Class of solutions for flow near a stagnation point

This paper considers a class of solutions for flow of a perfect gas near the stagnation point on a two-dimensional obstacle, where the flow is rotational far upstream from the obstacle. It is shown that the potential flow near the stagnation point is a special case of this class of solutions. Solutions accounting for the rotationality of the outer flow are obtained for flow in the mixing layer with an obstacle, and these solutions differ appreciably from the analogous Jimenez solution for potential flow near the stagnation point on a two-dimensional obstacle.     

Viscosity of Strain Gradient Effects on the Kinetics of Propagating Phase Boundaries in Solids

The theory of thermoelastic materials undergoing solid-solid phase transformations requires constitutive information that governs the evolution of a phase boundary. This is known as a kinetic relation which relates a driving traction to the speed of propagation of a phase boundary. The kinetic relation is prescribed in the theory from the onset. Here, though, a special kinetic relation is derived from an augmented theory that includes viscous, strain gradient and heat conduction effects. Based on a special class of solutions, namely travelling waves, the kinetic relation is inherited from the augmented theory as the viscosity, strain gradient and heat conductivity are removed by a suitable limit process.     

On the numerical solution of partial differential equations of the elliptic type. I

Summary The potential equation and some connected problems in which the unknown function is given on the boundary is solved by using the properties of a special class of matrices which have the same structure as the coefficient matrix of the system of linear difference equations resulting from the differential equation.     

Multimode laws of control of rigid body motions

The problem of control of motion of a rigid body (aircraft, satellite, or landing module) is studied. A multimode control law that can stabilize not only one prescribed motion of the body but any motion in a sufficiently broad class is constructed. The problem is solved in nonlinear setting under indeterminacy conditions on the basis of Lyapunov functions. The control law is constructed in the class of bounded discontinuous laws, special zero-overshoot response modes are constructed, and the specific character of mechanical systems is used.     

Two-dimensional flows of a viscous binary fluid between moving solid boundaries

A class of exact solutions of hydrodynamic equations with additional Korteweg stresses is obtained which is characterized by a linear dependence of part of the velocity components on the space variable. In this class, exact solutions of two problems of binary fluid flow between moving flat solid boundaries was found. A family of particular exact solutions is obtained for the problem of viscous fluid flow between planes which approach or move away from each other according to a special law.     

Complete exceptionality, constitutive laws and symmetric form for a non-linear inelastic rod

In this paper we consider quasilinear constitutive laws characterizing ‘Maxwellian Materials’ in the case of a one-dimensional inelastic rod. By using the complete exceptionality condition, we are able to determine the most general class of quasilinear constitutive relations by which a weak discontinuity wave propagating along characteristics cannot evolve into a non- linear shock. The last part of the paper is devoted to point out some properties connected with the special class of constitutive relations where the material functions do not depend on the strain. In such a case by means of a field variables transformation, we are able to reduce the fundamental system of equations to a symmetric hyperbolic system where the coefficient of the field spatial derivative is a constant matrix. This special symmetric form is very useful to study shocks.     

Various forms of the strain-displacement relations applied to experimental strain analysis

The purpose of this paper is to present the strain-displacement relations in a general way and to develop modified forms for three special cases which have application in experimental strain analysis:

1. 1.
   Small rotations—large strains     
   
   

On robust stability of a class of polynomial families

In this paper,we discuss the robust stability of a class of polynomial families more general than the interval polynomial family and diamond polynomial family.We prove that the Hurwitz stability of some special cases of this class of polynomial families can be determined by checking finite polynomials.We also give an example to illustrate that it is not always possible to determine the Hurwitz stability of all this class of polynomial families by checking finite polynomials.     

The analysis of thermoplastic characteristics of special polymer sulfur composite

Specific chemical environments step out in the industry objects. Portland cement composites (concrete and mortar) were impregnated by using the special polymerized sulfur and technical soot as a filler (polymer sulfur composite). Sulfur and technical soot was applied as the industrial waste. Portland cement composites were made of the same aggregate, cement and water. The process of special polymer sulfur composite applied as the industrial waste is a thermal treatment process in the temperature of about 150–155 \(^{\circ }\hbox {C}\). The result of such treatment is special polymer sulfur composite in a liquid state. This paper presents the plastic constants and coefficients of thermal expansion of special polymer sulfur composites, with isotropic porous matrix, reinforced by disoriented ellipsoidal inclusions with orthotropic symmetry of the thermoplastic properties. The investigations are based on the stochastic differential equations of solid mechanics. A model and algorithm for calculating the effective characteristics of special polymer sulfur composites are suggested. The effective thermoplastic characteristics of special polymer sulfur composites, with disoriented ellipsoidal inclusions, are calculated in two stages: First, the properties of materials with oriented inclusions are determined, and then effective constants of a composite with disoriented inclusions are determined on the basis of the Voigt or Rice scheme. A brief summary of new products related to special polymer sulfur composites is given as follows: Impregnation, repair, overlays and precast polymer concrete will be presented. Special polymer sulfur as polymer coating impregnation, which has received little attention in recent years, currently has some very interesting applications.     

Problem of Capillary Displacement for One Model of Three-Phase Filtration

The class of capillary pressures corresponding to a triangular tensor of capillary diffusion in a three-phase fluid is studied. Filtration with such a tensor is described by a parabolic system of equations degenerating on solutions. This system is integrodifferential because the desired quantities are the total flow rate and the phase-saturation distribution under conditions of a specified pressure drop on the boundaries of the flow region in one of the phases. It is shown that in the problem of capillary displacement, the degenerate system can be studied using a special maximum principle.     

Fractional empirical mode decomposition energy entropy based on segmentation and its application to the electrocardiograph signal

In this paper, based on the Hirota bilinear method, a kind of lump solutions and two classes of interaction solutions are discussed to the \((2+1)\)-dimensional generalized KdV equation with the aid of symbolic computation system Mathematica. Analyticity is naturally guaranteed by taking special choices of the involved parameters to achieve a positive constant term. Particularly, these solutions with special values of the included parameters are plotted, as illustrative example.     

Recent developments in multiphysics computational models of physiological flows

A mini-symposium on computational modeling of fluid–structure interactions and other multiphysics in physiological flows was held at the 11th World Congress on Computational Mechanics in July 2014 in Barcelona, Spain. This special issue of Theoretical and Computational Fluid Dynamics contains papers from among the participants of the mini-symposium. The present paper provides an overview of the mini-symposium and the special issue.     

Small-diameter parallel plate rheometry: a simple technique for measuring rheological properties of glass-forming liquids in shear

The rheological characterization of glass-forming liquids is challenging due to their extreme temperature dependence and high stiffness at low temperatures. This study focuses on the special precautions that need to be taken to accommodate high sample stiffness and torsional instrument compliance in shear rheological experiments. The measurement errors due to the instrument compliance can be avoided by employing small-diameter parallel plate (SDPP) rheometry in combination of numerical instrument compliance corrections. Measurements of that type demonstrate that accurate and reliable rheological data can be obtained by SDPP rheometry despite unusually small diameter-to-gap (d/h) ratios. Specimen preparation for SDPP requires special attention, but then experiments show excellent repeatability. Advantages and some current applications of SDPP rheometry are briefly reviewed. SDPP rheometry is seen as a simple and versatile way to measure rheological properties of glass-forming liquids especially near their glass transition temperature.     

Dynamics of a 3D autonomous quadratic system with an invariant algebraic surface

An invariant algebraic surface is calculated for a 3D autonomous quadratic system. Also, the dynamics near finite singularities and near infinite singularities on the invariant algebraic surface is analyzed. Furthermore, pitchfork bifurcation is analyzed using center manifold theorem and a first integral of this quadratic system for some special parameters is provided. Finally, the dynamics of this system at infinity using the Poincare compactification in \(R^3\) is investigated and the singularly degenerate heteroclinic cycles are presented by a first integral and verified by numerical simulations.     

Special class of solutions of the kinetic equation of a bubbly fluid

A new class of solutions is constructed for the kinetic model of bubble motion in a perfect fluid proposed by Russo and Smereka. These solutions are characterized by a linear relationship between the Riemann integral invariants. Using the expressions following from this relationship, the construction of solutions in the special class is reduced to the integration of a hyperbolic system of two differential equations with two independent variables. Exact solutions in the class of simple waves are obtained, and their physical interpretation is given.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 33–43, March–April, 2005.     

On the positive definiteness of a class of operators

In this paper, a proof of the positive definiteness for a class of operators is given. The operators considered are general enough to include those in two- and three-dimensional elasticity, thin plates and shells as their special cases.     

Shift of shock position for a class of nonlinear singularly perturbed problems

Thenonlinearsingularlyperturbedproblemisaveryattentiveobjectofstudyintheinternationalacademiccircles[1].Recently ,manyscholarsstudiedagreatdealofwork .Forexample,Boh啨[2 ],ButuzovandSmurov[3],O’Malley ,Jr.[4 ],Butuzov ,NefedovandSchneider[5 ]andKelley[6 ]andsoon .TheauthorconsideredaclassofsingularlyperturbednonlinearboundaryvalueproblemsfortheordinarydifferentialequationinRefs .[7～ 1 0 ] ,reactiondiffusionequationsinRefs.[1 1～ 1 3 ] ,singularlyperturbedproblemswithnonlocalboundarycond…     

VARIATIONAL PRINCIPLE AND GENERALIZED VARIATIONAL PRINCIPLE IN HYDRODYNAMICS OF A CLASS OF NON－NEWTONIAN FLUID

ＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＡＮＤＧＥＮＥＲＡＬＩＺＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＩＮＨＹＤＲＯＤＹＮＡＭＩＣＳＯＦＡＣＬＡＳＳＯＦＮＯＮ－ＮＥＷＴＯＮＩＡＮＦＬＵＩＤＳｈｅｎＭｉｎ（沈敏）,ＳｕｎＱｉ－ｒｅｎ（孙其仁）（Ｓ...     

On the surface instability of a highly elastic half-space

The phenomenon of surface instability of an isotropic half-space under biaxial plane stress is studied for compressible elastic materials in finite strain. Euler's method is used to derive the general form of the stability criterion, and analytical details are exhibited by special application to the class of hyperelastic Hadamard materials in two complementary cases: (i) the full solution is derived for the compressible, neo-Hookean members, and (ii) the plane deformation solution is provided for every isotropic, elastic material and specific results are presented for the full Hadamard class. Results appropriate to incompressible Mooney-Rivlin materials are herein obtained as special limit cases. Several theorems are established and some of the conclusions are illustrated graphically.     

The Moments Sliding Vector Field on the Intersection of Two Manifolds

In this work, we consider a special choice of sliding vector field on the intersection of two co-dimension 1 manifolds. The proposed vector field, which belongs to the class of Filippov vector fields, will be called moments vector field and we will call moments trajectory the associated solution trajectory. Our main result is to show that the moments vector field is a well defined, and smoothly varying, Filippov sliding vector field on the intersection \(\Sigma \) of two discontinuity manifolds, under general attractivity conditions of \(\Sigma \). We also examine the behavior of the moments trajectory at first order exit points, and show that it exits smoothly at these points. Numerical experiments illustrate our results and contrast the present choice with other choices of Filippov sliding vector field.