Miscibility in a degenerate fermionic mixture induced by linear coupling

We consider a one-dimensional mean-field-hydrodynamic model of a two-component degenerate Fermi gas in an external trap, each component representing a spin state of the same atom. We demonstrate that the interconversion between them (linear coupling), imposed by a resonant electromagnetic wave, transforms the immiscible binary gas into a miscible state, if the coupling constant, kappa, exceeds a critical value, kappa(cr). The effect is predicted in a variational approximation, and confirmed by numerical solutions. Unlike the recently studied model of a binary Bose-Einsten condensate with the linear coupling, the components in the immiscible phase of the binary fermion mixture never fill two separated domains with a wall between them, but rather form antilocked (pi-phase-shifted) density waves. Another difference from the bosonic mixture is spontaneous breaking of symmetry between the two components in terms of the numbers of atoms in them, N(1) and N(2). The latter effect is characterized by the parameter nu equivalent to(N(1)-N(2))/(N(1)+N(2)) (only N(1)+N(2) is a conserved quantity), the onset of miscibility at kappa >=kappa(cr) meaning a transition to nu equivalent to 0. At kappa linear coupling, and the developing spatial structure resembles the known Larkin-Ovchinnikov-Fulde-Ferrell states in the Fermi mixture. Dynamical states, when kappa is suddenly switched from zero to a value exceeding kappa(cr), are considered too. In the latter case, the system features oscillatory relaxation to the mixed state.

Effects of time-periodic linear coupling on two-component Bose-Einstein condensates in two dimensions

We examine two-component Gross-Pitaevskii equations with nonlinear and linear couplings, assuming self-attraction in one species and self-repulsion in the other, while the nonlinear inter-species coupling is also repulsive. For initial states with the condensate placed in the self-attractive component, a sufficiently strong linear coupling switches the collapse into decay (in the free space). Setting the linear-coupling coefficient to be time-periodic (alternating between positive and negative values, with zero mean value) can make localized states quasi-stable for the parameter ranges considered herein, but they slowly decay. The 2D states can then be completely stabilized by a weak trapping potential. In the case of the high-frequency modulation of the coupling constant, averaged equations are derived, which demonstrate good agreement with numerical solutions of the full equations. (C) 2007 Elsevier B.V. All rights reserved.

Impact of linear mode coupling on the group delay spread in few-mode fibers

We report an investigation on the group delay spread in few-mode fibers operating in the weak and strong linear coupling regimes, and for the first time, we study the transition region between them. A single expression linking the group delay spread to the fiber correlation length is validated for any coupling regime, considering 3 guided modes.

On the group delay statistics of few-mode fibres with intermediate linear mode coupling

We report an investigation on the statistics of group delay for few-mode fibres operating in the weak and strong linear coupling regimes as well as in the intermediate coupling regime. A single expression linking the standard deviation of the group delay spread to the fibre linear mode coupling is validated for any coupling regime, considering up to six linearly polarized guided modes. Furthermore, the study of the probability density function of the group delays allowed deriving and validating an analytical estimation for the maximum group delay spread as a function of linear mode coupling.

Two-component gap solitons with linear interconversion

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the coupling of the self-dual field to dynamical U(1) matter and its dual theory

We consider arbitrary U (1) charged matter non-minimally coupled to the self-dual field in d = 2 + 1. The coupling includes a linear and a rather general quadratic term in the self-dual field. By using both Lagragian gauge embedding and master action approaches we derive the dual Maxwell Chern-Simons-type model and show the classical equivalence between the two theories. At the quantum level the master action approach in general requires the addition of an awkward extra term to the Maxwell Chern-Simons-type theory. Only in the case of a linear coupling in the self-dual field can the extra term be dropped and we are able to establish the quantum equivalence of gauge invariant correlation functions in both theories.

Suppression of nonlinear distortion in few-mode fibres using strong mode coupling

In this paper, we investigate the impact of linear mode coupling on the efficiency of intermodal four-wave mixing and on the group delay statistics in few-mode fibres. The investigation will include not only the weak or strong linear coupling regimes, but also the transition region between them, the intermediate coupling regime. This analysis will allow to assess the level of coupling strength require to suppress the nonlinear distortion in a few-mode fibre below the level of distortion for single-mode propagation without mode coupling.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

The impact of two coupled cirrus microphysics-radiation parameterizations on the temperature and specific humidity biases in the tropical tropopause layer in a climate model

The impact of two different coupled cirrus microphysics-radiation parameterizations on the zonally averaged temperature and humidity biases in the tropical tropopause layer (TTL) of a Met Office climate model configuration is assessed. One parameterization is based on a linear coupling between a model prognostic variable, the ice mass mixing ratio, qi, and the integral optical properties. The second is based on the integral optical properties being parameterized as functions of qi and temperature, Tc, where the mass coefficients (i.e. scattering and extinction) are parameterized as nonlinear functions of the ratio between qi and Tc. The cirrus microphysics parameterization is based on a moment estimation parameterization of the particle size distribution (PSD), which relates the mass moment (i.e. second moment if mass is proportional to size raised to the power of 2 ) of the PSD to all other PSD moments through the magnitude of the second moment and Tc. This same microphysics PSD parameterization is applied to calculate the integral optical properties used in both radiation parameterizations and, thus, ensures PSD and mass consistency between the cirrus microphysics and radiation schemes. In this paper, the temperature-non-dependent and temperature-dependent parameterizations are shown to increase and decrease the zonally averaged temperature biases in the TTL by about 1 K, respectively. The temperature-dependent radiation parameterization is further demonstrated to have a positive impact on the specific humidity biases in the TTL, as well as decreasing the shortwave and longwave biases in the cloudy radiative effect. The temperature-dependent radiation parameterization is shown to be more consistent with TTL and global radiation observations.

Self-energies for interacting fields with a compactified spatial dimension

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Transverse-Plane Ankle Rotation for Lower-Limb Amputees Using Two Novel Prostheses

Thesis (Ph.D.)--University of Washington, 2016-06

Distributed optimization and games over networks: a system theoretical perspective

Several decision and control tasks involve networks of cyber-physical systems that need to be coordinated and controlled according to a fully-distributed paradigm involving only local communications without any central unit. This thesis focuses on distributed optimization and games over networks from a system theoretical perspective. In the addressed frameworks, we consider agents communicating only with neighbors and running distributed algorithms with optimization-oriented goals. The distinctive feature of this thesis is to interpret these algorithms as dynamical systems and, thus, to resort to powerful system theoretical tools for both their analysis and design. We first address the so-called consensus optimization setup. In this context, we provide an original system theoretical analysis of the well-known Gradient Tracking algorithm in the general case of nonconvex objective functions. Then, inspired by this method, we provide and study a series of extensions to improve the performance and to deal with more challenging settings like, e.g., the derivative-free framework or the online one. Subsequently, we tackle the recently emerged framework named distributed aggregative optimization. For this setup, we develop and analyze novel schemes to handle (i) online instances of the problem, (ii) ``personalized'' optimization frameworks, and (iii) feedback optimization settings. Finally, we adopt a system theoretical approach to address aggregative games over networks both in the presence or absence of linear coupling constraints among the decision variables of the players. In this context, we design and inspect novel fully-distributed algorithms, based on tracking mechanisms, that outperform state-of-the-art methods in finding the Nash equilibrium of the game.

Modal coupling in linear control systems using robust eigenstructure assignment

Eigenvalue assignment methods are used widely in the design of control and state-estimation systems. The corresponding eigenvectors can be selected to ensure robustness. For specific applications, eigenstructure assignment can also be applied to achieve more general performance criteria. In this paper a new output feedback design approach using robust eigenstructure assignment to achieve prescribed mode input and output coupling is described. A minimisation technique is developed to improve both the mode coupling and the robustness of the system, whilst allowing the precision of the eigenvalue placement to be relaxed. An application to the design of an automatic flight control system is demonstrated.

Confining solutions of massive spin-0 bosons by a linear nonminimal vector coupling in the Duffin-Kemmer-Petiau theory

The Duffin-Kemmer-Petiau (DKP) equation, in the scalar sector of the theory and with a linear nominimal vector potential, is mapped into the nonrelativistic harmonic oscillator problem. The behavior of the solutions for this sort of vector DKP oscillator is discussed in detail.