Homoclinic orbits of the doubly periodic Davey-Stewartson equation

Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this note, the homoclinic orbits of the doubly periodic Davey-Stewartson equation are obtained by using the Hirota's bilinear methods, which is important to the study on the global property of the doubly periodic Davey-Stewartson equation.     

Space periodic solutions and rogue wave solution of the derivative nonlinear Schrödinger equation

The derivative nonlinear Schrödinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota’s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.     

Existence of solutions for the dynamic equation of ferrimagnets

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.     

Measurement of the Mie-Grüneisen equation of state for polyimide

An equation of state(EOS) is a thermodynamic equation describing the state of matter under a given set of physical conditions,and the Mie-Grüneisen EOS is a widely used EOS for solid materials.Polyimide is a typical complex high-molecular polymer of imide monomers which is widely used in the manufacture of parts for aerospace technology and for fabricating the inertial fusion energy shells(IFE).When a spacecraft collides with a meteoroids(or orbital debris) or the IFE shells are radiated by high power laser,the polyimide used in the equipment is in high pressure state.In order to study the safety of the spacecraft and IFE shells,the EOS of polyimide should be determined.In our research,the three key parameters of the Mie-Grüneisen EOS based on the shock adiabat for polyimide have been determined with two-stage light-gas gun experiments,i.e.the bulk speed of sound of polyimide is determined as 2.62±0.22 km/s,the linear Hugoniot slope coefficient is determined as 1.25±0.063,and the Grüneisen parameter at initial state is determined as 1.53±0.135.The Mie-Grüneisen EOS for polyimide is finally obtained,and the parameter values are proved reliable via the comparison of Grüneisen parameter value calculated from two different theoretical models using the experimental data.     

Existence of the classical solution and almost periodic solution for the Camassa-Holm type equations

Using Banach fixed point theorem and a priori estimate,the existence of periodic and almost periodic solutions of Ca massa-Holm type equation with a nonlinear boundary condition are respectively proved when g(x,t)is periodic or almost periodic function of time t.     

Exact n-width on the class of analytic functions in the space of continuous functions

Let ω(·) be a given concave modulus of continuity and ω(g,·) be the modulus of continuity of a function g∈C, where C is the space of 2π-periodic, continuous functions on R with norm ‖f‖C∶=maxt∈R|f(t)|, r,ω∞,β(r=0,1,2,…) denotes those 2π-periodic, real-valued functions f on R that are analytic in the strip Sβ∶=｛z∈C：|Imz|＜β｝, β＞0, and satisfy the restriction condition: ω(f(r),·)≤ω(·). In this paper, the exact n-width of the class of functions r,ω∞,β in the space C is determined.     

Effects of the internal waves on the time correlation of the acoustic fields in the East China Sea

Theactivitiesoftheinternalwavecanmakethetemperatureoftheseawatermassvarywithtimeandspace ,andthencanaffectthesoundpropagationinthesea[1～ 7] .Inaddition ,itcanreducethecorrela tiontimeoftheacousticfields .Forexample ,intheSWARM 95experiment,thecorrelationtimeatarangeof 4 0kmislessthan 2minutes[6 ] .InJune 2 0 0 1,theAsianSeasInternationalA cousticsExperiment (ASIAEX)wasperformedintheEastChinaSea (ECS) .Acombinedacoustic/ physicaloceanographicexperimentalmeasurementwas per formedtostu…     

Factors affecting runoff change in the upper reaches of the Yellow River

Riverrunoffisaffectedbycouplingactionofhumanactivityandnaturalconditions,includingclimaticchange,topographicalfeatures,soilandvegetationcover.Itsevolutionprocessshowsbothdeterministicrulesandstrongrandomness.Thechangeofrunoffcharacteristicscertainlyhasimpactondevelopmentandutilizationofwaterresources,andfurtheronsocialandeconomicdevelopment.Analysisontheevolutionprocessofriverrunoffwillnotonlybehelpfultounderstandingthecharacteristicofwaterresourcesandprovidingabasisforrationaldevelopmentandut…     

Effects of binders on the performance of electric double-layer capacitors of carbon nanotube electrodes

Polarizable electrodes of electric double layer capacitor (EDLCs) were made from carbon nanotubes. Effects of different binders, which are phenolic resin (PF) and polytetrafluoroethylene (PTFE), on the properties of polarizable electrodes are studied. Results indicate that the microstructure, pore size distribution and specific capacitance of the electrodes with PTFE binder are superior to those electrodes with PF binder after carbonization. The suitable binder (PTFE) for carbon nanotubes electrodes is proposed.     

Regularization strategy for the Cauchy problem of Laplace’s equation from the viewpoint of regularization theory

Within the framework of the regularization theory, a spectral regularization method is introduced and analyzed. The convergence estimate under an appropriate choice of regularization parameter is obtained. A numerical implementation is described. Numerical examples show that the proposed method is effective and stable.     

On the Cauchy problem of generalized complex Ginzburg-Landau equation in three dimensions

The generlized complex Ginzburg-Landau equation (CGL) under periodic boundary condition is studied. The existence of global solution for this equation is established under appropriate assumption on a nonlinear σ, which rigorously establishes the foundation for further investigation of this type of model.     

Variation of the FeMn ratio of ferromanganese crusts from the Central North Pacific: implication for paleoclimate changes

Contents of Fe, Mn and other elements in four ferromanganese crusts recovered from the central North Pacific are analyzed at high depth-resolution by electron microprobe for reconstructing factors controlling their deposition. Manganese (IV) in hydrogenetic ferromanganese crusts is mainly supplied as colloidal precipitates from the Oxygen Minimum Zone (OMZ), which concentrates high amounts of dissolved Mn (II). The iron is derived from carbonate dissolution and silicate particles of eolian dust. An increase in paleoproductivity during cooler climate would potentially lead to a decrease in Mn deposition due to enlargement of the OMZ which has a “temporary storage” effect for Mn. On the other hand, not affected by the OMZ, the iron entering the Fe-Mn crust would likely increase with the eolian dust input and surface productivity at glacial stages. As a result, the increasing FeMn ratio should indicate a cooling climate. This is supported by the following observations. In the profile of the past 1 Ma, the variations of FeMn ratio coincide with benthic oxygen isotope fluctuation in glacial-interglacial cycles. Three episodes with high FeMn ratios, approximately at 2.6, 1.8 and 0.8 Ma, are detected within the past 3 Ma and coincide with major climate transitions and cooling events. The secular evolution pattern of FeMn ratio in the Cenozoic is similar to the Pb isotope evolution which is mainly controlled by eolian dust and related to climate. The FeMn evolution pattern is also broadly consistent with the global deep-sea oxygen isotope records. Therefore, FeMn ratio recorded in the ferromanganese crusts may be a new proxy for climate change.     

Well-posedness of Cauchy problems for Korteweg-de Vries-Benjamin-Ono equation and Hirota equation

The well-posedness of the Cauchy problems to the Korteweg-de Vries-Benjamin-Ono equation and Hirota equation is considered. For the Korteweg-de Vries-Benjamin-Ono equation, local result is established for data in Hs(R)(s≥-1/8). Moreover, the global well-posedness for data in L2(R) can be obtained. For Hirota equation, local result is established for initial data in Hs(s≥1/4) .In addition, the local solution is proved to be global in Hs (s≥1) if the initial data are in Hs (s≥1) by energy inequality and the generalization of the trilinear estimates associated with the Fourier restriction norm method.     

Paleoecological implications of the nitrogen isotope signatures in the sediments amended by Antarctic seal excrements

Theanalysesofpaleoecologicalprocessesondifferenttemporalandspatialscales,thetimeexpansionofthetraditionalecology,areimportantforpredictingthefutureglobalchanges[1].However,itisdifficulttoperformsuchanalysesonalargetemporal,forexamplethousandyear,scale.Currentpaleoecologicalstudiesstronglyrelyonfossilrelicssuchasfootprint,moulage,reliquiae,boneandothermaterials,butthesematerialsarerarelyavailableanddifficulttopreserve.Recently,stableisotopeanalysishasbeenusedasaneffectivetechniqueforstudyingthe…     

Study on the bulk wave radiation of finite-length SAW devices using FEMBEM

Based on the distributions of stress and free charge on the interface of the surface acoustic wave (SAW) device calculated with the combination of boundary element method and finite element method(FEMBEM), the power of each of the three possible bulk waves radiated by the SAW device is calculated, and their contributions to the overall input conductance are separated respectively. Moreover, the formula of angular distributions of their power radiation into the substrate is derived. Consider the effect of mass loading, the resistance density，defined as a scalar, is extended to generalized resistance densities which can be written as three 4×4 tensors and for which the formulas are derived. The bulk wave radiations for a synchronous one-port resonator on 42°Y-rotated LiTaO3 are simulated. It is found that the radiated energy by slow shear wave contributes a very high proportion to input electrical energy in some frequency range.     

Node ordinal encoded genetic algorithm for the optimal allocation of water resources

A new method, node ordinal encoded genetic algorithm (NOEGA), is proposed for solving water resources optimal allocation problems, in which the capacity of water resources is split into a number of smaller parts so that successive operations can be overlapped. Our objective is to maximize the whole benefit function. To overcome the “dimensionality and algorithm complexity curse” while searching for solutions and looking for an optimal solution, the operations of one-point crossover operator, gene exchange operator, gene random operator, gene shift operator and node ordinal strings are established. It is proved to be an effective optimal method in searching for global solutions. The NOEGA does not need a diversity of initial population, and it does not have the problem of immature convergence. The results of two cases show that using NOEGA to solve the optimal allocation model is very efficient and robust. In addition, the algorithm complexity of NOEGA is discussed.     

Improvement of different source function expressions in SWAN model for the Bohai Sea

The simulating wave nearshore (SWAN) wave model has been widely used in coastal areas, lakes and estuaries. However, we found a poor agreement between modeling results and measurements in analyzing the chosen four typical cases when we used the default parameters of the source function formulas of the SWAN to make wave simulation for the Bohai Sea. Also, it was found that at the same wind process the simulated results of two wind generation expressions (Komen, Janssen) demonstrated a large difference. Further study showed that the proportionality coefficient α in linear growth term of wave growth source function plays an unperceived role in the process of wave development. Based on experiments and analysis, we thought that the coefficient α should change rather than be a constant. Therefore, the coefficient α changing with the variation of friction velocity U* was introduced into the linear growth term of wave growth source function. Four weather processes were adopted to validate the improvement in the linear growth term. The results from the improved coefficient α agree much better with the measurements than those from the default constant coefficient α. Furthermore, the large differences of results between Komen wind generation expression and Janssen wind generation expression were eliminated. We also experimented with the four weather processes to test the new white-capping mechanisms based on the cumulative steepness method. It was found that the parameters of the new white-capping mechanisms are not suitable for the Bohai Sea, but Alkyon's white-capping mechanisms can be applicable to the Bohai Sea after amendments, demonstrating that this improvement of parameter α can improve the simulated results of the Bohai Sea.     

A new class of variational equation problems

Abstract Applying an analysis method to a group of multivariable equations, a new class of variational equations are proved. Thismethod is more concise and more direct than the others. This result can be applied to some stochastic control models.     

Observation of ultra-microtexture of fault rocks in shearing-sliding zones

Based on scanning electronic microscopic observation of three fault rocks in ductile-brittle shearing-sliding zones (including one palimpsest mylonite sampled from deep bore cores of Cajon Pass, California, two flowing-structured carbargillites sampled from Shaancan Well 1 located in north Shaanxi, and Well NH located in Huanghai, respectively), micron- and nanometer-scaled ultra-fine grinding grain texture of fault rocks is discovered in this study. And the geological significance of grinding grain texture is discussed in terms of its particulate organization, rheology of particulate slipping, laminar petrography and micro dynamics including dynamothermal metamorphism, fluid transferring, particulate autorotation, and so on. In addition, the remaining problems to be solved and broad prospects in this new study field are also discussed.