Dynamic compaction of granular materials.

An Eulerian hyperbolic multiphase flow model for dynamic and irreversible compaction of granular materials is constructed. The reversible model is first constructed on the basis of the classical Hertz theory. The irreversible model is then derived in accordance with the following two basic principles. First, the entropy inequality is satisfied by the model. Second, the corresponding 'intergranular stress' coming from elastic energy owing to contact between grains decreases in time (the granular media behave as Maxwell-type materials). The irreversible model admits an equilibrium state corresponding to von Mises-type yield limit. The yield limit depends on the volume fraction of the solid. The sound velocity at the yield surface is smaller than that in the reversible model. The last one is smaller than the sound velocity in the irreversible model. Such an embedded model structure assures a thermodynamically correct formulation of the model of granular materials. The model is validated on quasi-static experiments on loading-unloading cycles. The experimentally observed hysteresis phenomena were numerically confirmed with a good accuracy by the proposed model.

Mathematical and numerical model for nonlinear viscoplasticity.

A macroscopic model describing elastic-plastic solids is derived in a special case of the internal specific energy taken in separable form: it is the sum of a hydrodynamic part depending only on the density and entropy, and a shear part depending on other invariants of the Finger tensor. In particular, the relaxation terms are constructed compatible with the von Mises yield criteria. In addition, Maxwell-type material behaviour is shown up: the deviatoric part of the stress tensor decays during plastic deformations. Numerical examples show the ability of this model to deal with real physical phenomena.

Many-photon dynamics of photobleaching.

A detailed dynamical theory of photobleaching by periodical sequences of laser pulses is presented. The theory is used for interpretation of recent experiments with pyrylium salts. Our simulations are based on first-principles simulations of photoabsorption cross-sections and on empirical rate constants. Two competitive channels of photobleaching, namely, photobleaching from the lowest excited singlet and triplet states and from higher excited states, are found to explain different intensity dependences of the photobleaching rates in different samples. The process includes two-photon excitation from the ground state to the first or second excited singlet states and one-photon excitation from the first singlet or triplet states to higher excited states. The fluorescence follows double-exponential dynamics with two characteristic times. The first and the shorter one is the equilibrium settling time between the ground and the lowest triplet states. The second characteristic time, the time of photobleaching, is responsible for the long-term dynamics. The effective rate of photobleaching from the first excited singlet and lowest triplet states depends differently on the irradiance in comparison with the photobleaching in higher states. The first channel is characterized by a quadratic intensity dependence in contrast to the second channel that shows a cubic dependence. The competition between these photobleaching channels is very sensitive to the rate constants as well as to the repetition rate, the pulse duration, and the peak intensity. The double-exponential decay of the fluorescence is explained by the spatial inhomogeneity of the light beam. The findings in this work are discussed in terms of the possibility of using many-photon-induced photobleaching for new three-dimensional read-write devices.

Modeling of the moving deformed triple contact line: influence of the fluid inertia.

For partial wetting, motion of the triple liquid-gas-solid contact line is influenced by heterogeneities of the solid surface. This influence can be strong in the case of inertial (e.g., oscillation) flows where the line can be pinned or move intermittently. A model that takes into account both surface defects and fluid inertia is proposed. The viscous dissipation in the bulk of the fluid is assumed to be negligible as compared to the dissipation in the vicinity of the contact line. The equations of motion and the boundary condition at the contact line are derived from Hamilton's principle. The rapid capillary rise along a vertical inhomogeneous wall is treated as an example.

Model of a liquid nanofilm on a solid substrate based on the van der Waals concept of capillarity.

Van der Waals attractive forces drastically change the material properties of thin liquid layers several nanometers when in contact with a solid. At this scale, the fluid is no longer homogeneous. Moreover, it has properties which are analogous to those of solids. In particular, in equilibrium the stress tensor is no longer spherical. For such fluids, we use a long-wave approximation to derive the evolution of a liquid nanofilm on a substrate. We establish that the driving pressure in the nanofilm should be associated with the mean value of the component of the pressure tensor tangential to the liquid interface (along the substrate). Finally, we derive the equation for nanofilm dynamics by using a mass conservation formulation. This is not a conventional, conservative equation for the position of the free surface normally used in the theory of thick films where the density is homogeneous, but rather a conservative equation for the liquid mass. The equation turns out to be a nonlinear parabolic equation with a diffusion coefficient of a "good" sign.