相关论文: Self-avoiding walks adsorbed at a surface and subj…

Understanding about both the range and the strength of the effective force between two hydrophobic surfaces suspended in water is important in many areas of natural science but unfortunately has remained imperfect. Even the experimental…

We consider a weighted lattice $Z^d$ with conductance $\mu_e=|e|^{-\alpha}$. We show that the heat kernel of a variable speed random walk on it satisfies a two-sided Gaussian bound by using an intrinsic metric. We also show that when $d=2$…

Active diffusiophoresis - swimming through interaction with a self-generated, neutral, solute gradient - is a paradigm for autonomous motion at the micrometer scale. We study this propulsion mechanism within a linear response theory.…

We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…

Building on a work by Alm, we consider a model of weighted self-avoiding walks on a lattice and develop a method for computing upper bounds on the corresponding weighted connective constant, which we implement in a publicly available…

We introduce a new type of discrete quantum walks, called vertex-face walks, based on orientable embeddings. We first establish a spectral correspondence between the transition matrix $U$ and the vertex-face incidence structure. Using the…

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…

We prove that self-avoiding walk on Z^d is sub-ballistic in any dimension d at least two. That is, writing ||u|| for the Euclidean norm of u \in Z^d, and SAW_n for the uniform measure on self-avoiding walks gamma:{0,...,n} \to Z^d for which…

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $\mu=\sqrt{2+\sqrt{2}}.$ A key identity used in…

We have investigated the motion of a single optically trapped colloidal particle close to a limiting wall at time scales where the inertia of the surrounding fluid plays a significant role. The velocity autocorrelation function exhibits a…

We study a simple random walk on Z^2 with constraints on the axis. Motivation comes from physics when particles (a gas for example, see [Dal88]) are submitted to a local field. In our case we assume that the particle evolves freely in the…

We reduce the problem of counting self-avoiding walks in the square lattice to a problem of counting the number of integral points in multidimensional domains. We obtain an asymptotic estimate of the number of self-avoiding walks of length…

We derive the trapping energy of a colloidal particle at a liquid interface with contact angle h and principal curvatures c1 and c2. The boundary conditions at the particle surface are significantly simplified by introducing the shift e of…

The fundamental role of hydrophobic interactions in nature and technology has motivated decades long research aimed at measuring the distance-dependent hydrophobic force and identifying its origin. This quest has nevertheless proved more…

In theoretical analyses of the moving contact line, an infinite force along the solid wall has been reported based off the non-integrable stress along a single interface. In this investigation we demonstrate that the stress singularity is…

Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…

Since the 1970's it has been known that black hole (and other) horizons are truly thermodynamic in nature. More generally, surfaces which are not horizons have also been conjectured to behave thermodynamically. Initially, for surfaces…

Rough surfaces immersed under water remain practically dry if the liquid-solid contact is on roughness peaks, while the roughness valleys are filled with gas. Mechanisms that prevent water from invading the valleys are well studied.…

We apply a phenomenological theory of polar liquids to calculate the interaction energy between two plane surfaces at nm-distances. We show that depending on the properties of the surface-liquid interfaces, the interacting surfaces induce…

We calculate the large deviation function of the end-to-end distance and the corresponding extension-versus-force relation for (isotropic) random walks, on and off-lattice, with and without persistence, and in any spatial dimension. For…