Prandtl-Meyer Reflection Configurations, Transonic Shocks, and Free Boundary Problems

We are concerned with the Prandtl-Meyer reflection configurations of unsteady global solutions for supersonic flow impinging upon a symmetric solid wedge. Prandtl (1936) first employed the shock polar analysis to show that there are two possible steady configurations: the steady weak/strong shock solutions, when a steady supersonic flow impinges upon the wedge whose angle is less than the detachment angle, and then conjectured that the steady weak shock solution is physically admissible. The fundamental issue of whether one or both of the steady wea/strong shocks are physically admissible has been vigorously debated over the past eight decades. On the other hand, the Prandtl-Meyer reflection configurations are core configurations in the structure of global entropy solutions of the 2-D Riemann problem, while the Riemann solutions themselves are local building blocks and determine local structures, global attractors, and large-time asymptotic states of general entropy solutions. In this sense, we have to understand the reflection configurations in order to understand fully the global entropy solutions of 2-D hyperbolic systems of conservation laws, including the admissibility issue for the entropy solutions. In this monograph, we address this longstanding open issue and present our analysis to establish the stability theorem for the steady weak shock solutions as the long-time asymptotics of the Prandtl-Meyer reflection configurations for unsteady potential flow for all the physical parameters up to the detachment angle. To achieve these, we first reformulate the problem as a free boundary problem involving transonic shocks and then obtain appropriate monotonicity properties and uniform a priori estimates for admissible solutions, which allow us to employ the Leray-Schauder degree argument to complete the theory for all the physical parameters up to the detachment angle.Comment: 192 pages; 17 figures; To appear in the AMS series "Memoirs of the American Mathematical Society", 202

Detecting the degree of macroscopic quantumness using an overlap measurement

We investigate how to experimentally detect a recently proposed measure to quantify macroscopic quantum superpositions [Phys. Rev. Lett. 106, 220401 (2011)], namely, "macroscopic quantumness" $\mathcal{I}$. Schemes based on overlap measurements for harmonic oscillator states and for qubit states are extensively investigated. Effects of detection inefficiency and coarse-graining are analyzed in order to assess feasibility of the schemes.Comment: 12 pages, 8 figures, to be published in J. Opt. Soc. Am.

Albumin-heparin microspheres as carriers for cytostatic agents

Much work has been done on adriamycin-loaded albumin microspheres (Alb-MS) for chemoembolization [1–4], the rationale being that site-specific drug delivery may increase the therapeutic efficacy of the drug. Alb-Ms are being investigated because of their biocompatibility and because the degradation products of these microspheres are non-toxic. However, these microspheres have some disadvantages (i.e. drug loading during the microsphere preparation, low payloads, large burst effects). These disadvantages can be overcome by the incorporation of heparin (a highly negatively charged mucopolysaccharide). Albumin-heparin microspheres were prepared (i) by crosslinking of soluble albumin and heparin first using 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC) and subsequently glutaraldehyde (Alb-Hep-MS) and (ii) by crosslinking a preformed soluble conjugate of heparin and albumin with glutaraldehyde (Alb-Hep-Conj-MS). Albumin-heparin microspheres could be loaded with adriamycin after microsphere preparation giving payloads of 15–30%. Preliminary in vitro adriamycin release experiments showed that Alb-Hep-Conj-MS exhibit sustained release properties. Furthermore ion-exchange properties could be observed both with Alb-Hep-MS and Alb-Hep-Conj-MS. In vitro and in vivo toxicity experiments with Alb-Hep-MS showed no adverse effects

Adriamycin loading and release characteristics of albumin-heparin conjugate microspheres

Biodegradable ion-exchange microspheres, prepared from a prefabricated conjugate of albumin and heparin were investigated as carriers for adriamycin. The ion-exchange microspheres could be loaded with adriamycin giving payloads up to 33% w/w, depending on the heparin content of the conjugate. In vitro adriamycin release depended on the ionic strength of the release medium. In ion containing media, for instance saline, 90% of the drug was released within 45 min, whereas in non-ionic media, such as distilled water, only 30% was released. Drug release profiles could be modelled by combining ion-exchange kinetics and diffusion controlled drug release models

Atomic and nano-scale characterization of a 50-year-old hydrated C3S paste

This paper investigates the atomic and nano-scale structures of a 50-year-old hydrated alite paste. Imaged by TEM, the outer product C-S-H fibers are composed of particles that are 1.5-2 nm thick and several tens of nanometers long. 29Si NMR shows 47.9% Q1 and 52.1% Q2, with a mean SiO4 tetrahedron chain length (MCL) of 4.18, indicating a limited degree of polymerization after 50 years' hydration. A Scanning Transmission X-ray Microscopy (STXM) study was conducted on this late-age paste and a 1.5 year old hydrated C3S solution. Near Edge X-ray Absorption Fine Structure (NEXAFS) at Ca L3,2-edge indicates that Ca2 + in C-S-H is in an irregular symmetric coordination, which agrees more with the atomic structure of tobermorite than that of jennite. At Si K-edge, multi-scattering phenomenon is sensitive to the degree of polymerization, which has the potential to unveil the structure of the SiO44 - tetrahedron chain

Adriamycin-loaded albumin-heparin conjugate microspheres for intraperitoneal chemotherapy

Adriamycin-loaded albumin-heparin conjugate microspheres (ADR-AHCMS) were evaluated as possible intraperitoneal (i.p.) delivery systems for site-specific cytotoxic action. The biocompatibility of the microspheres after intraperitoneal injection was tested first. 1 day after i.p. administration of empty as well as drug-loaded AHCMS to male Balb/c mice, only a moderate increase in i.p. neutrophils was measured. 3 days after injection neutrophil levels were comparable with the controls. No significant increases in the numbers of other cell types were observed, indicating an acute inflammatory response which can be considered to be mild. Antitumour efficacy was tested in an L1210 tumour-bearing mouse model and in a CC531 tumour-bearing rat model. The use of ADR-AHCMS leads to longer survival times of mice and improved tumour growth delay in rats, as compared with untreated controls and free drug treated animals. In both animal models higher adriamycin doses were initially tolerated if the drug was formulated in microspheres, although long-term adriamycin toxicity effects were evident in all treated groups. Doses and dosage schedules may be optimized to further reduce the toxic effects of the drug

Preparation and characterization of albumin-heparin microspheres

Albumin-heparin microspheres were prepared by a two-step process which involved the preparation of a soluble albumin-heparin conjugate, followed by formation of microspheres from this conjugate or by a double cross-linking technique involving both coupling of soluble albumin and heparin and microsphere stabilization in one step. The first technique was superior since it allowed better control over the composition and the homogeneity of the microspheres. Microspheres could be prepared with a diameter of 5¿35¿m. The size could be controlled by adjusting the emulsification conditions. The degree of swelling of the microspheres was sensitive to external stimuli, and increased with increasing pH and decreasing ionic strength of the medium

PAMELA's cosmic positron from decaying LSP in SO(10) SUSY GUT

We propose two viable scenarios explaining the recent observations on cosmic positron excess. In both scenarios, the present relic density in the Universe is assumed to be still supported by thermally produced WIMP or LSP (\chi). One of the scenarios is based on two dark matter (DM) components (\chi,X) scenario, and the other is on SO(10) SUSY GUT. In the two DM components scenario, extremely small amount of non-thermally produced meta-stable DM component [O(10^{-10}) < n_X /n_\chi] explains the cosmic positron excess. In the SO(10) model, extremely small R-parity violation for LSP decay to e^\pm is naturally achieved with a non-zero VEV of the superpartner of one right-handed neutrino (\tilde{\nu}^c) and a global symmetry.Comment: 6 pages, Talks presented in PASCOS, SUSY, and COSMO/CosPA in 201

Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order. We establish a first global theory of existence and regularity for this shock diffraction problem. In particular, we establish that the optimal regularity for the solution is $C^{0,1}$ across the degenerate sonic boundary. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.Comment: 50 pages;7 figure