Related papers: Equilibrium Probability Distribution for Number of…
We study the situation in which the distribution of temperature a body is due to its interaction with radiation. We consider the boundary value problem for the stationary radiative transfer equation under the assumption of the local…
The assumption that similar structures have similar folding probabilities ($p_{fold}$) leads naturally to a procedure to evaluate $p_{fold}$ for every snapshot saved along an equilibrium folding-unfolding trajectory of a structured peptide…
The Langmuir-McLean isotherm is often interpreted as providing an approximation to the most probable grain boundary segregation as a function of the bulk mole solute fraction $x_B$, even though $x_B$ is not an independant parameter in the…
The experimental emission probabilities of complex fragments by low energy compound nuclei and their dependence upon energy and atomic number are compared to the transition state rates. Intermediate-mass-fragment multiplicity distributions…
Langevin diffusion (LD) is one of the main workhorses for sampling problems. However, its convergence rate can be significantly reduced if the target distribution is a mixture of multiple densities, especially when each component…
The 'l-Doubling' phenomenon emanates from the coupling between molecular rotations and perpendicular vibrations (bending modes) in polyatomic molecules. This elusive phenomenon has been largely discarded in laser-induced molecular…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
Considering the interactions of two arbitrary particles, we obtain an internal energy expression of the complex system having long-range interactions. Based on the postulate of "equal-probability principle" for all microstates, the…
We consider some aspects of a standard model employed in studies of many-body localization: interacting spinless fermions with quenched disorder, for non-zero filling fraction, here on $d$-dimensional lattices. The model may be recast as an…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…
We investigate the equilibrium state of the model of Peng, \textit{et al.} for molecular breeding. In the model, a population of DNA sequences is successively culled by removing the sequences with the lowest binding affinity to a particular…
Complex systems, and in particular random neural networks, are often described by randomly interacting dynamical systems with no specific symmetry. In that context, characterizing the number of relevant directions necessitates fine…
The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of…
In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied…
The Boltzmann distribution describes a single parameter (temperature) family of probability distributions over a state space; at any given temperature, the ratio of probabilities of two states depends on their difference in energy. The same…
The Boltzmann distribution predicts the collective behavior of systems at thermodynamic equilibrium as a function of their constituent parts. Yet most systems in nature are not at equilibrium, and a unified theory of their behavior does not…
Nuclear reaction rates in plasmas depend on the overlap (contact) probability of the reacting ions. Path integral Monte Carlo (PIMC) calculations are used here to determine these contact probabilities, g(0), for the one component plasma…
The calculation of the SIR distribution at the typical receiver (or, equivalently, the success probability of transmissions over the typical link) in Poisson bipolar and cellular networks with Rayleigh fading is relatively straightforward,…
We present an analytical description of the Alchemical Transfer Method (ATM) for molecular binding using the Potential Distribution Theory (PDT) formalism. ATM models the binding free energy by mapping the bound and unbound states of the…