相关论文: Meanders: A Direct Enumeration Approach

Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…

In this paper we study analytically a one-dimensional model for a semiconductor-metal junction. We study the formation of Tamm states and how they evolve when the semi-infinite semiconductor and metal are coupled together. The non-linear…

We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a transition at some finite temperature, from a type of short range order to a fundamentally different…

We compute the number of ways a given permutation can be written as a product of exactly $k$ transpositions. We express this number as a linear combination of explicit geometric sequences, with coefficients which can be computed in many…

Tree graphs are routinely used in statistics. When estimating a Bayesian model with a tree component, sampling the posterior remains a core difficulty. Existing Markov chain Monte Carlo methods tend to rely on local moves, often leading to…

We study an extension of Duncan Watts' 2002 model of information cascades in social networks where edge weights are taken to be random, an innovation motivated by recent applications of cascade analysis to systemic risk in financial…

Transition path theory computes statistics from ensembles of reactive trajectories. A common strategy for sampling reactive trajectories is to control the branching and pruning of trajectories so as to enhance the sampling of low…

The polymer model framework is a classical tool from statistical mechanics that has recently been used to obtain approximation algorithms for spin systems on classes of bounded-degree graphs; examples include the ferromagnetic Potts model…

Estimating characteristics of large graphs via sampling is a vital part of the study of complex networks. Current sampling methods such as (independent) random vertex and random walks are useful but have drawbacks. Random vertex sampling…

We theoretically investigate the kinetics of the folding transition of a single semiflexible polymer. In the folding transition, the growth rate decrease with an increase in the number of monomers in a collapsed domain, suggesting that the…

The endpoint distribution and dynamics of semiflexible fibers is studied by numerical simulation. A brief overview is given over the analytical theory of flexible and semiflexible polymers. In particular, a closed expression is given for…

We consider a process of noncolliding $q$-exchangeable random walks on $\mathbb{Z}$ making steps $0$ (straight) and $-1$ (down). A single random walk is called $q$-exchangeable if under an elementary transposition of the neighboring steps…

We investigate numerically and analytically Potts models on ``thin'' random graphs -- generic Feynman diagrams, using the idea that such models may be expressed as the N --> 1 limit of a matrix model. The thin random graphs in this limit…

We study the statistics of branching polymers with excluded-volume interactions, by modeling them as single self-avoiding trees on a generic regular periodic lattice with coordination number $q$. Each lattice site can be occupied at most by…

This paper deals with simulation of flow and transport in porous media such as transport of groundwater contaminants. We first discuss how macro scale equations are derived and which terms have to be closed by models. The transport of…

We consider the problem of undirected polymers (tied at the endpoints) in random environment, also known as the unoriented first passage percolation on the hypercube, in the limit of large dimensions. By means of the multiscale refinement…

The authors apply the generalized master equation to analyze time-dependent transport through a finite quantum wire with an embedded subsystem. The parabolic quantum wire and the leads with several subbands are described by a continuous…

We introduced concept of meander knots, 2-component meander links and multi-component meander links and derived different families of meander knots and links from open meanders with at most 16 crossings. We also defined semi-meander knots…

We investigate electron transport through clean open quantum dots (quantum billiards). We present a semiclassical theory that allows to accurately reproduce quantum transport calculations. Quantitative agreement is reached for individual…

We propose a numerical procedure to study closure approximations for FENE dumbbells in terms of chosen macroscopic state variables, enabling to test straightforwardly which macroscopic state variables should be included to build good…