675 research outputs found
The Canonical Symmetry and Hamiltonian Formalism. II. Hamiltonian Operators
It is shown how the canonical symmetry is used to look for the hierarchy of
the Hamiltonian operators relevant to the system under consideration. It
appears that only the invariance condition can be used to solve the problem.Comment: 13 pages, LaTeX file, IHEP 93-6
Towards the ab initio based theory of the phase transformations in iron and steel
Despite of the appearance of numerous new materials, the iron based alloys
and steels continue to play an essential role in modern technology. The
properties of a steel are determined by its structural state (ferrite,
cementite, pearlite, bainite, martensite, and their combination) that is formed
under thermal treatment as a result of the shear lattice reconstruction "gamma"
(fcc) -> "alpha" (bcc) and carbon diffusion redistribution. We present a review
on a recent progress in the development of a quantitative theory of the phase
transformations and microstructure formation in steel that is based on an ab
initio parameterization of the Ginzburg-Landau free energy functional. The
results of computer modeling describe the regular change of transformation
scenario under cooling from ferritic (nucleation and diffusion-controlled
growth of the "alpha" phase to martensitic (the shear lattice instability
"gamma" -> "alpha"). It has been shown that the increase in short-range
magnetic order with decreasing the temperature plays a key role in the change
of transformation scenarios. Phase-field modeling in the framework of a
discussed approach demonstrates the typical transformation patterns
UV manifold and integrable systems in spaces of arbitrary dimension
The dimensional manifold with two mutually commutative operators of
differentiation is introduced. Nontrivial multidimensional integrable systems
connected with arbitrary graded (semisimple) algebras are constructed. The
general solution of them is presented in explicit form
On Z-graded loop Lie algebras, loop groups, and Toda equations
Toda equations associated with twisted loop groups are considered. Such
equations are specified by Z-gradations of the corresponding twisted loop Lie
algebras. The classification of Toda equations related to twisted loop Lie
algebras with integrable Z-gradations is discussed.Comment: 24 pages, talk given at the Workshop "Classical and Quantum
Integrable Systems" (Dubna, January, 2007
The Canonical Symmetry for Integrable Systems
The properties of discrete nonlinear symmetries of integrable equations are
investigated. These symmetries are shown to be canonical transformations. On
the basis of the considered examples, it is concluded, that the densities of
the conservation laws are changed under these transformations by spatial
divergencies.Comment: 17 pages, LaTeX, IHEP 92-14
Application of a Convective-Conductive Heat Transfer Model in the Heat Loss Analysis of a Heat Pipeline Under Flooding Conditions
This paper describes the numerical modeling of a convective-conductive heat transfer the area placing of a heat pipeline under flooding conditions. We have established that the heat loss of a heat pipeline under flooding conditions increases in the range from 1.5 to 64.3%, depending on the volume fraction of water in the insulation structure
A possible combinatorial point for XYZ-spin chain
We formulate and discuss a number of conjectures on the ground state vectors
of the XYZ-spin chains of odd length with periodic boundary conditions and a
special choice of the Hamiltonian parameters. In particular, arguments for the
validity of a sum rule for the components, which describes in a sense the
degree of antiferromagneticity of the chain, are given.Comment: AMSLaTeX, 15 page
Bethe roots and refined enumeration of alternating-sign matrices
The properties of the most probable ground state candidate for the XXZ spin
chain with the anisotropy parameter equal to -1/2 and an odd number of sites is
considered. Some linear combinations of the components of the considered state,
divided by the maximal component, coincide with the elementary symmetric
polynomials in the corresponding Bethe roots. It is proved that those
polynomials are equal to the numbers providing the refined enumeration of the
alternating-sign matrices of order M+1 divided by the total number of the
alternating-sign matrices of order M, for the chain of length 2M+1.Comment: LaTeX 2e, 12 pages, minor corrections, references adde
The Wave Functions for the Free-Fermion Part of the Spectrum of the Quantum Spin Models
We conjecture that the free-fermion part of the eigenspectrum observed
recently for the Perk-Schultz spin chain Hamiltonian in a finite
lattice with is a consequence of the existence of a
special simple eigenvalue for the transfer matrix of the auxiliary
inhomogeneous vertex model which appears in the nested Bethe ansatz
approach. We prove that this conjecture is valid for the case of the SU(3) spin
chain with periodic boundary condition. In this case we obtain a formula for
the components of the eigenvector of the auxiliary inhomogeneous 6-vertex model
(), which permit us to find one by one all components of
this eigenvector and consequently to find the eigenvectors of the free-fermion
part of the eigenspectrum of the SU(3) spin chain. Similarly as in the known
case of the case at our numerical and analytical
studies induce some conjectures for special rates of correlation functions.Comment: 25 pages and no figure
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