A Numerical Study of the Applicability of the Shear Compression Specimen to Parabolic Hardening Materials

This paper addresses quasi-static loading of the shear compression specimen (SCS), that has been especially developed to investigate the shear response of materials at various strain rates. Previous work [4, 5] addressed bi-linear hardening materials, whereas the present work concerns parabolic hardening materials. The investigation is done numerically using three-dimensional elastoplastic finite element simulations. The analyses show that the averaged von Mises stress ( ) and strain ( ) on a mid-section of the gauge reflect accurately the prescribed parabolic hardening model. A method for finding the parabolic hardening coefficients and reducing the measured load, P, and displacement, d, into equivalent stress and strain is introduced and tested. A very good agreement is observed, thus confirming the potential of the technique for large strain testing of parabolic hardening materials.     

On the Local Smoothness of Solutions of the Navier–Stokes Equations

We consider the Cauchy problem for incompressible Navier–Stokes equations with initial data in , and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have , as long as stays finite.     

Traveling Waves of a Singularly Perturbed System of Integral–Differential Equations Arising from Neuronal Networks

A nonlinear nonlocal model arising from synaptically coupled neuronal networks with two integral terms is considered. The existence and stability of several traveling wave solutions are established by using ideas in differential equations and functional analysis. Steady-state solutions of some inhomogeneous integral–differential equations are also investigated. We consider several types of kernel functions: (I) positive functions, such as and , where ρ>0 is a constant; (II) nonnegative kernels with compact supports, for examples, (i) 1$$" align="middle" border="0"> , and (ii) {\pi\over 2}$$" align="middle" border="0"> ; (III) Mexican hat type kernel functions, such as and , where A>B>0 and a>b>0 are constants.Dedicated to Professor Yulin Zhou and Professor Boling Guo on the Occassions of their birthdays.     

Unexpected Behavior of Nonautonomous Linear Dynamical Systems in Two Dimensions

We show two examples of systems in with such that |Z_t| is strictly decreasing in time for any n but as .     

Existence of Weak Solutions to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with Shear Rate Dependent Viscosity

In the present paper we prove the existence of weak solutions to the equations of non-stationary motion of an incompressible fluid with shear rate dependent viscosity in a cylinder Q = Ω × (0,T), where denotes an open set. For the power-low model with we are able to construct a weak solution with ∇ · u = 0.     

Superstable Manifolds of Semilinear Parabolic Problems

We investigate the dynamics of the semiflow φ induced on H₀¹(Ω) by the Cauchy problem of the semilinear parabolic equation

Dynamic Contact Behavior of a Golf Ball during an Oblique Impact

The oblique impact between a golf ball and a rigid steel target was studied using a high-speed video camera. Video images recorded before and after the impact were used to determine the inbound velocity v _i, rebound velocity v _r, inbound angle θ_i, rebound angle θ_r, and the coefficient of restitution e. The results showed that θ_r and e decreased as v _i increased. The maximum compression ratio η_c, contact time t _c, average angular velocity , and tangential velocity , along the target were determined from images obtained during the impact. The images demonstrated that η_c increased with v _i while t _c decreased. In addition, and increased almost linearly as v _i increased. A rigid body model was used to estimate the final angular velocity ω* and tangential velocity ν_t* at the end of the impact; these results were then compared with experimental data.     

Interface Vanishing for Solutions to Maxwell and Stokes Systems

This paper is concerned with the component-wise regularity of the solution to the stationary Maxwell or Stokes systems. We assume that there is a surface in R³, regarded as an interface, and the solution u to one of the systems is smooth except for this . Then, under these assumptions, we can show that some components of u are smooth across . In the Maxwell system, the normal component of u is always regular across . On the other hand, in the Stokes system, the singularity of u across can only arise to the normal derivatives of its tangential components. Furthermore, these results are shown to be optimal.     

Time-Averaged Photoelastic Stress Analysis of the Ultrasonic Wave in a Strip

In this paper, a digital photoelastic system was employed to observe the stress distribution generated by an ultrasonic wave impinged at the edge of a strip. According to the classical photoelastic theory, gray level distribution of the photoelastic fringe patterns was formulated and expressed in the form of , where J₀ is the zeroth-order Bessel function. This new technique is called the time-averaged photoelastic method. To verify the proposed method, the distribution of was superimposed onto the distribution of gray level of the experimentally obtained photoelastic fringe pattern caused by standing wave only. Except regions near the center of fringes, well-matched results were found.     

Stokes and Navier–Stokes Equations with Robin Boundary Conditions in a Half-Space

We study the initial-boundary value problem for the Stokes equations with Robin boundary conditions in the half-space It is proved that the associated Stokes operator is sectorial and admits a bounded H^∞-calculus on As an application we prove also a local existence result for the nonlinear initial value problem of the Navier–Stokes equations with Robin boundary conditions.     

Strong Solutions for Generalized Newtonian Fluids

We consider the motion of a generalized Newtonian fluid, where the extra stress tensor is induced by a potential with p-structure (p = 2 corresponds to the Newtonian case). We focus on the three dimensional case with periodic boundary conditions and extend the existence result for strong solutions for small times from \tfrac{5}{3}$$ " align="middle" border="0"> (see [16]) to \tfrac{7}{5}.$$ " align="middle" border="0"> Moreover, for we improve the regularity of the velocity field and show that for all 0.$$ " align="middle" border="0"> Within this class of regularity, we prove uniqueness for all \tfrac{7}{5}.$$ " align="middle" border="0"> We generalize these results to the case when p is space and time dependent and to the system governing the flow of electrorheological fluids as long as      

On the Deformation of the Circumflex Coronary Artery During Inflation Tests at Constant Length

Here we investigate whether the deformation observed in an experiment in which the porcine circumflex coronary artery is subjected to inflation at constant length included in the class, , , . We find that this is not the case and discuss its implications in the study of the mechanics of this artery. Moreover, we identify and quantify the uncertainty in the value of the invariants of the left Cauchy–Green tensor inferred from the 2D motion of markers affixed to the surface of the test specimen, and suggest that 3D tracking of markers is needed due to inherent bending and twisting induced by pressurization in vitro.     

Second Order Multiple Scales for Oscillators with Large Delay

We use the method of multiple scales (MMS) to study small perturbations, governed by a parameter , of a harmonic oscillator by a small term with a large delay. These systems differ significantly from others where small terms have delays; or an term has delay in a system near a Hopf bifurcation. Here, the slow flow in time t depends strongly on even at lowest order, and itself has an delay. The MMS has already been applied elsewhere for such systems, but only to first order and with attention restricted to periodic and quasiperiodic solutions. Here, we address transients as well as proceed to second order. The second order analysis holds unless a special resonance occurs (we assume it does not). Several numerical examples are presented. In each case, the slow flows are infinite-dimensional, show strong -dependence, require significantly less computation time than the full solutions, yet agree well with the same.     

Homologies of Intersections of Pseudomanifolds with Local Homotopic Conditions on Links of Strata

In terms of local homotopic properties of the links of strata of an n-dimensional PL-pseudomanifold X, we obtain a sufficient condition for the natural homomorphisms of the jth intersection homology groups with perversity multiindices and to be isomorphisms for all j i, where i < n – 3.     

Some Results on the <Emphasis Type="BoldItalic">m</Emphasis>-Laplace Equations with Two Growth Terms

We prove the existence of positive radial solutions of the following equation:

On Approximations of First Integrals for a Strongly Nonlinear Forced Oscillator

In this paper a strongly nonlinear forced oscillator will be studied. It will be shown that the recently developed perturbation method based on integrating factors can be used to approximate first integrals. Not onlyapproximations of first integrals will be given, butit will also be shown how, in a rather efficient way, the existence and stability oftime-periodic solutions can be obtained from these approximations. In additionphase portraits, Poincaré-return maps, and bifurcation diagrams for a set of values of the parameters will be presented. In particularthe strongly nonlinear forced oscillator equation will be studied in this paper. It will be shown that the presentedperturbation method not onlycan be applied to a weakly nonlinear oscillator problem (that is, when the parameter ) but also to a strongly nonlinear problem (that is, when ). The model equation as considered in this paper is related to the phenomenon of galloping ofoverhead power transmission lines on which ice has accreted.     

Density-Dependent Incompressible Fluids in Bounded Domains

This paper is devoted to the study of the initial value problem for density dependent incompressible viscous fluids in a bounded domain of with boundary. Homogeneous Dirichlet boundary conditions are prescribed on the velocity. Initial data are almost critical in term of regularity: the initial density is in W^1,q for some q > N, and the initial velocity has fractional derivatives in L^r for some r > N and arbitrarily small. Assuming in addition that the initial density is bounded away from 0, we prove existence and uniqueness on a short time interval. This result is shown to be global in dimension N = 2 regardless of the size of the data, or in dimension N ≥ 3 if the initial velocity is small. Similar qualitative results were obtained earlier in dimension N = 2, 3 by O. Ladyzhenskaya and V. Solonnikov in [18] for initial densities in W^1,∞ and initial velocities in with q > N.     

Relations Between Energy and Enstrophy on the Global Attractor of the 2-D Navier-Stokes Equations

We examine how the global attractor of the 2-D periodic Navier–Stokes equations projects in the normalized, dimensionless energy–enstrophy plane (e, E). We treat time independent forces, with the view of understanding how the attractor depends on the nature of the force. First we show that for any force, is bounded by the parabola E = e^1/2 and the line E=e. We then show that for to have points near enough to the parabola, the force must be close to an eigenvector of the Stokes operator A; it can intersect the parabola only when the force is precisely such an eigenvector, and does so at a steady state parallel to this force. We construct a thin region along the parabola, pinched at such steady states, that the attractor can never enter. We show that 0 cannot be on the attractor unless the force is in H^m for all m. Different lower bound estimates on the energy and enstrophy on are derived for both smooth and nonsmooth forces, as are bounds on invariant sets away from 0 and near the line E = e. Motivation for the particular attention to the regions near the parabola and near 0 comes from turbulence theory, as explained in the introduction. Mathematics Subject Classification (2000): 35Q30, 76F02.     

Periodic Trajectories near Degenerate Equilibria in the Hénon-Heiles and Yang-Mills Hamiltonian Systems

This paper deals with connected branches of nonstationary periodic trajectories of Hamilton equations