Asymptotic description of Dirac mass formation in kinetic equations for quantum particles

In this paper, the detailed asymptotic behaviour of the solutions of a kinetic equation for quantum particles is studied. It is shown that this behaviour is sensitive not only to the total mass of the initial data but also to its precise behaviour near the origin. In some cases, solutions develop a Dirac mass at the origin for long times in a self-similar manner that is analysed in detail.     

Visual detection of cysteine and homocysteine

The determination of cysteine and homocysteine levels is of great current interest for the monitoring of desease states. A new colorimetric method for the simultaneous detection of l-cysteine and l-homocysteine has been developed. A fluorescein derivative reacts with the above amino acids, producing their respective thiazolidines resulting in color changes. Interference from other amino acids and proteins is minimal.     

Multicanonical schemes for mapping out free-energy landscapes of single-component and multicomponent systems

Multicanonical (MUCA) sampling is a powerful approach for simulating large domains of thermodynamic macrostate space that relies on mapping out either the density of states or a free energy of the system as a function of a suitable "order parameter." The purpose of this study is to extend and apply to more complex systems the method introduced in a previous paper [M. K. Fenwick and F. A. Escobedo, J. Chem. Phys. 120, 3066 (2004)] that uses Bennett's acceptance ratio method for estimating MUCA free energies. Four types of MUCA schemes are considered according to what order parameter is adopted and how the macrostate space is traversed: a la grand canonical ensemble, a la semigrand canonical ensemble, a la semigrand isothermal-isobaric ensemble, and a la isothermal-isobaric ensemble. Two types of systems are studied, the first is a two-component Lennard-Jones mixture that exhibits a vapor-liquid transition, and the second is a hard-cuboid containing system that exhibits an isotropic-liquid crystalline transition. These systems are simulated with different MUCA schemes and the resulting free-energy profiles are used to determine phase-coexistence conditions. For the Lennard-Jones systems, it is also demonstrated that different types of MUCA simulations can be conveniently performed over different macrostate regions and the results can be subsequently pieced together into a continuous weighting function.     

On a Kinetic Equation for Coalescing Particles

Existence of global weak solutions to a spatially inhomogeneous kinetic model for coalescing particles is proved, each particle being identified by its mass, momentum and position. The large time convergence to zero is also shown. The cornestone of our analysis is that, for any nonnegative and convex function, the associated Orlicz norm is a Liapunov functional. Existence and asymptotic behaviour then rely on weak and strong compactness methods in L¹ in the spirit of the DiPerna-Lions theory for the Boltzmann equation.     

Macrocycle-Derived Functional Xanthenes and Progress Towards Concurrent Detection of Glucose and Fructose

The detection of saccharides in biological media is of great current importance for the monitoring of disease states. We have previously reported that solutions of boronic acid-functionalized macrocycles form acyclic oligomeric materials in situ. The oligomers contain fluorescent xanthene moieties. Current efforts are aimed at modulating the spectroscopic responses of these materials for the analysis of specific sugars. We describe conditions whereby the xanthene boronic acids exhibit high colorimetric fructose selectivity. In contrast, at physiological levels selective glucose monitoring can be achieved via fluorescence. Additionally, we describe a method which exhibits promise for detecting both glucose and fructose at dual wavelengths in the UV-Vis region. Mechanistic rationale for each of these findings is presented.     

A convenient preparation of xanthene dyes

A facile synthetic route utilizing readily available reagents affords a series of regioisomerically pure xanthene dye derivatives. Advantages include relatively mild conditions and good to excellent yields. Nonpolar, highly crystalline intermediates are isolable by standard chromatographic techniques. The intermediates are in the requisite xanthene oxidation state, thus avoiding the need for relatively inefficient oxidation chemistry and/or harsh conditions. During the course of this work, a new boron-mediated 1,2-aryl migration reaction was discovered.     

Overview of DWDM/ODC Project

Abstract

This article introduces the main achievements resulting from the DWDM/ODC project. The five areas of research activity within the DWDM/ODC project cover some of the main issues of design and development of dense wavelength division multiplexing systems for transparent optical networks. These issues are: performance assessment with arbitrary optical filtering; performance of signaling formats; dispersion compensation strategies for directly and externally modulated systems in presence of nonlinear transmission-induced degradation; and the impact of noise and crosstalk in the extent of transparent optical networks. All five areas of research activity have contributed significantly to a better understanding of the limitations present in dense wavelength division multiplexing systems.     

Simulation of the gyroid phase in off-lattice models of pure diblock copolymer melts

Particle-based molecular simulations of pure diblock copolymer (DBC) systems were performed in continuum space via dissipative particle dynamics and Monte Carlo methods for a bead-spring chain model. This model consisted of chains of soft repulsive particles often used with dissipative particle dynamics. The gyroid phase was successfully simulated in DBC melts at selected conditions provided that the simulation box size was commensurate with the gyroid lattice spacing. Simulations were concentrated at conditions where the gyroid phase is expected to be stable which allowed us to outline approximate phase boundaries. When more than one phase was observed by varying simulation box size, thermodynamic stability was discerned by comparing the Helmholtz free energy of the competing phases. For this purpose, chemical potentials were efficiently simulated via an expanded ensemble that gradually inserts/deletes a target chain to/from the system. These simulations employed a novel combination of Bennett's [J. Comput. Phys. 22, 245 (1976)] acceptance-ratio method to estimate free-energy differences and a recently proposed method to get biasing weights that maximize the number of times that the target chain is regrown. The analysis of the gyroid nodes revealed clear evidence of packing frustration in the form of an (entropically) unfavorably overstretching of chains, a phenomenon that has been suggested to provide the structural basis for the limited region of stability of the gyroid phase in the DBC phase diagram. Finally, the G phase and nodal chain stretching were also found in simulations with a completely different DBC particle-based model.     

A general framework for non-Boltzmann Monte Carlo sampling

Non-Boltzmann sampling (NBS) methods have been extensively employed in recent years, mainly due to their ability to enhance ergodicity in simulations of complex systems. In addition, they make possible reliable computation of equilibrium properties (ensemble averages, free-energy differences, and potentials of mean force) over continuous ranges of thermodynamic conditions. In this work, we put forward a general and systematic framework for NBS methods that allows a single set of equations and procedures to be applied to diverse systems. Moreover, we show how to exploit simulation data most effectively by obtaining continuous profiles of any mechanical properties, including structural quantities not directly related to the ensemble parameters. Finally, we demonstrate the usefulness of the developed formulation by applying it to spin systems, Lennard-Jones fluids, and a model protein molecule (both in isolation and in the proximity of a flat wall).