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

A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks. Here, we show an advance in the methodology of enumeration, making the process thousands or millions of…

We prove several rigorous results about the asymptotic behaviour of the numbers of polygons and self-avoiding walks confined to a square on the square lattice. Specifically we prove that the dominant asymptotic behaviour of polygons…

We study via Monte Carlo simulation a generalisation of the so-called vertex interacting self-avoiding walk (VISAW) model on the square lattice. The configurations are actually not self-avoiding walks but rather restricted self-avoiding…

We review the existence of the infinite length self-avoiding walk in the half plane and its relationship to bridges. We prove that this probability measure is also given by the limit as $\beta \rightarrow \beta_c-$ of the probability…

Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…

Thermodynamics tells us to expect underwater contact between two hydrophobic surfaces to result in stronger adhesion compared to two hydrophilic surfaces. However, presence of water changes not only energetics, but also the dynamic process…

We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating…

The present paper is dedicated to the 2-dimensional Interacting Partially Directed Self Avoiding Walk constrained to remain in the upper-half plan and interacting with the horizontal axis. The model has been introduced in \cite{F90} to…

We use the lattice model of directed walks to investigate the conformational as well as the adsorption properties of a semiflexible homopolymer chain immersed in a good solvent in two and three dimensions. To account for the stiffness in…

Let $X=(V\!X,E\!X)$ be an infinite, locally finite, connected graph without loops or multiple edges. We consider the edges to be oriented, and $E\!X$ is equipped with an involution which inverts the orientation. Each oriented edge is…

Lattice model of directed self avoiding walk has been solved analytically to investigate adsorption desorption phase transition behaviour of a semiflexible sequential copolymer chain on a two dimensional impenetrable surface perpendicular…

Consider $N$ particles performing random walks on the $\epsilon$-grid $(\epsilon Z)^d$, $\epsilon>0$ with branching and density-dependent selection: When one of the particles branches, a particle is removed from the most populated site. The…

We analyze, from the thermodynamical point of view, mechanical systems in which there is production of mechanical energy due to an internal source of energy, and compare that analysis with the similar one for the "symmetric" motion which…

We consider a self-avoiding walk model (SAW) on the faces of the square lattice $\mathbb{Z}^2$. This walk can traverse the same face twice, but crosses any edge at most once. The weight of a walk is a product of local weights: each square…

We consider a long-range version of self-avoiding walk in dimension $d > 2(\alpha \wedge 2)$, where $d$ denotes dimension and $\alpha$ the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to…

We report an experimental, numerical and theoretical study of the motion of a ball on a rough inclined surface. The control parameters are $D$, the diameter of the ball, $\theta$, the inclination angle of the rough surface and $E_{ki}$, the…

The thermally assisted detachment of a self-avoiding polymer chain from an adhesive surface by an external force applied to one of the chain ends is investigated. We perform our study in the "fixed height" statistical ensemble where one…

Aerosols are ubiquitous, and particle capture from particle-laden air as it flows past an obstacle is of widespread practical importance. Neglecting diffusion, previous work has shown that for a smooth curved surface in both Stokes flow and…

We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…

A superfluid flows without friction below a critical velocity, exhibiting zero drag force on impurities. Above this threshold, superfluidity breaks down, and the internal energy is redistributed into incoherent excitations such as vortices.…