Theoretical evidence for a dense fluid precursor to crystallization

We present classical density functional theory calculations of the free energy landscape for fluids below their triple point as a function of density and crystallinity. We find that for both a model globular protein and for a simple atomic fluid modeled with a Lennard-Jones interaction, it is free-energetically easier to crystallize by passing through a metastable dense fluid in accord with the Ostwald rule of stages but in contrast to the alternative of ordering and densifying at once as assumed in the classical picture of crystallization.Comment: 4 pages, 3 figure

Mechanism for the stabilization of protein clusters above the solubility curve

Pan, Vekilov and Lubchenko[\textit{J. Phys. Chem. B}, 2010, \textbf{114}, 7620] have proposed that dense stable protein clusters appearing in weak protein solutions above the solubility curve are composed of protein oligomers. The hypothesis is that a weak solution of oligomer species is unstable with respect to condensation causing the formation of dense, oligomer-rich droplets which are stabilized against growth by the monomer-oligomer reaction. Here, we show that such a combination of processes can be understood using a simple capillary model yielding analytic expressions for the cluster properties which can be used to interpret experimental data. We also construct a microscopic Dynamic Density Functional Theory model and show that it is consistent with the predictions of the capillary model. The viability of the mechanism is thus confirmed and it is shown how the radius of the stable clusters is related to physically interesting quantities such as the monomer-oligomer rate constants

The effect of the range of interaction on the phase diagram of a globular protein

Thermodynamic perturbation theory is applied to the model of globular proteins studied by ten Wolde and Frenkel (Science 277, pg. 1976) using computer simulation. It is found that the reported phase diagrams are accurately reproduced. The calculations show how the phase diagram can be tuned as a function of the lengthscale of the potential.Comment: 20 pages, 5 figure

Emergence of coherent motion in aggregates of motile coupled maps

In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are able to swing along the route to chaos. Thereby, each motile can display different types of behavior, i.e. from ordered to fully erratic motion, accordingly with its surrounding conditions. The appearance of patterns of collective motion is shown to be related to the emergence of interparticle synchronization and the degree of coherence of motion is quantified by means of a graph representation. The effects related to the density of particles and to interparticle distances are explored. It is shown that the higher degrees of coherence and group cohesion are attained when the system elements display a combination of ordered and chaotic behaviors, which emerges from a collective self-organization process.Comment: 33 pages, 12 figures, accepted for publication at Chaos, Solitons and Fractal

Null energy condition and superluminal propagation

We study whether a violation of the null energy condition necessarily implies the presence of instabilities. We prove that this is the case in a large class of situations, including isotropic solids and fluids relevant for cosmology. On the other hand we present several counter-examples of consistent effective field theories possessing a stable background where the null energy condition is violated. Two necessary features of these counter-examples are the lack of isotropy of the background and the presence of superluminal modes. We argue that many of the properties of massive gravity can be understood by associating it to a solid at the edge of violating the null energy condition. We briefly analyze the difficulties of mimicking $\dot H>0$ in scalar tensor theories of gravity.Comment: 46 pages, 6 figure

Dynamics of error growth in unstable systems

Analytic expressions of the mean error and of the error probability versus time are derived for chaotic attractors. The expressions are studied for the logistic and Bernoulli maps and for the Rössler flow. In all cases mean error growth follows a logisticlike curve, the characteristics of which are related to the intrinsic properties of the attractor. © 1991 The American Physical Society.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

From short-scale atmospheric variability to global climate dynamics: toward a systematic theory of averaging

info:eu-repo/semantics/publishe

Extreme events in multivariate deterministic systems

The probabilistic properties of extreme values in multivariate deterministic dynamical systems are analyzed. It is shown that owing to the intertwining of unstable and stable modes the effect of dynamical complexity on the extremes tends to be masked, in the sense that the cumulative probability distribution of typical variables is differentiable and its associated probability density is continuous. Still, there exist combinations of variables probing the dominant unstable modes displaying singular behavior in the form of nondifferentiability of the cumulative distributions of extremes on certain sets of phase space points. Analytic evaluations and extensive numerical simulations are carried out for characteristic examples of Kolmogorov-type systems, for low-dimensional chaotic flows, and for spatially extended systems. © 2012 American Physical Society.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Passage through a barrier with a slowly increasing control parameter

The kinetics of the passage through a barrier in a bistable system experiencing a supercritical pitchfork bifurcation is analyzed. The main effects of a ramp in the instability control parameter on the distribution of probability mass on both sides of the barrier are examined. An asymptotic expression is derived to represent the stochastic dynamics in the presence of the ramp, and the results are compared with the results of the Langevin and Fokker-Planck equations.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Normal form analysis of stochastically forced dynamical systems

The possibility of reducing the dynamics of a system undergoing a Hopf bifurcation and forced by multiplicative noise to a universal normal form is examined on a simple model of geophysical interest. It is shown that the normal form equations and the stationary probability distribution depend on the way the noise is coupled to the original system. The universality of the normal forms is thus severely limited in the presence of noise. © 1986, Taylor & Francis Group, LLC. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe