Structure-preserving analysis on Gaussian solitary wave solution of logarithmic-KdV equation

The existence of the Gaussian solitary wave solution in the logarithmic-KdV equation has aroused considerable interests recently. Focusing on the defects of the reported multi-symplectic analysis on the Gaussian solitary wave solution of the logarithmic-KdV equation and considering the dynamic symmetry breaking of the logarithmic-KdV equation, new approximate multi-symplectic formulations for the logarithmic-KdV equation are deduced and the associated structure-preserving scheme is constructed to simulate the evolution of the Gaussian solitary wave solution. In the structure-preserving simulation process of the Gaussian solitary wave solution, the residuals of three conservation laws are recorded in each step. Comparing with the reported numerical results, it can be found that the Gaussian solitary wave solution can be simulated with tiny numerical errors and three conservation laws are preserved perfectly in the simulation process by the structure-preserving scheme presented in this paper, which implies that the proposed structure-preserving scheme improved the precision as well as the structure-preserving properties of the reported multi-symplectic approach.

QUANTUM DYNAMICS OF THE CUBIT SYSTEM IN EXTERNAL FIELDS

A system of two dipole-dipole interacting two-level elements (qubits) in external fields is considered. It is shown that using the coherent states (CS) of the dynamic symmetry group of the SU(2)SU(2) system, the time evolution can be reduced to the "classical" dynamics of the complex parameters of the CS. The trajectories of the CS are constructed and the time dependences of the probability of finding qubits at the upper levels are calculated.

On One Method for Constructing a Programmed Trajectory in Problems of Stabilizing a Spacecraft

A method is proposed for constructing a programmed trajectory in the problems of stabilizing a spacecraft in a fixed time. The method allows constructing a programmed motion, because of which the spacecraft is stabilized in rotational motion around the axis of dynamic symmetry, and this axis is oriented along the local vertical. The proposed algorithm is based on the possibility of representing the unit sphere of quaternions in four-dimensional space as a ball with a radius in three-dimensional space. This makes it possible to obtain a visual representation of the spacecraft rotation trajectory.

Global Cities and Local Challenges: Booms and Busts in the London Real Estate Market

In this paper we investigate the dynamic features of house prices in London. Using a generalized smooth transition model (GSTAR) we show that dynamic symmetry in price cycles in the London housing market is strongly rejected. We also show that the GSTAR model is able to replicate the features of the observed cycle in the simulated data. Further, our results show that the proposed model performs well when compared to other linear and nonlinear specifications in a out-of-sample forecasting exercise.

Controlling the symmetry of inorganic ionic nanofilms with optical chirality

Manipulating symmetry environments of metal ions to control functional properties is a fundamental concept of chemistry. For example, lattice strain enables control of symmetry in solids through a change in the nuclear positions surrounding a metal centre. Light–matter interactions can also induce strain but providing dynamic symmetry control is restricted to specific materials under intense laser illumination. Here, we show how effective chemical symmetry can be tuned by creating a symmetry-breaking rotational bulk polarisation in the electronic charge distribution surrounding a metal centre, which we term a meta-crystal field. The effect arises from an interface-mediated transfer of optical spin from a chiral light beam to produce an electronic torque that replicates the effect of strain created by high pressures. Since the phenomenon does not rely on a physical rearrangement of nuclear positions, material constraints are lifted, thus providing a generic and fully reversible method of manipulating effective symmetry in solids.

A STUDY ON THE GROUND STATES STRUCTURE OF EVEN-EVEN 104−106Ru ISOTOPES

In this paper, even-even 104−106Ru isotopes have been studied the ground state bands using Matlab computer code (IBM-1.Mat). We apply the interacting boson model-1 (IBM-1) formula for O(6) symmetry in Ru isotopes with neutron N = 60, 62. The theoretical energy levels up to spin-parity 12+ have been obtained for 104−106Ru isotopes. The yrast states, gamma band, beta band, and B(E2) values are calculated for these nuclei. The published experimental and calculated R4/2 values indicate that the even-even 104−106Ru isotopes have O(6) dynamic symmetry. The present results have been compared to the published experimental data and are found good harmony with each other. The outcome of our investigation of the potential energy surfaces (PES) of both isotopes belonging to O(6) character.