Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreement with numerical simulations.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.

Valence-bond treatment of distortions in polyacene polymers

Distortions of polyacene polymers are studied within a many-body valence-bond framework using a powerful transfer-matrix technique for the valence-bond (or Heisenberg) model of the system. The computations suggest that the ground-state geometry is either totally symmetric or possibly exhibits a slight (A2 or B2 symmetry) bond-alternation distortion. The lowest-energy (nonsymmetric, in-plane) distortions are the A2 and B2 modes, which, within our approximations, are degenerate.

Dynamics of a paramagnetic colloidal particle driven on a magnetic-bubble lattice

We present a theoretical study of the recently observed dynamical regimes of paramagnetic colloidal particles externally driven above a regular lattice of magnetic bubbles [P. Tierno, T. H. Johansen, and T. M. Fischer, Phys. Rev. Lett. 99, 038303 (2007)]. An external precessing magnetic field alters the potential generated by the surface of the film in such a way to either drive the particle circularly around one bubble, ballistically through the array, or in triangular orbits on the interstitial regions between the bubbles. In the ballistic regime, we observe different trajectories performed by the particles phase locked with the external driving. Superdiffusive motion, which was experimentally found bridging the localized and delocalized dynamics, emerge only by introducing a certain degree of randomness into the bubbles size distribution.

The effect of lattice defects on Hele-Shaw flow over an etched lattice

We examine the patterns formed by injecting nitrogen gas into the center of a horizontal, radial Hele-Shaw cell filled with paraffin oil. We use smooth plates and etched plates with lattices having different amounts of defects (010 %). In all cases, a quantitative measure of the pattern ramification shows a regular trend with injection rate and cell gap, such that the dimensionless perimeter scales with the dimensionless time. By adding defects to the lattice, we observe increased branching in the pattern morphologies. However, even in this case, the scaling behavior persists. Only the prefactor of the scaling function shows a dependence on the defect density. For different lattice defect densities, we examine the nature of the different morphology phases.

Development of Bio-Based Polymers for Use in Asphalt, TR-639, 2014

Asphalt binder is typically modified with poly type (styrene-butadiene-styrene or SBS) polymers to improve its rheological properties and performance grade. The elastic and principal component of SBS polymers is butadiene. For the last decade, butadiene prices have fluctuated and significantly increased, leading state highway agencies to search for economically viable alternatives to butadiene based materials. This project reports the recent advances in polymerization techniques that have enabled the synthesis of elastomeric, thermoplastic, block-copolymers (BCPs) comprised of styrene and soybean oil, where the “B” block in SBS polymers is replaced with polymerized triglycerides derived from soybean oil. These new breeds of biopolymers have elastomeric properties comparable to well-established butadiene-based styrenic BCPs. In this report, two types of biopolymer formulations are evaluated for their ability to modify asphalt binder. Laboratory blends of asphalt modified with the biopolymers are tested for their rheological properties and performance grade. Blends of asphalt modified with the biopolymers are compared to blends of asphalt modified with two commonly used commercial polymers. The viscoelastic properties of the blends show that biopolymers improve the performance grade of the asphalt to a similar and even greater extent as the commercial SBS polymers. Results shown in this report indicate there is an excellent potential for the future of these biopolymers as economically and environmentally favorable alternatives to their petrochemically-derived analogs.

Analysis of experiments in square lattice with emphasis on variance components. i. Individual analysis

This paper focused on four alternatives of analysis of experiments in square lattice as far as the estimation of variance components and some genetic parameters are concerned: 1) intra-block analysis with adjusted treatment and blocks within unadjusted repetitions; 2) lattice analysis as complete randomized blocks; 3) intrablock analysis with unadjusted treatment and blocks within adjusted repetitions; 4) lattice analysis as complete randomized blocks, by utilizing the adjusted means of treatments, obtained from the analysis with recovery of interblock information, having as mean square of the error the mean effective variance of this same analysis with recovery of inter-block information. For the four alternatives of analysis, the estimators and estimates were obtained for the variance components and heritability coefficients. The classification of material was also studied. The present study suggests that for each experiment and depending of the objectives of the analysis, one should observe which alternative of analysis is preferable, mainly in cases where a negative estimate is obtained for the variance component due to effects of blocks within adjusted repetitions.

Cumulative Shapes of Knotted Polymers

We investigate the influence of knotting and chirality on the shape of knotted polygons forming trefoil knots compared to unknotted polygons by aligning independent configurations along their principal inertial axes. While for six edge polygons forming trefoil knots the chiral knotted structure is revealed in the isodensity profiles, the distinct chiral signature of the trefoil is significantly diminished with 24 edges. We observe that as the number of edges in the polygons increases, the cumulative shapes of trefoil knots progressively approach the cumulative shapes for unknotted polygons.

Polymers as carriers for rhizobial inoculant formulations

The aim of this work was to evaluate the efficiency of carboxymethyl cellulose (CMC) and starch blends as carrier materials of rhizobial inoculants regarding their capacity to maintain viable cells and promote cowpea (Vigna unguiculata) nodulation. The experimental design adopted was completely randomized, with three replicates. Forty different compositions of carboxymethyl cellulose (CMC) with starch, compatibilized or not with different proportions of MgO or ZnO, were evaluated regarding their ability of maintaining rhizobial viable cells during the storage period of one month at room temperature, in an initial screening. Thereafter, selected inoculant carrier blends were evaluated regarding their ability to maintain viable rhizobial cells for a period of 165 days, and their performance as inoculant carriers was compared to a peat-based inoculant carrier under greenhouse conditions. Rhizobial cells were better maintained in blends containing 50-60% CMC. Compatibilizing agents did not increase survival of rhizobial cells for 30 days of storage. The cowpea nodulation of polymer blends was statistically the same of peat-based inoculants. CMC/starch polymer blends are efficient carriers to rhizobial inoculants for up to 165 days of storage, when compatibilized with MgO (1%).

3D culture of postnatal retinal stem cells using self assembling polymers

PURPOSE We have previously shown that retinal stem cells (RSCs) can be isolated from the radial glia population of the newborn mouse retina (Angénieux et al., 2006). These RSCs have a great capacity to renew and to generate a large number of neurons including cells differentiated towards the photoreceptor lineage (Mehri-Soussi et al., 2006). However, recent published results from our lab revealed that such cells have a poor integration and survival rate after grafting. The uncontrolled environment of a retina seems to prevent good integration and survival after grafting in vivo. To bypass this problem, we are evaluating the possibility of generating in vitro a hemi-retinal tissue before transplantation. METHODS RSC were expanded and cells passaged <10 were seeded in a solution containing poly-ethylene-glycol (PEG) polymer based hydrogels crosslinked with peptides that are chosen to be substrates for matrix metalloproteinases. Various doses of cross linkers peptides allowing connections between PEG polymers were tested. Different growth factors were studied to stimulate cell proliferation and differentiation. RESULTS Cells survived only in the presence of EGF and FGF-2 and generated colonies with a sphere shape. No cells migrated within the gel. To improve the migration and the repartition of the cells in the gels, the integrin ligand RGDSP was added into the gel. In the presence of FGF-2 and EGF, newly formed cell clusters appeared by cell proliferation within several days, but again no outspreading of cells was observed. No difference was even seen when the stiffness of the hydrogels or the concentration of the integrin ligand RGDSP were changed. However, our preliminary results show that RSCs still form spheres when laminin is entrapped in the gel, but they started to spread out having a neuronal morphology after around 2 weeks. The neuronal population was assessed by the presence of the neuronal marker b-tubulin-III. This differentiation was achieved after successive steps of stimulations including FGF-2 and EGF, and then only FGF-2. Glial cells were also present. Further characterizations are under process. CONCLUSIONS RSC can be grown in 3D. Preliminary results show that neuronal cell phenotype acquisition can be instructed by exogenous stimulations and factors linked to the gel. Further developments are necessary to form a homogenous tissue containing retinal cells.

Monte Carlo study of a kinetic lattice model with random diffusion of disorder

We report Monte Carlo results for a nonequilibrium Ising-like model in two and three dimensions. Nearest-neighbor interactions J change sign randomly with time due to competing kinetics. There follows a fast and random, i.e., spin-configuration-independent diffusion of Js, of the kind that takes place in dilute metallic alloys when magnetic ions diffuse. The system exhibits steady states of the ferromagnetic (antiferromagnetic) type when the probability p that J>0 is large (small) enough. No counterpart to the freezing phenomena found in quenched spin glasses occurs. We compare our results with existing mean-field and exact ones, and obtain information about critical behavior.

Reaction-diffusion lattice gas: Theory and computer results

We report on the study of nonequilibrium ordering in the reaction-diffusion lattice gas. It is a kinetic model that relaxes towards steady states under the simultaneous competition of a thermally activated creation-annihilation $(reaction$) process at temperature T, and a diffusion process driven by a heat bath at temperature T?T. The phase diagram as one varies T and T, the system dimension d, the relative priori probabilities for the two processes, and their dynamical rates is investigated. We compare mean-field theory, new Monte Carlo data, and known exact results for some limiting cases. In particular, no evidence of Landau critical behavior is found numerically when d=2 for Metropolis rates but Onsager critical points and a variety of first-order phase transitions.

Ising critical behavior of a non-Halmiltonian lattice system

We study steady states in d-dimensional lattice systems that evolve in time by a probabilistic majority rule, which corresponds to the zero-temperature limit of a system with conflicting dynamics. The rule satisfies detailed balance for d=1 but not for d>1. We find numerically nonequilibrium critical points of the Ising class for d=2 and 3.