M. Vallade

Stress-Induced “3-q”-“1-q” Incommensurate Phase Transition in Quartz

The influence of a symmetry breaking field on the triangular 3-q incommensurate phase of quartz is discussed. The appearance of a 1-q stripe phase between the β phase and the 3-q phase is expected when a uniaxial stress σ is applied in the (001) plane. In the (σ, T)-plane the 1-q phase is bound by two transition lines which meet at Ti. Elastic-neutron-scattering experiments demonstrate that such a stress-induced 1-q phase is actually observed in quartz and the experimental phase diagram is in qualitative agreement with theory.

Inelastic neutron scattering study of quartz near the incommensurate phase transition

Abstract Inelastic neutron spectra of B quartz were recorded at various temperatures, using triple axis neutron spectrometry. Our observations confirm the existence of a very low-lying phonon branch along the ⟨1,0,0⟩ directions, which exhibits a marked temperature dependence, in particular near the Brillouin zone center. This branch is very anisotropic in the (0,0,1) plane. Within the B phase a maximum of quasi elastic scattering is observed for q ≃ 0.03a*, premonitory to the appearance of satellite reflexions in the modulated phase. In addition, a transverse acoustic mode exhibits an anisotropic behaviour which is attributed to a coupling with the soft-mode. The results are consistent with a phenomenological model of the incommensurate phase transition and with a lattice dynamical model involving rigid SiO4 tetrahedra motions.

Optical observations of coexistence states during 1st order transition in KD2PO4, quartz and NH4C1.

Abstract At a 1st order transition the two phases are in equilibrium. In a solid, transition strain discontinuities induce elastic stresses which are of long range nature. In order to minimize elastic energy the interface takes definite orientations. The interface shapes, nucleation and motion have been optically observed in 3 materials : NH4C1 around the pressure induced tricritical point, quartz and deuterated KDP, with application of an electric field. In these 3 cases, observed interface orientations are in agreement with the predictions of the theory of coherent inclusions in anisotropic elastic materials.

Phonon Dispersion and Mode Coupling in High-Quartz Near the Incommensurate Phase Transition

In order to test the possible dynamical origin of the incommensurate phase of quartz, the dispersion of low-energy phonon branches in high quartz has been determined by inelastic neutron scattering. The optical sof tmode associated with the α-β transition and the transverse acoustic mode corresponding to uxy strains exhibit a large anisotropy within the hexagonal plane. The relations of these results to the phenomenological gradient coupling model and to microscopic lattice dynamical models are discussed.

Selection for altruism through random drift in variable size populations

BackgroundAltruistic behavior is defined as helping others at a cost to oneself and a lowered fitness. The lower fitness implies that altruists should be selected against, which is in contradiction with their widespread presence is nature. Present models of selection for altruism (kin or multilevel) show that altruistic behaviors can have ‘hidden’ advantages if the ‘common good’ produced by altruists is restricted to some related or unrelated groups. These models are mostly deterministic, or assume a frequency dependent fitness.ResultsEvolutionary dynamics is a competition between deterministic selection pressure and stochastic events due to random sampling from one generation to the next. We show here that an altruistic allele extending the carrying capacity of the habitat can win by increasing the random drift of “selfish” alleles. In other terms, the fixation probability of altruistic genes can be higher than those of a selfish ones, even though altruists have a smaller fitness. Moreover when populations are geographically structured, the altruists advantage can be highly amplified and the fixation probability of selfish genes can tend toward zero. The above results are obtained both by numerical and analytical calculations. Analytical results are obtained in the limit of large populations.ConclusionsThe theory we present does not involve kin or multilevel selection, but is based on the existence of random drift in variable size populations. The model is a generalization of the original Fisher-Wright and Moran models where the carrying capacity depends on the number of altruists.

Exact results for a noise-induced bistable system.

A stochastic system where bistability is caused by noise has been recently investigated by Biancalani et al. [Phys. Rev. Lett. 112, 038101 (2014)]. They have computed the mean switching time for such a system using a continuous Fokker-Planck equation derived from the Taylor expansion of the master equation to estimate the parameter of such a system from experiment. In this article, we provide the exact solution for the full discrete system without resorting to continuous approximation and obtain the expression for the mean switching time. We further extend this investigation by solving exactly the master equation and obtaining the expression of other quantities of interests such as the dynamics of the moments and the equilibrium time.

Inelastic neutron scattering studies of the origin of the incommensurate phase of quartz

Abstract The origin of several incommensurate phases has been attributed to a gradient coupling between the order parameter and strain. High resolution inelastic neutron scattering measurements performed in the high temperature phase of quartz show that the origin of the incommensurate phase of quartz can be explained by this gradient coupling.

Fluctuation-induced first-order phase transitions near mean-field tricritical points in solids

The authors consider displacive phase transitions with a one-component order parameter near what would be a tricritical point (TCP) in the mean-field approximation. As the system in question is a solid, a continuous phase transition is generally impossible. Along a fairly large portion of the phase transition line, a fluctuation-induced first-order phase transition occurs within the region of applicability of the perturbation theory. Close to the mean-field TCP the first-order phase transition proves to be strong, i.e. the discontinuity of the order parameter is of the same order of magnitude as the order parameter at T=0. Below Tc the temperature dependence of the order parameter is given by an equation containing a non-analytical term related to the critical fluctuations, and the other thermodynamic anomalies are governed by this (renormalized) temperature dependence of the order parameter. The theory shows that first-order transitions which are accompanied by strong precursor anomalies in the symmetrical phase, as is the case for ammonium chloride and quartz, would very likely be second order in the mean-field approximation.

Phenomenological interpretation of the critical behaviour of KDP and NH4C1 near their tricritical point

Abstract Recent order parameter measurements in KDP and NH4C1 near their pressure-induced tricritical point are interpreted using a Landau type free energy expansion of the following form: Good fits are obtained with the simple assumption that the coefficients a and b vary linearly with P and T near the tricritical point where they vanish simultaneously.

Fisher waves: An individual-based stochastic model

The propagation of a beneficial mutation in a spatially extended population is usually studied using the phenomenological stochastic Fisher-Kolmogorov-Petrovsky-Piscounov (SFKPP) equation. We derive here an individual-based, stochastic model founded on the spatial Moran process where fluctuations are treated exactly. The mean-field approximation of this model leads to an equation that is different from the phenomenological FKPP equation. At small selection pressure, the front behavior can be mapped into a Brownian motion with drift, the properties of which can be derived from the microscopic parameters of the Moran model. Finally, we generalize the model to take into account dispersal kernels beyond migration to nearest neighbors. We show how the effective population size (which controls the noise amplitude) and the diffusion coefficient can both be computed from the dispersal kernel.