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Dissertations / Theses on the topic 'Classical mechanics'
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1
Harker, Shaun Russell. "Classical mechanics with dissipative constraints." Thesis, Montana State University, 2009. http://etd.lib.montana.edu/etd/2009/harker/HarkerS0809.pdf.
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The aim of this thesis is to consider the mathematical treatment of mechanical systems in the presence of constraints which are energetically dissipative. Constraints may be energetically dissipative due to impacts and friction. In the frictionless setting, we generalize Hamilton's principle of stationary action, central to the Lagrangian formulation of classical mechanics, to reflect optimality conditions in constrained spaces. We show that this generalization leads to the standard measure-theoretic equations for shocks in the presence of unilateral constraints. Previously, these equations were simply postulated; we derive them from a fundamental variational principle. We also present results in the frictional setting. We survey the extensive literature on the subject, which focusses on existence results and numerical schemes known as time- stepping algorithms. We consider a novel model of friction (which is more dissipative than standard Coulomb friction) for which we can give better well-posedness results than what is currently available for the Coulomb theory. To this end, we study multi-valued maps, differential inclusions, and optimization theory. We construct a differential inclusion we call the feedback problem, for which the multi-valued map is the solution set of a convex program. We give existence and uniqueness results regarding this feedback problem. We cast the persistent contact evolution problem of our novel model of friction into the form of a feedback problem to derive an existence result.
2
Wong, Leon Chih Wen. "Automated reasoning about classical mechanics." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/35408.
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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.<br>Includes bibliographical references (p. 105-107).<br>by Leon Chih Wen Wong.<br>M.S.
3
Römer, Sarah. "The Classical Limit of Bohmian Mechanics." Diss., lmu, 2010. http://nbn-resolving.de/urn:nbn:de:bvb:19-113148.
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Breuer, Thomas. "Classical observables, measurement, and quantum mechanics." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339726.
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Borgan, Sharry. "Classical and quantum mechanics with chaos." Thesis, Durham University, 1999. http://etheses.dur.ac.uk/4968/.
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This thesis is concerned with the study, classically and quantum mechanically, of the square billiard with particular attention to chaos in both cases. Classically, we show that the rotating square billiard has two regular limits with a mixture of order and chaos between, depending on an energy parameter, E. This parameter ranges from -2w(^2) to oo, where w is the angular rotation, corresponding to the two integrable limits. The rotating square billiard has simple enough geometry to permit us to elucidate that the mechanism for chaos with rotation or curved trajectories is not flyaway, as previously suggested, but rather the accumulation of angular dispersion from a rotating line. Furthermore, we find periodic cycles which have asymmetric trajectories, below the value of E at which phase space becomes disjointed. These trajectories exhibit both left and right hand curvatures due to the fine balance between Centrifugal and Coriolis forces. Quantum mechanically, we compare the spectral analysis results for the square billiard with three different theoretical distribution functions. A new feature in the study is the correspondence we find, by utilising the Berry-Robnik parameter q, between classical E and a quantum rotation parameter w. The parameter q gives the ratio of chaotic quantum phase volume which we can link to the ratio of chaotic phase volume found classically for varying values of E. We find good correspondence, in particular, the different values of q as w is varied reflect the births and subsequent destructions of the different periodic cycles. We also study wave packet dynamics, necessitating the adaptation of a one dimensional unitary integration method to the two dimensional square billiard. In concluding we suggest how this work may be used, with the aid of the chaotic phase volumes calculated, in future directions for research work.
6
Baldock, Robert John Nicholas. "Classical statistical mechanics with nested sampling." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709164.
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Nielsen, Steven Ole. "Mixed quantum-classical dynamics and statistical mechanics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63602.pdf.
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Lami, Ludovico. "Non-classical correlations in quantum mechanics and beyond." Doctoral thesis, Universitat Autònoma de Barcelona, 2017. http://hdl.handle.net/10803/457968.
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Aquesta tesis parteix d'una pregunta aparentment ingènua: Què passa
si es separen dos sistemes físics que estaven en contacte? Un dels descobriments
més rellevants del segle passat és que els sistemes que obeeixen
les lleis de la mecànica quàntica, en comptes de les lleis clàssiques, romanen
intrínsecament connectats fins i tot quan estan separats físicament.
Aquest fenomen és conegut com entrellaçament o entanglement. Aquí,
ens preguntem quelcom més profund: pertany l'entrellaçament exclusivament
als sistemes quàntics o és comú a totes les teories no clàssiques?
I, donat el cas, com es pot comparar l'entrellaçament quàntic amb l'entrella
çament que pertany a d'altres teories?
La primera part de la tesis tracta amb aquestes qüestions considerant
la teoria quàntica com a part d'un grup més ampli de teories físiques
anomenat general probabilistic theories (GPTs). El Capítol 1 repassa les
motivacions que hi ha darrera el formalisme GPT, contextualitzant el
Capítol 2, on plantegem les preguntes mencionades en conjectures formals
adjuntant-ne la nostre contribució cap a una solució completa. Al
Capítol 3, considerem l'entrellaçament a nivell de mesures i no d'estats,
la qual cosa ens porta cap a la investigació d'una de les seves principals
implicacions, data hiding. En aquest marc, determinem la màxima efi
ciència de el data hiding que un sistema quàntic pot exhibir i també el
màxim valor entre tots els GPTs, trobant que els primers escalen amb
l'arrel quadrada dels darrers.
En la segona part d'aquest manuscrit estudiem alguns problemes relacionats
amb l'entrellaçament quàntic. Al Capítol 4, discutim la seva resistència al soroll blanc, modelitzat amb canals que actuen tant local com
globalment. Aquests canals depenen d'un nombre limitat de paràmetres,
això fa que siguem capaços de respondre totes les preguntes bàsiques relacionades
amb les propietats de transformació de l'entrellaçament. El
Capítol 5 presenta la nostre visió sobre l'entrellaçament gaussià, amb
especial focus en el rol del anomenat `positive partial transposition cri-
terion' en aquest context. Extensament, fent servir tècniques d'anàlisis
de matrius com ara Schur complements i matrix means, presentem demostracions
de resultats clàssics generalitzant-los i resolent algun dels
problemes oberts existents en la matèria.
La tercera part de la tesis es basa en formes més generals de correlacions
no clàssiques en sistemes bipartits i de variable contínua. Al
Capítol 6 investiguem el Gaussian steering i problemes relacionats en la
seva quantificació, així com presentem un esquema general que permeti
consistentment classificar correlacions de sistemes bipartits gaussians
en `clàssiques' i `quàntiques'. Finalment, el Capítol 7 explora alguns
dels problemes relacionats amb strong subadditivity en desigualtats de
matrius que juga un paper clau en el nostre anàlisis de correlacions en
estats gaussians bipartits. Entre d'altres coses, la teoria que desenvolupem
ens serveix per concloure que una Rényi-2 versió gaussiana del difús
squashed entanglement coincideix amb el corresponent entrellaçament de
formació quan s'avalua en estats gaussians.<br>Esta tesis versa sobre una cuestión aparentemente naíf: ¿qué ocurre cuando
se separan dos sistemas físicos que estaban juntos previamente? Uno de los mayores
descubrimientos del siglo pasado es que los sistemas que obedecen leyes
mecano-cuánticas, en lugar de clásicas, permanecen ligados inextricablemente
incluso tras haber sido separados físicamente, un fenómeno conocido como
entrelazamiento. Aquí nos preguntamos algo más profundo si cabe: ¿es el entrelazamiento
una característica exclusiva de los sistemas cuánticos o es común a
todas las teorías no-clásicas? Y, si es este el caso, ¿cuán fuerte es el entrelazamiento
mecano-cuántico comparado con aquel exhibido por otras teorías?
La primera parte de esta tesis trata estas cuestiones considerando la teoría
cuántica como parte de un conjunto más amplio de teorías físicas, colectivamente
llamadas teorías probabilísticas generales (TPG). En el Capítulo 2 revisamos
la sólida motivación que subyace al formalismo TPG, preparando el terreno
para el Capítulo 2, donde traducimos las anteriores cuestiones a conjeturas precisas,
y donde presentamos nuestro progreso hacia una solución completa. En el
Capítulo 3 consideramos el entrelazamiento a nivel de medidas en vez de estados,
lo cual conduce a la investigación de una de sus implicaciones principales,
la ocultación de información. En este contexto, determinamos el máximo poder
de ocultación de información que puede exhibir un sistema mecano-cuántico,
así como el mayor valor entre todas las TPG, hallando que el primero crece
como la raíz cuadrada del segundo.
En la segunda parte de este manuscrito exploramos algunos de los problemas
relacionados con el entrelazamiento cuántico. En el Capítulo 4 discutimos
su resistencia al ruido blanco modelado por canales que actúan bien local o bien
globalmente. Debido al número limitado de parámetros de los que dependen
estos canales, somos capaces de responder todas las preguntas básicas que conciernen
a diversas propiedades de la transformación del entrelazamiento. En el
siguiente Capítulo 5 presentamos nuestra perspectiva sobre el tema del entrelazamiento
gaussiano, con un énfasis particular sobre el papel del célebre \criterio
de la transposición parcial positiva" en este contexto. Empleando extensivamente
herramientas del análisis matricial como los complementos de Schur y
las medias matriciales, presentamos pruebas unificadas de resultados clásicos,
extendiéndolos y cerrando algunos de los problemas abiertos en el campo.
La tercera parte de esta tesis se ocupa de formas más generales de correlaciones
no-clásicas en sistemas bipartitos de variable continua. En el Capítulo 6
estudiamos el \steering" gaussiano y problemas relacionados con su cuantificaci
ón, y dise~namos un esquema general que permite clasificar consistentemente
correlaciones de estados gaussianos bipartitos en \clásicas" y \cuánticas". Finalmente,
en el Capítulo 7 exploramos algunos problemas vinculados a una desigualdad
matricial de \subaditividad fuerte" que desempe~na un papel crucial
en nuestro análisis de las correlaciones en los estados gaussianos bipartitos. Entre
otras cosas, la teoría que desarrollamos nos permite concluir que una versión
Rényi-2 gaussiana del escurridizo squashed entanglement coincide en estados
gaussianos con el correspondiente entrelazamiento de formación<br>This thesis is concerned with a seemingly naive question: what happens when
you separate two physical systems that were previously together? One of the
greatest discovery of the last century is that systems that obey quantum me-
chanical instead of classical laws remain inextricably linked even after they are
physically separated, a phenomenon known as entanglement. This leads im-
mediately to another, deep question: is entanglement an exclusive feature of
quantum systems, or is it common to all non-classical theories? And if this is
the case, how strong is quantum mechanical entanglement as compared to that
exhibited by other theories?
The first part of the thesis deals with these questions by considering quan-
tum theory as part of a wider landscape of physical theories, collectively called
general probabilistic theories (GPTs). Chapter 1 reviews the compelling motiva-
tions behind the GPT formalism, preparing the ground for Chapter 2, where we
translate the above questions into precise conjectures, and present our progress
toward a full solution. In Chapter 3 we consider entanglement at the level of
measurements instead of states, which leads us to the investigation of one of its
main implications, data hiding. In this context, we determine the maximal data
hiding strength that a quantum mechanical system can exhibit, and also the
maximum value among all GPTs, finding that the former scales as the square
root of the latter.
In the second part of this manuscript we explore some problems connected
with quantum entanglement. In Chapter 4 we discuss its resistance to white
noise, as modelled by channels acting either locally or globally. Due to the
limited number of parameters on which these channels depend, we are able to
answer all the basic questions concerning various entanglement transformation
properties. The following Chapter 5 presents our view on the topic of Gaussian
entanglement, with particular emphasis on the role of the celebrated `positive
partial transposition criterion' in this context. Extensively employing matrix
analysis tools such as Schur complements and matrix means, we present unified
proofs of classic results, further extending them and closing some open problems
in the field along the way.
The third part of this thesis concerns more general forms of non-classical
correlations in bipartite continuous variable systems. In Chapter 6 we look into
Gaussian steering and problems related to its quantification, moreover devising
a general scheme that allows to consistently classify correlations of bipartite
Gaussian states into `classical' and `quantum' ones. Finally, Chapter 7 explores
some problems connected with a `strong subadditivity' matrix inequality that
plays a crucial role in our analysis of correlations in bipartite Gaussian states.
Among other things, the theory we develop allows us to conclude that a Rényi-2
Gaussian version of the elusive squashed entanglement coincides with the corre-
sponding entanglement of formation when evaluated on Gaussian states.
9
Hoyle, David Charles. "On the theory of simple classical fluids." Thesis, University of Bristol, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296397.
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Basak, Gancheva Inna. "Explicit integration of some integrable systems of classical mechanics." Doctoral thesis, Universitat Politècnica de Catalunya, 2011. http://hdl.handle.net/10803/125114.
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The main objective of the thesis is the analytical and geometrical study of several integrable finite-dimentional dynamical systems of classical mechanics,
which are closely related, namely:
- the classical generalization of the Euler top: the Zhukovski-Volterra (ZV) system describing the free motion of a gyrostat, i.e., a rigid body carrying
a symmetric rotator whose axis is fixed in the body;
- the Steklov-Lyapunov integrable case of the Kirchhoff equations describing the motion of a rigid body in an ideal incompressible liquid;
- a nontrivial integrable generalization of the Steklov-Lyapunov system found by V.Rubanovskii: it describes the motion of a gyrostat in an ideal
fluid in presence of a non-zero circulation.
In our study we obtained explicit solution of the Zhukovski-Volterra ([2] and the Steklov-Lyapunov systems in terms of sigma- or theta-functions,
and performed a bifurcation analysis of these systems, as well as of the Rubanovskii generalization.
One should note that the solution of the ZV system was first given by V. Volterra, who, however, presented only its structure, but not the explicit formulas.
The thesis gives a new alternative solution of this system by using an algebraic parametrization of the angular momentum. This allowed us to find
poles and zeros of angular momentum in an algebraic way. The parametrization was also used to find an explicit solution for the Euler precession angle,
and, as a consequence, to solve the Poisson equations describing the motion of the gyrostat in space.
Similarly, by giving a geometric interpretation of the separating variables, and using the Weierstrass root functions, we reconstructed the thetafunctional
solution of the Steklov-Lyapunov systems, which was first given by F. Kötter in 1899 without a derivation ([3]).
In the study of bifurcations and singularities of the ZV system we used its bi-Hamiltonian structure ([1]. According the new method, the solution is
critical, if there exist a parameter of corresponding family of Poisson brackets, for wich the rang of the brackets with this parameter drops. Applying
new technics, based on the property of the system of being bi-Hamiltonian, we construct the bifurcation diagram of the ZV system. We also find the
equilibrium points of the system, check the non-degeneracy condition for such points in the sense of the singularity theory of Hamiltonian systems,
determine the types of equilibria points, and verify whether they are stable or not. We also describe the topological type of common levels of the first
integrals of the ZV system. Similar problems have been discussed in many papers, but the goal of our work is to study the system and demonstrate the
above techniques. It is a remarkable fact that using the bi-Hamiltonian property makes it possible to answer all the above questions practically without
any difficult computations.
The same method is applied to construct the bifurcation diagram for the Steklov-Lyapunov system, describe the zones of real motion, and analyze
stability of critical periodic solutions. Then the bifurcation analysis is extended to the Rubanovskii generalizaton. Here the main difficulty is that the number of different types of the bifurcation diagram is quite high, so we only describe general properties of the bifurcation curves, do stability analysis for closed trajectories, and equilibria.<br>El objetivo principal de la tesis es el estudio analítico y geométrico de varios sistemas integrables dinámicos y finito-dimensionales de la mecánica clásica que están estrechamente vinculados, a saber:
-La generalización clásica de Euler top: el sistema Zhukovski-Volterra (ZV) que describe el movimiento libre de un giróstato, es decir, un cuerpo rígido que lleva un rotor simétrico cuyo eje es fijo al cuerpo.
- El caso del sistema integrable de Steklov-Lyapunov de las ecuaciones de Kirchhoff que describen el movimiento de un cuerpo rígido en un líquido incompresible ideal;
- Una generalización no trivial del sistema integrable de Steklov-Lyapunov encontrado por V. Rubanovskii que describe el movimiento de un giróstato en un fluido ideal en presencia de una circulación distinta de cero.
En nuestro estudio hemos obtenido una solución explícita de los sistemas de Zhukovski-Volterra [2] y de Steklov-Lyapunov en términos de funciones sigma- o theta y hemos realizado un análisis de la bifurcación de estos sistemas, así como de la generalización de Rubanovskii.
Hay que señalar que la solución del sistema de ZV fue dado por primera vez por V. Volterra, que, sin embargo, presenta sólo su estructura, pero no las fórmulas explícitas.
La tesis ofrece una nueva solución alternativa de este sistema mediante el uso de una parametrización algebraica del momento angular. Esto nos ha permitido encontrar polos y ceros del momento angular en forma algebraica. La parametrización también se utilizó para encontrar una solución explícita para el ángulo de precesión de Euler, y, en consecuencia, para resolver las ecuaciones de Poisson que describen el movimiento de un giróstato en el espacio.
Del mismo modo, al dar una interpretación geométrica de las variables de separación, y utilizando las funciones de las raíces Weierstrass, hemos reconstruido la solución thetafunctional de los sistemas de Steklov-Lyapunov, que fue dado por primera vez por F. Kotter en 1899 sin una derivación ([3]).
En el estudio de las bifurcaciones y las singularidades del sistema ZV hemos utilizado su estructura bi-Hamiltoniana ([1]). Según el nuevo método, la solución es crítica, si existe un parámetro de la familia correspondiente del paréntesis de Poisson, para que el rango de las paréntesis con este parámetro se disminuye. Aplicando las nuevas técnicas, basadas en la propiedad del sistema de ser bi-Hamiltoniana, construimos el diagrama de bifurcación del sistema ZV. También hemos encontrado los puntos de equilibrio del sistema, verificando la condición de no-degeneración de estos puntos, en el sentido de la teoría de singularidad de los sistemas hamiltonianos, determinando los tipos de puntos de equilibrio, y comprobando si son estables
o no. También hemos descrito el tipo topológico de los niveles comunes de los primeros integrales del sistema de ZV. Problemas similares se han discutido en muchas obras, pero el objetivo de nuestro trabajo es estudiar el sistema y demostrar las técnicas anteriormente mencionadas. Es un hecho notable que el uso de la propiedad bi-Hamilton permite responder a todas las preguntas anteriores, prácticamente sin ningún cálculo difícil.
El mismo método se aplica para construir el diagrama de bifurcación para el sistema de Steklov-Lyapunov, describir las zonas de movimiento real, y analizar la estabilidad de soluciones periódicas críticas.
A continuación, el análisis de bifurcación se extiende a la generalización Rubanovskii. Aquí la principal dificultad consiste en que el número de diferentes tipos del diagrama de bifurcación es bastante alto, por lo que sólo se describen las propiedades generales de las curvas de bifurcación, y el análisis de estabilidad se hace para trayectorias cerradas, y equilibrios .
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Inaba, Hajime. "Historical investigations into the development of classical statistical mechanics." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199009.
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Crawford, Michael G. A. "Generalized coherent states and classical limits in quantum mechanics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ53489.pdf.
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Spencer, Paul. "Variational problems arising in classical mechanics and nonlinear elasticity." Thesis, University of Bath, 1999. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323570.
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Oreborn, Ulf. "IR spectroscopy for vibrational modes : A semi-classical approach based on classical electrodynamicsand modern quantum mechanics." Thesis, Linnéuniversitetet, Institutionen för fysik och elektroteknik (IFE), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-78144.
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The atoms of a molecule are always restless and are constantly moving in one way or another.Apart from rotations and translations, they may vibrate in many different modes. They may moveradially toward or from each other, so called stretching. This can be done symmetrically or asymmetrically.The angels between a pair of atoms may change seen from a common atom, so calledbending. This may be done in a common plane like scissoring or rocking, or out of plane like waggingor twisting.Anyhow, it is of interest to study these movements — since they work as a fingerprint of themolecule. Two methods for studying these behavior are Raman- and IR-spectroscopy. Some vibrations,such as symmetric stretching, are mainly seen using Raman spectroscopy (Raman active); whilebending and asymmetric stretching are primarily detected by IR spectroscopy (IR active) However,all types of combinations exist, so there are no watertight compartments between them. Instead, themethods are complementary to each other.In this article, I build up a semi-classical model of the vibrations for the case of IR-spectroscopy,and implement it in Mathematica to test the model. It is based on classical physics such as vibratingspringmechanics and Maxwell’s electrodynamics, but the vibrations are computed using modernphysics quantum mechanics. Since there are several atoms involved (say N) and the vibrations betweenthese atoms are in 3 dimensions, this may be described by 3N coupled 1-dimensional harmonicoscillators. By suitable transformations these oscillators are uncoupled, but results in a wave functionwhich is the product of 3N eigenfunctions, one for each oscillator’s eigenfunction of a given mode.Adding a time varying electric field (the IR-illumination), we need the time dependent SchrödingerEquation, where the potential is time varying sinusoidally. Necessary perturbation theory for suchtime dependency is described in some details, and an expression for the dipole moment needed forthe estimation of the IR absorption by the molecule is given. However, the model also depend onthe electrons’ orbitals and the total bond energy within the molecule. These are given by a DFT(Density Functional Theory) computer code, which serve as input to my calculations.The standard approach to do IR-spectrum calculations is to use DFT also to move the atoms inthe directions of the vibrations and compute how the dipole moments for the molecules change. Mymethod is instead to use SE directly for the many vibrating particle problem based on the knownexact solutions to the one dimensional harmonic oscillator. This is followed by perturbation theoryfor the time dependency of the IR-field to get the dipole moments.The drawback with my approach is that the electron clouds around the atoms are not affectedat all by the vibrations, they just follow the nuclei. The DFT approach takes care of the changingelectron density functions. However, my approach solves the vibrational problem more directly withthe SE and takes care of the time dependent potential using perturbation theory.Computational results for seven molecules containing between 2 and 11 atoms are shown andcompared with spectroscopic parameters and measurements compiled by established references. Theconclusion is that my model and computational output are well in accordance with these references,and some shortcomings and possible enhancements are pointed out. The drawback with the electronclouds might affect the absorption levels of the vibrations rather than their energies and are possiblein future work to take into account.<br><p>Till minne av Ulf Oreborn (1957-2018)</p>
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Schlosshauer-Selbach, Maximilian. "The quantum-to-classical transition : decoherence and beyond /." Thesis, Connect to this title online; UW restricted, 2005. http://hdl.handle.net/1773/9673.
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Anastopoulos, Charalabos. "Emergence of classical behaviour in quantum systems." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243292.
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Bielenberg, James R. (James Ronald) 1976. "The ramifications of diffusive volume transport in classical fluid mechanics." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/30061.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2004.<br>Includes bibliographical references (leaves 160-166).<br>The thesis that follows consists of a collection of work supporting and extending a novel reformulation of fluid mechanics, wherein the linear momentum per unit mass in a fluid continuum, m, is supposed equal to the volume velocity v[sub]v. The latter differs from the barycentric velocity V[sub]m by the vector field j[sub]v, where j[sub]v = v[sub]v - v[sub]m represents the heretofore largely ignored diffusive transport of volume. We will begin by giving a motivating discussion containing example problems which point to the possible need for a change in the constitutive choice for in. This will be followed by a brief outline of the kinematic concepts necessary to understand and utilize volume transport, including a general expression for j[sub]v. We will conclude by presenting the modified governing equations that result from the constitutive choice m = v[sub]v. Upon completing the required overview of existing ideas, a detailed linear irreversible thermodynamic study of the modified governing equations which result from the choice m = v[sub]v is presented. This analysis yields, inter alia, an expression for the entropy production per unit volume in the fluid which requires that the deviatoric stress tensor be expressed in terms of the volume velocity. Furthermore, an expression for the diffusive flux of internal energy is derived that differs from classical results by a term proportional to the diffusive flux of volume. This change in the internal energy flux stems from the explicit recognition of a diffusive volume flux, and precedes any specific choice of constitutive expression for the molecular flux of heat or species.<br>(cont.) The remainder of the thesis, which constitutes the bulk of the work performed, focuses on testing the proposed equation set against known experimental data. Each of the physically measurable phenomena treated herein was previously believed outside the realm of classical continuum fluid dynamics. We begin by considering the thermophoretic and diffusiophoretic motion of particles suspended in gases or liquids. We continue by studying the thermo-molecular pressure drop which results from applying a temperature gradient across the ends of a closed capillary. We conclude by presenting a hydrodynamic/Brownian motion model of thermal diffusion in liquids, wherein theoretical predictions for the Soret coefficient in a binary liquid system are presented that may be evaluated from readily available physicochemical data. It is shown, in each case, that the predictions of our modified theory are in agreement with experimental data. The final chapter of this dissertation is dedicated to utilizing the results derived in the previous chapters to comment on the veracity of the claim that the specific linear momentum in a fluid is given by the volume, rather than the barycentric, velocity. General arguments supporting this claim are presented and then followed by a list of questions which remain to be answered. Finally, a list of proposed experiments are detailed which could further test the predictions made herein.<br>by James R. Bielenberg.<br>Ph.D.
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Mata, Ricardo André Fernandes da. "Local correlation methods in classical and quantum mechanics hybrid schemes." [S.l. : s.n.], 2007. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-33346.
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Giardina, Ronald Joseph Jr. "General Nonlinear-Material Elasticity in Classical One-Dimensional Solid Mechanics." ScholarWorks@UNO, 2019. https://scholarworks.uno.edu/td/2666.
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We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation for stress and strain ubiquitous in engineering mechanics and define a general internal bending moment for which this expression, and several others, are special cases. We will then apply this general bending moment to some one-dimensional Euler beam-columns along with the continuous, periodic functions we developed with regard to the generalized ellipse. This will allow us to construct new solutions for critical buckling loads of Euler columns and deflections of beam-columns under very general engineering material requirements without some of the usual assumptions associated with the Ramberg-Osgood relation.
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Siegwart, David Kevin. "Classical and quantum chaos of dynamical systems : rotating billiards." Thesis, Durham University, 1990. http://etheses.dur.ac.uk/6228/.
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The theory of classical chaos is reviewed. From the definition of integrable systems using the Hamilton-Jacobi equation, the theory of perturbed systems is developed and the Kolmogorov-Arnold-Moser (KAM) theorem is explained. It is shown how chaotic motion in Hamiltonian systems is governed by the in tricate connections of stable and unstable invariant manifolds, and how it can be catagorised by algorithmic complexity and symbolic dynamics, giving chaotic measures such as Lyapunov exponents and Kolmogorov entropy. Also reviewed is Gutzwiller's semiclassical trace formula for strongly chaotic systems, torus quantisation for integrable systems, the asymptotic level density for stationary billiards, and random matrix theories for describing spectral fluctuation properties. The classical theory is applied to rotating billiards, particularly the free motion of a particle in a circular billiard rotating uniformly in its own plane about a point on its edge. Numerically, it is shown that the system's classical behaviour ranges from fully chaotic at intermediate energies, to completely integrable at very low and very high energies. It is shown that the strong chaos is due to discontinuities in the Poincare map, caused by trajectories which just glance the boundary-an effect of the curvature of trajectories. Weaker chaos exists due to the usual folding and stretching of the Hamiltonian flow. Approximate invariant curves for integrable motion are found, valid far from the presence of glancing trajectories. The major structures of phase space are investigated: a fixed point and its bifurcation into a two-cycle, and their stabilities. Lyapunov exponents for trajectories are calculated and the chaotic volume for a wide range of energies is measured. Quantum mechanically, the energy spectrum of the system is found numerically. It is shown that at the energies where the classical system is completely integrable the levels do not repel, and at those energies where it is completely chaotic there is strong level repulsion. The nearest neighbour level spacing distributions for various ranges of energy and values of Planck's constant are found. In the semiclassical limit, it is shown that, for energies where the classical system is completely chaotic, the level spacing statistics are Wigner, and where it is completely integrable, the level spacing statistics are Poisson. A model is described for the spacing distributions where the levels can be either Wigner or Poisson, which is useful for showing the transition from one to the other, and ad equately describes the statistics. Theoretically, the asymptotic level density for rotating billiards is calculated, and this is compared with the numerical results with good agreement, after modification of the method to include all levels.
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Tomsah, Ibrahim Basharei Ibrahim. "Quantum and classical aspects of molecular dynamics studied by NMR spectroscopy." Thesis, University of Nottingham, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241072.
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Sahm, David Karl. "The classical mechanics of mode-mode energy transfer in polyatomic molecules." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/29997.
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Di, Salvo Rosa. "Dynamics of Classical Systems in the Operator Algebra of Quantum Mechanics." Doctoral thesis, Università di Catania, 2017. http://hdl.handle.net/10761/3846.
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The use of the formalism and the operatorial techniques typical of quantum mechanics proved in recent years to be an effective approach for the description of even macroscopic systems characterized by complex interactions in several contexts with interesting applications both in the bioecological and in the socioeconomic area.
The operatorial approach, based on raising and lowering operators, especially using the number representation, provides useful tools for modeling collective dynamics of spatially distributed physical systems in a completely general and precise way. Quantum-like models (not necessarily related to the microscopic approach) offer an interesting mathematical insight into phenomena and processes even at macroscopic scales in several situations in which some quantities changing discontinuously are well described in terms of the integer eigenvalues of certain self-adjoint operators useful for a complete description of the system under consideration (the so-called observables of the system itself).
Moreover, according to the innovative approach called rule-induced dynamics, the derivation of the dynamics in the operator algebra of quantum mechanics from a time-independent Hamiltonian operator may be enriched by means of the repeated application of specific ''rules'' including in the dynamics meaningful effects occurring during the time evolution of the system and, therefore, producing an adjustment of the model itself as a consequence of its evolution. This method is of great interest to describe systems for which a nontrivial and sufficiently regular asymptotic behavior is expected.
The original contributions of this thesis, besides the construction and the numerical investigation of operatorial models to describe complex systems of interest in many areas (mathematics, physics, ecology, social sciences), are concerned with the introduction and exploitation of the so called (H, rho)-induced dynamics. The combined action of the Hamiltonian and of some rules allowed to take into account in the model relevant effects that can not be described by a time independent self-adjoint Hamiltonian. This strategy, which provides a powerful strategy to simulate the effect of using a time-dependent Hamiltonian, revealed capable of greatly enriching the dynamics of the considered models still with simple quadratic Hamiltonians without additional computational costs.
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Chen, Feng. "Mixed quantum/classical dynamics of photodissociation of H20 and ar-H20." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1095782886.
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Thesis (Ph. D.)--Ohio State University, 2004.<br>Title from first page of PDF file. Document formatted into pages; contains xvii, 105 p.; also includes graphics (some col.). Includes bibliographical references (p. 101-105).
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Rouvinez, Christophe. "Classical and quantum mechanics of a chaotic Hamiltonian system : the wedge billiard /." [S.l.] : [s.n.], 1995. http://library.epfl.ch/theses/?nr=1352.
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Tarama, Daisuke. "Classical and Quantum Mechanics, and Complex Algebraic Geometry of Free Rigid Bodies." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157481.
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Weidig, Tom. "Classical and quantum aspects of topological solitons (using numerical methods)." Thesis, Durham University, 1999. http://etheses.dur.ac.uk/4277/.
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In Introduction, we review integrable and topological solitons. In Numerical Methods, we describe how to minimize functionals, time-integrate configurations and solve eigenvalue problems. We also present the Simulated Annealing scheme for minimisation in solitonic systems. In Classical Aspects, we analyse the effect of the potential term on the structure of minimal- energy solutions for any topological charge n. The simplest holomorphic baby Skyrme model has no known stable minimal-energy solution for n > 1. The one-vacuum baby Skyrme model possesses non-radially symmetric multi-skyrmions that look like 'skyrmion lattices' formed by skyrmions with n = 2. The two-vacua baby Skyrme model has radially symmetric multi- skyrmions. We implement Simulated Annealing and it works well for higher order terms. We find that the spatial part of the six-derivative term is zero. In Quantum Aspects, we find the first order quantum mass correction for the Ф(^4) kink using the semi-classical expansion. We derive a trace formula which gives the mass correction by using the eigenmodes and values of the soliton and vacuum perturbations. We show that the zero mode is the most important contribution. We compute the mass correction of Ф(^4) kink and Sine-Gordon numerically by solving the eigenvalue equations and substituting into the trace formula.
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Junior, Jayme Vaz. "Sobre uma classe de teorias da mecânica." Universidade de São Paulo, 1990. http://www.teses.usp.br/teses/disponiveis/43/43133/tde-19062015-190623/.
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Neste trabalho mostra-se que uma devida reinteração das leis da Mecânica quando formuladas como um princípio variacional define uma classe de funcionais que as satisfazem. Cada funcional define uma teoria da Mecânica, chamada Mecânica Generalizada, que descreve uma particular dinâmica. A Mecânica Clássica, que descreve uma dinâmica chamada conjuntiva, baseia-se em uma escolha chamada trivial deste funcional. Escolhas não-triviais definem teorias que descrevem dinâmicas chamadas convolutivas. Uma dessas escolhas não-triviais define uma teoria que descreve uma dinâmica convolutica que se pode chamar quântica. Essa teoria é formalmente idêntica à Mecânica Quântica mas apresenta um conteúdo epistemológico diferente. A interpretação probabilística da Mecânica Quântica surge como uma interpretação suficiente mas não necessária desse formalismo.<br>In this work it is shown that a proper reinterpretation of the laws of Mechanics when formulated as a variational principle defines a class of functionals wich satisfies them. Each functional defines one theory of Mechanics, called Generalized Mechanics, which describes a particular dynamics. The Classical Mechanics, which describes to so called conjunctive dynamics, is based on a trivial choice of this functiona. Non-trivial choices define theories which describe the so called convolutive dynamics. One of these non-trivial choices define a convolutive theory which may be called quantic. This theory is formally identical to Quantum Mechanics but it displays a different epistemological content. The probabilistic interpretation of Quantum Mechanics emerges as a sufficient but not necessary interpretation of this formalism.
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Van, Laerhoven Christa Lynn. "Multi-planet Extra-solar Systems: Tides and Classical Secular Theory." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/321296.
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In a multi-planet system, gravitational interactions cause orbital eccentricity variations. For non-resonant systems, classical secular theory reveals that the eccentricities are vector sums of contributions from several eigenmodes. Examination of the eigenvectors often reveals subsets of planets that interact especially strongly as dynamical groups. Perturbations from other sources, such as tides, are shared among the planets through the secular interactions. If one planet's eccentricity is tidally damped, all the eigenmodes damp so as to leave a signature on their amplitudes. Therefore, if one desires to include some a priori tidal damping in an orbital fit, solutions should not assume the current eccentricity of that planet to be low, but rather for the eigenmodes that damp quickly to have low amplitude. The tidally perturbed planet may retain a substantial eccentricity, because some eigenmodes will be longer-lived. The secular eigenmodes, including relative damping rates, have been calculated for all 72 non-resonant extra-solar systems with adequate data. Tides also affect evolution of planets' semi-major axes, which is coupled with eccentricity evolution. A planet that, alone, would be quickly circularized so as to not experience much semi-major axis migration, could rapidly be forced into the star in the presence of an outer planet. Also, though such an inner planet may now be gone, the eccentricity of the outer planet could have been damped due to tides that acted on the inner planet. Any inferences about the primordial orbits of observed planets must consider these effects. For systems where the inner planet has not yet reached the star, the planets' eccentricities can be constrained for any particular assumed tidal dissipation factor Q', e.g. for the KOI-543 system, if the inner planet is rocky, the eccentricities must be<0.001. The habitable zone around low-mass stars is close to the star, precisely where tides are important. Low-mass stars are very long lived, and can be very old currently. A habitable planet likely needs tectonics for cycles that regulate the atmosphere, but a planet's internal heat will decay over long timescales. However, an outer planet could maintain the inner planet's eccentricity, allowing tidal heating to maintain long-term habitability. Secular interactions, coupled with tidal effects, may be critical for planetary habitability.
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Mullan, James Vincent. "Applications of relativistic and non-relativistic classical and quantum mechanics to heavy-particle collisions." Thesis, Queen's University Belfast, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337023.
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Brodlie, Alastair Robert. "Relationships between quantum and classical mechanics using the representation theory of the Heisenberg group." Thesis, University of Leeds, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410635.
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McCloud, Paul James. "Symmetry in classical and quantum field theory : an application of the theory of jets." Thesis, King's College London (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321679.
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Egloff, Dario [Verfasser]. "Non-classical processes in quantum mechanics : a resource theory approach to characterize coherence / Dario Egloff." Ulm : Universität Ulm, 2020. http://d-nb.info/1204481210/34.
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Alamino, Roberto Castro. "Aprendizado em modelos de Markov com variáveis de estado escondidas." Universidade de São Paulo, 2005. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-14112013-135303/.
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Neste trabalho estudamos o aprendizado em uma classe específica de modelos probabilísticos conhecidos como modelos de Markov com variáveis de estado escondidas (em inglês, Hidden Markov Models ou HMMs). Primeiramente discutimos sua teoria básica e em seguida fazemos um estudo detalhado do comportamento de cinco diferentes algoritmos de aprendizado, dois deles já conhecidos na literatura e os outros três propostos por nós neste trabalho. Os cinco algoritmos estão descritos abaixo e são estudados na seqüência apresentada: Algoritmo de Baum-Welch (BW): consiste em um célebre algoritmo off-line obtido através da aplicação do algoritmo EM ao caso particular dos HMMs. Na literatura, é comum referir-se a ele pelo nome de Fórmulas de Reestimação de BaumWelch. Algoritmo de Baum-Welch On-line (BWO): versão on-line de BW proposta por nós. Algoritmo de Baldi-Chauvin (BC): algoritmo on-line proposto por Baldi e Chauvin em [5] onde uma representação do tipo softma:x é utilizada para as probabilidades dos HMMs e cujo objetivo é, a cada passo de iteração, maximizar a verossimilhança do modelo. Algoritmo Bayesiano On-line (BKL): algoritmo desenvolvido por nós baseado numa proposta de Opper [74], onde, após a atualização da distribuição de probabilidades do modelo a cada novo dado, projeta-se a densidade obtida em uma família paramétrica de distribuições tratáveis minimizando-se a distância de KullbackLeibler entre as duas. Algoritmo Posterior Média (PM): uma simplificação de BKL onde a projeção após a atualização é feita na distribuição posterior média. Para cada um dos algoritmos acima, obtemos curvas de aprendizado através de simulações onde utilizamos duas medidas distintas de erro de generalização: a distância de Kullback-Leibler (dKL) e a distância euclideana (d IND. E). Com exceção do algoritmo BW, que só pode ser utilizado em situações de aprendizado off-line, estudamos para todos os outros algoritmos as curvas de aprendizado tanto para a situação on-line quanto para a off-line. Comparamos as performances dos algoritmos entre si e discutimos os resultados obtidos mostrando que, apesar de um tempo de computação maior, o algoritmo bayesiano PM, proposto por nós, é superior aos outros algoritmos não-bayesianos quanto à generalização em situações de aprendizado estáticas e possui uma performance muito próxima do algoritmo bayesiano BKL. Fazemos, também, uma comparação entre os algoritmos PM e BC em situações de aprendizado variáveis com o tempo, com dados gerados artificialmente e em uma situação com dados reais, porém com um cenário simplificado, onde os utilizamos para prever o comportamento do índice da bolsa de valores de São Paulo (IBOVESPA), mostrando que, embora necessitem de um período longo de aprendizado, após essa fase inicial as previsões obtidas por esses algoritmos são surpreendentemente boas. Por fim, apresentamos uma discussão sobre aprendizado e quebra de simetria baseada nos estudos feitos.<br>In this work we study learning in a specific class of probabilistic models known as Hidden Markov Models (HMMs). First we discuss its basic theory and after we make a detailed study of the behavior of five different learning algorithms, two of them already known in the literature and the other three proposed by us in this work. The five algorithms are described below in the sequence they are presented in the thesis: Baum-Welch Algorithm(BW): consists of a renowed offline algorithm obtained by applying the EM-algorithm to the particular case of HMMs. Through the literature it is common to refer to it by the name Baum-Welch Reestimation Formulas. Baum-Welch Online Algorithm (BWO): online version of BW proposed by us. Baldi-Chauvin Algorithm (BC): online algorithm proposed by Baldi and Chauvin in [5] where a softmax representation for the probabilities of the HMMs is used and where the aim is to maximize the model likelihood at each iteration step. Online Bayesian Algorithm (BKL): an algorithm developed by us based on the work of Opper [74] where, after updating the probability distribution of the model with each new data, the obtained density is projected into a parametric family of tractable distributions minimizing the Kullback-Leibler distance between both. Mean Posterior Algorithm (PM): a simplification of BKL where the projection after the update is made on the mean posterior distribution. For each one of the above algorithms, we obtain learning curves by means of simulations where we use two distinct measures of generalization error: the Kullback-Leibler distance (dKL) and the Euclidian distance (dE). With exception of the BW algorithm, which can be used only in offline learning situations, we study for all the other algorithms the learning curves for both learning situations: online and offiine. We compare the performance of the algorithms with one another and discuss the results showing that, besides its larger computation time, the bayesian algorithm PM, proposed by us, is superior to the other non-bayesian algorithms with respect to the generalization in static learning situations and that it has a performance that is very close to the bayesian algorithm BKL. We also make a comparison between algorithms PM and BC in learning situations that change with time using artificially generated data and in one situation with real data, with a simplified scenario, where we use them to predict the behavior of the São Paulo Stock Market Index (BOVESPA) showing that, although they need a large learning period, after that initial phase the predictions obtained by both algorithms are surprisingly good. Finally, we present a discussion about learning and symmetry breaking based on the presented studies.
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Tyukov, Alexei Evgen'evich. "Stochastic and asymptotic analysis applied to the study of stochastic models of classical and quantum mechanics." Thesis, Nottingham Trent University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366087.
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Shojaei, Barjoui Arman. "On the coupling of peridynamics with the classical theory of continuum mechanics in a meshless framework." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3423156.
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The classical theory of solid mechanics employs partial derivatives in the equation of motion and hence requires the differentiability of the displacement field. Such an assumption breaks down when simulation of problems containing discontinuities, such as cracks, comes into the picture. peridynamics is considered to be an alternative and promising nonlocal theory of solid mechanics that is formulated suitably for discontinuous problems. Peridynamics is well designed to cope with failure analysis as the theory deals with integral equations rather than partial differential equations. Indeed, peridynamics defines the equation of motion by substituting the divergence of the stress tensor, involved in the formulation of the classical theory, with an integral operator. One of the most common techniques to discretize and implement the theory is based on a meshless approach. However, the method is computationally more expensive than some meshless methods based on the classical theory. This originates from the fact that in peridynamics, similar to other nonlocal theories, each computational node interacts with many neighbors over a finite region. To this end, performing realistic numerical simulations with peridynamics entails a vast amount of computational resources. Moreover, the application of boundary conditions in peridynamics is nonlocal and hence it is more challenging than the application of boundary conditions adopted by methods based on the classical continuum theory. This issue is well-known to scientists working on peridynamics.
Therefore, it is reasonable to couple computational methods based on classical continuum mechanics with others based on peridynamics to develop an approach that applies different computational techniques where they are most suited for. The main purpose of this dissertation is to develop an effective coupled nonlocal/local meshless technique for the solution of two-dimensional elastodynamic problems involving brittle crack propagation. This method is based on a coupling between the peridynamic meshless method, and other meshless methods based on the classical continuum theory. In this study, two different meshless methods, the Meshless Local Exponential Basis Functions and the Finite Point Method are chosen as both are classified within the category of strong form meshless methods, which are simple and computationally cheap. The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only peridynamics is applied, one in which only the meshless method is applied and a transition zone where a transition between the two approaches takes place. The coupling adopts a local/nonlocal framework that benefits from the full advantages of both methods while overcoming their limitations. The parts of the domain where cracks either exist or are likely to propagate are described by peridynamics; the remaining part of the domain is described by the meshless method that requires less computational effort. We shall show that the proposed approach is suited for adaptive coupling of the strategies in the solution of crack propagation problems. Several static and dynamic examples are performed to demonstrate the capabilities of the proposed approach.<br>La teoria classica del continuo applicata ai solidi è basata sull’uso di equazioni differenziali del moto, pertanto viene ipotizzata la differenziabilità del campo degli spostamenti. Questa ipotesi viene meno quando nella risoluzione del problema compaiono delle discontinuità quali le cricche. La Peridynamics è una promettente teoria non locale del continuo che permette di gestire la presenza e l’evoluzione di discontinuità in un corpo solido. Questa nuova teoria è formulata per mezzo di equazioni integrali e pertanto può essere applicata anche allo studio della propagazione di cricche e dei fenomeni di rottura.La teoria Peridynamics utilizza un operatore integrale in sostituzione della divergenza del tensore delle tensioni, impiegata invece nella formulazione classica. Una delle tecniche di discretizzazione della Peridynamics maggiormente utilizzate è basata su un approccio di tipo meshless.
Da un punto di vista computazionale questo approccio si rivela, però, più oneroso rispetto a quanto richiesto dall’uso di altri metodi meshless comunemente impiegati per lo studio della teoria classica del continuo. Questo è dovuto al fatto che in Peridynamics, in maniera analoga a quanto avviene in altre teorie non locali, ogni nodo interagisce con molti altri nodi vicini ed all’interno di una regione di dimensioni finite. Un altro svantaggio della Peridynamics è legato alla modalità con cui le condizioni di vincolo e di carico sono applicate rispetto ai metodi abitualmente utilizzati nella teoria classica. Questo problema è ben noto agli scienziati che studiano questa nuova teoria non locale.
È quindi conveniente, accoppiare metodi basati sulla teoria classica con quelli che utilizzano la Peridynamics. Si svilupperà, in tal modo, un approccio in grado di utilizzare le diverse strategie computazionali nelle regioni del corpo solido in cui queste teorie si rivelano più adeguate.
Lo scopo principale di questa tesi è di sviluppare una tecnica efficace per accoppiare metodi meshless di tipo non locale e locale per lo studio di problemi elasto-dinamici bidimensionali in materiali fragili anche in presenza di propagazione di cricche. Questa tecnica sarà basata sull’accoppiamento della teoria Peridynamics (nella sua formulazione meshless) con la teoria classica del continuo studiata per mezzo di metodi di tipo meshless. In particolare sono stati scelti due metodi meshless, basati sulla teoria classica del continuo, il “Meshless Local Exponential Basis Functions” ed il “Finite Point Method”. Entrambi appartengono alla categoria “strong form meshless methods”, sono di semplice implementazione e non sono particolarmente onerosi da un punto di vista computazionale.
L’accoppiamento è stato realizzato grazie ad un unico schema meshless. Il dominio è suddiviso in tre regioni: una in cui si usa solamente la teoria Peridynamics, una in cui si utilizza solo il metodo meshless ed infine è prevista una regione di transizione che realizza il passaggio fra i due approcci di calcolo. La strategia proposta e sviluppata in questo elaborato, è in grado di accoppiare la teoria del continuo locale con la teoria del continuo non locale permettendo di trarre vantaggio dagli aspetti positivi delle due teorie e di superarne le rispettive limitazioni. La porzione del dominio in cui sono presenti delle cricche o in cui potrebbero propagarsi, è descritta impiegando la Peridynamics, mentre la restante porzione del dominio è descritta impiegando uno dei due metodi meshless citati in precedenza, che richiedono un minor onere computazionale. L’efficienza dell’approccio proposto sarà migliorata dall’uso di tecniche di accoppiamento adattativo: quest’ultima estensione permetterà di studiare diversi fenomeni di propagazione delle cricche con un limitato utilizzo di risorse di calcolo.
Le prestazioni del metodo di accoppiamento ideato saranno descritte per mezzo di molteplici esempi con analisi sia statiche che dinamiche.
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Römer, Sarah. "The Classical limit of bohmian mechanics : semiclassical wave packets and an application to many particle scattering theory /." Tönning [u.a.] : Der Andere Verlag, 2010. http://edoc.ub.uni-muenchen.de/11314/.
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Nazaikinskii, Vladimir, Bert-Wolfgang Schulze, and Boris Sternin. "Quantization methods in differential equations : Chapter 2: Exactly soluble commutation relations (The simplest class of classical mechanics)." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2579/.
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Zheng, Yindong. "Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor." Thesis, University of North Texas, 2005. https://digital.library.unt.edu/ark:/67531/metadc4824/.
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The de Broglie-Bohm (BB) approach to quantum mechanics gives trajectories similar to classical trajectories except that they are also determined by a quantum potential. The quantum potential is a "fictitious potential" in the sense that it is part of the quantum kinetic energy. We use quantum trajectories to treat quantum chaos in a manner similar to classical chaos. For the kicked rotor, which is a bounded system, we use the Benettin et al. method to calculate both classical and quantum Lyapunov exponents as a function of control parameter K and find chaos in both cases. Within the chaotic sea we find in both cases nonchaotic stability regions for K equal to multiples of π. For even multiples of π the stability regions are associated with classical accelerator mode islands and for odd multiples of π they are associated with new oscillator modes. We examine the structure of these regions. Momentum diffusion of the quantum kicked rotor is studied with both BB and standard quantum mechanics (SQM). A general analytical expression is given for the momentum diffusion at quantum resonance of both BB and SQM. We obtain agreement between the two approaches in numerical experiments. For the case of nonresonance the quantum potential is not zero and must be included as part of the quantum kinetic energy for agreement. The numerical data for momentum diffusion of classical kicked rotor is well fit by a power law DNβ in the number of kicks N. In the anomalous momentum diffusion regions due to accelerator modes the exponent β(K) is slightly less than quadratic, except for a slight dip, in agreement with an upper bound (K2/2)N2. The corresponding coefficient D(K) in these regions has three distinct sections, most likely due to accelerator modes with period greater than one. We also show that the local Lyapunov exponent of the classical kicked rotor has a plateau for a duration that depends on the initial separation and then decreases asymptotically as O(t-1lnt), where t is the time. This behavior is consistent with an upper bound that is determined analytically.
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Capela, Matheus. "Kolmogorov-Sinai entropy and dissipation in driven classical hamiltonian systems." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8216.
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Previous issue date: 2018-02-23<br>Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq<br>Diversas relações entre física e teoria de informação foram estabelecidas desde o trabalho de Shannon. Entropia é um elemento essencial nesta conexão, quantificando a informação transferida em um experimento. Mecânica estatística está conectada à teoria de informação através do princípio de máxima entropia, definindo as distribuições de probabilidade de estados de equilíbrio como aquelas que maximizam a entropia sujeita as condições físicas apropriadas. A energia dissipada em um processo clássico está conectada a divergência de Kullback-Leibler. Recentemente, Still e colaboradores mostraram que a ineficiência energética em um processo estocástico Markoviano é equivalente a ineficiência do modelo, definida como a diferença em informação que o estado do sistema compartilha com as variáveis externas no futuro e passado. Isto sugere que imprevisibilidade e ineficiência energética estejam relacionadas no âmbito da física clássica. O objetivo deste trabalho é estabelecer uma relação entre o comportamento randômico de sistemas clássicos, quantificado pela entropia de Kolmogorov-Sinai, com a ineficiência energética.<br>Many connections between physics and information theory have been revealed since the development of classical information theory by Shannon. A key concept in this connection is entropy, which represents the amount of information transferred to the observer who performs measurements in an experiment. Statistical mechanics is a physical theory deeply connected to information by Jaynes’ Maximum Entropy principle, which defines equilibrium probability distributions as the ones that maximizes entropy under some physical constraints. In this way, these distributions are the less unbiased probabilities that can be assignment to an event. Following this path, the dissipated energy in a classical Hamiltonian process (also known as the thermodynamic entropy production) was connected to the relative entropy between the forward and backward probability densities. A recent work by Still et al. has revealed that energetic inefficiency and model inefficiency are equivalent concepts in Markovian processes, where the latter is defined as the difference in mutual information that the system’s state shares with the future and past environmental variables. This raises the question whether model unpredictability and energetic inefficiency are connected in the framework of classical physics. The aim of this study is to connect the concepts of random behavior of a classical Hamiltonian system with its energetic inefficiency. The random behavior of a classical system is quantified by the Kolmogorov-Sinai entropy associated with its dynamics, an information-theoretic approach to chaos, whereas energetic inefficiency is measured by the dissipated work.
41
Bagwell, Ross David. "Bifurcation and Stability of a Ring Problem Motivated by the Mechanics of Double-Walled Carbon Nanotubes." University of Akron / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=akron1335288394.
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42
PEREA, CÓRDOBA MILTÓN HENRY. "On the semiclassical limit of emergent quantum mechanics, as a classical thermodynamics of irreversible processes in the linear regime." Doctoral thesis, Universitat Politècnica de València, 2015. http://hdl.handle.net/10251/54840.
Full textAbstract:
[EN] Motivated by the conceptual problems concerning the quantisation of gravity, the
Dutch theoretical physicist G. 't Hooft (1999 Nobel prize in physics) put forward the
notion that quantum mechanics must be the emergent theory of some underlying, deterministic
theory. This proposal usually goes by the name quantum mechanics as an
emergent phenomenon. This research line, initiated by 't Hooft in the late 1990's, has
been the subject of intense research over the last 15 years, by 't Hooft himself as well as
by many other researchers. In this PhD thesis we present our own approach to quantum
mechanics as an emergent phenomenon.
According to the emergence paradigm for quantum mechanics, information-loss
effects in the underlying deterministic theory lead to the arrangement of states of the
latter into equivalence classes, that one identifies as quantum states of the emergent
quantum mechanics. In brief, quantisation is dissipation, according to 't Hooft.
Moreover it has been argued in the literature that, in the presence of weak gravitational
fields, quantum effects must be indistinguishable from thermal effects. Since
the latter are typically dissipative in nature, the presence of a weak gravitational field
should provide a framework in which quantum effects can be explained as due to thermal,
dissipative fluctuations. Furthermore, since gravitational effects can be locally
gauged away (thanks to the equivalence principle), there should exist some kind of
equivalence principle for quantum effects, i.e., some kind of relativity principle for the
notion of quantumness as opposed to the notion of classicality. In this PhD thesis we
elaborate on this idea.
Once a reference frame is fixed, however, quantum effects cannot be gauged away,
and the statement quantisation is dissipation lends itself to a thermodynamical treatment.
In this thesis we also present one mechanism whereby quantum mechanics
is seen to emerge, thus explicitly realising 't Hooft's proposal. This mechanism is
based on a dictionary between semiclassical quantum mechanics, on the one hand, and
the classical theory of irreversible thermodynamics in the linear regime, on the other.
This thermodynamical formalism, developed by Nobel prize winners Onsager and Prigogine,
can be easily mapped into that of semiclassical quantum mechanics.<br>[ES] Motivado por los problemas conceptuales relativos a la cuantización de la gravedad,
el físico teórico holandés G. 't Hooft (premio Nobel de física en 1999) sugirió la noción
de que la mecánica cuántica pudiera ser la teoría emergente de alguna otra teoría determinista
subyacente. Dicha propuesta se conoce como la mecánica cuántica en tanto
que teoría emergente. Esta línea de investigación, iniciada por 't Hooft a finales de
los años 90, ha sido objeto de intenso estudio a lo largo de los últimos 15 años, tanto
por el mismo 't Hooft como por numerosos otros investigadores. En esta tesis doctoral
presentamos nuestra propia aproximación a la mecánica cuántica como fenómeno
emergente.
De acuerdo con este paradigma emergente para la mecánica cuántica, son efectos
de pérdida de información en la teoría determinista subyacente los que conducen a que
los estados de ésta última se agrupen en clases de equivalencia, las cuales clases se
identifican con los estados cuánticos de la mecánica cuántica emergente. En breve, la
cuantización es disipación, según 't Hooft.
Asimismo se ha argumentado en la literatura que, en presencia de campos gravitatorios
débiles, los efectos cuánticos son indistinguibles de los efectos térmicos. Dado
que éstos últimos son típicamente disipativos por naturaleza, la presencia de un campo
gravitatorio débil debería proporcionar un entorno en el cual los efectos cuánticos
puedan entenderse como debidos a fluctuaciones térmicas, disipativas. Además, dado
que los campos gravitatorios pueden eliminarse localmente (gracias al principio de
equivalencia), debería existir algún tipo de principio de equivalencia para los efectos
cuánticos, i.e., algún tipo de principio de relatividad para la noción de cuanticidad, por
oposición a la noción de clasicidad. En esta tesis doctoral elaboramos estas ideas.
Sin embargo, una vez fijado un sistema de referencia, los efectos gravitatorios ya
no pueden eliminarse, y la afirmación de que la cuantización es disipación se presta a
un tratamiento termodinámico. En esta tesis también presentamos un mecanismo mediante
el cual la mecánica cuántica se ve emerger, comprobándose así explícitamente
la propuesta de 't Hooft. Este mecanismo se basa en un diccionario entre la mecánica
cuántica semiclásica, por un lado, y la teoría clásica de la termodinámica irreversible
en el régimen lineal, por otro lado. Dicho formalismo termodinámico, desarrollado por
los premios Nobel Onsager y Prigogine, puede trasladarse fácilmente a la mecánica
cuántica semiclásica.<br>[CAT] Motivat pels problemes conceptuals en relació a la quantització de la gravetat, el físic teóric holandés G. 't Hooft (premi Nobel de física en 1999) va suggerir la noció de que la mecànica quàntica pogués ser la teoria emergent d ' alguna altra teoria determinista subjacent. A questa proposta es coneix com a mecanica quantica en tant que teoria emergent. Aquesta línia d ' investigació, iniciada per 't Hooft a final dels anys 90, ha sigut intensament estudiada durant els últims 15 anys , tant pel mateix 't Hooft com per nombrosos altres investigadors. En aquesta tesi doctoral presentem la nostra própia aproximació a la mecànica quàntica com a fenomen emergent.
D ' acord amb aquest paradigma emergent per a la mecànica quàntica, són efectes de pérdua d ' informació en la teoria determinista, subjacent els que condueixen a que els estats d ' aquesta última s ' agrupen en classes d ' equivalència, les quals s ' identifiquen amb els estats quàntics de la mecànica quàntica emergent. Breument, la quantització es dissipació segons 't Hooft.
Aixímateix, s ' ha argumentat a la literatura que, en presència de camps gravitatoris febles, els efectes quàntics són indistingibles dels efectes tèrmics. Com aquests últims són típicament dissipatius per naturalesa, la presència d ' un camp gravitatori feble hauria de proporcionar un entorn en el qual els efectes quàntico es puguen entendre com deguts a fluctuacions tèrmiques, dissipatives. A més a més, com que els camps gravitatoris poden eliminar-se localment (gràcies al principi d ' equivalència), hauria d ' existir algun tipus de principi d ' equivalència per als efectes quàntics, i.e. , algun tipus de principi de relativitat per a la noció de quanticitat, per oposició a la noció de classicitat. En aquesta tesi doctoral elaborem aquestes idees.
En canvi, una vegada fixat el sistema de referència, els efectes gravitatoris ja no poden eliminar-se, i l ' afirmació de que la quantització és dissipació es presta a un tractament termodinàmic. En aquesta tesi també presentem un mecanisme mitjançant el qual la mecànica quàntica es veu emergir, comprovant-se explícitament la proposta de 't Hooft. A quest mecanisme es basa en un diccionari entre la mecànica quàntica semiclàssica, d ' una banda, i la teoria clàssica de la termodinàmica irreversible en el règim lineal, d ' una altra banda. A quest formalisme termodinàmic, desenvolupat pels premis Nobel Onsager i Prigogine, pot traslladar-se fàcilment a la mecànica quàntica semiclàssica.<br>Perea Córdoba, MH. (2015). On the semiclassical limit of emergent quantum mechanics, as a classical thermodynamics of irreversible processes in the linear regime [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/54840<br>TESIS
43
Nilsson, Daniel. "The Ratio of Reality : A study of the gyromagnetic ratio in theories ranging from classical mechanics to string theory." Thesis, Uppsala universitet, Teoretisk fysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-448767.
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In this project a theoretical study of the so called gyromagnetic ratio was done by investigating classical mechanics, Dirac theory and string theory. The gyromagnetic ratio is a constant term appearing in the coupling between angular momentum and magnetic moment for a particle. A universality in quantum field theory claiming g = 2 regardless of spin is known to exist which also agrees with the found values (g = 2) of the Dirac and string theory. The proof of the aforementioned universality in quantum field theory was sketched in the project by showing that the W-boson Lagrangian is well behaved in the massless limit. Furthermore it is shown that the spin equations of motion for a particle is greatly reduced if g = 2 regardless of spin.<br>I det här projektet utfördes en teoretisk studie av den så kallade gyromagnetsika kvoten genom att undersöka klassisk mekanik, Dirac-teori och strängteori. Den gyromagnetiska kvoten är en konstant term som visar sig i kopplingen mellan rörelsemängsmoment och magnetiskt moment för en partikel. I kvantfältsteori existerar en universalitet som hävdar att g = 2 oberoende av spin. Denna universalitet stämmer överens med de funna värden på g från Dirac-teori och strängtoeri. Beviset för denna universalitet testades genom ett exempel där Lagrangianen för W-bosonen i kvantfältsteori visades bete sig som förväntat när massan för partikeln tilläts gå mot noll. Vidare undersöktes rörelseekvationerna för ett system helt bestämt av dess spin. I dessa kan det visas att ett universellt värde på g oavsett spin reducerar dessa ekvationer avsevärt.
44
Morita, Kohei. "Model Relative Emergence in Physics." Kyoto University, 2020. http://hdl.handle.net/2433/253017.
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45
Gleisner, Frida. "Three solutions to the two-body problem." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-26781.
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The two-body problem consists of determining the motion of two gravitationally interacting bodies with given masses and initial velocities. The problem was first solved by Isaac Newton in 1687 using geometric arguments. In this thesis, we present selected parts of Newton's solution together with an alternative geometric solution by Richard Feynman and a modern solution using differential calculus. All three solutions rely on the three laws of Newton and treat the two bodies as point masses; they differ in their approach to the the three laws of Kepler and to the inverse-square force law. Whereas the geometric solutions aim to prove some of these laws, the modern solution provides a method for calculating the positions and velocities given their initial values. It is notable that Newton in his most famous work Principia, where the general law of gravity and the solution to the two-body problem are presented, used mathematics that is not widely studied today. One might ask if today's low emphasis on classical geometry and conic sections affects our understanding of classical mechanics and calculus.
46
Hase, Masayuki Oka. "Desordem e competição em modelos de rede - Resultados exatos." Universidade de São Paulo, 2005. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-14112013-142827/.
Full textAbstract:
Resultados exatos são estabelecidos em dois trabalhos distintos. O primeiro tema é uma análise da dinâmica de Langevin para um modelo esférico médio com interações competitivas, investigando fenômenos de não equilíbrio como \"aging\" e violação do teorema flutuação-dissipação. O segundo trabalho é uma contribuição ao diagrama de fases do estado fundamental de um ferromagneto diluído e sujeito a um campo externo aleatório regido por uma distribuição bimodal; uma abordagem analítica, embora parcial, indica uma estabilidade da solução réplica-simétrica.<br>Exact results are established for two distinct works. The first of them is an analysis of Langevin dynamics for a mean spherical model with competiting interactions, searching for non-equilibrium phenomena as aging and the violation of the fluctuation-dissipation theorem. The second work is a contribution to the ground state\'s phase diagram of a diluted ferromagnet under a random external field obeying a bimodal distribution; an analytic study, although partial, indicates a stability of the replica-symmetric solution.
47
Wallrapp, Frank. "Mixed quantum and classical simulation techniques for mapping electron transfer in proteins." Doctoral thesis, Universitat Pompeu Fabra, 2011. http://hdl.handle.net/10803/22685.
Full textAbstract:
El
objetivo
de
esta
tesis
se
centra
en
el
estudio
de
la
transferencia
de
electrones
(ET),
una
de
las
reacciones
más
simples
y
cruciales
en
bioquímica.
Para
dichos
procesos,
obtener
información
directa
de
los
factores
que
lo
promueves,
asi
como
del
camino
de
transferencia
electronica,
no
es
una
tarea
trivial.
Dicha
información
a
un
nivel
de
conocimiento
detallado
atómico
y
electrónico,
sin
embargo,
es
muy
valiosa
en
términos
de
una
mejor
comprensión
del
ciclo
enzimático,
que
podría
conducir,
por
ejemplo,
a
un
diseño
más
eficaz
de
inhibidores.
El
objetivo
principal
de
esta
tesis
es
el
desarrollo
de
una
metodología
para
el
estudio
cuantitativo
de
la
ET
en
los
sistemas
biológicos.
En
este
sentido,
hemos
desarrollado
un
nuevo
método
para
obtener
el
camino
de
transferencia
electrónico,
llamado
QM/MM
e-‐
Pathway,
que
se
puede
aplicar
en
sistemas
complejos
con
ET
de
largo
alcance.
El
método
se
basa
en
una
búsqueda
sucesiva
de
residuos
importantes
para
la
ET,
utilizando
la
modificación
de
la
región
quantica
en
métodos
mixtos
QM/MM,
y
siguiendo
la
evolución
de
la
densidad
de
espín
dentro
de
la
zona
de
transferencia.
Hemos
demostrado
la
utilidad
y
la
aplicabilidad
del
algoritmo
en
el
complejo
P450cam/Pdx,
identificando
el
papel
clave
de
la
Arg112
(en
P450cam)
y
del
Asp48
(en
Pdx),
ambos
conocidos
en
la
literatura.
Además
de
obtener
caminos
de
ET,
hemos
cuantificado
su
importancia
en
términos
del
acoplamiento
electrónico
entre
el
dador
y
aceptor
para
los
diferentes
caminos.
En
este
sentido,
se
realizaron
dos
estudios
de
la
influencia
del
solvente
y
de
la
temperatura
en
el
acoplamiento
electrónico
para
sistemas
modelo
oligopéptidos.
Ambos
estudios
revelaron
que
los
valores
del
acoplamiento
electrónico
fluctúan
fuertemente
a
lo
largo
de
las
trayectorias
de
dinámica
molecular
obtenidas,
y
el
mecanismo
de
transferencia
de
electrones
se
ve
ampliamente
afectado
por
el
espacio
conformacional
del
sistema.
La
combinación
del
QM/MM
e-‐pathway
y
de
los
cálculos
de
acoplamiento
electronico
fueron
utilizados
finalmente
para
investigar
la
ET
en
el
complejo
CCP/Cytc.
Nuestros
hallazgos
indican
el
papel
fundamental
del
Trp191
en
localizar
un
estadio
intermedio
para
la
transferencia
electronica,
así
como
el
camino
ET
principal
que
incluye
Ala194,
Ala193,
Gly192
y
Trp191.
Ambos
hallazgos
fueron
confirmados
a
través
de
la
literatura.
Los
resultados
obtenidos
para
el
muestro
de
manios
de
ET,
junto
con
su
evaluación
a
través
de
cálculos
de
acoplamiento
electrónico,
sugieren
un
enfoque
sencillo
y
prometedor
para
investigar
ET
de
largo
alcance
en
proteínas.<br>The
focus
of
this
PhD
thesis
lies
on
electron
transfer
(ET)
processes,
belonging
to
the
simplest
but
most
crucial
reactions
in
biochemistry.
Getting
direct
information
of
the
forces
driving
the
process
and
the
actual
electron
pathway
is
not
a
trivial
task.
Such
atomic
and
electronic
detailed
information,
however,
is
very
valuable
in
terms
of
a
better
understanding
of
the
enzymatic
cycle,
which
might
lead,
for
example,
to
more
efficient
protein
inhibitor
design.
The
main
objective
of
this
thesis
was
the
development
of
a
methodology
for
the
quantitative
study
of
ET
in
biological
systems.
In
this
regard,
we
developed
a
novel
approach
to
map
long-‐range
electron
transfer
pathways,
called
QM/MM
e-‐Pathway.
The
method
is
based
on
a
successive
search
for
important
ET
residues
in
terms
of
modifying
the
QM
region
following
the
evolution
of
the
spin
density
of
the
electron
(hole)
within
a
given
transfer
region.
We
proved
the
usefulness
and
applicability
of
the
algorithm
on
the
P450cam/Pdx
complex,
indicating
the
key
role
of
Arg112
of
P450cam
and
Asp48
of
Pdx
for
its
ET
pathway,
both
being
known
to
be
important
from
the
literature.
Besides
only
identifying
the
ET
pathways,
we
further
quantified
their
importance
in
terms
of
electronic
coupling
of
donor
and
acceptor
incorporating
the
particular
pathway
residues.
Within
this
regard,
we
performed
two
systematic
evaluations
of
the
underlying
reasons
for
the
influence
of
solvent
and
temperature
onto
electronic
coupling
in
oligopeptide
model
systems.
Both
studies
revealed
that
electronic
coupling
values
strongly
fluctuate
throughout
the
molecular
dynamics
trajectories
obtained,
and
the
mechanism
of
electron
transfer
is
affected
by
the
conformational
space
the
system
is
able
to
occupy.
Combining
both
ET
mapping
and
electronic
coupling
calculations,
we
finally
investigated
the
electron
transfer
in
the
CcP/Cytc
complex.
Our
findings
indicate
the
key
role
of
Trp191
being
the
bridge-‐localized
state
of
the
ET
as
well
as
the
main
pathway
consisting
of
Ala194,
Ala193,
Gly192
and
Trp191
between
CcP
and
Cytc.
Both
findings
were
confirmed
through
the
literature.
Moreover,
our
calculations
on
several
snapshots
state
a
nongated
ET
mechanism
in
this
protein
complex.
The
methodology
developed
along
this
thesis,
mapping
ET
pathways
together
with
their
evaluation
through
electronic
coupling
calculations,
suggests
a
straightforward
and
promising
approach
to
investigate
long-‐range
ET
in
proteins.
48
Semerjian, Guilhem. "Mean-field disordered systems : glasses and optimization problems, classical and quantum." Habilitation à diriger des recherches, Ecole Normale Supérieure de Paris - ENS Paris, 2013. http://tel.archives-ouvertes.fr/tel-00785924.
Full textAbstract:
Ce mémoire présente mes activités de recherche dans le domaine de la mécanique statistique des systèmes désordonnés, en particulier sur les modèles de champ moyen à connectivité finie. Ces modèles présentent de nombreuses transitions de phase dans la limite thermodynamique, avec des applications tant pour la physique des verres que pour leurs liens avec des problèmes d'optimisation de l'informatique théorique. Leur comportement sous l'effet de fluctuations quantiques est aussi discuté, en lien avec des perspectives de calcul quantique.
49
Luo, Yu. "Studies on generalizations of the classical orthogonal polynomials where gaps are allowed in their degree sequences." Kyoto University, 2020. http://hdl.handle.net/2433/253419.
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50
Rodriguez-Fernandez, Alberto. "Classical dynamics of gas-surface scattering : fundamentals and applications." Thesis, Bordeaux, 2021. http://www.theses.fr/2021BORD0038.
Full textAbstract:
L’objet de cette thèse est l’étude théorique de processus réactifs et non réactifs se produisant à l’interface gaz-solide. Deux méthodes de trajectoires classiques, différentes et complémentaires, ont été utilisées afin de simuler la dynamique de ces processus. La première met en jeu un ensemble conséquent de trajectoires classiques obtenues en résolvant numériquement les équations de Hamilton sur une surface d’énergie potentielle (SEP) construite au préalable. Ces trajectoires sont pondérées par des poids statistiques conformément à deux contraintes semiclassiques: la pondération gaussienne et la correction d’adiabaticité. Cette approche, dans un esprit quantique, a été appliquée à la collision entre H2 et la surface de Pd(111). Dans un premier temps, nous nous sommes limités au cas où H2 se trouve dans son état rovibrationnel fondamental. Nous avons par la suite considéré ses états rotationnels excités. Il nous est alors apparu nécessaire de modifier la correction d’adiabaticité sur la base d’arguments semiclassiques rigoureux. Dans les deux cas, les prédictions des probabilités de collage et de réflexion résolues en états se sont avérées être en accord remarquable avec celles obtenues par des calculs quantiques exacts, contrairement aux prédictions classiques standards. L’approche classique dans un esprit quantique pourrait ainsi s’avérer d’une grande utilité pour les études à venir.La seconde méthode utilisée dans ce travail, connu sous le vocable de Ab-Initio Molecular Dynamics (AIMD), permet de calculer les forces entre noyaux à partir de la théorie de la fonctionnelle densité et d’en déduire classiquement leurs déplacements. Contrairement à l’approche précédente, l’AIMD n’exige pas la construction généralement difficile d’une SEP (le prix à payer, toutefois, est que le coût numérique de chaque trajectoire est nettement plus élevé qu’avec la méthode précédente). L’AIMD nous a permis d’étudier le processus de dissociation de H2 sur la surface de W(110). La fonctionnelle utilisée inclut un terme de van der Waals, qui provoque un accroissement de l’attraction à longue distance, compensé par une augmentation de la répulsion à courte distance. La combinaison des deux effets diminue de façon appréciable la probabilité de dissociation, alors en meilleur accord avec le résultat expérimental obtenu à l’aide d’une surface propre. Lorsque des atomes d’oxygène sont adsorbés au préalable sur la surface, la probabilité de dissociation chute considérablement. Cet effet est d’autant plus fort que la quantité d’oxygène adsorbé est forte. Un modèle de phase ordonnée a été utilisé afin d’expliquer l’absence de collage pour le taux de couverture Θ > 0.35 ML observé expérimentalement. Les atomes d’oxygène dévient les molécules H2 des étroits passages conduisant au collage en l’absence des atomes d’oxygène. Ceci élimine toute chance de collage pour de forts taux de recouvrement. En revanche, pour de faible taux, on s’attend à ce qu’une dynamique similaire à celle sur la surface propre se produise au dessus des atomes de tungstène, et à une distance suffisamment grande des atomes d’oxygène<br>This thesis manuscript is devoted to the theoretical study of several reactive and non-reactive processes that take place at the gas-solid interface. Two classical trajectory methods, different and complementary, were used to simulate the dynamics of these processes. The first one relies on large sets of classical paths obtained by numerically solving Hamilton equations on a previously constructed potential energy surface (PES). Classical paths are then assigned statistical weights based on two semiclassical corrections: Gaussian binning and the adiabaticity correction. This approach, in a quantum spirit, was applied to the scattering of H2 on a Pd(111) surface. First, the study focused on collisions where H2 is initially in the rovibrational ground state. Then, rotationally excited states were considered. On this occasion, a variation of the adiabaticity correction based on firmer semiclassical grounds was introduced. In both cases, the predictions of the sticking and state-resolved reflection probabilities were found to be in remarkably good agreement with those obtained through exact quantum time-dependent calculations, contrary to standard quasi-classical trajectory predictions. The classical approach in a quantum spirit could thus be very useful for future studies.The second method used in this work, known as Ab-Initio Molecular Dynamics (AIMD), calculates the inter-nuclear forces from density functional theory and uses them to classically move the nuclei. Contrary to the previous approach, AIMD does not require the very demanding construction of a PES (the price to pay, however, is that the numerical cost of each trajectory is much higher than with the previous method). AIMD allowed us to study the dissociation process of H2 on W(110) surfaces.The functional we used includes a van der Waals term which provokes an increase of the far distance attraction that is compensated by a stronger repulsion at short distances. The combination of both effects appreciably decreases the value of the dissociation probability, bringing it closer to the experimental result when a clean surface is used. When oxygen atoms are previously adsorbed on the surface, the dissociation probability drops considerably. This effect increases with the amount of oxygen on the surface. A model ordered phase is used to explain the nonexistent sticking probability for coverages Θ > 0.35 ML observed experimentally. The oxygen atoms push the H2 molecules away from the narrow bottlenecks leading to the surface in the absence of oxygen atoms. This effectively eliminates any chance of dissociation in the surface for high coverages. At low coverages, it is expected that similar dynamics compared to the clean surface case arise on top of W atoms at a sufficiently large distance from O atoms