Speed of pattern appearance in reaction-diffusion models: Implications in the pattern formation of limb bud mesenchyme cells

It has been postulated that fibroblast growth factor (FGF) treatment of cultured limb bud mesenchyme cells reinforces the lateral inhibitory effect, but the cells also show accelerated pattern appearance. In the present study, we analyze how a small change in a specific parameter affects the speed of pattern appearance in a Turing reaction-diffusion system using linear stability analysis. It is shown that the sign of the change in appearance speed is qualitatively decided if the system is under the diffusion-driven instability condition, and this is confirmed by numerical simulations. Numerical simulations also show that a small change in parameter value induced easily detectable differences in the appearance speed of patterns. Analysis of the Gierer-Meinhardt model revealed that a change in a single parameter can explain two effects of FGF on limb mesenchyme cells—reinforcement of lateral inhibition and earlier appearance of pattern. These qualitative properties and easy detectability make this feature a promising tool to elucidate the underlying mechanisms of biological pattern formationwhere the quantitative parameters are difficult to obtain

Mixed mode pattern in Doublefoot mutant mouse limb - Turing reaction-diffusion model on a growing domain during limb development

It has been suggested that the Turing reaction–diffusion model on a growing domain is applicable during limb development, but experimental evidence for this hypothesis has been lacking. In the present study, we found that in Doublefoot mutant mice, which have supernumerary digits due to overexpansion of the limb bud, thin digits exist in the proximal part of the hand or foot, which sometimes become normal abruptly at the distal part. We found that exactly the same behaviour can be reproduced by numerical simulation of the simplest possible Turing reaction–diffusion model on a growing domain. We analytically showed that this pattern is related to the saturation of activator kinetics in the model. Furthermore, we showed that a number of experimentally observed phenomena in this system can be explained within the context of a Turing reaction–diffusion model. Finally, we make some experimentally testable predictions

Structural Transition of Li2RuO3 Induced by Molecular-Orbit Formation

A pseudo honeycomb system Li2RuO3 exhibits a second-order-like transition at temperature T=Tc=540 K to a low-T nonmagnetic phase with a significant lattice distortion forming Ru-Ru pairs. For this system, we have calculated the band structure, using the generalized gradient approximation (GGA) in both the high- and low- T phases, and found that the results of the calculation can naturally explain the insulating behavior observed in the low-T phase. The detailed characters of the Ru 4d t2g bands obtained by the tight-binding fit to the calculated dispersion curves show clear evidence that the structural transition is driven by the formation of the Ru-Ru molecular-orbits, as proposed in our previous experimental studies.Comment: 5 pages, 5 figures, 4 tables, submitted to J. Phys. Soc. Jp

On the particle spectrum and the conformal window

We study the SU(3) gauge theory with twelve flavours of fermions in the fundamental representation as a prototype of non-Abelian gauge theories inside the conformal window. Guided by the pattern of underlying symmetries, chiral and conformal, we analyze the two-point functions theoretically and on the lattice, and determine the finite size scaling and the infinite volume fermion mass dependence of the would-be hadron masses. We show that the spectrum in the Coulomb phase of the system can be described in the context of a universal scaling analysis and we provide the nonperturbative determination of the fermion mass anomalous dimension gamma*=0.235(46) at the infrared fixed point. We comment on the agreement with the four-loop perturbative prediction for this quantity and we provide a unified description of all existing lattice results for the spectrum of this system, them being in the Coulomb phase or the asymptotically free phase. Our results corroborate the view that the fixed point we are studying is not associated to a physical singularity along the bare coupling line and estimates of physical observables can be attempted on either side of the fixed point. Finally, we observe the restoration of the U(1) axial symmetry in the two-point functions.Comment: 40 pages, 22 figure

One,Two,Zero: Scales of Strong Interactions

We discuss our results on QCD with a number of fundamental fermions ranging from zero to sixteen. These theories exhibit a wide array of fascinating phenomena which have been under close scrutiny, especially in recent years, first and foremost is the approach to conformality. To keep this review focused, we have chosen scale generation, or lack thereof as a guiding theme, however the discussion will be set in the general framework of the analysis of the phases and phase transitions of strong interactions at zero and nonzero temperature.Comment: 15 pages, prepared for IJMPA Special Issue 'Recent Nonperturbative Developments in QCD-like Theories

Chiral symmetry restoration in QCD with many flavours

We discuss the phases of QCD in the parameter space spanned by the number of light flavours and the temperature with respect to the realisation of chiral and conformal symmetries. The intriguing interplay of these symmetries is best studied by means of lattice simulations, and some selected results from our recent work are presented here.Comment: 10 pages, proceedings of the 9th International Workshop on Critical Point and Onset of Deconfinement, 17-21 November, 2014, ZiF, Bielefeld, German

QCD phase diagram with 2-flavor lattice fermion formulations

We propose a new framework for investigating two-flavor lattice QCD with finite temperature and density. We consider the Karsten-Wilczek fermion formulation, in which a species-dependent imaginary chemical potential term can reduce the number of species to two without losing chiral symmetry. This lattice discretization is useful for study on finite-($T$,$\mu$) QCD since its discrete symmetries are appropriate for the case. To show its applicability, we study strong-coupling lattice QCD with temperature and chemical potential. We derive the effective potential of the scalar meson field and obtain a critical line of the chiral phase transition, which is qualitatively consistent with the phenomenologically expected phase diagram. We also discuss that $O(1/a)$ renormalization of imaginary chemical potential can be controlled by adjusting a parameter of a dimension-3 counterterm.Comment: 21 pages, 11 figure

Synthesis and Properties of Dipyridylcyclopentenes

A short and general route to the substituted dipyridylcyclopentenes was explored and several new compounds belonging to this new group of diarylethenes were synthesized. The study of their photochromic and thermochromic properties shows that the rate of the thermal ring opening is strongly dependent on the polarity of the solvent.

A KdV-like advection-dispersion equation with some remarkable properties

We discuss a new non-linear PDE, u_t + (2 u_xx/u) u_x = epsilon u_xxx, invariant under scaling of dependent variable and referred to here as SIdV. It is one of the simplest such translation and space-time reflection-symmetric first order advection-dispersion equations. This PDE (with dispersion coefficient unity) was discovered in a genetic programming search for equations sharing the KdV solitary wave solution. It provides a bridge between non-linear advection, diffusion and dispersion. Special cases include the mKdV and linear dispersive equations. We identify two conservation laws, though initial investigations indicate that SIdV does not follow from a polynomial Lagrangian of the KdV sort. Nevertheless, it possesses solitary and periodic travelling waves. Moreover, numerical simulations reveal recurrence properties usually associated with integrable systems. KdV and SIdV are the simplest in an infinite dimensional family of equations sharing the KdV solitary wave. SIdV and its generalizations may serve as a testing ground for numerical and analytical techniques and be a rich source for further explorations.Comment: 15 pages, 4 figures, corrected sign typo in KdV Lagrangian above equation 3