Phase conjugator with two coherent beams in a BaTiO3:Ce crystal

A phase conjugator which includes two coherent beams that are incident upon one of a-faces of a BaTiO3:Ce crystal without internal reflection is performed experimentally. Based on the four-wave mixing, the mechanism of this conjugator is investigated numerically. In comparison with the corresponding self-pumped phase conjugator, the phase-conjugate behavior of this conjugator is established much more quickly, its phase conjugate reflectivity is greater in some cases and the intensity threshold is lower by over two orders of magnitude. The configuration of this conjugator is easy to perform because the output response exists over a wide range of angular and lateral positions of the two incident beams on the crystal.     

Analysis of weak solutions for the phase-field model for lithium-ion batteries

We study a phase-field model for lithium-ion batteries of olivine LiFePO₄. During electrochemical cycling the fundamental behavior of the crystal is the diffusion of Li which controls the movement of the phase boundary without changing the olivine topology. This model with diffusive phase interfaces consists of two nonlinear parabolic equations of second order. We first prove the existence of global solutions to an initial-boundary value problem of this model. Numerical experiments of the model are then performed to simulate the evolution of lithium concentration and of phase interfaces.     

Novel energy stable schemes for Swift-Hohenberg model with quadratic-cubic nonlinearity based on the H−1-gradient flow approach

The Swift-Hohenberg model is a very important phase field crystal model which can be described many crystal phenomena. This model with quadratic-cubic nonlinearity based on the H^??1-gradient flow approach is a sixth-order system which satisfies mass conservation and energy dissipation law. The negative energy of this model will bring huge difficulties to energy stability for many existing approaches. In this paper, we consider two linear, second-order and unconditionally energy stable schemes by linear invariant energy quadratization (LIEQ) and modified scalar auxiliary variable (MSAV) approaches. These two schemes will be effective for all negative E₁. Furthermore, we proved that all the semi-discrete schemes are unconditionally energy stable with respect to a modified energy. Finally, we present various 2D numerical simulations to demonstrate the stability and accuracy.

     

Electron paramagnetic resonance of Mn2+ in (NH4)2SO4 single crystal

Electron paramagnetic resonance investigation of Mn²⁺ in (NH₄)₂SO₄ single crystal is discussed both in paraelectric and ferroelectric phases of the crystal. Mn²⁺ is found to substitute one of the two possible types (α andβ) of NH ₄ ⁺ ions and get associated with the second type of NH ₄ ⁺ vacancy, the vacancy being the second distant neighbour in thebc-plane. As The line joining Mn²⁺ substituted NH ₄ ⁺ site and NH ₄ ⁺ vacancy lies at an angle of 18° from the crystallographicb-axis in thebc-plane. As the temperature is lowered to ? 56° C the crystal becomes ferroelectric and the spectrum in the paraelectric phase splits into two from which it appears that two sets of Mn²⁺ sites which are magnetically equivalent in the paraelectric phase become inequivalent in the ferroelectric phase. The spin Hamiltonian analysis is presented for the spectrum in the paraelectric phase.     

Distribution sensitivity in a highway flow model

We examine a model of traffic flow on a highway segment, where traffic can be impaired by random incidents (usually, collisions). Using analytical and numerical methods, we show the degree of sensitivity that the model exhibits to the distributions of service times (in the queueing model) and incident clearance times. Its sensitivity to the distribution of time until an incident is much less pronounced. Our analytical methods include an M/G_t/∞ analysis (G_t denotes a service process whose distribution changes with time) and a fluid approximation for an M/M/c queue with general distributions for the incident clearance times. Our numerical methods include M/PH₂/c/K models with many servers and with phase‐type distributions for the time until an incident occurs or is cleared. We also investigate different time scalings for the rate of incident occurrence and clearance. Copyright © 2009 John Wiley & Sons, Ltd.     

Radioactive ion beam line in Lanzhou

Radioactive ion beam line in Lanzhou (RIBLL) has been constructed for the production of short-lived radioactive nuclei and studies of exotic nuclei far from the β-stability line. It has been put into operation recently at the National Laboratory of Heavy Ion Accelerator Lanzhou. RIBLL consists of two doubly achromatic parts with a solid acceptance ΔΩ⩾6.5 msr, momentum acceptance Δp/p=±5% and maximum magnetic rigidityBp _max=4.2 Tm. The second part of RIBLL serving as a spectrometer gives an element resolutionZ/ΔZ>150 and mass resolutionA/ΔA>300. The polarized secondary beams can be obtained by using a swinger dipole magnet to change the incident direction of primary projectile from 0° to 5°. The shortest lift time for secondary beams on RIBLL is less than 1 μs. First experiments were performed with neutron rich nuclei for understanding the properties of halo nuclei and exotic nuclear reactions. Project supported by the Chinese Academy of Sciences, the State Science and Technology Commission of China, the National Natural Science Foundation of China (Grant No. 19675055).     

A new type of edge-derived vertex coloring

We study the minimum number of weights assigned to the edges of a graph G with no component K₂ so that any two adjacent vertices have distinct sets of weights on their incident edges. The best possible upper bound on this parameter is proved.     

Conditions for quasi Cerenkov radiation,generated by optical second harmonic polarisation in a nonlinear cristal

The analogy between classical Cerenkov radiation and quasi Cerenkov radiation, induced by intense laser light in a nonlinear crystal, is described. The effect is compared with noncollinear phase matching. In certain cases of interaction in birefringent crystals only second harmonic light within a restricted angular region with respect to the optic crystal axis can be generated by quasi Cerenkov radiation, whereas for all other directions the noncollinear phase matching condition can be fulfilled. A calculation shows that in addition to fulfilment of the Cerenkov condition there exists for quasi Cerenkov radiation a restriction on the nonlinear crystal. This restriction corresponds to the laser intensity inside the nonlinear crystal. This restriction corresponds to the fact that for quasi Cerenkov radiation virtually only longitudinal momentum is conserved. As an example, second harmonic generation in LiNbO₃ with an Nd: glass laser is discussed.     

Phase transition in layered perovskite-like manganate Ca3Mn2O7 under high pressure

In situ high pressure energy dispersive X-ray diffraction measurements on the layered perovskite-like manganate Ca₃Mn₂O₇ powder under pressures were performed by using the diamond anvil cell with synchrotron radiation. The results show that the structure of layered perovskite-like manganate Ca₃Mn₂O₇ is unstable under pressure due to the easy compression of NaCl-type blocks. The structure of Ca₃Mn₂O₇ underwent two phase transitions under pressures in the range of 0–35 GPa. One was at about 1.3 GPa with the crystal structure changing from tetragonal to orthorhombic. The other was at about 9.5 GPa with the crystal structure changing from orthorhombic back to another tetragonal.     

Experimental study on the non- specularly reflected ultrasonic beam on a liquid- solid interface

The reflected fields of a slightly divergent ultrasonic beam on a liquid-solid interface are recorded by a Schlieren system, and the lateral beam displacements on the interface are measured. The range of the incident angle_i is around the Rayleigh angle_c. The displacements are found to decrease as the incident angle increases. Theoretical calculation reveals that the displacements decrease with the increase in the incident angle for a divergent incident beam, but increase with that for a convergent one. The calculated curve of- _i are in agreement with the experimental results.     

Growth morphology and structural characteristic of C70 single crystals

Large size C₇₀ single crystals with the dimension of more than 5 mm are grown from the vapor phase by controlling nucleation. X-ray diffraction and electron diffraction confirm that in the C₇₀ single crystal a phase of the hexagonal close-packed (hcp) structure coexists with a minor face-center-cubic (fcc) phase at room temperature. The morphologies and their formation mechanism of the C₇₀ single crystals are investigated by means of scanning electron micrascopy and optical microscopy. The influence of growth conditions on the morphologies of C₇₀ single crystals is discussed. Project supported by the National Natural Science Foundation of China (Grant No. 59772026).     

A classification of a class of C3 geometries

The purpose of this paper is to classify the class of Tits geometries of type C₃ in which any line is incident with precisely two planes. We show that any such geometry is either a building or a quotient of a building by a group of automorphisms of order 2. Our knowledge of buildings of this type enables us to list explicitly all possibilities.     

Control of a network of Euler-Bernoulli beams

The aim is to study the boundary controllability of a system modeling the vibrations of a network of N Euler-Bernoulli beams connected by n vibrating point masses. Using the classical Hilbert Uniqueness Method, the control problem is reduced to the obtention of an observability inequality. The solution is then expressed in terms of Fourier series so that it is also enough to show that the distance between two consecutive large eigenvalues of the spatial operator involved in this evolution problem is superior to a minimal fixed value. This property called spectral gap holds as soon as the roots of a function denoted by f_∞ (and giving the asymptotic behaviour of the eigenvalues) are all simple. For a network of N=2 different beams, this assumption on the multiplicity of the roots of f_∞ (denoted by (A)) is proved to be satisfied and controllability follows. For higher values of N, a numerical approach allows one to prove (A) in many situations and no counterexample has been found but the problem of giving a general proof of controllability remains open.     

Photo-production of pion pairs by polarised nucleons

The problems of production of pion pairs by polarised photon beams on polarised nucleons is examined. It is found that the angular distribution of pion pairs is sensitive to the state of polarisation of the incident photon beam.     

Colliding dissipative pulses—The shooting manifold

We study multi-pulse solutions in excitable media. Under the assumption that a single pulse is asymptotically stable, we show that there is a well-defined “shooting manifold,” consisting of two pulses traveling towards each other. In phase space, the two-dimensional manifold is a graph over the manifold of linear superpositions of two pulses located at x₁ and x₂, with x₁−x₂?1. It is locally invariant under the dynamics of the reaction-diffusion system and uniformly asymptotically attracting with asymptotic phase. The main difficulty in the proof is the fact that the linearization at the leading order approximation is strongly non-autonomous since pulses approach each other with speed of order one.     

Numerical simulation of oblique and multidirectional wave propagation and breaking on steep slope based on FEM model of Boussinesq equations

Creating a representative numerical simulation of the propagation and breaking of waves along slopes is an important problem in engineering design. Most studies on wave breaking have focused on the propagation of normal incident waves on gentle slopes. In practice, however, waves on steep slopes are obliquely incident or multidirectional irregular waves. In this paper, the eddy viscosity term is introduced to the momentum equation of the improved Boussinesq equations to model wave dissipation caused by breaking and friction, and a numerical model based on an unstructured finite element method (FEM) is established based on the governing equations. It is applied to simulate wave propagation on a steep slope of 1:5. Parallel physical experiments are conducted for comparative analysis that considered a large number of cases, including those featuring of normal and oblique incident regular and irregular waves, and multidirectional waves. The heights of the incident wave increase for different periods to represent different kinds of waves breaking. Based on examination, the effectiveness and accuracy of the numerical model is verified through a comprehensive comparison between the numerical and the experimental results, including in terms of variation in wave height, wave spectrum, and nonlinear parameters. Satisfactory agreement between the numerical and experimental values shows that the proposed model is effective in representing the breaking of oblique incident regular waves, irregular waves, and multidirectional incident irregular waves. However, the initial threshold of the breaking parameter η_t^(I) takes different values for oblique and multidirectional waves. This needs to be paid attention when the breaking of waves is simulated using the Boussinesq equations.     

Crystal Bases and Monomials for U q (G 2)-Modules

In this article, we give a new realization of crystal bases for irreducible highest weight modules over U _q (G ₂) in terms of monomials. We also discuss the natural connection between the monomial realization and tableau realization.

Communicated by K. Misra