Related papers: Understanding and Controlling Regime Switching in …
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
We use a large single particle tracking data set to analyze the short time and small spatial scale motion of quantum dots labeling proteins in cell membranes. Our analysis focuses on the jumps which are the changes in the position of the…
This paper proposes an effective phase diffusion method to analyze chemical exchange in nuclear magnetic resonance (NMR). The chemical exchange involves spin jumps around different sites where the spin angular frequencies vary, which leads…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
Diffusion involving atom transport from one location to another governs many important processes and behaviors such as precipitation and phase nucleation. Local chemical complexity in compositionally complex alloys poses challenges for…
In this paper we consider the problem of calculating the quantiles of a risky position, the dynamic of which is described as a continuous time regime-switching jump-diffusion, by using Fourier Transform methods. Furthermore, we study a…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of single molecules in living cells. Such inference allows to determine the organization and function of the cell. The…
The intrinsic length scales of a reaction diffusion system (Gierer-Meinhardt model)is varied by quasi-statically changing the diffusion constant of the activator and a transition from rolls to hexagon is detected. The transition is…
Diffusion processes have been applied with great success to model the dynamics of large populations throughout science, in particular biology. One advantage is that they bridge two different scales: the microscopic and the macroscopic one.…
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…
In the last years, a few experiments in the fields of biological and soft matter physics in colloidal suspensions have reported normal diffusion with a Laplacian probability distribution in the particles displacements (i.e., Brownian yet…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
We analyze the influence of boundary conditions on numerical simulations of the diffusive properties of a two dimensional granular gas. We show in particular that periodic boundary conditions introduce unphysical correlations in time which…
The rates of activated processes, such as escape from a metastable state and nucleation, are exponentially sensitive to an externally applied field. We describe how this applies to modulation by high-frequency fields and illustrate it with…
"Quantum trajectories" are solutions of stochastic differential equations of non-usual type. Such equations are called "Belavkin" or "Stochastic Schr\"odinger Equations" and describe random phenomena in continuous measurement theory of Open…
Analysis of signal fluctuations of a locally fixed probe, caused by molecules diffusing under the probe, can be used to determine diffusion coefficients. Theoretical treatments so far have been limited to point-like particles or to…
Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…