8,282 research outputs found
Magnetohydrodynamic activity inside a sphere
We present a computational method to solve the magnetohydrodynamic equations
in spherical geometry. The technique is fully nonlinear and wholly spectral,
and uses an expansion basis that is adapted to the geometry:
Chandrasekhar-Kendall vector eigenfunctions of the curl. The resulting lower
spatial resolution is somewhat offset by being able to build all the boundary
conditions into each of the orthogonal expansion functions and by the
disappearance of any difficulties caused by singularities at the center of the
sphere. The results reported here are for mechanically and magnetically
isolated spheres, although different boundary conditions could be studied by
adapting the same method. The intent is to be able to study the nonlinear
dynamical evolution of those aspects that are peculiar to the spherical
geometry at only moderate Reynolds numbers. The code is parallelized, and will
preserve to high accuracy the ideal magnetohydrodynamic (MHD) invariants of the
system (global energy, magnetic helicity, cross helicity). Examples of results
for selective decay and mechanically-driven dynamo simulations are discussed.
In the dynamo cases, spontaneous flips of the dipole orientation are observed.Comment: 15 pages, 19 figures. Improved figures, in press in Physics of Fluid
Local estimates for entropy densities in coupled map lattices
We present a method to derive an upper bound for the entropy density of
coupled map lattices with local interactions from local observations. To do
this, we use an embedding technique being a combination of time delay and
spatial embedding. This embedding allows us to identify the local character of
the equations of motion. Based on this method we present an approximate
estimate of the entropy density by the correlation integral.Comment: 4 pages, 5 figures include
Orthogonal, solenoidal, three-dimensional vector fields for no-slip boundary conditions
Viscous fluid dynamical calculations require no-slip boundary conditions.
Numerical calculations of turbulence, as well as theoretical turbulence closure
techniques, often depend upon a spectral decomposition of the flow fields.
However, such calculations have been limited to two-dimensional situations.
Here we present a method that yields orthogonal decompositions of
incompressible, three-dimensional flow fields and apply it to periodic
cylindrical and spherical no-slip boundaries.Comment: 16 pages, 2 three-part figure
Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere
Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations
are reported for the interior of a rotating, perfectly-conducting, rigid
spherical shell that is insulator-coated on the inside. A previously-reported
spectral method is used which relies on a Galerkin expansion in
Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in
this set of computations is the rigid rotation of the sphere. After a few
purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial
waves), attention is focused on selective decay and the MHD dynamo problem. In
dynamo runs, prescribed mechanical forcing excites a persistent velocity field,
usually turbulent at modest Reynolds numbers, which in turn amplifies a small
seed magnetic field that is introduced. A wide variety of dynamo activity is
observed, all at unit magnetic Prandtl number. The code lacks the resolution to
probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn
out to be plentiful in those parts of parameter space in which the code is
accurate. The key control parameters seem to be mechanical and magnetic
Reynolds numbers, the Rossby and Ekman numbers (which in our computations are
varied mostly by varying the rate of rotation of the sphere) and the amount of
mechanical helicity injected. Magnetic energy levels and magnetic dipole
behavior are exhibited which fluctuate strongly on a time scale of a few eddy
turnover times. These seem to stabilize as the rotation rate is increased until
the limit of the code resolution is reached.Comment: 26 pages, 17 figures, submitted to New Journal of Physic
Reactive Control Improvisation
Reactive synthesis is a paradigm for automatically building
correct-by-construction systems that interact with an unknown or adversarial
environment. We study how to do reactive synthesis when part of the
specification of the system is that its behavior should be random. Randomness
can be useful, for example, in a network protocol fuzz tester whose output
should be varied, or a planner for a surveillance robot whose route should be
unpredictable. However, existing reactive synthesis techniques do not provide a
way to ensure random behavior while maintaining functional correctness. Towards
this end, we generalize the recently-proposed framework of control
improvisation (CI) to add reactivity. The resulting framework of reactive
control improvisation provides a natural way to integrate a randomness
requirement with the usual functional specifications of reactive synthesis over
a finite window. We theoretically characterize when such problems are
realizable, and give a general method for solving them. For specifications
given by reachability or safety games or by deterministic finite automata, our
method yields a polynomial-time synthesis algorithm. For various other types of
specifications including temporal logic formulas, we obtain a polynomial-space
algorithm and prove matching PSPACE-hardness results. We show that all of these
randomized variants of reactive synthesis are no harder in a
complexity-theoretic sense than their non-randomized counterparts.Comment: 25 pages. Full version of a CAV 2018 pape
Dimension of interaction dynamics
A method allowing to distinguish interacting from non-interacting systems
based on available time series is proposed and investigated. Some facts
concerning generalized Renyi dimensions that form the basis of our method are
proved. We show that one can find the dimension of the part of the attractor of
the system connected with interaction between its parts. We use our method to
distinguish interacting from non-interacting systems on the examples of
logistic and H\'enon maps. A classification of all possible interaction schemes
is given.Comment: 15 pages, 14 (36) figures, submitted to PR
Evolution of Ultracold, Neutral Plasmas
We present the first large-scale simulations of an ultracold, neutral plasma,
produced by photoionization of laser-cooled xenon atoms, from creation to
initial expansion, using classical molecular dynamics methods with open
boundary conditions. We reproduce many of the experimental findings such as the
trapping efficiency of electrons with increased ion number, a minimum electron
temperature achieved on approach to the photoionization threshold, and
recombination into Rydberg states of anomalously-low principal quantum number.
In addition, many of these effects establish themselves very early in the
plasma evolution ( ns) before present experimental observations begin.Comment: 4 pages, 3 figures, submitted to PR
Just plain Wronga?: a multimodal critical analysis of online payday loan discourse
Payday loans constitute one of the most rapidly expanding and controversial forms of consumer lending today. Payday lending – the selling of high-interest, short-term credit – has thrived in the wake of the decline of the traditional high street banking system and the reluctance on the part of many mainstream credit services, following the 2007/8 Global Financial Crisis, to lend to low income earners. This study critically examines the website of the industry leader in the UK, Wonga, a payday lender which recently rebranded and relaunched itself (in 2015) after being embroiled in a series of financial scandals. Our analysis centres on the new Wonga website, the gateway to its financial services, and identifies three inter-related discursive strategies through which the lender, in the wake of its financial misconduct, seeks to present itself as a reputable financial service provider, namely by (1) constructing the empowered and responsible borrower, (2) de-stigmatising both its service provision and its prospective customers, the payday borrower, and (3) minimising the consequences and risks associated with payday borrowing. We argue that, collectively, these strategies constitute an artful response by Wonga to the changing legislative and socio-economic contexts in which it and other payday lenders are now required to operate, permitting it to continue marketing and selling its high-interest rate financial services
Compressibility of titanosilicate melts
The effect of composition on the relaxed adiabatic bulk modulus (K0) of a range of alkali- and alkaline earth-titanosilicate [X 2 n/n+ TiSiO5 (X=Li, Na, K, Rb, Cs, Ca, Sr, Ba)] melts has been investigated. The relaxed bulk moduli of these melts have been measured using ultrasonic interferometric methods at frequencies of 3, 5 and 7 MHz in the temperature range of 950 to 1600°C (0.02 Pa s < s < 5 Pa s). The bulk moduli of these melts decrease with increasing cation size from Li to Cs and Ca to Ba, and with increasing temperature. The bulk moduli of the Li-, Na-, Ca- and Ba-bearing metasilicate melts decrease with the addition of both TiO2 and SiO2 whereas those of the K-, Rb- and Cs-bearing melts increase. Linear fits to the bulk modulus versus volume fraction of TiO2 do not converge to a common compressibility of the TiO2 component, indicating that the structural role of TiO2 in these melts is dependent on the identity of the cation. This proposition is supported by a number of other property data for these and related melt compositions including heat capacity and density, as well as structural inferences from X-ray absorption spectroscopy (XANES). The compositional dependence of the compressibility of the TiO2 component in these melts explains the difficulty incurred in previous attempts to incorporate TiO2 in calculation schemes for melt compressibility. The empirical relationship KV-4/3 for isostructural materials has been used to evaluate the compressibility-related structural changes occurring in these melts. The alkali metasilicate and disilicate melts are isostructural, independent of the cation. The addition of Ti to the metasilicate composition (i.e. X2TiSiO5), however, results in a series of melts which are not isostructural. The alkaline-earth metasilicate and disilicate compositions are not isostructural, but the addition of Ti to the metasilicate compositions (i.e. XTiSiO5) would appear, on the basis of modulus-volume systematics, to result in the melts becoming isostructural with respect to compressibility
Scale Invariance in the Nonstationarity of Physiological Signals
We introduce a segmentation algorithm to probe temporal organization of
heterogeneities in human heartbeat interval time series. We find that the
lengths of segments with different local values of heart rates follow a
power-law distribution. This scale-invariant structure is not a simple
consequence of the long-range correlations present in the data. We also find
that the differences in mean heart rates between consecutive segments display a
common functional form, but with different parameters for healthy individuals
and for patients with heart failure. This finding may provide information into
the way heart rate variability is reduced in cardiac disease.Comment: 13 pages, 5 figures, corrected typo
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