I study stable spatial Langmuir solitons in plasma based on nonlinear radial oscillations of charged particles. I discuss two situations when a Langmuir soliton can be stable. In the former case the stability of solitons against the collapse is due to electron-electron interactions which result in the nonlocal terms in the nonlinear Schr\"{o}dinger equation. In the latter situation I derive the new cubic-quintic nonlinear Schr\"{o}dinger equation with accounts for the interaction of induced dipole moments of diatomic ions with a rapidly oscillating electric field and show that the collapse of Langmuir waves can be also arrested. In both cases I find the numerical solutions of the nonlinear Schr\"{o}dinger equation and analyze their stability using the Vakhitov-Kolokolov criterion. I discuss the application of my results for the description of long-lived atmospheric plasma structures. I show that, using my model, one can explain the existence of atmospheric plasmoids in the upper ionosphere. It is also demonstrated that Langmuir solitons described by the cubic-quintic nonlinear Schr\"{o}dinger equation can describe atmospheric plasmoids at the initial stages of their evolution. Note that, besides the modeling of atmospheric plasma structures...

We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pdf in the region of low values of volatility whereas the Hull and White model better approximates the empirical pdf for large values of volatility. Both models fails in describing the empirical pdf over a moderately large volatility range.; Comment: 6 pages, 2 figures

If a new heavy particle phi is produced in association with the top quark in a hadron collider, the production cross section exhibits a collinear singularity of the form log(m_phi/m_t), which can be resummed by introducing a top quark parton distribution function (PDF). We reassess the necessity of such resummation in the context of a high energy pp collider. We find that the introduction of a top PDF typically has a small effect at sqrt(S) ~ 100 TeV due to three factors: 1) alpha_s at the scale mu = m_phi is quite small when log(m_phi/m_t) is large, 2) the Bjorken x << 1 for m_phi < ~10 TeV, and 3) the kinematic region where log(m_phi/m_t) >> 1 is suppressed by phase space. We show that the effect of a top PDF is generically smaller than that of a bottom PDF in the associated production of b phi and consider the example of pp -> t H+ at next-to-leading logarithm order.; Comment: 26 pages, 7 figures; minor changes, version accepted by PRD

The choice of data that enters a global QCD analysis can have a substantial impact on the resulting parton distributions and their predictions for collider observables. One of the main reasons for this has to do with the possible presence of inconsistencies, either internal within an experiment or external between different experiments. In order to assess the robustness of the global fit, different definitions of a conservative PDF set, that is, a PDF set based on a maximally consistent dataset, have been introduced. However, these approaches are typically affected by theory biases in the selection of the dataset. In this contribution, after a brief overview of recent NNPDF developments, we propose a new, fully objective, definition of a conservative PDF set, based on the Bayesian reweighting approach. Using the new NNPDF3.0 framework, we produce various conservative sets, which turn out to be mutually in agreement within the respective PDF uncertainties, as well as with the global fit. We explore some of their implications for LHC phenomenology, finding also good consistency with the global fit result. These results provide a non-trivial validation test of the new NNPDF3.0 fitting methodology, and indicate that possible inconsistencies in the fitted dataset do not affect substantially the global fit PDFs.; Comment: 6 pages...

Molecular Density Functional Theory (MDFT) offers an efficient implicit- solvent method to estimate molecule solvation free-energies whereas conserving a fully molecular representation of the solvent. Even within a second order ap- proximation for the free-energy functional, the so-called homogeneous reference uid approximation, we show that the hydration free-energies computed for a dataset of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by two to three orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canoni- cal to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justifcation to empirical partial molar volume corrections that have been proposed recently.; Comment: Version with correct equation numbers is here: http://compchemmpi.wikispaces.com/file/view/sergiievskyi_et_al.pdf/513575848/sergiievskyi_et_al.pdf Supporting information available online at: http://compchemmpi.wikispaces.com/file/view/SuppInf_sergiievskyi_et_al_07-04-2014.pdf/513576008/SuppInf_sergiievskyi_et_al_07-04-2014.pdf

We report resonant multiple Andreev relections in a multiwall carbon nanotube quantum dot coupled to superconducting leads. The position and magnitude of the subharmonic gap structure is found to depend strongly on the level positions of the single-electron states which are adjusted with a gate electrode. We discuss a theoretical model of the device and compare the calculated differential conductance with the experimental data. (pdf including figures, see: www.unibas.ch/phys-meso/Research/Papers/2003/MAR-MWNT.pdf); Comment: pdf including figures, see: http://www.unibas.ch/phys-meso/Research/Papers/2003/MAR-MWNT.pdf

We measure the matter probability distribution function (PDF) via counts in cells in a volume limited subsample of the Sloan Digital Sky Survey Luminous Red Galaxy Catalog on scales from $30 h^{-1}$Mpc to $150 h^{-1}$Mpc and estimate the linear Integrated Sachs--Wolfe effect produced by supervoids and superclusters in the tail of the PDF. We characterize the PDF by the variance, $S_3$, and $S_4$, and study in simulations the systematic effects due to finite volume, survey shape and redshift distortion. We compare our measurement to the prediction of $\Lambda$CDM with linear bias and find a good agreement. We use the moments to approximate the tail of the PDF with analytic functions. A simple Gaussian model for the superstructures appears to be consistent with the claim by Granett et al. that density fluctuations on $100 h^{-1}$Mpc scales produce hot and cold spots with $\Delta T \approx 10\mu K$ on the cosmic microwave background.; Comment: 9 pages, 9 figures, 2 tables, Updates to match the article accepted to ApJ

We show that the parton distribution functions (PDF) described by the statistical model have very interesting physical properties which help to understand the structure of partons. The role of the quark helicity components is emphasized as they represent the building blocks of the PDF. In the model the sign of the polarized quarks PDF comes out in a quite natural way once the thermodynamical potentials with a given helicity are known. Introducing the concept of entropy we study the states madeof |2u + d >, |u +d +s > and $|2\bar u +\bar d >$, for a fixed Q^2, the variation with x shows that the first state has a dominant entropy due to the effect of u quark. We prove that the PDF parameters obtained from experiments give in fact an optimal solution of an entropy equation subject to constraints. We develop a new approach of the polarized gluon density based on a neural model which explains its property, in particular, a large positivity value and an agreement with the positvity constraint. An extension of this neural approach is applied to quarks giving a coherent description of the partons structure.; Comment: 22 pages, 19 figures, new results added

We revisit the one dimensional discrete time quantum walk with 3 states and the Grover coin. We derive analytic expressions for observed the localization, an long time approximation for the probability density function (PDF). We also connect the time averaged approximation to the PDF found by Inui et. al. to a spatial average of the walk. We show that this smooth approximation constitutes a proper PDF that predicts moments of the real PDF accurately.; Comment: 8 pages, revtex, for related information see http://www.physics.emory.edu/faculty/boettcher/ v2: minor changes, references added

Extending the statistical approach proposed in a parallel paper \cite% {Tessarotto2008-aa}, purpose of this work is to propose a stochastic inverse kinetic theory for small-scale hydrodynamic turbulence based on the introduction of a suitable \textit{local phase-space probability density function} (pdf). In particular, we pose the problem of the construction of Fokker-Planck kinetic models of hydrodynamic turbulence. The approach here adopted is based on the so-called IKT approach (inverse kinetic theory), developed by Ellero et al. (2004-2008) which permits an exact phase-space description of incompressible fluids based on the adoption of a local pdf. We intend to show that for prescribed models of stochasticity the present approach permits to determine uniquely the time evolution of the stochastic fluid fields. The stochastic-averaged local pdf is shown to obey a kinetic equation which, although generally non-Markovian, locally in velocity-space can be approximated by means of a suitable Fokker-planck kinetic equation. As a side result, the same pdf is proven to have generally a non-Gaussian behavior.; Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008)

We present three new sets of next-to-leading order parton distribution functions (PDFs) determined by global fits to a wide variety of data for hard scattering processes. The analysis includes target mass and higher twist corrections needed for the description of deep inelastic scattering data at large x and low Q^2, and nuclear corrections for deuterium targets. The PDF sets correspond to three different models for the nuclear effects, and provide a more realistic uncertainty range for the d quark PDF, in particular, compared with previous fits. We describe the PDF error sets for each choice of the nuclear corrections, and provide a user interface for utilizing the distributions.; Comment: 25 pages, 7 figures, 2 tables. Extended discussion of PDF parametrizations and conventions

We provide a set of general tools for studying the alignments of dark matter halos and galaxies with respect to the large scale structure. The statistics of the positioning of these objects is represented by a Probability Distribution Function (PDF) of their Euler angles. The PDF corresponding to halos located in the shells of the cosmic voids is inferred from previous results. This PDF is used to show how to recover the outcomes found for the alignments of the axes of these halos in simulations. We also explore the orientation of the angular momentum of the halos, both with respect to the halo axes and with respect to the large scale structure. We present an expression which describes well numerical results for the alignment of the angular momentum of the halo with respect to the halo axes for randomly chosen halos. We also propose a model that relates the orientation of the angular momentum with the halos axes accounting for the orientation of the halo axes with the large scale structure. This model is shown to recover accurately the observed PDF of the halo angular momentum with respect to the void radial direction. In addition, we give an expression for determining the degradation of the angular momentum intrinsic alignment when observational errors are accounted. This expression is also used to determine the departure of the observed value of the alignment from the initial expectation (as provided by the tidal torque theory) due to the rotation of the angular momentum of the halo with respect to the initial torque. For voids...

We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gaussian limit distribution in the limit T-->0. Our analysis resolves the question of temperature dependence of the PDF in this regime, for which conflicting results have been reported. We show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously-derived graphical expansion. This is confirmed by numerical simulations on two controlled approximations to the 2dXY model: the Harmonic and ``Harmonic XY'' models. The Harmonic model has no Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes progressively less skewed with increasing temperature until it closely approximates a Gaussian function above T ~ 4\pi. Near to that temperature we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity.; Comment: 15 pages, 5 figures and 1 table

We propose a global optimization algorithm based on the Sequential Monte Carlo (SMC) sampling framework. In this framework, the objective function is normalized to be a probabilistic density function (pdf), based on which a sequence of annealed target pdfs is designed to asymptotically converge on the set of global optima. A sequential importance sampling (SIS) procedure is performed to simulate the resulting targets, and the maxima of the objective function is assessed from the yielded samples. The disturbing issue lies in the design of the importance sampling (IS) pdf, which crucially influences the IS efficiency. We propose an approach to design the IS pdf online by embedding a posterior exploration (PE) procedure into each iteration of the SMC framework. The PE procedure can also explore the important regions of the parameter space supported by the target pdf. A byproduct of the PE procedure is an adaptive mechanism to design the annealing temperature schedule online. We compare the performance of the proposed algorithm with those of several existing related alternatives by applying them to over a dozen standard benchmark functions. The result demonstrates the appealing properties of our algorithm.; Comment: 14 pages, 10 figures

When a coin falls in water, its trajectory is one of four types determined by its dimensionless moment of inertia $I^\ast$ and Reynolds number Re: (A) steady; (B) fluttering; (C) chaotic; or (D) tumbling. The dynamics induced by the interaction of the water with the surface of the coin, however, makes the exact landing site difficult to predict a priori. Here, we describe a carefully designed experiment in which a coin is dropped repeatedly in water, so that we can determine the probability density functions (pdf) associated with the landing positions for each of the four trajectory types, all of which are radially symmetric about the center-drop line. In the case of the steady mode, the pdf is approximately Gaussian distributed, with variances that are small, indicating that the coin is most likely to land at the center, right below the point it is dropped from. For the other falling modes, the center is one of the least likely landing sites. Indeed, the pdf's of the fluttering, chaotic and tumbling modes are characterized by a "dip" around the center. For the tumbling mode, the pdf is a ring configuration about the center-line, with a ring width that depends on the dimensionless parameters $I^\ast$ and Re and height from which the coin is dropped. For the chaotic mode...

Without assuming any pdf for some measured parameter, we derive a predictive pdf for the outcome of a second measurement, given the outcome of the first measurement and two common assumptions about the noise. These are that (1) it is additive, and (2) it is of some known pdf. The argument is based on a Bayesian analysis of the noise when no pdf is provided for the value of the parameter. In this way we avoid assuming an ad-hoc prior. We clarify how this method of direct predictive inference is distinct from fiducial prediction. We specify the distinct flaw in the fiducial argument, and outline the importance of this development in the foundations of probability and statistics. Keywords: nonparametric predictive inference, direct pivotal argument, pivotal argument, fiducial argument, fiducial prediction, Bayesian inference, reference prior, reference class.; Comment: 7 pages

We study the classical thermodynamics of the double sinh-Gordon (DSHG) theory in 1+1 dimensions. This model theory has a double well potential, thus allowing for the existence of kinks and antikinks. Though it is nonintegrable, the DSHG model is remarkably amenable to analysis. Below we obtain exact single kink and kink lattice solutions as well as the asymptotic kink-antikink interaction. In the continuum limit, finding the classical partition function is equivalent to solving for the ground state of a Schrodinger-like equation obtained via the transfer integral method. For the DSHG model, this equation turns out to be quasi-exactly solvable. We exploit this property to obtain exact energy eigenvalues and wavefunctions for several temperatures both above and below the symmetry breaking transition temperature. The availability of exact results provides an excellent testing ground for large scale Langevin simulations. The probability distribution function (PDF) calculated from Langevin dynamics is found to be in striking agreement with the exact PDF obtained from the ground state wavefunction. This validation points to the utility of a PDF-based computation of thermodynamics utilizing Langevin methods. In addition to the PDF, field-field and field fluctuation correlation functions were computed and also found to be in excellent agreement with the exact results.; Comment: 10 pages...

We report on recent progress in the NNPDF framework of global PDF analysis. The NNPDF2.3 set is the first and only available PDF set with includes LHC data. A recent benchmark comparison of NNPDF2.3 and all other modern NNLO PDF sets with LHC data was performed. We have also studied theoretical uncertainties due to heavy quark renormalization schemes, higher twists and deuterium corrections in PDFs. Finally, we report on the release of positive definite PDF sets, based on the NNPDF2.3 analysis, specially suited for use in Monte Carlo event generators.; Comment: 4 pages, 3 figures, to appear in the proceedings of Rencontres de Moriond 2013, QCD and High Energy Interactions

Random advection of Lagrangian tracer scalar field $\theta (t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations are maintained by a source concentrated at the integral scale $L$. The statistical properties of both scalar differences and the dissipation field are analytically determined, exploiting the dynamical formulation of the model. The Gaussianity known to be present at small scales for incompressible velocity fields emerges here at large scales ($x\gg L$). These scales are shown to be excited by an inverse cascade of $\theta ^{2}$ and the probability distribution function (PDF) of the corresponding scalar differences to approach the Gaussian form, as larger and larger scales are considered. Small scales ($x\ll L$) statistics is shown to be strongly non-Gaussian. Collapse of scaling exponents for scalar structure functions\thinspace takes place: moments of order $p\ge 1$ scale all linearly, independently of the order $p$. Smooth scaling $x^{p}$ is found for $-1

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Schinzel's original problem was to describe when an expression f(x)-g(y), with f,g nonconstant and having complex coefficients, is reducible. We call such an (f,g) a Schinzel pair if this happens nontrivially: f(x)-g(y) is newly reducible. Fried accomplished this as a special case of a result in "http://www.math.uci.edu/~mfried/paplist-ff/dav-red.pdf">dav-red.pdf, when f is indecomposable. That work featured using primitive permutation representations. Even after 42 years going beyond using primitivity is a challenge to the monodromy method despite many intervening related papers (see http://www.math.uci.edu/~mfried/paplist-ff/UMStory.pdf">UMStory.pdf. Here we develop a formula for branch cycles that characterizes Schinzel pairs satisfying a condition of Avanzi, Gusic and Zannier and relate it to this ongoing story.; Comment: 15 pages, 1 figure, to Appear in Acta Arithmetica early 2012 for the 75th birthday volume for Andrzej Schinzel