Related papers: Directed polymer in random environment and two poi…
We study the trajectories of a single colloidal particle as it hops between two energy wells A and B, which are sculpted using adjacent optical traps by controlling their respective power levels and separation. Whereas the dynamical…
We derive a combinatorial multisum expression for the number $D(n,k)$ of partitions of $n$ with Durfee square of order $k$. An immediate corollary is therefore a combinatorial formula for $p(n)$, the number of partitions of $n$. We then…
The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either $\pm\sigma$ is obtained. We find the electrostatic energy of…
Using the well known position-dependent mass (PDM) von Roos Hamiltonian, Dutra and Oliveira (2009 J. Phys. A: Math. Theor. 42 025304) have studied the problem of two-dimensional PDM particles in the presence of magnetic fields. They have…
We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…
In this paper, we establish the super Poincar\'e inequality for the two-parameter Dirichlet process when the partition number of the state space is finite. Furthermore, if the partition number is infinite, the super Poincar'e inequality…
We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…
In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting…
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…
In this paper, we study a model of directed polymers in random environment, where the environment is restricted to a time-space tube whose spatial width grows polynomially with time. It can be viewed as an interpolation between the…
We discuss various aspects of the randomly interacting directed polymers with emphasis on the phases and phase transition. We also discuss the behaviour of overlaps of directed paths in a random medium.
Recently, the fractional Fokker-Planck equations (FFPEs) with multiple internal states are built for the particles undergoing anomalous diffusion with different waiting time distributions for different internal states, which describe the…
We study the persistence probability for some discrete-time, time-reversible processes. In particular, we deduce the persistence exponent in a number of examples: first, we deal with random walks in random sceneries (RWRS) in any dimension…
We study the large distance behavior of a steady distribution of two Brownian particles under external driving in a two-dimensional space. Employing a method of perturbative system reduction, we analyze a Fokker-Planck equation that…
We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data…
Using the observation that configurations of N polymers with hard core interactions on a closed random surface correspond to random surfaces with N boundary components we calculate the free energy of a gas of polymers interacting with fully…
A disorder-dependent Gaussian variational approach is applied to the problem of a $d$ dimensional polymer chain in a random medium (or potential). Two classes of variational solutions are obtained. For $d<2$, these two classes may be…
We study the maximum $\phi_N^*$ of the partition function of the two dimensional (subcritical) Gaussian directed polymer over an $\sqrt N \times \sqrt N$ box. We show that $\phi_N^*/\log N$ converges towards a constant $\sigma^*$, which we…
A new high order accurate semi-implicit space-time Discontinuous Galerkin method on staggered grids, for the simulation of viscous incompressible flows on two-dimensional domains is presented. The designed scheme is of the Arbitrary…
We present a simple solution to enhance the separation ability of deterministic lateral displacement (DLD) systems by expanding the two-dimensional nature of these devices and driving the particles into size-dependent, fully…