Related papers: Optimal estimates of diffusion coefficients from m…
Mathematically modeling complex transport phenomena at the molecular level can be a powerful tool for identifying transport mechanisms and predicting macroscopic properties. We use two different stochastic time series models, parameterized…
The Mean Square Displacement is a central tool in the analysis of Single Particle Tracking experiments, shedding light on various biophysical phenomena. Frequently, parameters are extracted by performing time-averages on single particle…
Depending on their mechanism of self-propulsion, active particles can exhibit a time-dependent, often periodic, propulsion velocity. The precise propulsion velocity profile determines their mean square displacement and their effective…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…
The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged…
Recently, there has been interest in determining the viscoelastic properties of polymeric liquids and other complex fluids by means of Diffusing Wave Spectroscopy (DWS). In this technique, light-scattering spectroscopy is applied to highly…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
A molecular dynamics (MD) simulation of planar Couette flow is presented for the minimal channel in which turbulence structures can be sustained. Evolution over a single breakdown and regeneration cycle is compared to computational fluid…
Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide…
Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNN) can efficiently…
Diffusion models are the go-to method for Text-to-Image generation, but their iterative denoising processes has high inference latency. Quantization reduces compute time by using lower bitwidths, but applies a fixed precision across all…
We propose a method for obtaining the intrinsic, long time mean square displacement (MSD) of atoms and molecules in proteins from finite time molecular dynamics (MD) simulations. Typical data from simulations are limited to times of 1 to 10…
A tracer particle is called anomalously diffusive if its mean squared displacement grows approximately as $\sigma^2 t^{\alpha}$ as a function of time $t$ for some constant $\sigma^2$, where the diffusion exponent satisfies $\alpha \neq 1$.…
Consider a diffusion process X=(X_t), with t in [0,1], observed at discrete times and high frequency, solution of a stochastic differential equation whose drift and diffusion coefficients are assumed to be unknown. In this article, we focus…
Volume limitations and low yield thresholds of biological fluids have led to widespread use of passive microparticle rheology. The mean-squared-displacement (MSD) statistics of bead position time series (bead paths) are either applied…
We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval $[0,T]$ sampled with a time step $\Delta$. Our main contribution…
The problem of a spatially discontinuous diffusion coefficient ($D(\boldsymbol x)$) is one that may be encountered in hydrogeologic systems due to natural geological features or as a consequence of numerical discretization of flow…