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We prove uniform H\"older regularity estimates for a transport-diffusion equation with a fractional diffusion operator,and a general advection field in BMO, as long as the order of the diffusion dominates the transport term at small…
In this letter, we introduce a geometric model to explain the origin of the observed shallow levels in semiconductors threaded by a dislocation density. We show that a uniform distribution of screw dislocations acts as an effective uniform…
The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N…
An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape…
We consider the covariant Lyapunov vectors (CLV) of a high-dimensional Hamiltonian flow in the case of long range potential, namely the Hamiltonian Mean Field (HMF) problem, by studying the behavior of the Lyapunov spectra and the…
Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of $N$ globally coupled particles moving on…
In the paper [G.Pantsulaia, On Uniformly Distributed Sequences on [-1/2,1/2], Georg. Inter. J. Sci. Tech.,4(3) (2013), 21--27], it was shown that $\mu$-almost every element of $\mathbf{R}^{\infty}$ is uniformly distributed in…
Stability perserving is an important topic in approximation of systems, e.g.\ model reduction. If the original system is stable, we often want the approximation to be stable. But even if an algorithm preserves stability the resulting system…
The 2D half-filled Hubbard model is studied by a nonperturbative analytic theory of correlator projection. The original dynamical mean-field approximation (DMFA) is reproduced at the first-order projection and then improved by systematic…
Infinite sets of inequalities which generalize all the known inequalities that can be used in the majorization step of the Approximating Hamiltonian method are derived. They provide upper bounds on the difference between the quadratic…
In this paper we present a new approach to the solution to a generalized version of Hughes' models for pedestrian movements based on a follow-the-leader many particle approximation. In particular, we provide a rigorous global existence…
We introduce a model with diffusive and evaporation/condensation processes, depending on 3 parameters obeying some inequalities. The model can be solved in the sense that all correlation functions can be computed exactly without the use of…
An established strategy for material modeling is provided by energy-based principles such that evolution equations in terms of ordinary differential equations can be derived. However, there exist a variety of material models that also need…
We introduce Fermi Sets, a universal and physically interpretable neural architecture for fermionic many-body wavefunctions. Building on a ``parity-graded'' representation [1], we prove that any continuous fermionic wavefunction on a…
Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance. When integrated into…
We studied several aspects of the Mott metal-insulator transition in the disordered case. The model on which we based our analysis is the disordered Hubbard model, which is the simplest model capable of capturing the Mott metal-insulator…
The paper presents novel results, obtained on the basis of the modified theory of hydraulic fractures (HF). The theory underlines significance of the speed equation. When applied to numerical simulation of HF, the theory reveals three…
This article consists of two parts. The main objectives of Part 1 are to postulate a new principle of representation invariance (PRI), and to refine the unified field model of four interactions, derived using the principle of interaction…
For S=1 system with general isotropic nearest-neighbor exchange, we derive the low-energy description of the spin nematic phase in terms of the RP^{2} nonlinear sigma-model. In one dimension, quantum fluctuations destroy long-range nematic…
The equation of motion for Berkovits' WZW-like open (super)string field theory is shown to be integrable in the sense that it can be written as the compatibility condition ("zero-curvature condition") of some linear equations. Employing a…