PERSISTENCE AND GLOBAL STABILITY FOR TWO-SPECIES NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY

In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.     

NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE

The nonlocal initial problem for nonlinear nonautonomous evolution equati-ons in a Banach space is considered. It is assumed that the nonlinearities havethe local Lipschitz properties. The existence and uniqueness of mild solutionsare proved. Applications to integro-differential equations are discussed.The main tool in the paper is the normalizing mapping (the generalizednorm).     

Domain size equilibration in sphere‐forming block copolymers

The kinetics of domain size equilibration were studied for asymmetric poly(ethylene‐alt‐propylene)‐b‐poly(dimethyl siloxane) (EPDMS) and polyisoprene‐b‐poly(dimethyl siloxane) (IDMS) block copolymers in the body‐centered cubic ordered phase. Small‐angle X‐ray scattering measurements of the principal peak position (q*) were made as a function of time after temperature jumps within the ordered state. The equilibration times were remarkably long, especially on cooling and for temperatures below 100 °C. For example, after a quench to 40 °C, q* for EPDMS had not fully equilibrated even after several weeks of annealing; IDMS required several days to equilibrate at the same temperature. In contrast, a lamella‐forming EPDMS sample was able to adjust q* within the timescale of the measurements (i.e., minutes) with both heating and cooling over the same temperature range. Measurements of tracer diffusion indicated that chain mobility was not the rate‐limiting step, although differences in mobility did account for the differences between EPDMS and IDMS. Rather, the limiting step was the required reduction in the number density of spheres on cooling; the disappearance of spheres, either by evaporation or by fusion, provided a large kinetic barrier. Lamellae, however, could adjust domain dimensions simply by local displacements of individual chains. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 715–724, 2003     

Collisional Relaxation of Luminescence Anisotropy in Rarefied Gases in the Condensed Phase

The orientational relaxation of optically induced anisotropy in rarefied gases and at a damped rotation has been investigated. It has been found that the anisotropy relaxation in rarefied gases is described by a reduced kinetic equation depending only on free rotation integrals. The behavior of the integral anisotropy of luminescence for free symmetric and asymmetric top molecules has been elucidated. The law of luminescence depolarization has been obtained for asymmetric top molecules in the Gordon J-diffusion model. It represents the sum of two Stern–Volmer-type dependences, whose relative contribution is determined by the orientation of the dipole moments of transitions with absorption and emission of light in the molecular coordinate system and by the principal moments of inertia of the molecular top. It has been established that in the limit of a strongly damped rotation, kinetic equations of the general form reduce to equations of rotational diffusion. A number of modified diffusion equations correctly describing the contribution of inertial effects to the orientational relaxation of anisotropy have been obtained.     

Fluctuation Theory for a Three-Dimensional Model of Maxwellian Molecules

Under suitable assumptions, a functional central limit theorem is obtained for a three-dimensional model of Maxwellian molecules. This model is related to a nonlinear Boltzmann-type equation. It will be proved that the family of the distributions induced by fluctuation processes converges weakly.     

Molecular modeling study on surface,thermal, mechanical and gas diffusion properties of chitosan

The motivation of this work is to provide reliable and accurate modeling studies of the physical (surface, thermal, mechanical and gas diffusion) properties of chitosan (CS) polymer. Our computational efforts have been devoted to make a comparison of the structural bulk properties of CS with similar type of polymers such as chitin and cellulose through cohesive energy density, solubility parameter, hydrogen bonding, and free volume distribution calculations. Atomistic modeling on CS polymer using molecular mechanics (MM) and molecular dynamics (MD) simulations has been carried out in three dimensionally periodic and effective two dimensionally periodic condensed phases. From the equilibrated structures, surface energies were computed. The equilibrium structure of the films shows an interior region of mass density close to the value in the bulk state. Various components of energetic interactions have been examined in detail to acquire a better insight into the interactions between bulk structure and the film surface. MD simulation (NPT ensemble) has also been used to obtain polymer specific volume as a function of temperature. It is demonstrated that these V–T curves can be used to locate the volumetric glass transition temperature (T_g) reliably. The mechanical properties of CS have been obtained using the strain deformation method. Diffusion coefficients of O₂, N₂, and CO₂ gas molecules at 300 K in CS have been estimated. The calculated properties of CS are comparable with the experimental values reported in the literature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1260–1270, 2007     

Nonlinear Diffusion Processes

We study elliptic systems of strongly nonlinear first-order differential equations in complex form on the plane. For such systems we develop the theory of Hilbert boundary value problems which is very much similar to the well-known theory for a holomorphic vector. Systems of nonlinear elliptic equations describe problems of interaction of several nonlinear stationary processes in the diffusive and convective mass and heat transport by hydrodynamic fluid flows.     

Analogues of Coherent and Dissipative Structures in Social and Historical Processes

An analogy between social and hydrodynamic processes is developed. The relation of the state system to the passionarity theory suggested by L. N. Gumilev is discussed.     

Generation of large fifth-order nonlinear phase shifts by use of lossless χ(2) cascaded nonlinear processes

It is shown that the cascaded fifth-order nonlinear phase shifts will increase with energy loss in the cascaded processes. Essentially different from the multi-photon absorption accompanied with inherent material nonlinearities, the loss of fundamental wave in a cascaded process is controllable and suppressible. By introducing difference frequencies generated from the reaction between the fundamental and its second harmonic after the cascaded processes, the fundamental wave can be free of energy loss, while the large cascaded fifth-order nonlinear phase shift is maintained.