Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions.

Many imaging techniques for biological systems-like fixation of cells coupled with fluorescence microscopy-provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems.

Inferring stochastic rates from heterogeneous snapshots of particle positions.

Many imaging techniques for biological systems - like fixation of cells coupled with fluorescence microscopy - provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems.

Vacuum Friction on a Rotating Pair of Atoms.

Zero-point quantum fluctuations of the electromagnetic vacuum create the widely known London-van der Waals attractive force between two atoms. Recently, there has been a revived interest in the interaction of rotating matter with the quantum vacuum. Here, we consider a rotating pair of atoms maintained by London-van der Waals forces and calculate the frictional torque they experience due to zero-point radiation.

Statistical mechanical foundation of the peridynamic nonlocal continuum theory: energy and momentum conservation laws.

The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction.

Continuous-time random walks on bounded domains.

A useful perspective to take when studying anomalous diffusion processes is that of a continuous-time random walk and its associated generalized master equation. We derive the generalized master equations for continuous-time random walks that are restricted to a bounded domain and compare numerical solutions with kernel-density estimates of the probability-density function computed from simulations. The numerical solution of the generalized master equation represents a powerful tool in the study of continuous-time random walks on bounded domains.

Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background.

The current 'standard model' of cosmology posits an infinite flat universe forever expanding under the pressure of dark energy. First-year data from the Wilkinson Microwave Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but the largest scales. Temperature correlations across the microwave sky match expectations on angular scales narrower than 60 degrees but, contrary to predictions, vanish on scales wider than 60 degrees.

Production and evolution of light elements in active star-forming regions.

Collisions between cosmic rays (energetic protons and alpha-particles) and carbon, nitrogen and oxygen in the interstellar medium have been considered to be the main source of lithium, beryllium and boron, through fragmentation of the larger nuclei. But this mechanism is unable to account for the observed Solar System abundances of the isotopes 7Li and 11B. The recent detection of an excess of gamma-rays in the direction of the star-forming region in the Orion cloud has been interpreted as arising from the excitation of carbon and oxygen nuclei ejected from supernovae when they collide with the surrounding gas, which is primarily molecular and atomic hydrogen.