Dispersion processes

We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step, each of these particles moves to a neighbour of $v$ chosen independently and uniformly at random. The dispersion process ends once the particles have all stopped moving, i.e. at the first step at which each vertex is occupied by at most one particle. For the complete graph $K_n$ and star graph $S_n$, we show that for any constant $\delta>1$, with high probability, if $M \le n/2(1-\delta)$, then the process finishes in $O(\log n)$ steps, whereas if $M \ge n/2(1+\delta)$, then the process needs $e^{\Omega(n)}$ steps to complete (if ever). We also show that an analogous lazy variant of the process exhibits the same behaviour but for higher thresholds, allowing faster dispersion of more particles. For paths, trees, grids, hypercubes and Cayley graphs of large enough sizes (in terms of $M$) we give bounds on the time to finish and the maximum distance traveled from the origin as a function of the number of particles $M$

Neutrino processes with power law dispersion relations

We compute various processes involving neutrinos in the initial and/or final state and we assume that neutrinos have energy momentum relation with a general power law $E^2 =p^2+ \xi_n p^n$ correction due to Lorentz invariance violation. We find that for $n>2$ the bounds on $\xi_n$ from direct time of flight measurement are much more stringent than from constraining the neutrino Cerenkov decay process.Comment: 13 pages, 1 figure, Title change, replacement matches version accepted in Phys. Rev.

Dispersion relations and subtractions in hard exclusive processes

We study analytical properties of the hard exclusive processes amplitudes. We found that QCD factorization for deeply virtual Compton scattering and hard exclusive vector meson production results in the subtracted dispersion relation with the subtraction constant determined by the Polyakov-Weiss $D$-term. The relation of this constant to the fixed pole contribution found by Brodsky, Close and Gunion and defined by parton distributions is proved, while its manifestation is spoiled by the small $x$ divergence. The continuation to the real photons limit is considered and the numerical correspondence between lattice simulations of $D$-term and low energy Thomson amplitude is found.Comment: 4 pages, journal versio

Interfacial Phenomena and Natural Local Time

This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of phenomena in the geophysical and biological sciences pertaining to dispersion in the presence of an interface of discontinuity in dispersion coefficients. The results illustrate new ways in which to use the theory of stochastic processes to infer macro scale parameters and behavior from micro scale observations in particular heterogeneous environments

Taylor Dispersion with Adsorption and Desorption

We use a stochastic approach to show how Taylor dispersion is affected by kinetic processes of adsorption and desorption onto surfaces. A general theory is developed, from which we derive explicitly the dispersion coefficients of canonical examples like Poiseuille flows in planar and cylindrical geometries, both in constant and sinusoidal velocity fields. These results open the way for the measurement of adsorption and desorption rate constants using stationary flows and molecular sorting using the stochastic resonance of the adsorption and desorption processes with the oscillatory velocity field.Comment: 6 pages, 4 figure

Nonlocal Dynamics of Passive Tracer Dispersion with Random Stopping

We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion equation with a memory term. We have shown the exponential decay of the passive tracer concentration, under suitable conditions for the velocity field and the probability distribution of random stopping time.Comment: 7 page

What drives the velocity dispersion of ionized gas in star-forming galaxies?

We analyze the intrinsic velocity dispersion properties of 648 star-forming galaxies observed by the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, to explore the relation of intrinsic gas velocity dispersions with star formation rates (SFRs), SFR surface densities ($\rm{\Sigma_{SFR}}$), stellar masses and stellar mass surface densities ($\rm{\Sigma_{*}}$). By combining with high z galaxies, we found that there is a good correlation between the velocity dispersion and the SFR as well as $\rm{\Sigma_{SFR}}$. But the correlation between the velocity dispersion and the stellar mass as well as $\rm{\Sigma_{*}}$ is moderate. By comparing our results with predictions of theoretical models, we found that the energy feedback from star formation processes alone and the gravitational instability alone can not fully explain simultaneously the observed velocity-dispersion/SFR and velocity-dispersion/$\rm{\Sigma_{SFR}}$ relationships.Comment: 11 pages, 11 figures. Accepted for publication in MNRA

Urban air pollution dispersion model

Three-dimensional integrated puff model simulates smoke plume dispersion processes and estimates pollutant concentration during periods of low wind speed. Applications for model are given