305,342 research outputs found
Monte-Carlo Approach to Calculating the Fragmentation Functions in NJL-Jet Model
Recent studies of the fragmentation functions using the Nambu--Jona-Lasinio
(NJL) - Jet model have been successful in describing the quark fragmentation
functions to pions and kaons. The NJL-Jet model employs the integral equation
approach to solve for the fragmentation functions in quark-cascade description
of the hadron emission process, where one assumes that the initial quark has
infinite momentum and emits an infinite number of hadrons. Here we introduce a
Monte Carlo (MC) simulation method to solve for the fragmentation functions,,
that allows us to relax the above mentioned approximations. We demonstrate that
the results of MC simulations closely reproduce the solutions of the integral
equations in the limit where a large number of hadrons are emitted in the quark
cascade. The MC approach provides a strong foundation for the further
development of the NJL-Jet model that might include many more hadronic emission
channels with decays of the possible produced resonances, as well as inclusion
of the transverse momentum dependence (TMD), all of which are of considerable
importance to the experimental studies of the transverse structure of hadrons.Comment: 5 pages, 3 figures, Proceedings of "TROPICAL QCD II Workshop
A Poincare-Covariant Parton Cascade Model for Ultrarelativistic Heavy-Ion Reactions
We present a new cascade-type microscopic simulation of nucleus-nucleus
collisions at RHIC energies. The basic elements are partons (quarks and gluons)
moving in 8N-dimensional phase space according to Poincare-covariant dynamics.
The parton-parton scattering cross sections used in the model are computed
within perturbative QCD in the tree-level approximation. The Q^2 dependence of
the structure functions is included by an implementation of the DGLAP mechanism
suitable for a cascade, so that the number of partons is not static, but varies
in space and time as the collision of two nuclei evolves. The resulting parton
distributions are presented, and meaningful comparisons with experimental data
are discussed.Comment: 30 pages. 11 figures. Submitted to Phys.Rev.
Log-Poisson Cascade Description of Turbulent Velocity Gradient Statistics
The Log-Poisson phenomenological description of the turbulent energy cascade
is evoked to discuss high-order statistics of velocity derivatives and the
mapping between their probability distribution functions at different Reynolds
numbers. The striking confirmation of theoretical predictions suggests that
numerical solutions of the flow, obtained at low/moderate Reynolds numbers can
play an important quantitative role in the analysis of experimental high
Reynolds number phenomena, where small scales fluctuations are in general
inaccessible from direct numerical simulations
Anisotropic fluxes and nonlocal interactions in MHD turbulence
We investigate the locality or nonlocality of the energy transfer and of the
spectral interactions involved in the cascade for decaying magnetohydrodynamic
(MHD) flows in the presence of a uniform magnetic field at various
intensities. The results are based on a detailed analysis of three-dimensional
numerical flows at moderate Reynold numbers. The energy transfer functions, as
well as the global and partial fluxes, are examined by means of different
geometrical wavenumber shells. On the one hand, the transfer functions of the
two conserved Els\"asser energies and are found local in both the
directions parallel (-direction) and perpendicular (-direction)
to the magnetic guide-field, whatever the -strength. On the other
hand, from the flux analysis, the interactions between the two
counterpropagating Els\"asser waves become nonlocal. Indeed, as the -intensity is increased, local interactions are strongly decreased and the
interactions with small modes dominate the cascade. Most of the energy
flux in the -direction is due to modes in the plane at , while
the weaker cascade in the -direction is due to the modes with .
The stronger magnetized flows tends thus to get closer to the weak turbulence
limit where the three-wave resonant interactions are dominating. Hence, the
transition from the strong to the weak turbulence regime occurs by reducing the
number of effective modes in the energy cascade.Comment: Submitted to PR
Mixing in Supersonic Turbulence
In many astrophysical environments, mixing of heavy elements occurs in the
presence of a supersonic turbulent velocity field. Here we carry out the first
systematic numerical study of such passive scalar mixing in isothermal
supersonic turbulence. Our simulations show that the ratio of the scalar mixing
timescale, , to the flow dynamical time,
(defined as the flow driving scale divided by the rms velocity), increases with
the Mach number, , for M \lsim3, and becomes essentially constant for M
\gsim3. This trend suggests that compressible modes are less efficient in
enhancing mixing than solenoidal modes. However, since the majority of kinetic
energy is contained in solenoidal modes at all Mach numbers, the overall change
in is less than 20\% over the range 1 \lsim M
\lsim 6. At all Mach numbers, if pollutants are injected at around the flow
driving scale, is close to This suggests that
scalar mixing is driven by a cascade process similar to that of the velocity
field. The dependence of on the length scale at which pollutants
are injected into flow is also consistent with this cascade picture. Similar
behavior is found for the variance decay timescales for scalars without
continuing sources. Extension of the scalar cascade picture to the supersonic
regime predicts a relation between the scaling exponents of the velocity and
the scalar structure functions, with the scalar structure function becoming
flatter as the velocity scaling steepens with Mach number. Our measurements of
the volume-weighted velocity and scalar structure functions confirm this
relation for M\lsim 2, but show discrepancies at M \gsim 3.Comment: Accepted by Ap
Scale Dependence of Multiplier Distributions for Particle Concentration, Enstrophy and Dissipation in the Inertial Range of Homogeneous Turbulence
Turbulent flows preferentially concentrate inertial particles depending on
their stopping time or Stokes number, which can lead to significant spatial
variations in the particle concentration. Cascade models are one way to
describe this process in statistical terms. Here, we use a direct numerical
simulation (DNS) dataset of homogeneous, isotropic turbulence to determine
probability distribution functions (PDFs) for cascade multipliers, which
determine the ratio by which a property is partitioned into sub-volumes as an
eddy is envisioned to decay into smaller eddies. We present a technique for
correcting effects of small particle numbers in the statistics. We determine
multiplier PDFs for particle number, flow dissipation, and enstrophy, all of
which are shown to be scale dependent. However, the particle multiplier PDFs
collapse when scaled with an appropriately defined local Stokes number. As
anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach
an asymptote for sufficiently small spatial scales. From the DNS measurements,
we derive a cascade model that is used it to make predictions for the radial
distribution function (RDF) for arbitrarily high Reynolds numbers, ,
finding good agreement with the asymptotic, infinite inertial range theory
of Zaichik and Alipchenkov [New Journal of Physics 11, 103018 (2009)]. We
discuss implications of these results for the statistical modeling of the
turbulent clustering process in the inertial range for high Reynolds numbers
inaccessible to numerical simulations.Comment: 21 pages, 14 figures, accepted for publication in Physical Review
Fusion Rules in Turbulent Systems with Flux Equilibrium
Fusion rules in turbulence specify the analytic structure of many-point
correlation functions of the turbulent field when a group of coordinates
coalesce. We show that the existence of flux equilibrium in fully developed
turbulent systems combined with a direct cascade induces universal fusion
rules. In certain examples these fusion rules suffice to compute the
multiscaling exponents exactly, and in other examples they give rise to an
infinite number of scaling relations that constrain enormously the structure of
the allowed theory.Comment: Submitted to PRL on July 95, 4 pages, REVTe
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