Non-linear damage rheology and wave resonance in rocks

We address various deformational aspects of damaged materials with theoretical analyses and numerical simulations based on a non-linear continuum damage model. Quasi-static simulations of damage accumulation under cyclic load reproduce the laboratory-observed increase in the difference between tensile and compressive elastic moduli with ongoing deformation beyond the elastic regime. Modelling of wave propagation effects reproduces the observed relations between the resonance frequency and wave amplitude. In agreement with laboratory experiments, the simulated resonant curves are asymmetric, with gradual decrease of wave amplitudes for frequencies higher than the resonance value and strong reduction for lower frequencies. The predicted shift of the resonance frequency with increasing wave amplitude under constant material damage is only a few per cent, whereas the resonance frequency shift associated with increasing material damage may reach tens of per cent. The results show that the employed continuum damage rheology model provides a self-consistent treatment for multiple manifestations of non-linear elastic and brittle deformation of solids

Neutrino Fluxes from CMSSM LSP Annihilations in the Sun

We evaluate the neutrino fluxes to be expected from neutralino LSP annihilations inside the Sun, within the minimal supersymmetric extension of the Standard Model with supersymmetry-breaking scalar and gaugino masses constrained to be universal at the GUT scale (the CMSSM). We find that there are large regions of typical CMSSM $(m_{1/2}, m_0)$ planes where the LSP density inside the Sun is not in equilibrium, so that the annihilation rate may be far below the capture rate. We show that neutrino fluxes are dependent on the solar model at the 20% level, and adopt the AGSS09 model of Serenelli et al. for our detailed studies. We find that there are large regions of the CMSSM $(m_{1/2}, m_0)$ planes where the capture rate is not dominated by spin-dependent LSP-proton scattering, e.g., at large $m_{1/2}$ along the CMSSM coannihilation strip. We calculate neutrino fluxes above various threshold energies for points along the coannihilation/rapid-annihilation and focus-point strips where the CMSSM yields the correct cosmological relic density for tan(beta) = 10 and 55 for $\mu$ > 0, exploring their sensitivities to uncertainties in the spin-dependent and -independent scattering matrix elements. We also present detailed neutrino spectra for four benchmark models that illustrate generic possibilities within the CMSSM. Scanning the cosmologically-favored parts of the parameter space of the CMSSM, we find that the IceCube/DeepCore detector can probe at best only parts of this parameter space, notably the focus-point region and possibly also at the low-mass tip of the coannihilation strip.Comment: 32 pages, 13 figures. v2: updated/expanded discussion of IceCube/DeepCor

Correlation for Sessile Drop Evaporation Over a Wide Range of Drop Volatilities, Ambient Gases and Pressures

A correlation for the evaporation of sessile drops over a very broad range of conditions was developed based on measured evaporation rate data obtained for drops of acetone, methanol, and six hydrocarbons ranging from hexane to isooctane, evaporating in air, helium, argon, and krypton, over a range of ambient pressures from 96 kPa to 615 kPa. The experiments were designed to produce a large variation in the rates of diffusion and buoyancy-induced (natural) convection of the vapor phase amongst the experimental conditions. The correlation, which fits the measurements with an RMS relative error of 5.2%, is a simple equation involving conventional parameters for diffusive and convective transport and is applicable to conditions for which vapor transport limits the rate of evaporation. Application of the correlation requires knowledge of eight basic properties: the ambient pressure and temperature, the equilibrium vapor pressure of the evaporating component, the diffusion coefficient for the evaporating component in the ambient gas, the viscosity of the ambient gas, the radius of the sessile drop, and the molecular weights of the evaporating component and the ambient gas. The correlation is much easier to implement than a computational model based on the coupled conservation equations of mass, energy, and momentum for the two phases, and it offers a single mathematical expression that provides valuable insight into how the roles of diffusive and convective transport change with physical and geometrical parameters. The correlation can be a valuable tool to aid in the analyses of applications involving sessile drop evaporation and to support the validation of complex computational models. The range of experimental conditions resulted in a large variation in the rates of diffusive and naturally convective transport of the vapor. Over the range of experimental conditions, the liquid volatility, as indicated by the equilibrium vapor pressure, was varied by a factor of 16.7, the mass diffusivity by a factor of 52.2, the density difference ratio (the impetus for natural convection) by a factor of 3,557, and the drop radius by a factor of 22. In terms of the Rayleigh number, the experimental data covers a range from 5 to 361,000. Consequently, the correlation is applicable to a very broad range of conditions. To our knowledge these evaporation rate measurements of sessile drops in gases other than air and at pressures above one atmosphere are the first to be reported in the literature

Controlling Effect of Geometrically Defined Local Structural Changes on Chaotic Hamiltonian Systems

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a new and minimal method for achieving control of a chaotic system

Scaling relations of earthquakes, aseismic deformation and evolving fault structures in a damage rheology model

see Abstract Volum

Phase transitions in contagion processes mediated by recurrent mobility patterns

Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations and recurrent flows and poorly modeled by the random diffusive dynamics generally used to study them. Here we develop a theoretical framework to analyze contagion within a network of locations where individuals recall their geographic origins. We find a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected. This transition cannot be uncovered by continuous deterministic models due to the stochastic features of the contagion process and defines an invasion threshold that depends on mobility parameters, providing guidance for controlling contagion spread by constraining mobility processes. We recover the threshold behavior by analyzing diffusion processes mediated by real human commuting data.Comment: 20 pages of Main Text including 4 figures, 7 pages of Supplementary Information; Nature Physics (2011

Event-related alpha suppression in response to facial motion

This article has been made available through the Brunel Open Access Publishing Fund.While biological motion refers to both face and body movements, little is known about the visual perception of facial motion. We therefore examined alpha wave suppression as a reduction in power is thought to reflect visual activity, in addition to attentional reorienting and memory processes. Nineteen neurologically healthy adults were tested on their ability to discriminate between successive facial motion captures. These animations exhibited both rigid and non-rigid facial motion, as well as speech expressions. The structural and surface appearance of these facial animations did not differ, thus participants decisions were based solely on differences in facial movements. Upright, orientation-inverted and luminance-inverted facial stimuli were compared. At occipital and parieto-occipital regions, upright facial motion evoked a transient increase in alpha which was then followed by a significant reduction. This finding is discussed in terms of neural efficiency, gating mechanisms and neural synchronization. Moreover, there was no difference in the amount of alpha suppression evoked by each facial stimulus at occipital regions, suggesting early visual processing remains unaffected by manipulation paradigms. However, upright facial motion evoked greater suppression at parieto-occipital sites, and did so in the shortest latency. Increased activity within this region may reflect higher attentional reorienting to natural facial motion but also involvement of areas associated with the visual control of body effectors. © 2014 Girges et al