Stability boundaries of roll and square convection in binary fluid mixtures with positive separation ratio

Rayleigh-B\'{e}nard convection in horizontal layers of binary fluid mixtures heated from below with realistic horizontal boundary conditions is studied theoretically using multi-mode Galerkin expansions. For positive separation ratios the main difference between the mixtures and pure fluids lies in the existence of stable three dimensional patterns near onset in a wide range of the parameter space. We evaluated the stationary solutions of roll, crossroll, and square convection and we determined the location of the stability boundaries for many parameter combinations thereby obtaining the Busse balloon for roll and square patterns.Comment: 19 pages + 15 figures, accepted by Journal of Fluid Mechanic

Ferromagnetic Domain Structure of La0.78Ca0.22MnO3 Single Crystals

The magneto-optical technique has been employed to observe spontaneous ferromagnetic domain structures in La0.78Ca0.22MnO3 single crystals. The magnetic domain topology was found to be correlated with the intrinsic twin structure of the investigated crystals. With decreasing temperature the regular network of ferromagnetic domains undergoes significant changes resulting in apparent rotation of the domain walls in the temperature range of 70-150 K. The apparent rotation of the domain walls can be understood in terms of the Jahn-Teller deformation of the orthorhombic unit cell, accompanied by additional twinning.Comment: 7 pages, 5 figures, to be published in PR

Classical Scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set

We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate Poincare surface of section. We find the development parameters that describe the hyperbolic component of the chaotic invariant set. In addition, we show that the hierarchical structure of the fractal set of singularities of the scattering functions is the same as the structure of the chaotic invariant set. Finally, we construct a symbolic encoding of the hierarchical structure of the set of singularities of the scattering functions and use concepts from the thermodynamical formalism to obtain one of the measures of chaos of the fractal set of singularities, the topological entropy.Comment: accepted in Phy. Rev.

Neutrino oscillation signatures of oxygen-neon-magnesium supernovae

We discuss the flavor conversion of neutrinos from core collapse supernovae that have oxygen-neon-magnesium (ONeMg) cores. Using the numerically calculated evolution of the star up to 650 ms post bounce, we find that, for the normal mass hierarchy, the electron neutrino flux in a detector shows signatures of two typical features of an ONeMg-core supernova: a sharp step in the density profile at the base of the He shell and a faster shock wave propagation compared to iron core supernovae. Before the shock hits the density step (t ~ 150 ms), the survival probability of electron neutrinos is about 0.68, in contrast to values of 0.32 or less for an iron core supernova. The passage of the shock through the step and its subsequent propagation cause a decrease of the survival probability and a decrease of the amplitude of oscillations in the Earth, reflecting the transition to a more adiabatic propagation inside the star. These changes affect the lower energy neutrinos first; they are faster and more sizable for larger theta_13. They are unique of ONeMg-core supernovae, and give the possibility to test the speed of the shock wave. The time modulation of the Earth effect and its negative sign at the neutronization peak are the most robust signatures in a detector.Comment: 14 pages, 10 figures (16 figure files). Text and graphics added for illustration and clarification; Results unchanged. Version accepted for publication in Physical Review

Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems

The statistics of transitions between the metastable states of a periodically driven bistable Brownian oscillator are investigated on the basis of a two-state description by means of a master equation with time-dependent rates. The results are compared with extensive numerical simulations of the Langevin equation for a sinusoidal driving force. Very good agreement is achieved both for the counting statistics of the number of transitions and the residence time distribution of the process in either state. The counting statistics corroborate in a consistent way the interpretation of stochastic resonance as a synchronisation phenomenon for a properly defined generalized Rice phase.Comment: 15 pages, 9 figure

Standing wave oscillations in binary mixture convection: from onset via symmetry breaking to period doubling into chaos

Oscillatory solution branches of the hydrodynamic field equations describing convection in the form of a standing wave (SW) in binary fluid mixtures heated from below are determined completely for several negative Soret coefficients. Galerkin as well as finite-difference simulations were used. They were augmented by simple control methods to obtain also unstable SW states. For sufficiently negative Soret coefficients unstable SWs bifurcate subcritically out of the quiescent conductive state. They become stable via a saddle-node bifurcation when lateral phase pinning is exerted. Eventually their invariance under time-shift by half a period combined with reflexion at midheight of the fluid layer gets broken. Thereafter they terminate by undergoing a period-doubling cascade into chaos

Self-trapped Exciton and Franck-Condon Spectra Predicted in LaMnO3_3

Because the ground state has cooperative Jahn-Teller order, electronic excitations in LaMnO$_3$ are predicted to self-trap by local rearrangement of the lattice. The optical spectrum should show a Franck-Condon series, that is, a Gaussian envelope of vibrational sidebands. Existing data are reinterpreted in this way. The Raman spectrum is predicted to have strong multiphonon features.Comment: 5 pages with two embedded postscript figure

Collective dynamics of two-mode stochastic oscillators

We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the parameter space the periodicity of the collective output is enhanced by the considered coupling. This system can be used as a new model to describe synchronization-like phenomena in systems of units with two or more oscillation modes. The model can also explain how periodic dynamics can be generated by coupling largely stochastic units. Similar systems could be responsible for the emergence of rhythmic behavior in complex biological or sociological systems.Comment: 4 pages, RevTex, 5 figure

Gain in Stochastic Resonance: Precise Numerics versus Linear Response Theory beyond the Two-Mode Approximation

In the context of the phenomenon of Stochastic Resonance (SR) we study the correlation function, the signal-to-noise ratio (SNR) and the ratio of output over input SNR, i.e. the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of Linear Response Theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both, the correlation function and the SNR can deviate substantially from the predictions of LRT and yet, the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analogue simulation results by Gingl et al. in Refs. [18, 19].Comment: 22 pages, 5 eps figures, submitted to PR

Suppression of Higgsino mediated proton decay by cancellations in GUTs and strings

A mechanism for the enhancement for proton lifetime in supersymmetric/supergravity (SUSY/SUGRA) grand unified theories (GUTs) and in string theory models is discussed where Higgsino mediated proton decay arising from color triplets (anti-triplets) with charges $Q=-1/3(1/3)$ and $Q=-4/3(4/3)$ is suppressed by an internal cancellation due to contributions from different sources. We exhibit the mechanism for an SU(5) model with $45_H+\bar{45}_H$ Higgs multiplets in addition to the usual Higgs structure of the minimal model. This model contains both $Q=-1/3(1/3)$ and $Q=-4/3(4/3)$ Higgs color triplets (anti-triplets) and simple constraints allow for a complete suppression of Higgsino mediated proton decay. Suppression of proton decay in an SU(5) model with Planck scale contributions is also considered. The suppression mechanism is then exhibited for an SO(10) model with a unified Higgs structure involving $144_H+\bar{144}_H$ representations.The SU(5) decomposition of $144_H+\bar{144}_H$ contains $5_H+\bar 5_H$ and $45_H+\bar{45}_H$ and the cancellation mechanism arises among these contributions which mirrror the SU(5) case. The cancellation mechanism appears to be more generally valid for a larger class of unification models. Specifically the cancellation mechanism may play a role in string model constructions to suppress proton decay from dimension five operators. The mechanism allows for the suppression of proton decay consistent with current data allowing for the possibility that proton decay may be visible in the next round of nucleon stability experiment.Comment: 26 pages, no figures. Revtex 4. To appear in Physical Review