Narrow Results

We present a mathematical model for cell-induced gel contraction in vitro. The core of the model consists of conservation equations for the mass of the gel and the number of cells, coupled to a force balance on the gel. On the basis of previously reported experimental findings for collagen gels, which are frequently used experimentally, the gel is treated as a compressible viscous fluid while inertial effects are neglected. The flow is assumed to be isothermal, and a linear pressure–density relation is adopted. The force exerted on the gel by cells is assumed to depend upon the local environment surrounding the cell: influences can include the cell and extracellular matrix density, and the concentration of a diffusible chemical produced by the cells. We consider the simple, but experimentally relevant, case of spherically symmetric gels. For cell-free gels, we show how simple experiments might be used to determine the parameters in the model. When the cell-derived forces are given by a prescribed function of position, we are able to obtain the early time and steady-state behavior of the solution analytically. We perform numerical simulations which generate predictions of how the gel density evolves during compaction under differing assumptions concerning the factors influencing the force exerted by the cells. These results are compared with some previous observations reported in the literature.

In this paper, we study the self-propelled motion of a single deformable body in a viscous compressible fluid which occupies whole three-dimensional Euclidean space. The considered governing system for the fluid is the isentropic compressible Navier–Stokes equation. The main result of this paper is the existence of a weak solution on a time interval $(0,+\infty )$.

We consider the fluctuation modes around a hypersurface ${\mathrm{\Sigma }}_c$ in a $(d+2)$-dimensional product Einstein manifold, with ${\mathrm{\Sigma }}_c$ taken either near the horizon or at some finite cutoff from the horizon. By mapping the equations that govern the lowest nontrivial order of the fluctuation modes into a system of partial differential equations on a flat Newtonian spacetime, a system of compressible, forced viscous fluid is realized. This result generalizes the nonbulk/boundary holographic duality constructed by us recently to the case of a different background geometry.

This paper presents the results of studies on natural vibrations of circular cylindrical shells containing liquid and resting on an elastic foundation, which is described by the Pasternak two-parameter model. In the meridional direction, the elastic medium is nonuniform and represents an alternation of sections in which the foundation is present or absent. The behavior of the elastic structure and the compressible fluid is described in the framework of classical shell theory based on the Kirchhoff–Love hypothesis and the Euler equations. The equations of motion of the shell are reduced to a system of ordinary differential equations with respect to new unknowns. The wave equation written for pressure in the fluid also reduces to a system of ordinary differential equations using the straight line method. The solution of the formulated boundary value problem is found by the Godunov orthogonal sweep method. The validity of the results obtained is confirmed by comparison with the known numerical-analytical solutions. The dependences of the minimum vibration frequencies on the characteristics of elastic medium with variable nonuniformity along the length of the structure have been obtained for cylindrical shells with different boundary conditions. It has been found that the violation of smoothness of the derived dependences is caused by a change of the vibration mode with minimum frequency and is determined both by the ratio of the size of the elastic foundation to the entire length of the shell and its stiffness, and also by a combination of boundary conditions set at the edges of the thin-walled structure.

The peristaltic flow of Jeffrey fluid in a microchannel with compliant wall has been investigated. The rheological effects and compressibility of the fluid are given proper attention. Perturbation approach has been employed when the ratio of the wave amplitude to the radius of the pore is small. Expressions of perturbation function, mean axial velocity distribution, mean velocity at the boundaries and critical values are derived. The variations of various interesting parameters are shown and examined very carefully.

We consider a system coupling the compressible Navier–Stokes equations to the Vlasov–Fokker–Planck equation on three-dimensional torus. The coupling arises from a drag force exerted by each other. We establish the existence of the global classical solutions close to an equilibrium, and further prove that the solutions converge to the equilibrium exponentially fast.

This paper presents the results of investigation of the natural vibrations and stability of circular vertical multilayered cylindrical shells, fully or partially filled with a quiescent compressible fluid subjected to hydrostatic and external static loads. The behavior of the elastic structure and fluid medium is described based on the classical shell theory and Euler’s equations. The linearized equations of motion of the shell, together with the corresponding geometrical and physical relations are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the method of generalized differential quadrature. The solution of the formulated boundary value problem is developed using Godunov’s orthogonal sweep method. The dependences of the lowest vibration frequencies and critical external pressure on the ply angle and the filling level of two-layer and three-layer cylindrical shells are analyzed in detail. It is demonstrated that, in contrast to the ply angle and a given combination of boundary conditions, the lay-up scheme of composite materials plays different parts in the problems of maximizing the fundamental frequency of vibrations and extending the stability boundaries.

Model and simulation study is the starting point for engineering design and development, especially for developing vehicle control systems. This paper presents a methodology to develop models for application of smart struts for vehicle suspension control development. The modeling approach is based on decomposition of the testing data. Per the strut functions, the data is dissected according to both control and physical variables. Then the data sets are characterized to represent different aspects of the strut working behaviors. Next different mathematical equations can be built and optimized to best fit the corresponding data sets, respectively. In this way, the model optimization can be facilitated in comparison to a traditional approach to find out a global optimum set of model parameters for a complicated nonlinear model from a series of testing data. Finally, two struts are introduced as examples for this modeling study: magneto-rheological (MR) dampers and compressible fluid (CF) based struts. The model validation shows that this methodology can truly capture macro-behaviors of these struts.

Finite volume schemes are widely used in the numerical solution of conservation laws such as those occuring in C.F.D. Finite element approximations are naturally well suited to second-order operators like those modelling diffusion terms. Then an attractive approach for solving time-dependent convection-dominated diffusion problems consists in combining finite volume for convection and finite element for diffusion. In this paper, we propose to provide a review and a numerical comparison of these approaches in the framework of triangular meshes in two-dimension. New methods for combining finite volumes and finite elements are also defined.