Distribution ofK α L n satellite yields for mediumZ elements bombarded with16O ions

K _α X-ray spectra were measured with a Du Mond type curves crystal spectrometer for₄₂Mo and₄₆Pd targets bombarded with oxygen ions at 5.5 MeV/u energy (i.e. at velocity closely matching those of the targetL-shell electrons). The distribution ofL-shell vacancies produced in collisions with simultaneousK-shell ionization is deduced from the measured yield distribution of theK _α X-ray satellites. The distribution shows deviations from the binomial ones. The deviations can be accounted for by assuming that theL-shell vacancy production is due to two uncorrelated processes: the direct ionization by impact and the electron capture from theL-shell of the target atom into theK-shell of the projectile, both occurring at nearly central collisions. The corresponding probability values are deduced using simple statistical considerations.     

On the cases of equality in Bobkov's inequality and Gaussian rearrangement

We determine all of the cases of equality in a recent inequality of Bobkov that implies the isoperimetric inequality on Gauss space. As an application we determine all of the cases of equality in the Gauss space analog of the Faber-Krahn inequality. Received June 21, 1999 / Accepted June 12, 2000 / Published online November 9, 2000     

Molecular dynamics simulation of nanocolloidal amorphous silica particles: Part II

Explicit molecular dynamics simulations were applied to a pair of amorphous silica nanoparticles with diameter of 3.2 nm immersed in a background electrolyte. Mean forces acting between the pair of silica nanoparticles were extracted at four different background electrolyte concentrations. The dependence of the interparticle potential of mean force on the separation and the silicon to sodium ratio, as well as on the background electrolyte concentration, are demonstrated. The pH was indirectly accounted for via the ratio of silicon to sodium used in the simulations. The nature of the interaction of the counterions with charged silica surface sites (deprotonated silanols) was also investigated. The effect of the sodium double layer on the water ordering was investigated for three Si : Na(+) ratios. The number of water molecules trapped inside the nanoparticles was investigated as the Si : Na(+) ratio was varied. Differences in this number between the two nanoparticles in the simulations are attributed to differences in the calculated electric dipole moment. The implications of the form of the potentials for aggregation are also discussed.     

Entropy production by block variable summation and central limit theorems

We prove a strict lower bound on the entropy produced when independent random variables are summed and rescaled. Using this, we develop an approach to central limit theorems from a dynamical point of view in which the entropy is a Lyapunov functional governing approach to the Gaussian limit. This dynamical approach naturally extends to cover dependent variables, and leads to new results in pure probability theory as well as in statistical mechanics. It also provides a unified framework within which many previous results are easily derived.Partially supported by an NSF postdoctoral fellowshipPartially supported by NSF grant DMS-8905772; A. P. Sloan Fellow in Mathematics     

Molecular dynamics simulation of nanocolloidal amorphous silica particles: Part I

Explicit molecular dynamics simulations were applied to a pair of amorphous silica nanoparticles in aqueous solution, with diameter of 4.4 nm and with four different background electrolyte concentrations, to extract the mean force acting between the two silica nanoparticles. Dependences of the interparticle forces on the separation and the background electrolyte concentration were demonstrated. The nature of the interaction of the counterions with charged silica surface sites (deprotonated silanols) was investigated. A "patchy" double layer of adsorbed sodium counterions was observed. Dependences of the interparticle potential of mean force on the separation and the background electrolyte concentration were demonstrated. Direct evidence of the solvation forces is presented in terms of changes of the water ordering at the surfaces of the isolated and double nanoparticles. The nature of the interaction of the counterions with charged silica surface sites (deprotonated silanols) was investigated in terms of quantifying the effects of the number of water molecules separately inside each pair of nanoparticles by defining an impermeability measure. A direct correlation was found between the impermeability (related to the silica surface "hairiness") and the disruption of water ordering. Differences in the impermeability between the two nanoparticles are attributed to differences in the calculated electric dipole moment.     

On the Optimal Choice of Coefficients in a Truncated Wild Sum and Approximate Solutions for the Kac Equation

We study an approximate solution of the Boltzmann problem for Kac's caricature of a Maxwellian gas by using a truncated and modified expansion of Wild type. We choose the coefficients in the Wild sum approximation using a criterion based on exactly reproducing the behavior of the leading modes.     

A remainder term for Hölder’s inequality for matrices and quantum entropy inequalities

A labelled oriented graph (LOG) group is a group given by a presentation constructed in a certain way from a labelled oriented graph: examples include Wirtinger presentations of knot groups. We show how to obtain generators for the Schur Multiplier \(H_2(G)\) of a LOG group from the underlying LOG, and by exhibiting the n-string braid group \(B_n\) as a LOG group, we compute \(H_2(B_n)\).     

Approach to the Steady State in Kinetic Models with Thermal Reservoirs at Different Temperatures

We continue the investigation of kinetic models of a system in contact via stochastic interactions with several spatially homogeneous thermal reservoirs at different temperatures. Considering models different from those investigated in Carlen et al. (Braz J Probab Stat 29:372–386, 2015), we explicitly compute the unique spatially uniform non-equilibrium steady state (NESS) and prove that it is approached exponentially fast from any uniform initial state. This leaves open the question of whether there exist NESS that are not spatially uniform. Making a further simplification of our models, we then prove non-existence of such NESS and exponential approach to the unique spatially uniform NESS (with a computably boundable rate). The method of proof relies on refined Doeblin estimates and other probabilistic techniques, and is quite different form the analysis in Carlen et al. (Braz J Probab Stat 29:372–386, 2015) that was based on contraction mapping methods.     

Three-pion interferometry results from central Pb+Pb collisions at 158A GeV/c

Three-particle correlations have been measured for identified pi(-) from central 158A GeV Pb+Pb collisions by the WA98 experiment at CERN. A substantial contribution of the genuine three-body correlation has been found as expected for a mainly chaotic and symmetric source.     

Inner-shell ionization in near-central collisions of 6.7 MeV/amu4He ions with mid-Z atoms

We report a self consistent tight binding calculation of the cohesion energy of small MgO clusters, up to 12 atoms. We discuss the size variation of the charges, the bond lengths, the electronic gaps. For the first time, we predict the existence of a strong dimerization of the bond length in the small clusters. We underline the consequences of the competition between covalent and electrostatic effects in these ionocovalent systems.