Partial regularity for certain classes of polyconvex functionals related to nonlinear elasticity

Consider the variational integral where Ω⊂ℝ ⁿ andp≥n≥2. H: (0, ∞)→[0, ∞) is a smooth convex function such that . We approximateJ by a sequence of regularized functionalsJ _δ whose minimizers converge strongly to anJ-minimizing function and prove partial regularity results forJ _δ-minimizers.     

Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point

We consider the two-dimensional stochastic Ising model in finite square with free boundary conditions, at inverse temperature >₀ and zero external field. Using duality and recent results of Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of , with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.     

Fubini theorem for anticipating stochastic integrals in Hilbert space

Let (X,l,) be a measure space, letW be a cylindrical Hilbert-Wiener process, and let be an anticipating integrable process-valued function onX. We prove, under natural assumptions on, that there exists a measurable version Y_x,x X, of the anticipating integral of(x) such that the integral _x Y_x(dx) is a version of the anticipating integral of _X (x)(dx). We apply this anticipating Fubini theorem to study solutions of a class of stochastic evolution equations in Hilbert space.     

Droplet dynamics for asymmetric Ising model

Nucleation from a metastable state is studied for an anisotropic Ising model at very low temperatures. It turns out that the critical nucleus as well as configurations on a typical path to it differ from the Wulff shape of an equilibrium droplet.     

RHEOLOGICAL CHARACTERIZATION OF PROCESSABILITY OF UNVULCANIZED POLYBUTADIENE

Rheological investigation on a series ot unvulcamzed polybutadiene elastomers of different processability has been carried out by means of a capillary extrusion rheometer. It is found that the processability of unvulcanized polybutadiene can be correlated with the occurrence of unsteady flow and the wall stress, dependence of the dimensionless number e characterizing the entrance elongational elasticity which has been found to be sensitive to the branching structure and the molecular weight distribution of the samples. Interpretations based on the structural data of unvulcanized polybutadiene were discussed.     

Kinetics of the surface tension of micellar solutions: Comparison of different experimental techniques

The kinetics of the surface tension of micellar solutions of nonionic surfactant Triton X-100 is measured experimentally by means of three different techniques: oscillating jet, maximum bubble pressure and inclined plate. They allow to study the micellization kinetics at various time scales (from a few milliseconds to a few seconds) in fairly large concentration region up to 50 times CMC. The experimental data are satisfactorily explained by a theoretical model accounting for the kinetics of micellization, diffusion of surfactant species and expansion of the bubble interface. By this model are computed the characteristic times of diffusion and micellization, which are of comparable magnitude (about 5 to 200 ms), and the Gibbs' elasticity. The micellization time constant corresponds to the slow relaxation process known to coincide with the disintegration of micelles. Comparing our data with other data from literature one can conclude that more realistic information for the micellization kinetics is obtained by the maximum bubble pressure and the oscillating jet method. The inclined plate seems too slow to measure the relaxation processes in micellar solutions of this surfactant.     

内噪声作用下的随机共振算法对弱信号的检测

基于随机共振理论提出了一种简便、有效地检测弱信号的方法。在内噪声协同作用下，通过调节输入噪声信号的大小能较好地提高系统输出信号的信噪比，从而实现检测背景噪声很强的弱信号的目的。应用于模拟信号和实验信号的结果证明了方法是可行的。     

Surface viscoelasticity of phospholipid monolayers at the air/water interface

The surface viscoelastic properties of monolayers of two phospholipids DPPC (L--dipalmitoylphosphatidylcholine) and DMPE (L--dimyristoylphosphatidyl-ethanolamin), at the air-water interface have been investigated. Two techniques were used for the investigation. One involved use of an interfacial shear rheometer (torsion pendulum apparatus ISR1), to provide measurements of the shear viscosity _s as a function of surface pressure, and the second, a modified LB trough with an oscillating barrier to generate periodie dilation and compression so as to measure the dilational elastic modulusE as a function of surface area.Results indicate a strong dependence of _s andE upon monolayer phases. This suggests that the viscoelastic relaxation of monolayers can be understood as molecular rearrangements, domain exchange and molecular reorientations between different monolayer states.     

Shear flow experiments in an assembly of gel beads and modelling of bingham behavior

In this paper, we present a rheological study of a compact layer of highly swollen gel beads. The flow regimes of these systems are modelled by an elastic sinusoid moving in a Newtonian fluid. This model predicts a yield stress varying with the square root of the elastic modulus of the gel bead. The slope at the origin (at zero velocity) of the flow curve is expected to depend only on geometrical parameters and on the solvent viscosity. The experimental data are in qualitative agreement with the theoretical predictions.