Nonstandard Analysis and Lattice Statistical Mechanics: A Variational Principle
نویسندگان
چکیده
منابع مشابه
A Variational Principle for Quasistatic Mechanics
Quasistatic mechanical systems are those in which mass or acceleration are sufficientlysmall that the inertial term mu in F = mu is negligible compared to dissipative forces. In roboticsquasistatic mechanics may be used for systems with friction when motions are sufficiently slow. Here weconsider a general quasistatic system with constraints and both dissipative and conservative for...
متن کاملStatistical Mechanics of Lattice Systems
We study the thermodynamic limit for a classical system of particles on a lattice and prove the existence of infinite volume correlation functions for a "large" set of potentials and temperatures. §
متن کامل$(varphi_1, varphi_2)$-variational principle
In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm, such that $f + g $ attains its strong minimum on $X. $ This result extends some of the well-known varitional principles as that of Ekeland [On the variational principle, J. Ma...
متن کاملTransfer Principle Proof Tactic for Nonstandard Analysis
This paper describes a type constructor for nonstandard extensions of arbitrary types, generalizing the previous formalization of nonstandard analysis in Isabelle by Fleuriot and Paulson [1]. In addition to numeric types, nonstandard extensions of function spaces and set types also prove useful—they provide an elegant way to define internal functions and internal sets. The paper also describes ...
متن کاملDifference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This approach keeps both symplicticity and energy conservation discretely. We show that there exists the discrete version of the Euler-Lagrange cohomology in these...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1981
ISSN: 0002-9947
DOI: 10.2307/1998645