The (1+1) Dimensional Dirac Equation With Pseudoscalar Potentials: Path Integral Treatment

The supersymetric path integrals in solving the problem of relativistic spinning particle interacting with pseudoscalar potentials is examined. The relative propagator is presented by means of path integral, where the spin degrees of freedom are described by odd Grassmannian variables and the gauge invariant part of the effective action has a form similar to the standard pseudoclassical action given by Berezin and Marinov. After integrating over fermionic variables (Grassmannian variables), the problem is reduced to a nonrelativistic one with an effective supersymetric potential. Some explicit examples are considered, where we have extracted the energy spectrum of the electron and the wave functions. PACS numbers: 03.65. Ca-Formalism, 03.65. Db-Functional analytical methods, 03.65. Pm-Relativistic wave equations.     

The exponential characteristic of the Volterra integral operator with kernel depending on 2<Emphasis Type="Italic">N</Emphasis> variables

Exponential growth is estimated for integral operators with continuous periodic kernels of exponential type. The result is applied to the boundary-value problem for a general hyperbolic differential equation having periodic coefficients with Goursat boundary conditions. It is proved that the exponential characteristic for such a boundary-value problem has canonical form. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.     

On a certain nonlocal problem for a hyperbolic equation

The author proves the existence and uniqueness of a generalized solution of a nonlocal problem with an integral condition for a hyperbolic equation with n spatial variables. This work is a continuation of the studies started in [3–5], where the solvability problem of nonlocal problems with an integral condition was studied for hyperbolic equations on the plane. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.     

Slow cyclotron instability in a high-power backward-wave oscillator

The linear dispersion relation of a backward-wave oscillator (BWO), derived earlier by the authors, is modified to include effects of RF surface current at the beam-vacuum interface. This modified dispersion relation results in an unstable interaction between the slow cyclotron mode (SCM) and the structure mode in addition to the conventional Cherenkov instability caused by the slow space charge mode. Numerical analysis is then carried out using parameters of a BWO experiment at University of Maryland. Fine structure of the SCM instability is elucidated. The analysis indicates that BWO radiation would not be suppressed near cyclotron absorption in an infinitely long system.     

Insight into chain dimensions in PEO/water solutions

Small‐Angle Neutron Scattering has been performed from poly(ethylene oxide) in deuterated water at temperature ranging from 10 to 80 °C. A simple fitting model was used to obtain a correlation length and a Porod exponent. The correlation length L characterizes the average distance between entanglements in the semidilute region and is proportional to the individual coil sizes in the dilute region. L was found to increase with temperature in the semidilute region but it decreases with temperature in the dilute region. This decrease is the precursor to the single‐chain collapse which applies to very dilute polymer solutions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2196–2200, 2007     

Graphitic nanofillers in PMMA nanocomposites—An investigation of particle size and dispersion and their influence on nanocomposite properties

Mechanical, thermal, and electrical properties of graphite/PMMA composites have been evaluated as functions of particle size and dispersion of the graphitic nanofiller components via the use of three different graphitic nanofillers: “as received graphite” (ARG), “expanded graphite,” (EG) and “graphite nanoplatelets” (GNPs) EG, a graphitic materials with much lower density than ARG, was prepared from ARG flakes via an acid intercalation and thermal expansion. Subsequent sonication of EG in a liquid yielded GNPs as thin stacks of graphitic platelets with thicknesses of ～10 nm. Solution‐based processing was used to prepare PMMA composites with these three fillers. Dynamic mechanical analysis, thermal analysis, and electrical impedance measurements were carried out on the resulting composites, demonstrating that reduced particle size, high surface area, and increased surface roughness can significantly alter the graphite/polymer interface and enhance the mechanical, thermal, and electrical properties of the polymer matrix. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2097–2112, 2007     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007     

On the law of corresponding states for thermodynamic properties of a crystal

To study thermodynamic similarity of the properties of crystalline substances, we propose an approach connected with engaging of the metastable state region. Internal pressure and specific volume on the crystal’s stability boundary at T = 0 K are used as characteristic scales of thermodynamic variables. A semiempirical method of calculation of the stability boundary by the thermodynamic data related to the stable states region of a solid body is described. In the cases of argon and natrium, the stability boundary is calculated for a wide range of temperatures and pressures. Analysis of the properties of neon, argon, krypton, and xenon crystals in these variables indicates that the law of corresponding states holds for these substances.