6,152 research outputs found
Involutive constrained systems and Hamilton-Jacobi formalism
In this paper, we study singular systems with complete sets of involutive
constraints. The aim is to establish, within the Hamilton-Jacobi theory, the
relationship between the Frobenius' theorem, the infinitesimal canonical
transformations generated by constraints in involution with the Poisson
brackets, and the lagrangian point (gauge) transformations of physical systems
Hamilton-Jacobi formalism for Linearized Gravity
In this work we study the theory of linearized gravity via the
Hamilton-Jacobi formalism. We make a brief review of this theory and its
Lagrangian description, as well as a review of the Hamilton-Jacobi approach for
singular systems. Then we apply this formalism to analyze the constraint
structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit
The Kovacs effect in model glasses
We discuss the `memory effect' discovered in the 60's by Kovacs in
temperature shift experiments on glassy polymers, where the volume (or energy)
displays a non monotonous time behaviour. This effect is generic and is
observed on a variety of different glassy systems (including granular
materials). The aim of this paper is to discuss whether some microscopic
information can be extracted from a quantitative analysis of the `Kovacs hump'.
We study analytically two families of theoretical models: domain growth and
traps, for which detailed predictions of the shape of the hump can be obtained.
Qualitatively, the Kovacs effect reflects the heterogeneity of the system: its
description requires to deal not only with averages but with a full probability
distribution (of domain sizes or of relaxation times). We end by some
suggestions for a quantitative analysis of experimental results.Comment: 17 pages, 6 figures; revised versio
Trap models with slowly decorrelating observables
We study the correlation and response dynamics of trap models of glassy
dynamics, considering observables that only partially decorrelate with every
jump. This is inspired by recent work on a microscopic realization of such
models, which found strikingly simple linear out-of-equilibrium
fluctuation-dissipation relations in the limit of slow decorrelation. For the
Barrat-Mezard model with its entropic barriers we obtain exact results at zero
temperature for arbitrary decorrelation factor . These are then
extended to nonzero , where the qualitative scaling behaviour and all
scaling exponents can still be found analytically. Unexpectedly, the choice of
transition rates (Glauber versus Metropolis) affects not just prefactors but
also some exponents. In the limit of slow decorrelation even complete scaling
functions are accessible in closed form. The results show that slowly
decorrelating observables detect persistently slow out-of-equilibrium dynamics,
as opposed to intermittent behaviour punctuated by excursions into fast,
effectively equilibrated states.Comment: 29 pages, IOP styl
Cosmological parameters from strong gravitational lensing and stellar dynamics in elliptical galaxies
We show how the combination of observations related to strong gravitational
lensing and stellar dynamics in ellipticals offers a new way to measure the
cosmological matter and dark-energy density parameters. A gravitational lensing
estimate of the mass enclosed inside the Einstein circle can be obtained by
measuring the Einstein angle, once the critical density of the system is known.
A model-dependent dynamical estimate of this mass can also be obtained by
measuring the central velocity dispersion of the stellar component. By assuming
the well-tested homologous 1/r^{2} profile for the total density distribution
in the lens elliptical galaxies, these two mass measurements can be properly
compared. Thus, a relation between the Einstein angle and the central stellar
velocity dispersion is derived, and the cosmological matter and the dark-energy
density parameters can be estimated from this. We determined the accuracy of
the cosmological parameter estimates by means of simulations that include
realistic measurement uncertainties on the relevant quantities. Interestingly,
the expected constraints on the cosmological parameter plane are complementary
to those coming from other observational techniques. Then, we applied the
method to the data sets of the Sloan Lens ACS and the Lenses Structure and
Dynamics Surveys, and showed that the concordance value between 0.7 and 0.8 for
the dark-energy density parameter is included in our 99% confidence regions.
The small number of lenses available to date prevents us from precisely
determining the cosmological parameters, but it still proves the feasibility of
the method. When applied to samples made of hundreds of lenses that are
expected to become available from forthcoming surveys, this technique will be
an important tool for measuring the geometry of the Universe.Comment: 11 pages, 9 figures, accepted by Astronomy & Astrophysic
Active Brownian particles with velocity-alignment and active fluctuations
We consider a model of active Brownian particles with velocity-alignment in
two spatial dimensions with passive and active fluctuations. Hereby, active
fluctuations refers to purely non-equilibrium stochastic forces correlated with
the heading of an individual active particle. In the simplest case studied
here, they are assumed as independent stochastic forces parallel (speed noise)
and perpendicular (angular noise) to the velocity of the particle. On the other
hand, passive fluctuations are defined by a noise vector independent of the
direction of motion of a particle, and may account for example for thermal
fluctuations.
We derive a macroscopic description of the active Brownian particle gas with
velocity-alignment interaction. Hereby, we start from the individual based
description in terms of stochastic differential equations (Langevin equations)
and derive equations of motion for the coarse grained kinetic variables
(density, velocity and temperature) via a moment expansion of the corresponding
probability density function.
We focus here in particular on the different impact of active and passive
fluctuations on the onset of collective motion and show how active fluctuations
in the active Brownian dynamics can change the phase-transition behaviour of
the system. In particular, we show that active angular fluctuation lead to an
earlier breakdown of collective motion and to emergence of a new bistable
regime in the mean-field case.Comment: 5 figures, 22 pages, submitted to New Journal of Physic
The canonical structure of Podolsky's generalized electrodynamics on the Null-Plane
In this work we will develop the canonical structure of Podolsky's
generalized electrodynamics on the null-plane. This theory has second-order
derivatives in the Lagrangian function and requires a closer study for the
definition of the momenta and canonical Hamiltonian of the system. On the
null-plane the field equations also demand a different analysis of the
initial-boundary value problem and proper conditions must be chosen on the
null-planes. We will show that the constraint structure, based on Dirac
formalism, presents a set of second-class constraints, which are exclusive of
the analysis on the null-plane, and an expected set of first-class constraints
that are generators of a U(1) group of gauge transformations. An inspection on
the field equations will lead us to the generalized radiation gauge on the
null-plane, and Dirac Brackets will be introduced considering the problem of
uniqueness of these brackets under the chosen initial-boundary condition of the
theory
Linear and non linear response in the aging regime of the 1D trap model
We investigate the behaviour of the response function in the one dimensional
trap model using scaling arguments that we confirm by numerical simulations. We
study the average position of the random walk at time tw+t given that a small
bias h is applied at time tw. Several scaling regimes are found, depending on
the relative values of t, tw and h. Comparison with the diffusive motion in the
absence of bias allows us to show that the fluctuation dissipation relation is,
in this case, valid even in the aging regime.Comment: 5 pages, 3 figures, 3 references adde
Modelling elliptical galaxies: phase-space constraints on two-component (gamma1,gamma2) models
In the context of the study of the properties of the mutual mass distribution
of the bright and dark matter in elliptical galaxies, present a family of
two-component, spherical, self-consistent galaxy models, where one density
distribution follows a gamma_1 profile, and the other a gamma_2 profile
[(gamma_1,gamma_2) models], with different total masses and ``core'' radii. A
variable amount of Osipkov-Merritt (radial) orbital anisotropy is allowed in
both components. For these models, I derive analytically the necessary and
sufficient conditions that the model parameters must satisfy in order to
correspond to a physical system. Moreover, the possibility of adding a black
hole at the center of radially anisotropic gamma models is discussed,
determining analytically a lower limit of the anisotropy radius as a function
of gamma. The analytical phase-space distribution function for (1,0) models is
presented, together with the solution of the Jeans equations and the quantities
entering the scalar virial theorem. It is proved that a globally isotropic
gamma=1 component is consistent for any mass and core radius of the
superimposed gamma=0 model; on the contrary, only a maximum value of the core
radius is allowed for the gamma=0 model when a gamma=1 density distribution is
added. The combined effects of mass concentration and orbital anisotropy are
investigated, and an interesting behavior of the distribution function of the
anisotropic gamma=0 component is found: there exists a region in the parameter
space where a sufficient amount of anisotropy results in a consistent model,
while the structurally identical but isotropic model would be inconsistent.Comment: 29 pages, LaTex, plus 5 .eps figures and macro aaspp4.sty - accepted
by ApJ, main journa
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