Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction properties of two-soliton solutions.Comment: 2 figure

Exchange coupling in Eu monochalcogenides from first principles

Using a density functional method with explicit account for strong Coulomb repulsion within the 4f shell, we calculate effective exchange parameters and the corresponding ordering temperatures of the (ferro)magnetic insulating Eu monochalcogenides (EuX; X=O,S,Se,Te) at ambient and elevated pressure conditions. Our results provide quantitative account of the many-fold increase of the Curie temperatures with applied pressure and reproduce well the enhancement of the tendency toward ferromagnetic ordering across the series from telluride to oxide, including the crossover from antiferromagnetic to ferromagnetic ordering under pressure in EuTe and EuSe. The first and second neighbor effective exchange are shown to follow different functional dependencies. Finally, model calculations indicate a significant contribution of virtual processes involving the unoccupied f states to the effective exchange.Comment: 4 pages, 6 figure

On multidimensional analogs of Melvin's solution for classical series of Lie algebras

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra $\cal G$ is presented. The gravitational model contains n 2-forms and $l \geq n$ scalar fields, wheren is the rank of $\cal G$. The solution is governed by a set of n functions obeying n ordinary differential equations with certain boundary conditions. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). A program (in Maple) for calculating of these polynomials for classical series of Lie algebras is suggested (see Appendix). The polynomials corresponding to the Lie algebra D_4 are obtained. It is conjectured that the polynomials for A_n-, B_n- and C_n-series may be obtained from polynomials for D_{n+1}-series by using certain reduction formulas.Comment: 6 pages, based on a report at RUSGRAV-13 (23-28 June, 2008, PFUR, Moscow

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

On micro-structural effects in dielectric mixtures

The paper presents numerical simulations performed on dielectric properties of two-dimensional binary composites on eleven regular space filling tessellations. First, significant contributions of different parameters, which play an important role in the electrical properties of the composite, are introduced both for designing and analyzing material mixtures. Later, influence of structural differences and intrinsic electrical properties of constituents on the composite's over all electrical properties are investigated. The structural differences are resolved by the spectral density representation approach. The numerical technique, without any {\em a-priori} assumptions, for extracting the spectral density function is also presented.Comment: 24 pages, 8 figure and 7 tables. It is submitted to IEEE Transactions on Dielectrics and Electrical Insulatio

Matter-Wave Solitons in an F=1 Spinor Bose-Einstein Condensate

Following our previous work [J. Ieda, T. Miyakawa, M. Wadati, cond-mat/0404569] on a novel integrable model describing soliton dynamics of an F=1 spinor Bose--Einstein condensate, we discuss in detail the properties of the multi-component system with spin-exchange interactions. The exact multiple bright soliton solutions are obtained for the system where the mean-field interaction is attractive (c_0 < 0) and the spin-exchange interaction is ferromagnetic (c_2 < 0). A complete classification of the one-soliton solution with respect to the spin states and an explicit formula of the two-soliton solution are presented. For solitons in polar state, there exists a variety of different shaped solutions including twin peaks. We show that a "singlet pair" density can be used to distinguish those energetically degenerate solitons. We also analyze collisional effects between solitons in the same or different spin state(s) by computing the asymptotic forms of their initial and final states. The result reveals that it is possible to manipulate the spin dynamics by controlling the parameters of colliding solitons.Comment: 12 pages, 9 figures, to appear in J. Phys. Soc. Jpn. Vol.73 No.11 (2004

Observation of the Cabibbo-suppressed decay Xi_c+ -> p K- pi+

We report the first observation of the Cabibbo-suppressed charm baryon decay Xi_c+ -> p K- pi+. We observe 150 +- 22 events for the signal. The data were accumulated using the SELEX spectrometer during the 1996-1997 fixed target run at Fermilab, chiefly from a 600 GeV/c Sigma- beam. The branching fractions of the decay relative to the Cabibbo-favored Xi_c+ -> Sigma+ K- pi+ and Xi_c+ -> X- pi+ pi+ are measured to be B(Xi_c+ -> p K- pi+)/B(Xi_c+ -> Sigma+ K- pi+) = 0.22 +- 0.06 +- 0.03 and B(Xi_c+ -> p K- pi+)/B(Xi_c+ -> X- pi+ pi+) = 0.20 +- 0.04 +- 0.02, respectively.Comment: 5 pages, RevTeX, 3 figures (postscript), Submitted to Phys. Rev. Let

Quasi-molecular and atomic phases of dense solid hydrogen

The high-pressure phases of solid hydrogen are of fundamental interest and relevant to the interior of giant planets; however, knowledge of these phases is far from complete. Particle swarm optimization (PSO) techniques were applied to a structural search, yielding hitherto unexpected high-pressure phases of solid hydrogen at pressures up to 5 TPa. An exotic quasi-molecular mC24 structure (space group C2/c, stable at 0.47-0.59 TPa) with two types of intramolecular bonds was predicted, providing a deeper understanding of molecular dissociation in solid hydrogen, which has been a mystery for decades. We further predicted the existence of two atomic phases: (i) the oC12 structure (space group Cmcm, stable at > 2.1 TPa), consisting of planar H3 clusters, and (ii) the cI16 structure, previously observed in lithium and sodium, stable above 3.5 TPa upon consideration of the zero-point energy. This work clearly revised the known zero-temperature and high-pressure (>0.47 TPa) phase diagram for solid hydrogen and has implications for the constituent structures of giant planets.Comment: accepted in The Journal of Physical Chemistr