2,451 research outputs found
Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation
We present a numerical method for the Monte Carlo simulation of uncoupled
continuous-time random walks with a Levy alpha-stable distribution of jumps in
space and a Mittag-Leffler distribution of waiting times, and apply it to the
stochastic solution of the Cauchy problem for a partial differential equation
with fractional derivatives both in space and in time. The one-parameter
Mittag-Leffler function is the natural survival probability leading to
time-fractional diffusion equations. Transformation methods for Mittag-Leffler
random variables were found later than the well-known transformation method by
Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far
have not received as much attention; nor have they been used together with the
latter in spite of their mathematical relationship due to the geometric
stability of the Mittag-Leffler distribution. Combining the two methods, we
obtain an accurate approximation of space- and time-fractional diffusion
processes almost as easy and fast to compute as for standard diffusion
processes.Comment: 7 pages, 5 figures, 1 table. Presented at the Conference on Computing
in Economics and Finance in Montreal, 14-16 June 2007; at the conference
"Modelling anomalous diffusion and relaxation" in Jerusalem, 23-28 March
2008; et
Global magnetic cycles in rapidly rotating younger suns
Observations of sun-like stars rotating faster than our current sun tend to
exhibit increased magnetic activity as well as magnetic cycles spanning
multiple years. Using global simulations in spherical shells to study the
coupling of large-scale convection, rotation, and magnetism in a younger sun,
we have probed effects of rotation on stellar dynamos and the nature of
magnetic cycles. Major 3-D MHD simulations carried out at three times the
current solar rotation rate reveal hydromagnetic dynamo action that yields
wreaths of strong toroidal magnetic field at low latitudes, often with opposite
polarity in the two hemispheres. Our recent simulations have explored behavior
in systems with considerably lower diffusivities, achieved with sub-grid scale
models including a dynamic Smagorinsky treatment of unresolved turbulence. The
lower diffusion promotes the generation of magnetic wreaths that undergo
prominent temporal variations in field strength, exhibiting global magnetic
cycles that involve polarity reversals. In our least diffusive simulation, we
find that magnetic buoyancy coupled with advection by convective giant cells
can lead to the rise of coherent loops of magnetic field toward the top of the
simulated domain.Comment: 4 pages, 3 figures, from IAU 273: The Physics of Sun and Star Spot
New Imaging Protocols for New Single Photon Emission CT Technologies
Nuclear cardiology practitioners have several new technologies available with which to perform myocardial perfusion single photon emission CT (MPS). These include dedicated small-footprint cardiac scanners, new stationary or semi-stationary three-dimensional detectors, and advanced software algorithms for optimal image reconstruction. These new technologies have been employed to reduce imaging time and radiation exposure. They require less technologist and camera time and offer improved patient comfort. They have potential for the overall cost reduction of MPS and at the same time for improved accuracy by increased resolution, or accurate attenuation correction. Furthermore, these new technologies offer potential for new protocols such as simultaneous dual isotope, new combinations of isotopes, stress only MPS, or dynamic first-pass imaging. In addition, new imaging technologies in coronary CT angiography (CCTA) allow novel hybrid stress only MPS/CCTA protocols with reduced radiation burden. Additional developments further improving efficiency and diagnostic accuracy of MPS are on the horizon
Simultaneous calculation of the helical pitch and the twist elastic constant in chiral liquid crystals from intermolecular torques
We present a molecular simulation method that yields simultaneously the equilibrium pitch wave number q and the twist elastic constant K2 of a chiral nematic liquid crystal by sampling the torque density. A simulation of an untwisted system in periodic boundary conditions gives the product K2q; a further simulation with a uniform twist applied provides enough information to separately determine the two factors. We test our new method for a model potential, comparing the results with K2q from a thermodynamic integration route, and with K2 from an order fluctuation analysis. We also present a thermodynamic perturbation theory analysis valid in the limit of weak chirality
Leray and LANS- modeling of turbulent mixing
Mathematical regularisation of the nonlinear terms in the Navier-Stokes
equations provides a systematic approach to deriving subgrid closures for
numerical simulations of turbulent flow. By construction, these subgrid
closures imply existence and uniqueness of strong solutions to the
corresponding modelled system of equations. We will consider the large eddy
interpretation of two such mathematical regularisation principles, i.e., Leray
and LANS regularisation. The Leray principle introduces a {\bfi
smoothed transport velocity} as part of the regularised convective
nonlinearity. The LANS principle extends the Leray formulation in a
natural way in which a {\bfi filtered Kelvin circulation theorem},
incorporating the smoothed transport velocity, is explicitly satisfied. These
regularisation principles give rise to implied subgrid closures which will be
applied in large eddy simulation of turbulent mixing. Comparison with filtered
direct numerical simulation data, and with predictions obtained from popular
dynamic eddy-viscosity modelling, shows that these mathematical regularisation
models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure
The supernova-regulated ISM. II. The mean magnetic field
The origin and structure of the magnetic fields in the interstellar medium of
spiral galaxies is investigated with 3D, non-ideal, compressible MHD
simulations, including stratification in the galactic gravity field,
differential rotation and radiative cooling. A rectangular domain, 1x1x2
kpc^{3} in size, spans both sides of the galactic mid-plane. Supernova
explosions drive transonic turbulence. A seed magnetic field grows
exponentially to reach a statistically steady state within 1.6 Gyr. Following
Germano (1992) we use volume averaging with a Gaussian kernel to separate
magnetic field into a mean field and fluctuations. Such averaging does not
satisfy all Reynolds rules, yet allows a formulation of mean-field theory. The
mean field thus obtained varies in both space and time. Growth rates differ for
the mean-field and fluctuating field and there is clear scale separation
between the two elements, whose integral scales are about 0.7 kpc and 0.3 kpc,
respectively.Comment: 5 pages, 10 figures, submitted to Monthly Notices Letter
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