Spatially Ordered Research Articles

Continuous-time Monte Carlo and spatial ordering in driven lattice gases: Application to driven vortices in periodic superconducting networks

We consider the two dimensional (2D) classical lattice Coulomb gas as a model for magnetic field induced vortices in 2D superconducting networks. Two different dynamical rules are introduced to investigate driven diffusive steady states far from equilibrium as a function of temperature and driving force. The resulting steady states differ dramatically depending on which dynamical rule is used. We show that the commonly used driven diffusive Metropolis Monte Carlo dynamics contains unphysical intrinsic randomness that destroys the spatial ordering present in equilibrium (the vortex lattice) over most of the driven phase diagram. A continuous time Monte Carlo (CTMC) is then developed, which results in spatially ordered driven states at low temperature in finite sized systems. We show that CTMC is the natural discretization of continuum Langevin dynamics, and argue that it gives the correct physical behavior when the discrete grid represents the minima of a periodic potential. We use detailed finite size scaling methods to analyze the spatial structure of the steady states. We find that finite size effects can be subtle and that very long simulation times can be needed to arrive at the correct steady state. For particles moving on a triangular grid, we find that the ordered moving state is a transversely pinned smectic that becomes unstable to an anisotropic liquid on sufficiently large length scales. For particles moving on a square grid, the moving state is a similar smectic at large drives, but we find evidence for a possible moving solid at lower drives. We find that the driven liquid on the square grid has long range hexatic order, and we explain this as a specifically non-equilibrium effect. We show that, in the liquid, fluctuations are diffusive in both the transverse and longitudinal directions.

Nanostructure fabrication of InP by low energy ion beams

Spatially ordered dot structures with a size ranged between 30 and 60 nm and a height over 100 nm have been found on InP surfaces irradiated by 0.5–2 keV Ar ions. Their dependences on ion energy, dose, incident angle and sample temperature have been investigated from AFM and SEM observations. With an increase of dose, dot size increases, whereas its density decreases and finally saturate at 60 nm and 2.8 × 10 10/cm 2. Spatial ordering and size uniformity of dots seem to be superior after irradiation at 0.5 and 1 keV and degrade at higher energy. This is applicable as a simple fabrication technique for nanostructure with high density and uniformity compatible with crystal growth.

Spatial orders appearing at instabilities of synchronous chaos of spatiotemporal systems

Various spatial orders introduced by the instabilities of synchronous chaotic state of spatiotemporal systems are investigated by considering coupled map lattice and chaotic partial differential equation. In particular, the motions of on-off intermittent states at the onset of the instabilities are studied in detail. The chaotic desynchronized patterns can be described by a simple universal form, including three parts: the synchronous chaos; a spatially ordered pattern, determined by the unstable mode of the reference synchronous chaos; and on-off intermittency of the scale of this given pattern.

How does a periodic rotating wave emerge from high-dimensional chaos in a ring of coupled chaotic oscillators?

A route to typical rotating waves from high-dimensional chaos is investigated in diffusively coupled chaotic Rössler oscillators. By increasing the coupling from zero, a high-dimensional spatiotemporal chaos changes into a coherent state, which is periodic in time and well ordered in space, through consecutive transitions. A crossover transition from spatially random chaos to spatially ordered chaos with phase locking and orientational equality (for two directions) breaking is a crucial step for establishing the typical spatial order of the rotating wave.

Anisotropy of the spatial distribution of In(Ga)As quantum dots in In(Ga)As-GaAs multilayer heterostructures studied by X-ray and synchrotron diffraction and transmission electron microscopy

High-resolution X-ray and synchrotron (crystal truncation rods) diffraction methods and transmission electron microscopy have been employed to study MBE-grown multilayer In(Ga)As-GaAs heterostructures with arrays of vertically coupled In(Ga)As quantum dots (QDs) in a GaAs matrix. Additional (vertical and lateral) spatial ordering of QDs in perfect crystalline structures, giving rise to undulations of the crystalline planes and quasi-periodic elastic strain, was shown to be essentially anisotropic with respect to crystallographic directions of the [110] type. The anisotropy of the QD formational system of can be accounted for by assuming that the spatial ordering of the QDs and the corrugation of the crystal planes are the initial stages of relaxation of the elastic strain introduced into the system by the QDs. The anisotropic relief of the crystal planes (corrugated growth surface) results from the formation of a system of spatially ordered quantum quasi-wires uniformly filled with QDs. In a multilayer heterostructure with high crystal perfection, the anisotropic relief of the crystal planes is inherited by overlying layers and its amplitude decreases gradually with increasing distance from the source of elastic strain—the superstructure containing In(Ga)As QDs in the given case.

Spatial ordering of stacked quantum dots

We investigate the growth conditions necessary to form an ordered quantum dot crystal by capping spatially ordered quantum dots and growing a new layer of dots on top of the capping layer. Performing Monte Carlo simulations and developing analytic arguments based on the stress energy function, we demonstrate the existence of an optimal capping layer thickness, external flux, and temperature for the formation of quantum dot crystals.

Electrochemical approach to the dynamics of molecular recognition of redox enzyme sites by artificial cosubstrates in solution and in integrated systems.

Application of antigen-antibody technology allows the attachment to an electrode surface of an enzyme monolayer structure to which both the enzyme and the mediator are bound. As illustrated with the example of glucose oxidase and a ferrocene mediator, the enzyme preserves its full activity in such structures, which may be easily reproduced. In spite of their fixation to the structure, the mobility of the ferrocene heads is sufficient to ensure that its transport to the enzyme prosthetic group is not rate determining. The reaction is rather controlled by the prior formation of a complex between the ferrocenium ion and the flavin required for electron transfer to occur. The efficiency of this step is affected by steric hindrance and the various observations made with free-moving and attached ferrocene-ended poly(ethylene glycol) chains may be rationalized by the interplay of factors controlling their distribution and shape. Analyzing the dynamics of this system, in comparison with previous systems, was thus an occasion to shed further light on the recognition phenomenon. The enzyme monolayer integrated system is a good starting point for the step-by-step construction of spatially ordered multilayered assemblies with strong catalytic efficiencies. Fast responding systems are expected both in terms of electron transport and electron transfer between the mediator and the enzyme. The spatial order resulting from the step-by-step construction should allow a much more precise analysis of electron transport and electron transfer than in conventional assemblies of redox centers. Mastering both the construction and the functioning of such systems should help the design of more complex systems, integrating additional functionalities electrically controlled by means of their electron transport/electron transfer connection to the electrode surface.

Electron Transfer in Organized Assemblies of Biomolecules. Step-by-Step Avidin/Biotin Construction and Dynamic Characteristics of a Spatially Ordered Multilayer Enzyme Electrode

The avidin−biotin technology may be used successfully to build stable and spatially ordered assemblies of monomolecular enzyme layers on surfaces as illustrated with the example of glucose oxidase and glassy carbon electrodes. With ferrocene methanol as the cosubstrate, cyclic voltammetry allows a detailed analysis of the catalytic responses, thus providing a demonstration of the spatial order of the multilayer structure and an estimate of the average distance between monomolecular layers. The respective advantages of the avidin−biotin and antigen−antibody technologies are discussed.

The Genetic Sequence of Retinal Development in the Ciliary Margin of theXenopusEye

The ciliary marginal zone is a perpetually self-renewing proliferative neuroepithelium at the perimeter of the retina in amphibians and fish. In the ciliary marginal zone (CMZ), cells are spatially ordered with respect to cellular development, deep stem cells being most peripheral and differentiating retinal progenitors being most central. This spatial gradient in the CMZ recapitulates embryonic retinogenesis and provides a powerful system to examine the relative order of gene expression during this process. A number of neurogenic and proneural genes have been described to have interacting roles in the development of the vertebrate nervous system, and so it is of major importance to put these genes in a hierarchical pathway. In no other system yet described are the developmental stages of neurogenesis arrayed so clearly in a spatial pattern as in the CMZ. We have therefore taken advantage of this system, using doublein situhybridizations on cross sections of the CMZ, to compare the spatial patterns of 15 proneural, neurogenic, and other genes involved in early and late phases of retinal development. In addition, we have positioned these expression patterns with respect to cell division. What emerges from this work is a spatial ordering of gene expression that predicts a genetic hierarchy governing vertebrate retinogenesis. By injecting messenger RNA for some of these genes into blastomeres of theXenopusembryo and examining the effects on expression of the putative downstream genes, we have been able to corroborate some of the relationships between genes predicted to act sequentially.

Perfect Spatial Ordering of Self-Organized InGaAs/AlGaAs Quantum Disks on GaAs (311)B Substrate with Silicon-Nitride Dot Array

To control the position of self-organized InGaAs/AlGaAs quantum disks on a GaAs (311)B substrate, the use of fine silicon nitride dot array was examined. The pentagonally shaped hollow arrays were formed on the metal-organic vapor phase epitaxy grown AlGaAs layer by buried SiN dots due to the competition between the facet and the lateral growth. The following InGaAs layer grew preferentially in these hollows and self-organized quantum disks were formed during growth interruption. Successive growth of AlGaAs/InGaAs epi-layers induced the stacking of quantum disks right on top of the bottom disks. The upper quantum disks were perfectly spatially ordered when the pitch of the array was matched with the self-organized growth mode, with a simultaneous achievement of lateral positioning.

Theory and numerical simulations of defect ordering in irradiated materials.

A general theory for the spatial ordering of immobile clustered defects in irradiated materials is presented here. A vectorial form for the Fourier transforms of perturbations in the concentration of point and clustered defects is derived. Linear stability analysis indicates that, under conditions appropriate for void growth (high temperature), instabilities leading to spatially ordered microstructure are driven by vacancy cluster density fluctuations, which extends the range of validity of previous conclusions for microstructure with no void present (e.g., low temperature). The crucial importance of collision-cascade-induced vacancy cluster formation is clearly shown. Amplitude equations of the Ginzburg-Landau type are derived and used to discuss the qualitative features of microstructure pattern formation in the post-bifurcation regime. This is accompanied by numerical analysis of the space-time rate equations to test the validity of the weakly nonlinear analysis. Evolution of one- and two-dimensional patterns of the microstructure is illustrated by examples of typical reactor and accelerator irradiation conditions. The quasistatic approximation used in the weakly nonlinear analysis is shown to be adequate only for short irradiation doses. At larger times, higher mode generation leads to a wavelength selection that is somewhat insensitive to the dose, as observed experimentally. The role of interstitial diffusion anisotropy is shown to be significant in the alignment of microstructural patterns in parallel orientation to the directions of high interstitial mobility, in agreement with experiments. \textcopyright{} 1996 The American Physical Society.

Spatial Ordering of As Clusters Due to Indium Delta-Doping of LTMBE GaAs

AbstractWe have shown that two-dimensional layers of arsenic nano-clusters separated by cluster-free GaAs matrix can be formed using indium delta-doping of GaAs films grown by molecular beam epitaxy at low (200°C) temperature. Spatially ordered structures of As clusters have been obtained in the epitaxial LT GaAs films doped with Si donors, Be acceptors and undoped as well.

Discrimination between visual stimuli by variation of shape and relative position of volumetric primitives

To investigate the human ability to discriminate between simple volumetric objects differing in either elemental shape or relational structure a prototypical componential model representation for solid objects was initially developed. There were three principal subsections a set of global properties, a set of shape descriptions of the individual components, and a description of pairwise relations between components. Measures of similarity between objects were calcuated on the basis of an algorithm derived from relational database metrics. A picture/picture, same/different paradigm was employed to determine the ability of human subjects to discriminate between objects with single variations in either the shape or the relative position of components. Significant differences in correct response times and error rates were observed depending on the type of shape variation of individual components, and on the degree of lateral shift between them. Furthermore, a spatial order of processing was observed which could not be accounted for by individual component characteristics. This showed a primary effect from top to bottom of the presented stimulus. The findings are discussed in terms of models of object recognition and of other work on spatially ordered processing.

Trigeminal ganglion cell processes are spatially ordered prior to the differentiation of the vibrissa pad

The rodent trigeminal system is characterized by the punctate organization of its afferents and neurons that replicate the distribution of mystacial vibrissae and sinus hairs on the snout. We have examined the development of topographic equivalence between the sensory periphery on the snout and the brainstem trigeminal nuclei in rats. Lipophilic tracers Dil (1,1'-dioctodecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate) and DiA [4-(4-dihexadecylaminostyryl)-N-methylpyridinium iodide] were used to label trigeminal ganglion cells and their processes differentially from discrete regions of the presumptive vibrissa field in fixed embryos. Our results show that trigeminal ganglion cell processes are spatially ordered as they reach their peripheral and central targets on embryonic day 12 (E12). Peripheral processes of dorsomedially situated ganglion cells course dorsally toward the presumptive vibrissa field, and those of ventrolaterally situated ganglion cells project ventrally. On E13, the central processes of dorsomedially situated ganglion cells enter the brainstem medially whereas those of ventrolaterally situated ganglion cells enter laterally. This spatial order of trigeminal ganglion cell processes precedes the emergence of vibrissa rows in the periphery and the differentiation of brainstem trigeminal nuclei. Thus, the subsequent transfer of the vibrissa-related pattern to the brainstem trigeminal nuclei occurs along a preexisting, spatially aligned bridge formed by the trigeminal ganglion cells.

Spatially ordered void ensemble states at high irradiation temperatures

The physical mechanism of the spatially homogeneous void ensemble state instability with respect to small void size deviations induced by vacancy emission from voids is demonstrated by means of both the exact diffusion and chemical rate equations for the point defect concentrations in a volume containing voids. As it was shown in previous papers the corresponding instability conditions can be valid at rather high irradiation temperatures (higher than the swelling maximum). Here the nonlinear analysis of the void system response to small void size variations is carried out to obtain the qualitative characteristics of spatially ordered void distribution when the instability concerned takes place. Void ordering is the result of the spatially homogeneous void shrinkage after the completion of void nucleation process. Only “ordered” voids survive. The mathematical investigation is based on the conception of slowly and rapidly varying distributions, which is used to describe in unified fashion a spontaneous formation of ordered structures in a large class of nonequilibrium physical systems, whose properties depend on the parameters that differ in their spatial dispersion. In the case under consideration the spatial diffusion lengths of point defects and voids are such parameters. It is shown that the constructed periodical void distribution is stable in time with respect to small void size deviations. The roles of the anisotropic transport of self-interstitials in the void spatial ordering and the stochastic fluctuations of void growth rate in the expansion of the temperature range of the nonequilibrium phase transition from a spatially disordered to an ordered void system state are also discussed.

IR spectroscopic study of the molecular structure of highly filled systems of low molecular diene rubbers

The mechanism of interaction of low molecular butadiene and isoprene rubbers with KCl, an inactive filler, has been investigated by IR transmission spectroscopy and by the multiattenuated total internal reflection method (MTIR). Near the solid surface of filler particles polymer macromolecules are spatially ordered. The formation and growth of surface supermolecular structures near filler particles depend on formation of a chemical or physical network as well as on the molecular weight of the rubber and on its spatial ordering and microstructure.

Molecular Motion and Spatial Order in Liquids: The Aniline/Cyclohexane System

This work probes the relationship between molecular motion and spatial order in binary solutions. We deal with the aniline–cyclohexane system, in which the components are completely miscible above a critical solution temperature, Tc, of 29.5°C and separate into aniline-rich and cyclohexane-rich layers at lower temperatures. Previous light-scattering measurements indicate spatially ordered regions with dimensions of roughly 50 Å some 10° above Tc; the size of these regions increases to 1000–2000 Å at 0.1° above Tc. Spatial correlations between the positions of the aniline and cyclohexane molecules were examined through studies of: (1) the PMR solvent shift; (2) the intermolecular contribution to spin–lattice relaxation. The results indicate a statistical preference for aniline–aniline and cyclohexane–cyclohexane neighbors rather than aniline–cyclohexane pairings. The self-diffusion coefficients of both aniline and cyclohexane were determined by pulsed NMR methods over a wide range of temperature and concentration. We employed a sinusoidal time-dependent field gradient, locating the rf pulses at field-gradient nodes one cycle apart. Owing to the refocusing effect of the periodic gradient, multiple spin echoes can be generated from a simple 90–180 pulse sequence. The self-diffusion measurements indicate that the basic translational process involves the motion of individual aniline and cyclohexane molecules. We found no evidence for the translation of polymolecular aggregates. This is clearly a system of uncomplexed aniline and cyclohexane molecules that happen to translate in spatially ordered surroundings. We examined self-diffusion in the cloudy solutions characteristic of the phase-separation temperature. The experimental diffusion coefficients were indistinguishable from those determined at a temperature 1° higher. Evidently, the self-diffusion coefficients, Da, do not exhibit anomalous behavior near Tc, as does the mutual diffusion coefficient, Dm. These two quantities are related by the expression Dm = Da(∂ lna / ∂ lnc) and the experimental results are consistent since (∂ lna / ∂ lnc) becomes vanishingly small near Tc.