Some geometrically nonlinear problems of deformation of inelastic plates and shallow shells

This paper considers geometrically nonlinear problems of deformation of elastoplastic shallow shells and viscoelastoplastic plates where it is required to find kinematic loads for a given time interval such that a shell (plate) acquires prescribed residual deflections after these loads are applied and then removed. For some constraints, the correctness of the corresponding formulations (uniqueness of the solution and its continuous dependence on the problem data) is shown and iterative solution methods are justified.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 151–157, March–April, 2005.     

Non-gaussian diffusion modeling in composite porous media by homogenization: Tail effect

In the paper anomalous diffusion appearing in a porous medium composed of two porous components of considerably different diffusion characteristics is examined. The differences in diffusivities are supposed to result either from two medium types being present or from variations in pore size (double porosity media). The long-tail effect is predicted using the homogenization approach based on the application of multiple scale asymptotic developments. It is shown that, if the ratio of effective diffusion coefficients of two porous media is of the order of magnitude smaller or equal O( ²), where is a homogenization parameter, then the macroscopic behaviour of the composite may be affected by the presence of tail-effect. The results of the theoretical analysis were applied to a problem of diffusion in a bilaminate composite. Analytical calculations were performed to show the presence of the long-tail effect in two particular cases.Notations c _i the concentration of chemical species in water within the medium i - D _i the effective diffusion coefficient for the medium i - D _ij ^eff the macroscopic (or effective) diffusion tensor in the composite - ERV the elementary representative volume - h the thickness of the period - l a chracteristic length of the ERV or the periodic cell - L a characteristic macroscopic length - n the volumetric fraction of the material 2 - 1–n the volumetric fraction of the material 1 - N the unit vector normal to - t the time variable - x the macroscopic (or slow) space variable - y the microscopic (or fast) space variable - c _1c ,C _2c ,D _1c ,D _2c the characteristic quantities - T,T _1L ,T _2L ,T _1l ,T _2l the characteristic times - c ₁ ^* ,c ₂ ^* ,D ₁ ^* ,D ₂ ^* ,t ^* the non-dimensional variables - the homogenization parameter - ₁ the domain occupied by the material 1 - ₂ the domain occupied by the material 2 - the interface between the domains 1 and 2 - the total volume of the periodic cell - /x_i the gradient operator - the gradient operator     

Symbolic Sequences Generated by a Special Class of Discrete Systems With Discontinuity and Input

In this paper, we study the symbolic sequences generated by aclass of discrete systems. This class contains the double-modulators, a typical example of discretetime electronic systems with discontinuity and input. First we develop ageneral theory and then we apply it to some examples in order to obtainsets of inadmissible sequences.     

The modified Casson＇s equation and its application to pipe flows of shear-thickening fluid

A few additional data from our previous experiments were plotted to emphasize the shear-thickening behavior of deoxy sickle erythrocyte (SS) suspension. A constitutive equation (named as FX equation) was developed and applied to a cylindrical pipe flow of a shear-thickening fluid. A blunt velocity profile and its volume flow rate were calculated. The flow was non-viscous (potential) in the central part of the pipe (i.e. the central core or the central plug-flow), and became more and more viscous towards the wall of the pipe after a specific radial distance, which was determined by a critical shear rate of (named as Fungs shear rate). Furthermore, combining the FX equation with the original Cassons equation, the author obtained a modified Cassons equation by introducing .The English text was polished by Yunming Chen.     

Two Theoretical Elasticity Micromechanics Models

This study is concerned with the Composite Spheres (Cylinders) Model and the Generalized Self Consistent Method (GSCM). A detailed examination of the two models proves the two models are the same in the limited cases where they both give solutions. In this process of comparison between the two models, a new solution is found for the shear property of a closed cell foam type idealization.     

Piece-Wise Constant Approximations in the Membrane Problem

We present a technique for the approximation of quadratic variational problems of the first order in spaces of piece-wise constant functions. The method adopts ideas from the theory of -convergence as a guideline, and it differs from more traditional non-conforming techniques because it is based on the introduction of a suitable sequence of discrete functionals to be minimized with no constraints and without requiring that the spline functions fulfill any patch test condition.     

“Thermal layer” effect in MHD: Interaction of a parallel shock with a layer of decreased density

Interaction of a parallel fast MHD shock with a layer of decreased density is discussed using ideal MHD approach. This is an extrapolation of gas dynamic thermal layer effect on ideal MHD. Computer simulations show that a magnetic field of a moderate intensity ( 1) may change the character of the flow for intermediate Mach numbers (M 5) and a new raking regime may occur which is not observed in the absence of a magnetic field. Self similar precursor analogous to that in gas dynamics may develop in the case of highM and low density in the layer but magnetic forces essentially decrease its growth rate. This problem appears in connection with cosmical shock propagation where planetary magnetic tails play the role of the thermal layer, and it may also be observed in the laboratory when the shock is strong enough to heat the walls ahead of it.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Velocity Measurements in a One‐Dimensional Steady Flow by Methods of Emission Tomography

A new method for velocityfield measurements in a onedimensional steady flow is proposed. The method is based on principles of laserinduced fluorescence combined with emission tomography. Results of a numerical experiment are presented.     

On Ericksen’s Theorem for Unconstrained Hyperelastic Materials

After reviewing the proof of Ericksens theorem for the set of unconstrained, homogeneous, isotropic, hyperelastic materials, Ericksens result is sharpened to cover the subset of materials that possess a natural configuration and satisfy the empirical inequalities. Mathematics Subject Classifications (2000) 74B20.     

Design of a Beam with Controllable Force Elements

A method for solving the problem of design of an intellectual structure formulated for the pair optimal position of actuators, optimal control of actuators is developed. In the method proposed, physical and logical objects are treated as equivalent.     

Some Results on Dynamics of Special Double-Loop ΣΔ-Modulators

The dynamic behaviour of a specific two-dimensional state space model with discontinuity is studied. This model arises from the study of double-loop -modulators with constant input. Using mathematical tools we explain certain simulation results, and some properties are derived. Simulations based on time-varying input are also provided.     

On the Quasi‐Steadiness Hypothesis as Applied to Gas Exhaustion from a Receiver

A semiempirical method of determining the stabilization time for a quasisteady mode of gas exhaustion from a receiver after sudden opening of the nozzle and the time evolution of the real flow rate at the stage of the transitional process are considered. The numerical solution of the equations of exhaustion gas dynamics in a twodimensional formulation and the results of model experiments demonstrated that the method can be used to estimate the conditions of applicability of the quasisteadiness hypothesis and to determine the discharge coefficient of the nozzle with controlled accuracy.     

Effectiveness of Acidizing of the Vellbore Zone Taking into Account the Capillary Locking of Formation Water

The results of calculations of immiscible fluid flow to an operating well are compared for various formation parameters and states of the wellbore zone. Steadystate and unsteady filtration regimes are considered. The calculations show that acidizing of the wellbore zone increases the well flow rate.     

Numerical Experiments in Scalar Diffusion under Stochastic Convection

We study scalar diffusion, both from Eulerian and Lagrangian perspectives, advected by two dimensional flows. Emphasis is devoted to the problem of scalar diffusion under a synthetic turbulent flow. We present numerical and analytical results for the turbulent diffusion coefficient either from the influence of the turbulent synthetic field and a periodic array of eddies. Preliminary results concerning Lagrangian dispersion are also reported.     

Methods of Small and Large δ in the Nonlinear Dynamics – A Comparative Analysis

New asymptotic approaches for dynamical systems containing a power nonlinear term x ⁿ are proposed and analyzed. Two natural limiting cases are studied: n 1 + , 1 and n . In the firstcase, the 'small method' (SM)is used and its applicability for dynamical problems with the nonlinearterm sin as well as the usefulness of the SMfor the problem with small denominators are outlined. For n , a new asymptotic approach is proposed(conditionally we call it the 'large method' –LM). Error estimations lead to the followingconclusion: the LM may be used, even for smalln, whereas the SM has a narrow application area. Both of the discussed approaches overlap all values ofthe parameter n.     

The Devil’s Staircase Dimensions and Measure-Theoretical Entropy of Maps with Horizontal Gap

This work elucidates the measure-theoretical entropy and dimensions of a unimodal map with a horizontal gap. The measure-theoretical entropy and dimensions of the F_t (which is defined later) are shown to form a devils staircase structure with respect to the gap size t. Pesins formula for gap maps is also considered.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

Upscaling in Subsurface Transport Using Cluster Statistics of Percolation

Transport/flow problems in soils have been treated in random resistor network representations (RRNs). Two lines of argument can be used to justify such a representation. Solute transport at the pore-space level may probably be treated using a system of linear, first-order differential equations describing inter-pore probability fluxes. This equation is equivalent to a random impedance network representation. Alternatively, Darcys law with spatially variable hydraulic conductivity is equivalent to an RRN. Darcys law for the hydraulic conductivity is applicable at sufficiently low pressure head in saturated soils, but only for steady-state flow in unsaturated soils. The result given here will have two contributions, one of which is universal to any linear conductance problem, i.e., requires only the applicability of Darcys (or Ohms) law. The second contribution depends on the actual distribution of linear conductances appropriate. Although nonlinear effects in RRNs (including changes in resistance values resulting from current, analogous to changes in matric potential resulting from flow) have been treated within the framework of percolation theory, the theoretical development lags the corresponding development of the linear theory, which is, in principle, on a solid foundation. In practice, calculations of the nonlinear conductivity in relatively (compared with soils) well characterized solid-state systems such as amorphous or impure semiconductors, do not agree with each other or with experiment. In semiconductors, however, experiments do at least appear consistent with each other.In the limit of infinite system size the transport properties of a sufficiently inhomogeneous medium are best calculated through application of critical rate analysis with the system resistivity related to the critical (percolating) resistance value, R_c. Here well-known cluster statistics of percolation theory are used to derive the variability, W (R,x) in the smallest maximal resistance, R of a path spanning a volume x³ as well as to find the dependence of the mean value of the conductivity, (x). The functional form of the cluster statistics is a product of a power of cluster size, and a scaling function, either exponential or Gaussian, but which, in either case, cuts off cluster sizes at a finite value for any maximal resistance other than R_c. Either form leads to a maximum in W (R,x) at R=R_c. When the exponential form of the cluster statistics is used, and when individual resistors are exponential functions of random variables (as in stochastic treatments of the unsaturated zone by the McLaughlin group [see Graham and MacLaughlin (1991), or the series of papers by Yeh et al. (1985, 1995), etc.], or as is known for hopping conduction in condensed matter physics), then W (R,x) has a power law decay in R/R_c (or R_c/R, the power being an increasing function of x. If the statistics of the individual resistors are given by power law functions of random variables (as in Poiseiulles Law), then an exponential decay in R for W (R,x) is obtained with decay constant an increasing function of x. Use, instead, of the Gaussian cluster statistics alters the case of power law decay in R to an approximate power, with the value of the power a function of both R and x.     

Quasi-One-Dimensional Model of Heat and Mass Transfer During Sublimation of a Molecular Crystal Plate in a Plane Channel

An unsteady quasi-one-dimensional model is constructed for the process of sublimation of a monocrystalline plate of -diketonate in a uniform flow of an indifferent gas. A method of collocations and least squares is developed for solving heat-transfer problems. In contrast to the previous variants of the method, the algorithm proposed is designed for solving unsteady equations in partial derivatives with a phase transition. Numerical calculations are performed for various regimes of sublimation of chromium -diketonate; the results are in good agreement with the data of a physical experiment.