A one-parameter family of hamiltonian structures for the KP hierarchy and a continuous deformation of the nonlinear WKP algebra

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting W-algebra is a one-parameter deformation of W_KP admitting a central extension for generic values of the parameter, reducing naturally to W _n for special values of the parameter, and contracting to the centrally extended W₁₊, W and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic tow _KP. The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of which contracts to a new nonlinear algebra of the W-type.Address after October 1993: Queen Mary and Westfield College, UK     

Stability of benzoporphyrin photosensitizers in water/ethanol mixtures: pKa determination and self‐aggregation processes

Benzoporphyrin monoacid derivatives, here named B3A and B3B, are promising new drugs for photodynamic therapy. Although both isomers show interesting characteristics as photosensitizing compounds, they have some distinct physicochemical properties such as the tendency to self‐aggregate in water‐rich media. Because pH drives the presence of each species, the pK_a of these compounds assumes strategic importance. However, traditional micro‐titration methods and UV–Vis absorption techniques fail to give reliable pK_a values due to the characteristics of this highly complex system, such as the precipitation of hydrophobic species, close pK_a values, and high absorption band superposition. In the present work, chemometric tools are employed to evaluate pK_a, and the kinetic tendency of monomers to undergo self‐aggregation is investigated. In solvent mixtures at low water percentage in ethanol, both B3A and B3B are stabilized in a monomeric state. However, in mixtures with a high water content, self‐aggregation takes place, mainly under a mild pH acid condition (3 < pH < 6), in which the prevalent protolytic species of both isomers is the neutral charged form, compounds with carboxylic and porphyrin free‐base groups. It is demonstrated that both isomers can undergo aggregation following a self‐catalytic mechanism, which is 2000 times slower to B3A than B3B. For B3A, the aggregation is manifested by a decrease in the monomer band with the aggregation band probably superposed to that of the monomer. For B3B, together with the decrease in the monomer band, a new band related to self‐aggregates is observed. Copyright © 2010 John Wiley & Sons, Ltd.     

Nanorings in planar confinement: the role of repulsive surfaces on the formation of lacuna smectics

ABSTRACT

We study the structure and liquid-crystalline phase behaviour of a model of confined non-convex circular soft-repulsive nanorings in a planar slit geometry using molecular-dynamics simulation. The separation distance between the structureless parallel soft-repulsive walls is made large enough to allow for the formation of a distinct bulk phase in the central region of the box which is in coexistence with the adsorbed fluid thus allowing the analysis of single-wall effects. As the density of the particles is increased, the fluid adsorbs (wets) onto the planar surfaces leading to the formation of well-defined smectic-A layers with a spacing proportional to the diameter of the rings. An analysis of the nematic order parameter at distances perpendicular to the surface reveals that the particles in each layer exhibit anti-nematic behaviour and planar (edge-on) anchoring relative to the short symmetry axis of the rings. This behaviour is in stark contrast to the behaviour observed in convex disc-like particles that have the tendency to form nematic (discotic) structures with homeotropic (face-on) anchoring. The smectic phases formed by nanorings in the bulk and under confinement are characterised by the formation of low-density layered liquid-crystalline states with large voids, referred to here as lacuna smectic phases. In contrast to what is typically found for confined liquid-crystalline systems involving convex particles, no apparent biaxiality is found for nanorings in planar confinement. We argue that formation of the low-density lacuna smectic layers with planar anchoring is a consequence of the non-convex shape of the circular rings that allow for interpenetration between the particles as observed for nanorings under bulk conditions [C. Avendaño, G. Jackson, E.A. Müller and F.A. Escobedo, Proc. Natl. Acad. Sci. U.S.A. 113, 9699 (2016); H.H. Wensink and C. Avendaño, Phys. Rev. E 94, 062704 (2016)].     

Glass-specific behavior in the damping of acousticlike vibrations

High frequency sound is observed in lithium diborate glass, Li2O-2B2O3, using Brillouin scattering of light and x rays. The sound attenuation exhibits a nontrivial dependence on the wave vector, with a remarkably rapid increase towards a Ioffe-Regel crossover as the frequency approaches the boson peak from below. An analysis of literature results reveals that the boson-peak frequency is closely related with a Ioffe-Regel limit for sound in many glasses. We conjecture that this relation, specific to glassy materials, might be rather common among them.     

Models for the modern power grid

This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different aspects that co-determine the spatio-temporal multilayer dynamics of power system. We start our review by showing how the generation, transmission and distribution characteristics of the traditional power grids are already subject to complex behaviour appearing as a result of the the interplay between dynamics of the nodes and topology, namely synchronisation and cascade effects. When dealing with smart grids, the system complexity increases even more: on top of the physical network of power lines and controllable sources of electricity, the modernisation brings information networks, renewable intermittent generation, market liberalisation, prosumers, among other aspects. In this case, we forecast a dynamical co-evolution of the smart grid and other kind of networked systems that cannot be understood isolated. This review compiles recent results that model electric power grids as complex systems, going beyond pure technological aspects. From this perspective, we then indicate possible ways to incorporate the diverse co-evolving systems into the smart grid model using, for example, network theory and multi-agent simulation.     

Shakeup excitation during optical tunnel ionization

Shakeup of a two-electron system is investigated in the strong infrared laser field limit, both theoretically and experimentally. During tunnel ionization the electron shakes up a second electron to an excited bound state. Theoretically, a complete analytical theory of shakeup in intense laser fields is developed. We predict that shakeup produces one excited sigma(u) D(+)(2) state in approximately 10(5) ionization events. Shakeup is measured experimentally by using the molecular clock provided by the internuclear motion. The number of measured events is found to be in excellent agreement with theory.     

Tunable gold nanoparticles shape and size in reductive and structuring media containing protic ionic liquids

Herein, a facile method was developed for preparing high concentration of monodispersed gold nanoparticles (NPs) at room temperature from gold(III) chloride by using different media based on N,N-dimethylformamide or water solutions containing a protic ionic liquid (PIL), namely, the octylammonium formate or the bis(2-ethyl-hexyl)ammonium formate, based on which both PILs were used as redox-active structuring media. The formation of gold NPs in these systems was then characterized using UV–visible spectroscopy, transmission electron microscopy, and dynamic light scattering. From these investigations, it appears that the structure and aggregation pathway of PILs in selected solvents affect strongly the formation, growth, the shape, and the size of gold NPs. In fact, by using this approach, the shape-/ size-controlled gold NPs (branched and spherical) can be generated under mild condition. This approach suggests also a wealth of potential for these designer nanomaterials within the biomedical, materials, and catalysis communities by using designer and safer media based on PILs.     

Heat Release by Controlled Continuous-Time Markov Jump Processes

We derive the equations governing the protocols minimizing the heat released by a continuous-time Markov jump process on a one-dimensional countable state space during a transition between assigned initial and final probability distributions in a finite time horizon. In particular, we identify the hypotheses on the transition rates under which the optimal control strategy and the probability distribution of the Markov jump problem obey a system of differential equations of Hamilton-Jacobi-Bellman-type. As the state-space mesh tends to zero, these equations converge to those satisfied by the diffusion process minimizing the heat released in the Langevin formulation of the same problem. We also show that in full analogy with the continuum case, heat minimization is equivalent to entropy production minimization. Thus, our results may be interpreted as a refined version of the second law of thermodynamics.     

High-power laser with Nd:YAG single-crystal fiber grown by the micro-pulling-down technique

We present optical characterization and laser results achieved with single-crystal fibers directly grown by the micro-pulling-down technique. We investigate the spectroscopic and optical quality of the fiber, and we present the first laser results. We achieved a cw laser power of 10 W at 1064 nm for an incident pump power of 60 W at 808 nm and 360 kW peak power for 12 ns pulses at 1 kHz in the Q-switched regime. It is, to the best of our knowledge, the highest laser power ever achieved with directly grown single-crystal fibers.