Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

An unstructured CVFEM and moving interface algorithm for non-Newtonian Hele-Shaw flows in injection molding

Purpose - The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele-Shaw model. Design/methodology/approach - The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi-static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non-Newtonian. Findings - Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power-law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries. Research limitations/implications - With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so-called ""meshless"" scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill-time errors that might be addressed by introducing suitable projections. The general question of ""rate of convergence"" of these schemes requires analysis. Numerical results here suggest first-order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods. Originality/value - This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed ""on-the-fly"" for each ""active point"" to form a dynamic virtual mesh of active elements that evolves with the moving interface.

Upgrading a TCABR data analysis and acquisition system for remote participation using Java, XML, RCP and modern client/server communication/authentication

The TCABR data analysis and acquisition system has been upgraded to support a joint research programme using remote participation technologies. The architecture of the new system uses Java language as programming environment. Since application parameters and hardware in a joint experiment are complex with a large variability of components, requirements and specification solutions need to be flexible and modular, independent from operating system and computer architecture. To describe and organize the information on all the components and the connections among them, systems are developed using the extensible Markup Language (XML) technology. The communication between clients and servers uses remote procedure call (RPC) based on the XML (RPC-XML technology). The integration among Java language, XML and RPC-XML technologies allows to develop easily a standard data and communication access layer between users and laboratories using common software libraries and Web application. The libraries allow data retrieval using the same methods for all user laboratories in the joint collaboration, and the Web application allows a simple graphical user interface (GUI) access. The TCABR tokamak team in collaboration with the IPFN (Instituto de Plasmas e Fusao Nuclear, Instituto Superior Tecnico, Universidade Tecnica de Lisboa) is implementing this remote participation technologies. The first version was tested at the Joint Experiment on TCABR (TCABRJE), a Host Laboratory Experiment, organized in cooperation with the IAEA (International Atomic Energy Agency) in the framework of the IAEA Coordinated Research Project (CRP) on ""Joint Research Using Small Tokamaks"". (C) 2010 Elsevier B.V. All rights reserved.

Velocity-dependent KAM islands

We revisit the non-dissipative time-dependent annular billiard and we consider the chaotic dynamics in two planes of conjugate variables in order to describe the behavior of the growth, or saturation, of the mean velocity of an ensemble of particles. We observed that the changes in the 4-d phase space occur without changing any parameter. They occur depending on where the initial conditions start. The emerging KAM islands interfere in the behavior of the particle dynamics especially in the Fermi acceleration mechanism. We show that Fermi acceleration can be suppressed, without dissipation, even considering the non-dissipative energy context. (C) 2011 Published by Elsevier Ltd.

A dedicated setup for the measurement of the electron transport parameters in gases at large electric fields

Electron transport parameters are important in several areas ranging from particle detectors to plasma-assisted processing reactors. Nevertheless, especially at high fields strengths and for complex gases, relatively few data are published. A dedicated setup has been developed to measure the electron drift velocity and the first Townsend coefficient in parallel plate geometry. An RPC-like cell has been adopted to reach high field strengths without the risk of destructive sparks. The validation data obtained with pure Nitrogen will be presented and compared to a selection of the available literature and to calculations performed with Magboltz 2 version 8.6. The new data collected in pure Isobutane will then be discussed. This is the first time the electron drift velocity in pure Isobutane is measured well into the saturation region. Good agreement is found with expectations from Magboltz. (C) 2009 Elsevier B.V. All rights reserved.

Precambrian geotectonic units of the Rio de La Plata craton

The main Precambrian tectonic units of Uruguay include the Piedra Alta tectonostratigraphic terrane (PATT) and Nico Perez tectonostratigraphic terrane (NPTT), separated by the Sarandi del Yi high-strain zone. Both terranes are well exposed in the Rio de La Plata craton (RPC). Although these tectonic units are geographically small, they record a wide span of geologic time. Therefore improved geological knowledge of this area provides a fuller understanding of the evolution of the core of South America. The PATT is constituted by low-to medium-grade metamorphic belts (ca. 2.1 Ga); its petrotectonic associations such as metavolcanic units, conglomerates, banded iron formations, and turbiditic deposits suggest a back-arc or a trench-basin setting. Also in the PATT, a late to post-orogenic, arc-related layered mafic complex (2.3-1.9 Ga), followed by A-type granites (2.08 Ga), and finally a taphrogenic mafic dike swarm (1.78 Ga) occur. The less thoroughly studied NPTT consists of Palaeoproterozoic high-grade metamorphic sequences (ca. 2.2 Ga), mylonites and postorogenic and rapakivi granites (1.75 Ga). The Brasiliano-Pan African orogeny affected this terrane. Neoproterozoic cover occurs in both tectonostratigraphic terranes, but is more developed in the NPTT. Over the past 15 years, new isotopic studies have improved our recognition of different tectonic events and associated processes, such as reactivation of shear zones and fluids circulation. Transamazonian and Statherian tectonic events were recognized in the RPC. Based on magmatism, deformation, basin development and metamorphism, we propose a scheme for the Precambrian tectonic evolution of Uruguay, which is summarized in the first Palaeoproterozoic tectonic map of the Rio de La Plata craton.

Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

SPECIAL CHARACTERIZATIONS OF STANDARD DISCRETE MODELS

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic gamma : [0, 1] -> M joining p and U whose endpoints are conjugate along gamma. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.

ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

In this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

Maslov index in semi-Riemannian submersions

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the projected geodesic pi omicron gamma : I -> B in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

Picosecond Dynamics of the Prototropic Reactions of 7-Hydroxyflavylium Photoacids Anchored at an Anionic Micellar Surface

Three water-insoluble, micelle-anchored flavylium salts, 7-hydroxy-3-octyl-flavylium chloride, 4`-hexyl-7-hydroxyflavylium chloride, and 6-hexyl-7-hydroxy-4-methyl-flavylium chloride, have been employed to probe excited-state prototropic reactions in micellar sodium dodecyl sulfate (SDS). In SDS micelles, the fluorescence decays of these three flavylium salts are tetraexponential functions in the pH range from 1.0 to 4.6 at temperatures from 293 to 318 K. The four components of the decays are assigned to Four kinetically coupled excited species in the micelle: specifically, promptly deprotonable (AH(+)*) and nonpromptly deprotonable (AH(h)(+)*) orientations of the acid in the micelle. the base-proton geminate pair (A*center dot center dot center dot H(+)), and the free conjugate base (A*). The initial prompt deprotonation to form the germinate pair occurs at essentially the same rate (k(d) similar to 6-7 x 10(10) s(-1)) for all three photoacids. Recombination of the germinate pair is similar to 3-fold faster than the rate of proton escape from the pair (k(rec) similar to 3 x 10(10) s(-1) and k(diss) similar to 1 x 10(10) s(-1)), corresponding to an intrinsic recombination efficiency of the pair of similar to 75%. Finally, the reprotonation of the short-lived free A* (200-350 ps, depending oil the photoacid) has two components, only one of which depends oil the proton concentration in the intermicellar aqueous phase. Ultrafast transfer of the proton to water and substantial compartmentalization of the photogenerated proton at the micelle surface Oil the picosecond time scale strongly suggest preferential transfer of the proton to preformed hydrogen-bonded water bridges between the photoacid and the anionic headgroups. This localizes the proton in the vicinity of the excited base much more efficiently than ill bulk water, resulting ill the predominance of geminate re reprotonation at the micelle surface.

Modulation of trans-to-cis photoisomerization and photoluminescence of 1,2-bis(4-pyridyl)ethylene or 4-styrylpyridine coordinated to fac-tricarbonyl(5-chloro-1,10-phenathroline)rhenium(I)

Photochemical and photophysical properties of fac-[Re(CO)(3)(Clphen)(trans-L)](+) complexes, Clphen = 5-chloro-1,10-phenathroline and L = 1,2-bis(4-pyridyl)ethylene, bpe, or 4-styrylpyridine, stpy, were investigated to complement the understanding of intramolecular energy transfer process in tricarbonyl rhenium(I) complexes having an electron withdrawing group attached to polypyridyl ligands. These new compounds were synthesized, characterized and the photoisomerization quantum yields were accurately determined by (1)H NMR spectroscopy. The true quantum yields for fac-[Re(CO)(3)(Clphen) (trans-bpe)](+) were constant (Phi = 0.55) at all investigated irradiation wavelengths. However, for fac-[Re(CO)(3)(Clphen)(trans-stpy)](+), similar true quantum yields were observed only at higher energy irradiation (Phi(313 nm) = 0.53 and Phi(365 nm) = 0.57), but it decreased significantly at 404 nm (Phi = 0.41). These results indicated different deactivation pathways for the trans-stpy complex photoisomerization. Quantum yields decreased as the (3)IL(trans-L) and (3)MLCT(Re -> NN) excited states become closer and the behavior was discussed in terms of the excited state energy gaps. Additionally, luminescence properties of photoproducts, fac-[Re(CO)(3)(Clphen)(cis-L)](+), were also investigated in different environments to analyze the relative energy of the (3)MLCT(Re -> Clphen) excited state for each compound. (C) 2011 Elsevier B.V. All rights reserved.