Abundant multisoliton structures of the Konopelchenko-Dubrovsky equation

Using the homogenous balance method, the nonlinear transformations of the (2+1)-dimensional integrable Konopelchenko-Dubrovsky equation are given, and then some new special types of single solitary wave solution and the multisoliton solutions are constructed. The project is supported by the Natural Science Foundation of Shandong Province in China and the Natural Science Foundation of Liaocheng University.     

The study of soliton fission and fusion in (2+1)-dimensional nonlinear system

By means of a variable separation approach and an extended homogeneous balance method, a general variable separation excitation of a (2+1)-dimensional nonlinear system is derived. Based on the derived solution with arbitrary functions, we reveal soliton fission and fusion phenomena in the (2+1)-dimensional soliton system.     

Measurement of tortuosity in aluminum foams using airborne ultrasound

The slow compressional wave in air-saturated aluminum foams was studied by means of ultrasonic transverse transmission method over a frequency range from 0.2 MHz to 0.8 MHz. The samples investigated have three different cell sizes or pores per inch (5, 10 and 20 ppi) and each size has three aluminum volume fractions (5%, 8% and 12% AVF). Phase velocities show minor dispersion at low frequencies but remain constant after 0.7 MHz. Pulse broadening and amplitude attenuation are obvious and increase with increasing ppi. Attenuation increases considerably with AVF for 20 ppi foams. Tortuosity ranges from 1.003 to 1.032 and increases with AVF and ppi. However, the increase of tortuosity with AVF is very small for 10 and 20 ppi samples.     

Path integral solution of linear second order partial differential equations I: the general construction

A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schrödinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette.     

Properties and Phenomena: Basic Plasma Physics and Fusion Research in Postwar America

I review the changing conceptions of basic physics that the U.S. plasma-physics community put forward in postwar America. I give special attention to the tense relationship between fusion research and the more general study of plasmas in astrophysics, space science, and industry.Although fusion research often led to results that were regarded as basic plasma physics, its dominating influence tended to weaken other plasma work, as becomes evident when I compare the public statements and professional fortunes of plasma scientists during the 1960s, when fusion research experienced a downturn, with those of the 1970s, when fusion research flourished. I also show that the plasmaphysics community’s conceptions of basic physics were not highly regarded or easily understood by science administrators and the general physics community. To make this point, I contrast two general ideas of basic physics: the Big Questions conception and the Properties and Phenomena conception. Gary J.Weisel; Gary J.Weisel is Associate Professor of Physics at Penn State Altoona in Altoona, Pennsylvania. His historical research focuses on the development of subdisciplines in twentieth-century physics. He also carries out research in nuclear physics and materials science.     

A new construction of quasi-solvable quantum many-body systems of deformed Calogero-Sutherland type

We make a new multivariate generalization of the type A monomial space of a single variable. It is different from the previously introduced type A space of several variables which is an sl(M+1) module, and we thus call it type A′. We construct the most general quasi-solvable operator of (at most) second-order which preserves the type A′ space. Investigating directly the condition under which the type A′ operators can be transformed to Schrödinger operators, we obtain the complete list of the type A′ quasi-solvable quantum many-body systems. In particular, we find new quasi-solvable models of deformed Calogero-Sutherland type which are different from the Inozemtsev systems. We also examine a new multivariate generalization of the type C monomial space based on the type A′ scheme.     

Bose-Einstein solitons in time-dependent linear potential

In this paper, Bose-Einstein soliton solutions of the nonlinear Schrödinger equation with time-dependent linear potential are considered. Based on the F-expansion method, we present a number of Jacobian elliptic function solutions. Particular cases of these solutions, where the elliptic function modulus equals 1 and 0, are various localized solutions and trigonometric functions, respectively. Specially, for V_ext = ZF(T) = Z[mg + Hcos (ω₁T)], we discussed the Bose-Einstein condensate trapped in the coupling external field with considering the effect of gravity; for F(T) = constant, it describes the wave (Langmuir or electromagnetic) in a linearly inhomogeneous plasma with cubic nonlinearly.     

The measurement of the electronic g-factor in hydrogen-like ions --A promising tool for determining fundamental and nuclear constants

We describe a double-Penning-trap experiment suitable for testing QED in strong fields by determining the electronic g-factor of a single hydrogen-like ion in its ground state. Our measurements on ¹²C^{5 +} reach a relative accuracy of 2×10^-9, where the largest uncertainty results from the mass of the electron. Together with equally precise theoretical predictions therefore, it is possible to evaluate a new value for the electron's mass. The possibilities to obtain other fundamental constants and nuclear parameters are lined out. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: t.beier@gsi.de     

Investigation of heteroepitaxial diamond films by atomic force and scanning tunneling microscopy

We report on Atomic Force Microscopy (AFM) and Scanning Tunneling Microscopy (STM) investigations on chemical vapour deposited heteroepitaxial diamond films. Besides the good macroscopic crystal morphology a statistical tilt up to ±5.2° of the oriented crystallites has been found relative to the silicon substrates. By optimizing the process conditions, however, the crystal tilt of the films can be reduced, resulting in an improved film perfection. On crystallite (001)-surfaces a substructure of growth facets or islands has been found and high resolution STM images have established a 2×1 surface reconstruction on these growth facets. AFM and SEM were applied to study the morphology of diamond nuclei initially grown on the silicon substrate. Strong island like (Volmer-Weber) growth has been found, with a nucleus height to diameter ratio of 1:1. While the islands are growing in size with respect to time of nucleation, its aspect ratio does not change, due to the high surface free energy of the diamond relative to silicon.     

1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation

This Letter carries out the integration of the generalized Radhakrishnan, Kundu, Lakshmanan equation to obtain the 1-soliton solution. The solitary wave ansatz is used to carry out the integration, to obtain an exact solution of this equation.