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Relevant bibliographies by topics / Phase Space Formulation

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Academic literature on the topic 'Phase Space Formulation'

Author: Grafiati

Published: 10 March 2023

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Journal articles on the topic "Phase Space Formulation"

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CIRELLI, RENZO, ALESSANDRO MANIÀ, and LIVIO PIZZOCCHERO. "QUANTUM PHASE SPACE FORMULATION OF SCHRÖDINGER MECHANICS." International Journal of Modern Physics A 06, no. 12 (1991): 2133–46. http://dx.doi.org/10.1142/s0217751x91001064.

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We develop a geometrical approach to Schrödinger quantum mechanics, alternative to the usual one, which is based on linear and algebraic structures such as Hilbert spaces, operator algebras, etc. The starting point of this approach is the Kähler structure possessed by the set of the pure states of a quantum system. The Kähler manifold of the pure states is regarded as a “quantum phase space”, conceptually analogous to the phase space of a classical hamiltonian system, and all the constituents of the conventional formulation, in particular the algebraic structure of the observables, are reproduced using a suitable “Kähler formalism”. We also show that the probabilistic character of the measurement process in quantum mechanics and the uncertainty principle are contained in the geometrical structure of the quantum phase space. Finally, we obtain a characterization for quantum phase spaces which can be interpreted as a statement of uniqueness for Schrödinger quantum mechanics.

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Chruściński, Dariusz. "Phase-Space Approach to Berry Phases." Open Systems & Information Dynamics 13, no. 01 (2006): 67–74. http://dx.doi.org/10.1007/s11080-006-7268-3.

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We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light onto the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay angle with averaging over the classical torus and Berry phase with averaging over the entire classical phase space with respect to the corresponding Wigner function.

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ZACHOS, COSMAS. "DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE." International Journal of Modern Physics A 17, no. 03 (2002): 297–316. http://dx.doi.org/10.1142/s0217751x02006079.

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Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (e.g. quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides — coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.

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Wu, Xizeng, and Hong Liu. "Phase-space formulation for phase-contrast x-ray imaging." Applied Optics 44, no. 28 (2005): 5847. http://dx.doi.org/10.1364/ao.44.005847.

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Tosiek, J., and P. Brzykcy. "States in the Hilbert space formulation and in the phase space formulation of quantum mechanics." Annals of Physics 332 (May 2012): 1–15. http://dx.doi.org/10.1016/j.aop.2013.01.010.

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Kalmykov, Yuri P., and William T. Coffey. "Transition state theory for spins: phase-space formulation." Journal of Physics A: Mathematical and Theoretical 41, no. 18 (2008): 185003. http://dx.doi.org/10.1088/1751-8113/41/18/185003.

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Batalin, I. A., K. Bering, and P. H. Damgaard. "Superfield formulation of the phase space path integral." Physics Letters B 446, no. 2 (1999): 175–78. http://dx.doi.org/10.1016/s0370-2693(98)01537-8.

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Rosato, J. "A quantum phase space formulation of radiative transfer." Physics Letters A 378, no. 34 (2014): 2586–89. http://dx.doi.org/10.1016/j.physleta.2014.07.003.

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SOBOUTI, Y., and S. NASIRI. "A PHASE SPACE FORMULATION OF QUANTUM STATE FUNCTIONS." International Journal of Modern Physics B 07, no. 18 (1993): 3255–72. http://dx.doi.org/10.1142/s0217979293003218.

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Allowing for virtual paths in phase space permits an extension of Hamilton’s principle of least action, of lagrangians and of hamiltonians to phase space. A subsequent canonical quantization, then, provides a framework for quantum statistical mechanics. The classical statistical mechanics and the conventional quantum mechanics emerge as special case of this formalism. Von Neumann’s density matrix may be inferred from it. Wigner’s functions and their evolution equation may also be obtained by a unitary transformation.

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Torre, C. G. "Covariant phase space formulation of parametrized field theories." Journal of Mathematical Physics 33, no. 11 (1992): 3802–12. http://dx.doi.org/10.1063/1.529878.

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Dissertations / Theses on the topic "Phase Space Formulation"

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Meusburger, Catherine. "Phase space and quantisation of (2+1)-dimensional gravity in the Chern-Simons formulation." Thesis, Heriot-Watt University, 2004. http://hdl.handle.net/10399/320.

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Strandberg, Per Erik. "Mathematical models of bacteria population growth in bioreactors: formulation, phase space pictures, optimisation and control." Thesis, Linköping University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2337.

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<p>There are many types of bioreactors used for producing bacteria populations in commercial, medical and research applications. </p><p>This report presents a systematic discussion of some of the most important models corresponding to the well known reproduction kinetics such as the Michaelis-Menten kinetics, competitive substrate inhibition and competitive product inhibition. We propose a modification of a known model, analyze it in the same manner as known models and discuss the most popular types of bioreactors and ways of controlling them. </p><p>This work summarises much of the known results and may serve as an aid in attempts to design new models.</p>

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Lee, Ming-Tsung, and 李明聰. "Implications of Quantum Mechanics based on a Random Medium Model and a Stochastic Micro-Phase-Space Formulation." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/20811272010135150210.

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博士<br>國立臺灣大學<br>物理學研究所<br>90<br>Based on the framework of stochastic interpretation for quantum mechanics, two approaches are proposed to present several implications of quantum mechanics. One is the microscopic transport conservation approach for the random medium model. In this model, the quantum fluctuation of the microscopic object is assumed to arise from the collision between the microscopic object and the medion. Some assumptions for the object-medion collision are proposed to guarantee that the statistical ensemble manifestation of Schrodinger wave mechanics can be reproduced. According to this approach, several kinds of microscopic object energies and the local energy transport between the objects and the medions are studied. The other approach is the stochastic microscopic-phase-space formulation. A set of stochastic dynamic equations describing the motion of the individual object are proposed. According to this set of equations, a dynamic description for the von Neumann collapse is presented. Moreover, there exists the negativity of the microscopic-phase-space description in this formulation. The mechanism of the negativity is studied according to the stochastic dynamics. Some discussions on the significance of energy quantization and non-locality are also presented here.

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GIOVANNINI, ELISA. "A Wigner Equation with Decoherence." Doctoral thesis, 2020. http://hdl.handle.net/2158/1238624.

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Dopo un’introduzione sui fondamenti matematici della Meccanica Quantistica e la sua formulazione wigneriana, si ricava un’equazione 1-dimensionale di Wigner con termine di decoerenza partendo dalla descrizione dettagliata di R. Adami, M. Hauray, C. Negulescu per la decoerenza di una particella pesante che interagisce con una particella leggera. Si mostra che il modello ottenuto ne contiene, quali casi particolari, altri già utilizzati per descrivere il fenomeno della decoerenza quantistica, come ad esempio l’equazione di Wigner–Fokker–Planck o le funzioni di Wigner con lunghezza di coerenza finita. Si indaga l’effetto della decoerenza sulla dinamica delle quantità macroscopiche (densità, corrente, energia) attraverso le corrispondenti leggi di bilancio. Si applica poi il modello ricavato ad una situazione di interesse fisico mediante simulazioni numeriche: un processo di tunneling in ambiente decoerente. Si investiga la questione asintotica per tempi lunghi nel caso di soluzioni gaussiane e si accenna al caso generale spazio omogeneo. Si mostra che l’aggiunta di un termine di frizione quantistica di tipo Caldeira-Legget all’equazione di Wigner con decoerenza è capace di realizzare il comportamento asintotico prevedibile sulla base di considerazioni di natura fisica.

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Books on the topic "Phase Space Formulation"

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Mann, Peter. Noether’s Theorem for Fields. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0028.

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This is a unique chapter that discusses classical path integrals in both configuration space and phase space. It examines both Lagrangian and Hamiltonian formulations before qualitatively discussing some interesting features of gauge fixing. This formulation is then linked to superspace and Grassmann variables for a fermionic field theory. The chapter then shows that the corresponding operatorial formulation is none other than the Koopman–von Neumann theory. In parallel to quantum theory, the classical propagator or the transition amplitude between two classical states is given exactly by the phase space partition function. The functional Dirac delta is discussed, and the chapter closes by briefly mentioning Faddeev–Popov ghosts, which were introduced earlier in the chapter.

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Mann, Peter. Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0019.

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This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

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Deruelle, Nathalie, and Jean-Philippe Uzan. Hamiltonian mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0009.

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This chapter gives a brief overview of Hamiltonian mechanics. The complexity of the Newtonian equations of motion for N interacting bodies led to the development in the late 18th and early 19th centuries of a formalism that reduces these equations to first-order differential equations. This formalism is known as Hamiltonian mechanics. This chapter shows how, given a Lagrangian and having constructed the corresponding Hamiltonian, Hamilton’s equations amount to simply a rewriting of the Euler–Lagrange equations. The feature that makes the Hamiltonian formulation superior is that the dimension of the phase space is double that of the configuration space, so that in addition to point transformations, it is possible to perform more general transformations in order to simplify solving the equations of motion.

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Mann, Peter. Newton’s Three Laws. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0001.

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This chapter introduces Newton’s laws, the Newtonian formulation of mechanics and key concepts such as configuration space and phase space for later development. In 1687, the natural philosopher Sir Isaac Newton published the Principia Mathematica and, with it, sparked the revolutionary ideas key to all branches of classical physics. In this chapter, the system is the object of interest and is considered to be either a single or a collection of generic particles that are not governed by quantum mechanics, for quantum systems do not follow these laws explicitly. Results for systems of particles and conservation laws are presented as the invariance of a given quantity under time evolution. The N-body problem, first integrals, initial value problems and Galilean transformations are all introduced and the Picard iteration and the Verlet algorithm are discussed.

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Mann, Peter. Hamilton’s Equations & Routhian Reduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0016.

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In this chapter, the Poisson bracket and angular momentum are investigated and first integrals are used to develop conservation laws as a canonical Noether’s theorem. The Poisson bracket was developed by the French mathematician Poisson in the late nineteenth century and it is a reformulation, or at least a tidying up, of Hamilton’s equations into one neat package. The Poisson bracket of a quantity with the Hamiltonian describes the time evolution of that quantity as one moves along a curve in phase space. The Lie algebra structure of symmetries in mechanics is highlighted using this formulation. The classical propagator is derived using the Poisson bracket.

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Mercati, Flavio. Shape Dynamics and the Linking Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0012.

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This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

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Mann, Peter. Lagrangian Field Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0025.

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In this chapter, Hamiltonian field theory is derived classically via a Hamiltonian density, using the zeroth component of a 4-momentum density. In field theory, space and time are considered to be on equal footing but, in the canonical formalism, time is treated as being special and therefore, by definition, it is not covariant. Consequently, most field theoretic models are built on Lagrangian formulations. A covariant canonical formalism is the subject of the de Donder–Weyl formalism, which is briefly discussed as a covariant Hamiltonian field theory. In addition, the chapter examines the case of a generalised Poisson bracket in the continuous form for two local smooth functionals of phase space.

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Kondrakiewicz, Dariusz. Prognozowanie i symulacje międzynarodowe. Instytut Europy Środkowej, 2021. http://dx.doi.org/10.36874/m21580.

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International forecasting and simulation is a study that summarizes research, in a shortened and integrated version. The thematic scope concerns the basic terminology and methodological issues of forecasts and the forecasting process itself, forecasting institutions and the final product, i.e. international forecasts. The main goal is to present and systematize basic knowledge in the field of forecasting in international relations. The book is generally aimed at all those interested in international affairs. However, the author hopes that the publication will also be helpful for researchers and analysts dealing with difficult issues of international forecasting in the field of their scientific research methodologies. The work consists of two parts – theoretical and empirical. The theoretical part includes two chapters. The first chapter begins by discussing the concepts of forecasting and simulation. Next, considerations were made about the place of forecasting in science, pointing out the existing dilemmas in this regard, and also discussed categories, classifications and functions of forecasting and simulation. The second chapter presents the main elements of the forecast and the phases of the forecasting process. Most space was devoted to the presentation of the most important methods of forecasting in international relations, not limiting itself only to discussing them, but also assessing their usefulness for formulating international forecasts. In the third chapter, which is of an empirical nature, the selected forecasting institutions are first discussed according to the division applied into typically research, university, governmental, international and private institutions. This classification is of a contractual nature, but corresponds to the basic functions performed by individual institutions. In the further part of this chapter, the most important – according to the author – ecological, demographic and political forecasts are presented, focusing on discussing the main consequences of their possible implementation for international relations.

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Book chapters on the topic "Phase Space Formulation"

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Ashtekar, Abhay, Luca Bombelli, and Rabinder Koul. "Phase space formulation of general relativity without a 3+1 splitting." In The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-17894-5_378.

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Schroeck, Franklin E. "Consequences of Formulating Quantum Mechanics on Phase Space." In Quantum Mechanics on Phase Space. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-017-2830-0_4.

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Kenkre, V. M. "Thermal Effects: Phase-Space and Langevin Formulations." In Interplay of Quantum Mechanics and Nonlinearity. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-94811-5_8.

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Attard, Phil. "Wave packet formulation." In Quantum Statistical Mechanics in Classical Phase Space. IOP Publishing, 2021. http://dx.doi.org/10.1088/978-0-7503-4055-7ch2.

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"The Phase Space Formulation of Quantum Mechanics." In Advanced Topics in Quantum Mechanics. Cambridge University Press, 2021. http://dx.doi.org/10.1017/9781108863384.004.

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Bracken, Paul. "Classical and Quantum Integrability: A Formulation That Admits Quantum Chaos." In Chaotic Systems [Working Title]. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.94491.

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The concept of integrability of a quantum system is developed and studied. By formulating the concepts of quantum degree of freedom and quantum phase space, a realization of the dynamics is achieved. For a quantum system with a dynamical group G in one of its unitary irreducible representative carrier spaces, the quantum phase space is a finite topological space. It is isomorphic to a coset space G/R by means of the unitary exponential mapping, where R is the maximal stability subgroup of a fixed state in the carrier space. This approach has the distinct advantage of exhibiting consistency between classical and quantum integrability. The formalism will be illustrated by studying several quantum systems in detail after this development.

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Zinn-Justin, Jean. "Quantum statistical physics: Functional integration formalism." In Quantum Field Theory and Critical Phenomena. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0004.

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The functional integral representation of the density matrix at thermal equilibrium in non-relativistic quantum mechanics (QM) with many degrees of freedom, in the grand canonical formulation is introduced. In QM, Hamiltonians H(p,q) can be also expressed in terms of creation and annihilation operators, a method adapted to the study of perturbed harmonic oscillators. In the holomorphic formalism, quantum operators act by multiplication and differentiation on a vector space of analytic functions. Alternatively, they can also be represented by kernels, functions of complex variables that correspond in the classical limit to a complex parametrization of phase space. The formalism is adapted to the description of many-body boson systems. To this formalism corresponds a path integral representation of the density matrix at thermal equilibrium, where paths belong to complex spaces, instead of the more usual position–momentum phase space. A parallel formalism can be set up to describe systems with many fermion degrees of freedom, with Grassmann variables replacing complex variables. Both formalisms can be generalized to quantum gases of Bose and Fermi particles in the grand canonical formulation. Field integral representations of the corresponding quantum partition functions are derived.

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"Lagrangian and phase-space formulations." In From Classical to Quantum Mechanics. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9780511610929.016.

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Kübler, Jürgen. "Energy-Band Theory." In Theory of Itinerant Electron Magnetism, 2nd Edition. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895639.003.0003.

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Various methods to calculate energy bands and the electronic structure of solids are described in detail. Although the emphasis lies on linear methods well known for their transparency and high numerical speed, traditional methods are described to supply historical background and to point the way to modern methods. After introducing Bloch electrons and the reciprocal space, plane waves, orthogonalized plane waves, and pseudopotentials are discussed, followed by the important augmented plane wave method (APW). Multiple scattering theory defines scattering phase shifts encoding atomic properties and the structure constants that describe the crystal lattice. Linear combination of atomic orbitals (LCAO) and linear combination of muffin-tin orbitals (LMTO) result in efficient and fast methods as does the related augmented spherical waves (ASW) method. The treatment of arbitrary spin configurations using the ASW method and the formulation of incommensurate spiral structures on the basis of the unitary SU(2) group are developed in detail.

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"- Hamiltonian Formulation of Mechanics: Descriptions of Motion in Phase Spaces." In Classical Mechanics. CRC Press, 2013. http://dx.doi.org/10.1201/b14745-8.

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Conference papers on the topic "Phase Space Formulation"

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Signorelli, Joel, Duane L. Bindschadler, Kathryn A. Schimmels, and Shin M. Huh. "Operability Engineering for Europa Clipper: Formulation Phase Results and Lessons." In 15th International Conference on Space Operations. American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-2629.

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Ivanco, Marie L., and Christopher A. Jones. "Assessing the Science Benefit of Space Mission Concepts in the Formulation Phase." In 2020 IEEE Aerospace Conference. IEEE, 2020. http://dx.doi.org/10.1109/aero47225.2020.9172755.

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Casey, Thomas M., Nerses V. Armani, Wes L. Alexander, et al. "The wide field infrared survey telescope (WFIRST) observatory: design formulation (phase-A) overview (Conference Presentation)." In Space Telescopes and Instrumentation 2018: Optical, Infrared, and Millimeter Wave, edited by Howard A. MacEwen, Makenzie Lystrup, Giovanni G. Fazio, Natalie Batalha, Edward C. Tong, and Nicholas Siegler. SPIE, 2018. http://dx.doi.org/10.1117/12.2313748.

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SHESTAKOVA, T. P. "THE FORMULATION OF GENERAL RELATIVITY IN EXTENDED PHASE SPACE AS A WAY TO ITS QUANTIZATION." In Proceedings of the MG12 Meeting on General Relativity. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814374552_0247.

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Vladimirov, Igor G. "A phase-space formulation of the Belavkin-Kushner-Stratonovich filtering equation for nonlinear quantum stochastic systems*." In 2016 IEEE Conference on Norbert Wiener in the 21st Century (21CW). IEEE, 2016. http://dx.doi.org/10.1109/norbert.2016.7547465.

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Melamed, Shlomo T., and Ehud Heyman. "Phase-space beam summation for time-harmonic and time-dependent radiation from extended apertures: 3-D formulation." In OE/LASE '92, edited by Howard E. Brandt. SPIE, 1992. http://dx.doi.org/10.1117/12.137134.

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Boledi, Leonardo, Benjamin Terschanski, Stefanie Elgeti, and Julia Kowalski. "A Space-Time FE Level-set method for convection coupled phase-change processes." In VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12329.

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Phase transition processes have great relevance for both engineering and scientific applications. In production engineering, for instance, metal welding and alloy solidification are topics of ongoing research.In this contribution we focus on the convection coupled solid-liquid phase change of a single species, e.g. water. The material is assumed to be incompressible within the two phases, but we account for density changes across the phase interface. To describe the process, we need to solve the incompressible Navier-Stokes equations and the heat equation for both phases over time. The position of the phase interface is tracked with a Level-set method. The Level-set function is advected according to the propagation speed of the phase interface. Such velocity field depends on local energy conservation across the interface and is modelled as the Stefan condition. This formulation requires us to approximate the heat flux discontinuity across the interface based on the evolving temperature and velocity fields.To model the temperature and velocity fields within each phase, we employ the Space-Time Finite Element method. However, commonly used interpolation functions, such as piecewise linear functions, fail to capture discontinuous derivatives over one element that are needed to assess the Level-set's transport term. Available solutions to this matter, such as local enrichment with Extended Finite Elements, are often not compatible with existing Space-Time Finite Element codes and require extensive implementation work. Instead, we consider a conceptually simpler method and we decide to extend the Ghost Cell technique to Finite Element meshes. The idea is that we can separate the two subdomains associated with each phase and solve two independent temperature problems. We prescribe the melting temperature at an additional node close to the interface and we retrieve the required heat flux.In this work we describe the Ghost Cell method applied to our Space-Time Finite Element solver. First, we verify numerical results against analytical solutions, then we demonstrate more complex test cases in 2D and 3D.

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Obeyesekere, Nihal U., Jonathan J. Wylde, Thusitha Wickramarachchi, and Lucious Kemp. "Formulation of High-Performance Corrosion Inhibitors in the 21St Century: Robotic High Throughput Experimentation and Design of Experiments." In SPE International Conference on Oilfield Chemistry. SPE, 2021. http://dx.doi.org/10.2118/204353-ms.

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Abstract Critical micelle concentration (CMC) is a known indicator for surfactants such as corrosion inhibitors’ ability to partition to water from two phase systems such as oil and water. Most corrosion inhibitors are surface active. At critical micelle concentration, the chemical is partitioned to water from the interface, physisorption on metallic surfaces and forms a physical barrier between steel and corrosive water. This protective barrier thus prevents corrosion initiating on the metal surface. When the applied chemical concentration is equal or higher than the CMC, the surfactant is partitioned to aqueous phase from the oil-water interface. This would lead to higher chemical availability of the inhibitor in water, preventing corrosion. Therefore, it was suggested that CMC can be used as an indicator to optimal chemical dose for corrosion control1-5. The lower the CMC of a corrosion inhibitor product, the better is this chemical for corrosion control as the availability of the chemical in the aqueous phase increases. This can achieve corrosion control with lesser amount of corrosion inhibitor product. Thus, increasing the performance of corrosion inhibitor product. In this work, the physical property, CMC, was used as an indicator to differentiate corrosion inhibitor performance. A vast array of corrosion inhibitor formulations was achieved by combinatorial chemical methods using Design of Experiment (DoE) methodologies and these arrays of chemical formulations were screened by utilizing high throughput screening (HTE)6-8, using CMC as the selection guide. To validate the concept, a known corrosion inhibitor formulation (Inhibitor Abz) was selected to optimize its efficacy. This formula contains several active ingredients and a solvent package. Three raw materials of this formulation were selected and varied in combinatorial fashion, keeping the solvents and other raw materials constant9. These three raw materials were blended in a random but in a controled manner utizing DoE and using combinatorial techniques. Instead of rapidly blending a large amount of formulations using robotics, the design of experiment (DoE) methods were utilized to constrain the number of blends. When attempting to discover the important factors, DoE gives a powerful suite of statistical methodologies10. In this work, Design Expert software utilizes DoE methods and this prediction model was used to explore a desired design space. The more relevant (not entirely random) formulations were generated by DoE methods, using Design Expert software that can effectively explore a desired design space. The Design of Experiment software mathematically analyzes the space in which fundamental properties are being measured. The development of an equally robust prescreening analysis was also developed. After blending a vast array of formulations by using automated workstation, these products were screened for CMC by utilizing an automated surface tension workstation. Several formulations with lower CMCs than the reference product (Inhibitor Abz) were discovered and identified for further study. The selected corrosion inhibitor formulations were blended in larger scales. The efficacy of these products was tested by classical laboratory testing methods such as rotating cylinder electrode (RCE) and rotating cage autoclave (RCA) to determine their performance as anti-corrosion agents. As the focus of this project was to optimize the corrosion Inhibitor Abz, this chemical was used as the reference product throughout of this work. The testing indicated that several new corrosion inhibitor formulations discovered from this work outperformed the original blend, thus validating the proof of concept.

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Shyue, Keh-Ming. "An Adaptive Moving-Mesh Relaxation Scheme for Compressible Two-Phase Barotropic Flow With Cavitation." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-04009.

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We describe a simple relaxation scheme for the efficient numerical resolution of compressible two-phase barotropic flow with and without cavitation on moving meshes. The algorithm uses a curvilinear-coordinate formulation of the relaxation model proposed by Saurel et al. (J. Comput. Phys. 228 (2009) 1678–1712) as the basis, and employs a wave-propagation based relaxed scheme to solve the model system on a mapped grid that is constructed by a conventional mesh-redistribution procedure for better solution adaptation. Sample numerical results in both one and two space dimensions are present that show the feasibility of the proposed method for practical problems.

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Flickinger, Daniel Montrallo, Jedediyah Williams, and Jeffrey C. Trinkle. "Evaluating the Performance of Constraint Formulations for Multibody Dynamics Simulation." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12265.

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Contemporary software systems used in the dynamic simulation of rigid bodies suffer from problems in accuracy, performance, and robustness. Significant allowances for parameter tuning, coupled with the careful implementation of a broad phase collision detection scheme is required to make dynamic simulation useful for practical applications. A geometrically accurate constraint formulation, the Polyhedral Exact Geometry method, is presented. The Polyhedral Exact Geometry formulation is similar to the well-known Stewart-Trinkle formulation, but extended to produce unilateral constraints that are geometrically correct in cases where polyhedral bodies have a locally non-convex free space. The PEG method is less dependent on broad-phase collision detection or system tuning than similar methods, demonstrated by several examples. Uncomplicated benchmark examples are presented to analyze and compare the new Polyhedral Exact Geometry formulation with the well-known Stewart-Trinkle and Anitescu-Potra methods. The behavior and performance for the methods are discussed. This includes specific cases where contemporary methods fail to match theorized and observed system states in simulation, and how they are ameliorated by PEG.

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