相关论文: Dimensional Reduction for Directed Branched Polyme…
The excluded volume effects of randomly branched polymers are investigated. To approach this problem we assume the Gaussian distribution of segments around the center of gravity. Once this approximation is introduced, we can make use of the…
We construct a $d$-dimensional Eddy Damped Quasi-Normal Markovian (EDQNM) Closure Model to study dynamo action in arbitrary dimensions. In particular, we find lower $d_L$ and upper $d_U$ critical dimensions for sustained dynamo action in…
We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…
We present a rigorous derivation of dimensionally reduced theories for thin sheets of nematic elastomers, in the finite bending regime. Focusing on the case of twist nematic texture, we obtain 2D and 1D models for wide and narrow ribbons…
We study a supposed model for branched polymers which was shown in two dimensions to be in the universality class of ordinary percolation. We confirm this by high statistics simulations and show that it is in the percolation universality…
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…
The critical exponents for a class of one-dimensional models of interface depinning in disordered media can be calculated through a mapping onto directed percolation (DP). In higher dimensions these models give rise to directed surfaces,…
Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like…
In dimensions 3 or larger, it is a classical fact that the directed polymer model has two phases: Brownian behavior at high temperature, and non-Brownian behavior at low temperature. We consider the response of the polymer to an external…
Recent progress in open many-body quantum systems has highlighted the importance of the Markov length, the characteristic scale over which conditional correlations decay. It has been proposed that non-equilibrium phases of matter can be…
We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair correlation function…
We present analytical results for the finite-size scaling in d--dimensional O(N) systems with strong anisotropy where the critical exponents (e.g. \nu_{||} and \nu_{\perp}) depend on the direction. Prominent examples are systems with…
Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…
Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d_c = 4. In the framework of single-species…
We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP.…
The Rouse model has recently been modified to take into account the excluded volume interactions that exist between various parts of a polymer chain by incorporating a narrow Gaussian repulsive potential between pairs of beads on the Rouse…
The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in…
Plastic deformation In crystalline materials is controlled by the motion and interactions of dislocations [AND 17]. Discrete Dislocation Dynamics (DDD) simulations have now existed for about 25 years to investigate plastic flow at the…