Removable sets for homogeneous linear partial differential equations in Carnot groups

Let L be a homogeneous left-invariant differential operator on a Carnot group. Assume that both L and L^t are hypoelliptic. We study the removable sets for L-solutions. We give precise conditions in terms of the Carnot- Caratheodory Hausdorff dimension for the removability for L-solutions under several auxiliary integrability or regularity hypotheses. In some cases, our criteria are sharp on the level of the relevant Hausdorff measure. One of the main ingredients in our proof is the use of novel local self-similar tilings in Carnot groups.     

A kinetic study of the formation of polystyrene stars using 1,2-bis(trichlorosilyl)ethane

The kinetics of formation of a chlorosilane-linked polystyrene six-arm star is reported. The precursor arm material (M_n = 88,000) was made using anionic polymerization in benzene. Prior to addition to the 1,2-bis(trichlorosilyl) ethane linking agent, the anions were endcapped with about five units of isoprene. Size exclusion chromatography using multiangle laser light scattering and viscosity detectors was utilized for characterization. This technique has allowed the molecular weights, radii of gyration, and intrinsic viscosities to be measured for star components in aliquots taken from the reactor at various times. It was found that four-arm star is formed within 30 min after the addition of the chlorosilane linking agent. There is a linear relationship between the logarithm of molecular weight of the star samples and logarithm of time of the reaction after the formation of the four-arm star. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 587–594, 1997     

A diagnostic tool for jet noise using a line-source approach and implicit large-eddy simulation data

In this work, we propose a cost-effective approach allowing one to evaluate the acoustic field generated by a turbulent jet. A turbulence-resolving simulation of an incompressible turbulent round jet is performed for a Reynolds number equal to $460,000$ thanks to the massively parallel high-order flow solver Incompact3d. Then a formulation of Lighthill's solution is derived, using an azimuthal Fourier series expansion and a compactness assumption in the radial direction. The formulation then reduces to a line source theory, which is cost-effective to implement and evaluate. The accuracy of the radial compactness assumption, however, depends on the Strouhal number, the Mach number, the observation elevation angle, and the radial extent of the source. Preliminary results are showing that the proposed method approaches the experimental overall sound pressure level by less than 4 dB for aft emission angles below 50°.     

F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories

We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S³ partition functions. An explicit illustration based on the known analytic solution of the Chern-Simons matrix model is presented.     

Modeling of the shape of infrared stimulated luminescence signals in feldspars

This paper presents a new empirical model describing infrared (IR) stimulation phenomena in feldspars. In the model electrons from the ground state of an electron trap are raised by infrared optical stimulation to the excited state, and subsequently recombine with a nearest-neighbor hole via a tunneling process, leading to the emission of light. The model explains the experimentally observed existence of two distinct time intervals in the luminescence intensity; a rapid initial decay of the signal followed by a much slower gradual decay of the signal with time.The initial fast decay region corresponds to a fast rate of recombination processes taking place along the infrared stimulated luminescence (IRSL) curves. The subsequent decay of the simulated IRSL signal is characterized by a much slower recombination rate, which can be described by a power-law type of equation.Several simulations of IRSL experiments are carried out by varying the parameters in the model. It is found that the shape of the IRSL signal is remarkably stable when the kinetic parameters are changed within the model; this is in agreement with several previous studies of these signals on feldspars, which showed that the shape of the IRSL curves does not change significantly under different experimental conditions. The relationship between the simulated IRSL signal and the well-known power-law dependence of relaxation processes in solids is also explored, by fitting the IRSL signal at long times with a power-law type of equation. The exponent in this power-law is found to depend very weakly on the various parameters in the model, in agreement with the results of experimental studies. The results from the model are compared with experimental IRSL curves obtained using different IR stimulating power, and good quantitative agreement is found between the simulation results and experimental data.     

Superlinear dose response of thermoluminescence (TL) and optically stimulated luminescence (OSL) signals in luminescence materials: An analytical approach

The phenomenon of superlinear dose response of thermoluminescence (TL) and optically stimulated luminescence (OSL) signals has been reported for several important dosimetric materials. We develop new analytical equations for the filling of traps and centers during irradiation and for the read-out stage of annealed luminescence materials, within the context of a two-trap and two-center model. The equations are applicable for both TL and OSL signals in annealed dosimetric materials, and are derived under the assumptions of low irradiation doses and dominant strong retrapping (weak recombination) processes. For low doses all traps and centers display linear dose response, which leads to quadratic dose response of the integrated TL/OSL signals. A new analytical expression is presented for this well-known quadratic dose dependence, in terms of the kinetic parameters in the model. The effect of elevated irradiation temperature on the integrated TL/OSL signals is also considered, and analytical expressions are obtained for this situation as well. A new type of dose-rate effect is reported based on the modeling results, which is due to irradiation during elevated temperatures. The accuracy of the analytical expressions is verified by comparing with the results of numerical simulations.     

Lactate Biosensor Based on the Adsorption of Polyelectrolyte Stabilized Lactate Oxidase into Porous Conductive Carbon

 In this work the development a lactate biosensor is illustrated. Lactate oxidase is stabilized with the cationic polyelectrolyte diethylaminoethyl-dextran, and the resulting enzyme-polyelectrolyte complexes are physically absorbed into a highly porous and conductive carbon electrode for the construction of the biosensor. The amount of diethylaminoethyl-dextran used is optimized with respect to the sensor sensitivity and stability. Optimum results obtained with enzyme solution containing 0.5% w/v diethylaminoethyl-dextran and 200 U/ml lactate oxidase. The resulting biosensors present increased operational (over 240 hours of continuous polarization) and storage stability (more than 5 months), while the reproducibility was calculated to be better than 5.0% RSD.     

Resonance in viscous film flow over topography

We study viscous gravity-driven films flowing over periodically undulated substrates. Linear analysis describes resonance in steady flow along small bottom corrugations for films of arbitrary thickness. Depending on the dimensionless film thickness we find different regimes for the resonance, which is associated with the interaction of the undulated film with capillarygravity waves traveling against the flow. Nonlinear resonance produces higher harmonics and bistable resonance. The higher harmonics are due to higher harmonics resonance and due to the nonlinear coupling to lower harmonics. For the bistable resonance we derive a minimum model showing that the bistability corresponds essentially to that of the driven Duffing oscillator. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rod-coil block copolymers incorporating terfluorene segments for stable blue light emission

Spectroscopic studies on a series of rod-coil block copolymers with terfluorene as the rigid segment demonstrate that the main cause of color instability in fluorene oligomers and polymers is aggregate and/or excimer formation and not the presence alone of keto defects (fluorenone formation) along the molecular chain. Keto defects, when present, contribute to the appearance of the undesirable "green" emission band but are not the leading cause of color instability. Thus, the synthesis of materials where aggregation and/or interchain, intersegment interactions are inhibited is the key approach for the production of stable polymeric light-emitting devices (PLED's). The potential of this method is verified by the synthesis of photooxidative stable fluorene/styrene diblock copolymer blue emitters.     

New highly luminescent cationic polyelectrolytes based on poly(phenylenevinylene‐alt‐fluorenevinylene) or poly(fluorenevinylene) derivatives and their neutral precursors

Poly(phenylenevinylene‐alt‐fluorenevinylene) ( PF ) or poly(fluorenevinylene) ( F ) derivatives that carried alkyl chains with terminal tertiary amino groups were successfully synthesized via Heck coupling. They were postquaternized by reacting with bromoethane to the corresponding cationic polyelectrolytes PFQ and FQ . The neutral polymers PF and F as well as the quaternized polymer FQ were soluble in common organic solvents such as THF, chloroform, dichloromethane, and toluene. In contrast, the quaternized polymer PFQ did not dissolve in these solvents but was soluble in environmentally friendlier solvents like water and alcohols. The neutral precursors exhibited higher thermal stability and glass‐transition temperatures than the corresponding quaternized counterparts. All polymers emitted intense blue‐greenish light in solution (462–489 nm) with relatively high photoluminescence (PL) quantum yields 0.32–0.57, and as thin films (475–557 nm) with optical band gaps of 2.48–2.57 eV. The water soluble PFQ could find potential applications as chemo or biosensor. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1481–1491, 2007