324,261 research outputs found
Remarks on some vacuum solutions of scalar-tensor cosmological models
We present a class of exact vacuum solutions corresponding to de Sitter and
warm inflation models in the framework of scalar-tensor cosmologies. We show
that in both cases the field equations reduce to planar dynamical systems with
constraints. Then, we carry out a qualitative analysis of the models by
examining the phase diagrams of the solutions near the equilibrium points.Comment: 12 pages, 4 figures. To be published in the Brazilian Journal of
Physic
Comprehensive study of phase transitions in relaxational systems with field-dependent coefficients
We present a comprehensive study of phase transitions in single-field systems
that relax to a non-equilibrium global steady state. The mechanism we focus on
is not the so-called Stratonovich drift combined with collective effects, but
is instead similar to the one associated with noise-induced transitions a la
Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise
interpretation (e.g., Ito vs Stratonvich) merely shifts the phase boundaries.
With the help of a mean-field approximation, we present a broad qualitative
picture of the various phase diagrams that can be found in these systems. To
complement the theoretical analysis we present numerical simulations that
confirm the findings of the mean-field theory
Qualitative stability patterns for Lotka-Volterra systems on rectangles
We present a qualitative analysis of the Lotka-Volterra differential equation within rectangles that are transverse with respect to the flow. In similar way to existing works on affine systems (and positively invariant rectangles), we consider here nonlinear Lotka-Volterra n-dimensional equation, in rectangles with any kind of tranverse patterns. We give necessary and sufficient conditions for the existence of symmetrically transverse rectangles (containing the positive equilibrium), giving notably the method to build such rectangles. We also analyse the stability of the equilibrium thanks to this transverse pattern. We finally propose an analysis of the dynamical behavior inside a rectangle containing the positive equilibrium, based on Lyapunov stability theory. More particularly, we make use of Lyapunov-like functions, built upon vector norms. This work is a first step towards a qualitative abstraction and simulation of Lotka-Volterra systems
Stability of MultiComponent Biological Membranes
Equilibrium equations and stability conditions are derived for a general class of multicomponent biological membranes. The analysis is based on a generalized Helfrich energy that
accounts for geometry through the stretch and curvature, the composition, and the interaction between geometry and composition. The use of nonclassical differential operators and related integral theorems in conjunction with appropriate composition and mass conserving variations simplify the derivations. We show that instabilities of multicomponent membranes are significantly different from
those in single component membranes, as well as those in systems undergoing spinodal decomposition in flat spaces. This is due to the intricate coupling between composition and shape as well as the nonuniform tension in the membrane. Specifically, critical modes have high frequencies unlike single component vesicles and stability depends on system size unlike in systems undergoing spinodal
decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We show that the predictions of the analysis are in qualitative agreement with experimental observations
Distribution functions for clusters of galaxies from N-body simulations
We present the results of an attempt to adapt the distribution function
formalism to characterize large-scale structures like clusters of galaxies that
form in a cosmological N-body simulation. While galaxy clusters are systems
that are not strictly in equilibrium, we show that their evolution can
nevertheless be studied using a physically motivated extension of the language
of equilibrium stellar dynamics. Restricting our analysis to the virialized
region, a prescription to limit the accessible phase-space is presented, which
permits the construction of both the isotropic and the anisotropic distribution
functions and . The method is applied to models extracted from a
catalogue of simulated clusters. Clusters evolved in open and flat background
cosmologies are followed during the course of their evolution, and are found to
transit through a sequence of what we define as `quasi-equilibrium' states. An
interesting feature is that the computed is well fit by an exponential
form. We conclude that the dynamical evolution of a cluster, undergoing
relaxation punctuated by interactions and violent mergers with consequent
energy-exchange, can be studied both in a qualitative and quantitative fashion
by following the time evolution of .Comment: 16 pages, LaTeX file, all figures included, revised version, accepted
for publication in MNRA
Finite size corrections to random Boolean networks
Since their introduction, Boolean networks have been traditionally studied in
view of their rich dynamical behavior under different update protocols and for
their qualitative analogy with cell regulatory networks. More recently, tools
borrowed from statistical physics of disordered systems and from computer
science have provided a more complete characterization of their equilibrium
behavior. However, the largest part of the results have been obtained in the
thermodynamic limit, which is often far from being reached when dealing with
realistic instances of the problem. The numerical analysis presented here aims
at comparing - for a specific family of models - the outcomes given by the
heuristic belief propagation algorithm with those given by exhaustive
enumeration. In the second part of the paper some analytical considerations on
the validity of the annealed approximation are discussed.Comment: Minor correction
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