Exact time dependent Hopf solitons in 3+1 dimensions

We construct an infinite number of exact time dependent soliton solutions, carrying non-trivial Hopf topological charges, in a 3+1 dimensional Lorentz invariant theory with target space S2. The construction is based on an ansatz which explores the invariance of the model under the conformal group SO(4,2) and the infinite dimensional group of area preserving diffeomorphisms of S2. The model is a rare example of an integrable theory in four dimensions, and the solitons may play a role in the low energy limit of gauge theories. © SISSA 2006.

Plane waves in noncommutative fluids

We study the dynamics of the noncommutative fluid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear partial differential equations in which the variables are the fluid density and the fluid potentials. We show that these equations admit a set of solutions that are monochromatic plane waves for the fluid density and two of the potentials and a linear function for the third potential. The energy-momentum tensor of the plane waves is calculated. © 2013 Elsevier B.V.

Hopf bifurcation in the full repressilator equations

In this paper, we prove that the full repressilator equations in dimension six undergo a supercritical Hopf bifurcation.

Scattering equations, generating functions and all massless five point tree amplitudes

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

MOLECULAR DYNAMICS STUDIES OF SIMPLE MODEL FLUIDS AND WATER CONFINED IN CARBON NANOTUBE

Molecular Dynamics (MD) simulation is one of the most important computational techniques with broad applications in physics, chemistry, chemical engineering, materials design and biological science. Traditional computational chemistry refers to quantum calculations based on solving Schrodinger equations. Later developed Density Functional Theory (DFT) based on solving Kohn-Sham equations became the more popular ab initio calculation technique which could deal with ~1000 atoms by explicitly considering electron interactions. In contrast, MD simulation based on solving classical mechanics equations of motion is a totally different technique in the field of computational chemistry. Electron interactions were implicitly included in the empirical atom-based potential functions and the system size to be investigated can be extended to ~106 atoms. The thermodynamic properties of model fluids are mainly determined by macroscopic quantities, like temperature, pressure, density. The quantum effects on thermodynamic properties like melting point, surface tension are not dominant. In this work, we mainly investigated the melting point, surface tension (liquid-vapor and liquid-solid) of model fluids including Lennard-Jones model, Stockmayer model and a couple of water models (TIP4P/Ew, TIP5P/Ew) by means of MD simulation. In addition, some new structures of water confined in carbon nanotube were discovered and transport behaviors of water and ions through nano-channels were also revealed.

Rotating black holes in a Randall-Sundrum brane with a cosmological constant

In this work we have constructed axially symmetric vacuum solutions of the gravitational field equations in a Randall-Sundrum brane. A non-null effective cosmological constant is considered, and asymptotically de Sitter and anti-de Sitter spacetimes are obtained. The solutions describe rotating black holes in a four-dimensional brane. Optical features of the solutions are treated, emphasizing the rotation of the polarization vector along null congruences. DOI: 10.1103/PhysRevD.86.124047

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.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

Terahertz macrospin dynamics in insulating ferrimagnets

We investigate numerically the excitation of nonlinear magnetic interactions in a ferrite material by an energetic pump pulse of terahertz (THz) radiation. The calculations are performed by solving the coupled Maxwell and Landau-Lifshitz-Gilbert differential equations. In a time-resolved THz pump/THz probe scheme, it is demonstrated that Faraday rotation of a delayed THz probe pulse can be used to map these interactions. Our study is motivated by the ability of soft x-ray free electron lasers to perform time-resolved imaging of the magnetization process at the submicrometer and subpicosecond length and time scales.

Differential invariants of second-order ordinary differential equations

The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.

Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

An ethnographic study: Becoming a physics expert in a biophysics research group

Expertise in physics has been traditionally studied in cognitive science, where physics expertise is understood through the difference between novice and expert problem solving skills. The cognitive perspective of physics experts only create a partial model of physics expertise and does not take into account the development of physics experts in the natural context of research. This dissertation takes a social and cultural perspective of learning through apprenticeship to model the development of physics expertise of physics graduate students in a research group. I use a qualitative methodological approach of an ethnographic case study to observe and video record the common practices of graduate students in their biophysics weekly research group meetings. I recorded notes on observations and conduct interviews with all participants of the biophysics research group for a period of eight months. I apply the theoretical framework of Communities of Practice to distinguish the cultural norms of the group that cultivate physics expert practices. Results indicate that physics expertise is specific to a topic or subfield and it is established through effectively publishing research in the larger biophysics research community. The participant biophysics research group follows a learning trajectory for its students to contribute to research and learn to communicate their research in the larger biophysics community. In this learning trajectory students develop expert member competencies to learn to communicate their research and to learn the standards and trends of research in the larger research community. Findings from this dissertation expand the model of physics expertise beyond the cognitive realm and add the social and cultural nature of physics expertise development. This research also addresses ways to increase physics graduate student success towards their PhD. and decrease the 48% attrition rate of physics graduate students. Cultivating effective research experiences that give graduate students agency and autonomy beyond their research groups gives students the motivation to finish graduate school and establish their physics expertise.^

Toward equity through participation in Modeling Instruction in introductory university physics

We report the results of a five year evaluation of the reform of introductory calculus-based physics by implementation of Modeling Instruction (MI) at Florida International University (FIU), a Hispanic-serving institution. MI is described in the context of FIU’s overall effort to enhance student participation in physics and science broadly. Our analysis of MI from a “participationist” perspective on learning identifies aspects of MI including conceptually based instruction, culturally sensitive instruction, and cooperative group learning, which are consistent with research on supporting equitable learning and participation by students historically under-represented in physics (i.e., Black, Hispanic, women). This study uses markers of conceptual understanding as measured by the Force Concept Inventory (FCI) and odds of success as measured by the ratio of students completing introductory physics and earning a passing grade (i.e., C− or better) by students historically under-represented in physics to reflect equity and participation in introductory physics. FCI pre and post scores for students in MI are compared with lecture-format taught students. Modeling Instruction students outperform students taught in lecture-format classes on post instruction FCI (61.9% vs 47.9%, p