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Nemati, Navid. "Theorie macroscopique de propagation du son dans les milieux poreux 'à structure rigide permettant la dispersion spatiale: principe et validation." Phd thesis, Université du Maine, 2012. http://tel.archives-ouvertes.fr/tel-00848603.
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Ce travail présente et valide une théorie nonlocale nouvelle et généralisée, de la propagation acoustique dans les milieux poreux à structure rigide, saturés par un fluide viscothermique. Cette théorie linéaire permet de dépasser les limites de la théorie classique basée sur la théorie de l'homogénéisation. Elle prend en compte non seulement les phénomènes de dispersion temporelle, mais aussi ceux de dispersion spatiale. Dans le cadre de la nouvelle approche, une nouvelle procédure d'homogénéisation est proposée, qui permet de trouver les propriétés acoustiques à l'échelle macroscopique, en résolvant deux problèmes d'action-réponse indépendants, posés à l'échelle microscopique de Navier-Stokes-Fourier. Contrairement à la méthode classique d'homogénéisation, aucune contrainte de séparation d'échelle n'est introduite. En l'absence de structure solide, la procédure redonne l'équation de dispersion de Kirchhoff-Langevin, qui décrit la propagation des ondes longitudinales dans les fluides viscothermiques. La nouvelle théorie et procédure d'homogénéisation nonlocale sont validées dans trois cas, portant sur des microgéométries significativement différentes. Dans le cas simple d'un tube circulaire rempli par un fluide viscothermique, on montre que les nombres d'ondes et les impédances prédits par la théorie nonlocale, coïncident avec ceux de la solution exacte de Kirchhoff, connue depuis longtemps. Au contraire, les résultats issus de la théorie locale (celle de Zwikker et Kosten, découlant de la théorie classique d'homogénéisation) ne donnent que le mode le plus attenué, et encore, seulement avec le petit désaccord existant entre la solution simplifiée de Zwikker et Kosten et celle exacte de Kirchhoff. Dans le cas où le milieu poreux est constitué d'un réseau carré de cylindres rigides parallèles, plongés dans le fluide, la propagation étant regardée dans une direction transverse, la vitesse de phase du mode le plus atténué peut être calculée en fonction de la fréquence en suivant les approches locale et nonlocale, résolues au moyen de simulations numériques par la méthode des Eléments Finis. Elle peut être calculée d'autre part par une méthode complètement différente et quasi-exacte, de diffusion multiple prenant en compte les effets viscothermiques. Ce dernier résultat quasi-exact montre un accord remarquable avec celui obtenu par la théorie nonlocale, sans restriction de longueur d'onde. Avec celui de la théorie locale, l'accord ne se produit que tant que la longueur d'onde reste assez grande.
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Iwasaki, Masayuki. "Nonlocal potentials and nuclear resonance scattering /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu148726053195632.
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LOMBARDINI, LUCA. "MINIMIZATION PROBLEMS INVOLVING NONLOCAL FUNCTIONALS: NONLOCAL MINIMAL SURFACES AND A FREE BOUNDARY PROBLEM." Doctoral thesis, Università degli Studi di Milano, 2019. http://hdl.handle.net/2434/607164.
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This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the s-fractional perimeter and its minimizers, the s-minimal sets. We investigate the behavior of sets having (locally) finite fractional perimeter and we establish existence and compactness results for (locally) s-minimal sets. We study the s-minimal sets in highly nonlocal regimes, that correspond to small values of the fractional parameter s. We introduce a functional framework for studying those s-minimal sets that can be globally written as subgraphs. In particular, we prove existence and uniqueness results for minimizers of a fractional version of the classical area functional and we show the equivalence between minimizers and various notions of solution of the fractional mean curvature equation. We also prove a flatness result for entire nonlocal minimal graphs having some partial derivatives bounded from either above or below. Moreover, we consider a free boundary problem, which consists in the minimization of a functional defined as the sum of a nonlocal energy, plus the classical perimeter. Concerning this problem, we prove uniform energy estimates and we study the blow-up sequence of a minimizer---in particular establishing a Weiss-type monotonicity formula.
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Freitas, Pedro S. C. de. "Some problems in nonlocal reaction-diffusion equations." Thesis, Heriot-Watt University, 1994. http://hdl.handle.net/10399/1401.
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Magleby, Stephanie Allred. "The Violation of Bell's Inequality in a Deterministic but Nonlocal Model." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1197.pdf.
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Oterkus, Erkan. "Peridynamic Theory for Modeling Three-Dimensional Damage Growth in Metallic and Composite Structures." Diss., The University of Arizona, 2010. http://hdl.handle.net/10150/145366.
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A recently introduced nonlocal peridynamic theory removes the obstacles present in classical continuum mechanics that limit the prediction of crack initiation and growth in materials. It is also applicable at different length scales. This study presents an alternative approach for the derivation of peridynamic equations of motion based on the principle of virtual work. It also presents solutions for the longitudinal vibration of a bar subjected to an initial stretch, propagation of a pre-existing crack in a plate subjected to velocity boundary conditions, and crack initiation and growth in a plate with a circular cutout. Furthermore, damage growth in composites involves complex and progressive failure modes. Current computational tools are incapable of predicting failure in composite materials mainly due to their mathematical structure. However, the peridynamic theory removes these obstacles by taking into account non-local interactions between material points. Hence, an application of the peridynamic theory to predict how damage propagates in fiber reinforced composite materials subjected to mechanical and thermal loading conditions is presented. Finally, an analysis approach based on a merger of the finite element method and the peridynamic theory is proposed. Its validity is established through qualitative and quantitative comparisons against the test results for a stiffened composite curved panel with a central slot under combined internal pressure and axial tension. The predicted initial and final failure loads, as well as the final failure modes, are in close agreement with the experimental observations. This proposed approach demonstrates the capability of the PD approach to assess the durability of complex composite structures.
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Zhang, You-Kuan. "A quasilinear theory of time-dependent nonlocal dispersion in geologic media." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185039.
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A theory is presented which accounts for a particular aspect of nonlinearity caused by the deviation of plume "particles" from their mean trajectory in three-dimensional, statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities. Quasilinear expressions for the time-dependent nonlocal dispersivity and spatial covariance tensors of ensemble mean concentration are derived, as a function of time, variance σᵧ² of log hydraulic conductivity, degree of anisotropy, and flow direction. One important difference between existing linear theories and the new quasilinear theory is that in the former transverse nonlocal dispersivities tend asymptotically to zero whereas in the latter they tend to nonzero Fickian asymptotes. Another important difference is that while all existing theories are nominally limited to situations where σᵧ² is less than 1, the quasilinear theory is expected to be less prone to error when this restriction is violated because it deals with the above nonlinearity without formally limiting σᵧ². The theory predicts a significant drop in dimensionless longitudinal dispersivity when σᵧ² is large as compared to the case where σᵧ² is small. As a consequence of this drop the real asymptotic longitudinal dispersivity, which varies in proportion to σᵧ² when σᵧ² is small, is predicted to vary as σᵧ when σᵧ² is large. The dimensionless transverse dispersivity also drops significantly at early dimensionless time when σᵧ² is large. At late time this dispersivity attains a maximum near σᵧ² = 1, varies asymptotically at a rate proportional to σᵧ² when σᵧ² is small, and appears inversely proportional to σᵧ when σᵧ² is large. The actual asymptotic transverse dispersivity varies in proportion to σᵧ⁴ when σᵧ² is small and appears proportional to σᵧ when σᵧ² is large. One of the most interesting findings is that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the orientation of longitudinal spread is generally offset from μ toward the direction of largest log hydraulic conductivity correlation scale. When local dispersion is active, a plume starts elongating parallel to μ. With time the long axis of the plume rotates toward the direction of largest correlation scale, then rotates back toward μ, and finally stabilizes asymptotically at a relatively small angle of deflection. Application of the theory to depth-averaged concentration data from the recent tracer experiment at Borden, Ontario, yields a consistent and improved fit without any need for parameter adjustment.
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AUGELLO, RICCARDO. "Advanced FEs for the micropolar and geometrical nonlinear analyses of composite structures." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2872330.
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Foghem, Gounoue Guy Fabrice [Verfasser]. "$L^2$-Theory for nonlocal operators on domains / Guy Fabrice Foghem Gounoue." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1219215139/34.
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BRASSEUR, JULIEN. "ANALYSIS OF SOME NONLOCAL MODELS IN POPULATION DYNAMICS." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/597755.
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This thesis is mainly devoted to the mathematical analysis of some nonlocal models arising in population dynamics. In general, the study of these models meets with numerous difficulties owing to the lack of compactness and of regularizing effects. In this respect, their analysis requires new tools, both theoretical and qualitative. We present several results in this direction.
In the first part, we develop a functional analytic toolbox which allows one to handle some quantities arising in the study of these models. In the first place, we extend the characterization of Sobolev spaces due to Bourgain, Brezis and Mironescu to low regularity function spaces of Besov type. This results in a new theoretical framework that is more adapted to the study of some nonlocal equations of Fisher-KPP type. In the second place, we study the regularity of the restrictions of these functions to hyperplanes. We prove that, for a large class of Besov spaces, a surprising loss of regularity occurs. Moreover, we obtain an optimal characterization of the regularity of these restrictions in terms of spaces of so-called “generalized smoothness”.
In the second part, we study qualitative properties of solutions to some nonlocal
reaction-diffusion equations set in (possibly) heterogeneous domains. In collaboration with J. Coville, F. Hamel and E. Valdinoci, we consider the case of a perforated domain which consists of the Euclidean space to which a compact set, called an “obstacle”, is removed. When the latter is convex (or close to being convex), we prove that the solutions are necessarily constant. In a joint work with J. Coville, we study in greater detail the influence of the geometry of the obstacle on the classification of the solutions. Using tools of the type of those developed in the first part of this thesis, we construct a family of counterexamples when the obstacle is no longer convex. Lastly, in a work in collaboration with S. Dipierro, we study qualitative properties of solutions to nonlinear elliptic systems in variational form. We establish various monotonicity results in a fairly general setting that covers both local and fractional operators.
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Nersisyan, Henrik [Verfasser], and Luca [Akademischer Betreuer] Amendola. "Infrared Nonlocal Gravity Theories : Optimizing Science Return to Euclid Satellite Mission / Henrik Nersisyan ; Betreuer: Luca Amendola." Heidelberg : Universitätsbibliothek Heidelberg, 2017. http://d-nb.info/117801066X/34.
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Savin, Anton Yu, та Boris Yu Sternin. "Index defects in the theory of nonlocal boundary value problems and the η-invariant". Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2614/.
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The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincaré duality in the K-theory of the corresponding manifolds with singularities.
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Cao, Xinlin. "Geometric structures of eigenfunctions with applications to inverse scattering theory, and nonlocal inverse problems." HKBU Institutional Repository, 2020. https://repository.hkbu.edu.hk/etd_oa/754.
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Inverse problems are problems where causes for desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development, including radar/sonar, medical imaging, geophysical exploration, invisibility cloaking and remote sensing, to name just a few. In this thesis, we focus on the theoretical study and applications of some intriguing inverse problems. Precisely speaking, we are concerned with two typical kinds of problems in the field of wave scattering and nonlocal inverse problem, respectively. The first topic is on the geometric structures of eigenfunctions and their applications in wave scattering theory, in which the conductive transmission eigenfunctions and Laplacian eigenfunctions are considered. For the study on the intrinsic geometric structures of the conductive transmission eigenfunctions, we first present the vanishing properties of the eigenfunctions at corners both in R2 and R3, based on microlocal analysis with the help of a particular type of planar complex geometrical optics (CGO) solution. This significantly extends the previous study on the interior transmission eigenfunctions. Then, as a practical application of the obtained geometric results, we establish a unique recovery result for the inverse problem associated with the transverse electromagnetic scattering by a single far-field measurement in simultaneously determining a polygonal conductive obstacle and its surface conductive parameter. For the study on the geometric structures of Laplacian eigenfunctions, we separately discuss the two-dimensional case and the three-dimensional case. In R2, we introduce a new notion of generalized singular lines of Laplacian eigenfunctions, and carefully investigate these singular lines and the nodal lines. The studies reveal that the intersecting angle between two of those lines is closely related to the vanishing order of the eigenfunction at the intersecting point. We provide an accurate and comprehensive quantitative characterization of the relationship. In R3, we study the analytic behaviors of Laplacian eigenfunctions at places where nodal or generalized singular planes intersect, which is much more complicated. These theoretical findings are original and of significant interest in spectral theory. Moreover, they are applied directly to some physical problems of great importance, including the inverse obstacle scattering problem and the inverse diffraction grating problem. It is shown in a certain polygonal (polyhedral) setup that one can recover the support of the unknown scatterer as well as the surface impedance parameter by finitely many far-field patterns. Our second topic is concerning the fractional partial differential operators and some related nonlocal inverse problems. We present some prelimilary knowledge on fractional Sobolev Spaces and fractional partial differential operators first. Then we focus on the simultaneous recovery results of two interesting nonlocal inverse problems. One is simultaneously recovering potentials and the embedded obstacles for anisotropic fractional Schrödinger operators based on the strong uniqueness property and Runge approximation property. The other one is the nonlocal inverse problem associated with a fractional Helmholtz equation that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. The main method utilized here is the low-frequency asymptotics combining with the variational argument. In sharp contrast, these unique determination results are unknown in the local case, which would be of significant importance in thermo- and photo-acoustic tomography.
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Hollender, Julian. "Lévy-Type Processes under Uncertainty and Related Nonlocal Equations." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-211795.
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The theoretical study of nonlinear expectations is the focus of attention for applications in a variety of different fields — often with the objective to model systems under incomplete information. Especially in mathematical finance, advances in the theory of sublinear expectations (also referred to as coherent risk measures) lay the theoretical foundation for modern approaches to evaluations under the presence of Knightian uncertainty. In this book, we introduce and study a large class of jump-type processes for sublinear expectations, which can be interpreted as Lévy-type processes under uncertainty in their characteristics. Moreover, we establish an existence and uniqueness theory for related nonlinear, nonlocal Hamilton-Jacobi-Bellman equations with non-dominated jump terms.
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Kilic, Bahattin. "Peridynamic Theory for Progressive Failure Prediction in Homogeneous and Heterogeneous Materials." Diss., The University of Arizona, 2008. http://hdl.handle.net/10150/193658.
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The classical continuum theory is not capable of predicting failure without an external crack growth criteria and treats the interface having zero thickness. Alternatively, a nonlocal continuum theory referred to as peridynamic theory eliminates these shortcomings by utilizing formulation that uses displacements, rather than derivatives of displacements, and including material failure in its constitutive relations through the response functions. This study presents a new response function as part of the peridynamic theory to include thermal loading. Furthermore, an efficient numerical algorithm is presented for solution of peridynamic equations. Solution method relies on the discretization of peridynamic equations at collocation points resulting in a set of ordinary differential equations with respect to time. These differential equations are then integrated using explicit methods. In order to improve numerical efficiency of the computations, spatial partitioning is introduced through uniform grids as arrays of linked lists. Furthermore, the domain of interest is divided into subunits each of which is assigned to a specific processor to utilize parallel processing using OpenMP. In order to obtain the static solutions, the adaptive dynamic relaxation method is developed for the solution of peridynamic equations. Furthermore, an approach to couple peridynamic theory and finite element analysis is introduced to take advantage of their salient features. The regions in which failure is expected are modeled using peridynamics while the remaining regions are modeled utilizing finite element method. Finally, the present solution method is utilized for damage prediction of many problems subjected to mechanical, thermal and buckling loads.
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Ried, Tobias [Verfasser], and D. [Akademischer Betreuer] Hundertmark. "On some nonlinear and nonlocal effective equations in kinetic theory and nonlinear optics / Tobias Ried ; Betreuer: D. Hundertmark." Karlsruhe : KIT-Bibliothek, 2017. http://d-nb.info/1147485097/34.
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Hafezi, Mohammad Hadi, and Mohammad Hadi Hafezi. "Peridynamic Modeling and Extending the Concept to Peri-Ultrasound Modeling." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/625456.
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In this dissertation, a novel fast modeling technique called peri-ultrasound that can model both linear and nonlinear ultrasonic behavior of materials is developed and implemented. Nonlinear ultrasonic response can detect even very small material non- linearity. Quantification of the material nonlinearity at the early stages of damage is important to avoid catastrophic failure and reduce repair costs. The developed model uses the nonlocal continuum-based peridynamic theory which was found to be a good simulation tool for handling crack propagation modeling, in particular when multiple cracks grow simultaneously. The developed peri-ultrasound modeling tool has been used to model the ultrasonic response at the interface of two materials in presence of an interface crack. Also, the stress wave propagation in a half-space (or half-plane for a 2-dimensional problem) with boundary loading is investigated using peri-ultrasound modeling. In another simulation, well-established two-dimensional Lamb's problem is investigated where the results are verified against available analytical solution. Also, the interaction between the surface wave and a surface breaking crack is studied.
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Agwai, Abigail G. "A Peridynamic Approach for Coupled Fields." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/204892.
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Peridynamics is an emerging nonlocal continuum theory which allows governing field equations to be applicable at discontinuities. This applicability at discontinuities is achieved by replacing the spatial derivatives, which lose meaning at discontinuities, with integrals that are valid regardless of the existence of a discontinuity. Within the realm of solid mechanics, the peridynamic theory is one of the techniques that has been employed to model material fracture. In this work, the peridynamic theory is used to investigate different fracture problems in order to establish its fidelity for predicting crack growth. Various fracture experiments are modeled and analyzed. The peridynamic predictions are made and compared against experimental findings along with predictions from other commonly used numerical fracture techniques. Additionally, this work applies the peridynamic framework to model heat transfer. Generalized peridynamic heat transfer equation is formulated using the Lagrangian formalism. Peridynamic heat conduction quantites are related to quanties from the classical theory. A numerical procedure based on an explicit time stepping scheme is adopted to solve the peridynamic heat transfer equation and various benchmark problems are considered for verification of the model. This paves the way for the coupling of thermal and structural fields within the framework of peridynamics. The fully coupled peridynamic thermomechanical equations are derived based on thermodynamic considerations, and a nondimensional form of the coupled thermomechanical peridynamic equations is also presented. An explicit staggered algorithm is implemented in order to numerically approximate the solution to these coupled equations. The coupled thermal and structural responses of a thermoelastic semi-infinite bar and a thermoelastic vibrating bar are subsequently investigated.
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Hori, Kumiko, and Shigeo Yoshida. "Nonlocal memory effects of the electromotive force by fluid motion with helicity and two-dimensional periodicity." Taylor & Francis, 2008. http://hdl.handle.net/2237/13015.
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Iwata, Natsumi. "Nonlocal theory of relativistic ponderomotive force in high intensity lasers based on the phase space Lagrangian and the role in the interaction with various mediums." Kyoto University, 2014. http://hdl.handle.net/2433/188822.
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Khamitova, Raisa. "Symmetries and conservation laws." Doctoral thesis, Växjö : Växjö University Press, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-2587.
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Seitenfuss, Alan Bourscheidt. "On the behavior of a linear elastic peridynamic material." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-22062017-100938/.
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The peridynamic theory is a generalization of classical continuum mechanics and takes into account the interaction between material points separated by a finite distance within a peridynamic horizon δ. The parameter δ corresponds to a length scale and is treated as a material property related to the microstructure of the body. Since the balance of linear momentum is written in terms of an integral equation that remains valid in the presence of discontinuities, the peridynamic theory is suitable for studying the material behavior in regions with singularities. The first part of this work concerns the evaluation of the properties of a linear elastic peridynamic material in the context of a three-dimensional state-based peridynamic theory, which uses the difference displacement quotient field in the neighborhood of a material point and considers both length and relative angle changes. This material model is based upon a free energy function that contains four material constants, being, therefore, different from other peridynamic models found in the literature, which contain only two material constants. Using convergence results of the peridynamic theory to the classical linear elasticity theory in the limit of small horizons and a correspondence argument between the free energy function and the strain energy density function from the classical theory, expressions were obtained previously relating three peridynamic constants to the classical elastic constants of an isotropic linear elastic material. To calculate the fourth peridynamic material constant, which couples both bond length and relative angle changes, the correspondence argument is used once again together with the strain field of a linearly elastic beam subjected to pure bending. The expression for the fourth constant is obtained in terms of the Poisson\'s ratio and the shear elastic modulus of the classical theory. The validity of this expression is confirmed through the consideration of other experiments in mechanics, such as bending of a beam by terminal loads and anti-plane shear of a circular cylinder. In particular, numerical results indicate that the expressions for the constants are independent of the experiment chosen. The second part of this work concerns an investigation of the behavior of a one-dimensional linearly elastic bar of length L in the context of the peridynamic theory; especially, near the ends of the bar, where it is expected that the behavior of the peridynamic bar may be very different from the behavior of a classical linear elastic bar. The bar is in equilibrium without body force, is fixed at one end, and is subjected to an imposed displacement at the other end. The bar has micromodulus C, which is related to the Young\'s modulus E in the classical theory through different expressions found in the literature. Depending on the expression for C, the displacement field may be singular near the ends, which is in contrast to the linear behavior of the displacement field observed in classical linear elasticity. In spite of the above, it is also shown that the peridynamic displacement field converges to its classical counterpart as the peridynamic horizon tends to zero.<br>A teoria peridinâmica é uma generalização da teoria clássica da mecânica do contínuo e considera a interação de pontos materiais devido a forças que agem a uma distância finita entre si, além da qual considera-se nula a força de interação. Por ter o balanço de momento linear formulado como uma equação integral que permanece válida na presença de descontinuidades, a teoria peridinâmica é adequada para o estudo do comportamento de materiais em regiões com singularidades. A primeira parte deste trabalho consiste no cálculo das propriedades de um material peridinâmico elástico linear no contexto de uma teoria peridinâmica de estado, linearmente elástica e tridimensional, que utiliza o campo quociente de deslocamento relativo na vizinhança de um ponto material e leva em conta mudanças relativas angulares e de comprimento. Esse modelo utiliza uma função energia livre que apresenta quatro constantes materiais, sendo, portanto, diferente de outros modelos peridinâmicos investigados na literatura, os quais contêm somente duas constantes materiais. Utilizando resultados de convergência da teoria peridinâmica para a teoria de elasticidade linear clássica no limite de pequenos horizontes e um argumento de correspondência entre as funções energia livre proposta e densidade de energia de deformação da teoria clássica, expressões para três constantes peridinâmicas foram obtidas em função das constantes de um material elástico e isotrópico da teoria clássica. O argumento de correspondêmcia, em conjunto com o campo de deformações de uma viga submetida à flexão pura, é utilizado para calcular a quarta constante peridinâmica do material, que relaciona mudanças angulares relativas e de comprimentos das ligações entre as partículas. Obtem-se uma expressão para a quarta constante em termos do coeficiente de Poisson e do módulo de elasticidade ao cisalhamento da teoria clássica. A validade dessa expressão é confirmada por meio da consideração de outros experimentos da mecânica, tais como flexão de um viga por cargas terminais e cisalhamento anti-plano de um eixo cilíndrico. Em particular, os resultados numéricos indicam que as expressões para as constantes são independentes do experimento escolhido. A segunda parte deste trabalho consiste em uma investigação do comportamento de uma barra unidimensional linearmente elástica de comprimento L no contexto da teoria peridinâmica; especialmente, próximo às extremidades da barra, onde espera-se que o comportamento da barra peridinâmica possa ser muito diferente do comportamento de uma barra elástica linear clássica. A barra está em equilíbrio e sem força de corpo, fixa em uma extremidade, e sujeita a deslocamento imposto na outra extremidade. A barra possui micromódulo C, o qual está relacionado ao módulo de Young E da teoria clássica por meio de diferentes expressões encontradas na literatura. Dependendo da expressão para C, o campo de deslocamento pode ser singular próximo às extremidades, o que contrasta com o comportamento linear do campo de deslocamento observado na elasticidade linear clássica. Apesar disso, é mostrado também que o campo de deslocamento peridinâmico converge para o campo de deslocamento da teoria clássica quando o horizonte peridinâmico tende a zero.
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Henning, Soeren. "Elektronendynamik und Phasendiagramme in Vielteilchen-Modellen des Magnetismus." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2013. http://dx.doi.org/10.18452/16803.
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Der erste Teil dieser Arbeit ist dem Kondogittermodell gewidmet. Für ein Elektron, das in einen ferromagnetisch gesättigten Hintergrund aus lokalen Spinmomenten eingebracht wird (ferromagnetisches Polaron), wird die stationäre Schrödingergleichung gelöst und das vollständige Eigenwertspektrum im endlichen und unendlichen Gitter abgeleitet. Danach wird die zeitabhängige Schrödingergleichung für beliebige Anfangsbedingungen gelöst und eine detaillierte Analyse des Down-Elektron-Zerfalls vorgenommen. Für endliche Bandfüllungen wird im Anschluss das magnetische Grundzustandsphasendiagramm mit Hilfe einer Molekularfeldtheorie bestimmt. Der Einfluss von Verdünnung/Unordnung im lokalen Momentensystem auf die auftretenden Phasen wird analysiert. Im zweiten Teil der Arbeit wird das Hubbardmodell untersucht. Für dieses wird mit Hilfe einer modifizierten Störungstheorie (englisch: modified perturbation theory, MPT) eine wellenzahlabhängige (nicht-lokale) Selbstenergie abgeleitet, die sowohl für schwache als auch für starke Coulombwechselwirkungen gute Ergebnisse liefert. Mit dieser werden dann Spektraldichten und Quasiteilchenzustandsdichten berechnet, wobei insbesondere die nicht-lokalen Korrelationseffekte im Fokus stehen. Daneben werden Ergebnisse für die optische Leitfähigkeit, die in einer renormierten diagrammatischen Ein-Schleifen-Näherung berechnet wurden, besprochen. Es wird dann gezeigt, dass nur unter Beachtung der nicht-lokalen Korrelationseffekte ein ferromagnetisches Phasendiagramm konstruiert werden kann, das in Einklang mit dem Mermin-Wagner-Theorem steht.<br>The first part of this work deals with the Kondo-lattice model. The stationary Schrödinger equation is solved for the case of one electron in a ferromagnetically saturated local moment system (the magnetic polaron). The complete eigensystem is derived for the finite and infinite lattice. The time-dependent Schrödinger equation is then solved for arbitrary initial conditions and a detailed analysis of the down-electron decay dynamics is given. For finite band occupations the magnetic ground-state phase diagram is constructed within a mean-field theory. The effect of disorder/dilution in the local moment system on the phase diagram is discussed. The second part concentrates on the investigation of the Hubbard model. A nonlocal self-energy is derived within a modified perturbation theory that interpolates between weak and strong Coulomb repulsion. Results for the spectral density and quasiparticle density of states are shown with special attention to the effects of nonlocal correlations. Results for the optical conductivity within a renormalized one-loop approximation are also discussed. The main result of this section is the importance of nonlocal correlations for the fulfillment of the Mermin-Wagner theorem. A phase diagram that shows regions of ferromagnetic order is calculated for the simple cubic lattice.
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Nikola, Despotović. "Стабилност и осциловање запремински оптерећене правоугаоне нано-плоче уз коришћење нелокалне теорије еластичности". Phd thesis, Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, 2018. https://www.cris.uns.ac.rs/record.jsf?recordId=107567&source=NDLTD&language=en.
Full textAbstract:
У овој тези проучене су осцилације и стабилност запремински оптерећене правоугаоненано-плоче уз коришћење Ерингенове теорије еластичности. Запреминско оптерећењеје константно са правцем који је у равни плоче. Гранични услови су моделовани каопокретна укљештења. Класична теорија плоча и Карманова теорија плоча, које сунадограђене Ерингеновом теоријом еластичности, искоришћене су за формирањедиференцијалне једначине стабилности и осциловања нано-плоче. Галеркиновомметодом одређене су сопствене фреквенције трансверзалних осцилација нано-плоче узависности од ефеката запреминског оптерећења и нелокалности. Одређене сукритичне вредности параметра запреминског оптерећења при којима нано-плоча губистабилност. Приказан је утицај ефеката запреминског оптерећења и нелокалности нанеколико облика осциловања. Верификација резултата извршена је помоћу методедиференцијалних квадратура.<br>U ovoj tezi proučene su oscilacije i stabilnost zapreminski opterećene pravougaonenano-ploče uz korišćenje Eringenove teorije elastičnosti. Zapreminsko opterećenjeje konstantno sa pravcem koji je u ravni ploče. Granični uslovi su modelovani kaopokretna uklještenja. Klasična teorija ploča i Karmanova teorija ploča, koje sunadograđene Eringenovom teorijom elastičnosti, iskorišćene su za formiranjediferencijalne jednačine stabilnosti i oscilovanja nano-ploče. Galerkinovommetodom određene su sopstvene frekvencije transverzalnih oscilacija nano-ploče uzavisnosti od efekata zapreminskog opterećenja i nelokalnosti. Određene sukritične vrednosti parametra zapreminskog opterećenja pri kojima nano-ploča gubistabilnost. Prikazan je uticaj efekata zapreminskog opterećenja i nelokalnosti nanekoliko oblika oscilovanja. Verifikacija rezultata izvršena je pomoću metodediferencijalnih kvadratura.<br>In this thesis, the problem of stability and vibration of a rectangular single-layer graphenesheet under body force is studied using Eringen’s theory. The body force is constant andparallel with the plate. The boundary conditions correspond to the dynamical model of ananoplate clamped at all its sides. Classical plate theory and von Kármán plate theory,upgraded with nonlocal elasticity theory, is used to formulate the differential equation ofstability and vibration of the nanoplate. Natural frequencies of transverse vibrations,depending on the effects of body load and nonlocality, are obtained using Galerkin’s method.Critical values of the body load parameter, i.e., the values of the body load parameter whenthe plate loses its stability, are determined for different values of nonlocality parameter. Themode shapes of nanoplate under influences of body load and nonlocality are presented aswell. Differential quadrature method is used for verification of obtained results.
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Theeten, Marc. "Semi-microscopic and microscopic three-body models of nuclei and hypernuclei." Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210268.
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De nombreux noyaux atomiques et hypernoyaux se modélisent comme des structures à trois corps. C'est le cas, par exemple, de noyaux à halo, comme 6He, ou de noyaux stables, comme 12C et 9Be. <p>En effet, 6He se caractérise comme un système à trois corps, formé d'un coeur (une particule alpha) et de deux neutrons de valence faiblement liés. Le noyau de 12C peut s'étudier comme un système lié formé de trois particules alphas, tandis que 9Be peut être décrit comme la liaison de deux particules alphas et d'un neutron.<p><p>Dans les exemples précédents, les particules alphas sont des amas de nucléons. Elles possèdent donc une structure interne dont il faut tenir compte en raison du principe de Pauli.<p><p>Les modèles les plus réalistes pour décrire les structures à trois corps sont les modèles "microscopiques". Ces modèles prennent en compte explicitement tous les nucléons et respectent exactement le principe d'antisymétrisation de Pauli. Cependant, l'application de ces modèles est fortement limitée en pratique, car ils exigent de trop nombreux et trop longs calculs.<p>Par conséquent, pour simplifier considérablement les calculs et permettre l'étude des structures à trois corps, des modèles moins détaillés, de type "semi-microscopiques", sont également développés. Dans ces modèles, on représente les amas de nucléons comme de simples particules ponctuelles. Dans ce cas, la modélisation consiste à construire les potentiels effectifs entre les amas, puis à les employer dans les modèles à trois corps.<p><p>Dans ce travail, nous avons développé les modèles "semi-microscopiques à trois corps". Les potentiels effectifs entre amas sont directement déduits des forces entre nucléons (selon la RGM à 2 corps). Ces potentiels sont "non-locaux", et dépendent des énergies des amas qui interagissent. Ils permettent de simuler le principe de Pauli et les échanges de nucléons entre les amas. La dépendance en l'énergie se révèle être un inconvénient dans les modèles à trois corps. Les potentiels effectifs sont par conséquent transformés en de nouveaux potentiels (non-locaux) indépendants de l'énergie, bien adaptés aux modèles à trois corps. Les modèles "semi-microscopiques" sont beaucoup plus simples et plus rapides que les modèles "microscopiques". Ils fournissent les fonctions d'onde des états liés à trois corps des noyaux légers et hypernoyaux. Cela permet d'une part de comprendre les propriétés spectroscopiques nucléaires, et d'autre part, cela ouvre la voie pour de futurs modèles de réactions nucléaires impliquant les structures à trois corps.<p><p>/<p><p>Several atomic nuclei and hypernuclei can be modelled as three-body structures: e.g. two-neutron halo nuclei, such as 6He, and other nuclei, such as 12C and 9Be.<p>Indeed 6He can be represented as a three-body system, made up of a core (an alpha particle) and two weakly bound valence neutrons. The 12C nucleus can be studied as a bound system formed by three alpha particles, while the 9Be nucleus can be described as the binding of two alpha particles and one neutron.<p><p>In these typical examples, the alpha particles are clusters of nucleons. They have an internal structure that must be taken into account because of the Pauli principle.<p><p>The most realistic models are the "microscopic models". In these models, all the nucleons are taken into account, and the Pauli antisymmetrisation principle is fully respected. However, the application of the "microscopic models" is limited in practice, because they require too many laborious calculations.<p>Therefore, in order to greatly simplify the calculations, "semi-microscopic models" are developed. In those models, the clusters of nucleons are treated as ("structureless") pointlike particles. The models then consist in determining the effective potentials between the clusters, and in using them in three-body models.<p><p>In the present work, we have developed "semi-microscopic models". The effective potentials between the clusters are directly obtained from the interactions between nucleons (according to the two-cluster RGM). These potentials are "nonlocal", and depend on the energy of the interacting clusters. The non-locality is a direct consequence of the Pauli principle and the exchanges of nucleons between the clusters. The energy-dependence of the potentials turns out to be a drawback in three-body models. Therefore, the effective potentials are transformed into energy-independent potentials, which can be used in three-body models. The "semi-microscopic models" are much simpler and faster than the "microscopic models". They provide the three-body bound-state wave functions (i.e. the spectroscopic properties and the structure) of light nuclei and hypernuclei. Such wave functions are also the basic ingredient that will be used in future reactions models.<br>Doctorat en Sciences de l'ingénieur<br>info:eu-repo/semantics/nonPublished
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Koloğlu, Murat. "Light and Heat: Nonlocal Aspects in Conformal Field Theories." Thesis, 2019. https://thesis.library.caltech.edu/11576/8/Kologlu_Murat_2019.pdf.
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<p>This thesis is dedicated to certain nonlocal aspects of conformal quantum field theories (CFTs). Two main directions are the study of CFTs on a particular globally-nontrivial spacetime corresponding to finite temperature, and the study of particular nonlocal CFT observables localized on light-rays. Specifically, we introduce bootstrap techniques for determining finite-temperature data of CFTs, and make novel predictions for the 2+1-dimensional Ising model. We propose the “stringy equivalence principle”, stating that coincident gravitational shocks commute, as a generalization of the strong equivalence principle of Einstein’s General Relativity that must hold in all consistent theories of gravity. We prove it in Anti-de Sitter (AdS) spacetimes by studying light-ray operators in the holographically dual CFT. We also derive an operator product expansion (OPE) for light-ray operators in CFT, by which two light-ray operators on the same light-sheet can be expanded as a sum of single light-ray operators. Light-ray operators model detectors — such as calorimeters. We use the light-ray OPE to compute energy event shape observables suitable for conformal collider physics.</p>
<p>An additional part of this thesis determines the low-energy vacua of two-dimensional maximal super-Yang-Mills theory, which describes the dynamics of stacks of D-strings in Type IIB string theory. By computing an invariant of the renormalization group (RG) flow from high to low energy — a modified thermal partition function named the refined elliptic genus — we prove the existence of multiple vacua, and identify the superconformal field theories capturing their dynamics. The vacua correspond to bound states of (p,q)-strings in Type IIB string theory. Our computation serves as a check of the strong-weak S-duality of the Type IIB string.</p>
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Jung-JenYu and 余榮仁. "Free Vibration Analysis of Multi-walled Nanobeams using Eringen’s Nonlocal Elasticity Theory." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/7qtj94.
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碩士<br>國立成功大學<br>土木工程學系<br>107<br>This article is intended to present free vibration analysis of single-, double-, and multi-walled (SW-, DW-, and MW-) carbon nanotubes (CNTs) with combinations of simply-supported, free, and clamped edge conditions embedded or non-embedded in an elastic medium. Based on the principle of virtual displacements (PVD) and Reissner’s mixed variational theorem (RMVT), the corresponding strong- and weak-form formulations of the local Timoshenko beam theory(TBT) are reformulated for the free vibration analysis of SW-, DW-, and MW-CNTs, and presented for illustrative purposes.
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Nahan, Matthew F. "A nonlocal damage theory for laminated plate with application to aircraft damage tolerance." Thesis, 1997. http://hdl.handle.net/1957/34015.
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Design of commercial aircraft structure, composed of composite material, requires the
prediction of failure loads given large scale damage. In particular, a fuselage of
graphite/epoxy lamination was analyzed for damage tolerance given a standard large
crack that severed both skin and internal structure. Upon loading, a zone of damage is
known to develop in front of a crack-tip in composite laminates; and, its material
behavior within the damage zone is characterized as strain softening. This investigation
sought to develop a computational model that simulates progressive damage growth and
predicts failure of complex laminated shell structures subject to combined tensile and
flexural load conditions. This was accomplished by assuming a macroscopic definition
of orthotropic damage that is allowed to vary linearly through the shell thickness. It was
further proposed that nonlocal plate strain and curvature act to force damage growth
according to a set of uniaxial criteria. Damage induced strain softening is exhibited by
degradation of laminate stiffness. An expression for the damage reduced laminated
plate stiffness was derived which assumed the familiar laminated plate [AM] stiffness
matrix format. The model was implemented in a finite element shell program for
simulation of fracture and evaluation of damage tolerance. Laminates were characterized
for damage resistance according to material parameters defining nonlocal strain and
the damage growth criteria. These parameters were selected using an inverse method to
correlate simulation with uniaxial strength and fracture test results. A novel combined
tension-plus-flexure fracture test was developed to facilitate this effort. Analysis was
performed on a section of pressurized composite fuselage containing a large crack.
Good agreement was found between calculations and test results.<br>Graduation date: 1998
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Abdelhamid, Ahmed. "A non-gradient heuristic topology optimization approach using bond-based peridynamic theory." Thesis, 2017. https://dspace.library.uvic.ca//handle/1828/8452.
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Peridynamics (PD), a reformulation of the Classical Continuum Mechanics (CCM), is a new and promising meshless and nonlocal computational method in solid mechanics. To permit discontinuities, the PD integro-differential equation contains spatial integrals and time derivatives. PD can be considered as the continuum version of molecular dynamics. This feature of PD makes it a good candidate for multi-scale analysis of materials. Concurrently, the topology optimization has also been rapidly growing in view of the need to design lightweight and high performance structures. Therefore, this thesis presents the potential for a peridynamics-based topology optimization approach. To avoid the gradient calculations, a heuristic topology optimization method is employed. The minimization of the PD strain energy density is set as the objective function. The structure is optimized based on a modified solid isotropic material with a penalization approach and a projection scheme is utilized to obtain distinct results. Several test cases have been studied to analyze the suitability of the proposed method in topology optimization.<br>Graduate
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Faruk, Abu N. "Prediciting Size Effects and Determing Length Scales in Small Scale Metaliic Volumes." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-05-7981.
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The purpose of this study is to develop an understanding of the behavior of metallic structures in small scales. Structural materials display strong size dependence when deformed non-uniformly into the inelastic range. This phenomenon is widely known as size effect. The primary focus of this study is on developing analytical models to predict some of the most commonly observed size effects in structural metals and validating them by comparing with experimental results. A nonlocal rate-dependent and gradient dependent theory of plasticity on a thermodynamically consistent framework is adopted for this purpose.
The developed gradient plasticity theory is applied to study size effects observed in biaxial and thermal loading of thin films and indentation tests. One important intrinsic material property associated with this study is material length scale. The work also presents models for predicting length scales and discusses their physical interpretations. It is found that the proposed theory is successful for the interpretation of indentation size effects in micro/nano-hardness when using pyramidal or spherical indenters and gives sound interpretation of the size effects in thin films under biaxial or thermal loading.
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(6368468), Daesung Kim. "Stability for functional and geometric inequalities and a stochastic representation of fractional integrals and nonlocal operators." Thesis, 2019.
Find full textAbstract:
<div>The dissertation consists of two research topics.</div><div><br></div><div>The first research direction is to study stability of functional and geometric inequalities. Stability problem is to estimate the deficit of a functional or geometric inequality in terms of the distance from the class of optimizers or a functional that identifies the optimizers. In particular, we investigate the logarithmic Sobolev inequality, the Beckner-Hirschman inequality (the entropic uncertainty principle), and isoperimetric type inequalities for the expected lifetime of Brownian motion. </div><div><br></div><div>The second topic of the thesis is a stochastic representation of fractional integrals and nonlocal operators. We extend the Hardy-Littlewood-Sobolev inequality to symmetric Markov semigroups. To this end, we construct a stochastic representation of the fractional integral using the background radiation process. The inequality follows from a new inequality for the fractional Littlewood-Paley square function. We also prove the Hardy-Stein identity for non-symmetric pure jump Levy processes and the L^p boundedness of a certain class of Fourier multiplier operators arising from non-symmetric pure jump Levy processes. The proof is based on Ito's formula for general jump processes and the symmetrization of Levy processes. <br></div>
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Chang, Lara Hector Andres. "Regularity for solutions of nonlocal fully nonlinear parabolic equations and free boundaries on two dimensional cones." 2013. http://hdl.handle.net/2152/21668.
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On the first part, we consider nonlinear operators I depending on a family of nonlocal linear operators [mathematical equations]. We study the solutions of the Dirichlet initial and boundary value problems [mathematical equations]. We do not assume even symmetry for the kernels. The odd part bring some sort of nonlocal drift term, which in principle competes against the regularization of the solution. Existence and uniqueness is established for viscosity solutions. Several Hölder estimates are established for u and its derivatives under special assumptions. Moreover, the estimates remain uniform as the order of the equation approaches the second order case. This allows to consider our results as an extension of the classical theory of second order fully nonlinear equations. On the second part, we study two phase problems posed over a two dimensional cone generated by a smooth curve [mathematical symbol] on the unit sphere. We show that when [mathematical equation] the free boundary avoids the vertex of the cone. When [mathematical equation]we provide examples of minimizers such that the vertex belongs to the free boundary.<br>text
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Ming-XianLin and 林明賢. "Application of Hybrid Differential Transformation / Finite Difference Method to the Vibration Analysis of Nonlocal Elasticity Theory of Graphene Micro-Nano Beam." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/97779268490021859937.
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碩士<br>國立成功大學<br>機械工程學系<br>103<br>In this study, the hybrid differential transformation/finite difference method is used to analyze the dynamic characteristic of micro / nano beams, which are electrostatically actuated under the influence of the coupling effect, the residual stress and the fringing field effect between the micro / nano system and electrostatic field. Furthermore, the nonlocal continuum field theory is applied to analyze the dynamic behavior of micro / nano beams.
To obtain the natural frequencies of the micro / nano beam, the governing equation is transformed to the algebraic equation by differential transformation. The effect of pull-in voltage by the residual stress and the squeeze damping is discussed by using hybrid differential transformation/finite difference method.
The results of this study show that the natural frequency of micro / nano beam under different boundary conditions is consistent with the literatures by the errors within 0.003%. The nonlocal elasticity theory is employed to analyze the behavior of an electrostatically actuated graphene micro / nano beams. It indicates that the results by traditional elasticity theory and nonlocal elasticity theory are the same as the beams subjected to residual stress and squeeze-film damping. However, unlike the residual stress, the effect of squeeze-film damping on pull-in voltage is very small. By consideration of the interaction on nanoscale, the data can be more real by adjustment of the nonlocal parameter. Therefore, the hybrid differential transformation / finite difference method is simpler and faster on nonlinear partial differential equations than other methods, especially on complex equation of nonlocal continuum field.
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Jyun-YuLiou and 柳俊宇. "An RMVT-based nonlocal Timoshenko beam theory for the buckling analysis of an embedded single-walled carbon nanotube with various boundary conditions." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/99607173933453639211.
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碩士<br>國立成功大學<br>土木工程學系<br>104<br>On the basis of Reissner’s mixed variational theory (RMVT), a nonlocal Timoshenko beam theory (TBT) is developed for the stability analysis of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium, with various boundary conditions and under axial loads. Eringen’s nonlocal elasticity theory is used to account for the small length scale effect. The strong formulations of the RMVT- based nonlocal TBT and its associated possible boundary conditions are presented. The interaction between the SWCNT and its surrounding elastic medium is simulated using the Pasternak foundation models. The critical load parameters of the embedded SWCNT with different boundary conditions are obtained using the differential quadrature (DQ) method, in which the locations of np sampling nodes are selected as the roots of np-order Chebyshev polynomials.
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Wei-WenLai and 賴偉文. "Mechanical behavior of a single-walled carbon nanotube embedded in an elastic medium and using the RMVT-based nonlocal Timoshenko beam theory." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/66470633858657958041.
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碩士<br>國立成功大學<br>土木工程學系<br>103<br>A nonlocal Timoshenko beam theory (TBT), based on the Reissner mixed variational theorem (RMVT), is developed for the analysis of a single-walled carbon nanotube (SWCNT) embedded in an elastic medium and with various boundary conditions. The comparisons between the results obtained by using the RMVT-based nonlocal TBT and those of principle of virtual displacement (PVD)-based one. The strong formulations of the RMVT- and PVD-based nonlocal TBTs are derived by using Hamilton’s principle, in which Eringen’s nonlocal constitutive relations are used to account for the small-scale effect. The interaction between the SWCNT and its surrounding elastic medium is simulated using the Winkler and Pasternak foundation models. The static and free vibration of the embedded SWCNT are thus investigated by using these nonlocal TBT combined with the meshless collocation methods, in which the shape functions are constructed by either the differential reproducing kernel (DRK) interpolation method or the differential quadrature (DQ) one. In the implementation of these meshless colocation methods, the results show the performance of RMVT-based nonlocal TBT is superior to that of the PVD-based one. A parametric study with regard to some crucial effects on the static and free vibration characteristics of the embedded SWCNT is undertaken, such as different boundary conditions, nonlocal parameters, aspect ratios, spring constants and shear modulus of the foundation.
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Dvořák, Jan. "Asociativní odtržení elektronu při srážce záporného iontu." Master's thesis, 2017. http://www.nusl.cz/ntk/nusl-365180.
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Low-energy resonant processes in collisions of electrons, atoms, ions and molecules significantly contributed to the evolution of the early Universe. Much attention has not yet been paid to processes involving lithium atoms and ions. In this thesis, we present the theoretical description of two associa- tive detachment processes of Li with H− and H with Li− within the nonlocal resonant theory. The nonlocal resonant models were constructed from poten- tial energy curves computed by the MOLPRO package of ab initio programs and from electron-molecule scattering data obtained from R-matrix calcula- tions by the UK molecular R-matrix suite of codes. The Lippman-Schwinger equation describing the nuclear motion was solved by the Schwinger-Lanczos algorithm. We developed a new method, which is based on the singular value decomposition method and separates the coupling potential. We predict sev- eral orders of magnitude difference between the temperature-dependent rate constants of the studied collisions at temperatures below 1000 K.
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Cheng-ChihChou and 周承志. "Mechanical behavior of a single-walled carbon nanotube embedded in an elastic medium and using the RMVT-based nonlocal Euler-Bernoulli beam theory." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/98001727377042867400.
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碩士<br>國立成功大學<br>土木工程學系<br>103<br>A Reissner’s mixed variational theorem (RMVT)-based nonlocal Euler-Bernoulli beam theory (EBT) is developed for the bending, free vibration and buckling analyses of a single-layered nanobeam (SLNB) (or a single-walled carbon nanotube, SWCNT) embedded in an elastic medium and with combinations of simply-supported and clamped edges. The interaction effect between the SLNB/SWCNT and its surrounding elastic medium is simulated using either a Winkler or a Pasternak foundation model. The SLNB/SWCNT’s equations of motion and the associated possible boundary conditions are derived by using Hamilton’s principle combined with Eringen’s nonlocal constitutive relations. A meshless collocation method is applied to obtain the deflection and stress-resultant components induced in a loaded SLNB/SWCNT, frequency parameters of an unloaded SLNB/SWCNT, and critical load parameters of an axially-loaded one, in which a differential reproducing kernel interpolation method is used to construct the shape functions of each field variable.
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Arash, Behrouz. "Molecular dynamics studies on application of carbon nanotubes and graphene sheets as nano-resonator sensors." 2013. http://hdl.handle.net/1993/22278.
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The main objective of the research is to study the potential application of carbon nanotubes and graphene sheets as nano-resonator sensors in the detection of atoms/molecules with vibration and wave propagation analyses. It is also aimed to develop and examine new methods in the design of nano-resonator sensors for differentiating distinct gas atoms and different macromolecules, such as DNA molecules. The hypothesis in the detection techniques is that atoms or molecules attached on the surface of the nano-resonator sensors would induce a recognizable shift in the resonant frequency of or wave velocity in the sensors. With this regard, a sensitivity index based on the shift in resonant frequency of the sensors in the vibration analysis and/or a shift in wave velocity in the sensors in the wave propagation analysis is defined and examined.
In order to achieve the objective, the vibration characteristics of carbon nanotubes and graphenes are studied using molecular dynamics simulations to first propose nano-resonator sensors, which are able to differentiate distinct gas atoms with high enough resolutions even at low concentration. It is also indicated that the nano-resonator sensors are effective devices to identify different genes even with the same number of nucleobases in the structure of single-strand DNA macromolecules. The effect of various parameters such as size and restrained boundary conditions of the sensors, the position of attached atoms/molecules being detected, and environment temperature on the sensitivity of the sensors is investigated in detail.
Following the studies on vibration-based sensors, the wave propagation analysis in carbon nanotubes and graphene sheets is first investigated by using molecular dynamics simulations to design nano-resonator sensors. Moreover, a nonlocal finite element model is presented and calibrated for the first time to model propagation of mechanical waves in graphene sensors attached with atoms through a verification process with atomistic results. The simulation results reveal that the nano-resonator sensors are able to successfully detect distinct types of noble gases with the same mass density or at the same environmental condition of temperature and pressure.
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Broadbent, Anne Lise. "Quantum nonlocality, cryptography and complexity." Thèse, 2008. http://hdl.handle.net/1866/6448.
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