双层桥梁耦合系统的强迫振动

本文研究作为双层桥模型的梁方程耦合系统，利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ不动点定理，得到了一个关于这种系统的解的存在性定理，它类似于ＭｃＫｅｎｎａ和Ｗａｌｔｅｒ文２中关于吊桥方程的一个定理。     

Anomalous dispersion in the Belousov-Zhabotinsky reaction: Experiments and modeling

We report results on dispersion relations and instabilities of traveling waves in excitable systems. Experiments employ solutions of the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction confined to thin capillary tubes which create a pseudo-one-dimensional system. Theoretical analyses focus on a three-variable reaction-diffusion model that is known to reproduce qualitatively many of the experimentally observed dynamics. Using continuation methods, we show that the transition from normal, monotonic to anomalous, single-overshoot dispersion curves is due to an orbit flip bifurcation of the solitary pulse homoclinics. In the case of “wave stacking”, this anomaly induces attractive pulse interaction, slow solitary pulses, and faster wave trains. For “wave merging”, wave trains break up in the wake of the slow solitary pulse due to an instability of wave trains at small wavelength. A third case, “wave tracking” is characterized by the non-existence of solitary waves but existence of periodic wave trains. The corresponding dispersion curve is a closed curve covering a finite band of wavelengths.     

一阶线性模糊微分方程的解

利用文[8]中的扩展原理求解了一阶线性模糊微分方程,给出了解可表示的条件,讨论了同其他求解方法之间的关系,最后给出了具体算例。     

Existence and Uniqueness of Solutions for a Class of Reaction-diffusion Systems

61.Intr0ducti0nInthispaper,wediscussareactionnetinacombusti0nmodel:V={R,,R2},whereR,andR2aredistinctreacti0nprocesses:Rl:A1+A,-A,,R2:A2+A3-P,A,(j=1,2,3)denotesthereactant,andPdenotestheinertproduct.Thesereactionsareexothermicreactions-LetQ,,Q2standforheatenergiesandU=(U,,U,,U,,U,)forstatevariablesdescribingreactions,whereUoisreactiontemporature,andU,(j=1,2,3)isthemolarityofthej-threactant.AssumethatV,(i=1,2)isthereactantvariablefortheithreactionpr0cess:V,=(Q,,1,-l,l)",V2=(Q,,O,-l,-…     

一个广义Bihari型不等式及其应用

本文对定义于一定有序局部紧空间上的向量值函数建立一个Ｂｉｈａｒｉ型积分不等式，并给出其对于非线性Ｖｏｌｔｅｒｒａ型积分方程的若干应用。     

几类非线性差分方程的对称和精确解

本文将微分方程的Lie变换群方法推广到差分方程,给出了三类非线性差分方程的不变变换,利用这种变换由差分方程的平凡解得到非平凡的单参数解族。     

Localization and Screening Enhancement in Asymmetric Binary Ionic Mixtures

The equation of state of binary ionic mixtures of similar ions, such as nitrogen, oxygen and carbon, has been extensively studied. The study of dense asymmetric mixtures, where Z₂ >> Z₁, has primarily focused on mixtures of hydrogen and iron at solar conditions. Using molecular dynamics simulations, we examine the behavior of highly asymmetric binary ionic mixtures, where the coupling of the high‐Z species may be orders of magnitude higher than the coupling of the low‐Z species. For the conditions we have studied, we find that strong correlations and signatures of solidification occur in the high‐Z species, while the low‐Z species exists as a freely flowing fluid within the high‐Z solid matrix. Solidification of the low‐Z species is correlated with the coupling between the two components. Using the Widom expansion method, we compute the plasma screening enhancement of the nuclear reaction rates for Z = 1 in a high‐Z matrix. We also provide some estimates of the coefficient of binary diffusion in the mixture. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

RN上的临界非齐次多重调和方程的多解存在性

讨论了 RN上带非负扰动的临界非齐次多重调和方程的多解存在性 .首先由泛函弱连续性方法获得方程的第一个解 ,再由山路引理获得方程的第二个解 .本文的这种求解方法和这些结果不仅适用于 RN 上的二阶椭圆方程 ,而且也适用于尚未解决的 RN 上的双调和方程     

Spatial chaotic structure of attractors of reaction-diffusion systems

The dynamics described by a system of reaction-diffusion equations with a nonlinear potential exhibits complicated spatial patterns. These patterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. The estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem.

     

Ultrahigh pressure equation of state of tantalum to 310 GPa

ABSTRACT

The isothermal compression of transition metal tantalum (Ta) was studied in a diamond anvil cell by X-ray diffraction utilizing rhenium (Re) and gold (Au) as internal X-ray pressure standards. The Re pressure marker was employed during non-hydrostatic compression to pressures up to 310?GPa while the Au pressure marker was used during quasi-hydrostatic compression in a neon pressure-transmitting medium to 80?GPa. Two ultra-high pressure experiments were conducted on Ta and Re mixtures utilizing focused-ion beam machined toroidal diamond anvils with central flats varying from 8 microns to 16 microns in diameter. The Ta metal was observed to be stable in the body-centered-cubic phase to a volume compression V/V₀?=?0.581. The measured equations of state (EOS) of Ta using two different calibrations of the Re pressure marker are compared with the ambient temperature isotherm derived from shock compression data. We provide a detailed analysis of EOS fit parameters for Ta under quasi-hydrostatic and non-hydrostatic conditions.