Metastability, Mode Coupling and the Glass Transition

Mode coupling theory (MCT) has been successful in explaining the observed sequence of time relaxations in dense fluids. Previous expositions of this theory showing this sequence have required the existence of an ideal glass transition temperature $T_0$. Recent experiments show no evidence of $T_0$. We show here how the theory can be reformulated, in a fundamental way, such that one retains this sequence of relaxation behaviors but with a smooth temperature dependence and without any indication of $T_0$. The key ingredient in the reformulation is the inclusion of the metastable nature of the glass transition problem through a coupling of the mass density to the defect density. A main result of our theory is that the exponents governing the sequence of time relaxations are weak functions of the temperature in contrast to the results from conventional MCT.Comment: 14 pages (2 figures upon request), REVTEX

Density fluctuations and single-particle dynamics in liquid lithium

The single-particle and collective dynamical properties of liquid lithium have been evaluated at several thermodynamic states near the triple point. This is performed within the framework of mode-coupling theory, using a self-consistent scheme which, starting from the known static structure of the liquid, allows the theoretical calculation of several dynamical properties. Special attention is devoted to several aspects of the single-particle dynamics, which are discussed as a function of the thermodynamic state. The results are compared with those of Molecular Dynamics simulations and other theoretical approaches.Comment: 31 pages (in preprint format), 14 figures. Submitted to Phys. Rev.

Prospective evaluation of voice outcome during the first two years in male patients treated by radiotherapy or laser surgery for T1a glottic carcinoma

In this prospective cohort study, we assessed voice outcome in patients before and up to 2 years after treatment for early glottic cancer either by radiotherapy or by laser surgery; 106 male patients, treated for T1aN0M0 glottic cancer either by endoscopic laser surgery (n = 67) or by radiotherapy (n = 39), participated in the study. Patients’ voices were recorded and analysed pre-treatment and 3, 6, 12 and 24 months post-treatment at their routine visit at the outpatient clinic. Average fundamental frequency (F0), percent jitter, percent shimmer and normalized noise energy (NNE) were determined. After 2 years, local control rate was 95% in the radiotherapy group and 97% in the laser surgery group. Larynx preservation rate was 95% after radiotherapy and 100% after laser surgery. Voice outcome recovers more quickly in patients treated with laser surgery in comparison to radiotherapy: 3 months after laser surgery there is no longer a difference with regard to normal voices except for the fundamental frequency, which remains higher pitched, even in the longer term. For patients treated with radiotherapy it takes longer for jitter, shimmer and NNE to become normal, where jitter remains significantly different from normal voices even after 2 years. According to these results, we believe that laser surgery is the first treatment of choice in the treatment of selected cases of T1a glottic carcinomas with good functional and oncological results

The evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wave length and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wave length with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by X-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.Comment: 50 pages, 17 postscript files including 18 figures, to be published in Phys. Rev.

Universal and non-universal features of glassy relaxation in propylene carbonate

It is demonstrated that the susceptibility spectra of supercooled propylene carbonate as measured by depolarized-light-scattering, dielectric-loss, and incoherent quasi-elastic neutron-scattering spectroscopy within the GHz window are simultaneously described by the solutions of a two-component schematic model of the mode-coupling theory (MCT) for the evolution of glassy dynamics. It is shown that the universal beta-relaxation-scaling laws, dealing with the asymptotic behavior of the MCT solutions, describe the qualitative features of the calculated spectra. But the non-universal corrections to the scaling laws render it impossible to achieve a complete quantitative description using only the leading-order-asymptotic results.Comment: 37 pages, 16 figures, to be published in Phys. Rev.

Evidence for Unusual Dynamical Arrest Scenario in Short Ranged Colloidal Systems

Extensive molecular dynamics simulation studies of particles interacting via a short ranged attractive square-well (SW) potential are reported. The calculated loci of constant diffusion coefficient $D$ in the temperature-packing fraction plane show a re-entrant behavior, i.e. an increase of diffusivity on cooling, confirming an important part of the high volume-fraction dynamical-arrest scenario earlier predicted by theory for particles with short ranged potentials. The more efficient localization mechanism induced by the short range bonding provides, on average, additional free volume as compared to the hard-sphere case and results in faster dynamics.Comment: 4 pages, 3 figure

Metastable Dynamics above the Glass Transition

The element of metastability is incorporated in the fluctuating nonlinear hydrodynamic description of the mode coupling theory (MCT) of the liquid-glass transition. This is achieved through the introduction of the defect density variable $n$ into the set of slow variables with the mass density $\rho$ and the momentum density ${\bf g}$. As a first approximation, we consider the case where motions associated with $n$ are much slower than those associated with $\rho$. Self-consistently, assuming one is near a critical surface in the MCT sense, we find that the observed slowing down of the dynamics corresponds to a certain limit of a very shallow metastable well and a weak coupling between $\rho$ and $n$. The metastability parameters as well as the exponents describing the observed sequence of time relaxations are given as smooth functions of the temperature without any evidence for a special temperature. We then investigate the case where the defect dynamics is included. We find that the slowing down of the dynamics corresponds to the system arranging itself such that the kinetic coefficient $\gamma_v$ governing the diffusion of the defects approaches from above a small temperature-dependent value $\gamma^c_v$.Comment: 38 pages, 14 figures (6 figs. are included as a uuencoded tar- compressed file. The rest is available upon request.), RevTEX3.0+eps

Critical Decay at Higher-Order Glass-Transition Singularities

Within the mode-coupling theory for the evolution of structural relaxation in glass-forming systems, it is shown that the correlation functions for density fluctuations for states at A_3- and A_4-glass-transition singularities can be presented as an asymptotic series in increasing inverse powers of the logarithm of the time t: $\phi(t)-f\propto \sum_i g_i(x)$, where $g_n(x)=p_n(\ln x)/x^n$ with p_n denoting some polynomial and x=ln (t/t_0). The results are demonstrated for schematic models describing the system by solely one or two correlators and also for a colloid model with a square-well-interaction potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions", Messina, Italy, December 2003 (submitted

Dynamic Habitat Disturbance and Ecological Resilience (DyHDER): Modeling Population Responses to Habitat Condition

Understanding how populations respond to spatially heterogeneous habitat disturbance is as critical to conservation as it is challenging. Here, we present a new, free, and open‐source metapopulation model: Dynamic Habitat Disturbance and Ecological Resilience (DyHDER), which incorporates subpopulation habitat condition and connectivity into a population viability analysis framework. Modeling temporally dynamic and spatially explicit habitat disturbance of varying magnitude and duration is accomplished through the use of habitat time‐series data and a mechanistic approach to adjusting subpopulation vital rates. Additionally, DyHDER uses a probabilistic dispersal model driven by site‐specific habitat suitability, density dependence, and directionally dependent connectivity. In the first application of DyHDER, we explore how fragmentation and projected climate change are predicted to impact a well‐studied Bonneville cutthroat trout metapopulation in the Logan River (Utah, USA). The DyHDER model predicts which subpopulations are most susceptible to disturbance, as well as the potential interactions between stressors. Further, the model predicts how populations may be expected to redistribute following disturbance. This information is valuable to conservationists and managers faced with protecting populations of conservation concern across landscapes undergoing changing disturbance regimes. The DyHDER model provides a valuable and generalizable new tool to explore metapopulation resilience to spatially and temporally dynamic stressors for a diverse range of taxa and ecosystems