相关论文: Tangential Tensor Fields on Deformable Surfaces --…

We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances,…

The transport of energy in a moving fluid with a simply connected free surface is analyzed, taking into account the contribution of surface tension. This is done by following a "control volume" with arbitrary, specified velocity,…

Incompressible flows of an ideal two-dimensional fluid on a closed orientable surface of positive genus are considered. Linear stability of harmonic, i.e. irrotational and incompressible, solutions to the Euler equations is shown using the…

In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism,…

Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…

The paper addresses the question if there exists a finite stopping time for an unforced motion of a yield stress fluid with free surface. A variation inequality formulation is deduced for the problem of yield stress fluid dynamics with a…

We propose new formulations of geometric curvature flows -- referred to as \emph{dual formulations} -- that are equivalent to the original formulations but provide a novel framework for constructing linearly implicit and energy-stable…

We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…

A pressure-driven two-layer channel flow of a Newtonian fluid with constant viscosity (top layer) and a fluid with a time-dependent viscosity (bottom layer) is numerically investigated. The bottom layer goes through an aging process in…

Computing the electromagnetic field due to a periodic grating is critical for assessing the performance of thin film solar voltaic devices. In this paper we investigate the computation of these fields in the time domain (similar problems…

A particle is thrown tangentially on a surface. It is shown that for some surfaces and for special initial velocities the thrown particle leaves immediately the surface, and for special conditions it never leaves the surface. The conditions…

The time dependent Schrodinger equation inclusive of curvature effects is developed for a spinless electron constrained to motion on a toroidal surface and subjected to circularly polarized and linearly polarized waves in the microwave…

We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system…

Many viscous liquids behave effectively as incompressible under high pressures but display a pronounced dependence of viscosity on pressure. The classical incompressible Navier-Stokes model cannot account for both features, and a simple…

We present a second-order strictly length-preserving and unconditionally energy-stable rotational discrete gradient (Rdg) scheme for the numerical approximation of the Oseen-Frank gradient flows with anisotropic elastic energy functional.…

We use a database of direct numerical simulations to evaluate parametrizations for energy dissipation rate in stably stratified flows. We show that shear-based formulations are more appropriate for stable boundary layers than commonly used…

We study the energy flow of dissipative dynamics on infinite lattices, allowing the total energy to be infinite and considering formally gradient dynamics. We show that in spatial dimensions 1,2, the flow is for almost all times arbitrarily…

We propose a covariant, gauge-independent construction of foliation-based scalar-tensor theories, yielding diffeomorphism-invariant operators involving only gradients on the hypersurfaces where the scalar field is constant, assumed to be…

We re-examine the nature of the turbulent magnetic diffusivity tensor of mean field electrodynamics and show that an inconsistency arises if it is calculated via consideration of time-independent magnetic fields. Specifically, the predicted…

The properties of one-dimensional superconductors are strongly influenced by topological fluctuations of the order parameter, known as phase slips, which cause the decay of persistent current in superconducting rings and the appearance of…