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Primordial Black Holes in non-linear perturbation theory

Hidalgo, Juan Carlos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/10/2009 Português
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This thesis begins with a study of the origin of cosmological fluctuations with special attention to those cases in which the non-Gaussian correlation functions are large. The analysis shows that perturbations from an almost massless auxiliary field generically produce large values of the non-linear parameter f_NL. The effects of including non-Gaussian correlation functions in the statistics of cosmological structure are explored by constructing a non-Gaussian probability distribution function (PDF). Such PDF is derived for the comoving curvature perturbation from first principles in the context of quantum field theory, with n-point correlation functions as the only input. The non-Gaussian PDF is then used to explore two important problems in the physics of primordial black holes (PBHs): First, to compute non-Gaussian corrections to the number of PBHs generated from the primordial curvature fluctuations. The second application concerns new cosmological observables. The formation of PBHs is known to depend on two main physical characteristics: the strength of the gravitational field produced by the initial curvature inhomogeneity and the pressure gradient at the edge of the curvature configuration. We account for the probability of finding these configurations by using two parameters: The amplitude of the inhomogeneity and its second radial derivative...

Particle drift in turbulent flows: the influence of local structure and inhomogeneity

Reeks, Michael W.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The way particles interact with turbulent structures, particularly in regions of high vorticity and strain rate, has been investigated in simulations of homogeneous turbulence and in simple flows which have a periodic or persistent structure e.g. separating flows and mixing layers. The influence on both settling under gravity and diffusion has been reported and the divergence (compressibility) of the underlying particle velocity field along a particle trajectory has been recognized as an important quantity in quantifying these features. This paper shows how these features can be incorporated in a formal way into a two-fluid model of the dispersed particle phase. In particular the PDF equation for the particle velocity and position is formerly derived on the basis of a stochastic process that involves the statistics of both the particle velocity and local compressibility along particle trajectories. The PDF equation gives rise to contributions to both the drift and particle diffusion coefficient that depend upon the correlation of these quantities with the local carrier flow velocity. Key Words: turbulent structures, particle dispersion, drift, PDF approach; Comment: 14 pages, 2 figures,4th Int. Conf. on Multiphase Flow, N. Orleans USA May 27-June 1...

Non-Gaussian Statistics of Multiple Filamentation

Lushnikov, Pavel M.; Vladimirova, Natalia
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/05/2010 Português
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We consider the statistics of light amplitude fluctuations for the propagation of a laser beam subjected to multiple filamentation in an amplified Kerr media, with both linear and nonlinear dissipation. Dissipation arrests the catastrophic collapse of filaments, causing their disintegration into almost linear waves. These waves form a nearly-Gaussian random field which seeds new filaments. For small amplitudes the probability density function (PDF) of light amplitude is close to Gaussian, while for large amplitudes the PDF has a long power-like tail which corresponds to strong non-Gaussian fluctuations, i.e. intermittency of strong optical turbulence. This tail is determined by the universal form of near singular filaments and the PDF for the maximum amplitudes of the filaments.

Scaled unscented transform Gaussian sum filter: theory and application

Luo, Xiaodong; Moroz, Irene M.; Hoteit, Ibrahim
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/05/2010 Português
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In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem...

The advection-condensation model and water vapour PDFs

Sukhatme, Jai; Young, William R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/05/2011 Português
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The statistically steady humidity distribution resulting from an interaction of advection, modeled as an uncorrelated random walk of moist parcels on an isentropic surface, and a vapour sink, modeled as immediate condensation whenever the specific humidity exceeds a specified saturation humidity, is explored with theory and simulation. A source supplies moisture at the deep-tropical southern boundary of the domain, and the saturation humidity is specified as a monotonically decreasing function of distance from the boundary. The boundary source balances the interior condensation sink, so that a stationary spatially inhomogeneous humidity distribution emerges. An exact solution of the Fokker-Planck equation delivers a simple expression for the resulting probability density function (PDF) of the water vapour field and also of the relative humidity. This solution agrees completely with a numerical simulation of the process, and the humidity PDF exhibits several features of interest, such as bimodality close to the source and unimodality further from the source. The PDFs of specific and relative humidity are broad and non-Gaussian. The domain averaged relative humidity PDF is bimodal with distinct moist and dry peaks, a feature which we show agrees with middleworld isentropic PDFs derived from the ERA interim dataset.; Comment: 13 pages...

Primordial Non-Gaussianity and Extreme-Value Statistics of Galaxy Clusters

Chongchitnan, Sirichai; Silk, Joseph
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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What is the size of the most massive object one expects to find in a survey of a given volume? In this paper, we present a solution to this problem using Extreme-Value Statistics, taking into account primordial non-Gaussianity and its effects on the abundance and the clustering of rare objects. We calculate the probability density function (pdf) of extreme-mass clusters in a survey volume, and show how primordial non-Gaussianity shifts the peak of this pdf. We also study the sensitivity of the extreme-value pdfs to changes in the mass functions, survey volume, redshift coverage and the normalization of the matter power spectrum, {\sigma}_8. For 'local' non-Gaussianity parametrized by f_NL, our correction for the extreme-value pdf due to the bias is important when f_NL > O(100), and becomes more significant for wider and deeper surveys. Applying our formalism to the massive high-redshift cluster XMMUJ0044.0-2-33, we find that its existence is consistent with f_NL = 0, although the conclusion is sensitive to the assumed values of the survey area and {\sigma}_8. We also discuss the convergence of the extreme-value distribution to one of the three possible asymptotic forms, and argue that the convergence is insensitive to the presence of non-Gaussianity.; Comment: Revised version...

A QCD analysis of ZEUS data including DIS inclusive cross sections with longitudinally polarised leptons and data run at lower proton beam energies

Cooper-Sarkar, A M
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/07/2009 Português
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New ZEUS data are added into the NLO QCD analysis of the ZEUS-JETS PDF fit. The addition of high-$Q^2$ NC and CC $e^-p$ inclusive cross-section data improves the determination of the $u$-valence quark at high $x$. The addition of high-$Q^2$ CC $e^+p$ inclusive cross-section data improves the determination of the $d$-valence quark at high $x$. The addition of lower-$Q^2$ NC $e^+p$ inclusive cross-section data, run at three different proton beam energies, improves the determination of the sea and gluon PDFs at small $x$. The new PDF fit is called the ZEUS09 PDF fit.; Comment: Invited talk on behalf of the ZEUS Collaboration at DIS 2009, The 17th International Workshop on Deep Inelastic Scattering, Madrid, April 2009. % pages, 6 figures

Recovering the topology of the IGM at z~2

Caucci, S.; Colombi, S.; Pichon, C.; Rollinde, E.; Petitjean, P.; Sousbie, T.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/01/2008 Português
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We investigate how well the 3D density field of neutral hydrogen in the Intergalactic Medium (IGM) can be reconstructed using the Lyman-alpha absorptions observed along lines of sight to quasars separated by arcmin distances in projection on the sky. We use cosmological hydrodynamical simulations to compare the topologies of different fields: dark matter, gas and neutral hydrogen optical depth and to investigate how well the topology of the IGM can be recovered from the Wiener interpolation method implemented by Pichon et al. (2001). The global statistical and topological properties of the recovered field are analyzed quantitatively through the power-spectrum, the probability distribution function (PDF), the Euler characteristics, its associated critical point counts and the filling factor of underdense regions. The local geometrical properties of the field are analysed using the local skeleton by defining the concept of inter-skeleton distance. At scales larger than ~1.4 , where is the mean separation between lines of sight, the reconstruction accurately recovers the topological features of the large scale density distribution of the gas, in particular the filamentary structures. At scales larger than the intrinsic smoothing length of the inversion procedure...

Scaling in Gravitational Clustering, 2D and 3D Dynamics

Munshi, D.; Bernardeau, F.; Melott, A. L.; Schaeffer, R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/07/1997 Português
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Perturbation Theory (PT) applied to a cosmological density field with Gaussian initial fluctuations suggests a specific hierarchy for the correlation functions when the variance is small. In particular quantitative predictions have been made for the moments and the shape of the one-point probability distribution function (PDF) of the top-hat smoothed density. In this paper we perform a series of systematic checks of these predictions against N-body computations both in 2D and 3D with a wide range of featureless power spectra. In agreement with previous studies, we found that the reconstructed PDF-s work remarkably well down to very low probabilities, even when the variance approaches unity. Our results for 2D reproduce the features for the 3D dynamics. In particular we found that the PT predictions are more accurate for spectra with less power on small scales. The nonlinear regime has been explored with various tools, PDF-s, moments and Void Probability Function (VPF). These studies have been done with unprecedented dynamical range, especially for the 2D case, allowing in particular more robust determinations of the asymptotic behaviour of the VPF. We have also introduced a new method to determine the moments based on the factorial moments. Results using this method and taking into account the finite volume effects are presented.; Comment: 13 pages...

Stochastic Approach to Plasticity and Yield in Amorphous Solids

Hentschel, H. G. E.; Jaiswal, Prabhat K.; Procaccia, Itamar; Sastry, Srikanth
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/09/2015 Português
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We focus on the probability distribution function (pdf) $P(\Delta \gamma; \gamma)$ where $\Delta \gamma$ are the {\em measured} strain intervals between plastic events in an athermal strained amorphous solids, and $\gamma$ measures the accumulated strain. The tail of this distribution as $\Delta \gamma\to 0$ (in the thermodynamic limit) scales like $\Delta \gamma^\eta$. The exponent $\eta$ is related via scaling relations to the tail of the pdf of the eigenvalues of the {\em plastic modes} of the Hessian matrix $P(\lambda)$ which scales like $\lambda^\theta$, $\eta=(\theta-1)/2$. The numerical values of $\eta$ or $\theta$ can be determined easily in the unstrained material and in the yielded state of plastic flow. Special care is called for in the determination of these exponents between these states as $\gamma$ increases. Determining the $\gamma$ dependence of the pdf $P(\Delta \gamma; \gamma)$ can shed important light on plasticity and yield. We conclude that the pdf's of both $\Delta \gamma$ and $\lambda$ are not continuous functions of $\gamma$. In slowly quenched amorphous solids they undergo two discontinuous transitions, first at $\gamma=0^+$ and then at the yield point $\gamma=\gamma_{_{\rm Y}}$ to plastic flow. In quickly quenched amorphous solids the second transition is smeared out due to the non existing stress peak before yield. The nature of these transitions and scaling relations with the system size dependence of $\langle \Delta \gamma\rangle$ are discussed.; Comment: 8 pages...

Quantitative size-dependent structure and strain determination of CdSe nanoparticles using atomic pair distribution function analysis

Masadeh, A. S.; Bozin, E.; Farrow, C. L.; Paglia, G.; Juhas, P.; Karkamkar, A.; Kanatzidis, M. G.; Billinge, S. J. L.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The size-dependent structure of CdSe nanoparticles, with diameters ranging from 2 to 4 nm, has been studied using the atomic pair distribution function (PDF) method. The core structure of the measured CdSe nanoparticles can be described in terms of the wurtzite atomic structure with extensive stacking faults. The density of faults in the nanoparticles ~50% . The diameter of the core region was extracted directly from the PDF data and is in good agreement with the diameter obtained from standard characterization methods suggesting that there is little surface amorphous region. A compressive strain was measured in the Cd-Se bond length that increases with decreasing particle size being 0.5% with respect to bulk CdSe for the 2 nm diameter particles. This study demonstrates the size-dependent quantitative structural information that can be obtained even from very small nanoparticles using the PDF approach.; Comment: 10 pages, 7 figures and 3 tables. Phys. Rev. B, submitted (2007)

Review of AdS/CFT Integrability: An Overview

Beisert, Niklas; Ahn, Changrim; Alday, Luis F.; Bajnok, Zoltan; Drummond, James M.; Freyhult, Lisa; Gromov, Nikolay; Janik, Romuald A.; Kazakov, Vladimir; Klose, Thomas; Korchemsky, Gregory P.; Kristjansen, Charlotte; Magro, Marc; McLoughlin, Tristan; Min
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection we present an overview of the achievements and the status of this subject as of the year 2010.; Comment: 31 pages, v2: reference added, references to other chapters updated, v3: footnote 1 on location of references added, v4: minor changes, references added, accepted for publication in Lett. Math. Phys, v5: minor corrections, links to chapters updated, attached IntAdS.pdf with all chapters in one file, see http://arxiv.org/src/1012.3982/anc/IntAdS.pdf or http://www.phys.ethz.ch/~nbeisert/IntAdS.pdf

The Nyquist-Shannon sampling theorem and the atomic pair distribution function

Farrow, Christopher L.; Shaw, Margaret; Kim, Hyunjeong; Juhas, Pavol; Billinge, Simon J. L.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/04/2011 Português
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We have systematically studied the optimal real-space sampling of atomic pair distribution data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we demonstrate that the optimal sampling is bounded by the Nyquist interval described by the Nyquist-Shannon sampling theorem. Near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty prediction. Furthermore, refinements using sparsely sampled data may run many times faster than using oversampled data. This investigation establishes a theoretically sound limit on the amount of information contained in the PDF, which has ramifications towards how PDF data are modeled.; Comment: 10 pages, 4 figures

The rule for a subdiffusive particle in an extremely diverse environment

Flomenbom, Ophir
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The dynamics of a subdiffusive continuous time random walker in an inhomogeneous environment is analyzed. In each microscopic jump, a random time is drawn from a waiting time probability density function (WT-PDF) that decays as a power law: phi(t;k)~k/(1+kt)^(1+beta), 0 beta;, mu=beta, but when 1-gamma

Dissecting the spin distribution of Dark Matter halos

Antonuccio-Delogu, V.; Dobrotka, A.; Becciani, U.; Cielo, S.; Giocoli, C.; Maccio', A. V.; Romeo, A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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(Abridged) We apply a very general statistical theorem introduced by Cramer (1936) to study the origin of the deviations of the halo spin PDF from the reference lognormal shape. We find that these deviations originate from correlations between two quantities entering the definition of spin, namely the ratio $J/M^{5/2}$ (which depends only on mass) and the total gravitational binding energy $E$. To reach this conclusion, we have made usage of the results deduced from two high spatial- and mass resolution simulations. Our simulations cover a relatively small volume and produce a sample of more than 16.000 gravitationally bound halos, each traced by at least 300 particles. We verify that our results are stable to different systematics, by comparing our results with those derived by the GIF2 and by a more recent simulation performed by Maccio' et al. We find that the spin probability distribution function shows systematic deviations from a lognormal, at all redshifts z <= 1. These deviations depend on mass and redshift: at small masses they change little with redshift, and also the best lognormal fits are more stable. The J-M relationship is well described by a power law of exponent $\alpha$ very near to the linear theory prediction (alpha=5/3)...

Lyman Break Galaxies and the Lyman-alpha Forest

Kollmeier, Juna A.; Weinberg, David H.; Dave', Romeel; Katz, Neal
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We use hydrodynamic simulations to predict correlations between Lya forest absorption and galaxies at redshift z~3. The probability distribution function (PDF) of Lya flux decrements shifts systematically towards higher values in the vicinity of galaxies, reflecting the overdense environments in which these galaxies reside. The predicted signal remains strong in spectra smoothed over 50-200 km/s, allowing tests with moderate resolution quasar spectra. The strong bias of high redshift galaxies towards high density regions imprints a clear signature on the flux PDF, but the predictions are not sensitive to galaxy baryon mass or star formation rate, and they are similar for galaxies and for dark matter halos. The dependence of the flux PDF on galaxy proximity is sensitive to redshift determination errors, with rms errors of 150-300 km/s substantially weakening the predicted trends. On larger scales, the mean galaxy overdensity in a cube of 5 or 10 Mpc/h (comoving) is strongly correlated with the mean Lya flux decrement on a line of sight through the cube center. The slope of the correlation is ~3 times steeper for galaxies than for dark matter as a result of galaxy bias. The predicted large scale correlation is in qualitative agreement with recently reported observational results. However...

The distribution of annihilation luminosities in dark matter substructure

Koushiappas, Savvas M.; Zentner, Andrew R.; Kravtsov, Andrey V.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We calculate the probability distribution function (PDF) of the expected annihilation luminosities of dark matter subhalos as a function of subhalo mass and distance from the Galactic center using a semi-analytical model of halo evolution. We find that the PDF of luminosities is relatively broad, exhibiting a spread of as much as an order of magnitude at fixed subhalo mass and halo-centric distance. The luminosity PDF allows for simple construction of mock samples of gamma-ray luminous subhalos and assessment of the variance in among predicted gamma-ray signals from dark matter annihilation. Other applications include quantifying the variance among the expected luminosities of dwarf spheroidal galaxies, assessing the level at which dark matter annihilation can be a contaminant in the expected gamma-ray signal from other astrophysical sources, as well as estimating the level at which nearby subhalos can contribute to the antimatter flux.; Comment: 10 pages, 5 figures. Replaced with version accepted for publication in Phys. Rev. D

Finite-Horizon Parameterizing Manifolds, and Applications to Suboptimal Control of Nonlinear Parabolic PDEs

Chekroun, Mickaël D.; Liu, Honghu
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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This article proposes a new approach based on finite-horizon parameterizing manifolds (PMs) for the design of low-dimensional suboptimal controllers to optimal control problems of nonlinear partial differential equations (PDEs) of parabolic type. Given a finite horizon $[0,T]$ and a low-mode truncation of the PDE, a PM provides an approximate parameterization of the uncontrolled high modes by the controlled low ones so that the unexplained high-mode energy is reduced, in an $L^2$-sense, when this parameterization is applied. Analytic formulas of such PMs are derived by application of the method of pullback approximation of the high-modes (Chekroun, Liu, and Wang, 2013, http://arxiv.org/pdf/1310.3896v1.pdf). These formulas allow for an effective derivation of reduced ODE systems, aimed to model the evolution of the low-mode truncation of the controlled state variable, where the high-mode part is approximated by the PM function applied to the low modes. A priori error estimates between the resulting PM-based low-dimensional suboptimal controller $u_R^\ast$ and the optimal controller $u^*$ are derived. These estimates demonstrate that the closeness of $u_R^\ast$ to $u^*$ is mainly conditioned on two factors: (i) the parameterization defect of a given PM...

Robust Distributed Maximum Likelihood Estimation with Dependent Quantized Data

Shen, Xiaojing; Varshney, Pramod K.; Zhu, Yunmin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic parameters. The parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe dependence of observations across sensors. Since MLE with a single quantizer is sensitive to the choice of thresholds due to the uncertainty of pdf, we concentrate on MLE with multiple groups of quantizers (which can be determined by the use of prior information or some heuristic approaches) to fend off against the risk of a poor/outlier quantizer. The asymptotic efficiency of the MLE scheme with multiple quantizers is proved under some regularity conditions and the asymptotic variance is derived to be the inverse of a weighted linear combination of Fisher information matrices based on multiple different quantizers which can be used to show the robustness of our approach. As an illustrative example, we consider an estimation problem with a bivariate non-Gaussian pdf that has applications in distributed constant false alarm rate (CFAR) detection systems. Simulations show the robustness of the proposed MLE scheme especially when the number of quantized measurements is small.; Comment: submitted to journal

Trajectory statistics of confined L\'{e}vy flights and Boltzmann-type equilibria

Zaba, Mariusz; Garbaczewski, Piotr; Stephanovich, Vladimir
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/03/2013 Português
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We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise, where Langevin representation is absent. In view of the L\'{e}vy noise sensitivity to environmental inhomogeneities, the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Here, we infer pdf $\rho (x,t)$ based on numerical path-wise simulation of the underlying jump-type process. A priori given data are jump transition rates entering the master equation for $\rho (x,t)$ and its target pdf $\rho_*(x)$. To simulate the above processes, we construct a suitable modification of the Gillespie algorithm, originally invented in the chemical kinetics context. We exemplified our algorithm simulating different jump-type processes and discuss the dynamics of real physical systems where it can be useful.; Comment: Presented at 25th Marian Smoluchowski Symposium on Statistical Physics, Cracow, Sept. 10-13, 2012