Persistence problem in two-dimensional fluid turbulence

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter Λ to distinguish between vortical and extensional regions. We then use a direct numerical simulation of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent θ=2.9±0.2.     

Vector boson production in pPb and PbPb collisions at the LHC and its impact on <Emphasis FontCategory="NonProportional">nCTEQ15</Emphasis> PDFs

We provide a comprehensive comparison of \(W^\pm / Z\) vector boson production data in pPb and PbPb collisions at the LHC with predictions obtained using the nCTEQ15 PDFs. We identify the measurements which have the largest potential impact on the PDFs, and estimate the effect of including these data using a Bayesian reweighting method. We find this data set can provide information as regards both the nuclear corrections and the heavy flavor (strange quark) PDF components. As for the proton, the parton flavor determination/separation is dependent on nuclear corrections (from heavy target DIS, for example), this information can also help improve the proton PDFs.     

Cascade-like and scaling behavior of wind velocity increments in the atmospheric surface layer

By using a large amount of data collected in the atmospheric surface layer, we analyze the probability density functions (PDFs), the probability of return and the moments of wind velocity increments. Results show that the PDFs change from the non-Gaussian long-tailed distributions to Gaussian with the increase of time scales. This is similar to what has been observed and interpreted as an indication of cascade in the fully developed homogeneous and isotropic turbulence. Besides, both the probability of return and the moments are found to be scaling with time scales. We then compare above results with the truncated Lévy flights and the log-normal PDF model. It is found that although both models show the cascade-like behavior in the PDFs and the scaling behavior in the probability of return and the moments under some conditions, they are not good enough for quantitatively describing the random process of wind velocity increments.     

A comparison of new MC-adapted parton densities

A selection of the latest and most frequently used parton distribution functions (PDFs) is incorporated in Pythia8, including the Monte Carlo-adapted PDFs from the MSTW and CTEQ collaborations. This article examines the differences in PDFs as well as the effect they have on results of simulations and compare with data collected by the CDF experiment. Monte Carlo-adapted PDFs do a better job than leading- and next-to-leading order PDFs for many observables, but there is room for further improvements.     

Probability density functions of quantum mechanical observable uncertainties

We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the uncertainties of arbitrary qubit observables. Based on these PDFs, the uncertainty regions of the observables are characterized by the support of the PDFs. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions, which opens a new vista for studying state-independent uncertainty relations. Our results may be generalized to multiple observable cases in higher dimensional spaces.     

Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry

Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Carlo (MC) simulation of SDEs. Specifically, we develop a new MC SDE method to overcome the challenges in calculating a time-dependent PDF and information geometric diagnostics and to speed up simulations by utilizing GPU computing. Using MC SDE simulations, we reproduce Information Geometric scaling relations found from the Fokker–Planck method for the case of a stochastic process with linear and cubic damping terms. We showcase the advantage of MC SDE simulation over FPE solvers by calculating unequal time joint PDFs. For the linear process with a linear damping force, joint PDF is found to be a Gaussian. In contrast, for the cubic process with a cubic damping force, joint PDF exhibits a bimodal structure, even in a stationary state. This suggests a finite memory time induced by a nonlinear force. Furthermore, several power-law scalings in the characteristics of bimodal PDFs are identified and investigated.     

Steady-state probability density function in wave turbulence under large volume limit

We investigate the possibility for two-mode probability density function(PDF) to have a non-zero flux steady state solution.We take the large volume limit so that the space of modes becomes continuous.It is shown that in this limit all the steady-state two-or higher-mode PDFs are the product of one-mode PDFs.The flux of this steady-state solution turns out to be zero for any finite mode PDF.     

Extreme waves statistics for the Ablowitz-Ladik system

We examine statistics of waves for the problem of modulation instability development in the framework of discrete integrable Ablowitz-Ladik (AL) system. Modulation instability depends on one free parameter h that has the meaning of the coupling between the nodes on the lattice. For strong coupling h ? 1, the probability density functions (PDFs) for waves amplitudes coincide with that for the continuous classical nonlinear Schrödinger equation; the PDFs for both systems are very close to Rayleigh ones. When the coupling is weak h ～ 1, there appear highly localized waves with very large amplitudes, that drastically change the PDFs to significantly non-Rayleigh ones, with so-called “fat tails” when the probability of a large wave occurrence is by several orders of magnitude higher than that predicted by the linear theory. Evolution of amplitudes for such rogue waves with time is similar to that of the Peregrine solution for the classical nonlinear Schrödinger equation.     

Universal impedance fluctuations in wave chaotic systems

We experimentally investigate theoretical predictions of universal impedance fluctuations in wave chaotic systems using a microwave analog of a quantum chaotic infinite square well potential. We emphasize the use of the radiation impedance to remove the nonuniversal effects of the particular coupling between the outside world and the scatterer. Specific predictions that we test include the probability density functions (PDFs) of the real and imaginary parts of the universal impedance, the equality of the variances of these PDFs, and the dependence of these PDFs on a single loss parameter.     

Impact of LHCb 13 TeV W and Z pseudo-data on the parton distribution functions

We study the potential of the LHCb 13 TeV single W±and Z boson pseudo-data for constraining the parton distribution functions(PDFs)of the proton.As an example,we demonstrate the sensitivity of the LHCb 13 TeV data,collected with integrated luminosities of 5fb^-1 and 300 fb^-1 ,to reducing the PDF uncertainty bands of the CT14HERA2 PDFs,using the error PDF updating package EPUMP.The sensitivities of various experimental observables are compared.Generally,sizable reductions in PDF uncertainties can be observed in the 300fb^-1 data sample,particularly in the small-x region.The double-differential cross section measurement of Z boson pT and rapidity can greatly reduce the uncertainty bands of u and d quarks in almost the whole x range,as compared to various single observable measurements.     

Polarised Drell-Yan measurements at COMPASS-II

The spin structure of the nucleon and its Parton Distribution Functions (PDFs) are important topics studied by the COMPASS experiment at CERN. So far, the transverse momentum dependent PDFs (TMD PDFs) of the proton and deuteron have been studied in Semi-Inclusive Deep Inelastic Scattering (SIDIS). The Drell-Yan (DY) process is a complementary way to access the TMD PDFs, using a transversely polarised target. Studying the angular distributions of dimuons from the DY events produced in the collisions of a π^? beam with 190 GeV/c momentum off a transversely polarised proton target (NH₃) we are able to extract the azimuthal spin asymmetries, which are generated by 4 out of the 8 TMD PDFs needed to describe the nucleon structure at leading order QCD. The expected sign change in Sivers and Boer-Mulders functions when accessed from DY and SIDIS will be checked [1]. The opportunity to study, in the same experiment, the TMD PDFs from both SIDIS and DY processes is unique at COMPASS. The COMPASS II Proposal [2] was approved by CERN including one year for polarised DY measurements; the beginning of the DY data taking is scheduled for 2014. The feasibility of the measurement was proven by several beam tests performed so far.     

QCD analysis of CMS W+ charm measurements at LHC with s~(1/2)=7 TeV and implications for strange PDF

We calculate cross-sections and cross-section ratios of a charm quark production in association with a W gauge boson at next-to-leading order QCD using MadGraph and CTIONNLO,CT14 NNLO,and MSTW2008 NNLO PDFs.We compare the results with measurements from the CMS detector at the LHC at a center-of-mass energy of 7 TeV.Moreover,we calculate absolute and normalized differential cross-sections as well as differential cross-section ratios as a function of the lepton pseudorapidity from the W boson decay.The correlation between the CT14 NNLO PDFs and Predictions for W+charm data are studied as well.Furthermore,by employing the error PDF updating method proposed by the CTEQ-TEA group,we update CT14 NNLO PDFs,and analyze the impact of CMS 7 TeV W+charm production data to the original CT14 NNLO PDFs.By comparison of the g(x,Q),s(x,Q),u(x,Q),d(x,Q),u(x,Q),and d(x,Q) PDFs at Q=1.3 GeV and Q=100 GeV for the CT14 NNLO and CT14 NNLO+Wc,we see that the error band of the s(x,Q) PDF is reduced in the region x 0.4,and the error band of g(x,Q) PDF is also slightly reduced at region 0.01 x 0.1.     

Transversity and T-odd PDFs from Drell–Yan processes with <Emphasis Type="Italic">pp</Emphasis>, <Emphasis Type="Italic">pD</Emphasis> and <Emphasis Type="Italic">DD</Emphasis> collisions

We estimate the single-spin asymmetries (SSA) which provide the access to transversity as well as to Boer–Mulders and Sivers PDFs via investigation of the single-polarized Drell–Yan (DY) processes with pp, pD and DD collisions available to RHIC, NICA, COMPASS, and J-PARC. The feasibility of these SSA is studied with the new generator of polarized DY events. The estimations performed demonstrate that there exist kinematical regions where SSA are presumably measurable. Most useful for PDFs extraction are the limiting kinematical ranges, where one can neglect the sea PDFs contributions which occur at large values of the Bjorken variable x. It is of interest that, contrary to the Sivers PDF, the transversity PDF is presumably accessible only in a particular kinematical region. Contrary to the option with the symmetric collider mode (RHIC, NICA), this is of importance for the COMPASS experiment and the future J-PARC facility, where the fixed-target mode is available.     

Statistical effect in the parton distribution functions of the nucleon

A new and simple statistical approach is performed to calculate the parton distribution functions (PDFs) of the nucleon in terms of light-front kinematic variables. We do not put in any extra arbitrary parameter or corrected term by hand, which guarantees the stringency of our approach. Analytic expressions of the x-dependent PDFs are obtained in the whole x   region [0,1]$[0,1]$, and some features, especially the low-x rise, are more agreeable with experimental data than those in some previous instant-form statistical models in the infinite-momentum frame (IMF). Discussions on heavy-flavored PDFs are also presented.     

Uncertainties in air showers from small-x pQCD mini-jets

To investigate uncertainties in air shower simulations caused by the small-x regime, a model including leading-twist hard pQCD plus soft processes was built, which are separated by an energy dependent transverse momentum cut-off. We provide a fit of the cut-off to the total pp cross section for different PDFs using the eikonal formalism and show that for modern PDF sets there is only a small uncertainty in the mini-jet cross section, and hence in the finalstate multiplicity and the number of produced muons.     

Preferred numbers and the distributions of trade sizes and trading volumes in the Chinese stock market

The distributions of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individualstocks exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the “q-Gamma” function for fitting the distribution by the Cramér-von Mises criterion. The empirical PDFs of tradingvolumes at different timescales Δt ranging from 1 min to 240 min can be well modeled. The applicability of the q-Gamma functions for multiple trades is restricted to the transaction numbers Δn≤ 8. We find that all the PDFs have power-law tails for large volumes. Using careful estimation of the average tail exponents α of the distributions of trade sizes and trading volumes, we get α> 2, well outside the Lévy regime.     

Multifractal PDF analysis for intermittent systems

The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy transfer rates, etc., and it is shown that the formula actually explains various PDFs extracted from direct numerical simulations and experiments performed in a wind tunnel. It is also shown that the formula with appropriate zooming increment corresponding to experimental situation gives a new route to obtain the scaling exponents of velocity structure function, including intermittency exponent, out of PDFs of velocity fluctuations.     

Parton distribution functions from the precise NNLO QCD fit

We report on the parton distribution functions (PDFs) determined from the NNLO QCD analysis of the world inclusive DIS data with account for the precise NNLO QCD corrections to the evolution equations kernel. The value of the strong coupling constant α _s ^NNLO (M _Z ) = 0.1141 ± 0.0014 (exp.), in fair agreement with the one obtained using the earlier approximate NNLO kernel by van Neerven-Vogt. The intermediate bosons rates calculated in the NNLO using the obtained PDFs are in agreement with the latest Run II results.     

Connection formulas between the different QCD orders in application to the valence parton distribution functions

Formulas directly connecting parton distribution functions (PDFs) at the leading (LO) and next to leading (NLO) QCD orders are applied with respect to both unpolarized and polarized valence PDFs. It is shown that the connection formulas allow without any restriction on the allowed Q ² range for the analyzed data to produce improved LO results on valence PDFs, which strongly differ from the standard parametrizations on these quantities, and which could be obtained within the standard approach only by using the data produced at very high Q ² values (that is hardly possible in reality).