24,656 research outputs found
IFSM representation of Brownian motion with applications to simulation
Several methods are currently available to simulate paths of the Brownian
motion. In particular, paths of the BM can be simulated using the properties of
the increments of the process like in the Euler scheme, or as the limit of a
random walk or via L2 decomposition like the Kac-Siegert/Karnounen-Loeve
series.
In this paper we first propose a IFSM (Iterated Function Systems with Maps)
operator whose fixed point is the trajectory of the BM. We then use this
representation of the process to simulate its trajectories. The resulting
simulated trajectories are self-affine, continuous and fractal by construction.
This fact produces more realistic trajectories than other schemes in the sense
that their geometry is closer to the one of the true BM's trajectories. The
IFSM trajectory of the BM can then be used to generate more realistic solutions
of stochastic differential equations
Symmetries of the Einstein Equations
Generalized symmetries of the Einstein equations are infinitesimal
transformations of the spacetime metric that formally map solutions of the
Einstein equations to other solutions. The infinitesimal generators of these
symmetries are assumed to be local, \ie at a given spacetime point they are
functions of the metric and an arbitrary but finite number of derivatives of
the metric at the point. We classify all generalized symmetries of the vacuum
Einstein equations in four spacetime dimensions and find that the only
generalized symmetry transformations consist of: (i) constant scalings of the
metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms.
Our results rule out a large class of possible ``observables'' for the
gravitational field, and suggest that the vacuum Einstein equations are not
integrable.Comment: 15 pages, FTG-114-USU, Plain Te
Transverse-momentum resummation for heavy-quark hadroproduction
We consider the production of a pair of heavy quarks () in
hadronic collisions. When the transverse momentum of the heavy-quark pair
is much smaller than its invariant mass, the QCD perturbative expansion is
affected by large logarithmic terms that must be resummed to all-orders. This
behavior is well known from the simpler case of hadroproduction of colourless
high-mass systems, such as vector or Higgs boson(s). In the case of
production, the final-state heavy quarks carry colour charge and are
responsible for additional soft radiation (through direct emission and
interferences with initial-state radiation) that complicates the evaluation of
the logarithmically-enhanced terms in the small- region. We present the
all-order resummation structure of the logarithmic contributions, which
includes colour flow evolution factors due to soft wide-angle radiation.
Resummation is performed at the completely differential level with respect to
the kinematical variables of the produced heavy quarks. Soft-parton radiation
produces azimuthal correlations that are fully taken into account by the
resummation formalism. These azimuthal correlations are entangled with those
that are produced by initial-state collinear radiation. We present explicit
analytical results up to next-to-leading order and next-to-next-to-leading
logarithmic accuracy.Comment: Some comments expanded and references added. Version published on NP
Translation-Rotation Coupling in Transient Grating Experiments : Theoretical and Experimental Evidences
The results of a Transient Grating experiment in a supercooled molecular
liquid of anisotropic molecules and its theoretical interpretation are
presented. These results show the existence of two distinct dynamical
contributions in the response function of this experiment, density and
orientation dynamics. These dynamics can be experimentally disentangled by
varying the polarisation of the probe and diffracted beams and they have been
identified and measured in a Heterodyne Detected experiment performed on
m-toluidine. The results of the theory show a good qualitative agreement with
the measurements at all temperatures.Comment: PDF format, 14 pages including 4 figures, accepted for publication in
EPL. minor modification
Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids
In a fluid subject to a magnetic field the viscous stress tensor has a
dissipationless antisymmetric component controlled by the so-called Hall
viscosity. We here propose an all-electrical scheme that allows a determination
of the Hall viscosity of a two-dimensional electron liquid in a solid-state
device.Comment: 12 pages, 4 figure
Gurses' Type (b) Transformations are Neighborhood-Isometries
Following an idea close to one given by C. G. Torre (private communication),
we prove that Riemannian spaces (M,g) and (M,h) that are related by a Gurses
type (b) transformation [M. Gurses, Phys. Rev. Lett. 70, 367 (1993)] or,
equivalently, by a Torre-Anderson generalized diffeomorphism [C. G. Torre and
I. M. Anderson, Phys. Rev. Lett. xx, xxx (1993)] are neighborhood-isometric,
i.e., every point x in M has a corresponding diffeomorphism phi of a
neighborhood V of x onto a generally different neighborhood W of x such that
phi*(h|W) = g|V.Comment: 10 pages, LATEX, FJE-93-00
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