Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.     

氯化钠水溶液结构的研究

利用上海光源(SSRF)的第三代同步辐射光源测定室温下摩尔浓度分别为0.172 mol/L、0.343 mol/L、0.699 mol/L、1.064 mol/L、2.832 mol/L、3.910 mol/L、5.289 mol/L的NaCl水溶液的X射线散射数据。由X射线散射数据可知,随着NaCl水溶液浓度的增大,X射线散射曲线的特征峰由12.6°到13.4°发生偏移。运用Pair Distribution Function(PDF)理论对X射线散射数据进行处理,得到了不同浓度NaCl水溶液及纯水的差值对分布函数,其中的O-O峰随着浓度的增大逐渐分裂为两峰,O-O峰位在0.282 nm处。利用分子动力学模拟研究不同浓度的NaCl水溶液,表明Na+、Cl-的引入对水分子的氢键结构有一定的破坏,当浓度大于15%时,这种效果尤其明显。Na+、Cl-均存在两层水化层,各离子间配位数随浓度的增大而减少。H2O分子的自扩散系数远大于Na+和Cl-的自扩散系数,后两者的值随浓度的增大逐渐减少,Na+和Cl-的水化半径均随浓度增大而降低。     

Precise lattice parameter measurements in CsCl-Br solid solutions between room temperature and 90°K by powder x-ray diffraction

Solid solutions of CsCl-Br in five different concentrations were prepared in sealed quartz tubes by heating the mixture to 1123°K for 6–8 hr and quenching to room temperature. X-ray diffractograms were taken at eight different temperatures between room temperature and 90°K for these solid solutions using the YPC50NM powder diffractometer and a continuous flow cryostat. The observed lattice parameters for each sample at each temperature obtained from the powder diffractograms were then extrapolated to give the true lattice parameters using the least square method with Nelson-Riley extrapolation scheme. The values of the true lattice parameters at each concentration and at each temperature were tabulated and the results discussed. It is shown that the lattice parameters vs temperature for some concentrations exhibit an anomalous behaviour. Contribution No. 691     

Variations on a theme by Mark Kac

Mark Kac's theorem on the mean recurrence time in a stationary stochastic process in discrete time with discrete states is taken as the starting point for a series of variations, most of which are formulated in terms of 0–1 processes. Whereas the original theorem deals with the mean recurrence time of a given state under the condition that the state is realized at time 0, this condition is dropped in part of the variations; two others refer to the variance of the recurrence time and two to the Poincaré cycle of a dynamical system. Most variations consist in inequalities and formal identities for the mean first-arrival time and subsequent recurrence times for the given state.     

Randomly transitional phenomena in the system governed by Duffing's equation

This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon.     

Analysis of polymer adsorption onto colloidal particles

The structure of the layer formed after polymer adsorption onto a spherical particle is numerically studied by means of the application of the Single-Chain Mean-Field theory. We have determined several overall layer properties including the monomer volume fraction profiles, the layer thickness, adsorbances related to loops and to tails, as well as the variation of the crossover distance between loops and tails for different particle radii and fixed polymer length. When the radius of the sphere is small enough to affect the loop layer, one enters a single-adsorbed-chain regime, characterized by a critical sphere radius. In this regime, structural changes in the adsorbed layer arise. For such small sphere, the loop layer is confined to a region whose thickness is of the order of the radius of the adsorbing sphere, and two long tails dominate the outer layer and the adsorbance due to tails dominates that due to loops. An analysis of the structure of the outer tail layer for this small sphere case is also presented.     

Towards a general solution of the Hamiltonian constraints of General Relativity

The present work has a double aim. On the one hand, we call attention on the relationship existing between the Ashtekar formalism and other gauge-theoretical approaches to gravity, in particular the Poincaré Gauge Theory. On the other hand, we study two kinds of solutions for the constraints of General Relativity, consisting of two mutually independent parts, namely a general three-metric-dependent contribution to the extrinsic curvature K _ab in terms of the Cotton–York tensor, and besides it further metric independent contributions, which we analyze in particular in the presence of isotropic three-metrics.     

Darboux Transformation for Tzitzeica Equation

We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem. The explicit solution of Tzitzeica equation is obtained.     

New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method

In this paper, the nonlinear Boussinesq equations with the conformable time-fractional derivative are solved analytically using the well-established modified Kudryashov method. As a consequence, a number of new exact solutions for this type of equations are formally derived. It is believed that the method is one of the most effective techniques for extracting new exact solutions of nonlinear fractional differential equations.     

Multiple exp-function method for soliton solutions of nonlinear evolution equations

We applied the multiple exp-function scheme to the(2+1)-dimensional Sawada-Kotera(SK) equation and(3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model.