26,861 research outputs found
Uranium(III) coordination chemistry and oxidation in a flexible small-cavity macrocycle
U(III) complexes of the conformationally flexible, small-cavity macrocycle trans-calix[2]benzene[2]pyrrolide (L)2–, [U(L)X] (X = O-2,6-tBu2C6H3, N(SiMe3)2), have been synthesized from [U(L)BH4] and structurally characterized. These complexes show binding of the U(III) center in the bis(arene) pocket of the macrocycle, which flexes to accommodate the increase in the steric bulk of X, resulting in long U–X bonds to the ancillary ligands. Oxidation to the cationic U(IV) complex [U(L)X][B(C6F5)4] (X = BH4) results in ligand rearrangement to bind the smaller, harder cation in the bis(pyrrolide) pocket, in a conformation that has not been previously observed for (L)2–, with X located between the two ligand arene rings
High momentum lepton pairs from jet-plasma interactions
We discuss the emission of high momentum lepton pairs (p_T>4 GeV) with low
invariant masses (M << p_T) in central Au+Au collisions at RHIC
(\sqrt{s_{NN}}=200 GeV). The spectra of dileptons produced through interactions
of quark and antiquark jets with the quark-gluon plasma (QGP) have been
calculated. Annihilation and Compton scattering processes, as well as processes
benefitting from collinear enhancement, including Landau-Pomeranchuk-Migdal
(LPM) effects, are calculated and convolved with a one dimensional hydrodynamic
expansion. The jet-induced contributions are compared to thermal dilepton
emission and Drell-Yan processes, and are found to dominate around p_T=4 GeV.Comment: Parallel talk given at QM2006, Shanghai November 2006. 4 pages, 3
figure
Real-time Chern-Simons term for hypermagnetic fields
If non-vanishing chemical potentials are assigned to chiral fermions, then a
Chern-Simons term is induced for the corresponding gauge fields. In thermal
equilibrium anomalous processes adjust the chemical potentials such that the
coefficient of the Chern-Simons term vanishes, but it has been argued that
there are non-equilibrium epochs in cosmology where this is not the case and
that, consequently, certain fermionic number densities and large-scale
(hypermagnetic) field strengths get coupled to each other. We generalise the
Chern-Simons term to a real-time situation relevant for dynamical
considerations, by deriving the anomalous Hard Thermal Loop effective action
for the hypermagnetic fields, write down the corresponding equations of motion,
and discuss some exponentially growing solutions thereof.Comment: 13 page
An Exact Universal Gravitational Lensing Equation
We first define what we mean by gravitational lensing equations in a general
space-time. A set of exact relations are then derived that can be used as the
gravitational lens equations in all physical situations. The caveat is that
into these equations there must be inserted a function, a two-parameter family
of solutions to the eikonal equation, not easily obtained, that codes all the
relevant (conformal) space-time information for this lens equation
construction. Knowledge of this two-parameter family of solutions replaces
knowledge of the solutions to the geodesic equations.
The formalism is then applied to the Schwarzschild lensing problemComment: 12 pages, submitted to Phys. Rev.
Pesin's Formula for Random Dynamical Systems on
Pesin's formula relates the entropy of a dynamical system with its positive
Lyapunov exponents. It is well known, that this formula holds true for random
dynamical systems on a compact Riemannian manifold with invariant probability
measure which is absolutely continuous with respect to the Lebesgue measure. We
will show that this formula remains true for random dynamical systems on
which have an invariant probability measure absolutely continuous to the
Lebesgue measure on . Finally we will show that a broad class of
stochastic flows on of a Kunita type satisfies Pesin's formula.Comment: 35 page
Instabilities in complex mixtures with a large number of components
Inside living cells are complex mixtures of thousands of components. It is
hopeless to try to characterise all the individual interactions in these
mixtures. Thus, we develop a statistical approach to approximating them, and
examine the conditions under which the mixtures phase separate. The approach
approximates the matrix of second virial coefficients of the mixture by a
random matrix, and determines the stability of the mixture from the spectrum of
such random matrices.Comment: 4 pages, uses RevTeX 4.
A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis
Angiogenesis, the process by which new blood capillaries grow into a tissue from surrounding parent vessels, is a key event in dermal wound healing, malignant-tumour growth, and other pathologic conditions. In wound healing, new capillaries deliver vital metabolites such as amino acids and oxygen to the cells in the wound which are involved in a complex sequence of repair processes. The key cellular constituents of these new capillaries are endothelial cells: their interactions with soluble biochemical and insoluble extracellular matrix (ECM) proteins have been well documented recently, although the biological mechanisms underlying wound-healing angiogenesis are incompletely understood. Considerable recent research, including some continuum mathematical models, have focused on the interactions between endothelial cells and soluble regulators (such as growth factors). In this work, a similar modelling framework is used to investigate the roles of the insoluble ECM substrate, of which collagen is the predominant macromolecular protein. Our model consists of a partial differential equation for the endothelial-cell density (as a function of position and time) coupled to an ordinary differential equation for the ECM density. The ECM is assumed to regulate cell movement (both random and directed) and proliferation, whereas the cells synthesize and degrade the ECM. Analysis and numerical solutions of these equations highlights the roles of these processes in wound-healing angiogenesis. A nonstandard approximation analysis yields insight into the travel ling-wave structure of the system. The model is extended to two spatial dimensions (parallel and perpendicular to the plane of the skin), for which numerical simulations are presented. The model predicts that ECM-mediated random motility and cell proliferation are key processes which drive angiogenesis and that the details of the functional dependence of these processes on the ECM density, together with the rate of ECM remodelling, determine the qualitative nature of the angiogenic response. These predictions are experimentally testable, and they may lead towards a greater understanding of the biological mechanisms involved in wound-healing angiogenesis
A Computational Study of the Weak Galerkin Method for Second-Order Elliptic Equations
The weak Galerkin finite element method is a novel numerical method that was
first proposed and analyzed by Wang and Ye for general second order elliptic
problems on triangular meshes. The goal of this paper is to conduct a
computational investigation for the weak Galerkin method for various model
problems with more general finite element partitions. The numerical results
confirm the theory established by Wang and Ye. The results also indicate that
the weak Galerkin method is efficient, robust, and reliable in scientific
computing.Comment: 19 page
Surface magnetic canting in a ferromagnet
The surface magnetic canting (SMC) of a semi-infinite film with ferromagnetic
exchange interaction and competing bulk and surface anisotropies is
investigated via a nonlinear mapping formulation of mean-field theory
previously developed by our group [L. Trallori et al., Int. J. Mod. Phys. B 10,
1935-1988 (1996)], and extended to the case where an external magnetic field is
applied to the system. When the field H is parallel to the film plane, the
condition for SMC is found to be the same as that recently reported by Popov
and Pappas [Phys. Rev. B 64, 184401 (2001)]. The case of a field H applied
perpendicularly to the film plane is also investigated. In both cases, the
zero-temperature equilibrium configuration is easily determined by our
theoretical approach.Comment: 4 pages, 3 figure
Low-lying bifurcations in cavity quantum electrodynamics
The interplay of quantum fluctuations with nonlinear dynamics is a central
topic in the study of open quantum systems, connected to fundamental issues
(such as decoherence and the quantum-classical transition) and practical
applications (such as coherent information processing and the development of
mesoscopic sensors/amplifiers). With this context in mind, we here present a
computational study of some elementary bifurcations that occur in a driven and
damped cavity quantum electrodynamics (cavity QED) model at low intracavity
photon number. In particular, we utilize the single-atom cavity QED Master
Equation and associated Stochastic Schrodinger Equations to characterize the
equilibrium distribution and dynamical behavior of the quantized intracavity
optical field in parameter regimes near points in the semiclassical
(mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that
the semiclassical limit sets are qualitatively preserved in the quantum
stationary states, although quantum fluctuations apparently induce phase
diffusion within periodic orbits and stochastic transitions between attractors.
We restrict our attention to an experimentally realistic parameter regime.Comment: 13 pages, 10 figures, submitted to PR
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