A coupled immersed boundary‐lattice Boltzmann method with smoothed point interpolation method for fluid‐structure interaction problems

The immersed boundary‐lattice Boltzmann method has been verified to be an effective tool for fluid‐structure interaction simulation associated with thin and flexible bodies. The newly developed smoothed point interpolation method (S‐PIM) can handle the largely deformable solids owing to its softened model stiffness and insensitivity to mesh distortion. In this work, a novel coupled method has been proposed by combining the immersed boundary‐lattice Boltzmann method with the S‐PIM for fluid‐structure interaction problems with large‐displacement solids. The proposed method preserves the simplicity of the lattice Boltzmann method for fluid solvers, utilizes the S‐PIM to establish the realistic constitutive laws for nonlinear solids, and avoids mesh regeneration based on the frame of the immersed boundary method. Both two‐ and three‐dimensional numerical examples have been carried out to validate the accuracy, convergence, and stability of the proposed method in consideration of comparative results with referenced solutions.     

Stable blow-up dynamics in the -critical and -supercritical generalized Hartree equation

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: First, we consider the -critical case in dimensions and obtain that a generic blow-up has a self-similar structure and exhibits not only the square root blowup rate , but also the log-log correction (via asymptotic analysis and functional fitting), thus, behaving similarly to the stable blow-up regime in the -critical nonlinear Schrödinger equation. In this setting, we also study blow-up profiles and show that generic blow-up solutions converge to the rescaled , a ground state solution of the elliptic equation . We also consider the -supercritical case in dimensions . We derive the profile equation for the self-similar blow-up and establish the existence and local uniqueness of its solutions. As in the NLS -supercritical regime, the profile equation exhibits branches of nonoscillating, polynomially decaying (multi-bump) solutions. A numerical scheme of putting constraints into solving the corresponding ordinary differential equation is applied during the process of finding the multi-bump solutions. Direct numerical simulation of solutions to the generalized Hartree equation by the dynamic rescaling method indicates that the is the profile for the stable blow-up. In this supercritical case, we obtain the blow-up rate without any correction. This blow-up happens at the focusing level , and thus, numerically observable (unlike the -critical case). In summary, we find that the results are similar to the behavior of stable self-similar blowup solutions in the corresponding settings for the nonlinear Schrödinger equation. Consequently, one may expect that the form of the nonlinearity in the Schrödinger-type equations is not essential in the stable formation of singularities.     

Integrated Digital Image Correlation considering gray level and blur variations: Application to distortion measurements of IR camera

The acquisition of images with different modalities may involve different alterations with respect to an ideal model. Inhomogeneous brightness and contrast, blur due to non-ideal focusing, distortions are common. It is proposed herein to account for such effects for instance by registering a calibration target image with an actual optical image to measure lens distortions. An Integrated Digital Image Correlation (I-DIC) algorithm is proposed to account for the above artifacts and the algorithm is detailed. The resolution and uncertainty of the technique are first investigated on synthetic images, and then applied to the measurement of distortions for infrared (IR) images. The procedure is shown to reduce drastically the residual level assessing the validity of the image formation model, but more importantly allowing for a much improved registration of images.     

Reflection of plane waves in generalized thermoelasticity of type III with nonlocal effect

The generalized thermoelasticity theory based upon the Green and Naghdi model III of thermoelasticity as well as the Eringen's nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves, which are dispersive in nature and experience attenuation. In addition to the coupled waves, there also exists one independent vertically shear-type wave, which is dispersive but experiences no attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear-type wave is found to face a critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients and the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted.     

On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data that can be extended as holomorphic functions in a strip around the x‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity given by , where can be taken arbitrarily small and c is a positive constant.     

Nonexistence of nontrivial global solutions for nonlocal in time differential inequalities

In this paper, some nonlocal in time differential inequalities of Sobolev type are considered. Using the nonlinear capacity method, sufficient conditions for the nonexistence of nontrivial global classical solutions are provided.     

Mixed convection unsteady stagnation point flow over a stretching sheet with heat transfer in the presence of variable free stream

An analysis is performed for the unsteady mixed convection flow of an incompressible viscous fluid about a stagnation point on a stretching sheet in the presence of a variable free stream. The equations of motion and energy are transformed into the ordinary differential equations by using similarity transformations. Homotopy analysis method is used for the solution of the governing problem. The results have been discussed by plots. The present values of the function are shown very close to the previous limiting solutions. Copyright © 2011 John Wiley & Sons, Ltd.     

A vectorial algorithm with finite element method for prediction of powder segregation in metal injection molding

The design of the mold and the choice of the injection parameters for metal injection molding (MIM) is required to maintain homogeneity of the filled mixture. However, powder segregation is unavoidable in MIM because of the significant difference in densities of the metallic powder and the polymer binder. To achieve an effective prediction of segregation effect, a biphasic model based on mixture theory is employed. The viscous behaviors of each phase and the interaction coefficient between the flows of the two phases should be determined. The solution of two coupled Navier–Stokes equations results in a tremendous computation effort. The previous development of an explicit algorithm makes the biphasic simulation much faster than that of the classic methods. However, it is strongly desired to reduce or even eliminate the numerous global solutions for pressure fields at each time step. Hence, a new vectorial algorithm is proposed and developed to perform the simulation only by vectorial operations. It provides the anticipated efficiency in the simulation of biphasic modeling, and the advantage to use the classic elements of equal‐order interpolations. Some results produced by the two algorithms are compared with the experimental values to validate the new vectorial algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

NONUNIQUENESS AND SINGULAR RADIAL SOLUTIONS OF SYSTEMS OF CONSERVATION LAWS Dedicated to Professor Constantine M. Dafcrmos on the occasion of his 70th birthday

The case of a radial initial state for a family of hyperbolic systems of conservation laws with several spatial dimensions is considered.It will be shown that the singularity at the origin introduces multiple solutions outside of the traditional admissible classes.