725 research outputs found
Are ghost surfaces quadratic-flux-minimizing?
Two candidates for "almost-invariant" toroidal surfaces passing through
magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost
surfaces, use families of periodic pseudo-orbits (i.e. paths for which the
action is not exactly extremal). QFMin pseudo-orbits, which are
coordinate-dependent, are field lines obtained from a modified magnetic field,
and ghost-surface pseudo-orbits are obtained by displacing closed field lines
in the direction of steepest descent of magnetic action, . A generalized Hamiltonian definition of ghost
surfaces is given and specialized to the usual Lagrangian definition. A
modified Hamilton's Principle is introduced that allows the use of Lagrangian
integration for calculation of the QFMin pseudo-orbits. Numerical calculations
show QFMin and Lagrangian ghost surfaces give very similar results for a
chaotic magnetic field perturbed from an integrable case, and this is explained
using a perturbative construction of an auxiliary poloidal angle for which
QFMin and Lagrangian ghost surfaces are the same up to second order. While
presented in the context of 3-dimensional magnetic field line systems, the
concepts are applicable to defining almost-invariant tori in other
degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.Comment: 8 pages, 3 figures. Revised version includes post-publication
corrections in text, as described in Appendix C Erratu
Novel Transversity Properties in Semi-Inclusive Deep Inelastic Scattering
The -odd distribution functions contributing to transversity properties of
the nucleon and their role in fueling nontrivial contributions to azimuthal
asymmetries in semi-inclusive deep inelastic scattering are investigated. We
use a dynamical model to evaluate these quantities in terms of HERMES
kinematics.Comment: 5 pages revtex; 5 eps figures. References added. To appear as a Rapid
Communication in Physical Review
Probing Quark Fragmentation Functions for Spin-1/2 Baryon Production in Unpolarized Annihilation
We study the measurement of the quark fragmentation functions for spin-1/2
baryon production ( and , in particular) in unpolarized
annihilation. The spin-dependent fragmentation functions
and can be probed in the process as a result of quark-antiquark
spin correlation and the weak decay of the baryons. The relevant cross section
is expressed as a product of the two-jet cross-section, the fragmentation
functions, and the differential width of the hyperon decay.Comment: 17 pages, ReVTeX with (1 figure available from authors), MIT-CTP:
#236
Partially ordered models
We provide a formal definition and study the basic properties of partially
ordered chains (POC). These systems were proposed to model textures in image
processing and to represent independence relations between random variables in
statistics (in the later case they are known as Bayesian networks). Our chains
are a generalization of probabilistic cellular automata (PCA) and their theory
has features intermediate between that of discrete-time processes and the
theory of statistical mechanical lattice fields. Its proper definition is based
on the notion of partially ordered specification (POS), in close analogy to the
theory of Gibbs measure. This paper contains two types of results. First, we
present the basic elements of the general theory of POCs: basic geometrical
issues, definition in terms of conditional probability kernels, extremal
decomposition, extremality and triviality, reconstruction starting from
single-site kernels, relations between POM and Gibbs fields. Second, we prove
three uniqueness criteria that correspond to the criteria known as bounded
uniformity, Dobrushin and disagreement percolation in the theory of Gibbs
measures.Comment: 54 pages, 11 figures, 6 simulations. Submited to Journal of Stat.
Phy
Action-gradient-minimizing pseudo-orbits and almost-invariant tori
Transport in near-integrable, but partially chaotic,
degree-of-freedom Hamiltonian systems is blocked by invariant tori and is
reduced at \emph{almost}-invariant tori, both associated with the invariant
tori of a neighboring integrable system. "Almost invariant" tori with rational
rotation number can be defined using continuous families of periodic
\emph{pseudo-orbits} to foliate the surfaces, while irrational-rotation-number
tori can be defined by nesting with sequences of such rational tori. Three
definitions of "pseudo-orbit," \emph{action-gradient--minimizing} (AGMin),
\emph{quadratic-flux-minimizing} (QFMin) and \emph{ghost} orbits, based on
variants of Hamilton's Principle, use different strategies to extremize the
action as closely as possible. Equivalent Lagrangian (configuration-space
action) and Hamiltonian (phase-space action) formulations, and a new approach
to visualizing action-minimizing and minimax orbits based on AGMin
pseudo-orbits, are presented.Comment: Accepted for publication in a special issue of Communications in
Nonlinear Science and Numerical Simulation (CNSNS) entitled "The mathematical
structure of fluids and plasmas : a volume dedicated to the 60th birthday of
Phil Morrison
Probing Yukawian gravitational potential by numerical simulations. I. Changing N-body codes
In the weak field limit general relativity reduces, as is well known, to the
Newtonian gravitation. Alternative theories of gravity, however, do not
necessarily reduce to Newtonian gravitation; some of them, for example, reduce
to Yukawa-like potentials instead of the Newtonian potential. Since the
Newtonian gravitation is largely used to model with success the structures of
the universe, such as for example galaxies and clusters of galaxies, a way to
probe and constrain alternative theories, in the weak field limit, is to apply
them to model the structures of the universe. In the present study, we consider
how to probe Yukawa-like potentials using N-body numerical simulations.Comment: 17 pages, 11 figures. To appear in General Relativity and Gravitatio
Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics
We study fractional configurations in gravity theories and Lagrange
mechanics. The approach is based on Caputo fractional derivative which gives
zero for actions on constants. We elaborate fractional geometric models of
physical interactions and we formulate a method of nonholonomic deformations to
other types of fractional derivatives. The main result of this paper consists
in a proof that for corresponding classes of nonholonomic distributions a large
class of physical theories are modelled as nonholonomic manifolds with constant
matrix curvature. This allows us to encode the fractional dynamics of
interactions and constraints into the geometry of curve flows and solitonic
hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and
up-dated reference
A mechanism for the T-odd pion fragmentation function
We consider a simple rescattering mechanism to calculate a leading twist
-odd pion fragmentation function, a favored candidate for filtering the
transversity properties of the nucleon. We evaluate the single spin azimuthal
asymmetry for a transversely polarized target in semi-inclusive deep inelastic
scattering (for HERMES kinematics). Additionally, we calculate the double
-odd asymmetry in this framework.Comment: 6 pages revtex, 7 eps figures, references added and updated in this
published versio
Hopping motion of lattice gases through nonsymmetric potentials under strong bias conditions
The hopping motion of lattice gases through potentials without
mirror-reflection symmetry is investigated under various bias conditions. The
model of 2 particles on a ring with 4 sites is solved explicitly; the resulting
current in a sawtooth potential is discussed. The current of lattice gases in
extended systems consisting of periodic repetitions of segments with sawtooth
potentials is studied for different concentrations and values of the bias.
Rectification effects are observed, similar to the single-particle case. A
mean-field approximation for the current in the case of strong bias acting
against the highest barriers in the system is made and compared with numerical
simulations. The particle-vacancy symmetry of the model is discussed.Comment: 8 pages (incl. 6 eps figures); RevTeX 3.
Transversity distributions in the nucleon in the large-N_c limit
We compute the quark and antiquark transversity distributions in the nucleon
at a low normalization point of 600 MeV in the large- limit, where the
nucleon can be described as a soliton of an effective chiral theory (chiral
quark-soliton model). The flavor-nonsinglet distributions, and , appear in leading order
of the -expansion, while the flavor-singlet distributions, and , are non-zero only in
next-to-leading order. The transversity quark and antiquark distributions are
found to be significantly different from the longitudinally polarized
distributions and , respectively, in contrast to the prediction of the naive
non-relativistic quark model. We show that this affects the predictions for the
spin asymmetries in Drell-Yan pair production in transversely polarized pp and
ppbar collisions.Comment: 45 pages, 16 figure
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