1,037 research outputs found
Solution of the generalized periodic discrete Toda equation II; Theta function solution
We construct the theta function solution to the initial value problem for the
generalized periodic discrete Toda equation.Comment: 11 page
Two dimensional periodic box-ball system and its fundamental cycle
We study a 2-dimensional Box-Ball system which is a ultradiscrete analog of
the discrete KP equation. We construct an algorithm to calculate the
fundamental cycle, which is an important conserved quantity of the 2-dim.
Box-Ball system with periodic boundary condition, by using the tropical curve
theory.Comment: 16 pages, 5 figure
Tropical Krichever construction for the non-periodic box and ball system
A solution for an initial value problem of the box and ball system is
constructed from a solution of the periodic box and ball system. The
construction is done through a specific limiting process based on the theory of
tropical geometry. This method gives a tropical analogue of the Krichever
construction, which is an algebro-geometric method to construct exact solutions
to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur
Ultradiscretization of the solution of periodic Toda equation
A periodic box-ball system (pBBS) is obtained by ultradiscretizing the
periodic discrete Toda equation (pd Toda eq.). We show the relation between a
Young diagram of the pBBS and a spectral curve of the pd Toda eq.. The formula
for the fundamental cycle of the pBBS is obtained as a colloraly.Comment: 41 pages; 7 figure
Bilinear Equations and B\"acklund Transformation for Generalized Ultradiscrete Soliton Solution
Ultradiscrete soliton equations and B\"acklund transformation for a
generalized soliton solution are presented. The equations include the
ultradiscrete KdV equation or the ultradiscrete Toda equation in a special
case. We also express the solution by the ultradiscrete permanent, which is
defined by ultradiscretizing the signature-free determinant, that is, the
permanent. Moreover, we discuss a relation between B\"acklund transformations
for discrete and ultradiscrete KdV equations.Comment: 11 page
Solution of the genaralized periodic discrete Toda equation
A box-ball system with more than one kind of balls is obtained by the
generalized periodic discrete Toda equation (pd Toda eq.). We study the pd Toda
equation in view of algebraic geometry. The time evolution of pd Toda eq. is
linearized on an algebraic variety, and theta function solutions are obtained.Comment: 18pages, 1figur
Uncomputably noisy ergodic limits
V'yugin has shown that there are a computable shift-invariant measure on
Cantor space and a simple function f such that there is no computable bound on
the rate of convergence of the ergodic averages A_n f. Here it is shown that in
fact one can construct an example with the property that there is no computable
bound on the complexity of the limit; that is, there is no computable bound on
how complex a simple function needs to be to approximate the limit to within a
given epsilon
Isotopic dependence of the giant monopole resonance in the even-A ^{112-124}Sn isotopes and the asymmetry term in nuclear incompressibility
The strength distributions of the giant monopole resonance (GMR) have been
measured in the even-A Sn isotopes (A=112--124) with inelastic scattering of
400-MeV particles in the angular range
--. We find that the experimentally-observed GMR energies
of the Sn isotopes are lower than the values predicted by theoretical
calculations that reproduce the GMR energies in Pb and Zr very
well. From the GMR data, a value of MeV is obtained
for the asymmetry-term in the nuclear incompressibility.Comment: Submitted to Physical Review Letters. 10 pages; 4 figure
Creation of ballot sequences in a periodic cellular automaton
Motivated by an attempt to develop a method for solving initial value
problems in a class of one dimensional periodic cellular automata (CA)
associated with crystal bases and soliton equations, we consider a
generalization of a simple proposition in elementary mathematics. The original
proposition says that any sequence of letters 1 and 2, having no less 1's than
2's, can be changed into a ballot sequence via cyclic shifts only. We
generalize it to treat sequences of cells of common capacity s > 1, each of
them containing consecutive 2's (left) and 1's (right), and show that these
sequences can be changed into a ballot sequence via two manipulations, cyclic
and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various
kink-like structures are traveling along the system like particles under the
time evolution of this rule.Comment: 31 pages. Section 1 changed and section 5 adde
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