Irreversible phase transitions induced by an oscillatory input

A novel kind of irreversible phase transitions (IPT's) driven by an oscillatory input parameter is studied by means of computer simulations. Second order IPT's showing scale invariance in relevant dynamic critical properties are found to belong to the universality class of directed percolation. In contrast, the absence of universality is observed for first order IPT's.Comment: 18 pages (Revtex); 8 figures (.ps); submitted to Europhysics Letters, December 9th, 199

On the regularity of the distance near the boundary of an obstacle

We study the regularity of the Euclidean distance function from a given point-wise target of a n-dimensional vector space in the presence of a compact obstacle bounded by a smooth hypersurface. It is known that such a function is semiconcave with fractional modulus one half. We provide a geometrical explanation of the exponent one half. Furthermore, under a natural (weak) assumption on the position of the point-wise target relatively to the obstacle, we show that there exists a point in the boundary of the obstacle so that no better regularity result holds near such a point. As a consequence of this result, we show that the Euclidean metric cannot be extended to a tubular neighborhood of the obstacle, as a Riemannian metric, keeping the property that the associated distances coincide outside the obstacle

Study of the one-dimensional off-lattice hot-monomer reaction model

Hot monomers are particles having a transient mobility (a ballistic flight) prior to being definitely absorbed on a surface. After arriving at a surface, the excess energy coming from the kinetic energy in the gas phase is dissipated through degrees of freedom parallel to the surface plane. In this paper we study the hot monomer-monomer adsorption-reaction process on a continuum (off-lattice) one-dimensional space by means of Monte Carlo simulations. The system exhibits second-order irreversible phase transition between a reactive and saturated (absorbing) phases which belong to the directed percolation (DP) universality class. This result is interpreted by means of a coarse-grained Langevin description which allows as to extend the DP conjecture to transitions occurring in continuous media.Comment: 13 pages, 5 figures, final version to appear in J. Phys.

Analysis and Insights from a Dynamical Model of Nuclear Plant Safety Risk

In this paper, we expand upon previously reported results of a dynamical systems model for the impact of plant processes and programmatic performance on nuclear plant safety risk. We utilize both analytical techniques and numerical simulations typical of the analysis of nonlinear dynamical systems to obtain insights important for effective risk management. This includes use of bifurcation diagrams to show that period doubling bifurcations and regions of chaotic dynamics can occur. We also investigate the impact of risk mitigating functions (equipment reliability and loss prevention) on plant safety risk and demonstrate that these functions are capable of improving risk to levels that are better than those that are represented in a traditional risk assessment. Next, we analyze the system response to the presence of external noise and obtain some conclusions with respect to the allocation of resources to ensure that safety is maintained at optimal levels. In particular, we demonstrate that the model supports the importance of management and regulator attention to plants that have demonstrated poor performance by providing an external stimulus to obtain desired improvements. Equally important, the model suggests that excessive intervention, by either plant management or regulatory authorities, can have a deleterious impact on safety for plants that are operating with very effective programs and processes. Finally, we propose a modification to the model that accounts for the impact of plant risk culture on process performance and plant safety risk. We then use numerical simulations to demonstrate the important safety benefits of a strong risk culture.Nonlinear Dynamical Systems, Process Model, Risk Management

An interpolation problem in the Denjoy–Carleman classes

Inspired by some iterative algorithms useful for proving the real analyticity (or the Gevrey regularity) of a solution of a linear partial differential equation with real-analytic coefficients, we consider the following question. Given a smooth function defined on [a,b]subset of R$[a,b]\subset {\mathbb {R}}$ and given an increasing divergent sequence dn$d_n$ of positive integers such that the derivative of order dn$d_n$ of f has a growth of the type Mdn$M_{d_n}$, when can we deduce that f is a function in the Denjoy-Carleman class CM([a,b])C<^>M([a,b])? We provide a positive result and show that a suitable condition on the gaps between the terms of the sequence dn$d_n$ is needed

The distance function in the presence of an obstacle

We study the Riemannian distance function from a fixed point (a point-wise target) of Euclidean space in the presence of a compact obstacle bounded by a smooth hypersurface. First, we show that such a function is locally semiconcave with a fractional modulus of order one half and that, near the obstacle, this regularity is optimal. Then, in the Euclidean setting, we prove that the singularities of the distance function propagate, in the sense that each singular point belongs to a nontrivial singular continuum. Finally, we investigate the lack of differentiability of the distance function when a convex obstacle is present

Dynamic Critical approach to Self-Organized Criticality

A dynamic scaling Ansatz for the approach to the Self-Organized Critical (SOC) regime is proposed and tested by means of extensive simulations applied to the Bak-Sneppen model (BS), which exhibits robust SOC behavior. Considering the short-time scaling behavior of the density of sites ($\rho(t)$) below the critical value, it is shown that i) starting the dynamics with configurations such that $\rho(t=0) \to 0$ one observes an {\it initial increase} of the density with exponent $\theta = 0.12(2)$; ii) using initial configurations with $\rho(t=0) \to 1$, the density decays with exponent $\delta = 0.47(2)$. It is also shown that he temporal autocorrelation decays with exponent $C_a = 0.35(2)$. Using these, dynamically determined, critical exponents and suitable scaling relationships, all known exponents of the BS model can be obtained, e.g. the dynamical exponent $z = 2.10(5)$, the mass dimension exponent $D = 2.42(5)$, and the exponent of all returns of the activity $\tau_{ALL} = 0.39(2)$, in excellent agreement with values already accepted and obtained within the SOC regime.Comment: Rapid Communication Physical Review E in press (4 pages, 5 figures

Numerical study of a first-order irreversible phase transition in a CO+NO catalyzed reaction model

The first-order irreversible phase transitions (IPT) of the Yaldran-Khan model (Yaldran-Khan, J. Catal. 131, 369, 1991) for the CO+NO reaction is studied using the constant coverage (CC) ensemble and performing epidemic simulations. The CC method allows the study of hysteretic effects close to coexistence as well as the location of both the upper spinodal point and the coexistence point. Epidemic studies show that at coexistence the number of active sites decreases according to a (short-time) power law followed by a (long-time) exponential decay. It is concluded that first-order IPT's share many characteristic of their reversible counterparts, such as the development of short ranged correlations, hysteretic effects, metastabilities, etc.Comment: 17 pages, 10 figure

Damage Spreading in a Driven Lattice Gas Model

We studied damage spreading in a Driven Lattice Gas (DLG) model as a function of the temperature $T$, the magnitude of the external driving field $E$, and the lattice size. The DLG model undergoes an order-disorder second-order phase transition at the critical temperature $T_c(E)$, such that the ordered phase is characterized by high-density strips running along the direction of the applied field; while in the disordered phase one has a lattice-gas-like behaviour. It is found that the damage always spreads for all the investigated temperatures and reaches a saturation value $D_{sat}$ that depends only on $T$. $D_{sat}$ increases for $TT_c(E=\infty)$ and is free of finite-size effects. This behaviour can be explained as due to the existence of interfaces between the high-density strips and the lattice-gas-like phase whose roughness depends on $T$. Also, we investigated damage spreading for a range of finite fields as a function of $T$, finding a behaviour similar to that of the case with $E=\infty$.Comment: 13 pages, 7 figures. Submitted to "Journal of Statistical Mechanics: Theory and Experiment