Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces

We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal fluctuation $\sim \sqrt{2/(\pi K)} \ln N$ and the asymptotic behavior of the whole distribution $P(m) \sim N^2 e^{-{\rm (const)} N^2 e^{-\sqrt{2\pi K} m} - \sqrt{2\pi K} m}$ for $m$ finite with $N^2$ and $K$ the interface size and tension, respectively. The standardized form of $P(m)$ does not depend on $N$ or $K$, but shows a good agreement with Gumbel's first asymptote distribution with a particular non-integer parameter. The effects of the correlations among individual fluctuations on the extreme value statistics are discussed in our findings.Comment: 4 pages, 4 figures, final version in PR

Distribution of meteoric smoke ? sensitivity to microphysical properties and atmospheric conditions

International audienceMeteoroids entering the Earth's atmosphere experience strong deceleration and ablate, whereupon the resulting material is believed to re-condense to nanometre-size "smoke particles". These particles are thought to be of great importance for many middle atmosphere phenomena, such as noctilucent clouds, polar mesospheric summer echoes, metal layers, and heterogeneous chemistry. The properties and distribution of meteoric smoke depend on poorly known or highly variable factors such as the amount, composition and velocity of incoming meteoric material, the efficiency of coagulation, and the state and circulation of the atmosphere. This work uses a one-dimensional microphysical model to investigate the sensitivities of meteoric smoke properties to these poorly known or highly variable factors. The resulting uncertainty or variability of meteoric smoke quantities such as number density, mass density, and size distribution are determined. It is found that the two most important factors are the efficiency of the coagulation and background vertical wind. The seasonal variation of the vertical wind in the mesosphere implies strong global and temporal variations in the meteoric smoke distribution. This contrasts the simplistic picture of a homogeneous global meteoric smoke layer, which is currently assumed in many studies of middle atmospheric phenomena. In particular, our results suggest a very low number of nanometre-sized smoke particles at the summer mesopause where they are thought to serve as condensation nuclei for noctilucent clouds

Sensitivity of meteoric smoke distribution to microphysical properties and atmospheric conditions

International audienceMeteoroids entering the Earth's atmopsphere experience strong deceleration and ablate, whereupon the resulting material is believed to re-condense to nanometre-size "smoke particles". These particles are thought to be of great importance for many middle atmosphere phenomena, such as noctilucent clouds, polar mesospheric summer echoes, metal layers, and heterogeneous chemistry. The properties and distribution of meteoric smoke depend on poorly known or highly variable factors such as the amount, composition and velocity of incoming meteoric material, the efficiency of coagulation, and the state and circulation of the atmosphere. This work uses a one-dimensional microphysical model to investigate the sensitivities of meteoric smoke properties to these poorly known or highly variable factors. The resulting uncertainty or variability of meteoric smoke quantities such as number density, mass density, and size distribution are determined. It is found that the two most important factors are the efficiency of the coagulation and background vertical wind. The seasonal variation of the vertical wind in the mesosphere implies strong global and temporal variations in the meteoric smoke distribution. This contrasts the simplistic picture of a homogeneous global meteoric smoke layer, which is currently assumed in many studies of middle atmospheric phenomena. In particular, our results suggest a very low number of nanometre-sized smoke particles at the summer mesopause where they are thought to serve as condensation nuclei for noctilucent clouds

Ensemble averageability in network spectra

The extreme eigenvalues of connectivity matrices govern the influence of the network structure on a number of network dynamical processes. A fundamental open question is whether the eigenvalues of large networks are well represented by ensemble averages. Here we investigate this question explicitly and validate the concept of ensemble averageability in random scale-free networks by showing that the ensemble distributions of extreme eigenvalues converge to peaked distributions as the system size increases. We discuss the significance of this result using synchronization and epidemic spreading as example processes.Comment: 4 pages, 4 figure

Mapping of Coulomb gases and sine-Gordon models to statistics of random surfaces

We introduce a new class of sine-Gordon models, for which interaction term is present in a region different from the domain over which quadratic part is defined. We develop a novel non-perturbative approach for calculating partition functions of such models, which relies on mapping them to statistical properties of random surfaces. As a specific application of our method, we consider the problem of calculating the amplitude of interference fringes in experiments with two independent low dimensional Bose gases. We calculate full distribution functions of interference amplitude for 1D and 2D gases with nonzero temperatures.Comment: final published versio

Record statistics in random vectors and quantum chaos

The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records that is non-universal but tends to the Gumbel distribution asymptotically. The quantum standard map is used to study these statistics for the effect of correlations apart from normalization. It is seen that in the mixed phase space regime the number of intensity records is a power law in the dimensionality of the state as opposed to the logarithmic growth for random states.Comment: figures redrawn, discussion adde

Role of disorder in the size-scaling of material strength

We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and another controlled by stress-concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone. Its existence and scaling properties are only revealed by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.Comment: 4 pages 5 figure

Relative Importance of Nitric Oxide Physical Drivers in the Lower Thermosphere

Nitric oxide (NO) observations from the Solar Occultation for Ice Experiment and Student Nitric Oxide Explorer satellite instruments are investigated to determine the relative importance of drivers of short‐term NO variability. We study the variations of deseasonalized NO anomalies by removing a climatology, which explains between approximately 70% and 90% of the total NO budget, and relate them to variability in geomagnetic activity and solar radiation. Throughout the lower thermosphere geomagnetic activity is the dominant process at high latitudes, while in the equatorial region solar radiation is the primary source of short‐term NO changes. Consistent results are obtained on estimated geomagnetic and radiation contributions of NO variations in the two data sets, which are nearly a decade apart in time. The analysis presented here can be applied to model simulations of NO to investigate the accuracy of the parametrized physical drivers

In-depth analysis of the Naming Game dynamics: the homogeneous mixing case

Language emergence and evolution has recently gained growing attention through multi-agent models and mathematical frameworks to study their behavior. Here we investigate further the Naming Game, a model able to account for the emergence of a shared vocabulary of form-meaning associations through social/cultural learning. Due to the simplicity of both the structure of the agents and their interaction rules, the dynamics of this model can be analyzed in great detail using numerical simulations and analytical arguments. This paper first reviews some existing results and then presents a new overall understanding.Comment: 30 pages, 19 figures (few in reduced definition). In press in IJMP

Right tail expansion of Tracy-Widom beta laws

Using loop equations, we compute the large deviation function of the maximum eigenvalue to the right of the spectrum in the Gaussian beta matrix ensembles, to all orders in 1/N. We then give a physical derivation of the all order asymptotic expansion of the right tail Tracy-Widom beta laws, for all positive beta, by studying the double scaling limit.Comment: 23 page