相关论文: Long time behaviour of generalised gradient flows …

Recently we proposed a microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures. It was based on the method of collective variables (CV) with a reference system. The approach allowed us…

The collective behaviour of statistical systems close to critical points is characterized by an extremely slow dynamics which, in the thermodynamic limit, eventually prevents them from relaxing to an equilibrium state after a change in the…

We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that…

This paper addresses the gradient flow -- the continuous-time representation of the gradient method -- with the smooth approximation of a non-differentiable objective function and presents convergence analysis framework. Similar to the…

In this note we study the singular vanishing-viscosity limit of a gradient flow set in a finite-dimensional Hilbert space and driven by a smooth, but possibly non convex, time-dependent energy functional. We resort to ideas and techniques…

We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the…

Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Total variation gradient flows are important in several applied fields, including image analysis and materials science. In this paper, we review a few basic topics including definition of a solution, explicit examples and the notion of…

We study the limit of the joint distribution of a multidimensional Generalized Tempered Stable (GTS) process and its quadratic covariation process when the stable index tends to two. Under a proper scaling, the GTS processes converges to a…

Critical behaviour of a system, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. Specifically, relaxational stochastic dynamics of a non-conserved multicomponent order…

The persistent problem posed by the glass transition is to develop a general atomic level description of a solidification process that is not associated with any change in the symmetry of the atomic structure. The answer proposed in this…

This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalised by the relative entropy. We identify suitable metric space on which we construct a gradient flow for the…

Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…

The purpose of this article is to study the hydrodynamic limit of the symmetric exclusion process with long jumps and in contact with infinitely extended reservoirs for a particular critical regime. The jumps are given in terms of a…

In the field of machine learning, comprehending the intricate training dynamics of neural networks poses a significant challenge. This paper explores the training dynamics of neural networks, particularly whether these dynamics can be…

In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…

The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…

The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation.…

We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry. We then discuss what the phase space and the Hamiltonian of general…