396 research outputs found
Inertial manifolds for Burgers' original model system of turbulence
AbstractThe existence of inertial manifolds for Burgers' original mathematical model system of turbulence is investigated. The system consists of two equations and enjoys the characteristic quantity: the Reynolds number. Our object in this article is to express the existence in terms of this Reynolds number. The difficulty of first order derivatives is circumvented by the method originally due to M. Kwak
A Model with Simultaneous Dynamical Breaking of Supersymmetry and GUT Gauge Symmetry
We try to construct a model in which supersymmetry and grand unified gauge
symmetry are dynamically broken at the same time. In this model SUSY breaking
is mediated mainly by massive vector multiplet, and a new solution for the mu
problem is proposed.Comment: 9 pages; a reference adde
Partially Solvable Anisotropic t-J Model with Long-Range Interactions
A new anisotropic t-J model in one dimension is proposed which has long-range
hopping and exchange. This t-J model is only partially solvable in contrast to
known integrable models with long-range interaction. In the high-density limit
the model reduces to the XXZ chain with the long-range exchange. Some exact
eigenfunctions are shown to be of Jastrow-type if certain conditions for an
anisotropy parameter are satisfied. The ground state as well as the excitation
spectrum for various cases of the anisotropy parameter and filling are derived
numerically. It is found that the Jastrow-type wave function is an excellent
trial function for any value of the anisotropy parameter.Comment: 10 pages, 3 Postscript figure
Dynamical Structure Factors of the S=1/2 Bond-Alternating Spin Chain with a Next-Nearest-Neighbor Interaction in Magnetic Fields
The dynamical structure factor of the S=1/2 bond-alternating spin chain with
a next-nearest-neighbor interaction in magnetic field is investigated using the
continued fraction method based on the Lanczos algorithm. When the plateau
exists on the magnetization curve, the longitudinal dynamical structure factor
shows a large intensity with a periodic dispersion relation, while the
transverse one shows a large intensity with an almost dispersionless mode. The
periodicity and the amplitude of the dispersion relation in the longitudinal
dynamical structure factor are sensitive to the coupling constants. The
dynamical structure factor of the S=1/2 two-leg ladder in magnetic field is
also calculated in the strong interchain-coupling regime.
The dynamical structure factor shows gapless or gapful behavior depending on
the wave vector along the rung.Comment: 8 pages, 4 figures, to appear in Journal of the Physical Society of
Japan, vol. 69, no. 10, (2000
Spiral solutions for a weakly anisotropic curvature flow equation
The presence of steps associated with screw dislocations plays a key role for the growth of crystal surfaces. In geometric model the motion of curves describing location of steps is governed by curvature flow equations with a driving force term. We show the existence of spiral-shaped solutions for such an equation when anisotropic effect is small. Such a spiral-shaped solution is ahown to be stable and unique up to translation of the time
Nonlinear Parabolic Equations arising in Mathematical Finance
This survey paper is focused on qualitative and numerical analyses of fully
nonlinear partial differential equations of parabolic type arising in financial
mathematics. The main purpose is to review various non-linear extensions of the
classical Black-Scholes theory for pricing financial instruments, as well as
models of stochastic dynamic portfolio optimization leading to the
Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both
problems can be represented by solutions to nonlinear parabolic equations.
Qualitative analysis will be focused on issues concerning the existence and
uniqueness of solutions. In the numerical part we discuss a stable
finite-volume and finite difference schemes for solving fully nonlinear
parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387
Spin Wave Response in the Dilute Quasi-one Dimensional Ising-like Antiferromagnet CsCo_{0.83}Mg_{0.17}Br_3
Inelastic neutron scattering profiles of spin waves in the dilute
quasi-one-dimensional Ising-like antiferromagnet CsCo_{0.83}Mg_{0.17}Br_3 have
been investigated. Calculations of S^{xx}(Q,omega), based on an effective spin
Hamiltonian, accurately describe the experimental spin wave spectrum of the 2J
mode. The Q dependence of the energy of this spin wave mode follows the
analytical prediction
omega_{xx}(Q)=(2J)(1-5epsilon^{2}cos^{2}Qa+2epsilon^{2})^{1/2}, calculated by
Ishimura and Shiba using perturbation theory.Comment: 13 pages, 4 figure
Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF6
Thermodynamic properties and elementary excitations in
one-dimensional Heisenberg antiferromagnet KCuGaF were investigated by
magnetic susceptibility, specific heat and ESR measurements. Due to the
Dzyaloshinsky-Moriya interaction with alternating -vectors and/or the
staggered -tensor, the staggered magnetic field is induced when subjected to
external magnetic field. Specific heat in magnetic field clearly shows the
formation of excitation gap, which is attributed to the staggered magnetic
field. The specific heat data was analyzed on the basis of the quantum
sine-Gordon (SG) model. We observed many ESR modes including one soliton and
three breather excitations characteristic of the quantum SG model.Comment: 4 pages, 5 figures, to appear in J. Phys. Soc. Jpn., vol. 76, no.
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