Related papers: A variational principle for nonlinear local pressu…

In this note, we show several variational principles for metric mean dimension. First we prove a variational principles in terms of Shapira's entropy related to finite open covers. Second we establish a variational principle in terms of…

We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…

In this paper, unstable metric entropy, unstable topological entropy and unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. A version of Shannon-McMillan-Breiman Theorem is established, and a…

Using monotonicity theory we investigate the continuous dependence on parameters for the discrete BVPs which can be written in a form of a nonlinear system.

Nonlinear topology has been much less inquired compared to its linear counterpart. Existing advances have focused on nonlinearities of limited magnitudes and fairly homogeneous types. As such, the realizations have rarely been concerned…

We discuss different definitions of pressure for a system of active spherical particles driven by a non-thermal coloured noise. We show that mechanical, kinetic and free-energy based approaches lead to the same result up to first order in…

We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…

In a previous article by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems by starting with the first variation functional instead of an action functional. In this…

Many advancements have been made in the field of topological mechanics. The majority of the works, however, concerns the topological invariant in a linear theory. We, in this work, present a generic prescription of defining topological…

We recall the classical theory of capillarity, describing the shape of a liquid droplet in a container, and present a recent approach which aims at accounting for long-range particle interactions. This nonlocal setting recovers the…

Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…

A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…

Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…

We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…

In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology that classifies their global shape.…

We present variational and Hamiltonian formulations of incompressible fluid dynamics with free surface and nonvanishing odd viscosity. We show that within the variational principle the odd viscosity contribution corresponds to geometric…

Computer simulations of inhomogeneous soft matter systems often require accurate methods for computing the local pressure. We present a simple derivation, based on the virial relation, of two equivalent expressions for the local (atomistic)…

We present a method for performing multithermal-multibaric molecular dynamics simulations that sample entire regions of the temperature-pressure (TP) phase diagram. The method uses a variational principle [Valsson and Parrinello, Phys. Rev.…

A new inequality for a nonlinear surface layer integral is proved for minimizers of causal variational principles. This inequality is applied to obtain a new proof of the positive mass theorem with volume constraint. Next, a positive mass…

General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…