相关论文: Extended objects with edges

In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its application to the problem of the existence in the space-time of compact and complete spacelike hypersurface.

I discuss the relationship between edge exponents in the statistics of work done, dynamical phase transitions, and the role of different kinds of excitations appearing when a non-equilibrium protocol is performed on a closed, gapped,…

We show that a mobility edge exists in 1D random potentials provided specific long-range correlations. Our approach is based on the relation between binary correlator of a site potential and the localization length. We give the algorithm to…

We formulate a Euclidean theory of edge length dynamics based on a notion of Ricci curvature on graphs with variable edge lengths. In order to write an explicit form for the discrete analog of the Einstein-Hilbert action, we require that…

Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions.…

In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with…

This paper presents a new method for modelling the dynamic behaviour of developable ribbons, two dimensional strips with much smaller width than length. Instead of approximating such surface with a general triangle mesh, we characterize it…

In this note, we showcase some recent results concerning the stickiness properties of nonlocal minimal graphs in the plane. To start with, the nonlocal minimal graphs in the plane enjoy an enhanced boundary regularity, since boundary…

We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence…

An analysis of the generalised Raychaudhuri equations for string world sheets is shown to lead to the notion of focusing of timelike worldsheets in the classical Nambu-Goto theory of strings. The conditions under which such effects can…

We have simulated the dynamics of a 2D gas of hard needles by event-oriented molecular dynamics. Various quantities namely translational and rotational diffusion constants and intermediate self scattering function have been explored and…

We extend our recently identified dynamical edge mode boundary condition to $p$-form gauge theories, revealing their edge modes as Goldstone bosons arising from gauge transformations with support on the boundary. The symplectic conjugates…

We study the behavior of a semi-infinite monolayer, which is placed initially on a half of an infinite in both directions, ideal crystalline surface, and then evolves in time due to random motion of the monolayer particles. Particles…

The concept of smooth deformation of Riemannian manifolds associated with the extrinsic curvature is explained and applied to the FLRW cosmology. We show that such deformation can be derived from Einstein-Hilbert-like dynamical principle…

We prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a global existence…

In this molecular dynamics study, we examine the local surface geometric effects of the normal impact force between two approximately spherical nanoparticles that collide in a vacuum. Three types of surface geometries, facets, sharp crystal…

We consider an electrodiffusion model describing the evolution of $N$ ionic species in a three-dimensional fluid flowing through a porous medium and forced by added body charges. We address the global well-posedness and long-time dynamics…

The single-file problem of N particles in one spatial dimension is analyzed, when each particle has a randomly distributed diffusion constant D sampled in a density $\rho(D)$. The averaged one-particle distributions of the edge particles…

We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…

A finite photonic lattice with two bands and a random gap is considered. Using a two-dimensional Dirac equation, the effect of a random sign of the Dirac mass is studied numerically. The edge state at the sample boundary has a strong…