Large deviations for stochastic partial differential equations driven by a Poisson random measure

Stochastic partial differential equations driven by Poisson random measures (PRMs) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential equation (PDE). A systematic framework for the study of probabilities of deviations of the stochastic PDE from the deterministic PDE is through the theory of large deviations. The goal of this work is to develop the large deviation theory for small Poisson noise perturbations of a general class of deterministic infinite dimensional models. Although the analogous questions for finite dimensional systems have been well studied, there are currently no general results in the infinite dimensional setting. This is in part due to the fact that in this setting solutions may have little spatial regularity, and thus classical approximation methods for large deviation analysis become intractable. The approach taken here, which is based on a variational representation for nonnegative functionals of general PRMs, reduces the proof of the large deviation principle to establishing basic qualitative properties for controlled analogues of the underlying stochastic system. As an illustration of the general theory, we consider a particular system that models the spread of a pollutant in a waterway.     

Large deviations for multiscale diffusion via weak convergence methods

We study the large deviations principle for locally periodic SDEs with small noise and fast oscillating coefficients. There are three regimes depending on how fast the intensity of the noise goes to zero relative to homogenization parameter. We use weak convergence methods which provide convenient representations for the action functional for all regimes. Along the way, we study weak limits of controlled SDEs with fast oscillating coefficients. We derive, in some cases, a control that nearly achieves the large deviations lower bound at prelimit level. This control is useful for designing efficient importance sampling schemes for multiscale small noise diffusion.     

Coupled-channel calculation of nonelastic cross sections using a density-functional structure model

A microscopic calculation of reaction cross sections for nucleon-nucleus scattering was performed by coupling the elastic channel to all particle-hole excitations in the target and one-nucleon pickup channels. The particle-hole states may be regarded as doorway states through which the flux flows to more complicated configurations, and subsequently to long-lived compound nucleus resonances. Target excitations for (40,48)Ca, 58Ni, 90Zr, and 144Sm were described in a random-phase framework using a Skyrme functional. Reaction cross sections obtained agreed very well with experimental data and predictions of a fitted optical potential. Couplings between inelastic states were found to be negligible, while the pickup channels contribute significantly. For the first time observed absorptions are completely accounted for by explicit channel coupling, for incident energies between 10 and 40 MeV.     

Maximal orbital analysis of molecular wavefunctions

We describe a new way to decompose one-electron orbitals of a molecule into atom-centered or fragment-centered orbitals by an approach that we call “maximal orbital analysis” (MOA). The MOA analysis is based on the corresponding orbital transformation (COT) that has the unique mathematical property of maximizing any sub-trace of the overlap matrix, in Hilbert metric sense, between two sets of nonorthogonal orbitals. Here, one set comprises the molecule orbitals (Hartree–Fock, Kohn–Sham, complete-active-space, or any set of orthonormal molecular orbitals), the other set comprises the basis functions associated with an atom or a group of atoms. We show in prototypical molecular systems such as a water dimer, metal carbonyl complexes, and a mixed-valent transition metal complex, that the MOA orbitals capture very well key aspects of wavefunctions and the ensuing chemical concepts that govern electronic interactions in molecules. © 2019 Wiley Periodicals, Inc.     

Simulation of an Ultrahigh-Pressure Short-Arc Xenon Discharge Plasma

Technical Physics - We have studied a high- (ultrahigh-) pressure short-arc discharge in xenon with thoriated tungsten cathodes. A system of equations formulated based on earlier experimental data...     

Non-perturbative renormalization-group approach to lattice models

The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a φ⁴ theory defined on a d-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve the flow equations and obtain the renormalized dispersion epsilon(q) over the whole Brillouin zone of the reciprocal lattice. In the long-distance limit, where the lattice does not matter any more, we reproduce the usual flow equations of the continuum model. We show how the numerical solution of the flow equations can be simplified by expanding the dispersion in a finite number of circular harmonics.     

Peptide-Mediated Targeted Delivery of Aloe-Emodin as Anticancer Drug

Breast cancer is one of the most diffuse cancers in the world and despite the availability of the different drugs employed against it, the need for new and particularly more specific molecules is ever growing. In this framework, natural products are increasingly assuming an important role as new anticancer drugs. Aloe-emodin (AE) is one of the best characterized molecules in this field. The functionalization of bioactive natural products with selected peptide sequences to enhance their bioavailability and specificity of action is a powerful and promising strategy. In this study, we analyzed the cell specificity, cell viability effects, intracellular distribution, and immune cell response of a new peptide conjugate of Aloe-emodin in SKBR3 and A549 cell lines by means of viability tests, flow cytometry, and confocal microscopy. The conjugate proved to be more effective at reducing cell viability than AE in both cell lines. Furthermore, the results showed that it was mainly internalized within the SKBR3 cells, showing a nuclear localization, while A459 cells displayed mainly a cytoplasmic distribution. A preserving effect of the conjugate on NKs’ cell function was also observed. The designed conjugate showed a promising specific activity towards HER2-expressing cells coupled with an enhanced water solubility and a higher cytotoxicity; thus, the resulting proof-of-concept molecule can be further improved as an anticancer compound.     

Asymmetric intramolecular Diels-Alder reactions of N-acyl-camphor-sultam trienes.

Treatment of triene-imides 4 with EtAlCl₂ at ?20° gave crystalline cycloadducts 5 which furnished enantiomerically pure bicyclic alcohols 9 with regeneration of the chiral auxiliary.