Numerical analysis of the Toda lattice equations

Numerical solutions to three systems of integrable evolutionary equations from the Toda lattice hierarchy are analyzed. These are the classical Toda lattice, the second local dispersive flow, and the second extended dispersive flow. Special attention is given to the properties of soliton solutions. For the equations of the second local flow, two types of solitons interacting in a special manner are found. Solutions corresponding to various initial data are qualitatively outlined.     

JET: Preparing the future in fusion

JET (Joint European Torus) is the largest tokamak in the world and the only fusion facility able to operate with Tritium, the fusion fuel, and Beryllium, the ITER first wall material. JET also features the most complete remote handling equipment for invessel maintenance. As a multinational research center, JET provides logistic experience in preparing for operation of the global facility, tokamak ITER.Experiments on JET are focused on ITER-relevant studies, in particular on detailing the operational scenarios (EL My H-modes and advanced regimes), on enhancing the heating systems, on developing diagnostics for burning plasmas etc. Pioneering real-time control techniques have been implemented that maximize performance and minimize internal disturbances of JET plasmas. In helium plasmas, ion cyclotron heating (ICRH) created fast α-particles, mimicking their populations in future burning plasmas. The recent successful Trace Tritium campaign provided important new data on fuel transport. Current enhancements on JET include a new ITER-like ELM-resilient high power ICRH antenna (7 MW) and over twenty new diagnostics that will further extend the JET scientific capabilities and push the facility even closer to the ITER parameters.A special mention is given to the involvement of the fusion experts from Association EURATOM-IPP.CR, who have been actively participating in the collective use of JET facility for more than three years.     

On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method

For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P ₀ and Q ₀.     

Phase Diagrams of Polytype Transformations in Close-Packed Crystals Including Metastable States

The paper offers a method for calculating phase diagrams of polytype transformations in close-packed crystals based on the generalized axial Ising's model of finite dimensions at non-zero temperatures. Using the Metropolis algorithm, the behavior of systems with polytype transitions is studied under the conditions of changing external shear stress and temperature. The longest polytype period considered here is taken to be 30 close-packed planes.     

Self-consistent treatment of the Anderson model

TheN-fold degenerate Anderson single impurity model in the infiniteU limit is treated by means of the irreducible Green functions method. In this approach a derivation of an exact Dyson equation and an exact self-energy operator is possible. The necessity of introducing auxiliary fields, such as slave-bosons is avoided.     

Periodic solutions of difference Runge-Kutta schemes

Translated from Matematicheskie Zametki, Vol. 49, No. 6, pp. 92–97, June, 1991.     

A symmetry-adapted force-constant lattice-dynamical model for single-walled carbon nanotubes

We develop a lattice-dynamical model based on the screw symmetry of single-walled carbon nanotubes that allows for reducing the size of the dynamical matrix to six, for all tube chiralities. The model uses force constants derived from fitting to the phonon dispersion of 2D graphite. We present the calculation procedure in a clear and transparent way, making the model easier to follow. We calculate the phonon dispersions of a number of nanotubes of different chiralities. The splitting of two highest Raman active modes and the radial breathing mode frequency are studied by changing the tube diameter and chirality.     

Quantum graph of Sierpinski gasket type: Computational experiment

A continuous model of the Sierpinski gasket (SG) is suggested. The Laplace operator on the SG is defined. An effective computational algorithm for solving the scattering problem is suggested. The self-similarity of the graph of transmission coefficient via the wave number k is observed. A violation of symmetry of the SG is considered. The results are compared with the discrete SG model. In memoriam V. A. Geyler