An effective medium approach to the asymptotics of the statistical moments of the parabolic Anderson model and Lifshitz tails

Originally introduced in solid state physics to model amorphous materials and alloys exhibiting disorder induced metal-insulator transitions, the Anderson model $H_{\omega}= -\Delta + V_{\omega}$ on l^2(\bZ^d) has become in mathematical physics as well as in probability theory a paradigmatic example for the relevance of disorder effects. Here $\Delta$ is the discrete Laplacian and V_{\omega} = \{V_{\omega}(x): x \in \bZ^d\} is an i.i.d. random field taking values in \bR. A popular model in probability theory is the parabolic Anderson model (PAM), i.e. the discrete diffusion equation $\partial_t u(x,t) =-H_{\omega} u(x,t)$ on \bZ^d \times \bR_+, $u(x,0)=1$, where random sources and sinks are modelled by the Anderson Hamiltonian. A characteristic property of the solutions of (PAM) is the occurrence of intermittency peaks in the large time limit. These intermittency peaks determine the thermodynamic observables extensively studied in the probabilistic literature using path integral methods and the theory of large deviations. The rigorous study of the relation between the probabilistic approach to the parabolic Anderson model and the spectral theory of Anderson localization is at least mathematically less developed. We see our publication as a step in this direction. In particular we will prove an unified approach to the transition of the statistical moments $$ and the integrated density of states from classical to quantum regime using an effective medium approach. As a by-product we will obtain a logarithmic correction in the traditional Lifshitz tail setting when $V_{\omega}$ satisfies a fat tail condition

Lawsuits in context

The study of Roman procedure has benefited enormously from the discovery of wooden tablets near Pompeii. They are variously referred to as 'the Murecine tablets' (after the Agro Murecine, their place of discovery), 'the Pompeian tablets' (after the ancient site near their place of discovery), 'the Puteoli tablets' (after the ancient site from which they were removed in antiquity), or 'the archive of the Sulpicii' (after the presumed owner of the archive in antiquity). Unfortunately, the tablets are sometimes misinterpreted, for the simple reason that the procedures they describe do not always match the procedures which more familiar sources have (wrongly) led us to believe existed. The tablets, in fact, give us the rare opportunity to revise our understanding of procedure, particularly when taken together with another remarkable find, the lex Irnitana. This article gives a sketch of the 'new' Roman civil procedure now available to us as a result of these exciting finds

Assessing a macroalgal foundation species: community variation with shifting algal assemblages

Thesis (M.S.) University of Alaska Fairbanks, 2018Foundation species provide critical food and habitat to their associated communities. Consequently, they are disproportionately important in shaping community structure, promoting greater biodiversity and increased species abundance. In the Aleutian archipelago, once extensive kelp forests are now relatively rare and highly fragmented. This is due to unregulated urchin grazing shifting the majority of nearshore rocky-reefs from kelp forests to either urchin barrens or "transition forests" - kelp forests devoid of understory algae. The algal communities within kelp forests, transition forests, and urchin barrens represent a stepwise loss in fleshy algal guilds, a regression from a full algal community, to having only canopy kelp, to areas largely denuded of all fleshy algae. This stepwise loss of algal guilds was used to test the designation of the resident canopy-forming kelp, Eualaria fistulosa, as a foundation species--a species that has strong, positive effects on communities where it occurs. Therefore, I assessed the impact that E. fistulosa's occurrence had on faunal community structure (in terms of species diversity, abundance and biomass, and percent bottom cover)and invertebrate size-structure. This study found that the presence of E. fistulosa does not correspond to strong differences in invertebrate size-structure or faunal community structure. However, in kelp forests where E. fistulosa exists in tandem with a variety of subcanopy macroalgae, faunal communities are more species rich, have significantly different community structures with notably higher abundance, biomass, and percent cover of filter feeding taxa, and support sea urchin populations containing significantly higher proportions of larger individuals. Consequently, this study stresses the context dependent role of foundation species and suggests their strong, positive effects on associated communities may change with perturbations to ecosystems. To that end, this study suggests that we may need to reconsider the designation of E. fistulosa as a foundation species following the extensive fragmentation and range restriction that has occurred throughout much of the Aleutian Archipelago

New Bose-Einstein Results from L3

In hadronic Z decays, we compare Bose-Einstein correlations in \Pgpz pairs with those in identical charged pion pairs. We also measure Bose-Einstein correlations in triplets of identical charged pions. From the first study, the source radius is found to be smaller for \Pgpz-\Pgpz than for \Pgppm-\Pgppm, as would be expected, e.g., in a string model. However, the second study shows that the data are consistent with the pion production being completely incoherent. Both studies use data collected by the L3 collaboration at LEP.Comment: 4 pages, 3 figures in eps, talk given at XXXI International Symposium on Multiparticle Dynamics, Sept 1-7, 2001, Datong China. see http://ismd31.ccnu.edu.cn

Bose-Einstein and Other Correlations in Hadronic Z Decay

In hadronic Z decays, Bose-Einstein correlations in neutral pion pairs are compared to those in identical charged pion pairs. Bose-Einstein correlations are also measured in triplets of identical charged pions, and comparison with those in pairs of pions indicates that pion production is completely incoherent. Further, factorial cumulants are used to compare correlations among like-sign as well as among all particles with those of several Monte Carlo models.Comment: 4 pages, 3 figures, Rencontres de Moriond - QCD 200

Low Cell pH Depresses Peak Power in Rat Skeletal Muscle Fibres at Both 30°C and 15°C: Implications for Muscle Fatigue

Historically, an increase in intracellular H+ (decrease in cell pH) was thought to contribute to muscle fatigue by direct inhibition of the cross-bridge leading to a reduction in velocity and force. More recently, due to the observation that the effects were less at temperatures closer to those observed in vivo, the importance of H+ as a fatigue agent has been questioned. The purpose of this work was to re-evaluate the role of H+ in muscle fatigue by studying the effect of low pH (6.2) on force, velocity and peak power in rat fast-and slow-twitch muscle fibres at 15°C and 30°C. Skinned fast type IIa and slow type I fibres were prepared from the gastrocnemius and soleus, respectively, mounted between a force transducer and position motor, and studied at 15°C and 30°C and pH 7.0 and 6.2, and fibre force (P0), unloaded shortening velocity (V0), force–velocity, and force–power relationships determined. Consistent with previous observations, low pH depressed the P0 of both fast and slow fibres, less at 30°C (4–12%) than at 15°C (30%). However, the low pH-induced depressions in slow type I fibre V0 and peak power were both significantly greater at 30°C (25% versus 9% for V0 and 34% versus 17% for peak power). For the fast type IIa fibre type, the inhibitory effect of low pH on V0 was unaltered by temperature, while for peak power the inhibition was reduced at 30°C (37% versus 18%). The curvature of the force–velocity relationship was temperature sensitive, and showed a higher a/P0 ratio (less curvature) at 30°C. Importantly, at 30°C low pH significantly depressed the ratio of the slow type I fibre, leading to less force and velocity at peak power. These data demonstrate that the direct effect of low pH on peak power in both slow-and fast-twitch fibres at near-in vivo temperatures (30°C) is greater than would be predicted based on changes in P0, and that the fatigue-inducing effects of low pH on cross-bridge function are still substantial and important at temperatures approaching those observed in vivo

Nuclear-dominated accretion and subluminous supernovae from the merger of a white dwarf with a neutron star or black hole

We construct one dimensional steady-state models of accretion disks produced by the tidal disruption of a white dwarf (WD) by a neutron star (NS) or stellar mass black hole (BH). At radii r <~ 1e8.5-1e9 cm the midplane density and temperature are sufficiently high to burn the initial white dwarf material into increasingly heavier elements (e.g. Mg, Si, S, Ca, Fe, and Ni) at sequentially smaller radii. When the energy released by nuclear reactions is comparable to that released gravitationally, we term the disk a nuclear-dominated accretion flow (NuDAF). At small radii <~1e7 cm Fe photo-disintegrates into He and then free nuclei, and cooling by neutrinos may be efficient. At the high accretion rates of relevance ~ 0.1-1e-4 Msun/s, most of the disk is radiatively inefficient and prone to outflows powered by viscous dissipation and nuclear burning. Outflow properties are calculated by requiring that material in the midplane be marginally bound (Bernoulli constant <~ 0), due (in part) to cooling by matter escaping the disk. For reasonable assumptions regarding the properties of disk winds, we show that a significant fraction >50-80 per cent of the total WD mass is unbound. The ejecta composition is predominantly O, C, Si, Mg, Ne, Fe, and S [He, C, Si, S, Ar, and Fe], in the case of C-O [He] WDs, respectively, along with a small quantity ~1e-3-1e-2 Msun of radioactive Ni56 and, potentially, a trace amount of H. We use our results to evaluate possible EM counterparts of WD-NS/BH mergers, including optical transients powered by the radioactive decay of Ni56 and radio transients powered by the interaction of the ejecta with the interstellar medium. We address whether recently discovered subluminous Type I supernovae result from WD-NS/BH mergers. Our results also have implications for accretion following the core collapse of massive stars in collapsar models for gamma-ray bursts.Comment: 13 pages, 7 figures, 2 tables, now accepted to MNRA