Investigation of Scattering Property for An Anisotropic Dielectric Circular Cylinder

Utilizing the scales theory of electromagnetic theory, the anisotropic dielectric material is reconstructed into an isotropic medium. The analytic expressions of scattering field and the scattering breadth for an anisotropic material cylinder are first presented. Their validities are checked theoretically. The influences induced by the dielectric constant tensor etc. on the scattering breadth are simulated. The results show that the scatterings both in the forward direction and vertical direction to the incident direction are strong. The dielectric constant in the polarizing direction has a biggish effect on scattering field. The mechanism of results is presente

The continuum limit of perturbative coefficients calculated with a large field cutoff

We report MC calculations of perturbative coefficients for lattice scalar field theory in dimensions 1, 2 and 3, where the large field contributions are cutoff. This produces converging (instead of asymptotic) perturbative series. We discuss the statistical errors and the lattice effects and show that accurate calculations are possible even in a crossover region where no approximation works. We show that the field cutoff is also a UV regulator. We point out the relevance for QCD questions discussed by Tomboulis and Trottier at this conference.Comment: 3 pages, 4 figs., Lattice2003(theory

Universal Crossover in Perturbation Theory with a Large Field Cutoff

For lambda phi^4 models, the introduction of a large field cutoff improves significantly the accuracy that can be reached with perturbative series but the calculation of the modified coefficients remains a challenging problem. We show that this problem can be solved numerically, and in the limits of large and small field cutoffs, for the ground state energy of the anharmonic oscillator. For the two lowest orders, the approximate formulas obtained in the large field cutoff limit extend unexpectedly far in the low field cutoff region. For the higher orders, the transition between the small field cutoff regime and the large field cutoff regime can be described in terms of a universal function.Comment: 6 pages, 4 figures, uses iopar

Large Field Cutoffs in Lattice Gauge Theory

In pure gauge SU(3) near beta = 6, weak and strong coupling expansions break down and the MC method seems to be the only practical alternative. We discuss the possibility of using a modified version of perturbation theory which relies on a large field cutoff and has been successfully applied to the double-well potential (Y. M., PRL 88 141601). Generically, in the case of scalar field theory, the weak coupling expansion is unable to reproduce the exponential suppression of the large field configurations. This problem can be solved by introducing a large field cutoff. The value of this cutoff can be chosen to reduce the discrepancy with the original problem. This optimization can be approximately performed using the strong coupling expansion and bridges the gap between the two expansions. We report recent attempts to extend this procedure for SU(3) gauge theory on the lattice. We compare gauge invariant and gauge dependent (in the Landau gauge) criteria to sort the configurations into ``large-field'' and ``small-field'' configurations. %We discuss the effects of discarding the large field configurations. We discuss the convergence of lattice perturbation theory and the way it can be modified in order to obtain results similar to the scalar case.Comment: 12 pages, 8 figures; talk presented by Y. Meurice at the Workshop on QCD in Extreme Environments, Argonne National Laboratory, 29th June to 3rd July, 2

A study of large field configurations in MC simulations

We discuss a new approach of scalar field theory where the small field contributions are treated perturbatively and the large field configurations (which are responsible for the asymptotic behavior of the perturbative series) are neglected. In two Borel summable lambda phi ^4 problems improved perturbative series can be obtained by this procedure. The modified series converge towards values exponentially close to the exact ones. For lambda larger than some critical value, the method outperforms Pade approximants and Borel summations. The method can also be used for series which are not Borel summable such as the double-well potential series and provide a perturbative approach of the instanton contribution. Semi-classical methods can be used to calculate the modified Feynman rules, estimate the error and optimize the field cutoff. We discuss Monte Carlo simulations in one and two dimensions which support the hypothesis of dilution of large field configurations used in these semi-classical calculations. We show that Monte Carlo methods can be used to calculate the modified perturbative series.Comment: 3 pages, lattice2002(spin

A Tractable Example of Perturbation Theory with a Field Cutoff: the Anharmonic Oscillator

For lambda phi^4 models, the introduction of a large field cutoff improves significantly the accuracy that can be reached with perturbative series but the calculation of the modified coefficients remains a challenging problem. We show that this problem can be solved numerically, and analytically in the limits of large and small field cutoffs, for the ground state energy of the anharmonic oscillator. For the two lowest orders in lambda, the approximate formulas obtained in the large field cutoff limit extend unexpectedly far in the low field cutoff region and there is a significant overlap with the small field cutoff approximation. For the higher orders, this is not the case, however the shape of the transition between the small field cutoff regime and the large field cutoff regime is approximately order independent.Comment: 16 pages, 9 figs., uses iopart.cl

Observation of flux tube crossings in the solar wind

Current sheets are ubiquitous in the solar wind.They are a major source of the solar wind MHD turbulence intermittency. They may result from non-linear interactions of the solar wind MHD turbulence or are the boundaries of flux tubes that originate from the solar surface. Some current sheets appear in pairs and are the boundaries of transient structures such as magnetic holes and reconnection exhausts, or the edges of pulsed Alfv\'{e}n waves. For an individual current sheet, discerning whether it is a flux tube boundary or due to non-linear interactions, or the boundary of a transient structure is difficult. In this work, using data from the {\sl Wind} spacecraft, we identify two three-current-sheet events. Detailed examination of these two events suggest that they are best explained by the flux tube crossing scenario. Our study provides a convincing evidence supporting the scenario that the solar wind consists of flux tubes where distinct plasmas reside.Comment: 5 figure

Research of Mechanical Properties of Ni-Ti-Nb Alloyson Low Temperature and Restriction Behavior

Mechanical Properties of Ni-Ti-Nb alloys with these conditions of cold-drawing, non-vacuum heat treatment and vacuum heat treatment were measured at low temperature, and Mechanical Properties of Ni47Ti44Nb9 alloys of restricting recover was compared with the one of alloys of non-restricting recover, and these rules of the mechanical performance between them was analyzed. Experiment indicates that, mechanical Properties of vacuum heat treatment's alloys was more excellent than the other two (non-vacuum heat treatment and cold-drawing), and the stress curves of alloys of restricting recover haven't the evident yield band, and the stress of alloys of restricting recover was higher than the ones of alloys of non-restricting recover, but the stress of alloys of restricting recover was lower than the ones of alloys of non-restricting recover.Comment: e.g.: 5pages, 4 figures, conferenc

Bilinear forms on Green rings of finite dimensional Hopf algebras

In this paper, we study the Green ring and the stable Green ring of a Hopf algebra $H$ by means of bilinear forms. We show that the Green ring of a Hopf algebra of finite representation type is a Frobenius algebra over $\mathbb{Z}$ with a dual basis associated to almost split sequences. On the stable Green ring we define a new bilinear form which is more accurate to determine the bi-Frobenius property of the stable Green ring. We show that the complexified stable Green ring (or algebra) is a group-like algebra, and hence a bi-Frobenius algebra, if the bilinear form on the stable Green ring is non-degenerate.Comment: Section 4 and 5 revise

Structure and thermodynamic properties of a weakly-coupled antiferromagnetic spin-1/2 chain compound (C5H12N)CuBr3

Single crystals of a metal organic complex \ce{(C5H12N)CuBr3} (\ce{C5H12N} = piperidinium, pipH for short) have been synthesized and the structure was determined by single-crystal X-ray diffraction. \ce{(pipH)CuBr3} crystallizes in the monoclinic group $C$2/$c$. Edging-sharing \ce{CuBr5} units link to form zigzag chains along the $c$ axis and the neighboring Cu(II) ions with spin-1/2 are bridged by bi-bromide ions. Magnetic susceptibility data down to 1.8 K can be well fitted by the Bonner-Fisher formula for antiferromagnetic spin-1/2 chain, giving the intrachain magnetic coupling constant $J$ $\sim$ 17 K. At zero field, \ce{(pipH)CuBr3} shows three-dimensional (3D) order below $T_N$ = 1.68 K. Calculated by the mean-field theory, the interchain coupling constant $J'$ = 0.65 K is obtained and the ordered magnetic moment $m_0$ is about 0.20 $\mu_B$. This value of $m_0$ makes \ce{(pipH)CuBr3} a rare compound suitable to study the dimensional crossover problem in magnetism, since both 3D order and one-dimensional (1D) quantum fluctuations are prominent. In addition, specific heat measurements reveal two successive magnetic transitions with lowering temperature when external field $H \geq$ 3 T is applied along the $a'$ axis. The $H$ - $T$ phase diagram of \ce{(pipH)CuBr3} is roughly constructed. The interplay between exchange interactions, dimensionality, Zeeman energy and possible Dzyaloshinkii-Moriya interaction should be the driving force for the multiple phase transitions.Comment: 5 pages, 4 figure