Formation Of Spatio-temporal Structures Research Articles

Simulation of Membrane Fabrication via Solvent Evaporation and Nonsolvent-Induced Phase Separation.

Block copolymer membranes offer a bottom-up approach to form isoporous membranes that are useful for ultrafiltration of functional macromolecules, colloids, and water purification. The fabrication of isoporous block copolymer membranes from a mixed film of an asymmetric block copolymer and two solvents involves two stages: First, the volatile solvent evaporates, creating a polymer skin, in which the block copolymer self-assembles into a top layer, comprised of perpendicularly oriented cylinders, via evaporation-induced self-assembly (EISA). This top layer imparts selectivity onto the membrane. Subsequently, the film is brought into contact with a nonsolvent, and the exchange between the remaining nonvolatile solvent and nonsolvent through the self-assembled top layer results in nonsolvent-induced phase separation (NIPS). Thereby, a macroporous support for the functional top layer that imparts mechanical stability onto the system without significantly affecting permeability is fabricated. We use a single, particle-based simulation technique to investigate the sequence of both processes, EISA and NIPS. The simulations identify a process window, which allows for the successful in silico fabrication of integral-asymmetric, isoporous diblock copolymer membranes, and provide direct insights into the spatiotemporal structure formation and arrest. The role of the different thermodynamic (e.g., solvent selectivity for the block copolymer components) and kinetic (e.g., plasticizing effect of the solvent) characteristics is discussed.

Perturbative field-theoretical analysis of three-species cyclic predator-prey models

We apply a perturbative Doi–Peliti field-theoretical analysis to the stochastic spatially extended symmetric Rock-paper-Scissors (RPS) and May–Leonard (ML) models, in which three species compete cyclically. Compared to the two-species Lotka–Volterra predator-prey (LV) model, according to numerical simulations, these cyclical models appear to be less affected by intrinsic stochastic fluctuations. Indeed, we demonstrate that the qualitative features of the ML model are insensitive to intrinsic reaction noise. In contrast, and although not yet observed in numerical simulations, we find that the RPS model acquires significant fluctuation-induced renormalizations in the perturbative regime, similar to the LV model. We also study the formation of spatio-temporal structures in the framework of stability analysis and provide a clearcut explanation for the absence of spatial patterns in the RPS system, whereas the spontaneous emergence of spatio-temporal structures features prominently in the LV and the ML models.

Plastic Flow as Spatiotemporal Structure Formation. Part I. Qualitative and Quantitative Patterns

Plastic Flow as Spatiotemporal Structure Formation. Part I. Qualitative and Quantitative Patterns

Plastic Flow as Spatiotemporal Structure Formation. Part II. Two-Level Description

Plastic Flow as Spatiotemporal Structure Formation. Part II. Two-Level Description

Acceleration of chemical reaction fronts

Chemical fronts and waves travelling in reaction-diffusion systems frequently induce hydrodynamic flow. This adds an additional transport process to the mechanism of spatio-temporal structure formation and can lead to an acceleration of the chemical (reaction) front. We report on the acceleration of travelling chemical fronts elicited by convection, as caused by the Marangoni effect in the monostable iodate-arsenous acid reaction in a thin liquid film. At a stoichiometric excess of iodate over arsenous acid, the reaction produces a large amount of iodine, which is surface-active. At the reaction front, iodine is transferred from the bulk to the surface inducing spatio-temporal gradients of surface tension that lead to capillary flows. These flows, in turn, promote further iodine adsorption at the surface through hydrodynamic mixing effects. As a consequence, an acceleration of the chemical fronts is observed, even if the concentration difference across the front is constant. After the transient acceleration of the reaction front, it settles at a constant propagation velocity, which is assumed to be regulated by a balance in the mass transfer between the bulk and the surface.

Pattern formation during electrodeposition of copper-antimony alloys

<p class="PaperAbstract"><span lang="EN-GB">Aim of the present study is to establish the conditions of the electrolysis for the preparation of structured and unstressed purple-pink coatings of copper-antimony alloys, including their phase characterization. Also the task of the present investigation is, by changing drastically the metal content in the methanesulfonic electrolyte to find out the conditions of electrolysis where the self-organization of the different phases is expressed by higher-order structures - not only waves but also spirals and targets. The possibility to obtain copper-antimony alloy with up to 80 wt. % Sb from methanesulfonic acid is shown. The deposition rate, morphology and the phase composition of the obtained coatings are established. The phenomena of formation of spatio-temporal structures in this alloy are described.It is determined that the observed structures consist of Cu<sub>2</sub>Sb and Cu<sub>11</sub>Sb<sub>3</sub> intermetallic phases.</span></p>

New examples of electrodeposited alloy systems with pattern formation

The experience in the pattern formation during electrodeposition of alloys is summarized. The possibility of formation of spatio-temporal structures due to the spontaneous co-deposition of different phases and their self-organization in ordered structures is demonstrated in some new not investigated in this aspect alloy systems, like Cu-Sb, Ag-Sn, Pd-In and Au-In.

Technique for Determining Fluids Motion Characteristics in the Vicinity of Ferromagnetic Solids Under Magneto-Chemical Treatment

We report on new technique for determining and visualization of fluids motion in the vicinity of magnetized ferromagnetic surfaces under chemical dissolution and autocatalytic formation of spatiotemporal structures. The proposed method of obtaining data on the motion of fluids does not require the use of additional inclusions and allows to avoid the distortions caused by such inclusions or other changes in the nature of the reaction. The developed technique allows to obtain both the integral dependences and time frequencies distributions of the fluids over the volume of the medium under investigation.

Self-organisation phenomena during electrodeposition of palladium–indium alloys

The present investigation was focussed on determining the appropriate electrolyte for the deposition of palladium–indium alloy in a wide range of indium content and to investigate the possibility of observing spatio-temporal structures on the electrode surface. From polarisation experiments, it was established that the palladium–indium phase deposits at more positive potentials than the pure metals and this results at low current densities (0.1–0.3 A dm−2) in the content of the coatings being about 9–17 wt-% In. In the coatings obtained the formation of spatio-temporal structures during electrodeposition of palladium–indium alloys was observed for the first time. The period of the structures is 50–200 µm. The optically different areas of the structures show similar elemental and phase content as well as similar morphology. X-ray analysis of the sample with spatio-temporal structures shows superposition and coincidence of the spectra of the phases Pd and Pd0.85In0.15. This result is in agreement with those obtained during investigation of other electrodeposited alloys (Аg–In, Ag–Sb, Ag–Cd, In–Co, etc.) with spatio-temporal structures, which appear when simultaneously deposition of two phases with identical crystal lattice takes place.

Bifurcation of learning and structure formation in neuronal maps

Most learning processes in neuronal networks happen on a much longer time scale than that of the underlying neuronal dynamics. It is therefore useful to analyze slowly varying macroscopic order parameters to explore a network's learning ability. We study the synaptic learning process giving rise to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable states as well. A simple time translation of the learning window function shifts the bifurcation point of structure formation and goes along with traveling waves in the map, without changing the animal's sound localization performance.

Electrodeposition of Silver-Indium Alloys from Non-Cyanide Electrolytes / Elektoosadzanie Stopów Srebrowo-Indowych Z Elektrolitów Nie Zawierajacych Cyjanków

Non-cyanide electrolytes for silver-indium alloys deposition investigated in order to adjust electrolysis conditions thus to observe the formation of spatio-temporal structures onto the electrode surface. It was established that the electrolytes for silver-indium deposition prepared with the excess of thiocyanate and iodide complexing agents are stable in time. The alloy electrodeposition is of a regular type where the silver is the more positive metal. The observed oscillations of the potential during galvanostatic deposition of indium in the thiocyanate solution are suggested to appears due to the formation/destruction of some passive layers on the electrode surface. Spatio-temporal structures could be observed during electrodeposition of the alloy from thiocyanate electrolytes.

Pattern formation during electrodeposition of alloys

The increase in the content of the alloying element in electrodeposited alloys reflects in the changes of their phase composition, when the saturation limit of the lattice of the basic metal is reached. At higher percentages, the excess amount of the alloying element forms one or more new, richer in this element phases. The coatings become multi-phase, heterogeneous and their physical–mechanical properties change. Sometimes an ordered distribution of the different phases of the heterogeneous alloy coating could be observed. Examples of self-organization phenomena during electrodeposition of different alloy systems, such as Ag-Sb, Ag-Bi, Ag-In, Ag-Sn, Ag-Cd, Cu-Sb and In-Co, resulting in pattern formation and formation of spatio-temporal structures on the surface of the obtained coatings are presented and compared. Instabilities resulting in potential or current oscillations are registered in most of the investigated systems. The phase composition of the alloy coatings and especially of the observed pattern is determined and some similarities in the structure of the phases forming the pattern are registered. The pattern formation is registered on the cathode not only in cyanide silver alloys electrolytes, but also during deposition of other alloy systems in acidic electrolytes like Cu-Sb and In-Co. The effect of the natural convection in non-agitated electrolytes on the pattern formation is discussed. The possibility of formation of periodic structured coatings without applying external electrical pulses which could result in appropriate modification of some properties of the electrodeposited alloys is demonstrated. The hypothesis that similar pattern formation could be observed in agitated electrolytes at different hydrodynamic and electrolysis conditions, when the same percentage or the same phase composition of the alloy is reached was examined for Ag-Cd, In-Co and Ag-Sb alloys in jet-plating experiments.

Phase identification in electrodeposited Ag–Cd alloys by anodic linear sweep voltammetry and X-ray diffraction techniques

During electrodeposition of Ag–Cd alloy coatings phenomena of self-organization and formation of spatio-temporal structures can be observed. The difficulties in the determination of the local phase composition in the observed structures are mostly connected with the strong heterogeneity of the coatings consisting of several alloy phases. The results obtained with electrochemical techniques, such as anodic linear sweep voltammetry (ALSV) are compared with results obtained by X-ray analysis and SEM. In the proposed electrolyte for dissolution of Ag–Cd alloy coatings (12 M LiCl + 0.1 M HCl) the dissolution peaks of the pure metals, Ag and Cd, have a potential difference of about 700 mV. The peaks, corresponding to the alloy phases, are situated between the dissolution potentials of Ag and Cd, their height depending on the deposition current density, i.e. on the percentage content of the alloy. Different phases (Ag, Ag 3Cd, AgCd, AgCd 3 and pure Cd) are observed in the coatings deposited at different cathodic potentials. A good correlation between the XRD spectra of the Ag–Cd alloy coatings and the ALSV data obtained during their dissolution is established.

Phase identification in electrodeposited Ag–In alloys by ALSV technique

During electrodeposition of Ag–In alloy coatings phenomena of self-organization and formation of spatio-temporal structures can be observed. The difficulties in the determination of the local phase composition in the observed structures are mostly connected with the strong heterogeneity of the coatings consisting of several alloy phases. The results obtained with electrochemical techniques, such as anodic linear sweep voltammtery (ALSV) are compared with results obtained by X-ray analysis and SEM. In the proposed electrolyte for dissolution of Ag–In alloy coatings (12 M LiCl + 0.1 M HCl) the dissolution peaks of the pure metals, Ag and In, have a potential difference of about 650 mV. The peaks, corresponding to the alloy phases, are situated between the dissolution potentials of Ag and In, their height depending on the deposition current density, i.e. on the percentage content of the alloy. Each ALSV peak is ascribed to a separate phase as a result of very good agreement between the alloy characterization by ALSV technique and by X-ray technique. This opens the possibility for ASLV identification of the phase composition in the different regions of the microscopically observed structures.

Composition and Structure of Silver-Indium Alloy Coatings Electrodeposited from Cyanide Electrolytes

The electrodeposition of Ag-In alloys from cyanide electrolytes was investigated. The resulting coatings were characterized by cyclic voltammetry, scanning electron microscopy, energy-dispersive X-ray, and X-ray diffraction. The effect of current density on the structure and coating phase composition was established. With increasing current density heterogeneous, more indium-rich alloy coatings were deposited, containing different phases such as Ag, and During electrodeposition in exhausted electrolytes, spatiotemporal structures were observed on the coating surface. A linear relationship between the concentration ratio of both metals in the electrolyte and the current density was found. According to this relation, the formation of spatiotemporal structures during electrodeposition in a fresh electrolyte is possible. © 2005 The Electrochemical Society. All rights reserved.

A space-time state-space model of phytoplankton allelopathy

An integro-differential equation system with nonlocal effects of interspecific allelopathic interaction has been studied to investigate the formation of spatio-temporal structures in toxin producing phytoplankton population. The model is inherently more realistic than the usual kind of reaction-diffusion model. Bifurcation from uniform steady-state solution has been examined. Evolution of steady-state spatially periodic structure and periodic standing waves have been studied. The model helps to investigate the blooms, pulses and succession in different patches of phytoplankton population. Numerical simulations for a hypothetical set of parameter values and experimental observations have been presented to substantiate the analytical findings.

Hydroacoustical interaction of bubble clouds

Acoustically driven cavitation bubble fields consist of typically 104 micron-sized bubbles. Due to their nonlinear hydroacoustical interaction, these extended multiscale systems exhibit the phenomenon of spatiotemporal structure formation. Apart from its significance for the theory of self-organization, it plays a major role in design and control of many industrial and medical applications. Prominent examples are ultrasound cleaning, sono-chemistry and medical diagnostics. From a fundamental point of view the key question to ask is ‘‘How does the fast dynamics on small length scales determine the global slow dynamics of the bubble field?’’ To clarify the complex interplay of acoustical and hydrodynamical forces acting on the bubbles, we employ high-speed particle tracking velocimetry. This technique allows the three-dimensional reconstruction of the bubbles’ trajectories on small and fast scales as well as the measurement of the bubble density on large and slow scales. A theoretical model is derived that describes the nonlinear radial and translational dynamics of the individual bubbles and their interaction. The numerical solution of this N body problem is presented.

SELF-MODULATION AND CHAOTIC REGIMES OF GENERATION IN A RELATIVISTIC BACKWARD-WAVE OSCILLATOR WITH END REFLECTIONS

We study self-modulation and chaotic regimes of generation in a relativistic backward-wave oscillator in the presence of reflections of radiation from the boundaries of a slow-wave structure. The onset of self-modulation is examined in detail in the cases of weak and strong reflections. A numerical simulation of transition-to-chaos scenarios is performed over a wide range of parameters. The relation of bifurcation transitions between different regimes to the formation of spatio-temporal structures in the electron beam is discussed.

Time series analysis of cavitation bubble fields

Acoustical cavitation bubble fields exhibit spatio–temporal structure formation on multiple scales involved. The temporal scales are the fast, medium, and slow scales given by the period of the driving, the typical relaxation time of the individual bubble motion, and the drift of the filaments, respectively. The spatial scales are the microscopic, mesoscopic, and macroscopic scales given by the bubbles’ mean radii, typical bubble distances, and the wavelength of macroscopic disturbances (e.g., sound waves). Prominent examples of the observed structures are, for example, period doubling on a fast temporal scale and a slowly drifting filamentlike bubble distribution on the macroscopic spatial scale. These structures are experimentally investigated using simultaneously measured sequences of images (CCD camera) and acoustic time series (hydrophones). Based on these data the experimentally observed patterns are characterized using image processing techniques (e.g., principal component analysis) and by means of methods of nonlinear time series analysis (e.g., test for stationarity, dimension estimates, surrogate data analysis). The investigations focus on the correlation between spatial and temporal structures on different scales and transitions between them. [Work supported by ‘‘Graduiertenkolleg Strömungsinstabilität und Turbulenz.’’]

Formation of dynamic domains in strongly driven ferromagnets.

Based on the dissipative Landau-Lifshitz equation, the spatiotemporal structure formation problem is investigated in the region far above the transverse ferromagnetic resonance instability. Apart from the external fields, the model contains an isotropic exchange field, a shape demagnetization field, and an anisotropy field. Numerical simulations exhibit in the rotating frame a stationary domain structure with a precessing motion in the wall regimes. Employing analytical methods, characteristic elements of this structure are explained. This driven dissipative system shows similarities to equilibrium systems of coexisting phases and organizes itself in such a way that the local dynamics tends to become Hamiltonian.