Consider randomly picked points inside the n-dimensional unit hypersphere centered at the origin of the Cartesian coordinate system. The Cartesian coordinates of the points are random variables, which form an n-dimensional vector for each point. Observing only the x-coordinate I obtained its probability density function (PDF). I show that it is related to the Gaussian distribution: in limit its companion PDF?? converges to the PDF of the standard normal distribution.; Comment: 7 pages, 3 figures

We consider a one dimensional asymmetric random walk whose jumps are identical, independent and drawn from a distribution \phi(\eta) displaying asymmetric power law tails (i.e. \phi(\eta) \sim c/\eta^{\alpha +1} for large positive jumps and \phi(\eta) \sim c/(\gamma |\eta|^{\alpha +1}) for large negative jumps, with 0 < \alpha < 2). In absence of boundaries and after a large number of steps n, the probability density function (PDF) of the walker position, x_n, converges to an asymmetric L\'evy stable law of stability index \alpha and skewness parameter \beta=(\gamma-1)/(\gamma+1). In particular the right tail of this PDF decays as c n/x_n^{1+\alpha}. Much less is known when the walker is confined, or partially confined, in a region of the space. In this paper we first study the case of a walker constrained to move on the positive semi-axis and absorbed once it changes sign. In this case, the persistence exponent \theta_+, which characterizes the algebraic large time decay of the survival probability, can be computed exactly and we show that the tail of the PDF of the walker position decays as c \, n/[(1-\theta_+) \, x_n^{1+\alpha}]. This last result can be generalized in higher dimensions such as a planar L\'evy walker confined in a wedge with absorbing walls. Our results are corroborated by precise numerical simulations.; Comment: 16 pages...

This thesis discusses the search for supersymmetry at the future Large Hadron Collider (LHC) and the ongoing construction of one of the four large LHC experiments, the Compact Muon Solenoid (CMS), and focuses on the detection of signals from the annihilation of supersymmetric dark matter in the spectra of cosmic rays. Measurements of cosmic ray antiparticles, such as positrons, can impose strong constraints on the nature of new physics beyond the Standard Model. However, cosmic ray positron measurements are experimentally very challenging due to the vast proton background. A novel approach of positron identification with the space-borne AMS-01 experiment, namely through the detection of bremsstrahlung conversion in a silicon microstrip detector, is introduced. Bremsstrahlung from protons is suppressed by a factor of more than 3*10^6 with respect to positrons. The results of the positron measurement show that the bremsstrahlung approach extends the sensitivity range of AMS-01 to positron momenta up to 50 GeV/c, which is far beyond the original scope of the experiment. At momenta above 8 GeV/c there is indication for a positron overabundance with respect to model predictions for purely secondary positron production. Therefore, the AMS-01 data lend further weight to the hints of a positron overabundance seen in the data from earlier experiments. The positron fraction measurements from the most recent experiments are combined with the results of this analysis...

An analytical expression of probability density function (PDF) of velocity fluctuation is derived with the help of the statistics based on generalized entropy (the Tsallis entropy or the R\'{e}nyi entropy). It is revealed that the derived PDF explains the detailed structure of experimentally observed PDF as well as the scaling exponents of velocity structure function. Every parameters appeared in the analysis, including the index proper to the Tsallis entropy or the R\'{e}nyi entropy, are determined, self-consistently, by making use of observed value of intermittency exponent. The experiments conducted by Lewis and Swinney (1999) are analyzed.; Comment: 4 pages, 6 figures

The Sunyaev Zel'dovich (SZ) signal is highly non-Gaussian, so the SZ power spectrum (along with the mean $y$ parameter) does not provide a complete description of the SZ effect. Therefore, SZ-based constraints on cosmological parameters and on cluster gastrophysics which assume Gaussianity will be biased. We derive an analytic expression for the $n$-point joint PDF of the SZ power spectrum. Our derivation, which is based on the halo model, has several advantages: it is expressed in an integral form which allows quick computation; it is applicable to any given survey and any given angular scale; it is straightforward to incorporate many of the complexities which arise when modeling the SZ signal. To illustrate, we use our expression to estimate $p(C_\ell)$, the one-point PDF of the SZ power spectrum. For small sky coverage (applicable to BIMA/CBI and the Sunyaev Zel'dovich Array experiments), our analysis shows that $p(C_\ell)$ on the several arc-minute scale is expected to be strongly skewed, peaking at a value well below the mean and with a long tail which extends to tail high $C_\ell$ values. In the limit of large sky coverage (applicable to the South Pole Telescope and Planck), $p(C_\ell)$ approaches a Gaussian form. However, even in this limit...

The production of artificial light curves with known statistical and variability properties is of great importance in astrophysics. Consolidating the confidence levels during cross-correlation studies, understanding the artefacts induced by sampling irregularities, establishing detection limits for future observatories are just some of the applications of simulated data sets. Currently, the widely used methodology of amplitude and phase randomisation is able to produce artificial light curves which have a given underlying power spectral density (PSD) but which are strictly Gaussian distributed. This restriction is a significant limitation, since the majority of the light curves e.g. active galactic nuclei, X-ray binaries, gamma-ray bursts show strong deviations from Gaussianity exhibiting `burst-like' events in their light curves yielding long-tailed probability distribution functions (PDFs). In this study we propose a simple method which is able to precisely reproduce light curves which match both the PSD and the PDF of either an observed light curve or a theoretical model. The PDF can be representative of either the parent distribution or the actual distribution of the observed data, depending on the study to be conducted for a given source. The final artificial light curves contain all of the statistical and variability properties of the observed source or theoretical model i.e. same PDF and PSD...

We study the relative velocity of inertial particles suspended in turbulent flows and discuss implications for dust particle collisions in protoplanetary disks. We simulate a weakly compressible turbulent flow, evolving 14 particle species with friction timescale, tau_p, covering the entire range of scales in the flow. The particle Stokes numbers, St, measuring the ratio of tau_p to the Kolmogorov timescale, are in the range from ~0.1 to ~800. Using simulation results, we show that the model by Pan & Padoan (PP10) gives satisfactory predictions for the rms relative velocity between identical particles. The probability distribution function (PDF) of the relative velocity is found to be highly non-Gaussian. The PDF tails are well described by a 4/3 stretched exponential function for particles with tau_p ~ 1-2 T_L, where T_L is the Lagrangian correlation timescale, consistent with a prediction based on PP10. The PDF approaches Gaussian only for very large particles with tau_p >~ 54 T_L. We split particle pairs at given distances into two types with low and high relative speeds, referred to as continuous and caustic types, respectively, and compute their contributions to the collision kernel. Although amplified by the effect of clustering...

We consider bosons in a harmonic trap and investigate the fluctuations of the work performed by an adiabatic change of the trap curvature. Depending on the reservoir conditions such as temperature and chemical potential that provide the initial equilibrium state, the exponentiated work average (EWA) defined in the context of the Crooks relation and the Jarzynski equality may diverge if the trap becomes wider. We investigate how the probability distribution function (PDF) of the work signals this divergence. It is shown that at low temperatures the PDF is highly asymmetric with a steep fall off at one side and an exponential tail at the other side. For high temperatures it is closer to a symmetric distribution approaching a Gaussian form. These properties of the work PDF are discussed in relation to the convergence of the EWA and to the existence of the hypothetical equilibrium state to which those thermodynamic potential changes refer that enter both the Crooks relation and the Jarzynski equality.; Comment: 9 pages, 4 figures

We use deep $8\:\mu m$ Spitzer-IRAC imaging of a massive Infrared Dark Cloud (IRDC) G028.37+00.07 to construct a Mid-Infrared (MIR) extinction map that probes mass surface densities up to $\Sigma\:\sim 1\:\rm{g~cm^{-2}}$ ($A_V\sim200\:$mag), amongst the highest values yet probed by extinction mapping. Merging with a NIR extinction map of the region, creates a high dynamic range map that reveals structures down to $A_V\sim1\:$mag. We utilize the map to: (1) Measure a cloud mass $\sim7\times10^4\:M_\odot$ within a radius of $\sim8\:$pc. $^{13}$CO kinematics indicate that the cloud is gravitationally bound. It thus has the potential to form one of the most massive young star clusters known in the Galaxy. (2) Characterize the structures of 16 massive cores within the IRDC, finding they can be fit by singular polytropic spheres with $\rho\propto{r}^{-k_\rho}$ and $k_\rho=1.3\pm0.3$. They have $\overline{\Sigma}\simeq0.1-0.4\:\rm{g~cm^{-2}}$ --- relatively low values that, along with their measured cold temperatures, suggest magnetic fields, rather than accretion-powered radiative heating, are important for controlling fragmentation of these cores. (3) Determine the $\Sigma$ (equivalently column density or $A_V$) probability distribution function (PDF) for a region that is near complete for $A_V>3\:$mag. The PDF is well fit by a single log-normal with mean $\overline{A}_V\simeq9\:$mag...

In this paper, we present an analytical approach in obtaining the probability density function (pdf) of the random decision variable Y, formed at the output of power-cubic all-optical nonlinear preprocessor followed by the photodetector. Our approach can be used to accurately evaluate the performance of ultrafast pulse detection in the presence of Gaussian noise. Through rigorous Monte-Carlo simulation, the accuracy of widely used Gaussian approximation of decision variable Y is refuted. However, in this paper we show that the so called Log-Pearson type-3 probability density function (LP3 pdf) is an excellent representation for the decision variable Y . Three distinguishable parameters of the LP3 pdf are obtained through analytical derivation of three moments of the decision variable Y . Furthermore, toward a more realistic model, in addition to ASE Gaussian noise, the effects of shot and thermal noises are also included. Finally, using the presented analytical approach, it is shown that power-cubic preprocessor outperforms its quadratic counterparts, i.e., Second Harmonic Generation (SHG) and Two Photon Absorption (TPA) devices, in high power regime where shot and thermal noises can be neglected.

Using self-gravitational hydrodynamical numerical simulations, we investigated the evolution of high-density turbulent molecular clouds swept by a colliding flow. The interaction of shock waves due to turbulence produces networks of thin filamentary clouds with a sub-parsec width. The colliding flow accumulates the filamentary clouds into a sheet cloud and promotes active star formation for initially high-density clouds. Clouds with a colliding flow exhibit a finer filamentary network than clouds without a colliding flow. The probability distribution functions (PDFs) for the density and column density can be fitted by lognormal functions for clouds without colliding flow. When the initial turbulence is weak, the column density PDF has a power-law wing at high column densities. The colliding flow considerably deforms the PDF, such that the PDF exhibits a double peak. The stellar mass distributions reproduced here are consistent with the classical initial mass function with a power-law index of $-1.35$ when the initial clouds have a high density. The distribution of stellar velocities agrees with the gas velocity distribution, which can be fitted by Gaussian functions for clouds without colliding flow. For clouds with colliding flow...

We present a method to produce mock galaxy catalogues with efficient perturbation theory schemes, which match the number density, power spectra and bispectra in real and in redshift space from N-body simulations. The essential contribution of this work is the way in which we constrain the bias parameters in the PATCHY-code. In addition of aiming at reproducing the two-point statistics, we seek the set of bias parameters, which constrain the univariate halo probability distribution function (PDF) encoding higher-order correlation functions. We demonstrate that halo catalogues based on the same underlying dark matter field with a fix halo number density, and accurately matching the power spectrum (within 2%), can lead to very different bispectra depending on the adopted halo bias model. A model ignoring the shape of the halo PDF can lead to deviations up to factors of 2. The catalogues obtained additionally constraining the shape of the halo PDF can significantly lower the discrepancy in the three-point statistics, yielding closely unbiased bispectra both in real and in redshift space; which are in general compatible with those corresponding to an N-body simulation within 10% (deviating at most up to 20%). Our calculations show that the constant linear bias of ~2 for Luminous Red Galaxy (LRG) like galaxies seen in the power spectrum...

The main focus of this thesis is the IR spectral regime, which since the 70's and 80's has revolutionised our understanding of the Universe. A multi-wavelength analysis on Extremely Red Galaxy populations is first presented in one of the most intensively observed patch of the sky, the Chandra Deep Field South. By adopting a purely statistical methodology, we consider all the photometric and spectroscopic information available on large samples of Extremely Red Objects (EROs, 553 sources), IRAC EROs (IEROs, 259 sources), and Distant Red Galaxies (DRGs, 289 sources). We derive general properties: redshift distributions, AGN host fraction, star-formation rate densities, dust content, morphology, mass functions and mass densities. The results point to the fact that EROs, IEROs, and DRGs all belong to the same population, yet seen at different phases of galaxy evolution. The second part of this thesis is dedicated to the AGN selection in the IR, with particular relevance to the James Webb Space Telescope, to be launched in 2018. We develop an improved IR criterion (using K and IRAC bands) as an alternative to existing IR AGN criteria for the z<2.5 regime, and develop another IR criterion which reliably selects AGN hosts at 0

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We present a study of the results obtained combining LO partonic matrix elements with either LO or NLO partons distributions. These are compared to the best prediction using NLO for both matrix elements and parton distributions. The aim is to determine which parton distributions are most appropriate to use in those cases where only LO matrix elements are available, e.g. as in many Monte Carlo generators. Both LO and NLO parton distributions have flaws, sometimes serious, for some processes, so a modified optimal LO set is suggested. We investigate a wide variety of process, and the LO* pdf works at least as well as, and often better than, both LO and NLO pdfs in nearly all cases.The LO* pdf set is now available in the LHAPDF package.; Comment: 40 pages, 29 figures as .ps or .eps files, the LO* pdf set is now available in LHAPDF

Protostellar jets and outflows are signatures of star formation and promising mechanisms for driving supersonic turbulence in molecular clouds. We quantify outflow-driven turbulence through three-dimensional numerical simulations using an isothermal version of the robust total variation diminishing code. We drive turbulence in real-space using a simplified spherical outflow model, analyse the data through density probability distribution functions (PDF), and investigate the Core Formation Rate per free-fall time (CFR_ff). The real-space turbulence driving method produces a negatively skewed density PDF possessing an enhanced tail on the low-density side. It deviates from the log-normal distributions typically obtained from Fourier-space turbulence driving at low densities, but can provide a good fit at high-densities, particularly in terms of mass weighted rather than volume weighted density PDF. Due to this fact, we suggest that the CFR_ff determined from a Fourier-driven turbulence model could be comparable to that of our particular real-space driving model, which has a ratio of solenoidal to compressional components from the resulting turbulence velocity fields of ~0.6.; Comment: 5 pages, 3 figures, accepted for publication in MNRASL

The contribution of physical degrees of freedom to the one-loop amplitudes of Euclidean supergravity is here evaluated in the case of flat Euclidean backgrounds bounded by a three-sphere, recently considered in perturbative quantum cosmology. The physical degrees of freedom (denoted by PDF) are picked out by imposing the supersymmetry constraints and choosing a gauge condition. Remarkably, for the massless gravitino field the PDF method and local boundary conditions lead to a result for the trace anomaly which is equal to the PDF value one obtains using spectral boundary conditions on a 3-sphere.; Comment: 23 pages, plain-tex, recently appearing in Int. J. Mod. Phys. D, volume 3, pages 593-607, September 1994. The Author would like to apologize for the delay in circulating the paper, due to technical problems now fixed

We show that the tails of the single-point velocity probability distribution function (PDF) are generally non-Gaussian in developed turbulence. By using instanton formalism for the Navier-Stokes equation, we establish the relation between the PDF tails of the velocity and those of the external forcing. In particular, we show that a Gaussian random force having correlation scale $L$ and correlation time $\tau$ produces velocity PDF tails $\ln{\cal P}(v)\propto-v^4$ at $v\gg v_{rms}, L/\tau$. For a short-correlated forcing when $\tau\ll L/v_{rms}$ there is an intermediate asymptotics $\ln {\cal P}(v)\propto-v^3$ at $L/\tau\gg v\gg v_{rms}$.; Comment: 9 pages, revtex, no figures

We describe two complementary formalisms designed for the description of probability density function (PDF) of the gradients of turbulent fields. The first approach, we call it adiabatic, describes PDF at the values much less than dispersion. The second, instanton, approach gives the tails of PDF at the values of the gradient much larger than dispersion. Together, both approaches give satisfactory description of gradient PDFs, as illustrated here by an example of a passive scalar advected by a one-dimensional compressible random flow.; Comment: 4 pages, RevTeX, submitted to PRE

We investigated the effects of Schmidt number on passive scalar transport in forced compressible turbulence. In the inertial-convective range the scalar spectrum followed the k^{-5/3} power law. For Sc >> 1, there appeared a k^{-1} power law in the viscous-convective range, while for Sc << 1, a k^{-17/3} power law was identified in the inertial-diffusive range. The scaling constant for the mixed third-order structure function of velocity-scalar increment grew over Sc, and the effect of compressibility made it smaller than the classical 4/3 value. At small amplitudes, the PDF of scalar fluctuations collapsed to the Gaussian distribution, whereas at large amplitudes it decayed more quickly than Gaussian. At large scales, the PDF of scalar increment behaved similarly to that of scalar fluctuation, while at small scales it resembled the PDF of scalar gradient. The scalar dissipation occurring at large magnitudes was found to grow with Sc. Due to low molecular diffusivity, for Sc >> 1, the scalar field rolled up and got mixed sufficiently. However, for Sc << 1, the scalar field lost the small-scale structures by high molecular diffusivity, and retained only the large-scale, cloudlike structures. The spectral densities of scalar advection and dissipation in both Sc >> 1 and Sc << 1 flows followed the k^{-5/3} scaling. This indicated that in compressible turbulence the processes of advection and dissipation except that of scalar-dilatation coupling might defer to the Kolmogorov picture. It then showed that at high wavenumbers...

We formalize a classification of pair interactions based on the convergence properties of the {\it forces} acting on particles as a function of system size. We do so by considering the behavior of the probability distribution function (PDF) P(F) of the force field F in a particle distribution in the limit that the size of the system is taken to infinity at constant particle density, i.e., in the "usual" thermodynamic limit. For a pair interaction potential V(r) with V(r) \rightarrow \infty) \sim 1/r^a defining a {\it bounded} pair force, we show that P(F) converges continuously to a well-defined and rapidly decreasing PDF if and only if the {\it pair force} is absolutely integrable, i.e., for a > d-1, where d is the spatial dimension. We refer to this case as {\it dynamically short-range}, because the dominant contribution to the force on a typical particle in this limit arises from particles in a finite neighborhood around it. For the {\it dynamically long-range} case, i.e., a \leq d-1, on the other hand, the dominant contribution to the force comes from the mean field due to the bulk, which becomes undefined in this limit. We discuss also how, for a \leq d-1 (and notably, for the case of gravity, a=d-2) P(F) may, in some cases, be defined in a weaker sense. This involves a regularization of the force summation which is generalization of the procedure employed to define gravitational forces in an infinite static homogeneous universe. We explain that the relevant classification in this context is...