Academic literature on the topic 'Classical scattering dynamics'
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Journal articles on the topic "Classical scattering dynamics"
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BRUHN, B., and B. P. KOCH. "CHAOTIC SCATTERING IN CLASSICAL TRIATOMIC MOLECULAR DYNAMICS." International Journal of Bifurcation and Chaos 03, no. 04 (August 1993): 999–1012. http://dx.doi.org/10.1142/s0218127493000829.
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The classical scattering dynamics of two coupled Morse systems is investigated by analytical and numerical methods. If a McGehee type transformation and the Melnikov method are applied to the invariant manifolds of a nonhyperbolic fixed point at infinity, a proof of the appearance of chaotic scattering is obtained. Furthermore, we study the occurrence of hyperbolic and elliptic periodic orbits under perturbation using the subharmonic Melnikov approach. The analytical predictions regarding the range of the scattering function where chaotic scattering appears are compared with numerical results. Moreover, we investigate the threshold for channel transitions and discuss some mechanisms for this transition.
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Marković, Nikola, and Andreas Bäck. "Mixed Quantum−Classical Scattering Dynamics of CF3Br†." Journal of Physical Chemistry A 108, no. 41 (October 2004): 8765–71. http://dx.doi.org/10.1021/jp049138k.
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Schultz, David G., Samuel B. Wainhaus, Luke Hanley, Pascal de Sainte Claire, and William L. Hase. "Classical dynamics simulations of SiMe3+ ion–surface scattering." Journal of Chemical Physics 106, no. 24 (June 22, 1997): 10337–48. http://dx.doi.org/10.1063/1.474069.
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LANDAU, D. P., ALEX BUNKER, and KUN CHEN. "SPIN DYNAMICS SIMULATIONS OF CLASSICAL, THREE-DIMENSIONAL HEISENBERG MAGNETS." International Journal of Modern Physics C 07, no. 03 (June 1996): 401–8. http://dx.doi.org/10.1142/s012918319600034x.
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Spin dynamics simulations have been used to study dynamic critical behavior of classical Heisenberg magnets. The temporal evolutions of the spin configurations were determined numerically from coupled equations of motion by a fourth-order predictor corrector method, with initial spin configurations generated by Monte-Carlo simulations. The neutron scattering function, S (q, ω), was calculated from the space and time displaced spin-spin correlation function and the dynamic critical exponent z was extracted using dynamic finite size scaling theory. For both ferromagnetic and antiferromagnetic models we find good agreement with theoretical predictions and experimental results.
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McCluskey, Andrew R., James Grant, Adam R. Symington, Tim Snow, James Doutch, Benjamin J. Morgan, Stephen C. Parker, and Karen J. Edler. "An introduction to classical molecular dynamics simulation for experimental scattering users." Journal of Applied Crystallography 52, no. 3 (May 7, 2019): 665–68. http://dx.doi.org/10.1107/s1600576719004333.
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Classical molecular dynamics simulations are a common component of multi-modal analyses of scattering measurements, such as small-angle scattering and diffraction. Users of these experimental techniques often have no formal training in the theory and practice of molecular dynamics simulation, leading to the possibility of these simulations being treated as a `black box' analysis technique. This article describes an open educational resource (OER) designed to introduce classical molecular dynamics to users of scattering methods. This resource is available as a series of interactive web pages, which can be easily accessed by students, and as an open-source software repository, which can be freely copied, modified and redistributed by educators. The topics covered in this OER include classical atomistic modelling, parameterizing interatomic potentials, molecular dynamics simulations, typical sources of error and some of the approaches to using simulations in the analysis of scattering data.
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Fejoz, Jacques, Andreas Knauf, and Richard Montgomery. "Classical n-body scattering with long-range potentials." Nonlinearity 34, no. 11 (October 14, 2021): 8017–54. http://dx.doi.org/10.1088/1361-6544/ac288d.
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Abstract We consider the scattering of n classical particles interacting via pair potentials which are assumed to be ‘long-range’, i.e. of order O ( r − α ) as r tends to infinity, for some α > 0. We define and focus on the ‘free region’, the set of states leading to well-defined and well-separated final states at infinity. As a first step, we prove the existence of an explicit, global surface of section for the free region. This surface of section allows us to prove the smoothness of the map sending a point to its final state and to establish a forward conjugacy between the n-body dynamics and free dynamics.
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Bäck, Andreas, and Nikola Marković. "Comparison of classical and quantum dynamics for collinear cluster scattering." Journal of Chemical Physics 122, no. 14 (April 8, 2005): 144711. http://dx.doi.org/10.1063/1.1875072.
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Poppe, D. "Classical dynamics of rotationally inelastic scattering of atoms with molecules." Chemical Physics 111, no. 1 (January 1987): 21–31. http://dx.doi.org/10.1016/0301-0104(87)87004-0.
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Tamura, Hideo. "Semi-classical bounds on scattering cross sections in two dimensional magnetic fields." Nagoya Mathematical Journal 147 (September 1997): 25–61. http://dx.doi.org/10.1017/s0027763000006309.
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AbstractWe prove the uniform boundedness of averaged total cross sections or of quantities related to scattering into cones in the semi-classical limit for scattering by two dimensional magnetic fields. We do not necessarily assume that the energy under consideration is in a non-trapping energy range in the sense of classical dynamics.
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Trugman, S. A. "Complex Classical and Quantum Scattering Dynamics and the Quantum Hall Effect." Physical Review Letters 62, no. 5 (January 30, 1989): 579–82. http://dx.doi.org/10.1103/physrevlett.62.579.
Full textDissertations / Theses on the topic "Classical scattering dynamics"
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Rodriguez-Fernandez, Alberto. "Classical dynamics of gas-surface scattering : fundamentals and applications." Thesis, Bordeaux, 2021. http://www.theses.fr/2021BORD0038.
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L’objet de cette thèse est l’étude théorique de processus réactifs et non réactifs se produisant à l’interface gaz-solide. Deux méthodes de trajectoires classiques, différentes et complémentaires, ont été utilisées afin de simuler la dynamique de ces processus. La première met en jeu un ensemble conséquent de trajectoires classiques obtenues en résolvant numériquement les équations de Hamilton sur une surface d’énergie potentielle (SEP) construite au préalable. Ces trajectoires sont pondérées par des poids statistiques conformément à deux contraintes semiclassiques: la pondération gaussienne et la correction d’adiabaticité. Cette approche, dans un esprit quantique, a été appliquée à la collision entre H2 et la surface de Pd(111). Dans un premier temps, nous nous sommes limités au cas où H2 se trouve dans son état rovibrationnel fondamental. Nous avons par la suite considéré ses états rotationnels excités. Il nous est alors apparu nécessaire de modifier la correction d’adiabaticité sur la base d’arguments semiclassiques rigoureux. Dans les deux cas, les prédictions des probabilités de collage et de réflexion résolues en états se sont avérées être en accord remarquable avec celles obtenues par des calculs quantiques exacts, contrairement aux prédictions classiques standards. L’approche classique dans un esprit quantique pourrait ainsi s’avérer d’une grande utilité pour les études à venir.La seconde méthode utilisée dans ce travail, connu sous le vocable de Ab-Initio Molecular Dynamics (AIMD), permet de calculer les forces entre noyaux à partir de la théorie de la fonctionnelle densité et d’en déduire classiquement leurs déplacements. Contrairement à l’approche précédente, l’AIMD n’exige pas la construction généralement difficile d’une SEP (le prix à payer, toutefois, est que le coût numérique de chaque trajectoire est nettement plus élevé qu’avec la méthode précédente). L’AIMD nous a permis d’étudier le processus de dissociation de H2 sur la surface de W(110). La fonctionnelle utilisée inclut un terme de van der Waals, qui provoque un accroissement de l’attraction à longue distance, compensé par une augmentation de la répulsion à courte distance. La combinaison des deux effets diminue de façon appréciable la probabilité de dissociation, alors en meilleur accord avec le résultat expérimental obtenu à l’aide d’une surface propre. Lorsque des atomes d’oxygène sont adsorbés au préalable sur la surface, la probabilité de dissociation chute considérablement. Cet effet est d’autant plus fort que la quantité d’oxygène adsorbé est forte. Un modèle de phase ordonnée a été utilisé afin d’expliquer l’absence de collage pour le taux de couverture Θ > 0.35 ML observé expérimentalement. Les atomes d’oxygène dévient les molécules H2 des étroits passages conduisant au collage en l’absence des atomes d’oxygène. Ceci élimine toute chance de collage pour de forts taux de recouvrement. En revanche, pour de faible taux, on s’attend à ce qu’une dynamique similaire à celle sur la surface propre se produise au dessus des atomes de tungstène, et à une distance suffisamment grande des atomes d’oxygèneThis thesis manuscript is devoted to the theoretical study of several reactive and non-reactive processes that take place at the gas-solid interface. Two classical trajectory methods, different and complementary, were used to simulate the dynamics of these processes. The first one relies on large sets of classical paths obtained by numerically solving Hamilton equations on a previously constructed potential energy surface (PES). Classical paths are then assigned statistical weights based on two semiclassical corrections: Gaussian binning and the adiabaticity correction. This approach, in a quantum spirit, was applied to the scattering of H2 on a Pd(111) surface. First, the study focused on collisions where H2 is initially in the rovibrational ground state. Then, rotationally excited states were considered. On this occasion, a variation of the adiabaticity correction based on firmer semiclassical grounds was introduced. In both cases, the predictions of the sticking and state-resolved reflection probabilities were found to be in remarkably good agreement with those obtained through exact quantum time-dependent calculations, contrary to standard quasi-classical trajectory predictions. The classical approach in a quantum spirit could thus be very useful for future studies.The second method used in this work, known as Ab-Initio Molecular Dynamics (AIMD), calculates the inter-nuclear forces from density functional theory and uses them to classically move the nuclei. Contrary to the previous approach, AIMD does not require the very demanding construction of a PES (the price to pay, however, is that the numerical cost of each trajectory is much higher than with the previous method). AIMD allowed us to study the dissociation process of H2 on W(110) surfaces.The functional we used includes a van der Waals term which provokes an increase of the far distance attraction that is compensated by a stronger repulsion at short distances. The combination of both effects appreciably decreases the value of the dissociation probability, bringing it closer to the experimental result when a clean surface is used. When oxygen atoms are previously adsorbed on the surface, the dissociation probability drops considerably. This effect increases with the amount of oxygen on the surface. A model ordered phase is used to explain the nonexistent sticking probability for coverages Θ > 0.35 ML observed experimentally. The oxygen atoms push the H2 molecules away from the narrow bottlenecks leading to the surface in the absence of oxygen atoms. This effectively eliminates any chance of dissociation in the surface for high coverages. At low coverages, it is expected that similar dynamics compared to the clean surface case arise on top of W atoms at a sufficiently large distance from O atoms
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Chism, William Wesley. "Nonlinear classical dynamics in intense laser-atom physics /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.
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McCrudden, Garreth. "Vector correlations in gas-phase inelastic collision dynamics." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:967fbe54-98a9-48e9-a0b2-707811804d7a.
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This thesis presents a joint experimental and theoretical study of vector correlations in the electronically, vibrationally, and rotationally inelastic collisions of simple molecules with rare-gas atoms. In the first instance, empirical and calculated data are presented for rotationally inelastic scattering in the NO(X)+Ar and ND3(X̃)+Ar systems at collision energies in the range 405-2210 cm-1. These experiments - the first to be conducted on a newly commissioned crossed-molecular beam machine - measured the k-k' correlation, i.e. that between the vectors describing the relative velocities before and after collision, respectively. The empirical data were subjected to rigorous comparison with both quantum-mechanical and quasi-classical trajectory (QCT) calculations. For both the NO(X)+Ar and ND3(X̃)+Ar systems, there is generally good agreement between experiment and theory at all four collision energies investigated. Two chapters of this thesis focus on the development of trajectory surface-hopping (TSH) QCT models of the OH(A, v = 0)+Kr and OH(A, v = 0)+Xe systems. Experimental data relating to scalar quantities (rotational energy transfer (RET) and electronic quenching) and to the j-j' correlation (which quantifies the depolarisation of the angular momentum of the OH(A) radical) are compared to variable-collision-energy TSH QCT calculations in which the length of the OH bond is fixed. The algorithms involve all three PESs of the OH(A/X)+Kr system, and the full range of electrostatic and roto-electronic mechanisms that couple them, for the first time. The most complete model succeeded in accounting for 93% of experimentally observed quenching. For the OH(A/X)+Xe system, coupling matrix elements were estimated from those of OH(A/X)+Kr, and the most complete model recovered 63% of experimentally observed quenching. This thesis also presents a novel theoretical study of rotationally inelastic dynamics in the OH(A, v = 1)+Kr system. Provisional results from adiabatic calculations in which the OH bond length is allowed to vary over the course of a trajectory are presented alongside experimental data that were reported previously. To date, these calculations continue to underestimate the extent of empirical RET data. Reasons for the observed discrepancy, and suggestions to resolve it, are outlined in detail.
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Alexander, William Andrew. "Theoretical and experimental studies of energy transfer dynamics in collisions of atomic and molecular species with model organic surfaces." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/26857.
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A full understanding of chemical reaction dynamics at the gas/organic-surface interface requires knowledge of energy-transfer processes that happen during the initial gas/surface collision. We have examined the influence of mass and rovibrational motion on the energy-transfer dynamics of gas-phase species scattering from model organic surfaces using theory and experiment. Molecular-beam scattering techniques were used to investigate the rare gases, Ne, Ar, Kr, and Xe, and the diatomics, N2 and CO, in collisions with CH3- and CF3-terminated self-assembled monolayer (SAM) surfaces. Complementary molecular-dynamics simulations were employed to gain an atomistic view of the collisions and elucidate mechanistic details not observable with our current experimental apparatus. We developed a systematic approach for obtaining highly accurate analytic intermolecular potential-energy surfaces, derived from high-quality ab initio data, for use in our classical-trajectory simulations. Results of rare gas scattering experiments and simulations indicate mass to be the determining factor in the energy-transfer dynamics, while other aspects of the potential-energy surface play only a minor role. Additionally, electronic-structure calculations were used to correlate features of the potential-energy surface with the energy-transfer behavior of atoms and small molecules scattering from polar and non-polar SAM surfaces. Collisions of diatomic molecules with SAMs are seen to be vibrationally adiabatic, however translational energy transfer to and from rotational modes of the gas species, while relatively weak, is readily apparent. Examination of the alignment and orientation of the final rotational angular momentum of the gas species reveals that the collisions induce a stereodynamic preference for the expected "cartwheel" motion, as well as a surprising propensity for "corkscrew" or "propeller" motion. The calculated stereodynamic trends suggest that the CH3-SAM is effectively more corrugated than the CF3-SAM. Finally, the feasibility for collisional-energy promoted, direct gas/organic-surface reactions was interrogated using the 1,3-dipolar azide-alkyne cycloaddition reaction. We found that geometrical constraints prevented the reaction from proceeding at the probed conditions.Ph. D.
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Gibson, D. J. "A High-Energy, Ultrashort-Pulse X-Ray System for the Dynamic Study of Heavy, Dense Materials." Washington, D.C : Oak Ridge, Tenn. : United States. Dept. of Energy ; distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2004. http://www.osti.gov/servlets/purl/15011626-GeBNVt/native/.
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Thesis (Ph.D.); Submitted to Univ. of California, Davis, CA (US); 17 Sep 2004.Published through the Information Bridge: DOE Scientific and Technical Information. "UCRL-TH-207378" Gibson, D J. 09/17/2004. Report is also available in paper and microfiche from NTIS.
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Barr, Alexander Michael. "Chaos, quasibound states, and classical periodic orbits in HOCI." Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-05-3029.
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We study the classical nonlinear dynamics and the quantum vibrational energy eigenstates of the molecule HOCl. The classical vibrational dynamics, at energies below the HO+Cl dissociation energy, contains several saddle-center and period doubling bifurcations. The saddle-center bifurcations are shown to be due to a 2:1, and at higher energies a 3:1, nonlinear resonance between bend and stretch motions in various periodic orbits. The sequence of bifurcations takes the system from nearly integrable at low energies to almost completely chaotic at energies near the HO+Cl dissociation energy. At energies above dissociation we study the chaotic scattering of the Cl atom off the HO dimer. This scattering is governed by a homoclinic tangle formed by the stable and unstable manifolds of a parabolic periodic orbit at infinity. We construct the first three segments of the homoclinic tangle in phase space and use scattering functions to investigate its higher-order structure.
For the quantum system we use a discrete variable representation to efficiently calculate the Hamiltonian matrix. We find 365 even and 357 odd parity eigenstates with energies below the dissociation energy. By plotting the eigenstates in configuration space we show that almost every quantum eigenstate can be associated with one or more of the classical periodic orbits. The classical bifurcations that give rise to new periodic orbits are manifest quantum mechanically through the sudden appearance of new classes of eigenstates. Despite the high degree of chaos in the classical dynamics at energies near the dissociation energy most quantum eigenstates remain highly ordered with recognizable nodal patterns.
We use R-matrix theory together with a discrete variable representation to calculate quasibound states with energies above the dissociation energy. We find quasibound states with lifetimes ranging over 5 orders of magnitude. Using configuration space plots and Husimi distributions we show that the long-lived quasibound states are supported by unstable periodic orbits in the classical dynamics and medium-lived quasibound states are spread throughout the chaotic region of the classical phase space. Short-lived quasibound states show some similarity to unstable periodic orbits that stretch along the dissociation channel.text
Books on the topic "Classical scattering dynamics"
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Beigie, Darin. Dynamics associated with classical multi-degree-of-freedom scattering phenomena. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1996.
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Henriksen, Niels Engholm, and Flemming Yssing Hansen. Bimolecular Reactions, Dynamics of Collisions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805014.003.0004.
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This chapter discusses the dynamics of bimolecular collisions within the framework of (quasi-)classical mechanics as well as quantum mechanics. The relation between the cross-section and the reaction probability, which can be calculated theoretically from a (quasi-)classical or quantum mechanical description of the collision, is described in terms of classical trajectories and wave packets, respectively. As an introduction to reactive scattering, classical two-body scattering is described and used to formulate simple models for chemical reactions, based on reasonable assumptions for the reaction probability. Three-body (and many-body) quasi-classical scattering is formulated and the numerical evaluation of the reaction probability is described. The relation between scattering angles and differential cross-sections in various frames is emphasized. The chapter concludes with a brief description of non-adiabatic dynamics, that is, situations beyond the Born–Oppenheimer approximation where more than one electronic state is in play. A discussion of the so-called Landau–Zener model is included.
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Morawetz, Klaus. Interacting Systems far from Equilibrium. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.001.0001.
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In quantum statistics based on many-body Green’s functions, the effective medium is represented by the selfenergy. This book aims to discuss the selfenergy from this point of view. The knowledge of the exact selfenergy is equivalent to the knowledge of the exact correlation function from which one can evaluate any single-particle observable. Complete interpretations of the selfenergy are as rich as the properties of the many-body systems. It will be shown that classical features are helpful to understand the selfenergy, but in many cases we have to include additional aspects describing the internal dynamics of the interaction. The inductive presentation introduces the concept of Ludwig Boltzmann to describe correlations by the scattering of many particles from elementary principles up to refined approximations of many-body quantum systems. The ultimate goal is to contribute to the understanding of the time-dependent formation of correlations. Within this book an up-to-date most simple formalism of nonequilibrium Green’s functions is presented to cover different applications ranging from solid state physics (impurity scattering, semiconductor, superconductivity, Bose–Einstein condensation, spin-orbit coupled systems), plasma physics (screening, transport in magnetic fields), cold atoms in optical lattices up to nuclear reactions (heavy-ion collisions). Both possibilities are provided, to learn the quantum kinetic theory in terms of Green’s functions from the basics using experiences with phenomena, and experienced researchers can find a framework to develop and to apply the quantum many-body theory straight to versatile phenomena.
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Steane, Andrew M. Relativity Made Relatively Easy Volume 2. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.001.0001.
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This is a textbook on general relativity and cosmology for a physics undergraduate or an entry-level graduate course. General relativity is the main subject; cosmology is also discussed in considerable detail (enough for a complete introductory course). Part 1 introduces concepts and deals with weak-field applications such as gravitation around ordinary stars, gravimagnetic effects and low-amplitude gravitational waves. The theory is derived in detail and the physical meaning explained. Sources, energy and detection of gravitational radiation are discussed. Part 2 develops the mathematics of differential geometry, along with physical applications, and discusses the exact treatment of curvature and the field equations. The electromagnetic field and fluid flow are treated, as well as geodesics, redshift, and so on. Part 3 then shows how the field equation is solved in standard cases such as Schwarzschild-Droste, Reissner-Nordstrom, Kerr, and internal stellar structure. Orbits and related phenomena are obtained. Black holes are described in detail, including horizons, wormholes, Penrose process and Hawking radiation. Part 4 covers cosmology, first in terms of metric, then dynamics, structure formation and observational methods. The meaning of cosmic expansion is explained at length. Recombination and last scattering are calculated, and the quantitative analysis of the CMB is sketched. Inflation is introduced briefly but quantitatively. Part 5 is a brief introduction to classical field theory, including spinors and the Dirac equation, proceeding as far as the Einstein-Hilbert action. Throughout the book the emphasis is on making the mathematics as clear as possible, and keeping in touch with physical observations.
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Tiwari, Sandip. Semiconductor Physics. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198759867.001.0001.
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A graduate-level text, Semiconductor physics: Principles, theory and nanoscale covers the central topics of the field, together with advanced topics related to the nanoscale and to quantum confinement, and integrates the understanding of important attributes that go beyond the conventional solid-state and statistical expositions. Topics include the behavior of electrons, phonons and photons; the energy and entropic foundations; bandstructures and their calculation; the behavior at surfaces and interfaces, including those of heterostructures and their heterojunctions; deep and shallow point perturbations; scattering and transport, including mesoscale behavior, using the evolution and dynamics of classical and quantum ensembles from a probabilistic viewpoint; energy transformations; light-matter interactions; the role of causality; the connections between the quantum and the macroscale that lead to linear responses and Onsager relationships; fluctuations and their connections to dissipation, noise and other attributes; stress and strain effects in semiconductors; properties of high permittivity dielectrics; and remote interaction processes. The final chapter discusses the special consequences of the principles to the variety of properties (consequences of selection rules, for example) under quantum-confined conditions and in monolayer semiconductor systems. The text also bring together short appendices discussing transform theorems integral to this study, the nature of random processes, oscillator strength, A and B coefficients and other topics important for understanding semiconductor behavior. The text brings the study of semiconductor physics to the same level as that of the advanced texts of solid state by focusing exclusively on the equilibrium and off-equilibrium behaviors important in semiconductors.
Book chapters on the topic "Classical scattering dynamics"
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Billing, Gert Due. "Classical Path Approach to Inelastic and Reactive Scattering." In Supercomputer Algorithms for Reactivity, Dynamics and Kinetics of Small Molecules, 339–56. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-0945-8_20.
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Gibbons, John. "The Zabolotskaya-Khokhlov Equation and the Inverse Scattering Problem of Classical Mechanics." In Dynamical Problems in Soliton Systems, 36–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-02449-2_6.
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"SCATTERING AND LINEAR OSCILLATIONS." In Classical Dynamics, 147–200. Cambridge University Press, 1998. http://dx.doi.org/10.1017/cbo9780511803772.005.
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GASPARD, P. "Scattering and Resonances: Classical and Quantum Dynamics." In Quantum Chaos, 307–83. Elsevier, 1993. http://dx.doi.org/10.1016/b978-0-444-81588-0.50013-4.
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Boothroyd, Andrew T. "Nuclear Scattering." In Principles of Neutron Scattering from Condensed Matter, 127–84. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198862314.003.0005.
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This chapter contains an overview of the different types of structural dynamics found in condensed matter, and the associated neutron scattering cross-sections. The scattering dynamics of the harmonic oscillator is discussed, and an expression for the Debye-Waller factor is obtained. In the case of crystalline solids, the vibrational spectrum in the harmonic approximation is described, including the phonon dispersion and the cross-sections for one-phonon coherent and incoherent scattering. Multi-phonon scattering is discussed briefly. For non-crystalline matter, the time-dependent van Hove correlation and response functions are introduced, and their relation to the scattering cross-section established. An approximate expression for the correlation function is obtained from the classical form. Partial correlation and response functions are defined for multicomponent systems. The technique of neutron Compton scattering as a probe of single-particle recoil dynamics is described. Quasielastic and neutron spin-echo spectroscopy are introduced, as well as examples of relaxational dynamics which these techniques can measure.
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Raff, Lionel, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam. "Fitting Potential Energy Hypersurfaces." In Neural Networks in Chemical Reaction Dynamics. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199765652.003.0005.
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Molecular dynamics (MD) and Monte Carlo (MC) simulations are the two most powerful methods for the investigation of dynamic behavior of atomic and molecular motions of complex systems. To date, such studies have been used to investigate chemical reaction mechanisms, energy transfer pathways, reaction rates, and product yields in a wide array of polyatomic systems. In addition, MD/MC methods have been successfully applied for the investigation of gas-surface reactions, diffusion on surfaces and in the bulk, membrane transport, and synthesis of diamond using chemical vapor deposition (CVD) techniques. The structure of vapor deposited rare gas matrices has been studied using trajectories procedures. If the chemical reaction of interest contains three atoms or fewer, various types of quantum and semiclassical calculations can be brought to bear on the problem. These methods include wave packet studies, close-coupling calculations at various levels of accuracy, and S-matrix theory. Several excellent review articles have been published describing the principal techniques and problems involved in conducting MD studies; the reader may wish to consult these as background material for this discussion. With the advent of relatively inexpensive, powerful personal computers, MD/MC simulations have become routine. Once the potential-energy hypersurface for the system has been obtained, the computations are straightforward, though time-consuming. In the majority of cases, the computational time required is on the order of hours to a few days. However, the accuracy of these simulations depends critically on the accuracy of the potential hypersurface used. The major problem associated with MD/MC investigations is the development of a potential-energy hypersurface whose topographical features are sufficiently close to those of the true, but unknown, surface that the results of the calculations are experimentally meaningful. Once the potential surface is chosen or computed, all the results from any quantum mechanical, semiclassical, or classical scattering or equilibrium calculation are determined. The only purpose of the MD calculations is to ascertain what these results are. Therefore, the most critical part of any MD/MC study is the development of the potential-energy hypersurface and the associated force field.
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Pierrus, J. "Electromagnetic radiation." In Solved Problems in Classical Electromagnetism. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821915.003.0011.
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This chapter begins by expressing the multipole expansion of the dynamic vector potential A ( r, t) in terms of electric and magnetic multipole moments. Differentiation of A ( r, t) leads directly to the fields E ( r, t) and B ( r, t), which have a component transporting energy away from the sources to infinity. This component is called electromagnetic radiation and it arises only when electric charges experience an acceleration. A range of questions deal with the various types of radiation, including electric dipole and magnetic dipole–electric quadrupole. Larmor’s formula is applied in both its non-relativistic and relativistic forms. Also considered are some applications involving antennas, antenna arrays and the scattering of radiation by a free electron.
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PINE, D. J., D. A. WEITZ, G. MARET, P. E. WOLF, E. HERBOLZHEIMER, and P. M. CHAIKIN. "DYNAMICAL CORRELATIONS OF MULTIPLY SCATTERED LIGHT." In Scattering and Localization of Classical Waves in Random Media, 312–72. WORLD SCIENTIFIC, 1990. http://dx.doi.org/10.1142/9789814340687_0006.
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Tossell, John A., and David J. Vaughan. "Theoretical Methods." In Theoretical Geochemistry. Oxford University Press, 1992. http://dx.doi.org/10.1093/oso/9780195044034.003.0005.
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In this chapter, the most important quantum-mechanical methods that can be applied to geological materials are described briefly. The approach used follows that of modern quantum-chemistry textbooks rather than being a historical account of the development of quantum theory and the derivation of the Schrödinger equation from the classical wave equation. The latter approach may serve as a better introduction to the field for those readers with a more limited theoretical background and has recently been well presented in a chapter by McMillan and Hess (1988), which such readers are advised to study initially. Computational aspects of quantum chemistry are also well treated by Hinchliffe (1988). In the section that follows this introduction, the fundamentals of the quantum mechanics of molecules are presented first; that is, the “localized” side of Fig. 1.1 is examined, basing the discussion on that of Levine (1983), a standard quantum-chemistry text. Details of the calculation of molecular wave functions using the standard Hartree-Fock methods are then discussed, drawing upon Schaefer (1972), Szabo and Ostlund (1989), and Hehre et al. (1986), particularly in the discussion of the agreement between calculated versus experimental properties as a function of the size of the expansion basis set. Improvements on the Hartree-Fock wave function using configuration-interaction (CI) or many-body perturbation theory (MBPT), evaluation of properties from Hartree-Fock wave functions, and approximate Hartree-Fock methods are then discussed. The focus then shifts to the “delocalized” side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field Xα method (MS-SCF-Xα) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is followed by discussion of empirical simulation, and we conclude by mentioning a recent approach incorporating density-functional theory and molecular dynamics (Car and Parrinello, 1985).
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Tiwari, Sandip. "Hamiltonians and solution techniques." In Semiconductor Physics, 6–57. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198759867.003.0001.
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Chapter 1 introduces several of the common principles, techniques and approximations that will be employed throughout the text. Classically, the Hamiltonian is the sum of kinetic energy and potential energy. In quantum mechanics, it is an operator that, by operating on the statefunction, leads to the energy observable. The chapter begins with a preliminary description of the crystal’s Hamiltonian and then introduces approximation techniques that permit useful solutions. Beginning with the simple jellium model, Hartree and Hartree-Fock approaches are developed, exchange interactions and correlation effects are explored, and both time-independent perturbation and time-dependent perturbation techniques discussed. Examples illustrate scattering by perturbation as well as adiabatic evolution. The centrality of fast-and-slow interactions is stressed, the Born-Oppenheimer approximation is illustrated through the configuration coordinate diagram, and interacting electron systems are analyzed. The multi-electron aspects are stressed by discussing static screening, dynamic screening and the meaning of permittivity therein.
Conference papers on the topic "Classical scattering dynamics"
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Choi, Woon Ih, Kwiseon Kim, and Sreekant Narumanchi. "Molecular Dynamics Modeling of Thermal Conductance at Atomically Clean and Disordered Silicon/Aluminum Interfaces." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-65409.
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Thermal resistance between layers impedes effective heat dissipation in electronics packaging applications. Thermal conductance for clean and disordered interfaces between silicon (Si) and aluminum (Al) was computed using realistic Si/Al interfaces and classical molecular dynamics with the modified embedded atom method potential. These realistic interfaces, which include atomically clean as well as disordered interfaces, were obtained using density functional theory. At 300 K, the magnitude of interfacial conductance due to phonon-phonon scattering obtained from the classical molecular dynamics simulations was approximately five times higher than the conductance obtained using analytical elastic diffuse mismatch models. Interfacial disorder reduced the thermal conductance due to increased phonon scattering with respect to the atomically clean interface. Also, the interfacial conductance, due to electron-phonon scattering at the interface, was greater than the conductance due to phonon-phonon scattering. This suggests that phonon-phonon scattering is the bottleneck for interfacial transport at the semiconductor/metal interfaces. The molecular dynamics modeling predictions for interfacial thermal conductance for a 5 nm disordered interface between Si/Al are in-line with recent experimental data in the literature.
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Stevens, Robert J., Pamela M. Norris, and Leonid V. Zhigilei. "Molecular Dynamics Study of Thermal Boundary Resistance: Evidence of Strong Inelastic Scattering Transport Channels." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60334.
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With the ever-decreasing size of microelectronics, growing applications of superlattices, and development of nanotechnology, thermal resistances of interfaces are becoming increasingly central to thermal management. Although there has been much success in understanding thermal boundary resistance (TBR) at low temperature, the current models for room temperature TBR are not adequate. This work examines TBR using molecular dynamics (MD) simulations of a simple interface between two FCC solids. The simulations reveal a temperature dependence of TBR, which is an indication of inelastic scattering in the classical limit. Introduction of point defects and lattice-mismatch-induced disorder in the interface region is found to assist the energy transport across the interface. This is believed to be due to the added sites for inelastic scattering and optical phonon excitation. A simple MD experiment was conducted by directing a phonon wave packet towards the interface. Inelastic scattering, which increases transport across the interface, was directly observed. Another mechanism of energy transport through the interface involving localization of optical phonon modes at the interface was also revealed in the simulations.
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Sipkens, T. A., K. J. Daun, J. T. Titantah, and M. Karttunen. "Quantifying the Thermal Accommodation Coefficient for Iron Surfaces Using Molecular Dynamics Simulations." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52150.
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With nanotechnology becoming an increasingly important field in contemporary science, there is a growing demand for a better understanding of energy exchange on the nanoscale. Techniques, such as time-resolved laser-induced incandescence, for example, require accurate models of gas-surface interaction to correctly predict nanoparticle characteristics. The present work uses molecular dynamics to define the thermal accommodation coefficient of various gases on iron surfaces. A more in depth analysis examines the scattering distributions from the surfaces and examines how well existing scattering kernels and classical theories can represent these distributions. The molecular dynamics-derived values are also compared to recent experimental time-resolved laser-induced incandescence studies aimed at evaluating the thermal accommodation coefficient across a range of surface-gas combinations.
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Mabuchi, Takuya, and Takashi Tokumasu. "Molecular Dynamics Study of Proton and Water Transport in Nafion Membrane." In ASME 2013 11th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icnmm2013-73084.
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Polymer electrolyte fuel cells (PEFCs) are highly expected as a next-generation power supply system due to the purity of its exhaust gas, its high power density and high efficiency. The polymer electrolyte membrane is a critical component for the performance of the PEFCs and it is important to understand the nanostructure in the membrane to enhance proton transport. We have performed an atomistic analysis of the vehicular transport of hydronium ions and water molecules in the nanostructure of hydrated Nafion membrane by systematically changing the hydration level which provides insights into a connection between the nanoscopic and mesoscopic structure of ion clusters and the dynamics of hydronium ions and water molecules in the hydrated Nafion membrane. In this study, classical molecular dynamics simulations are implemented using a model of Nafion membrane which is based on DREIDING force field and newly modified and validated by comparing the density, water diffusivity, and Nafion morphology with experimental data. The simulated final density after the annealing procedure agrees with experiment within 1.3 % for various water contents and the trends that density decreases with increasing hydration level are reproduced. In addition to determination of diffusion coefficients of solvent molecules as a function of hydration level (from λ = 1 up to λ = 18), we have also calculated radial distribution functions and static structure factors not only to clarify the structure of water molecules and hydronium ions around the first solvation shell of sulfonate groups but also to validate the mesoscopic periodic structure among water clusters. The diffusion coefficient of water molecules increases with increasing hydration level and is found to be in good agreement with experimental data. The diffusion coefficient of hydronium ions has showed that general trends in the experimental data are reproduced by the simulations although the classical models have the limitation of probing hydronium dynamics. The static structure factors of liquid molecules at low wave length provide insights into the periodic structure of the inter-water clusters. These results are consistent with the Gebel’s model based on small-angle X-ray scattering that considers the dry membrane to be made of isolated spherical ionic clusters of radius ∼7.5 Å that swell with increasing hydration.
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Thompson, Lonny L. "A Multi-Field Space-Time Finite Element Method for Structural Acoustics." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0395.
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Abstract A Computational Structural Acoustics (CSA) capability for solving scattering, radiation, and other problems related to the acoustics of submerged structures has been developed by employing some of the recent algorithmic trends in Computational Fluid Dynamics (CFD), namely time-discontinuous Galerkin Least-Squares finite element methods. Traditional computational methods toward simulation of acoustic radiation and scattering from submerged elastic bodies have been primarily based on frequency domain formulations. These classical time-harmonic approaches (including boundary element, finite element, and finite difference methods) have been successful for problems involving a limited range of frequencies (narrow band response) and scales (wavelengths) that are large compared to the characteristic dimensions of the elastic structure. Attempts at solving large-scale structural acoustic systems with dimensions that are much larger than the operating wavelengths and which are complex, consisting of many different components with different scales and broadband frequencies, has revealed limitations of many of the classical methods. As a result, there has been renewed interest in new innovative approaches, including time-domain approaches. This paper describes recent advances in the development of a new class of high-order accurate and unconditionally stable space-time methods for structural acoustics which employ finite element discretization of the time domain as well as the usual discretization of the spatial domain. The formulation is based on a space-time variational equation for both the acoustic fluid and elastic structure together with their interaction. Topics to be discussed include the development and implementation of higher-order accurate non-reflecting boundary conditions based on the exact impedance relation through the. Dirichlet-to-Neumann (DtN) map, and a multi-field representation for the acoustic fluid based on independent pressure and velocity potential variables. Numerical examples involving radiation and scattering of acoustic waves are presented to illustrate the high-order accuracy achieved by the new methodology for CSA.
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Popkov, Vyacheslav, Alexander Sterenberg, Vladimir Gusev, and Andrey Tyutyaev. "COGNITIVE GEOLOGY OF SUPERIMPOSED SCATTERING OF MOBILE ORE ELEMENTS, PROPER FORMS OF MULTISCALE STRUCTURAL STRESS STABILITY, BIOGENETIC ACCESS CODE OF RESOURCES AND FIELD ARTEFACTS." In GEOLINKS International Conference. SAIMA Consult Ltd, 2020. http://dx.doi.org/10.32008/geolinks2020/b1/v2/11.
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The authors present the theory is numerical / analytical method of multi-scaled 4D geomechanics – geo-dynamics of energy integration in geo-physical rhythms of Eigen-solution of Navier-Stokes equations for multi-level geological time space of evolution in structural compacted mass transfer at the basis of Newton’s Differential Law ∫V∫TρdS·∂2ξ/∂t2 following the integration formula of A. Einstein E(u,t)=ρVC2+∫V∫Tρ‹uv›dtdx. Сreate the theory (Restoration) and Maintenance of Water Eco-System with Given Parameters. They establish the geophysical seismic rhythms of geological cycles in deep structural formations of the Volga-Urals and Siberia and Kamchatka at dissipative emission, adsorption and nuclear magnetic resonance. The authors propose the systematic velocity model of convective diffusion drift of ρ<uv> in deep phase components of heterogenic structures with complexly structured geology in off-shore and global aeration of Middle Ridges from the Urals to the Rocky Mountains. They have also considered the energy time space of more than 4,5 billion years to find the organic markers of quantum photo-synthesis and multiple circulating energy waves in physical and chemical reactions of compacted formation genesis in fissile and relict shales, including the facies with symmetrical absolutely-saturated porosity of classical fields. They establish the geophysical seismic rhythms of geological cycles in deep structural formations of the Volga-Urals and Siberia and Kamchatka at dissipative emission, adsorption and nuclear magnetic resonance. The authors propose the systematic velocity model of convective diffusion drift of ρ‹uv› in deep phase components of heterogenic structures with complexly structured geology in off-shore and global aeration of Middle Ridges from the Urals to the Rocky Mountains. They have also considered the energy time space of more than 4.5 billion years to find the organic markers of quantum photo-synthesis and multiple circulating energy waves in physical and chemical reactions of compacted formation genesis in fissile and relict shales, including the facies with symmetrical absolutely-saturated porosity of classical fields’ cognitive geology, artefacts.
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Gillet, Jean-Numa, and Sebastian Volz. "Atomic-Scale Three-Dimensional Phononic Crystals With a Large Thermoelectric Figure of Merit." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68381.
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The design of thermoelectric materials led to extensive research on superlattices with a low thermal conductivity. Indeed, the thermoelectric figure of merit ZT varies with the inverse of the thermal conductivity but is directly proportional to the power factor. Unfortunately, as nanowires, superlattices cancel heat conduction in only one main direction. Moreover they often show dislocations owing to lattice mismatches, which reduces their electrical conductivity and avoids a ZT larger than unity. Self-assembly is a major epitaxial technology to design ultradense arrays of germanium quantum dots (QDs) in silicon for many promising electronic and photonic applications as quantum computing. Accurate positioning of the self-assembled QD can now be achieved with few dislocations. We theoretically demonstrate that high-density three-dimensional (3-D) arrays of self-assembled Ge QDs, with a size of only some nanometers, in a Si matrix can also show an ultra-low thermal conductivity in the three spatial directions. This property can be considered to design new CMOS-compatible thermoelectric devices. To obtain a realistic and computationally-manageable model of these nanomaterials, we simulate their thermal behavior with atomic-scale 3-D phononic crystals. A phononic-crystal period (supercell) consists of diamond-like Si cells. At each supercell center, we substitute Si atoms by Ge atoms to form a box-like nanoparticle. Since this phononic crystal is periodic, we compute its phonon dispersion curves by classical lattice dynamics. Non-periodicities can be introduced with statistical distributions. From the flat dispersion curves, we obtain very small group velocities; this reduces the thermal conductivity in our phononic crystal compared to bulk Si. However, owing to the wave-particle duality at very small scales in quantum mechanics, another reduction arises from multiple scattering of the particle-like phonons in nanoparticle clusters. At room temperature, the thermal conductivity in an example phononic crystal can be reduced by a factor of at least 165 compared to bulk Si or below 0.95 W/mK. This value, which is lower than the classical Einstein limit of single crystalline Si, is an upper limit of the thermal conductivity since we use an incoherent-scattering approach for the nanoparticles. Because of its very low thermal conductivity, we hope to obtain a much larger ZT than unity in our atomic-scale 3-D phononic crystal. Indeed, this silicon-based nanomaterial is crystalline with a power factor that can be optimized by doping using CMOS-compatible processes. Future research on the phononic-crystal electrical conductivity has to be performed in order to compute the full ZT with a good accuracy.
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Gillet, Jean-Numa, Yann Chalopin, and Sebastian Volz. "Atomic-Scale Three-Dimensional Phononic Crystals With a Lower Thermal Conductivity Than the Einstein Limit of Bulk Silicon." In ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/ht2008-56403.
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Extensive research about superlattices with a very low thermal conductivity was performed to design thermoelectric materials. Indeed, the thermoelectric figure of merit ZT varies with the inverse of the thermal conductivity but is directly proportional to the power factor. Unfortunately, as nanowires, superlattices reduce heat transfer in only one main direction. Moreover, they often show dislocations owing to lattice mismatches. Therefore, fabrication of nanomaterials with a ZT larger than the alloy limit usually fails with the superlattices. Self-assembly is a major epitaxial technology to fabricate ultradense arrays of germaniums quantum dots (QD) in a silicon matrix for many promising electronic and photonic applications as quantum computing. We theoretically demonstrate that high-density three-dimensional (3-D) periodic arrays of small self-assembled Ge nanoparticles (i.e. the QDs), with a size of some nanometers, in Si can show a very low thermal conductivity in the three spatial directions. This property can be considered to design thermoelectric devices, which are compatible with the complementary metal-oxide-semiconductor (CMOS) technologies. To obtain a computationally manageable model of these nanomaterials, we simulate their thermal behavior with atomic-scale 3-D phononic crystals. A phononic-crystal period (supercell) consists of diamond-like Si cells. At each supercell center, we substitute Si atoms by Ge atoms in a given number of cells to form a box-like Ge nanoparticle. The phononic-crystal dispersion curves, which are computed by classical lattice dynamics, are flat compared to those of bulk Si. In an example phononic crystal, the thermal conductivity can be reduced below the value of only 0.95 W/mK or by a factor of at least 165 compared to bulk silicon at 300 K. Close to the melting point of silicon, we obtain a larger decrease of the thermal conductivity below the value of 0.5 W/mK, which is twice smaller than the classical Einstein Limit of single crystalline Si. In this paper, we use an incoherent-scattering approach for the nanoparticles. Therefore, we expect an even larger decrease of the phononic-crystal thermal conductivity when multiple-scattering effects, as multiple reflections and diffusions of the phonons between the Ge nanoparticles, will be considered in a more realistic model. As a consequence of our simulations, a large ZT could be achieved in 3-D ultradense self-assembled Ge nanoparticle arrays in Si. Indeed, these nanomaterials with a very small thermal conductivity are crystalline semiconductors with a power factor that can be optimized by doping using CMOS-compatible technologies, which is not possible with other recently-proposed nanomaterials.
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Sakiyama, Yukinori, Shu Takagi, and Yoichiro Matsumoto. "Multiscale Analysis of Silicon LPCVD Reactor." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72051.
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We demonstrate the multiscale analysis of the transport phenomena in a low pressure reactor. In this method, the macroscopic phenomena such as the temperature and the density distribution are related to the microscopic electronic structure of atom/molecule. By connecting the different scales with physical models, the macroscopic properties are obtained starting from the first principle calculation without any empirical parameters. Here, we take the silicon epitaxial growth from a gas mixture of silane and hydrogen as an example. As the first step of this method, we calculated the intermolecular potential energy of SiH4/H2 using the ab initio molecular orbital calculations. Then, an analytical pair potential model was constructed to reproduce the potential energy surface obtained from the ab initio calculation. We have confirmed the validation of the potential model by comparing the experimental data of the transport properties with the molecular dynamics simulation using the potential model. Subsequently, the binary molecular collision models were constructed by the classical trajectory calculation using the potential model as the second step of the multiscale analysis. The trajectory calculations were conducted for the various combinations of the initial translational and the rotational energy. Through the statistical analysis of the trajectory calculations, the elastic/inelastic collision cross section and the scattering angle model were constructed. Finally, the direct simulation Monte Carlo simulation of flow field in a low parssure reactor was executed. The thin film thickness distribution was also investigated and discussed. This method was extended to analyze the surface reaction, which is an ongoing research work and only the current progress is reported here.
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Liu, Yen-Chen, and Nikhil Chopra. "A New Architecture for Set-Point Control of Robotic Manipulators With Time-Varying Input/Output Delays." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-6188.
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In this paper we study the classical set-point control problem for rigid robots when there are time-varying delays in the input-output channels. It has been demonstrated earlier that scattering variables together with additional gains can be utilized to stabilize the closed loop system in the presence of time-varying delays. However, this architecture is not able to guarantee asymptotic regulation to the desired configuration, and the stability depends on the maximum rate of change of the time-varying delays in the communication. Hence, in this paper, we present a new architecture where scattering variables and position feedback are utilized to guarantee stability and asymptotic convergence of the regulation error to the origin while simultaneously relaxing a significant assumption on the rate of change of delays. The proposed algorithm is numerically verified on a two-degree-of-freedom manipulator.