Related papers: Dimensional Reduction for Directed Branched Polyme…
The relaxational dynamics of 1+1 dimensional directed polymer in random potential is studied by Monte Carlo simulation. A series of temperature quench experiments is performed changing waiting times. Clear crossover from quasi-equilibrium…
We study the relation between the directed polymer and the directed percolation models, for the case of a disordered energy landscape where the energies are taken from bimodal distribution. We find that at the critical concentration of the…
An explicit relation between the dimensional loss ($\Delta D$), entropy production and transport is established under thermal gradients, relating the microscopic and macroscopic behaviors of the system. The extensivity of $\Delta D$ in…
An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more commonly used soft-Coulomb interaction, the exponential…
A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to…
In recent years, a variety of novel measures of dependence have been introduced being capable of characterizing diverse types of directed dependence, hence diverse types of how a number of predictor variables $\mathbf{X} = (X_1, \dots,…
We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse…
We consider a directed polymer interacting with a diluted pinning potential restricted to a line. We characterize explicitely the set of disorder configurations that give rise to localization of the polymer. We study both relevant cases of…
We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model…
In this paper we apply both the procedure of dimension reduction and the incorporation of structured deformations to a three-dimensional continuum in the form of a thinning domain. We apply the two processes one after the other, exchanging…
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…
In D-dimensional spacetimes which can be foliated by n-dimensional homogeneous subspaces, a quantum field can be decomposed in terms of modes on the subspaces, reducing the system to a collection of (D-n)-dimensional fields. This allows one…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…
In addition to the double-dimensional reduction procedure that employs world-volume Killing symmetries of $p$-brane supergravity solutions and acts diagonally on a plot of $p$ versus spacetime dimension $D$, there exists a second procedure…
The equilibrium statistical mechanics of classical directed polymers in 2 dimensions is well known to be equivalent to the imaginary-time quantum dynamics of a 1+1-dimensional many-particle system, with polymer configurations corresponding…
Phase transition of strongly excited granular materials in 2D pipe is investigated numerically. By changing the ratio between width of the pipe and the height of the granular bed, we observe the transition between the 1 dimensional like…
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon…
We present a variational approach for directed polymers in $D$ transversal dimensions which is used to compute the corrections to the mean field theory predictions with broken replica symmetry. The trial function is taken to be a…