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The leading order terms in a curvature expansion of the surface tension, the Tolman length (first order), and rigidities (second order) have been shown to play an important role in the description of nucleation processes. This work presents…
The generalized spherical Radon transform associates the mean values over spherical tori to a function $f$ defined on $\mathbb{S}^3 \subset \mathbb{H}$, where the elements of $\mathbb{S}^3$ are considered as quaternions representing…
In order to account for competition and interplay of localized and itinerant magnetic behaviour in correlated many body systems with complex spectra the various types of spin-fermion models have been considered in the context of the…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…
The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties.…
A general problem of current interest is the analysis of diffusion problems in singularly perturbed domains, within which small subdomains are removed from the domain interior and boundary conditions imposed on the resulting holes. One…
We develop a method to evaluate the generalized degrees of freedom (GDF), which is a key quantity of a model selection criterion, for linear regression with sparse regularization. Using the replica method, GDF is expressed by the variables…
Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales…
We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems. We first investigate the physical origin of universality in these systems, before comparing RG…
The extensions of the classical Debye model of susceptibility of dielectric materials to the well-known Cole-Cole, Davidson- Cole, or the Havriliak-Negami models is done by introducing non-integer power parameters to the frequency-domain…
We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by…
We consider construction of effective Hamiltonians for periodically driven interacting systems in the case of resonant driving. The standard high-frequency expansion is not expected to converge due to the resonant creation of collective…
We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can…
We propose an analytical method for finding the time domain solution for the problem of electronic relaxation of a molecule in solution. The relaxation process is modeled by the decay of a diffusing probability distribution through an…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…
We propose a general methodology for recovering preference parameters from data on choices and response times. Our methods yield estimates with fast ($1/n$ for $n$ data points) convergence rates when specialized to the popular Drift…
We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose…