Progress in lattice gauge theory

Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g²-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a $\text{1}\text{N}$ expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed.     

Optimization of the Isolation of Some Taxoids from Yew Tissues

JPC – Journal of Planar Chromatography – Modern TLC - A new TLC procedure has been developed for the purification, separation, and isolation of paclitaxel and cephalomannine from yew...     

Electromagnetic and Thermal Properties of a Conductively Loaded Epoxy

We discuss the mechanical, thermal, and electromagnetic properties of a castable microwave absorber consisting of a mixture of stainless steel powder suspended in a commercially available epoxy. The resulting mixture is well suited for cryogenic applications. Its coefficient of thermal expansion closely matches most metals to reduce mechanical strain during cool down. The absorption can be tuned by varying the volume filling fraction of the stainless steel powder in the mixture and exhibits little change from room temperature to 4 K. We provide simple expressions for the real and imaginary parts of the dielectric permittivity as a function of frequency and the stainless steel filling fraction.     

Millimeter-wave whispering gallery modes in an ellipsoidal dielectric resonator with a small ellipticity

It is found that, when the shape of a dielectric sphere (hemisphere) operating under the whispering gallery mode conditions is perturbed by a surface curvature gradient (ellipticity), the unloaded Q factor of the sphere degrades and its resonance frequencies change. It is shown theoretically and experimentally that an elliptic irregularity removes frequency degeneracy of whispering gallery modes at millimeter waves.     

On the existence of optimal coefficient controls for a nonlinear Neumann boundary value problem

We study the solvability of an optimal control problem for a nonlinear elliptic equation with the Neumann conditions on the boundary for the case in which the coefficients in the main part of the differential operator play the role of control functions. We show that this problem is solvable in the class of generalized-solenoidal matrices.     

Effect of Functionalization of Colloidal Gold on Controlled Flocculation by the Ligand-Receptor Mechanism

Modification of colloidal gold particles with octadecanthiol and alkyl biotin, with the subsequent flocculation of these particles via introduction of a tetramer protein avidin, was studied.     

Optimal design of temperature regimes of reflecting systems

We solve the variational problem of determining the power of additional three-dimensional and surface heat sources to guarantee the minimization of the displacement field at the end of a finite circular cylinder on which a stationary heat flow is prescribed. Four figures. Bibliography: 5 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 73–77.     

High-order asymptotics of a solution of one problem of optimal control over a distributed system with rapidly oscillating coefficients

High-order asymptotics is constructed and justified for optimal control over parabolic systems with rapidly oscillating coefficients in the principal part that describes high-intensity heat transfer processes in inhomogeneous and periodic media. The investigation is based on the use of methods of multiscale asymptotic decomposition and some results of the theory of averaging.     

Simulation of deuterium reflection from plasma-sprayed tungsten

A method of computer simulation of the formation of plasma-sprayed tungsten surface is proposed. The dependencies of the reflection coefficients of hydrogen isotopes on the energy of incident particles in the range from 5 to 10⁴ eV were obtained for this surface. It is shown that, at energies about 10 eV, the reflection coefficient for the surface of plasma-sprayed tungsten is smaller than that for a smooth surface by a factor of 1.5; this decrease corresponds to the increase in the deuterium incorporation coefficient by a factor of 2.