Analytic solutions for nonlinear waves in coupled reacting systems

We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison is made between exact solutions and solutions of the piecewise linearized system, showing how the linearization affects the amplitude and frequency of the solutions.Comment: 5 pages, 5 figures, RevTeX 4 styl

Outflows at the Edges of an Active Region in a Coronal Hole: A Signature of Active Region Expansion?

Outflows of plasma at the edges of active regions surrounded by quiet Sun are now a common observation with the Hinode satellite. While there is observational evidence to suggest that the outflows are originating in the magnetic field surrounding the active regions, there is no conclusive evidence that reveals how they are driven. Motivated by observations of outflows at the periphery of a mature active region embedded in a coronal hole, we have used a three-dimensional simulation to emulate the active region's development in order to investigate the origin and driver of these outflows. We find outflows are accelerated from a site in the coronal hole magnetic field immediately surrounding the active region and are channelled along the coronal hole field as they rise through the atmosphere. The plasma is accelerated simply as a result of the active region expanding horizontally as it develops. Many of the characteristics of the outflows generated in the simulation are consistent with those of observed outflows: velocities up to 45 km per sec, properties akin to the coronal hole, proximity to the active region's draining loops, expansion with height, and projection over monopolar photospheric magnetic concentrations. Although the horizontal expansion occurs as a consequence of the active region's development in the simulation, expansion is also a general feature of established active regions. Hence, it is entirely possible and plausible that the expansion acceleration mechanism displayed in the simulation is occurring in active regions on the Sun and, in addition to reconnection, is driving the outflows observed at their edges.Comment: 19 pages, 9 figure

On the Emergence of Unstable Modes in an Expanding Domain for Energy-Conserving Wave Equations

Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{\"o}dinger equation in a finite domain and show how the expansion or contraction of the domain, under appropriate conditions, can destabilize its originally stable solutions through the modulational instability mechanism. Using both real and Fourier spacediagnostics, we monitor and control the crossing of the instability threshold and, hence, the activation of the instability. We also consider how the manifestation of this mechanism is modified in a spatially inhomogeneous setting, namely in the presence of an external parabolic potential, which is relevant to trapped Bose-Einstein condensates

A Family of Exact, Analytic Time Dependent Wave Packet Solutions to a Nonlinear Schroedinger Equation

We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The NRT non-linear equation admits plane wave-like solutions ($q$-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the $q$-generalized thermostatistical formalism, is characterized by a parameter $q$, and in the limit $q \to 1$ reduces to the standard, linear Schr\"odinger equation. The $q$-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known $q$-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the $q \to 1$ limit the $q$-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schr\"odinger equation. In the present work we also show that there are other families of nonlinear Schr\"odinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations

Anomalous diffusion with absorption: Exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a non extensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion and the absorption process are discussed.Comment: RevTex, 16 pgs, 4 figures. Accepted in Physical Review

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove

Population Dynamics and Non-Hermitian Localization

We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the Schroedinger-like operator which appears in linearized growth models. We illustrate the basic ideas by reviewing how convection affects the evolution of a population influenced by a simple square well growth profile. Results from discrete lattice growth models in both one and two dimensions are presented. A set of similarity transformations which lead to exact results for the spectrum and winding numbers of eigenfunctions for random growth rates in one dimension is described in detail. We discuss the influence of boundary conditions, and argue that periodic boundary conditions lead to results which are in fact typical of a broad class of growth problems with convection.Comment: 19 pages, 11 figure

γ-Cyclodextrin Metal-Organic Frameworks: Do Solvents Make a Difference?

Conventionally, methanol is the solvent of choice in the synthesis of gamma-cyclodextrin metal-organic frameworks (γ-CD-MOFs), but using ethanol as a replacement could allow for a more food-grade synthesis condition. Therefore, the aim of the study was to compare the γ-CD-MOFs synthesised with both methanol and ethanol. The γ-CD-MOFs were characterised by scanning electron microscopy (SEM), surface area and pore measurement, Fourier transform infrared spectroscopy (FTIR) and powder X-ray diffraction (PXRD). The encapsulation efficiency (EE) and loading capacity (LC) of the γ-CD-MOFs were also determined for curcumin, using methanol, ethanol and a mixture of the two as encapsulation solvent. It was found that γ-CD-MOFs synthesised by methanol and ethanol do not differ greatly, the most significant difference being the larger crystal size of γ-CD-MOFs crystallised from ethanol. However, the change in solvent significantly influenced the EE and LC of the crystals. The higher solubility of curcumin in ethanol reduced interactions with the γ-CD-MOFs and resulted in lowered EE and LC. This suggests that different solvents should be used to deliberately manipulate the EE and LC of target compounds for better use of γ-CD-MOFs as their encapsulating and delivery agents

Patient Outcomes at Twelve Months after Early Decompressive Craniectomy for Diffuse Traumatic Brain Injury in the Randomized DECRA Clinical Trial

Functional outcomes at 12 months were a secondary outcome of the randomized DECRA trial of early decompressive craniectomy for severe diffuse traumatic brain injury (TBI) and refractory intracranial hypertension. In the DECRA trial, patients were randomly allocated 1:1 to either early decompressive craniectomy or intensive medical therapies (standard care). We conducted planned secondary analyses of the DECRA trial outcomes at 6 and 12 months, including all 155 patients. We measured functional outcome using the Glasgow Outcome Scale-Extended (GOS-E). We used ordered logistic regression, and dichotomized the GOS-E using logistic regression, to assess outcomes in patients overall and in survivors. We adjusted analyses for injury severity using the International Mission for Prognosis and Analysis of Clinical Trials in TBI (IMPACT) model. At 12 months, the odds ratio (OR) for worse functional outcomes in the craniectomy group (OR 1.68; 95% confidence interval [CI]: 0.96-2.93; p = 0.07) was no longer significant. Unfavorable functional outcomes after craniectomy were 11% higher (59% compared with 48%), but were not significantly different from standard care (OR 1.58; 95% CI: 0.84-2.99; p = 0.16). Among survivors after craniectomy, there were fewer good (OR 0.33; 95% CI: 0.12-0.91; p = 0.03) and more vegetative (OR 5.12; 95% CI: 1.04-25.2; p = 0.04) outcomes. Similar outcomes in survivors were found at 6 months after injury. Vegetative (OR 5.85; 95% CI: 1.21-28.30; p = 0.03) and severely disabled outcomes (OR 2.49; 95% CI: 1.21-5.11; p = 0.01) were increased. Twelve months after severe diffuse TBI and early refractory intracranial hypertension, decompressive craniectomy did not improve outcomes and increased vegetative survivors

Nucleation of Al3Zr and Al3Sc in aluminum alloys: from kinetic Monte Carlo simulations to classical theory

Zr and Sc precipitate in aluminum alloys to form the compounds Al3Zr and Al3Sc which for low supersaturations of the solid solution have the L12 structure. The aim of the present study is to model at an atomic scale this kinetics of precipitation and to build a mesoscopic model based on classical nucleation theory so as to extend the field of supersaturations and annealing times that can be simulated. We use some ab-initio calculations and experimental data to fit an Ising model describing thermodynamics of the Al-Zr and Al-Sc systems. Kinetic behavior is described by means of an atom-vacancy exchange mechanism. This allows us to simulate with a kinetic Monte Carlo algorithm kinetics of precipitation of Al3Zr and Al3Sc. These kinetics are then used to test the classical nucleation theory. In this purpose, we deduce from our atomic model an isotropic interface free energy which is consistent with the one deduced from experimental kinetics and a nucleation free energy. We test di erent mean-field approximations (Bragg-Williams approximation as well as Cluster Variation Method) for these parameters. The classical nucleation theory is coherent with the kinetic Monte Carlo simulations only when CVM is used: it manages to reproduce the cluster size distribution in the metastable solid solution and its evolution as well as the steady-state nucleation rate. We also find that the capillary approximation used in the classical nucleation theory works surprisingly well when compared to a direct calculation of the free energy of formation for small L12 clusters.Comment: submitted to Physical Review B (2004