On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3

Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a surface with the Polyakov extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation. In other words, I show that the density of state of the partition function for the quantized Willmore surface is expressed by volume of a subspace of the moduli of the MNV equation.Comment: AMS-Tex Us

Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Due to the bilinearity of the energy functional,I have obtained its exact partition function.By investigation of the system,I conjectured that an expectation value at a critical point of this system obeys the Painlev\'e equation of the first kind and its related equations extended by the KdV hierarchy.Furthermore I also commented onthe relation between the MKdV hierarchy and BRS transformationin this system.Comment: AMS-Tex Us

Generalized Weierstrass Relations and Frobenius reciprocity

This article investigates local properties of the further generalized Weierstrass relations for a spin manifold $S$ immersed in a higher dimensional spin manifold $M$ from viewpoint of study of submanifold quantum mechanics. We show that kernel of a certain Dirac operator defined over $S$, which we call submanifold Dirac operator, gives the data of the immersion. In the derivation, the simple Frobenius reciprocity of Clifford algebras $S$ and $M$ plays important roles.Comment: 17pages. to be published in Mathematical Physics, Analysis and Geometr

Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions

Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given curve $y^2 = f(x)$ whose genus is three. This study was based upon the fact that about one hundred years ago (Acta Math. (1903) {\bf{27}}, 135-156), H. F. Baker essentially derived KdV hierarchy and KP equation by using bilinear differential operator ${\bold{D}}$, identities of Pfaffians, symmetric functions, hyperelliptic $\sigma$-function and $\wp$-functions; $\wp_{\mu \nu} = -\partial_\mu \partial_\nu \log \sigma$ $= - ({\bold{D}}_\mu {\bold{D}}_\nu \sigma \sigma)/2\sigma^2$. The connection between his theory and the modern soliton theory was also discussed.Comment: AMS-Tex, 12 page

Toda Equations and σ\sigma-Functions of Genera One and Two

We study the Toda equations in the continuous level, discrete level and ultradiscrete level in terms of elliptic and hyperelliptic $\sigma$ and $\psi$ functions of genera one and two. The ultradiscrete Toda equation appears as a discrete-valuation of recursion relations of $\psi$ functions.Comment: 16 page

Parametrically controlling solitary wave dynamics in modified Kortweg-de Vries equation

We demonstrate the control of solitary wave dynamics of modified Kortweg-de Vries (MKdV) equation through the temporal variations of the distributed coefficients. This is explicated through exact cnoidal wave and localized soliton solutions of the MKdV equation with variable coefficients. The solitons can be accelerated and their propagation can be manipulated by suitable variations of the above parameters. In sharp contrast with nonlinear Schr\"{o}dinger equation, the soliton amplitude and widths are time independent.Comment: 4 pages, 5 eps figure

Power-Gating Technique for Network-on-Chip Buffers

A new approach to reducing leakage power in network-on-chip buffers is presented. The non-uniformity of buffer utilisation is leveraged across the network and power-gating is applied to scarcely utilised buffers. Instead of turning-off the buffers completely, a buffer portion is kept turned-on. This design choice has a significant performance benefit because the buffer is always able to receive network packets. Design aspects and trade-offs in a 45 nm CMOS technology are discussed and results obtained over video application benchmarks are presented. It is shown that it is possible to reduce buffer leakage by 40% without performance penalt

On Some Classes of mKdV Periodic Solutions

We obtain exact periodic solutions of the positive and negative modified Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices through direct numerical simulations. While the positive mKdV breather lattice solutions are found to be unstable, the two-soliton lattice solution of the same equation is found to be stable. Similarly, a negative mKdV lattice solution is found to be stable. We also touch upon the implications of these results for the KdV equation.Comment: 8 pages, 3 figures, to appear in J. Phys.

Abelian functions associated with a cyclic tetragonal curve of genus six

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y^4 = x^5 + λ[4]x^4 + λ[3]x^3 + λ[2]x^2 + λ[1]x + λ[0]. We construct Abelian functions using the multivariate sigma-function associated with the curve, generalizing the theory of theWeierstrass℘-function. We demonstrate that such functions can give a solution to the KP-equation, outlining how a general class of solutions could be generated using a wider class of curves. We also present the associated partial differential equations satisfied by the functions, the solution of the Jacobi inversion problem, a power series expansion for σ(u) and a new addition formula

Breather lattice and its stabilization for the modified Korteweg-de Vries equation

We obtain an exact solution for the breather lattice solution of the modified Korteweg-de Vries (MKdV) equation. Numerical simulation of the breather lattice demonstrates its instability due to the breather-breather interaction. However, such multi-breather structures can be stabilized through the concurrent application of ac driving and viscous damping terms.Comment: 6 pages, 3 figures, Phys. Rev. E (in press