Related papers: Characteristic time scales for diffusion processes…
Let $L_t:=\Delta_t+Z_t$ for a $C^{1,1}$-vector field $Z$ on a differential manifold $M$ with boundary $\partial M$, where $\Delta_t$ is the Laplacian induced by a time dependent metric $g_t$ differentiable in $t\in [0,T_c)$. We first…
Multi-label classification has broad applications and depends on powerful representations capable of capturing multi-label interactions. We introduce \textit{Diff-Feat}, a simple but powerful framework that extracts intermediate features…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…
We derive a Thermodynamic Uncertainty Relation bounding the mean squared displacement of a Gaussian process with memory, driven out of equilibrium by unbalanced thermal baths and/or by external forces. Our bound is tighter with respect to…
Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct…
We generalize leading-order asymptotics of a form of the heat content of a submanifold (van den Berg & Gilkey 2015) to the setting of time-dependent diffusion processes in the limit of vanishing diffusivity. Such diffusion processes arise…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Radiative mixing layers arise wherever multiphase gas, shear, and radiative cooling are present. Simulations show that in steady state, thermal advection from the hot phase balances radiative cooling. However, many features are puzzling.…
Uchaikin suggested a mathematical model of an anomalous diffusion in a space was suggested. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
We discuss a new phenomenon of turbulent thermal diffusion associated with turbulent transport of aerosols in the atmosphere and in laboratory experiments. The essence of this phenomenon is the appearance of a nondiffusive mean flux of…
In temporal networks, both the topology of the underlying network and the timings of interaction events can be crucial in determining how some dynamic process mediated by the network unfolds. We have explored the limiting case of the speed…
The temporal fluctuations in global mean surface temperature is an example of a geophysical quantity which can be described using the notions of long-range persistence and scale invariance/scaling, but this description has suffered from…
We seek to give users precise control over diffusion-based image generation by modeling complex scenes as sequences of layers, which define the desired spatial arrangement and visual attributes of objects in the scene. Collage Diffusion…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…
We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature)…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…