Optimal random coding

We consider a stochastic method for representing a real number x by a finite sequence of bits. The method is symmetrical with respect to interchange of the bits: it is characterized by a single function p (x) which gives the probability that any particular bit is on as a function of the real number x that is being encoded. We then consider the problem of reconstructing x from its representation. In the limiting case in which the number of bits is large, we determine the function p (x) that minimizes the expected k-th power of the absolute error in this reconstruction. The optimal choice of p (x) is independent of k.     

EPR Studies of Tl0.5Pb0.5Sr1.6Ba0.4CaCu2?xRuxO7?δ Superconductor

Bulk superconducting samples of type Tl_0.5Pb_0.5Sr_1.6Ba_0.4CaCu_2−x Ru _x O_7−δ, (Tl, Pb)/Sr-1212, with 0.0 ≤ x ≤ 0.525 were prepared by the conventional one-step solid-state reaction technique. The prepared samples were investigated using X-ray powder diffraction, electrical resistivity and electron paramagnetic resonance (EPR) measurements. Enhancement of the phase formation, superconducting transition temperature T _c and hole carriers concentration P was observed up to x = 0.075. For x > 0.075, a reverse trend was observed. EPR spectra were measured at different temperatures (120–290 K) for all prepared samples. The number of spins N participating in the resonance and the paramagnetic susceptibility χ were calculated as a function of both Ru-content and temperature. N and χ increased as the Ru-content increased. A linear relationship between logN and 1/T was established, from which the activation energy E _a was calculated as a function of the Ru-content. The temperature dependence of χ was fitted according to Curie–Weiss type of magnetic behavior. Curie constant C, Curie temperature θ, the effective magnetic moment μ and the electronic specific heat γ were estimated as a function of the Ru-content.     

Analysis of the backward-euler/langevin method for molecular dynamics

This paper develops the theory of a recently introduced computational method for molecular dynamics. The method in question uses the backward-Euler method to solve the classical Langevin equations of a molecular system. Parameters are chosen to produce a cutoff frequency ω_c, which may be set equal to kT/h to simulate quantum-mechanical effects. In the present paper, an ensemble of identical Hamiltonian systems modeled by the backward-Euler/Langevin method is considered, an integral equation for the equilibrium phase-space density is derived, and an asymptotic analysis of that integral equation in the limit Δt → 0 is performed. The result of this asymptotic analysis is a second-order partial differential equation for the equilibrium phase-space density expressed as a function of the constants of the motion. This equation is solved in two special cases: a system of coupled harmonic oscillators and a diatomic molecule with a stiff bond.     

The solubility of oxygen in aqueous fluorocarbon emulsions

The solubility of oxygen in aqueous fluorocarbon emulsions has been measured directly for several perfluorocarbons and monobromo or monoiodo-perfluorocarbons. The measured oxygen solubilities are consistent with results for the solubility of oxygen in neat liquid perfluorinated organic compounds.     

Fiber architecture of the left ventricular wall: An asymptotic analysis

The goal of this paper is to derive the fiber architecture of the left ventricle from first principles. The principles used are (i) mechanical equilibrium, (ii) a stress tensor that is the sum of a hydrostatic pressure and a fiber stress, (iii) the assumption that fiber tubes have constant cross-sectional area along their length, (iv) axial symmetry, and (v) the approximation that the thickness of the ventricular wall is small in comparison with the other wall dimensions. From these hypotheses, it is deduced that the cardiac muscle fibers are approximate geodesics on a nested family of toroidal surfaces centered on a degenerate torus in the equatorial plane of the heart. (Exact geodesics are ruled out by the theory.) Formulae are derived for the fiber surfaces and the fiber-angle distribution through the wall, and a differential equation is derived for the shape of the middle surface of the left ventricle. The results are in substantial agreement with experimental observations.     

Molecular dynamics by the Backward-Euler method

This paper introduces a new computational method for molecular dynamics. The method combines the Backward-Euler scheme for the solution of stiff differential equations with a Langevin-equation approach to the establishment of thermal equilibrium. The method allows the user to choose a cutoff frequency ω_c. Vibrational modes with frequencies below ω_c will be fully excited (receive a mean energy of kT per mode), while modes with frequencies greater than ω_c will be effectively frozen by the method. By setting ω_c = kT/h, one can obtain reasonable agreement with the quantum-mechanical energy distribution among the various modes, despite the classical character of the computation.     

A constraint from B decay on models with no t quark

We show that if the b quark is assigned to a singlet representation of the weak interaction SU(2) symmetry and if it decays through the usual weak bosons W^± and Z⁰, then neutral current decays occur at such a rate that Λ(B→X?⁺?^?)/Λ(B→X?⁺ν)?0.12, even allowing arbitrarily many quarks with which the b can mix. We discuss the manner in which the experimental exlusion of this inequality would constrain the possibilities for t-free models.     

Analysis,Simulation, and Optimization of Stochastic Vesicle Dynamics in Synaptic Transmission

Synaptic transmission is the mechanism of information transfer from one neuron to another (or from a neuron to a muscle or to an endocrine cell). An important step in this physiological process is the stochastic release of neurotransmitter from vesicles that fuse with the presynaptic membrane and spill their contents into the synaptic cleft. We are concerned here with the formulation, analysis, and simulation of a mathematical model that describes the stochastic docking, undocking, and release of synaptic vesicles and their effect on synaptic signal transmission. The focus of this paper is on the parameter p₀, the probability of release for each docked vesicle when an action potential arrives. We study the influence of this parameter on the statistics of the release process and on the theoretical capability of the model synapse in reconstructing various desired outputs based on the timing and amount of neurotransmitter release. This theoretical capability is assessed by formulating and solving an optimal filtering problem. Methods for parameter identification are proposed and applied to simulated data. © 2019 Wiley Periodicals, Inc.     

Effect of IR laser radiation on the structure and optical properties of PC-PBT/Pd polymer nanocomposite films

ABSTRACT

Bayfol (PC-PBT blend ?lm) is a class of polymeric solid-state nuclear track detector which has a lot of applications in several radiation detection ?elds. It is a bisphenol-A polycarbonate PC blended with polybutylene terephthalate PBT. Bayfol/Palladium (PC-PBT/Pd) nanocomposite films have been deposited using the molding technique. It is worth mentioning that this report is almost the first one dealing with the topic of the changes of physical properties of Bayfol/Pd nanocomposite due to laser exposure. Samples from PC-PBT/Pd (5?wt%) nanocomposite were exposed to IR-pulsed laser of 5-W power, capable of producing 2000 pulses per second with pulse duration of 200?ns at 904?nm. The laser fluences were in the range 2–25?J/cm². The resultant modi?cations in the exposed nanocomposite samples have been studied as a function of fluence using different characterization techniques such as X-ray diffraction (XRD), UV spectroscopy and color difference studies. The results indicate the proper dispersion of Pd nanoparticles in the PC-PBT matrix that causes a strong intermolecular interaction between Pd and PC-PBT, resulted in an increase in refractive index and the amorphous phase. Also, it is found that the laser exposure reduces the optical energy gap that could be attributed to the increase in structural disorder of the exposed PC-PBT/Pd nanocomposites due to crosslinking. Further, the color intensity ΔE, which is the color difference between the exposed samples and the non-exposed one, was increased with increasing the laser fluence, convoyed by a significant increase in the green and yellow color components.