The Sedov self-similar point blast solutions in nonuniform media

The character of a spherical blast wave propagating radially outward in a pressureless medium with density decreasing as ^– changes dramatically as and the adiabatic index vary. Plots of the Sedov formulas for the density, velocity, and pressure profiles behind the shock front for a selection of different parameters illustrate this and suggest that some of the solutions satisfy the conditions for the Rayleigh-Taylor or convective instablity.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.     

Synthesis,surface property,micellization and pH responsivity of fluorinated gradient copolymers

In this work, fluorinated nonamphiphilic gradient copolymers of tert‐butyl acrylate (tBA) and 2,2,3,3,4,4,4‐heptafluorobutyl methacrylate (HFBMA) [poly(tBA‐grad‐HFBMA)] were first synthesized by semibatch atom transfer radical copolymerization of tBA and HFBMA. Their hydrolysis at acidic conditions led to amphiphilic poly(acrylic acid‐grad‐HFBMA). The chemical compositions and structures of these copolymers were characterized by proton nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy, and gel permeation chromatography. Their surface properties were evaluated with water contact angle measurement and x‐ray photoelectron spectroscopy. The micellization behaviors of amphiphilic copolymer were also studied by transmission electron microscopy and dynamic light scattering. The results showed that the fluorinated and amphiphilic gradient copolymers could self‐assemble in a dilute solution to form aggregates of morphologies. Furthermore, the effect of pH on the aggregates was investigated to verify that the resulting gradient copolymers were to some extent pH sensitive. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure

Elastic analysis of a functionally graded thick-walled cylindrical pressure vessel is analytically studied in the present research. Gradation is considered for all mechanical properties along the thickness direction based on a power function. The constitutive relations are developed in the general cylindrical coordinate system for an axisymmetric pressurized cylinder. For simulation of these two deformation components, first order shear deformation theory is considered. The FG cylinder is subjected to longitudinally non-uniform pressure along the length of the cylinder. The present problem is applicable for simulation of non-uniform pressurized cylinder by fluids or gases.     

Improving the sharpness of a non-uniformly illuminated image by an integral mask-filtering approach

We demonstrate an extended mask-filtering approach to improve the sharpness of an image with non-uniform illumination. The proposed method comprises two different masks which cope with higher and lower spatial frequencies respectively. By using this integral algorithm, the enhanced image has much better performance than that derived from the conventional technique.     

Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

The work continues and develops authors’ previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a “canonical” form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers).     

Free vibration of non-uniform column using DQM

Most of engineering problems are governed by a set of partial differential equations with proper boundary conditions. The present work is concerned with free vibration analysis of non-uniform column resting on elastic foundation and subjected to follower force. The used method of solution is the differential quadrature method (DQM). Formulation of the problem is introduced. The results obtained and compared with the exact solution and traditional numerical techniques such as finite element method. The parametric study is used to investigate the effect of column geometry on the natural frequencies, the mode shapes and the critical load.     

Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid

A study of the hydromagnetic flow due to a stretching sheet and heat transfer in an incompressible micropolar liquid is made. Temperature-dependent thermal conductivity and a non-uniform heat source/sink render the problem analytically intractable and hence a numerical study is made using the shooting method based on Runge-Kutta and Newton-Raphson methods. The two problems of horizontal and vertical stretching are considered to implement the numerical method. The former problem involves one-way coupling between linear momentum and heat transport equations and the latter involves two-way coupling. Further, both the problems involve two-way coupling between the non-linear equations of conservation of linear and angular momentums. A similarity transformation arrived at for the problem using the Lie group method facilitates the reduction of coupled, non-linear partial differential equations into coupled, non-linear ordinary differential equations. The algorithm for solving the resulting coupled, two-point, non-linear boundary value problem is presented in great detail in the paper. Extensive computation on velocity and temperature profiles is presented for a wide range of values of the parameters, for prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions.