New expression for the K-shell ionization

A new expression for the total K-shell ionization cross section by electron impact based on the relativistic extension of the binary encounter Bethe (RBEB) model, valid from ionization threshold up to relativistic energies, is proposed. The new MRBEB expression is used to calculate the K-shell ionization cross sections by electron impact for the selenium atom. Comparison with all, to our knowledge, available experimental data shows good agreement

The Ising-Sherrington-Kirpatrick model in a magnetic field at high temperature

We study a spin system on a large box with both Ising interaction and Sherrington-Kirpatrick couplings, in the presence of an external field. Our results are: (i) existence of the pressure in the limit of an infinite box. When both Ising and Sherrington-Kirpatrick temperatures are high enough, we prove that: (ii) the value of the pressure is given by a suitable replica symmetric solution, and (iii) the fluctuations of the pressure are of order of the inverse of the square of the volume with a normal distribution in the limit. In this regime, the pressure can be expressed in terms of random field Ising models

Central limit theorem for fluctuations in the high temperature region of the Sherrington-Kirkpatrick spin glass model

In a region above the Almeida-Thouless line, where we are able to control the thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are Gaussian, on the scale N^{-1/2}, for N large. The method we employ is based on the idea, we recently developed, of introducing quadratic coupling between two replicas. The proof makes use of the cavity equations and of concentration of measure inequalities for the free energy.Comment: 18 page

On the Stability Functional for Conservation Laws

This note is devoted to the explicit construction of a functional defined on all pairs of \L1 functions with small total variation, which is equivalent to the \L1 distance and non increasing along the trajectories of a given system of conservation laws. Two different constructions are provided, yielding an extension of the original stability functional by Bressan, Liu and Yang.Comment: 26 page

The replica symmetric behavior of the analogical neural network

In this paper we continue our investigation of the analogical neural network, paying interest to its replica symmetric behavior in the absence of external fields of any type. Bridging the neural network to a bipartite spin-glass, we introduce and apply a new interpolation scheme to its free energy that naturally extends the interpolation via cavity fields or stochastic perturbations to these models. As a result we obtain the free energy of the system as a sum rule, which, at least at the replica symmetric level, can be solved exactly. As a next step we study its related self-consistent equations for the order parameters and their rescaled fluctuations, found to diverge on the same critical line of the standard Amit-Gutfreund-Sompolinsky theory.Comment: 17 page

Photoexcitation of lasers and chemical reactions for NASA missions: A theoretical study

The possibility of obtaining CW laser oscillation by optical pumping in the infrared at an elevated gas pressure is reviewed. A specific example utilizing a mixture of CO and NO gases is included. The gas pressures considered are in excess of several atmospheres. Laser frequency tuning over a broad region becomes possible at such elevated gas pressures due to collisional broadening of the amplifying transitions. The prior-rate and surprisal analysis are applied to obtain detailed VV and VT rates for CO and NO molecules and the transfer rates in a CO-NO gas mixture. The analysis is capable of giving temperature dependence of the rate constants. Computer estimates of the rates are presented for vibrational levels up to v = 50. The results show that in the high-lying vibrational states the VV transfer rates with Delta nu = 2 become appreciable

Surface terms on the Nishimori line of the Gaussian Edwards-Anderson model

For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure, i.e., the difference between the pressure of a box and the sum of the pressures of adjacent sub-boxes in which the box can been decomposed. We show that all those terms indeed behave proportionally to the surface size and prove the existence in the thermodynamic limit of the adjacency pressure.Comment: Final version with minor corrections. To appear in Journal of Statistical Physic

The Compressible to Incompressible Limit of 1D Euler Equations: the Non Smooth Case

We prove a rigorous convergence result for the compressible to incompressible limit of weak entropy solutions to the isothermal 1D Euler equations.Comment: 16 page

The Impact of Prescribed Fire on Moth Assemblages in the Boston Mountains and Ozark Highlands, in Arkansas

In addition to the impacts of prescribed fires on forest vegetation, this ecosystem process also has dramatic impacts on associated insect assemblages. For herbivorous, terrestrial insects, fire predictably results in a cycle of initial insect population reduction followed by recovery and growth, in which these insect populations exceed pre-fire abundances. We sought to examine if fire-induced disturbance cycles make prescribed burned areas more or less suitable specifically for moths (order Lepidoptera), which is a major food source for, among others, multiple bat species. We surveyed moth assemblages at 20 burned and 20 unburned sites in the Boston Mountain and Ozark Highland ecoregions of Arkansas, to determine if biomass or abundance of moths differed between areas that had been burned in the past 10 years, and those areas that had never been burned. Samples were collected early (April to July) and late (August to November) in the growing season of 2017 (hereafter early season and late season, respectively). We compared biomass and abundance of all moths, and of five representative moth species, between burned and unburned sites. The five moth species were chosen and considered to be representative due to their high relative abundance, and ease of identification. The five chosen moth species included the banded tussock moth (Halysidota tessellaris), white-dotted prominent moth (Nadata gibbosa), ailanthus moth (Atteva aurea), grape leaffolder (Desmia funeralis), and painted lichen moth (Hypoprepia fucosa). Results from paired t-tests showed no significant difference in total biomass, or abundance of representative species between burned and unburned sites. However, generalized linear regression models showed significantly higher abundance of moths in areas with high basal area that had been previously burned (β = -0.038 ± 0.004 SE,