Application of variational principle to scattering problems

The validity of the variational principle for scattering problems is examined in the case of ionization of atomic hydrogen by electron impact. The effective charge seen by the scattered electron is determined mathematically in a rigorous way excluding any empirical assumptions. It is shown that the elaborated approach gives effective charge values that are reasonable and have clear physical meaning.     

Non-existence of a minimizer to the magnetic Hartree-Fock functional

In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization.      

Scattering measurements in nuclear emulsions and their application to measuring the charge of primary cosmic ray nuclei

Small local dislocations in processed emulsions give rise to spurious scattering whose effect on tracks is indistinguishable from the multiple scattering produced by coulomb interaction. Because of this effect the atomic number of fast primary cosmic ray nuclei will be underestimated in more than 50% of the cases in experiments where multiple scattering of tracks and ionization measurements are employed for charge determination. The spurious scattering was investigated by measuring the track contours of 100 very long tracks due to energetic primary particles; the effect was present in comparable strength in all plates and all types of emulsions which have been investigated. It is too small to affect measurements on medium energy particle tracks (protons with energy below 600 MeV and heavy nuclei with energy below 300 MeV/ nucleon). It dominates, however, other sources or error and noise for tracks of energetic particles although it does not preclude occasional observations of very low scattering values. New methods for measuring various forms of noise have also been developed in the course of this work and the noise level for scattering measurements has been reduced below previously accepted values. Spurious scattering is presumably largely responsible for the discrepancies which appear when one compares the primary charge and energy spectra derived from experiments involving scattering measurements with the corresponding spectra derived from numerous other experiments which employ different techniques. If the experiments based on scattering measurements are omitted, the remaining evidence strongly favours a spectrum in which the energy per nucleon is nearly independent of atomic number for all primaries. It also favours a charge distribution which has a pronounced minimum for charges 3≤ Z≤ 5 and, therefore, yields a fairly low upper limit for the amount of interstellar matter traversed by primary cosmic ray nuclei.     

Zustandsgrössen eines schweren Plasmas in Abhängigkeit von temperatur und Dichte

Summary Assuming thermodynamic equilibrium we calculate ion and electron densities of a uranium plasma in the temperature range between 0,5 keV and 50 keV for densities around 10²³ ions per cm³ using a simplified Saha equation. The ionization energies are found by extrapolation from known data or by a Slater approximation.The ratios of the partition functions of two successive stages of ionization are set equal to one. A depression of the ionization energies caused by electrostatic interactions is considered. The numerical results include the internal energy of the plasma as a function of temperature.     

Dynamics of desorption induced by electronic transitions: Desorption of neutrals from physisorbed layers

The dynamical theory of desorption from physisorbed layers irradiated by electrons or photons is presented. The basic steps of the microscopic mechanism are: ionization to a more strongly bound state, acceleration towards the surface, reneutralization, and finally, desorption. Desorption yields and the kinetic energy distributions of desorbing neutrals obtained in the classical and in the fully quantum-mechanical approach are numerically compared. Comparison with the existing experimental data is also made. Next, the classical trajectory approximation is applied to study the metal — adsorbate charge transfer process. The neutralization rate obtained is compared with the one following from the conventional perturbation theory. Viene presentata la teoria dinamica di desorbimento da strati fisisorbiti irraggiati da elettroni o fotoni. Le fasi basilari del meccanismo microscopico sono: ionizzazione ad uno stato più fortemente legato, accelerazione verso la superficie, rineutralizzazione ed infine, desorbimento. Vengono confrontati numericamente i rendimenti di desorbimento e le distribuzioni di energia cinetica delle specie neutre desorbite, ottenute nello schema classico e in quello totalmente quanto-mccanico. Si confrontano inoltre i dati sperimentali esistenti.     

Classical ionization for the aperiodic driven hydrogen atom

The classical ionization rate, for 1D hydrogen atom under intense field, was obtained for several almost-periodic (with different degrees of randomness) and random possibilities for the electric field amplitude; it was observed that the less effective is the ionization due to an amplitude sequence for weak intensity, the more effective it is for strong fields. Most numerical calculations were performed with simple adaptations of the Kepler map, which were supported by Hamiltonian calculations.     

Enhanced ionization of multi-well quantum systems in intense laser fields

The ionization dynamics of multi-well quantum systems in intense laser fields (~ 10¹⁴W/cm) has been numerically investigated through solving the time-dependent Schrodinger equation. The enhanced ionization effect at a critical inter-well distance is found as a general feature of multi-well quantum systems subjected to intense laser fields. It is well rationalized in terms of.the field-induced over-the-barriers ionization mechanism. With the number of wells increasing the whole ionization peak slightly shifts to small inter-well distance, but the enhanced ionization tendency still keeps. The ionization potential of multi-well systems is not the sole important factor of intense field-ionization of system.     

Existence and global bounds for a fluid model of plasma display technology

This article considers the fluid model for the discharge of plasma particle species in display technology. The fluid equations are coupled with Poisson's equation, which describes the effect of the charged particles on the electric field. The diffusion and mobility coefficients for the positive ion particles depend on the electric field, while those for the electrons depend on the electron mean energy. The reaction rates are proportional to the products of the densities of the reacting particles involved in the particular ionization, conversion or recombination reactions. Moreover, the ionization coefficients are dependent on the electric field, which varies spatially and temporally. The main ionization and discharge reactions are described by an initial-boundary value problem for a system of coupled parabolic–elliptic partial differential equations. The system is first analyzed by upper–lower solution method. By means of the a priori bounds obtained for an arbitrary time, the existence of solution for the initial-boundary value problem is proved in an appropriate Hölder space.     

山西省高速公路计重收费标准仿真研究

顺应全国统一治理公路非法超载超限运输的形势,结合山西省特点,确定适应山西省开放式干线公路计重收费的费率标准.建立开放式公路计重收费数学模型,通过Excel设置控件进行动态仿真,并对数学模型进行实证分析.     

Relativistic semi-classical theory of atom ionization in ultra-intense laser

A relativistic semi-classical theory (RSCT) of H-atom ionization in ultra-intense laser (UIL) is proposed. A relativistic analytical expression for ionization probability of H-atom in its ground state is given. This expression, compared with non-relativistic expression, clearly shows the effects of the magnet vector in the laser, the non-dipole approximation and the relativistic mass-energy relation on the ionization processes. At the same time, we show that under some conditions the relativistic expression reduces to the non-relativistic expression of non-dipole approximation. At last, some possible applications of the relativistic theory are briefly stated.     

On Equilibrium Shape of Charged Flat Drops

The equilibrium shapes of two‐dimensional charged, perfectly conducting liquid drops are governed by a geometric variational problem that involves a perimeter term modeling line tension and a capacitary term modeling Coulombic repulsion. Here we give a complete explicit solution to this variational problem. Namely, we show that at fixed total charge a ball of a particular radius is the unique global minimizer among all sufficiently regular sets in the plane. For sets whose area is also fixed, we show that balls are the only minimizers if the charge is less than or equal to a critical charge, while for larger charge minimizers do not exist. Analogous results hold for drops whose potential, rather than charge, is fixed. © 2018 Wiley Periodicals, Inc.     

Global Existence for the Vlasov-Poisson System with Steady Spatial Asymptotics

ABSTRACT

A collisionless plasma is modelled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge—dependant upon only velocity—is assumed. The situation in which mobile negative ions balance the positive charge as | x | → ∞ is considered. Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behavior for large | x |, which were previously shown to exist locally in time, are continued globally. This is done by showing that the charge density decays at least as fast as | x |^?6. This article also establishes decay estimates for the electrostatic field and its derivatives.     

Explicit solutions of the one‐dimensional Vlasov–Poisson system with infinite mass

A collisionless plasma is modelled by the Vlasov–Poisson system in one dimension. A fixed background of positive charge, dependent only upon velocity, is assumed and the situation in which the mobile negative ions balance the positive charge as |x| → ∞ is considered. Thus, the total positive charge and the total negative charge are infinite. In this paper, the charge density of the system is shown to be compactly supported. More importantly, both the electric field and the number density are determined explicitly for large values of |x|. Copyright © 2007 John Wiley & Sons, Ltd.     

Hypersonic flow past a sphere

The effects of dissociation or ionization of air on the analytical solution for hypersonic flow past a sphere are considered here, under certain assumptions. It has been assumed that the shock wave is in the shape of a sphere, that the density ratio across the shock is constant, that the flow behind the shock is at constant density and that dissociation or ionization only occurs behind the shock wave. Thus the effects of the compressibility of the air, variation of density ratio along the shock, and the department of the shock shape from being circular are not taken into account. Here the velocity, pressure, temperature, pressure coefficient and vorticity, etc., at any point between the shock and the surface of the sphere in the presence of dissociation or ionization are obtained. In addition, shock detachment distance, drag coefficient, stagnation point velocity gradient and sonic points on the shock and the surface have also been obtained. The results have been compared with the corresponding results obtained in the case when dissociation or ionization does not occur behind the shock.     

The Vlasov Poisson System with Steady Spatial Asymptotics

Abstract

A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the positive charge as |x|→∞ is considered. Hence the total positive charge and the total negative charge are infinite. Smooth solutions with appropriate asymptotic behavior are shown to exist locally in time. Conditions for continuation of these solutions are also established.     

NFFT-based extension of a particle simulation method using multigrid

In the calculation of electrostatic problems using multigrid methods, computationally the most expensive part is often the charge assignment to a grid. We show how to improve an existing multigrid method by using an NFFT-based scheme for this task. Numerical tests show that the new method outperforms the direct charge assignment schemes for the case where smooth charge distributions with large support are considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fermion pair creation by a strong Coulomb field in 2+1 dimensions

The creation of charged fermion pairs by a strong external Coulomb field in a space with two dimensions is investigated. Exact solutions to the Dirac equation are found for the Coulomb external field in 2+1 dimensions. The equation for determining the critical charge is obtained and is numerically solved for a simplified model. The critical charge for 2+1 dimensions is much less than the critical charge for the similar model with 3+1 dimensions. The influence of the vacuum polarization on the critical charge is studied in the one-loop approximation to the (2+1)-dimensional quantum electrodynamics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 2, pp. 277–287, August, 1998.     

On the structure of the fixed charge transportation problem

This work extends the theory of the fixed charge transportation problem (FCTP), currently based mostly on a forty-year-old publication by Hirsch and Danzig. This paper presents novel properties that need to be considered by those using existing, or those developing new methods for optimizing FCTP. It also defines the problem in an easier way, making it understandable to a wider spectrum of readers. While the analysis is limited to FCTP only, elements of it can easily be extended to the general fixed charge problem. Finally a novel, snap method for finding global minima for FCTPs with large fixed charge coefficients is introduced.     

Exponential decay and ionization thresholds in non-relativistic quantum electrodynamics

Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster Hamiltonians, and one in terms of minimal energies of non-localized states. We show that these two definitions agree, and that the electrons described by a state with energy below the ionization threshold are localized in a small neighborhood of the nuclei with a probability that approaches 1 exponentially fast with increasing radius of the neighborhood. The latter result is derived from a new, general result on exponential decay tailor-made for our problem, but applicable to many non-relativistic quantum systems outside quantum electrodynamics as well.     

Turbulent particle dispersion in an electrostatic precipitator

The behaviour of charged particles in turbulent gas flow in electrostatic precipitators (ESPs) is crucial information to optimise precipitator efficiency. This paper describes a strongly coupled calculation procedure for the rigorous computation of particle dynamics during ESP taking into account the statistical particle size distribution. The turbulent gas flow and the particle motion under electrostatic forces are calculated by using the commercial computational fluid dynamics (CFD) package FLUENT linked to a finite volume solver for the electric field and ion charge. Particle charge is determined from both local electrical conditions and the cell residence time which the particle has experienced through its path. Particle charge density and the particle velocity are averaged in a control volume to use Lagrangian information of the particle motion in calculating the gas and electric fields. The turbulent particulate transport and the effects of particulate space charge on the electrical current flow are investigated. The calculated results for poly-dispersed particles are compared with those for mono-dispersed particles, and significant differences are demonstrated.