Dynamic phase diagram of the REM

By studying the two-time overlap correlation function, we give a comprehensive analysis of the phase diagram of the Random Hopping Dynamics of the Random Energy Model (REM) on time-scales that are exponential in the volume. These results are derived from the convergence properties of the clock process associated to the dynamics and fine properties of the simple random walk in the $n$-dimensional discrete cube.Comment: This paper is in large part based on the unpublished work arXiv:1008.3849. In particular, the analysis of the overlap correlation function is new as well as the study of the high temperature and short time-scale transition line between aging and stationarit

Quantitative Theory of a Relaxation Function in a Glass-Forming System

We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally favored regions (clusters) which are long lived but each of which relaxes as a simple function of time. Without the clusters the relaxation of the background is simply determined by one typical length which we deduce from an elementary statistical mechanical argument. The total relaxation function (which depends on time in a nontrivial manner) is quantitatively determined as a weighted sum over the clusters and the background. The `fragility' in this system can be understood quantitatively since it is determined by the temperature dependence of the number fractions of the locally favored regions.Comment: 4 pages, 5 figure

The use of paleoclimate simulations to refine the environmental and chronological context of archaeological/paleontological sites

This study illustrates the strong potential of combining paleoenvironmental reconstructions and paleoclimate modeling to refine the paleoenvironmental and chronological context of archaeologicaland paleontological sites. We focus on the El Harhoura 2 cave (EH2), an archeological site located on the North-Atlantic coast of Morocco that covers a period from the Late Pleistocene to the mid-Holocene. On several stratigraphic layers, inconsistencies are observed between species- and isotope-based inferences used to reconstruct paleoenvironmental conditions. The stratigraphy of EH2 also shows chronological inconsistencies on older layers between age estimated by Optical Stimulated Luminescence (OSL) and Combination of Uranium Series and Electron Spin Resonance methods (combined US-ESR). We performed paleoclimate simulations to infer the global paleoclimate variations over the EH2 sequence in the area, and we conducted a consistency approach between paleoclimatereconstruction estimated from simulations and available from EH2 paleoenvironmental inferences. Our main conclusion show that the climate sequence based on combined US-ESR ages is more consistent with paleoenvironmental inferences than the climate sequence based on OSL ages. We also evidence that isotope-based inferences are more congruent with the paleoclimate sequence than species-based inferences. These results highlight the difference in scale between the information provided by each ofthese paleoenvironmental proxies. Our approach is transferable to other sites due to the increase number of available paleoclimate simulations.1 Introduction 2 Material and methods 2.1 El Harhoura 2 cave 2.1.1 Presentation of the site 2.1.2 Chronostratigraphy and dating hypotheses 2.1.3 Paleoenvironmental variables 2.2 Paleoclimate reconstruction 2.2.1 Climate model 2.2.2 Paleoclimate simulations 2.2.3 Sea-surface boundary conditions 2.2.4 A subset of key paleoclimate variables 2.3 Consistency analyses 3 Results 3.1. Simulated climate changes 3.2 Consistency between paleoclimate simulations and paleoenvironmental inferences 3.2.1 Association of paleoclimate simulations and stratigraphic layers 3.2.2 Consistency analyses 4 Discussion 4.1 Paleoclimate variation and underlying forcings 4.2 Paleoclimate simulations and chronostratigraphy 4.3 Paleoclimate simulations and paleoenvironmental inferences 5 Conclusion

The use of paleoclimatic simulations to refine the environmental and chronological context of archaeological/paleontological sites

To reconstruct the paleoenvironmental and chronological context of archaeological/paleontological sites is a key step to understand the evolutionary history of past organisms. Commonly used method to infer paleoenvironments rely on varied proxies such as faunal assemblages and isotopes. However, those proxies often show some inconsistencies. Regarding estimated ages of stratigraphic layers, they can vary depending on the dating method used. In this paper, we tested the potential of paleoclimate simulations to address this issue and contribute to the description of the environmental and chronological context of archaeological/paleontological sites. We produced a set of paleoclimate simulations corresponding to the stratigraphy of a Late-Pleistocene Holocene site, El Harhoura 2 (Morocco), and compared the climatic sequence described by these simulations to environmental inferences made from isotopes and faunal assemblages. Our results showed that in the studied site combined US-ESR ages were much more congruent with paleoenvironmental inferences than OSL ages. In addition, climatic variations were found to be more consistent with isotopic studies than faunal assemblages, allowing us to discuss unresolved discrepancies to date. This study illustrates the strong potential of our approach to refine the paleoenvironmental and chronological context of archaeological and paleontological sites.1 Introduction 2 Material and methods 2.1 El Harhoura 2 cave 2.2 Paleoclimate simulations 2.2.1 Pre-existing ensemble of simulations 2.2.2 Model 2.2.3 Sea-surface boundary conditions 2.3 Climate variations through EH2 sequence 3 Results 3.1 Paleoclimate simulations 3.2 Climate variations through EH2 sequence 4 Discussion 5 Conclusio

Universality of REM-like aging in mean field spin glasses

Aging has become the paradigm to describe dynamical behavior of glassy systems, and in particular spin glasses. Trap models have been introduced as simple caricatures of effective dynamics of such systems. In this Letter we show that in a wide class of mean field models and on a wide range of time scales, aging occurs precisely as predicted by the REM-like trap model of Bouchaud and Dean. This is the first rigorous result about aging in mean field models except for the REM and the spherical model.Comment: 4 page

Archaeological sites and palaeoenvironments of Pleistocene West Africa

African paleoanthropological studies typically focus on regions of the continent such as Eastern, Southern and Northern Africa, which hold the highest density of Pleistocene archaeological sites. Nevertheless, lesser known areas such as West Africa also feature a high number of sites. Here, we present a high-resolution map synthesising all well contextualised Pleistocene archaeological sites present in Sub-Saharan West Africa. A detailed elevation and ecoregional map was developed and correlated with palaeoanthropological sites. This map is supplemented with 1,000- and 2000-year interval climate reconstructions over the last 120,000 years for three subregions of high archaeological interest. The presented archaeological sites were compiled by reviewing published literature, and selected based on: (1) documented archaeological stratification or >10 characteristic artefacts, (2) published coordinates, and (3) published chronometric ages or relative dating. The data presented here elucidates the current state of knowledge of Pleistocene West Africa, highlighting the regional potential for human evolutionary studies.1. Introduction 2. Data and methods 3. Map description 4. Discussio

Slow movement of a random walk on the range of a random walk in the presence of an external field

In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions (d \geq 5). This demonstrates that, unlike in the supercritical percolation setting, a slowdown effect occurs as soon a non-trivial bias is introduced. The proof applies a decomposition of the underlying simple random walk path at its cut-times to relate the associated biased random walk to a one-dimensional random walk in a random environment in Sinai's regime

Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities

The aim of this paper is to discuss some basic notions regarding generic glass forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction we discuss the so called `glass transition' in which super-cooled amorphous state is formed, accompanied with a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length-scales we show that (i) the system remains ergodic at all temperatures. (ii) the number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N. (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N, showing that the graph of configurations has the `small world' property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0Comment: 10 pages, 9 figures, submitted to PR

Crossover from stationary to aging regime in glassy dynamics

We study the non-equilibrium dynamics of the spherical p-spin models in the scaling regime near the plateau and derive the corresponding scaling functions for the correlators. Our main result is that the matching between different time regimes fixes the aging function in the aging regime to $h(t)=\exp(t^{1-\mu})$. The exponent $\mu$ is related to the one giving the length of the plateau. Interestingly $1-\mu$ is quickly very small when one goes away from the dynamic transition temperature in the glassy phase. This gives new light on the interpretation of experiments and simulations where simple aging was found to be a reasonable but not perfect approximation, which could be attributed to the existence of a small but non-zero stretching exponent.Comment: 7 pages+2 figure

Metastability and small eigenvalues in Markov chains

In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.Comment: 5pp, AMSTe