Signature of mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

The decomposition of some RDX and HMX based materials in the one dimensional time to explosion apparatus. Part 2. Estimating the violence of the cook-off event

Various methods of assessment have been applied to the One Dimensional Time to Explosion (ODTX) apparatus and experiments with the aim of allowing an estimate of the comparative violence of the explosion event to be made. Non-mechanical methods used were a simple visual inspection, measuring the increase in the void volume of the anvils following an explosion and measuring the velocity of the sound produced by the explosion over 1 metre. Mechanical methods used included monitoring piezo-electric devices inserted in the frame of the machine and measuring the rotational velocity of a rotating bar placed on the top of the anvils after it had been displaced by the shock wave. This last method, which resembles original Hopkinson Bar experiments, seemed the easiest to apply and analyse, giving relative rankings of violence and the possibility of the calculation of a “detonation” pressure.

The decomposition of some RDX and HMX based materials in the one-dimensional time to explosion apparatus. Part 1. Time to explosion and apparent activation energy

A One-Dimensional Time to Explosion (ODTX) apparatus has been used to study the times to explosion of a number of compositions based on RDX and HMX over a range of contact temperatures. The times to explosion at any given temperature tend to increase from RDX to HMX and with the proportion of HMX in the composition. Thermal ignition theory has been applied to time to explosion data to calculate kinetic parameters. The apparent activation energy for all of the compositions lay between 127 kJ mol−1 and 146 kJ mol−1. There were big differences in the pre-exponential factor and this controlled the time to explosion rather than the activation energy for the process.

Comparison of polar ozone loss rates simulated by one-dimensional and three-dimensional models with Match observations in recent Antarctic and Arctic winters

Simulations of ozone loss rates using a three-dimensional chemical transport model and a box model during recent Antarctic and Arctic winters are compared with experimental loss rates. The study focused on the Antarctic winter 2003, during which the first Antarctic Match campaign was organized, and on Arctic winters 1999/2000, 2002/2003. The maximum ozone loss rates retrieved by the Match technique for the winters and levels studied reached 6 ppbv/sunlit hour and both types of simulations could generally reproduce the observations at 2-sigma error bar level. In some cases, for example, for the Arctic winter 2002/2003 at 475 K level, an excellent agreement within 1-sigma standard deviation level was obtained. An overestimation was also found with the box model simulation at some isentropic levels for the Antarctic winter and the Arctic winter 1999/2000, indicating an overestimation of chlorine activation in the model. Loss rates in the Antarctic show signs of saturation in September, which have to be considered in the comparison. Sensitivity tests were performed with the box model in order to assess the impact of kinetic parameters of the ClO-Cl2O2 catalytic cycle and total bromine content on the ozone loss rate. These tests resulted in a maximum change in ozone loss rates of 1.2 ppbv/sunlit hour, generally in high solar zenith angle conditions. In some cases, a better agreement was achieved with fastest photolysis of Cl2O2 and additional source of total inorganic bromine but at the expense of overestimation of smaller ozone loss rates derived later in the winter.

Coincidence Wecken homotopies versus Wecken homotopies relative to a fixed homotopy in one of the maps

We study the 1-parameter Wecken problem versus the restricted Wecken problem, for coincidence free pairs of maps between surfaces. For this we use properties of the function space between two surfaces and of the pure braid group on two strings of a surface. When the target surface is either the 2-sphere or the torus it is known that the two problems are the same. We classify most pairs of homotopy classes of maps according to the answer of the two problems are either the same or different when the target is either projective space or the Klein bottle. Some partial results are given for surfaces of negative Euler characteristic. (C) 2010 Elsevier B.V. All rights reserved.

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.

Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Experimental investigation of gravitational gas separation in an inclined annular channel

The oil industry uses gas separators in production wells as the free gas present in the suction of the pump reduces the pumping efficiency and pump lifetime. Therefore, free gas is one of the most important variables in the design of pumping systems. However, in the literature there is little information on these separators. It is the case of the inverted-shroud gravitational gas separator. It has an annular geometry due to the installation of a cylindrical container in between the well casing and pioduction pipe (tubing). The purpose of the present study is to understand the phenomenology and behavior of inverted-shroud separator. Experimental tests were performed in a 10.5-m-length inclinable glass tube with air and water as working fluids. The water flow rate was in the range of 8.265-26.117 l/min and the average inlet air mass flow rate was 1.1041 kg/h, with inclination angles of 15 degrees, 30 degrees, 45 degrees, 60 degrees, 75 degrees, 80 degrees and 85 degrees. One of the findings is that the length between the inner annular level and production pipe inlet is one of the most important design parameters and based on that a new criterion for total gas separation is proposed. We also found that the phenomenology of the studied separator is not directly dependent on the gas flow rate, but on the average velocity of the free surface flow generated inside the separator. Maps of efficiency of gas separation were plotted and showed that liquid flow rate, inclination angle and pressure difference between casing and production pipe outlet are the main variables related to the gas separation phenomenon. The new data can be used for the development of design tools aiming to the optimized project of the pumping system for oil production in directional wells. (C) 2012 Elsevier Inc. All rights reserved.

High-resolution electrophoretic simulations: performance characteristics of one-dimensional simulators

Three comprehensive one-dimensional simulators were used on the same PC to simulate the dynamics of different electrophoretic configurations, including two migrating hybrid boundaries, an isotachophoretic boundary and the zone electrophoretic separation of ten monovalent anions. Two simulators, SIMUL5 and GENTRANS, use a uniform grid, while SPRESSO uses a dynamic adaptive grid. The simulators differ in the way components are handled. SIMUL5 and SPRESSO feature one equation for all components, whereas GENTRANS is based on the use of separate modules for the different types of monovalent components, a module for multivalent components and a module for proteins. The code for multivalent components is executed more slowly compared to those for monovalent components. Furthermore, with SIMUL5, the computational time interval becomes smaller when it is operated with a reduced calculation space that features moving borders, whereas GENTRANS offers the possibility of using data smoothing (removal of negative concentrations), which can avoid numerical oscillations and speed up a simulation. SPRESSO with its adaptive grid could be employed to simulate the same configurations with smaller numbers of grid points and thus is faster in certain but not all cases. The data reveal that simulations featuring a large number of monovalent components distributed such that a high mesh is required throughout a large proportion of the column are fastest executed with GENTRANS.