The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.

Relativistic particle dynamics in D = 2+1

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and τ-reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables λα show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model. © SISSA 2006.

Sending classical information through relativistic quantum channels

We investigate how special relativity influences the transmission of classical information through quantum channels by evaluating the Holevo bound when the sender and the receiver are in (relativistic) relative motion. By using the spin degrees of freedom of spin-1/2 fermions to encode the classical information, we show that, for some configurations, the accessible information in the receiver can be increased when the spin detector moves fast enough. This is possible by allowing the momentum wave packet of one of the particles to be sufficiently wide while the momentum wave packets of other particles are kept relatively narrow. In this way, one can take advantage of the fact that boosts entangle the spin and momentum degrees of freedom of spin-1/2 fermions to increase the accessible information in the former. We close the paper with a discussion of how this relativistic quantum channel cannot in general be described by completely positive quantum maps. © 2013 American Physical Society.

Relativistic Coulomb scattering of spinless bosons

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Rho-omega mixing and the Nolen-Schiffer anomaly in relativistic nuclear models

We calculate within the framework of relativistic nuclear models the contribution of the ρ0 - ω mixing interaction to the binding energy differences of the mirror nuclei in the neighborhood of A = 16 and A = 40. We use two relativistic models for the nuclear structure, one with scalar and vector Woods-Saxon potentials, and the Walecka model. The ρ0 - ω interaction is treated in first order perturbation theory. When using the Walecka model the ρ- and ω-nucleon coupling constants are the same for calculating bound state wave functions and the perturbation due to the mixing. We find that the relativistic results on the average are of the same order as the ones obtained with nonrelativistic calculations.

Controlling chaos in wave-particle interactions

We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also use a method of control for near-integrable Hamiltonians that consists of the addition of a small and simple control term to the system. This control term creates invariant tori in phase space that prevent chaos from spreading to large regions, making the controlled dynamics more regular. We show numerically that the control term just slightly modifies the system but is able to drastically reduce chaos with a low additional cost of energy. Moreover, we discuss how the control of chaos and the consequent recovery of regular trajectories in phase space are useful to improve regular particle acceleration.

On the radial expansion of tubular structures in a quark-gluon plasma

We study the radial expansion of cylindrical tubes in a hot QGP. These tubes are treated as perturbations in the energy density of the system which is formed in heavy ion collisions at RHIC and LHC. We start from the equations of relativistic hydrodynamics in two spatial dimensions and cylindrical symmetry and perform an expansion of these equations in a small parameter, conserving the nonlinearity of the hydrodynamical formalism. We consider both ideal and viscous fluids and the latter are studied with a relativistic Navier-Stokes equation. We use the equation of state of the MIT bag model. In the case of ideal fluids we obtain a breaking wave equation for the energy density fluctuation, which is then solved numerically. We also show that, under certain assumptions, perturbations in a relativistic viscous fluid are governed by the Burgers equation. We estimate the typical expansion time of the tubes. (C) 2012 Elsevier B.V. All rights reserved.

Analysis and mathematical modeling of wave-structure interaction

The aim of this thesis, included within the THESEUS project, is the development of a mathematical model 2DV two-phase, based on the existing code IH-2VOF developed by the University of Cantabria, able to represent together the overtopping phenomenon and the sediment transport. Several numerical simulations were carried out in order to analyze the flow characteristics on a dike crest. The results show that the seaward/landward slope does not affect the evolution of the flow depth and velocity over the dike crest whereas the most important parameter is the relative submergence. Wave heights decrease and flow velocities increase while waves travel over the crest. In particular, by increasing the submergence, the wave height decay and the increase of the velocity are less marked. Besides, an appropriate curve able to fit the variation of the wave height/velocity over the dike crest were found. Both for the wave height and for the wave velocity different fitting coefficients were determined on the basis of the submergence and of the significant wave height. An equation describing the trend of the dimensionless coefficient c_h for the wave height was derived. These conclusions could be taken into consideration for the design criteria and the upgrade of the structures. In the second part of the thesis, new equations for the representation of the sediment transport in the IH-2VOF model were introduced in order to represent beach erosion while waves run-up and overtop the sea banks during storms. The new model allows to calculate sediment fluxes in the water column together with the sediment concentration. Moreover it is possible to model the bed profile evolution. Different tests were performed under low-intensity regular waves with an homogeneous layer of sand on the bottom of a channel in order to analyze the erosion-deposition patterns and verify the model results.

Higher-order perturbative relativistic corrections to energies and properties

Relativistic effects need to be considered in quantum-chemical calculations on systems including heavy elements or when aiming at high accuracy for molecules containing only lighter elements. In the latter case, consideration of relativistic effects via perturbation theory is an attractive option. Among the available techniques, Direct Perturbation Theory (DPT) in its lowest order (DPT2) has become a standard tool for the calculation of relativistic corrections to energies and properties.In this work, the DPT treatment is extended to the next order (DPT4). It is demonstrated that the DPT4 correction can be obtained as a second derivative of the energy with respect to the relativistic perturbation parameter. Accordingly, differentiation of a suitable Lagrangian, thereby taking into account all constraints on the wave function, provides analytic expressions for the fourth-order energy corrections. The latter have been implemented at the Hartree-Fock level and within second-order Møller-Plesset perturbaton theory using standard analytic second-derivative techniques into the CFOUR program package. For closed-shell systems, the DPT4 corrections consist of higher-order scalar-relativistic effects as well as spin-orbit corrections with the latter appearing here for the first time in the DPT series.Relativistic corrections are reported for energies as well as for first-order electrical properties and compared to results from rigorous four-component benchmark calculations in order to judge the accuracy and convergence of the DPT expansion for both the scalar-relativistic as well as the spin-orbit contributions. Additionally, the importance of relativistic effects to the bromine and iodine quadrupole-coupling tensors is investigated in a joint experimental and theoretical study concerning the rotational spectra of CH2BrF, CHBrF2, and CH2FI.

IMEX finite volume methods for the shallow water equations

Die Flachwassergleichungen (SWE) sind ein hyperbolisches System von Bilanzgleichungen, die adäquate Approximationen an groß-skalige Strömungen der Ozeane, Flüsse und der Atmosphäre liefern. Dabei werden Masse und Impuls erhalten. Wir unterscheiden zwei charakteristische Geschwindigkeiten: die Advektionsgeschwindigkeit, d.h. die Geschwindigkeit des Massentransports, und die Geschwindigkeit von Schwerewellen, d.h. die Geschwindigkeit der Oberflächenwellen, die Energie und Impuls tragen. Die Froude-Zahl ist eine Kennzahl und ist durch das Verhältnis der Referenzadvektionsgeschwindigkeit zu der Referenzgeschwindigkeit der Schwerewellen gegeben. Für die oben genannten Anwendungen ist sie typischerweise sehr klein, z.B. 0.01. Zeit-explizite Finite-Volume-Verfahren werden am öftersten zur numerischen Berechnung hyperbolischer Bilanzgleichungen benutzt. Daher muss die CFL-Stabilitätsbedingung eingehalten werden und das Zeitinkrement ist ungefähr proportional zu der Froude-Zahl. Deswegen entsteht bei kleinen Froude-Zahlen, etwa kleiner als 0.2, ein hoher Rechenaufwand. Ferner sind die numerischen Lösungen dissipativ. Es ist allgemein bekannt, dass die Lösungen der SWE gegen die Lösungen der Seegleichungen/ Froude-Zahl Null SWE für Froude-Zahl gegen Null konvergieren, falls adäquate Bedingungen erfüllt sind. In diesem Grenzwertprozess ändern die Gleichungen ihren Typ von hyperbolisch zu hyperbolisch.-elliptisch. Ferner kann bei kleinen Froude-Zahlen die Konvergenzordnung sinken oder das numerische Verfahren zusammenbrechen. Insbesondere wurde bei zeit-expliziten Verfahren falsches asymptotisches Verhalten (bzgl. der Froude-Zahl) beobachtet, das diese Effekte verursachen könnte.Ozeanographische und atmosphärische Strömungen sind typischerweise kleine Störungen eines unterliegenden Equilibriumzustandes. Wir möchten, dass numerische Verfahren für Bilanzgleichungen gewisse Equilibriumzustände exakt erhalten, sonst können künstliche Strömungen vom Verfahren erzeugt werden. Daher ist die Quelltermapproximation essentiell. Numerische Verfahren die Equilibriumzustände erhalten heißen ausbalanciert.rnrnIn der vorliegenden Arbeit spalten wir die SWE in einen steifen, linearen und einen nicht-steifen Teil, um die starke Einschränkung der Zeitschritte durch die CFL-Bedingung zu umgehen. Der steife Teil wird implizit und der nicht-steife explizit approximiert. Dazu verwenden wir IMEX (implicit-explicit) Runge-Kutta und IMEX Mehrschritt-Zeitdiskretisierungen. Die Raumdiskretisierung erfolgt mittels der Finite-Volumen-Methode. Der steife Teil wird mit Hilfe von finiter Differenzen oder au eine acht mehrdimensional Art und Weise approximniert. Zur mehrdimensionalen Approximation verwenden wir approximative Evolutionsoperatoren, die alle unendlich viele Informationsausbreitungsrichtungen berücksichtigen. Die expliziten Terme werden mit gewöhnlichen numerischen Flüssen approximiert. Daher erhalten wir eine Stabilitätsbedingung analog zu einer rein advektiven Strömung, d.h. das Zeitinkrement vergrößert um den Faktor Kehrwert der Froude-Zahl. Die in dieser Arbeit hergeleiteten Verfahren sind asymptotisch erhaltend und ausbalanciert. Die asymptotischer Erhaltung stellt sicher, dass numerische Lösung das "korrekte" asymptotische Verhalten bezüglich kleiner Froude-Zahlen besitzt. Wir präsentieren Verfahren erster und zweiter Ordnung. Numerische Resultate bestätigen die Konvergenzordnung, so wie Stabilität, Ausbalanciertheit und die asymptotische Erhaltung. Insbesondere beobachten wir bei machen Verfahren, dass die Konvergenzordnung fast unabhängig von der Froude-Zahl ist.

Time-domain modeling of high-frequency electromagnetic wave propagation, overhead wires, and earth

Prediction of radiated fields from transmission lines has not previously been studied from a panoptical power system perspective. The application of BPL technologies to overhead transmission lines would benefit greatly from an ability to simulate real power system environments, not limited to the transmission lines themselves. Presently circuitbased transmission line models used by EMTP-type programs utilize Carson’s formula for a waveguide parallel to an interface. This formula is not valid for calculations at high frequencies, considering effects of earth return currents. This thesis explains the challenges of developing such improved models, explores an approach to combining circuit-based and electromagnetics modeling to predict radiated fields from transmission lines, exposes inadequacies of simulation tools, and suggests methods of extending the validity of transmission line models into very high frequency ranges. Electromagnetics programs are commonly used to study radiated fields from transmission lines. However, an approach is proposed here which is also able to incorporate the components of a power system through the combined use of EMTP-type models. Carson’s formulas address the series impedance of electrical conductors above and parallel to the earth. These equations have been analyzed to show their inherent assumptions and what the implications are. Additionally, the lack of validity into higher frequencies has been demonstrated, showing the need to replace Carson’s formulas for these types of studies. This body of work leads to several conclusions about the relatively new study of BPL. Foremost, there is a gap in modeling capabilities which has been bridged through integration of circuit-based and electromagnetics modeling, allowing more realistic prediction of BPL performance and radiated fields. The proposed approach is limited in its scope of validity due to the formulas used by EMTP-type software. To extend the range of validity, a new set of equations must be identified and implemented in the approach. Several potential methods of implementation have been explored. Though an appropriate set of equations has not yet been identified, further research in this area will benefit from a clear depiction of the next important steps and how they can be accomplished. Prediction of radiated fields from transmission lines has not previously been studied from a panoptical power system perspective. The application of BPL technologies to overhead transmission lines would benefit greatly from an ability to simulate real power system environments, not limited to the transmission lines themselves. Presently circuitbased transmission line models used by EMTP-type programs utilize Carson’s formula for a waveguide parallel to an interface. This formula is not valid for calculations at high frequencies, considering effects of earth return currents. This thesis explains the challenges of developing such improved models, explores an approach to combining circuit-based and electromagnetics modeling to predict radiated fields from transmission lines, exposes inadequacies of simulation tools, and suggests methods of extending the validity of transmission line models into very high frequency ranges. Electromagnetics programs are commonly used to study radiated fields from transmission lines. However, an approach is proposed here which is also able to incorporate the components of a power system through the combined use of EMTP-type models. Carson’s formulas address the series impedance of electrical conductors above and parallel to the earth. These equations have been analyzed to show their inherent assumptions and what the implications are. Additionally, the lack of validity into higher frequencies has been demonstrated, showing the need to replace Carson’s formulas for these types of studies. This body of work leads to several conclusions about the relatively new study of BPL. Foremost, there is a gap in modeling capabilities which has been bridged through integration of circuit-based and electromagnetics modeling, allowing more realistic prediction of BPL performance and radiated fields. The proposed approach is limited in its scope of validity due to the formulas used by EMTP-type software. To extend the range of validity, a new set of equations must be identified and implemented in the approach. Several potential methods of implementation have been explored. Though an appropriate set of equations has not yet been identified, further research in this area will benefit from a clear depiction of the next important steps and how they can be accomplished.

A new set of relativistic screening constants for the screened hydrogenic model

AnewRelativisticScreenedHydrogenicModel has been developed to calculate atomic data needed to compute the optical and thermodynamic properties of high energy density plasmas. The model is based on anewset of universal screeningconstants, including nlj-splitting that has been obtained by fitting to a large database of ionization potentials and excitation energies. This database was built with energies compiled from the National Institute of Standards and Technology (NIST) database of experimental atomic energy levels, and energies calculated with the Flexible Atomic Code (FAC). The screeningconstants have been computed up to the 5p3/2 subshell using a Genetic Algorithm technique with an objective function designed to minimize both the relative error and the maximum error. To select the best set of screeningconstants some additional physical criteria has been applied, which are based on the reproduction of the filling order of the shells and on obtaining the best ground state configuration. A statistical error analysis has been performed to test the model, which indicated that approximately 88% of the data lie within a ±10% error interval. We validate the model by comparing the results with ionization energies, transition energies, and wave functions computed using sophisticated self-consistent codes and experimental data.

Relativistic description of 3He(e,e'p)2H

The relativistic distorted-wave impulse approximation is used to describe the 3He(e, e′ p)2H process. We describe the 3He nucleus within the adiabatic hyperspherical expansion method with realistic nucleon-nucleon interactions. The overlap between the 3He and the deuteron wave functions can be accurately computed from a three-body calculation. The nucleons are described by solutions of the Dirac equation with scalar and vector (S–V) potentials. The wave function of the outgoing proton is obtained by solving the Dirac equation with a S–V optical potential fitted to elastic proton scattering data on the residual nucleus. Within this theoretical framework, we compute the cross section of the reaction and other observables like the transverse-longitudinal asymmetry, and compare them with the available experimental data measured at JLab.

Wave-like Disturbances on the Downstream Wall of an Open Cavity

This contribution presents results of an incompressible two-dimensional flow over an open cavity of fixed aspect ratio (length/depth) L/D = 2 and the coupling between the three dimensional low frequency oscillation mode confined in the cavity and the wave-like disturbances evolving on the downstream wall of the cavity in the form of Tollmien-Schlichting waves. BiGlobal instability analysis is conducted to search the global disturbances superimposed upon a two-dimensional steady basic flow. The base solution is computed by the integration of the laminar Navier-Stokes equations in primitive variable formulation, while the eigenvalue problem (EVP) derived from the discretization of the linearized equations of motion in the BiGlobal framework is solved using an iterative procedure. The formulation of the BiGlobal EVP for the unbounded flow in the open cavity problem introduces additional difficulties regarding the flow-through boundaries. Local analysis has been utilized for the determination of the proper boundary conditions in the upper limit of the downstream region

Wave reflection at a stent

A simple analytical expression has been derived to calculate the characteristics of a wave that reflects at a stent implanted in a uniform vessel. The stent is characterized by its length and the wave velocity in the stented region. The reflected wave is proportional to the time derivative of the incident wave. The reflection coefficient is a small quantity of the order of the length of the stent divided by the wavelength of the unstented vessel. The results obtained coincide with those obtained numerically by Charonko et al. The main simplifications used are small amplitude of the waves so that equations can be linearized and that the length of the stent is small enough so that the values of the wave functions are nearly uniform along the stent. Both assumptions hold in typical situations.