Riemann boundary value problems and reflection of shock for the Chaplygin gas

In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp.     

A Renormalization Group Study of the Ising Model on a Triangular Lattice with Long-Range Interactions

The critical exponents of the triangular lattice Ising model with long-range interactions γ^-s are calculated by the real space renormalization group. Using the simplest Kadanoff blocks and the lowest approximation of cumulant expansion, it is shown that there exists a finite critical temperature when 4(1 - ㏑2/㏑3) < s < 4.     

A note on the spheroidal modes vibration of an elastic sphere in linear viscoelastic fluid

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing, and also to investigate materials mechanical properties. An analytical approach based on the exact theory has been developed in this paper, to establish a new accurate and simple generalized frequency equation to predict spheroidal vibration of an elastic nanosphere, in a compressible viscoelastic fluid using linear Maxwell fluid model. To demonstrate the accuracy of the present approach, a comparison is made with the published theoretical results in the literature in some particular cases, which shows a very good agreement. Thus, the obtained frequency equation can be very useful to interpret the experimental measurements of vibrational dynamics of nanospheres and can serve as benchmark solution in design of liquid sensors.     

On the integrability aspects of nonparaxial nonlinear Schrödinger equation and the dynamics of solitary waves

The integrability nature of a nonparaxial nonlinear Schrödinger (NNLS) equation, describing the propagation of ultra-broad nonparaxial beams in a planar optical waveguide, is studied by employing the Painlevé singularity structure analysis. Our study shows that the NNLS equation fails to satisfy the Painlevé test. Nevertheless, we construct one bright solitary wave solution for the NNLS equation by using the Hirota's direct method. Also, we numerically demonstrate the stable propagation of the obtained bright solitary waves even in the presence of an external perturbation in a form of white noise. We then numerically investigate the coherent interaction dynamics of two and three bright solitary waves. Our study reveals interesting energy switching among the colliding solitary waves due to the nonparaxiality.     

Exploring the Origin of Maximum Entropy States Relevant to Resonant Modes in Modern Chladni Plates

The resonant modes generated from the modern Chladni experiment are systematically confirmed to intimately correspond to the maximum entropy states obtained from the inhomogeneous Helmholtz equation for the square and equilateral triangle plates. To investigate the origin of maximum entropy states, the inhomogeneous Helmholtz equation is modified to consider the point interaction coming from the driving oscillator. The coupling strength associated with the point interaction is characterized by a dimensionless factor α. The δ potential of the point interaction is numerically modelled by a truncated basis with an upper index N. The asymptotic behavior for the upper index N is thoroughly explored to verify that the coupling strength of α = 1.0 can make the theoretical resonant modes agree excellently with the maximum entropy states as N→∞. It is further authenticated that nearly the same resonant modes can be obtained by using a larger coupling strength α when a smaller upper index N is exploited in the calculation.     

Dynamics of Self-Organized and Self-Assembled Structures,by Rashmi C. Desai and Raymond Kapral

The arrival of the first hard X-ray free electron laser facilities promises new advances in structural dynamics and nanoscale imaging that will have impact across the sciences. This introductory review is intended to cover the basic physics behind this potential and illustrate the current state-of-the-art by discussing a number of recent findings from the LCLS facility at the Stanford Linear Accelerator Centre (SLAC). We concentrate on the new science using these light sources rather than the new light source technology itself, although a brief introduction to the operation of LCLS is given. Emphasis is placed upon the new regime of high intensity X-ray matter interaction physics with ultrashort X-ray pulses. We discuss how the unique combination of X-ray parameters will open new opportunities for time resolved structural studies and how the high brightness enables a new class of coherent diffraction X-ray imaging. The potential importance of this new imaging method in the study of nanostructures and biological systems at the sub-cellular and molecular level will be outlined.     

Effect of Solute‐Polymer Interactions on Sorption and Diffusion in Polyacrylamide Gels

Solute‐polymer interactions can exert a large effect on selective sorption and permeation in polyacrylamide (PAAm) gels. In order to investigate this effect, three probe polyelectrolytes, sodium polystyrene sulphonate (PSS), polyvinylpyrrolidone (PVP), and sulfonated polyaniline (SPANI), were chosen as probe species in sorption, release, and permeation experiments in PAAm gels. For PAAm gels with trapped SPANI, FTIR spectroscopy has confirmed that there exists hydrogen‐bonding between SPANI and PAAm. In addition, rigid‐chain SPANI has an intense tendency to aggregate; it is likely that the effective chains of the PAAm matrices are enwrapped in these aggregates. Hydrogen‐bonding and aggregation resulted in that the release kinetics of SPANI from PAAm gels exhibited a remarkable “lag time”, as long as 100 h (lag period means that in the initial period there is no detectable SPANI released from PAAm gels.), the releasing rate of SPANI was very slow, and the selective sorption of SPANI in PAAm gels was extremely high. On the other hand, the release and permeation of PVP and PSS through PAAm gels were much faster than SPANI, and the selective sorption were close to unity. From these facts it could be deduced that there is no or only weak interaction between PAAm and PSS (or PVP). Adding of concentrated support electrolyte resulted in decrease of the release rate and a two‐magnitude decrease of the calculated diffusion coefficients of PSS; the effect of support electrolyte on release and permeation of PSS was partly attributed to the electrostatic interaction.     

Dissipative particle dynamics simulation for the effect of interaction on the self-assembly behaviours of heterogemini surfactant in aqueous solution

Self-assembly behaviours of heterogemini surfactant in aqueous solution have been explored by means of dissipative particle dynamics simulation. Five kinds of heterogemini molecules are involved and a variety of novel morphologies have been obtained. Results based on detailed analyses show that head–tail and tail–water interactions play different roles in the formation of six kinds of self-assembly morphologies. The key factors are tail–water and head–tail repulsions separately for morphology with small (sphere) and relatively large scales (rod, planar grid, lamella and tunnels). Besides, the appearance of network in only one system can be regarded as a particular type of intermediate state. Coexistence of several sphere micelles in an amplified dissipative particle dynamics system gives us a better understanding of interactions inside the soft matter. Our simulation results can provide a theoretical guide to further research towards self-assembly behaviours of heterogemini surfactants and practical applications of these matters.     

Magnetic properties of ferromagnetic diluted Zn x Cd1–x Cr2Se4 spinels are studied by Green's functions,mean field theory and high temperature series expansions theories

The field induced reorientation of the magnetization of ferromagnetic (or antiferromagnetic) structure is treated within the framework of many-body Green's function theory by considering all components of the magnetization. The mean field theory is used to calculate the nearest neighbour and the next-neighbour super-exchange J₁(Cr–Cr) and J₂(Cr–(Zn(Cd)–Se)–Cr), respectively, for the Zn_1–x Cd _x Cr₂Se₄ in the range 0 < x < 1. The intraplanar and the interplanar interactions are deduced. The high temperature series expansions (HTSEs) are derived for the magnetic susceptibility and the two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation (RPA). The magnetic phase diagram is deduced. A spin glass phase is predicted for intermediate range of concentration. The obtained results are comparable with those obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) have been deduced. The obtained values are comparable to those of 3D Heisenberg model.     

Interaction Between Pr3☎ Pairs and Excitons in CsCdBr3

CsCdBr₃ consists of linear chains of [CdBr₆]^4- octahedra separated by Cs^? ions. The excited states of the covalently bound [CdBr₆]^4- octahedra form the lowest excitonic states of the crystal lattice. The trivalent Pr ions substitute for the divalent Cd ions. For reasons of charge compensation in the linear Cd^2? chains, pair centers of the form Pr^3?-(Cd vacancy)-Pr^3? are predominantly formed. In CsCdBr₃ the optical band gap is wider than the electronic one. This allows to study the interaction between Pr^3? ions and excitons by means of optical spectroscopy. The interaction leads to quantum up- and down-conversion generating one photon from two lower ones in energy and vice versa. Related experiments are discussed.