The Dirac-Ramond operator on loops in flat space

In this paper, a rigorous construction of the S¹-equivariant Dirac operator (i.e., Dirac-Ramond operator) on the space of (mean zero) loops in is given and its equivariant L²-index computed. Essential use is made of infinite tensor product representations of the canonical anticommutation relations algebra.     

Computational singular perturbation with non-parametric tabulation of slow manifolds for time integration of stiff chemical kinetics

This paper presents a novel tabulation strategy for the adaptive numerical integration of chemical kinetics using the computational singular perturbation (CSP) method. The strategy stores and reuses CSP quantities required to filter out fast dissipative processes, resulting in a non-stiff chemical source term. In particular, non-parametric regression on low-dimensional slow invariant manifolds (SIMs) in the chemical state space is used to approximate the CSP vectors spanning the fast chemical subspace and the associated fast chemical time-scales. The relevant manifold and its dimension varies depending on the local number of exhausted modes at every location in the chemical state space. Multiple manifolds are therefore tabulated, corresponding to different numbers of exhausted modes (dimensions) and associated radical species. Non-parametric representations are inherently adaptive, and rely on efficient approximate-nearest-neighbor queries. As the CSP information is only a function of the non-radical species in the system and has relatively small gradients in the chemical state space, tabulation occurs in a lower-dimensional state space and at a relatively coarse level, thereby improving scalability to larger chemical mechanisms. The approach is demonstrated on the simulation of homogeneous constant pressure H₂–air and CH₄–air ignition, over a range of initial conditions. For CH₄–air, results are shown that outperform direct implicit integration of the stiff chemical kinetics while maintaining good accuracy.     

On the 2 and the 3-connectedness of ample divisors on a surface

Let X be a nonsingular complex projective surface and let D be an ample divisor on X such that the associated invertible sheaf is spanned by its global sections. We prove that D is 2-connected apart from a few cases we explicitly describe. We also provide a corresponding result for the 3-connectedness when D²10 and for the 4-connectedness when D²17 and D is very ample.     

Ond-folds whose canonical bundle is not numerically effective,according to Mori and Kawamata

Sunto In questo lavoro si studiano le varietà non singolari di dimensione d il cui divisore canonico non è numericamente effettivo e si estendono alcuni dei risultati ottenuti da Mori nel caso d=3. CiÒ viene ottenuto mediante un uso sistematico della teoria di Mori dei raggi estremali e di un forte teorema di Kawamata-Shokurov. Quest'ultimo risultato fornisce una varietà normale Y e un morfismo : X Y che contrae un raggio estremale R e che dá la struttura di X. Se R è numericamente effettivo, dimY     

Free differential algebras: Their use in field theory and dual formulation

The gauging of free differential algebras (FDA's) produces gauge field theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer equations of ordinary Lie algebras by incorporating p-form potentials (p>1). We study here the algebra of FDA transformations. To every p-form in the FDA, we associate an extended Lie derivative l generating a corresponding gauge transformation. The field theory based on the FDA is invariant under these new transformations. This gives geometrical meaning to the antisymmetric tensors. The algebra of Lie derivatives is shown to close and provides the dual formulation of FDA's.     

Biodegradable PLGA-b-PEG polymeric nanoparticles: synthesis, properties, and nanomedical applications as drug delivery system

Liquid sodium containing titanium nanoparticles (LSnanop) of 10-nm diameter was prepared by dispersing titanium nanoparticles (2 at.% Ti) into liquid sodium with the addition of stirring and ultrasonic sound wave. The titanium nanoparticles themselves were prepared by the vapor deposition method. This new liquid metal, LSnanop, shows a remarkable stability due to the Brownian motion of nanoparticles in liquid sodium medium. In addition, the difference of measured heat of reaction to water between this LSnanop and liquid sodium indicates the existence of cohesive energy between the liquid sodium medium and dispersed titanium nanoparticles. The origin of the cohesive energy, which serves to stabilize this new liquid metal, was explained by the model of screened nanoparticles in liquid sodium. In this model, negatively charged nanoparticles with transferred electrons from liquid sodium are surrounded by the positively charged screening shell, which may inhibit the gathering of nanoparticles by the ??Coulombic repulsion coating.?? The atomic volume of LSnanop shows the shrinkage from the linear law, which also suggests the existence of cohesive energy. The viscosity of LSnanop is almost the same as that of liquid sodium. This behavior was explained by the Einstein equation. The surface tension of LSnanop is 17?% larger than that of liquid sodium. The cohesive energy and the negative adsorption may be responsible to this increase. Titanium nanoparticles in liquid sodium seem to be free from the Coulomb fission. This new liquid metal containing nanoparticles suggests the possibility to prepare various stable suspensions with new properties.     

Minimalist landscape model of glass relaxation

The relaxation behavior of glass is of great scientific and technological importance. However, prediction of glass relaxation behavior using direct first principles techniques is currently infeasible for realistic laboratory time scales. The enthalpy landscape approach has proven to be successful in overcoming this time scale constraint and providing insights into the fundamental physics governing glass transition and relaxation behavior. However, it is still too computationally intensive to calculate representative enthalpy landscapes for multicomponent glasses of industrial interest. It is thus interesting to consider a simplified enthalpy landscape that captures the essential features of glass relaxation and can be solved analytically. Here, we present the analytical solution for such a “minimalist landscape” model that is complicated enough to capture both primary (α$\alpha$) and secondary (β$\beta$) relaxation processes, yet simple enough to offer a closed-form solution. Using this minimalist landscape, we perform model calculations to illustrate the relative impact of activation barriers and entropy on glass relaxation behavior. The results of our model show that α$\alpha$ and β$\beta$ relaxation processes are largely decoupled, in agreement with recently published experimental results.     

Short‐wavelength infrared defect emission as a probe of degradation processes in 980 nm single‐mode diode lasers

Infrared emission from 980‐nm single‐mode high power diode lasers is recorded and analyzed in the wavelength range from 0.8 to 8.0 μm. A pronounced short‐wavelength infrared (SWIR) emission band with a maximum at 1.3 μm originates from defect states located in the waveguide of the devices. The SWIR intensity is a measure of the non‐equilibrium carrier concentration in the waveguide, allowing for a non‐destructive waveguide mapping in spatially resolved detection schemes. The potential of this approach is demonstrated by measuring spatially resolved profiles of SWIR emission and correlating them with mid‐wavelength infrared (MWIR) thermal emission along the cavity of devices undergoing repeated catastrophic optical damage. The enhancement of SWIR emission in the damaged parts of the cavity is due to a locally enhanced carrier density in the waveguide and allows for an analysis of the spatial damage patterns. The figure shows a side view of a diode laser during catastrophic degradation as recorded by a thermocamera within 5 successive current pulses. The geometry of the device is given in grayscale. The position of the laser chip is indicated by the dotted line. The thermal signatures of the internal degradation of the diode laser are overlaid in color. The bi‐directional spread of the damage along the laser cavity is clearly visible.