Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems

We study the dynamics of scroll vortices in excitable reaction-diffusion systems analytically and numerically. We demonstrate that intrinsic three-dimensional instability of a straight scroll leads to the formation of helicoidal structures. This behavior originates from the competition between the scroll curvature and unstable core dynamics. We show that the obtained instability persists even beyond the meander core instability of two-dimensional spiral wave.Comment: 4 pages, 5 figures, revte

Anomalous relaxation and self-organization in non-equilibrium processes

We study thermal relaxation in ordered arrays of coupled nonlinear elements with external driving. We find, that our model exhibits dynamic self-organization manifested in a universal stretched-exponential form of relaxation. We identify two types of self-organization, cooperative and anti-cooperative, which lead to fast and slow relaxation, respectively. We give a qualitative explanation for the behavior of the stretched exponent in different parameter ranges. We emphasize that this is a system exhibiting stretched-exponential relaxation without explicit disorder or frustration.Comment: submitted to PR

Universal Scaling of Wave Propagation Failure in Arrays of Coupled Nonlinear Cells

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular coupling. We find the universal scaling of the field throughout the range of couplings, and show that the field becomes exponentially small for large couplings. Our method is generic and applicable to a wide class of cellular dynamics in chemical, biological, and engineering systems. We confirm our results by direct numerical simulations.Comment: 4 pages, 3 figures, RevTe

Metabolic syndrome severity score: range and associations with cardiovascular risk factors

Introduction: Metabolic Syndrome Severity Score (MSSS) is a new clinical prediction rule (CPR) for diagnostic and therapeutic decisions and employs available components (sex, age, race, systolic blood pressure, waistline circumference, high-density lipoprotein, triglycerides and fasting blood glucose). The aim of our work was to perform cross-sectional pilot trial on middle-aged healthy volunteers and patients with metabolic syndrome (MetS) with and without type 2 diabetes mellitus (T2DM) for studying feasibility and implementation of MSSS and its associations with cardiovascular risk factors.Material and methods: We approached 64 eligible participants from Bulgaria. The MSSS values, together with demographic, anthropometric, medical history, laboratory findings, CVD risk factors, QRISK2 score for 10-year cardiovascular risk and predicted heart age, were analysed. Descriptive statistics with tests for comparison (e.g., t-test, c2) between groups as well as ANOVA and logistic regression were applied. Results: We analysed data from 56 participants (aged 50.11 ±3.43 years). The MSSS was higher in MetS patients (including 6 T2DM patients) than in controls (n = 29; 51.8%) presented as percentiles (69.97% and 34.41%, respectively) and z-scores (0.60 and –0.45, respectively) (p < 0.05). The logistic regression model of MSSS indicated a positive association with MetS/T2DM cases (correctness > 85%, p < 0.01). For further validation purposes, positive correlations of MSSS with CVDrisk factor as diastolic blood pressure (Rho = 0.399; p < 0.003) and QRISK2 score (Rho = 0.524; p < 0.001) or predicted heart age (Rho = 0.368; p < 0.007) were also found.Conclusions: The pilot study of MSSS in Bulgaria indicated feasibility and consistency of its implementation among patients with metabolic syndrome and/or T2DM and healthy volunteers

Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications

In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral pattern, or retract causing the wave to vanish at boundaries. An asymptotic analysis of spiral motion and retraction is carried out in this weakly excitable large core regime starting from the free-boundary limit of the reaction-diffusion models, valid when the excited region is delimited by a thin interface. The wave description is shown to naturally split between the tip region and a far region that are smoothly matched on an intermediate scale. This separation allows us to rigorously derive an equation of motion for the wave tip, with the large scale motion of the spiral wavefront slaved to the tip. This kinematic description provides both a physical picture and exact predictions for a wide range of wave behavior, including: (i) steady rotation (frequency and core radius), (ii) exact treatment of the meandering instability in the free-boundary limit with the prediction that the frequency of unstable motion is half the primary steady frequency (iii) drift under external actions (external field with application to axisymmetric scroll ring motion in three-dimensions, and spatial or/and time-dependent variation of excitability), and (iv) the dynamics of multi-armed spiral waves with the new prediction that steadily rotating waves with two or more arms are linearly unstable. Numerical simulations of FitzHug-Nagumo kinetics are used to test several aspects of our results. In addition, we discuss the semi-quantitative extension of this theory to finite cores and pinpoint mathematical subtleties related to the thin interface limit of singly diffusive reaction-diffusion models

Parametrically forced sine-Gordon equation and domain walls dynamics in ferromagnets

A parametrically forced sine-Gordon equation with a fast periodic {\em mean-zero} forcing is considered. It is shown that $\pi$-kinks represent a class of solitary-wave solutions of the equation. This result is applied to quasi-one-dimensional ferromagnets with an easy plane anisotropy, in a rapidly oscillating magnetic field. In this case the $\pi$-kink solution we have introduced corresponds to the uniform ``true'' domain wall motion, since the magnetization directions on opposite sides of the wall are anti-parallel. In contrast to previous work, no additional anisotropy is required to obtain a true domain wall. Numerical simulations showed good qualitative agreement with the theory.Comment: 3 pages, 1 figure, revte

Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states

Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are seen to be unstable in different regions of parameter space. The corresponding bifurcations and bifurcated states are characterized by performing direct numerical simulations. In addition, computations of the adjoint linear stability operator eigenmodes are also performed and serve to obtain a number of matrix elements characterizing the long-wavelength deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.

Imbibition in Disordered Media

The physics of liquids in porous media gives rise to many interesting phenomena, including imbibition where a viscous fluid displaces a less viscous one. Here we discuss the theoretical and experimental progress made in recent years in this field. The emphasis is on an interfacial description, akin to the focus of a statistical physics approach. Coarse-grained equations of motion have been recently presented in the literature. These contain terms that take into account the pertinent features of imbibition: non-locality and the quenched noise that arises from the random environment, fluctuations of the fluid flow and capillary forces. The theoretical progress has highlighted the presence of intrinsic length-scales that invalidate scale invariance often assumed to be present in kinetic roughening processes such as that of a two-phase boundary in liquid penetration. Another important fact is that the macroscopic fluid flow, the kinetic roughening properties, and the effective noise in the problem are all coupled. Many possible deviations from simple scaling behaviour exist, and we outline the experimental evidence. Finally, prospects for further work, both theoretical and experimental, are discussed.Comment: Review article, to appear in Advances in Physics, 53 pages LaTe

Dynamics of Wetting Fronts in Porous Media

We propose a new phenomenological approach for describing the dynamics of wetting front propagation in porous media. Unlike traditional models, the proposed approach is based on dynamic nature of the relation between capillary pressure and medium saturation. We choose a modified phase-field model of solidification as a particular case of such dynamic relation. We show that in the traveling wave regime the results obtained from our approach reproduce those derived from the standard model of flow in porous media. In more general case, the proposed approach reveals the dependence of front dynamics upon the flow regime.Comment: 4 pages, 2 figures, revte

Ultimate attainment of anaphora resolution in L2 Chinese

The current study tests the Interface Hypothesis through forward and backward anaphora in complex sentences with temporal subordinate clauses in highly proficient English-speaking learners’ second-language (L2) Chinese. Forward anaphora is involved when the overt pronoun ta ‘he/she’ or a null element appears in the subject position of the main clause, whereas backward anaphora is involved when it is in the subject position of the temporal clause, because the main clause always follows the temporal clause in Chinese. Specifically, the article tests the syntactic and discourse constraints in the interpretation and representation of ta and the null element in complex sentences. Ta is constrained by the syntactic cyclic-c-command condition. Thus it is possible for ta to refer to the other sentential subject in forward anaphora, but not in backward anaphora in Chinese. Unlike English, Chinese allows a null element in subject positions of finite subordinate and main clauses. It is proposed in the article that the null element in these positions is a Øtopic, a syntax–discourse interface category. Results from an acceptability judgement task and a picture judgment task indicate that Øtopic at the external interface has been acquired, whereas the cyclic-c-command condition within narrow syntax is fossilized in L2 Chinese