Modeling study of migration-driven lateral instability in autocatalytic systems

The lateral stability of reaction fronts in simple autocatalytic models with the components carrying various charges is investigated when the system is exposed to an inhomogeneous electric field parallel to the direction of propagation. The enhanced migrational flux of the reactant destabilizes the planar front giving rise to a cellular structure because the electric field strength is greater on the reactant side of the reaction front. The onset of instability depends not only on the charge difference between the reactant and the autocatalyst but also on the variation of specific conductance in the course of the reaction, which results in a difference in electric field strength on the opposite sides of the reaction front.     

Development of Concentration-Dependent Diffusion Instability in Reactive Miscible Fluids Under Influence of Constant or Variable Inertia

In this work, we focus on the processes which accompany a frontal neutralization reaction occurring between two miscible fluids filling a vertical Hele-Shaw cell. We have found that chemically-induced changes of reagent concentrations coupled with concentration- dependent diffusion (CDD) can produce spatially localized low density areas which are sensitive to the external inertial field. In the case of static gravity we have demonstrated both experimentally and theoretically that it can give rise to the development of perfectly periodic convective structure. This scenario is strikingly different from the irregular density fingering, which is typically observed in the miscible systems. When the system is under the influence of the periodic low-frequency vibrations perpendicular to the reaction front, we found numerically the excitation of a mixed-mode instability combining the double-diffusion instabilities and the Rayleigh-Taylor mechanism of the convection within the low density areas.     

Self‐Organization of Thin Polymer Films Guided by Electrostatic Charges on the Substrate

The self‐organization of thin polymer films into functional patterns is important both scientifically and technologically. Electric fields have been exploited as an efficient and powerful means to induce the destabilization and self‐organization of soft materials. Previous attention, however, has mainly focused on externally applied electric fields. It is shown herein that the internal electric field is strong enough to guide the self‐organization of thin polymer films as well. Patterns of electrostatic charges with micrometer resolution are first introduced on a dielectric substrate. A thin polymer film is then spin‐coated onto the topographically flat substrate. Upon thermal annealing, the thin polymer film destabilizes due to a lateral gradient of electrostatic stress and flows away from the electroneutral regime to the charged area, resembling the patterns of charges on the substrate. Theoretical and numerical modeling based on the electrohydrodynamic instability shows excellent agreement with experimental observations both qualitatively and quantitatively. It is also demonstrated that the interplay between charge‐driven instability with spinodal dewetting and Rayleigh instabilities can generate finer and hierarchical polymeric patterns that are completely different from the charge patterns preintroduced on the substrate. This study provides direct evidence that the internal electric field caused by charges on the substrate is strong enough to destabilize thin polymeric films and generate patterns. This study also demonstrates new strategies for bottom‐up fabrication of structured functional materials.     

Oscillatory and chaotic wakes behind moving boundaries in reaction-diffusion systems

Oscillatory wakes occur in a wide range of reaction-diffusion systems, consisting of either periodic travelling waves or irregular spatiotemporal oscillations, behind a moving transition front. In this paper, the use of a finite boundary moving with an imposed speed to mimic the transition front is considered. For both λ-ω systems and standard predator-prey models, the solutions behind these moving boundaries agree very closely with the behaviour behind transition fronts, provided suitable end conditions are used on the moving boundary. This confirms that the transition front can be regarded as determining the solution, by forcing a particular periodic wave at the boundary of the wake region. In the case of λ-ω systems, a detailed numerical study of solutions on a fixed-length finite domain with a periodic wave solution forced at the boundaries is performed. As the domain length is varied as a parameter, the long-term temporal behaviour undergoes bifurcation sequences that are well known as routes to chaos in ordinary differential equations. This suggests that irregular wakes actually have the form of a perpetual transient in a progression towards chaos. Finally, the way in which the moving boundary results can be used to design an experimental verification of the oscillatory wakes phenomenon in a chemical system is discussed.     

Liquid-crystal Hartmann wave-front scanner

The liquid-crystal wave-front scanner (LCWS) is a highly sensitive wave-front sensor suited to the measurement of aberrations in optical systems and, more generally, of static wave fronts, and it is based on the Hartmann test. In the LCWS an incoming wave front is scanned sequentially by a programmable moving aperture that is implemented by use of a liquid-crystal display. The position of the diffraction spot is recorded behind an observation lens with a CCD detector and provides an estimation of the local slopes in two orthogonal directions at the aperture position. The wave front is then reconstructed from slope data by use of a least-squares method. Experiments are reported for nearly planar wave fronts as well as for strongly aberrated wave fronts, demonstrating both the large dynamic range and the great sensitivity of the LCWS. The LCWS is compared with the Shack-Hartmann wave-front sensor in terms of dynamic range and sensitivity.     

A two-level implicit scheme for the numerical solution of the linearized vorticity equation

A numerical scheme is developed to study the stability of the linearized vorticity equations. The linear growth rates of Kelvin-Helmholtz instabilities resulting from a velocity shear are calculated numerically. The theory of neutrally stable waves, in two dimensions, is extended to include the cases where the stream function is zero or periodic at the boundary, and is verified numerically for the case of a velocity profile having the shape of a cosine function. The instability growth rates of the oscillations in the neighbourhood of the neutrally stable waves are calculated numerically and are shown to be in very good agreement with the theory. The results are also of interest in relation to studies on the instabilities of a two-dimensional guiding-centre plasma, and also in the study of the diocotron instability in electronics.     

Landau and Dynamical Instabilities of Bose-Einstein Condensates in a Kronig-Penney Potential

We study elementary excitations of Bose-Einstein condensates in a one-dimensional periodic potential and discuss the stability of superfluid flow based on the Kronig-Penney model. We analytically solve the Bogoliubov equations and calculate the excitation spectrum. The Landau and dynamical instabilities occur in the first condensate band when the superfluid velocity exceeds certain critical values as in a sinusoidal potential. It is found that the onset of the Landau instability coincides with the point where the perfect transmission of low-energy excitations is forbidden, while the dynamical instability occurs when the effective mass is negative. The condensate band has a swallow-tail structure when the periodic potential is shallow compared to the mean-field energy. We find that the upper side of a swallow-tail is dynamically unstable although the excitation spectrum has a linear dispersion reflecting the positive effective mass.     

Non linear dynamics of dissipative wave patterns near a bifurcation point

Dissipative wave patterns are described in the vicinity of a bifurcation point by amplitude equations possessing neither gradient nor Hamiltonian structure, and therefore may exhibit complex dynamic behaviour. A detailed investigation of patterns composed of two propagating or standing waves shows that non-stationary amplitude states are realized in certain parametric domains, and demonstrates the existence of homoclinic orbits. Still more complex behaviour can be expected of multiwave patterns corresponding to quasiperiodic planforms. In addition to non-stationary behaviour retaining elements of spatial order, wave patterns can exhibit modulational, or self-focusing instability leading to spatially disordered states. Conditions of modulational stability are derived with the account of non-isotropic character of wave patterns.     

IS SEGREGATION-BY-PARTICLE-TYPE A GENERIC MECHANISM UNDERLYING FINGER FORMATION AT FRONTS OF FLOWING GRANULAR MEDIA?

The fronts of flowing granular media often manifest fingered patterns. For the case of a granular flow down an inclined plane, Pouliquen, Delour and Savage (1997) have proposed that such patterns are induced by the segregation of coarse irregularly shaped particles. Here, we consider a thin layer of a granular medium flowing within a cylinder that is rotated about its horizontal axis of symmetry. Our results show that—even when the medium is well-sieved and consists of nearly spherical grains—its leading edge may develop fingers. This suggests that, in general flow configurations, mechanisms other than segregation by particle type may be active in the instability of a straight front.     

Turing instability in an economic–demographic dynamical system may lead to pattern formation on a geographical scale

Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the emergence of densely populated areas at their present locations is widely believed to be linked to more favourable environmental and climatic conditions. In this paper, we challenge this point of view. We first identify a few areas at different parts of the world where the environmental conditions (quantified by the temperature, precipitation and elevation) show a relatively small variation in space on the scale of thousands of kilometres. We then examine the population distribution across those areas to show that, in spite of the approximate homogeneity of the environment, it exhibits a significant variation revealing a nearly periodic spatial pattern. Based on this apparent disagreement, we hypothesize that there may exist an inherent mechanism that may lead to pattern formation even in a uniform environment. We consider a mathematical model of the coupled demographic-economic dynamics and show that its spatially uniform, locally stable steady state can give rise to a periodic spatial pattern due to the Turing instability, the spatial scale of the emerging pattern being consistent with observations. Using numerical simulations, we show that, interestingly, the emergence of the Turing patterns may eventually lead to the system collapse.     

IS SEGREGATION-BY-PARTICLE-TYPE A GENERIC MECHANISM UNDERLYING FINGER FORMATION AT FRONTS OF FLOWING GRANULAR MEDIA?

ABSTRACT

The fronts of flowing granular media often manifest fingered patterns. For the case of a granular flow down an inclined plane, Pouliquen, Delour and Savage (1997) have proposed that such patterns are induced by the segregation of coarse irregularly shaped particles. Here, we consider a thin layer of a granular medium flowing within a cylinder that is rotated about its horizontal axis of symmetry. Our results show that—even when the medium is well-sieved and consists of nearly spherical grains—its leading edge may develop fingers. This suggests that, in general flow configurations, mechanisms other than segregation by particle type may be active in the instability of a straight front.     

Crack propagation along polymer/non-polymer interfaces

Mechanisms of the propagation of crack fronts along interfaces between a glassy polymer and metal or glass are discussed. Specifically, the systems studied are Poly-Ethylene Terephthalate (PETG) spin-coated on Al, PETG-glass and PETG hot-pressed on Cr-sputtered glass. Cracks studied propagate in an Assymetric Double Cantilever Beam (ADCB) geometry. Dependence of microscopic crack front geometry on propagation speed is found. The local stress state is found to have an impact on macroscopic as well as microscopic crack front geometry. Simple lattice model calculations of propagating crack fronts illustrate the impact of disorder and residual stress state on propagation mechanisms and macroscopic crack front shape respectively.     

Negative bias–temperature stress in non-self-aligned p-channel polysilicon TFTs

The electrical instabilities in p-channel polysilicon TFTs induced by negative bias temperature stress (NBTS) and self-heating have been investigated. From NBTS experiments performed at different temperatures and gate bias, we derived an empirical relationship that provides the T and electric field dependence of the interface state generation. To explain the device instability related to self-heating we considered a spatially non uniform interface state distribution, as a non uniform transverse electric field is present during bias stress. The interface state distribution can be deduced using the empirical relationship, determined from NBTS experiments, and considering the spatial distribution of the oxide electric field, obtained from numerical simulations. Using the so determined interface state distribution it was possible to perfectly reproduce not only the transfer characteristics but also the asymmetry observed in the output characteristics, when source/drain contacts are reverted after bias stress.     

Computational simulation of chemical dissolution‐front instability in fluid‐saturated porous media under non‐isothermal conditions

This paper primarily deals with the computational aspects of chemical dissolution‐front instability problems in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. After the dimensionless governing partial differential equations of the non‐isothermal chemical dissolution‐front instability problem are briefly described, the formulation of a computational procedure, which contains a combination of using the finite difference and finite element method, is derived for simulating the morphological evolution of chemical dissolution fronts in the non‐isothermal chemical dissolution system within two‐dimensional fluid‐saturated porous media. To ensure the correctness and accuracy of the numerical solutions, the proposed computational procedure is verified through comparing the numerical solutions with the analytical solutions for a benchmark problem. As an application example, the verified computational procedure is then used to simulate the morphological evolution of chemical dissolution fronts in the supercritical non‐isothermal chemical dissolution system. The related numerical results have demonstrated the following: (1) the proposed computational procedure can produce accurate numerical solutions for the planar chemical dissolution‐front propagation problem in the non‐isothermal chemical dissolution system consisting of a fluid‐saturated porous medium; (2) the Zhao number has a significant effect not only on the dimensionless propagation speed of the chemical dissolution front but also on the distribution patterns of the dimensionless temperature, dimensionless pore‐fluid pressure, and dimensionless chemical‐species concentration in a non‐isothermal chemical dissolution system; (3) once the finger penetrates the whole computational domain, the dimensionless pore‐fluid pressure decreases drastically in the non‐isothermal chemical dissolution system.     

Periodic image artifacts from continuous-tone laser scanners

Continuous-tone images produced by mechanically scanned analog modulated laser beams are susceptible to image artifacts in the form of spatially periodic density variations due to machine errors in film transport velocity, raster scan-line placement, and scan-line intensity. The human eye is particularly sensitive to periodic patterns and, in ideal conditions, can detect peak-to-peak density variations as small as approximately 0.005 for spatial frequencies around 2-5 cycles/deg. The stringent requirements that this implies for the scanner hardware are derived. Particular attention is paid to the rotating polygon-type scanner, since this device currently provides the best combination of speed, image quality, and cost.     

Detecting research fronts in OLED field using bibliographic coupling with sliding window

Research fronts represent cutting edge studies in specific fields. One can better understand current and future development trends in the relevant field when updated with trends in research fronts. This study uses bibliographic coupling and sliding window to explore the organic light-emitting diodes (OLED) research fronts from 2000 to 2009, and identifies eighteen research fronts that match those predicted by subject experts related to OLED materials. Closer observation of the evolution shows that among the eighteen research fronts, there are four emerging fronts, two growing fronts, eleven stable fronts, and one shrinking front. Bibliographic coupling with sliding window is an effective tool to track the generation, growth, decline, and disappearance of research fronts. Therefore, this analytical method has great potential in discovering the evolution of research fronts.     

Dynamics of interphase surface of self-sustaining evaporation front in liquid with additives of nanosized particles

The results of experimental research on dynamics of propagation of self-sustaining evaporation front in the conditions of large volume are presented. Investigations were carried out using Freon R21, and also in R21 with the addition of SiO₂ nanoparticles. The experimental data on the propagation velocity and structure of evaporation fronts were obtained. The spectral analysis of interphase boundary oscillations of evaporation front was obtained. The characteristic frequencies and oscillation amplitudes of interphase boundary depending on the temperature difference are determined. It is shown that the addition of nanoparticles considerably influences the initiation temperature of evaporation front, front velocity and the character of the oscillations of interphase boundary. The analysis of the results obtained is carried out from the perspective of the development of hydrodynamic instabilities in Landau formulation.     

The avalanche ionization rate in argon and krypton measured at the shockwave Mach numbers close to the flow instability development threshold

The ionization rates of argon and krypton were measured in a relaxation zone behind the shockwave front for the Mach numbers corresponding to stable flow regimes close to the threshold for development of the flow instability of types I and II. The experimental rates of the avalanche ionization exceed theoretical predictions. It is suggested that the discrepancy is related to the existence of an additional channel for the energy transfer between particles.     

Asymptotic properties of mathematical models of excitability

We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (Hodgkin & Huxley 1952 J. Physiol.117, 500-544) model of nerve axon, Noble (Noble 1962 J. Physiol.160, 317-352) model of heart Purkinje fibres and Courtemanche et al. (Courtemanche et al. 1998 Am. J. Physiol.275, H301-H321) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic time-scales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh-Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for breakups and self-termination of re-entrant waves in excitable media with Courtemanche et al. kinetics.     

Mesoscale fronts as foraging habitats: composite front mapping reveals oceanographic drivers of habitat use for a pelagic seabird

The oceanographic drivers of marine vertebrate habitat use are poorly understood yet fundamental to our knowledge of marine ecosystem functioning. Here, we use composite front mapping and high-resolution GPS tracking to determine the significance of mesoscale oceanographic fronts as physical drivers of foraging habitat selection in northern gannets Morus bassanus. We tracked 66 breeding gannets from a Celtic Sea colony over 2 years and used residence time to identify area-restricted search (ARS) behaviour. Composite front maps identified thermal and chlorophyll-a mesoscale fronts at two different temporal scales—(i) contemporaneous fronts and (ii) seasonally persistent frontal zones. Using generalized additive models (GAMs), with generalized estimating equations (GEE-GAMs) to account for serial autocorrelation in tracking data, we found that gannets do not adjust their behaviour in response to contemporaneous fronts. However, ARS was more likely to occur within spatially predictable, seasonally persistent frontal zones (GAMs). Our results provide proof of concept that composite front mapping is a useful tool for studying the influence of oceanographic features on animal movements. Moreover, we highlight that frontal persistence is a crucial element of the formation of pelagic foraging hotspots for mobile marine vertebrates.