Dynamics and Scaling of Noise-Induced Domain Growth

The domain growth processes originating from noise-induced nonequilibrium phase transitions are analyzed, both for non-conserved and conserved dynamics. The existence of a dynamical scaling regime is established in the two cases, and the corresponding growth laws are determined. The resulting universal dynamical scaling scenarios are those of Allen-Cahn and Lifshitz-Slyozov, respectively. Additionally, the effect of noise sources on the behaviour of the pair correlation function at short distances is studied.Comment: 11 pages (including 13 figures) LaTeX file. Accepted in EPJ

Antiferromagnetic effects in Chaotic Map lattices with a conservation law

Some results about phase separation in coupled map lattices satisfying a conservation law are presented. It is shown that this constraint is the origin of interesting antiferromagnetic effective couplings and allows transitions to antiferromagnetic and superantiferromagnetic phases. Similarities and differences between this models and statistical spin models are pointed out.Comment: 14 pages including 9 figure

Feedback Loops Between Fields and Underlying Space Curvature: an Augmented Lagrangian Approach

We demonstrate a systematic implementation of coupling between a scalar field and the geometry of the space (curve, surface, etc.) which carries the field. This naturally gives rise to a feedback mechanism between the field and the geometry. We develop a systematic model for the feedback in a general form, inspired by a specific implementation in the context of molecular dynamics (the so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized Lagrangian that allows for the coupling of the space's metric tensor (the first fundamental form) to the scalar field, and add terms motivated by RP-MD. We present two implementations of the scheme: one in which the metric is only time-dependent [which gives rise to ordinary differential equation (ODE) for its temporal evolution], and one with spatio-temporal dependence [wherein the metric's evolution is governed by a partial differential equation (PDE)]. Numerical results are reported for the (1+1)-dimensional model with a nonlinearity of the sine-Gordon type.Comment: 5 pages, 3 figures, Phys. Rev. E in pres

On the structure-properties relationship in montmorillonite-filled polyamide 6 nanocomposites

Polyamide 6/montmorillonite (MMT) nanocomposites were prepared by melt compounding method comprising 1–7.5 wt % of Nanomer I.24 TL or 5 and 10 wt % of Cloisite 15A organically modified nanoclays. The composite samples were characterized by synchrotron X-ray, thermal and FT-IR spectroscopy methods looking for changes in the micro- and nanostructure of both PA6 matrix and MMT reinforcement as a function of the clay content and type. These data were discussed in conjunction with the mechanical properties of the respective nanocomposites. Generally, the Young’s modulus was found to increase proportionally to the clay content being the highest in samples with strong aggregation of MMT at micron length scale. The tensile strength passed through a maximum at 2.5 wt % clay load presenting a homogeneous microstructure with almost no agglomeration. Increasing the amount of MMT produced less crystalline PA6 matrices, richer in gamma-PA6 polymorph and resulted in larger long spacings of PA6 due to expansion of both crystalline and amorphous domains.Fundação para a Ciência e a Tecnologia (FCT), Portugal; HASYALb at DESY, Hamburg, German

On the well-posedness of the stochastic Allen-Cahn equation in two dimensions

White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d \geq 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen-Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that a series of published numerical studies are problematic: shrinking the mesh size in these simulations does not lead to the recovery of a physically meaningful limit.Comment: 21 pages, 4 figures; accepted by Journal of Computational Physics (Dec 2011

Population rate codes carried by mean, fluctuation and synchrony of neuronal firings

A population of firing neurons is expected to carry information not only by mean firing rate but also by fluctuation and synchrony among neurons. In order to examine this possibility, we have studied responses of neuronal ensembles to three kinds of inputs: mean-, fluctuation- and synchrony-driven inputs. The generalized rate-code model including additive and multiplicative noise (H. Hasegawa, Phys. Rev. E {\bf 75} (2007) 051904) has been studied by direct simulations (DSs) and the augmented moment method (AMM) in which equations of motion for mean firing rate, fluctuation and synchrony are derived. Results calculated by the AMM are in good agreement with those by DSs. The independent component analysis (ICA) of our results has shown that mean firing rate, fluctuation (or variability) and synchrony may carry independent information in the population rate-code model. The input-output relation of mean firing rates is shown to have higher sensitivity for larger multiplicative noise, as recently observed in prefrontal cortex. A comparison is made between results obtained by the integrate-and-fire (IF) model and our rate-code model.Comment: 20 pages, 10 figures, accepted in Physica A (revised version of arXiv:0706.3489

Textured Minimal and Extended Supergravity Unification and Implications for Proton Stability

We construct a class of textured supergravity unified SU(5) models using Planck scale corrections. We show that the texture constraints in the Higgs doublet sector are insufficient in general to fully determine the textures in the Higgs triplet sector. A classification of textured minimal parameter models is given and their Higgs triplet textures computed under the constraint that they possess the Georgi-Jarlskog textures in the Higgs doublet sector. It is argued that additional dynamical assumptions are needed to remove the ambiguity.The recently proposed extension of supergravity unification to include a minimal exotic sector is free of this ambiguity and leads to unique textures in the Higgs triplet sector. Implications for proton stability are discussed.Comment: 14 pages, latex, no figure

Auxin Influx Carriers Control Vascular Patterning and Xylem Differentiation in Arabidopsis thaliana

Auxin is an essential hormone for plant growth and development. Auxin influx carriers AUX1/LAX transport auxin into the cell, while auxin efflux carriers PIN pump it out of the cell. It is well established that efflux carriers play an important role in the shoot vascular patterning, yet the contribution of influx carriers to the shoot vasculature remains unknown. Here, we combined theoretical and experimental approaches to decipher the role of auxin influx carriers in the patterning and differentiation of vascular tissues in the Arabidopsis inflorescence stem. Our theoretical analysis predicts that influx carriers facilitate periodic patterning and modulate the periodicity of auxin maxima. In agreement, we observed fewer and more spaced vascular bundles in quadruple mutants plants of the auxin influx carriers aux1lax1lax2lax3. Furthermore, we show AUX1/LAX carriers promote xylem differentiation in both the shoot and the root tissues. Influx carriers increase cytoplasmic auxin signaling, and thereby differentiation. In addition to this cytoplasmic role of auxin, our computational simulations propose a role for extracellular auxin as an inhibitor of xylem differentiation. Altogether, our study shows that auxin influx carriers AUX1/LAX regulate vascular patterning and differentiation in plants.Peer reviewe