The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories

The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown

A new gas discharge process for preparation of non-fouling surfaces on biomaterials

A non-fouling surface containing immobilized polyethylene oxide (PEO) was achieved using an argon radio-frequency glow discharge treatment (RFGD) of polyethylene films precoated with Brij hydrocarbon-PEO surfactants. Surface wettability of RFGD-treated and washed surfaces increased the most when PEO surfactants with unsaturated and/or long alkyl tails were used. ESCA measurements of treated and washed surfaces showed increases of surface O/C ratios and ether carbon peaks in high resolution Cls spectra. These results demonstrate the retention of the PEO surfactants on the treated surfaces. Fibrinogen adsorp tion on these treated surfaces was significantly reduced, from 500 to 50 ng/cm2, indicating the non-fouling properties of the RFGD-immobilized PEO surfactants

S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

Immobilization of Polyethylene Oxide Surfactants for Non-Fouling Biomaterial Surfaces Using an Argon Glow Discharge Treatment

A non-fouling (protein-resistant) polymer surface is achieved by the covalent immobilization of polyethylene oxide (PEO) surfactants using an inert gas discharge treatment. Treated surfaces have been characterized using electron spectroscopy for chemical analysis (ESCA), static secondary ion mass spectrometry (SSIMS), water contact angle measurement, fibrinogen adsorption, and platelet adhesion. This paper is intended to review our recent work in using this simple surface modification process to obtain wettable polymer surfaces in general, and non-fouling biomaterial surfaces in particular

Quantum planes and quantum cylinders from Poisson homogeneous spaces

Quantum planes and a new quantum cylinder are obtained as quantization of Poisson homogeneous spaces of two different Poisson structures on classical Euclidean group E(2).Comment: 13 pages, plain Tex, no figure

Small Noise Asymptotics for Invariant Densities for a Class of Diffusions: A Control Theoretic View (with Erratum)

The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (2009) " is flawed. We give here a corrected proof.Comment: 23 pages; Journal of Mathematical Analysis and Applications, 200

Ballistic Annihilation Kinetics: The Case of Discrete Velocity Distributions

The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean field limit, the densities of different velocity species decay in time with different power law rates for many initial conditions. For a one-dimensional symmetric system containing particles with velocity 0 and $\pm 1$, there is a particular initial state for which the concentrations of all three species as decay as $t^{-2/3}$. For the case of a fast ``impurity'' in a symmetric background of $+$ and $-$ particles, the impurity survival probability decays as $\exp(-{\rm const.}\times \ln^2t)$. In a symmetric 4-velocity system in which there are particles with velocities $\pm v_1$ and $\pm v_2$, there again is a special initial condition where the two species decay at the same rate, t^{-\a}, with \a\cong 0.72. Efficient algorithms are introduced to perform the large-scale simulations necessary to observe these unusual phenomena clearly.Comment: 18 text pages, macro file included, hardcopy of 9 figures available by email request to S

Quantized algebras of functions on homogeneous spaces with Poisson stabilizers

Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0<q<1. We study a quantization C(G_q/K_q) of the algebra of continuous functions on G/K. Using results of Soibelman and Dijkhuizen-Stokman we classify the irreducible representations of C(G_q/K_q) and obtain a composition series for C(G_q/K_q). We describe closures of the symplectic leaves of G/K refining the well-known description in the case of flag manifolds in terms of the Bruhat order. We then show that the same rules describe the topology on the spectrum of C(G_q/K_q). Next we show that the family of C*-algebras C(G_q/K_q), 0<q\le1, has a canonical structure of a continuous field of C*-algebras and provides a strict deformation quantization of the Poisson algebra \C[G/K]. Finally, extending a result of Nagy, we show that C(G_q/K_q) is canonically KK-equivalent to C(G/K).Comment: 23 pages; minor changes, typos correcte