相关论文: Exact Solution for a 1-dimensional model for Repta…

This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…

We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient…

In this paper, we present an approach to solving the Riemann problem in one-dimensional relativistic hydrodynamics, where the most computationally expensive steps of the exact solver are replaced by compact, highly specialized neural…

An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total…

We present a new strategy for introducing population balances into full-chain constitutive models of living polymers with linear chain architectures. We provide equations to describe a range of stress relaxation processes covering both…

Recurrent neural networks (RNNs) are capable of learning features and long term dependencies from sequential and time-series data. The RNNs have a stack of non-linear units where at least one connection between units forms a directed cycle.…

In this note, we present an exact solution for the structured singular value (SSV) of rank-one complex matrices with repeated complex full-block uncertainty. A key step in the proof is the use of Von Neumman's trace inequality. Previous…

In this work, we discuss kinetic descriptions of flocking models, of the so-called Cucker-Smale and Motsch-Tadmor types. These models are given by Vlasov-type equations where the interactions taken into account are only given long-range…

We compare the Rubinstein-Duke model for reptation to a model where the boundary dynamics is modified by calculating the viscosity of polymer melts. The question is investigated whether the viscosity is determined by details of the dynamics…

The consequences of discretization on the resulting viscosity for the necklace model are analyzed to find out the mechanisms by which this model leads to results different from what could be anticipated. In order to accomplish this, various…

The design of recurrent neural networks (RNNs) to accurately process sequential inputs with long-time dependencies is very challenging on account of the exploding and vanishing gradient problem. To overcome this, we propose a novel RNN…

Based on the Wilemski-Fixman approach (J. Chem. Phys. 60, 866 (1974)) we showed that for a flexible chain in theta solvent hydrodynamic interaction treated with an pre-averaging approximation makes ring closing faster if the chain is not…

A one dimensional XX spin chain of finite length coupled to reservoirs at both ends is solved exactly in terms of a matrix product state ansatz. An explicit representation of matrices of fixed dimension 4 independent of the chain length is…

We investigate the Rouse dynamics of a flexible ring polymer with a prime knot. Within a Monte Carlo approach, we locate the knot, follow its diffusion, and observe the fluctuations of its length. We characterise a topological time scale,…

We introduce two 1D tight-binding models based on the Tribonacci substitution, the hopping and on-site Tribonacci chains, which generalize the Fibonacci chain. For both hopping and on-site models, a perturbative real-space renormalization…

Using the transfer matrix method, we give the exact solution of a deterministic sandpile model for arbitrary $N$, where $N$ is the size of a single toppling. The one- and two-point functions are given in term of the eigenvalues of an $N…

We introduce a new model of preferential attachment with fitness, and establish a time reversed duality between the model and a system of branching-coalescing particles. Using this duality, we give a clear and concise explanation for the…

We present exact results for the dynamical structure function, i.e.~the density-density correlations for the 1/r^2 system of interacting particles at three special values of the coupling constant. The results are interpreted in terms of…

We consider the Keller--Rubinow model for Liesegang rings in one spatial dimension in the fast reaction limit as introduced by Hilhorst, van der Hout, Mimura, and Ohnishi in 2007. Numerical evidence suggests that solutions to this model…

Based on Richardson's exact solution of the pairing model and the Gaudin model for spin systems we derive a new class of exactly solvable models for finite boson system. As an example we solve a particular hamiltonian which displays a…