Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

Blurred femtoscopy in two-proton decay

We study the effects of final state interactions in two-proton emission by nuclei. Our approach is based on the solution the time-dependent Schrodinger equation. We show that the final relative energy between the protons is substantially influenced by the final state interactions. We also show that alternative correlation functions can be constructed showing large sensitivity to the spin of the diproton system. (c) 2008 Elsevier B.V. All rights reserved.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

Observational constraints on the dark energy and dark matter mutual coupling

We examine different phenomenological interaction models for Dark Energy and Dark Matter by performing statistical joint analysis with observational data arising from the 182 Gold type la supernova samples, the shift parameter of the Cosmic Microwave Background given by the three-year Wilkinson Microwave Anisotropy Probe observations, the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey and age estimates of 35 galaxies. Including the time-dependent observable, we add sensitivity of measurement and give complementary results for the fitting. The compatibility among three different data sets seem to imply that the coupling between dark energy and dark matter is a small positive value, which satisfies the requirement to solve the coincidence problem and the second law of thermodynamics, being compatible with previous estimates. (c) 2008 Elsevier B.V. All rights reserved.

Coherent and semiclassical states in a magnetic field in the presence of the Aharonov-Bohm solenoid

A new approach to constructing coherent states (CS) and semiclassical states (SS) in a magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy-plane; this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and then the time-dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2 + 1) and (3 + 1) dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.

Four-level systems and a universal quantum gate

We discuss the possibility of implementing a universal quantum XOR gate by using two coupled quantum dots subject to external magnetic fields that are parallel and slightly different. We consider this system in two different field configurations. In the first case, parallel external fields with the intensity difference at each spin being proportional to the time-dependent interaction between the spins. A general exact solution describing this system is presented and analyzed to adjust field parameters. Then we consider parallel fields with intensity difference at each spin being constant and the interaction between the spins switching on and off adiabatically. In both cases we adjust characteristics of the external fields (their intensities and duration) in order to have the parallel pulse adequate for constructing the XOR gate. In order to provide a complete theoretical description of all the cases, we derive relations between the spin interaction, the inter-dot distance, and the external field. (C) 2008 WILEYNCH Verlag GmbH & Co. KGaA. Weinheim.

Hierarchical spherical model from a geometric point of view

A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.

Probing the functionalization of gold surfaces and protein adsorption by PM-IRRAS

The control of morphology and coating of metal surfaces is essential for a number of organic electronic devices including photovoltaic cells and sensors. In this study, we monitor the functionalization of gold surfaces with 11-mercaptoundecanoic acid (MUA, HS(CH(2))(10)CO(2)H) and cysteamine, aiming at passivating the surfaces for application in surface plasmon resonance (SPR) biosensors. Using polarization-modulated infrared reflection-absorption spectroscopy (PM-IRRAS), cyclic voltammetry, atomic force microscopy and quartz crystal microbalance, we observed a time-dependent organization process of the adsorbed MUA monolayer with alkyl chains perpendicular to the gold surface. Such optimized condition for surface passivation was obtained with a systematic search for experimental parameters leading to the lowest electrochemical signal of the functionalized gold electrode. The ability to build supramolecular architectures was also confirmed by detecting with PM-IRRAS the adsorption of streptavidin on the MUA-functionalized gold. As the approaches used for surface functionalization and its verification with PM-IRRAS are generic, one may now envisage monitoring the fabrication of tailored electrodes for a variety of applications.

Generation of nonground-state condensates and adiabatic paradox

The problem of resonant generation of nonground-state condensates is addressed aiming at resolving the seeming paradox that arises when one resorts to the adiabatic representation. In this picture, the eigenvalues and eigenfunctions of a time-dependent Gross-Pitaevskii Hamiltonian are also functions of time. Since the level energies vary in time, no definite transition frequency can be introduced. Hence no external modulation with a fixed frequency can be made resonant. Thus, the resonant generation of adiabatic coherent modes is impossible. However, this paradox occurs only in the frame of the adiabatic picture. It is shown that no paradox exists in the properly formulated diabatic representation. The resonant generation of diabatic coherent modes is a well defined phenomenon. As an example, the equations are derived, describing the generation of diabatic coherent modes by the combined resonant modulation of the trapping potential and atomic scattering length.

Ligand dissociation from estrogen receptor is mediated by receptor dimerization: Evidence from molecular dynamics simulations

Estrogen Receptor (ER) is an important target for pharmaceutical design. Like other ligand-dependent transcription factors, hormone binding regulates ER transcriptional activity. Nevertheless, the mechanisms by which ligands enter and leave ERs and other nuclear receptors remain poorly understood. Here, we report results of locally enhanced sampling molecular dynamics simulations to identify dissociation pathways of two ER ligands [the natural hormone 17 beta-estradiol (E-2) and the selective ER modulator raloxifene (RAL)] from the human ER alpha ligand-binding domain in monomeric and dimeric forms. E-2 dissociation occurs via three different pathways in ER monomers. One resembles the mousetrap mechanism (Path I), involving repositioning of helix 12 (H12), others involve the separation of H8 and H11 (Path II), and a variant of this pathway at the bottom of the ligand-binding domain (Path II`). RAL leaves the receptor through Path I and a Path I variant in which the ligand leaves the receptor through the loop region between H11 and H12 (Path I`). Remarkably, ER dimerization strongly suppresses Paths II and II` for E-2 dissociation and modifies RAL escape routes. We propose that differences in ligand release pathways detected in the simulations for ER monomers and dimers provide an explanation for previously observed effects of ER quaternary state on ligand dissociation rates and suggest that dimerization may play an important, and hitherto unexpected, role in regulation of ligand dissociation rates throughout the nuclear receptor family.

Inhibition of myeloperoxidase-mediated protein nitration by tempol: Kinetics, mechanism, and implications

Despite the therapeutic potential of tempol (4-hydroxy-2,2,6,6-tetra-methyl-1-piperidinyloxy) and related nitroxides as antioxidants, their effects on peroxidase-mediated protein tyrosine nitration remain unexplored. This posttranslational protein modification is a biomarker of nitric oxide-derived oxidants, and, relevantly, it parallels tissue injury in animal models of inflammation and is attenuated by tempol treatment. Here, we examine tempol effects on ribonuclease (RNase) nitration mediated by myeloperoxidase (MPO), a mammalian enzyme that plays a central role in various inflammatory processes.. Some experiments were also performed with horseradish peroxidase (HRP). We show that tempol efficiently inhibits peroxidase-mediated RNase nitration. For instance, 10 mu M tempol was able to inhibit by 90% the yield of 290 mu M 3-nitrotyrosine produced from 370 mu M RNase. The effect of tempol was not completely catalytic because part of it was consumed by recombination with RNase-tyrosyl radicals. The second-order rate constant of the reaction of tempol with MPO compound I and 11 were determined by stopped-flow kinetics as 3.3 x 10(6) and 2.6 x 10(4) M-1 s(-1), respectively (pH 7.4, 25 degrees C); the corresponding HRP constants were orders of magnitude smaller. Time-dependent hydrogen peroxide and nitrite consumption and oxygen production in the incubations were quantified experimentally and modeled by kinetic simulations. The results indicate that tempol inhibits peroxidase-mediated RNase nitration mainly because of its reaction with nitrogen dioxide to produce the oxammonium cation, which, in turn, recycles back to tempol by reacting with hydrogen peroxide and superoxide radical to produce oxygen and regenerate nitrite. The implications for nitroxide antioxidant mechanisms are discussed.

Metal transport parameters of a gneiss saprolitic silty soil for liner design

Diffusion coefficients and retardation factors of two metal cations (Cd2+ and Pb2+) were measured for a compacted Brazilian saprolitic soil derived from gneiss, aiming to assess its geoenvironmental performance as a liner for waste disposal sites. This soil occurs extensively all over the country in very thick layers, but has not been used in liners because of its hydraulic conductivity, higher than 10(-9) m/s when compacted at optimum water content of standard Proctor energy, but which can be reduced by means of appropriate compaction techniques or additives. Batch, column, and diffusion tests were carried out with monospecies synthetic solutions at pH 1, 3, and 5.5. Measured diffusion coefficients varied between 0.5 and 4 X 10(-10) m(2)/s. Retardation factors show that cadmium, a very mobile cation, is not adsorbed at pH I but is significantly retained at pH 3 and pH 5.5, whereas lead is retained at all tested pH values though slightly at pH 1. Estimated retardation factors from batch tests were 1.3-2.3 times those resulting from column tests and at its highest when obtained by diffusion tests; whereas batch tests allow a more complete exposure of the soil grains to the solution, time-dependent nonspecific adsorption may take longer to occur. The importance of contact time was observed and should be considered in further investigations. Its significant retention of metals suggests a promising utilization of this soil as a bottom liner for wastes landfills.

Effects of hydroxyl group distribution on the reactivity, stability and optical properties of fullerenols

We investigate the impact of hydroxyl groups on the properties of C(60)(OH)(n) systems, with n = 1, 2, 3, 4, 8, 10, 16, 18, 24, 32 and 36 by means of first-principles density functional theory calculations. A detailed analysis from the local density of states has shown that adsorbed OH groups can induce dangling bonds in specific carbon atoms around the adsorption site. This increases the tendency to form polyhydroxylated fullerenes (fullerenols). The structural stability is analyzed in terms of the calculated formation enthalpy of each species. Also, a careful examination of the electron density of states for different fullerenols shows the possibility of synthesizing single molecules with tunable optical properties.

Evidence for diffusional coupling in electrochemical thin layers: implications for surface coverage calibration via electrochemical infrared spectroscopy

The time dependence of the concentration of CO2 in an electrochemical thin layer cavity is studied with Fourier transform infrared spectroscopy (FTIR) in order to evaluate the extent to which the thin layer cavity is diffusionally decoupled from the surrounding bulk electrolyte. For the model system of CO on Pt(111) in 0.1 M HClO4, it is found that the concentration of CO2, formed by electro-oxidation of CO, equilibrates rapidly with the surrounding bulk electrolyte. This rapid equilibration indicates that there is diffusion out of the thin layer, even on the short time scales of typical infrared experiments (1-3 min). However, since the measured CO2 absorbance intensity as a function of time is reproducible to within 10%, a new time-dependent method for surface coverage calibration using solution-phase species is proposed.