348 research outputs found
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 immersed in a higher dimensional
spin manifold from viewpoint of study of submanifold quantum mechanics. We
show that kernel of a certain Dirac operator defined over , which we call
submanifold Dirac operator, gives the data of the immersion. In the derivation,
the simple Frobenius reciprocity of Clifford algebras and 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 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 , identities of Pfaffians, symmetric
functions, hyperelliptic -function and -functions; . The connection between his theory and the modern
soliton theory was also discussed.Comment: AMS-Tex, 12 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
Toda Equations and -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 and
functions of genera one and two. The ultradiscrete Toda equation appears as a
discrete-valuation of recursion relations of functions.Comment: 16 page
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.
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
Annual variation in the levels of transcripts of sex-specific genes in the mantle of the common mussel, Mytilus edulis
Mytilus species are used as sentinels for the assessment of environmental health but sex or stage in the reproduction cycle is rarely considered even though both parameters are likely to influence responses to pollution. We have validated the use of a qPCR assay for sex identification and related the levels of transcripts to the reproductive cycle. A temporal study of mantle of Mytilus edulis found transcripts of male-specific vitelline coat lysin (VCL) and female-specific vitelline envelope receptor for lysin (VERL) could identify sex over a complete year. The levels of VCL/VERL were proportional to the numbers of sperm/ova and are indicative of the stage of the reproductive cycle. Maximal levels of VCL and VERL were found in February 2009 declining to minima between July - August before increasing and re-attaining a peak in February 2010. Water temperature may influence these transitions since they coincide with minimal water temperature in February and maximal temperature in August. An identical pattern of variation was found for a cryptic female-specific transcript (H5) but a very different pattern was observed for oestrogen receptor 2 (ER2). ER2 varied in a sex-specific way with male > female for most of the cycle, with a female maxima in July and a male maxima in December. Using artificially spawned animals, the transcripts for VCL, VERL and H5 were shown to be present in gametes and thus their disappearance from mantle is indicative of spawning. VCL and VERL are present at equivalent levels in February and July-August but during gametogenesis (August to January) and spawning (March to June) VCL is present at lower relative amounts than VERL. This may indicate sex-specific control mechanisms for these processes and highlight a potential pressure point leading to reduced reproductive output if environmental factors cause asynchrony to gamete maturation or release
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