Atomic step motion during the dewetting of ultra-thin films

We report on three key processes involving atomic step motion during the dewetting of thin solid films: (i) the growth of an isolated island nucleated far from a hole, (ii) the spreading of a monolayer rim, and (iii) the zipping of a monolayer island along a straight dewetting front. Kinetic Monte Carlo results are in good agreement with simple analytical models assuming diffusion-limited dynamics.Comment: 7 pages, 5 figure

Weakly versus highly nonlinear dynamics in 1D systems

We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order parameter, or a concentration profile. We show that two types of dynamics occur around the transition: weakly nonlinear dynamics, or highly nonlinear dynamics. The conditions under which highly nonlinear evolution equations appear are determined, and their generic form is derived. Finally, examples are discussed.Comment: to be published in Europhys. Let

Spin Glass Computations and Ruelle's Probability Cascades

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.Comment: 20 page

Persistence and survival in equilibrium step fluctuations

Results of analytic and numerical investigations of first-passage properties of equilibrium fluctuations of monatomic steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probability of persistent large deviations are considered. Results of experiments in which dynamical scanning tunneling microscopy is used to evaluate these first-passage properties for steps with different microscopic mechanisms of mass transport are also presented and interpreted in terms of theoretical predictions for appropriate models. Effects of discrete sampling, finite system size and finite observation time, which are important in understanding the results of experiments and simulations, are discussed.Comment: 30 pages, 12 figures, review paper for a special issue of JSTA

Short-range spin glasses and Random Overlap Structures

Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on $\Z^d$ with periodic boundary conditions are studied. ROSt's are $\N\times\N$ random matrices whose entries are the overlaps of spin configurations sampled from the Gibbs measure. Since the ROSt construction is the same for mean-field models (like the Sherrington-Kirkpatrick model) as for short-range ones (like the EA model), the setup is a good common ground to study the effect of dimensionality on the properties of the Gibbs measure. In this spirit, it is shown, using translation invariance, that the ROSt of the EA model possesses a local stability that is stronger than stochastic stability, a property known to hold at almost all temperatures in many spin glass models with Gaussian couplings. This fact is used to prove stochastic stability for the EA spin glass at all temperatures and for a wide range of coupling distributions. On the way, a theorem of Newman and Stein about the pure state decomposition of the EA model is recovered and extended.Comment: 27 page

The homotopy type of the loops on (n−1)(n-1)-connected (2n+1)(2n+1)-manifolds

For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are determined by the rank of the free Abelian part of the homology. Moreover, we show that these $p$-local homotopy groups can be expressed as a direct sum of $p$-local homotopy groups of spheres. The integral homotopy type of the loop space is also computed and shown to depend only on the rank of the free Abelian part and the torsion subgroup.Comment: Trends in Algebraic Topology and Related Topics, Trends Math., Birkhauser/Springer, 2018. arXiv admin note: text overlap with arXiv:1510.0519

MELODIE: A whole-farm model to study the dynamics of nutrients in dairy and pig farms with crops

In regions of intensive pig and dairy farming, nutrient losses to the environment at farm level are a source of concern for water and air quality. Dynamic models are useful tools to evaluate the effects of production strategies on nutrient flows and losses to the environment. This paper presents the development of a new whole-farm model upscaling dynamic models developed at the field or animal scale. The model, called MELODIE, is based on an original structure with interacting biotechnical and decisional modules. Indeed, it is supported by an ontology of production systems and the associated programming platform DIESE. The biotechnical module simulates the nutrient flows in the different animal, soil and crops and manure sub-models. The decision module relies on an annual optimization of cropping and spreading allocation plans, and on the flexible execution of activity plans for each simulated year. These plans are examined every day by an operational management sub-model and their application is context dependent. As a result, MELODIE dynamically simulates the flows of carbon, nitrogen, phosphorus, copper, zinc and water within the whole farm over the short and long-term considering both the farming system and its adaptation to climatic conditions. Therefore, it is possible to study both the spatial and temporal heterogeneity of the environmental risks, and to test changes of practices and innovative scenarios. This is illustrated with one example of simulation plan on dairy farms to interpret the Nitrogen farm-gate budget indicator. It shows that this indicator is able to reflect small differences in Nitrogen losses between different systems, but it can only be interpreted using a mobile average, not on a yearly basis. This example illustrates how MELODIE could be used to study the dynamic behaviour of the system and the dynamic of nutrient flows. Finally, MELODIE can also be used for comprehensive multi-criterion assessments, and it also constitutes a generic and evolving framework for virtual experimentation on animal farming systems. (Résumé d'auteur

Epidemics on contact networks: a general stochastic approach

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our systematic framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible (SIS) and susceptible-infectious-removed (SIR) dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.Comment: Main document: 16 pages, 7 figures. Electronic Supplementary Material (included): 6 pages, 1 tabl

Borcherds symmetries in M-theory

It is well known but rather mysterious that root spaces of the $E_k$ Lie groups appear in the second integral cohomology of regular, complex, compact, del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms) of toroidal compactifications of M theory. Their Borel subgroups are actually subgroups of supergroups of finite dimension over the Grassmann algebra of differential forms on spacetime that have been shown to preserve the self-duality equation obeyed by all bosonic form-fields of the theory. We show here that the corresponding duality superalgebras are nothing but Borcherds superalgebras truncated by the above choice of Grassmann coefficients. The full Borcherds' root lattices are the second integral cohomology of the del Pezzo surfaces. Our choice of simple roots uses the anti-canonical form and its known orthogonal complement. Another result is the determination of del Pezzo surfaces associated to other string and field theory models. Dimensional reduction on $T^k$ corresponds to blow-up of $k$ points in general position with respect to each other. All theories of the Magic triangle that reduce to the $E_n$ sigma model in three dimensions correspond to singular del Pezzo surfaces with $A_{8-n}$ (normal) singularity at a point. The case of type I and heterotic theories if one drops their gauge sector corresponds to non-normal (singular along a curve) del Pezzo's. We comment on previous encounters with Borcherds algebras at the end of the paper.Comment: 30 pages. Besides expository improvements, we exclude by hand real fermionic simple roots when they would naively aris