Axiomatic Theories of Intermediate Phases (IP) and Ideal Stretched Exponential Relaxation (SER)

Minimalist theories of complex systems are broadly of two kinds: mean-field and axiomatic. So far all theories of properties absent from simple systems and intrinsic to complex systems, such as IP and SER, are axiomatic. SER is the prototypical complex temporal property of glasses, discovered by Kohlrausch 150 years ago, and now observed almost universally in microscopically homogeneous, complex non-equilibrium materials (strong network and fragile molecular glasses, polymers and copolymers, even electronic glasses). The Scher-Lax trap model (1973) is paradigmatic for electronic SER; for molecular SER Phillips (3RCS 1995) identified two "magic" shape fractions \beta = 3/5 and 3/7, as confirmed by many later experiments here reviewed. In the dielectric SER frequency domain involving ion conduction, there are also special beta values for fused salts and glasses, slightly, but distinguishably, different because of the presence of a forcing electric field

Role of interference in MM-wave driven DC transport in two dimensional electron gas

In this paper we point out that in addition to the density of states effect proposed in Ref.\cite{durst,anderson} one should consider the effect of constructive interference between the multi-MM-wave-photon processes shown in Fig.2. This process enhances the dark value of the conductivity. When the sample is very pure, i.e., when the transport life time is very long, this interference effect quickly diminishes as the MM-wave frequency deviates from the cyclotron frequency. In this paper we also present the linear response theory in the presence of strong harmonic time-dependent perturbation

Signature of small rings in the Raman spectra of normal and compressed amorphous silica: A combined classical and ab initio study

We calculate the parallel (VV) and perpendicular (VH) polarized Raman spectra of amorphous silica. Model SiO2 glasses, uncompressed and compressed, were generated by a combination of classical and ab initio molecular-dynamics simulations and their dynamical matrices were computed within the framework of the density functional theory. The Raman scattering intensities were determined using the bond-polarizability model and a good agreement with experimental spectra was found. We confirm that the modes associated to the fourfold and threefold rings produce most of the Raman intensity of the D1 and D2 peaks, respectively, in the VV Raman spectra. Modifications of the Raman spectra upon compression are found to be in agreement with experimental data. We show that the modes associated to the fourfold rings still exist upon compression but do not produce a strong Raman intensity, whereas the ones associated to the threefold rings do. This result strongly suggests that the area under the D1 and D2 peaks is not directly proportional to the concentration of small rings in amorphous SiO2.Comment: 21 pages, 8 figures. Phys. Rev. B, in pres

Frequency-Rank Correlations of Rhodopsin Mutations with Tuned Hydropathic Roughness Based on Self-Organized Criticality

The behavior of disease-linked mutations of membrane proteins is especially simple in rhodopsin, where they are well-studied, as they are responsible for retinitis pigmentosa, RP (retinal degeneration). Here we show that the frequency of occurrence of single RP mutations is strongly influenced by their posttranslational survival rates, and that this survival correlates well (82%) with a long-range, non-local hydropathic measure of the roughness of the water interfaces of ex-membrane rhodopsin based on self-organized criticality (SOC). It is speculated that this concept may be generally useful in studying survival rates of many mutated proteins

Microscopic Aspects of Stretched Exponential Relaxation (SER) in Homogeneous Molecular and Network Glasses and Polymers

Because the theory of SER is still a work in progress, the phenomenon itself can be said to be the oldest unsolved problem in science, as it started with Kohlrausch in 1847. Many electrical and optical phenomena exhibit SER with probe relaxation I(t) ~ exp[-(t/{\tau}){\beta}], with 0 < {\beta} < 1. Here {\tau} is a material-sensitive parameter, useful for discussing chemical trends. The "shape" parameter {\beta} is dimensionless and plays the role of a non-equilibrium scaling exponent; its value, especially in glasses, is both practically useful and theoretically significant. The mathematical complexity of SER is such that rigorous derivations of this peculiar function were not achieved until the 1970's. The focus of much of the 1970's pioneering work was spatial relaxation of electronic charge, but SER is a universal phenomenon, and today atomic and molecular relaxation of glasses and deeply supercooled liquids provide the most reliable data. As the data base grew, the need for a quantitative theory increased; this need was finally met by the diffusion-to-traps topological model, which yields a remarkably simple expression for the shape parameter {\beta}, given by d*/(d* + 2). At first sight this expression appears to be identical to d/(d + 2), where d is the actual spatial dimensionality, as originally derived. The original model, however, failed to explain much of the data base. Here the theme of earlier reviews, based on the observation that in the presence of short-range forces only d* = d = 3 is the actual spatial dimensionality, while for mixed short- and long-range forces, d* = fd = d/2, is applied to four new spectacular examples, where it turns out that SER is useful not only for purposes of quality control, but also for defining what is meant by a glass in novel contexts. (Please see full abstract in main text

Relationship between dynamical heterogeneities and stretched exponential relaxation

We identify the dynamical heterogeneities as an essential prerequisite for stretched exponential relaxation in dynamically frustrated systems. This heterogeneity takes the form of ordered domains of finite but diverging lifetime for particles in atomic or molecular systems, or spin states in magnetic materials. At the onset of the dynamical heterogeneity, the distribution of time intervals spent in such domains or traps becomes stretched exponential at long time. We rigorously show that once this is the case, the autocorrelation function of the renewal process formed by these time intervals is also stretched exponential at long time.Comment: 8 pages, 4 figures, submitted to PR

Microscopic origin of collective exponentially small resistance states

The formation of "zero" (exponentially small) resistance states (ESRS) in high mobility two-dimensional electron systems (2DES) in a static magnetic field B and subjected to strong microwave (MW) radiation has attracted great theoretical interest. These states appear to be associated with a new kind of energy gap $\Delta$. Here I show that the energy gap $\Delta$ is explained by a microscopic quantum model that involves the Prime Number Theorem, hitherto reserved for only mathematical contexts.Comment: 9 pages, submitted to Solid State Communication

Marine benthic flora and fauna of Gourdon Bay and the Dampier Peninsula in the Kimberley region of North-Western Australia

Surveys undertaken to characterise the marine benthic habitats along the Dampier Peninsula and further south at Gourdon Bay in the Kimberley region of Western Australia were augmented with epibenthic sled sampling of soft and hard bottom habitats. This paper describes the species collected, their biomass and relative abundance for the main groups of marine macrophytes and invertebrates. Five localities were surveyed; Gourdon Bay, Quondong Point to Coulomb Point, Carnot Bay to Beagle Bay, Perpendicular Head and Packer Island. Sampling was limited to fifteen epibenthic dredge operations from a range of habitat types and was designed to target the most common habitat types and to obtain species identifications of the most important species and those which typified different habitat types. Surveys covered a total of 1,350 m 2 of seabed in depths between 11 and 23m. We identified 415 taxa comprising: 1 seagrass, 43 algae, 52 sponges, 30 ascidians, 10 hydroids, 14 scleractinian corals, 52 other cnidarians, 69 crustaceans, 73 molluscs and 71 echinoderms. Despite the limited nature of the sampling, a significant number of new species, range extensions and new records for Western Australia and Australia were recorded. Within the algae, one range extension (Halimeda cf. cuneata f. digitata not previously recorded in Western Australia) and one possible new species of Areschougia were recorded. Two range extensions were present in the ascidians; the solitary ascidian Polycarpa cf. intonata has previously only been recorded in Queensland and Cnemidocarpa cf. radicosa only in temperate Australian waters. There were several range extensions for the crustacea, for example, the sponge crab, Tumidodromia dormia, has only been recorded in Queensland. One species of holothurian of the genus Phyllophorus could not be identified from the literature available and may represent a new species. Similarly, a small species of the echinoid Gymnechinus could possibly be a new species. The collections of hydroids, hard corals, crinoids and molluscs contained no new species or range extensions. There was difficulty in identification of some groups to species level due to the status of the current taxonomic literature (e.g. Cnidaria, Porifera and ascidians) and there may be a number of new species among the material collected. Among the anthozoa, there is at least one new species of Chromonephthea and potentially 10 range extensions to Western Australia. Sinularia cf. acuta and Chromonephthea curvata are both new records for Australia with both previously recorded in Indonesia only. Among the better known taxa (e.g. molluscs, echinoderms, corals), most of the taxa identified to species level have been recorded to occur throughout north-western Australia, however the diversity recorded in this study is less than other parts of the Kimberley and this is almost certainly a result of the small overall area sampled and the single method of collection utilised. The most important species on soft bottom habitats in terms of biomass was the heart urchin Breynia desorii (up to 326 g.m -2). Sponges were the dominant fauna by biomass (up to 620 g.m -2) on hard bottom habitats and biomass was dominated a by a few large cup and massive sponge species (e.g. Pione velans and two unidentified Spheciospongia). The biomass of other filter feeders, especially ascidians (e.g. Aplidium cf. crateriferum), soft corals (e.g. Chromonephthea spp.), gorgonians (e.g. Junceella fragilis and Dichotella gemmacea) was also high, indicating the importance of these groups in characterising hard bottom habitats. Although low in biomass, crinoids such as Comaster multifidus and Comatula pectinata were abundant in samples that included a high biomass of other filter feeders