Geometric approach to Hamiltonian dynamics and statistical mechanics
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In this paper, a topological hypothesis was proposed to explain the chaotic behavior of the curvature of the configuration space of a dynamical system at a phase transition point, which can be qualitatively reproduced using geometric models.About:
This article is published in Physics Reports.The article was published on 2000-10-01 and is currently open access. It has received 240 citations till now. The article focuses on the topics: Hamiltonian system & Configuration space.read more
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Statistical mechanics and dynamics of solvable models with long-range interactions
TL;DR: In this article, a comprehensive review of the recent advances on the statistical mechanics and out-of-equilibrium dynamics of solvable systems with long-range interactions is presented, as exemplified by the exact solution, in the microcanonical and canonical ensembles, of mean-field type models.
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Nonstatistical dynamics in thermal reactions of polyatomic molecules.
TL;DR: A brief review is presented of post-RRKM models for unimolecular reaction kinetics, and a qualitative model for this behavior based on overlaps of transitional regions in the molecular phase space is discussed.
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Phase transitions and configuration space topology
TL;DR: In this paper, the authors studied the relationship between nonanalytic points of thermodynamic functions and topology changes in configuration space, and found that the non-analytic point in a thermodynamic function has some maximization procedure at its origin.
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Theorem on the Origin of Phase Transitions
Roberto Franzosi,Marco Pettini +1 more
TL;DR: For physical systems described by smooth, finite-range, and confining microscopic interaction potentials V with continuously varying coordinates, the proof of a theorem that establishes that the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature also in the N--> infinity limit is announced.
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Free motion around black holes with discs or rings: between integrability and chaos - I
Oldřich Semerák,Petra Suková +1 more
TL;DR: In this paper, the authors studied the time-like geodesic dynamics in exact static, axially and reflection symmetric space, describing the fields of a Schwarzschild black hole surrounded by thin discs or rings.
References
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Handbook of Mathematical Functions
Book
Phase Transitions and Critical Phenomena
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.
Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
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The classical theory of fields
TL;DR: The principle of relativity Relativistic mechanics Electromagnetic fields electromagnetic waves as discussed by the authors The propagation of light The field of moving charges Radiation of electromagnetic waves Particle in a gravitational field The gravitational field equation