Transitions among crystal, glass, and liquid in a binary mixture with changing particle size ratio and temperature

Using molecular dynamics simulation we examine changeovers among crystal, glass, and liquid at high density in a two dimensional binary mixture. We change the ratio between the diameters of the two components and the temperature. The transitions from crystal to glass or liquid occur with proliferation of defects. We visualize the defects in terms of a disorder variable "D_j(t)" representing a deviation from the hexagonal order for particle j. The defect structures are heterogeneous and are particularly extended in polycrystal states. They look similar at the crystal-glass crossover and at the melting. Taking the average of "D_j(t)" over the particles, we define a disorder parameter "D(t)", which conveniently measures the degree of overall disorder. Its relaxation after quenching becomes slow at low temperature in the presence of size dispersity. Its steady state average is small in crystal and large in glass and liquid.Comment: 7 pages, 10 figure

Factorization methods for Noncommutative KP and Toda hierarchy

We show that the solution space of the noncommutative KP hierarchy is the same as that of the commutative KP hierarchy owing to the Birkhoff decomposition of groups over the noncommutative algebra. The noncommutative Toda hierarchy is introduced. We derive the bilinear identities for the Baker--Akhiezer functions and calculate the $N$-soliton solutions of the noncommutative Toda hierarchy.Comment: 7 pages, no figures, AMS-LaTeX, minor corrections, final version to appear in Journal of Physics

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

Conserved Quantities in Noncommutative Principal Chiral Model with Wess-Zumino Term

We construct noncommutative extension of U(N) principal chiral model with Wess-Zumino term and obtain an infinite set of local and non-local conserved quantities for the model using iterative procedure of Brezin {\it et.al} \cite{BIZZ}. We also present the equivalent description as Lax formalism of the model. We expand the fields perturbatively and derive zeroth- and first-order equations of motion, zero-curvature condition, iteration method, Lax formalism, local and non-local conserved quantities.Comment: 14 Page

Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space

We consider the Dunne-Jackiw-Pi-Trugenberger model of a U(N) Chern-Simons gauge theory coupled to a nonrelativistic complex adjoint matter on noncommutative space. Soliton configurations of this model are related the solutions of the chiral model on noncommutative plane. A generalized Uhlenbeck's uniton method for the chiral model on noncommutative space provides explicit Chern-Simons solitons. Fundamental solitons in the U(1) gauge theory are shaped as rings of charge `n' and spin `n' where the Chern-Simons level `n' should be an integer upon quantization. Toda and Liouville models are generalized to noncommutative plane and the solutions are provided by the uniton method. We also define affine Toda and sine-Gordon models on noncommutative plane. Finally the first order moduli space dynamics of Chern-Simons solitons is shown to be trivial.Comment: latex, JHEP style, 23 pages, no figur

Noncommutative Vortex Solitons

We consider the noncommutative Abelian-Higgs theory and investigate general static vortex configurations including recently found exact multi-vortex solutions. In particular, we prove that the self-dual BPS solutions cease to exist once the noncommutativity scale exceeds a critical value. We then study the fluctuation spectra about the static configuration and show that the exact non BPS solutions are unstable below the critical value. We have identified the tachyonic degrees as well as massless moduli degrees. We then discuss the physical meaning of the moduli degrees and construct exact time-dependent vortex configurations where each vortex moves independently. We finally give the moduli description of the vortices and show that the matrix nature of moduli coordinates naturally emerges.Comment: 22 pages, 1 figure, typos corrected, a comment on the soliton size is adde

Noncommutative Burgers Equation

We present a noncommutative version of the Burgers equation which possesses the Lax representation and discuss the integrability in detail. We find a noncommutative version of the Cole-Hopf transformation and succeed in the linearization of it. The linearized equation is the (noncommutative) diffusion equation and exactly solved. We also discuss the properties of some exact solutions. The result shows that the noncommutative Burgers equation is completely integrable even though it contains infinite number of time derivatives. Furthermore, we derive the noncommutative Burgers equation from the noncommutative (anti-)self-dual Yang-Mills equation by reduction, which is an evidence for the noncommutative Ward conjecture. Finally, we present a noncommutative version of the Burgers hierarchy by both the Lax-pair generating technique and the Sato's approach.Comment: 24 pages, LaTeX, 1 figure; v2: discussions on Ward conjecture, Sato theory and the integrability added, references added, version to appear in J. Phys.

Examination of the Singapore Shift in Japan's Foreign Direct Investment in Services in ASEAN

Asia is fast becoming the largest recipient of Japan's foreign direct investment (FDI). Within the Asian region, the Association of Southeast Asian Nations (ASEAN) has been the major investment destination of Japan. In the manufacturing sectors, however, the investment flows from Japan to ASEAN - with Thailand being the largest recipient - has been declining. In contrast, Japan's FDI in the services sectors in ASEAN has been growing rapidly. The recent phenomenon of the Singapore Shift in Japan's FDI in the ASEAN services sectors proves interesting. The prominent strategy of Japanese companies is to establish a commercial presence in Singapore, which they expect to be the hub of Southeast Asia, thereby enabling them to supply services to the entire ASEAN region. The magnitude of the Singapore Shift varies for every services sub-sector. By comparing transport and logistics with finance and insurance industries, this paper considers the critical determinants of the Singapore Shift

Fuzzy sphere bimodule, ABS construction to the exact soliton solutions

In this paper, we set up the bi-module of the algebra ${\cal A}$ on fuzzy sphere. Based on the differential operators in moving frame, we generalize the ABS construction into fuzzy sphere case. The applications of ABS construction are investigated in various physical systems.Comment: Latex file without figure, 13 page

Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared