Acceleration waves analyzed by a new continuum model of solids incorporating microscopic thermal vibrations

Acceleration waves propagating in isotropic solids at finite temperatures are studied by applying the method of singular surfaces to a new continuum model derived statistical-mechanically from a three-dimensional lattice model. The continuum model explicitly takes into account the microscopic thermal vibrations of the constituent atoms as one of the field variables. The propagation speeds and the ratios of mechanical and thermal amplitudes for both longitudinal and transverse waves are consistently determined. The differential equations that govern the time variation of the amplitudes of the waves are also derived. The analytical results, which are valid over a wide temperature range that includes the melting point, are evaluated numerically for several materials, and their physical implications are discussed. One of the findings to be emphasized is that of the singularities of the characteristic quantities at the melting point.Received: 13 March 2003, Accepted: 20 June 2003PACS: 62.30. + d, 65.40.-bM. Sugiyama: Correspondence to Dedicated to Prof. Ingo Müller on the occasion of his 65th birthday.     

A novel electron scattering apparatus combining a laser photoelectron source and a triply differentially pumped supersonic beam target: characterization and results for the resonance

A novel electron scattering apparatus for high resolution studies of angle-differential elastic and inelastic electron scattering from atoms and molecules in the gas phase is described and its performance characterized. It combines a laser photoelectron source, a triply differentially pumped collimated supersonic beam target (half angle 0.015 rad, background to beam density ratio < 0.01), and several electron multipliers for simultaneous detection of elastically scattered electrons and metastable atoms (or molecules) due to inelastic scattering. In detailed test measurements of the yield for the production of metastable He^*(2³S₁) atoms around its threshold, the dependence of the overall energy width on various experimental parameters has been investigated. So far a resolution down to 7 meV (FWHM) has been obtained. Under such conditions we have investigated the profile of the He^- (1 s 2 s ^{2 2} S _1/2 ) resonance at the scattering angles 22 ^° , 45 ^° , and 90 ^° . From a consistent fit of the measured profiles by resonant scattering theory we determine a new value for the resonance energy ( E _r = 19.365(1) eV) and an accurate resonance width ( Γ = 11.2(5) meV). These results are consistent with the previously recommended values. Received 23 July 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: hotop@physik.uni-kl.de RID="b" ID="b"Permanent address: Department of Physics and Astronomy, Drake University, Des Moines, IA 50311, USA.     

Remarks on the Formulation of the Cosmological Constant/Dark Energy Problems

Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component while the new problem is related to this magnitude being of the same order of the matter energy density during the present epoch of cosmic evolution. Current plans to measure the equation of state or density parameters certainly constitute an important approach; however, as we discuss, this approach is faced with serious feasibility challenges and is limited in the type of conclusive answers it could provide. Therefore, is it really too early to seek actively for new tests and approaches to these problems? In view of the difficulty of this endeavor, we argue in this work that a good place to start is by questioning some of the assumptions underlying the formulation of these problems and finding new ways to put this questioning to the test. First, we calculate how much fine tuning the cosmic coincidence problem represents. Next, we discuss the potential of some cosmological probes such as weak gravitational lensing to identify novel tests to probe dark energy questions and assumptions and provide an example of consistency tests. Then, motivated by some theorems in General Relativity, we discuss if the full identification of the cosmological constant with vacuum energy is unquestionable. We discuss some implications of the simplest solution for the principles of General Relativity. Also, we point out the relevance of experiments at the interface of astrophysics and quantum field theory, such as the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions.     

Low-energy electron scattering from copper

Differential cross sections for the elastic scattering of electrons from the ground states of copper for the configuration 3d¹⁰ 4s and the excitation state ²D with the configuration 3d⁹ 4s² have been calculated. Local density approximations to the exchange and correlation potentials have been used in these calculations, and it is confirmed that Hara exchange coupled with a Hedin-Lundqvist electron-gas-type correlation potential joined to an adiabatic polarization potential gives good predictions for differential cross sections. A comparison of the calculated results with other experimental and theoretical data are presented and discussed.     

Application of R-matrix method to electron-H<Subscript>2</Subscript>S collisions in the low energy range

Electron-H₂S collision process is studied using the R-matrix method. Nine low-lying states of H₂S molecule are considered in the R-matrix formalism to obtain elastic integral, differential, momentum transfer and excitation cross sections for this scattering system. We have represented our target states using configuration interaction (CI) wavefunctions. We obtained adequate representation of vertical spectrum of the target states included in the scattering calculations. The cross sections are compared with the experiment and other theoretical results. We have obtained good agreement for elastic and momentum transfer cross sections with experiment for entire energy range considered. The differential cross sections are in excellent agreement with experiment in the range 3–15 eV. A prominent feature of this calculation is the detection of a shape resonance in ²B₂ symmetry which decays via dissociative electron attachment (DEA). Born correction is applied for the elastic and dipole allowed transition to account for higher partial waves excluded in the R-matrix calculation. The electron energy range is 0.025–15 eV.     

Accelerating flames in tubes—an analysis

Flame acceleration in tubes is studied. A tube filled with flammable mixture is closed at one end and open to the atmosphere at its second end. When ignition takes place near the closed end, it is well-known from experiments that the flame may accelerate, oscillate and eventually reach considerable speeds. A one-dimensional analysis is presented, based upon the assumption that the flame front propagates at a speed that is small compared to the speed of sound. The analysis leads to a construction of the complete unsteady solution. Results from the analysis and from a numerical simulation are compared. They are similar enough to validate the analysis. The tube acoustics are set in motion by the expansion of the fluid due to ignition at the closed end. Subsequently, both spectrum and amplitude evolve because of the motion of the temperature interface, and because of forcing by the flame front, which the analysis precisely quantifies. Oscillations in the front position are strong enough to result in flow reversal. In addition, the induced periodic acoustic acceleration of the temperature and density interface will periodically make the flame front Rayleigh–Taylor unstable, which should result in the dramatic increase in the propagation speed seen in experiments.     

Conduction of Strongly Coupled Electrons Through Narrow Channels on Liquid Helium Surface: Simulation

The conduction of electrons through narrow channels formed on the surface of liquid helium is analyzed by numerical simulations. It is shown that, when electrons are strongly coupled, we have nonlinear and even negative dependence of conductance on the width of the constriction which is controlled by the gate voltage (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于最小加速度原理的刚塑性动力问题

应用有限变形的最小加速度原理，推导出了小变形或有限变形构件受到刚性飞射物撞击时的刚塑性运动方程，指出该方法具有直接、简捷和可靠的特点。     

Intermodulation of transverse magnetoresistance oscillations in structures with strong intersubband interaction

In the Shubnikov–de Haas oscillation spectrum of doped InAs/AlSb structures, high-amplitude peaks are established at combination frequencies. It is demonstrated that they are caused by a significant contribution of intersubband scattering to the processes of electron-electron interaction. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 32–38, December, 2008.     

Function-valued Padé-type approximant via the formal orthogonal polynomials and its applications in solving integral equations

A kind of function-valued Padé-type approximant via the formal orthogonal polynomials (FPTAVOP) is introduced on the polynomial space and an algorithm is sketched by means of the formal orthogonal polynomials. This method can be applied to approximate characteristic values and the corresponding characteristic function of Fredholm integral equation of the second kind. Moreover, theoretical analyses show that FPTAVOP method is the most effective one for accelerating the convergence of a sequence of functions. In addition, a typical numerical example is presented to illustrate when the estimates of characteristic value and characteristic function by using this new method are more accurate than other methods.