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Asynchronous Variational Integration of Interaction Potentials for Contact Mechanics  [PDF]
Etienne Vouga,David Harmon,Rasmus Tamstorf,Eitan Grinspun
Mathematics , 2009,
Abstract: Asynchronous Variational Integrators (AVIs) have demonstrated long-time good energy behavior. It was previously conjectured that this remarkable property is due to their geometric nature: they preserve a discrete multisymplectic form. Previous proofs of AVIs' multisymplecticity assume that the potentials are of an elastic type, i.e., specified by volume integration over the material domain, an assumption violated by interaction-type potentials, such as penalty forces used to model mechanical contact. We extend the proof of AVI multisymplecticity, showing that AVIs remain multisymplectic under relaxed assumptions on the type of potential. The extended theory thus accommodates the simulation of mechanical contact in elastica (such as thin shells) and multibody systems (such as granular materials) with no drift of conserved quantities (energy, momentum) over long run times, using the algorithms in [3]. We present data from a numerical experiment measuring the long time energy behavior of simulated contact, comparing the method built on multisymplectic integration of interaction potentials to recently proposed methods for thin shell contact.
Geometrical aspects of a generalized statistical mechanics  [PDF]
M. Portesi,F. Pennini,A. Plastino
Physics , 2005, DOI: 10.1016/j.physa.2006.05.024
Abstract: We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics models. The thermodynamic stability of the system is the focus of attention in this geometric context.
Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability  [PDF]
Taksu Cheon,T. Shigehara,K. Takayanagi
Physics , 1998, DOI: 10.1143/JPSJ.69.345
Abstract: We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization. Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.Md
Contact Mechanics: Modeling the Interaction Between Surfaces with Nanoscale Asperities for MEMS via Online Simulations in NanoHUB  [PDF]
Petros Charalambides
JPUR : Journal of Purdue Undergraduate Research , 2012,
Abstract: Physics-based simulations are playing an increasingly important role in materials and device engineering, providing information that can help engineers understand current technology and optimize designs. We describe a model and simulation tool for the characterization of the interaction between surfaces with nanoscale asperities relevant in nano and micro-electromechanical systems (N/MEMS) whose operation involves periodic contacts. A mesoscale contact model was developed to characterize the interaction and adhesion between two surfaces in terms of surface topography and fundamental materials properties. The model computed the long-range van der Waals attractive forces and repulsive interactions originating from the contact between solid surface asperities. The tool has been deployed in nanoHUB.org and is available for fully interactive, free online simulations using a web browser.
Contact mechanics for randomly rough surfaces  [PDF]
Bo N. J. Persson
Physics , 2006, DOI: 10.1016/j.surfrep.2006.04.001
Abstract: When two solids are squeezed together they will in general not make atomic contact everywhere within the nominal (or apparent) contact area. This fact has huge practical implications and must be considered in many technological applications. In this paper I briefly review basic theories of contact mechanics. I consider in detail a recently developed contact mechanics theory. I derive boundary conditions for the stress probability distribution function for elastic, elastoplastic and adhesive contact between solids and present numerical results illustrating some aspects of the theory. I analyze contact problems for very smooth polymer (PMMA) and Pyrex glass surfaces prepared by cooling liquids of glassy materials from above the glass transition temperature. I show that the surface roughness which results from the frozen capillary waves can have a large influence on the contact between the solids. The analysis suggest a new explanation for puzzling experimental results [L. Bureau, T. Baumberger and C. Caroli, arXiv:cond-mat/0510232] about the dependence of the frictional shear stress on the load for contact between a glassy polymer lens and flat substrates. I discuss the possibility of testing the theory using numerical methods, e.g., finite element calculations.
Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction  [PDF]
Taksu Cheon,T. Shigehara
Physics , 1998, DOI: 10.1103/PhysRevLett.82.2536
Abstract: For a system of spinless one-dimensional fermions, the non-vanishing short-range limit of two-body interaction is shown to induce the wave-function discontinuity. We prove the equivalence of this fermionic system and the bosonic particle system with two-body $\delta$-function interaction with the reversed role of strong and weak couplings. KEYWORDS: one-dimensional system, $\epsilon$-interaction, solvable many-body problem, exact bosonization
Contact structures and supersymmetric mechanics  [PDF]
Andrew James Bruce
Mathematics , 2011,
Abstract: We reexamine the relation between contact structures on supermanifolds and supersymmetric mechanics in the superspace formulation. This allows one to use the language of contact geometry when dealing with the d = 1, N = 2 super-Poincare algebra.
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics  [PDF]
T. Shigehara,H. Mizoguchi,T. Mishima,Taksu Cheon
Physics , 1999,
Abstract: We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\delta$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called $\epsilon$ potential. It will be also shown that the scattering properties at high energy substantially differ between non-relativistic and relativistic cases.
Contact reductions, mechanics and duality  [PDF]
Pavol Severa
Mathematics , 1999,
Abstract: Contact reduction is very closely related to symplectic reduction, but it allows symmetries that are not manifest in Hamiltonian mechanics and moreover, solution of the reduced problems yields solution of the original problem without further integration.
On Generalized Functions in Adelic Quantum Mechanics  [PDF]
Branko Dragovich
Physics , 2004,
Abstract: Some aspects of adelic generalized functions, as linear continuous functionals on the space of Schwartz-Bruhat functions, are considered. The importance of adelic generalized functions in adelic quantum mechanics is demonstrated. In particular, adelic product formula for Gauss integrals is derived, and the connection between the functional relation for the Riemann zeta function and quantum states of the harmonic oscillator is stated.
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