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The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…
We construct loop soups for general Markov processes without transition densities and show that the associated permanental process is equal in distribution to the loop soup local time. This is used to establish isomorphism theorems…
The breakdown of dynamical scaling for a dilute polymer solution in 2D has been suggested by Shannon and Choy [Phys. Rev. Lett. {\bf 79}, 1455 (1997)]. However, we show here both numerically and analytically that dynamical scaling holds…
We consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that the corresponding stationary non-equilibrium solutions have a…
We present an analytical and computational study characterizing the structural and dynamical properties of an active filament confined in cylindrical channels. We first outline the effects of the interplay between confinement and polar…
Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…
The wormlike chain (WLC) model of DNA bending accurately reproduces single-molecule force-extension profiles of long (kilobase) chains. These bending statistics over large scales do not, however, establish a unique microscopic model for…
We present a Monte Carlo algorithm that provides efficient and unbiased sampling of polymer melts consisting of two chains of equal length that jointly visit all the sites of a cubic lattice with rod geometry L x L x rL and non-periodic…
We study the equilibrium dynamics of a single polymer chain under good solvent condition. Special emphasis is laid on varying the drag force experienced by the chain while it moves. To this end we model the solvent in a mesoscopic manner by…
DNA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
We study the dynamics of a monitored single particle in a one-dimensional, Anderson-localized system. The time evolution is governed by Hamiltonian dynamics for fixed time intervals, interrupted by local, projective measurements. The…
We present numerical and analytical results describing the effect of hydrodynamic interactions on the dynamics of a short polymer chain in solution. A molecular dynamics algorithm for the polymer is coupled to a direct simulation Monte…
In this paper, we show how the method of field theoretical renormalization group may be used to analyze universal shape properties of long polymer chains in porous environment. So far such analytical calculations were primarily focussed on…
Density functional theory offers accurate structure prediction at acceptable computational cost, but commonly used approximations suffer from delocalization error; this results in inaccurate predictions of quantities such as energy band…
We consider a one-dimensional sandpile model which mimics an elastic string of particles driven through a strongly pinning periodic environment with phase disorder. The evolution towards depinning occurs by the triggering of avalanches in…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
We investigate by means of a number of different dynamical Monte Carlo simulation methods the self-assembly of equilibrium polymers in dilute, semidilute and concentrated solutions under good-solvent conditions. In our simulations, both…
Mapping the electrostatic potential (ESP) distribution around ions in electrolyte solution is crucial for the establishment of a microscopic understanding of electrolyte solution properties. For solutions in the bulk phase, it has not been…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…