相关论文: Mean Back Relaxation for Position and Densities
We study how the finite-sized n-component model A with periodic boundary conditions relaxes near its bulk critical point from an initial nonequilibrium state with short-range correlations. Particular attention is paid to the universal…
We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer…
Lunar mean-motion resonances (MMRs) significantly shape cislunar dynamics beyond GEO, forming stable-unstable orbit pairs with corresponding intermingled chaotic and regular regions. The resonance zone is rigorously defined using the…
We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using Transportation Cost Inequalities for stochastic…
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…
The zero temperature relaxational dynamics of a particle in a short range correlated random potential is addressed. We derive a set of "two-times" mean-field dynamical equations, accounting for a possible mean displacement of the particle…
The constraints on departures from general relativity (GR) at cosmological length scales due to cosmic microwave background (CMB) data are discussed. The departure from GR is measured by the ratio, parameterized as $1 +\varpi_0 (1 +…
Mean-motion resonances (MMRs) are likely to play an important role both during and after the lifetime of a protostellar gas disk. We study the dynamical evolution and stability of planetary systems containing two giant planets on circular…
Using a new approximate strong-randomness renormalization group (RG), we study the many-body localized (MBL) phase and phase transition in one-dimensional quantum systems with short-range interactions and quenched disorder. Our RG is built…
We estimate the mean first time, called the mean rotation time (MRT), for a planar random polymer to wind around a point. This polymer is modeled as a collection of n rods, each of them being parameterized by a Brownian angle. We are led to…
Many-body perturbation theory (MBPT) based on Green's functions and Feynman diagrams provides a fundamental theoretical framework for various \emph{ab initio} computational approaches in molecular and materials science, including the random…
Diffusion through semipermeable interfaces has a wide range of applications, ranging from molecular transport through biological membranes to reverse osmosis for water purification using artificial membranes. At the single-particle level,…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…
The maximum-likelihood (ML) decoder for symbol detection in large multiple-input multiple-output wireless communication systems is typically computationally prohibitive. In this paper, we study a popular and practical alternative, namely…
The relativistic precession model (RPM) is widely-considered as a benchmark framework to interpret quasi-periodic oscillations (QPOs), albeit several observational inconsistencies suggest that the model remains incomplete. The RPM ensures…
A century after Prandtl's mixing length hypothesis, full-profile scaling of the mixing length in pressure-gradient turbulent boundary layers (PG TBLs) remains debated, especially for adverse pressure gradients (APGs). This work presents a…
We study a one-dimensional gas of $N$ Brownian particles that diffuse independently, but are {\it simultaneously} reset to the origin at a constant rate $r$. The system approaches a non-equilibrium stationary state (NESS) with long-range…
Future experiments will produce high-resolution temperature maps of the cosmic microwave background (CMB) and are expected to reveal the signature of gravitational lensing by intervening large-scale structures. We construct all-sky…
The dynamics of molecules are governed by rare event transitions between long-lived (metastable) states. To explore these transitions efficiently, many enhanced sampling protocols have been introduced that involve using simulations with…
A Bayesian method of moments/instrumental variable (BMOM/IV) approach is developed and applied in the analysis of the important mean and multiple regression models. Given a single set of data, it is shown how to obtain posterior and…