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.     

Third‐order WENO scheme with a new smoothness indicator

In this article, we have devised a new reference smoothness indicator for third‐order weighted essentially non‐oscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially non‐oscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the third‐order convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on three‐point stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier third‐order WENO schemes like WENO‐JS and WENO‐Z. Copyright © 2017 John Wiley & Sons, Ltd.     

A mathematical and physical Study of multiscale deconvolution models of turbulence

This work presents a rigorous analysis of mathematical and physical properties for solutions of multiscale deconvolution turbulence models. We show that solutions of these models exactly conserve model quantities for the integral invariants of fundamental physical importance: kinetic energy, helicity, and (in two dimensions) enstrophy. The kinetic energy conservation is the key that allows us to next apply the phenomenology of homogeneous, isotropic turbulence to establish the existence of a model energy cascade and, in particular, that the cascade exhibits enhanced energy dissipation in a secondary accelerated cascade, which ends at the model's microscale (which we establish is larger than the Kolmogorov microscale). We also prove that the model dissipates energy at the same rate as true turbulent flow, ～ O(U³ ∕ L), independent of Reynolds number. Lastly, we prove the existence of global attractors for the model solutions; the proof of which also shows that solutions are actually one degree of regularity higher than previously known. Copyright © 2012 John Wiley & Sons, Ltd.     

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

For nonlinear Schrödinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed.     

Density,viscosity and thermodynamic activation for viscous flow of water+sulfolane

Densities and viscosities for the system, water (W)?+?sulfolane (SFL), have been determined for the entire range of composition at temperatures ranging from 303.15 to 323.15?K. Density, excess molar volume, viscosity, excess viscosity and thermodynamic activation parameters for viscous flow have been calculated and plotted against the mole fraction of SFL. The measured properties and some of the derived properties have been fitted to appropriate polynomial equations. These have been explained in terms of such factors, as, dipole–dipole interaction, partial accommodation of water molecules into the structural network of SFL and H-bonding between SFL and H₂O.