2,609 research outputs found
A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling
Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK ‘Octopus’, EPSRC ‘Reactor Core-Structure Re-location Modelling for Severe Nuclear Accidents’) and Horizon 2020 ‘In-Vessel Melt Retention’. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC ‘Multi-Scale Exploration of Multi-phase Physics in Flows’. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.Peer reviewedPublisher PD
Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity
© 2016 .A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach
Predictability sieve, pointer states, and the classicality of quantum trajectories
We study various measures of classicality of the states of open quantum
systems subject to decoherence. Classical states are expected to be stable in
spite of decoherence, and are thought to leave conspicuous imprints on the
environment. Here these expected features of environment-induced superselection
(einselection) are quantified using four different criteria: predictability
sieve (which selects states that produce least entropy), purification time
(which looks for states that are the easiest to find out from the imprint they
leave on the environment), efficiency threshold (which finds states that can be
deduced from measurements on a smallest fraction of the environment), and
purity loss time (that looks for states for which it takes the longest to lose
a set fraction of their initial purity). We show that when pointer states --
the most predictable states of an open quantum system selected by the
predictability sieve -- are well defined, all four criteria agree that they are
indeed the most classical states. We illustrate this with two examples: an
underdamped harmonic oscillator, for which coherent states are unanimously
chosen by all criteria, and a free particle undergoing quantum Brownian motion,
for which most criteria select almost identical Gaussian states (although, in
this case, predictability sieve does not select well defined pointer states.)Comment: 10 pages, 13 figure
The Archean crust in the Wawa-Chapleau-Timmins region. A field guidebook prepared for the 1983 Archean Geochemistry-Early Crustal Genesis Field Conference
This guidebook describes the characteristics and interrelationships of Archean greenstone-granite and high-grade gneiss terrains of the Superior Province. A 300-km long west to east transect between Wawa and Timmins, Ontario will be used to illustrate regional-scale relationships. The major geological features of the Superior Province are described
Quantum noise and stochastic reduction
In standard nonrelativistic quantum mechanics the expectation of the energy
is a conserved quantity. It is possible to extend the dynamical law associated
with the evolution of a quantum state consistently to include a nonlinear
stochastic component, while respecting the conservation law. According to the
dynamics thus obtained, referred to as the energy-based stochastic Schrodinger
equation, an arbitrary initial state collapses spontaneously to one of the
energy eigenstates, thus describing the phenomenon of quantum state reduction.
In this article, two such models are investigated: one that achieves state
reduction in infinite time, and the other in finite time. The properties of the
associated energy expectation process and the energy variance process are
worked out in detail. By use of a novel application of a nonlinear filtering
method, closed-form solutions--algebraic in character and involving no
integration--are obtained for both these models. In each case, the solution is
expressed in terms of a random variable representing the terminal energy of the
system, and an independent noise process. With these solutions at hand it is
possible to simulate explicitly the dynamics of the quantum states of
complicated physical systems.Comment: 50 page
Problems and Aspects of Energy-Driven Wavefunction Collapse Models
Four problematic circumstances are considered, involving models which
describe dynamical wavefunction collapse toward energy eigenstates, for which
it is shown that wavefunction collapse of macroscopic objects does not work
properly. In one case, a common particle position measuring situation, the
apparatus evolves to a superposition of macroscopically distinguishable states
(does not collapse to one of them as it should) because each such
particle/apparatus/environment state has precisely the same energy spectrum.
Second, assuming an experiment takes place involving collapse to one of two
possible outcomes which is permanently recorded, it is shown in general that
this can only happen in the unlikely case that the two apparatus states
corresponding to the two outcomes have disjoint energy spectra. Next, the
progressive narrowing of the energy spectrum due to the collapse mechanism is
considered. This has the effect of broadening the time evolution of objects as
the universe evolves. Two examples, one involving a precessing spin, the other
involving creation of an excited state followed by its decay, are presented in
the form of paradoxes. In both examples, the microscopic behavior predicted by
standard quantum theory is significantly altered under energy-driven collapse,
but this alteration is not observed by an apparatus when it is included in the
quantum description. The resolution involves recognition that the statevector
describing the apparatus does not collapse, but evolves to a superposition of
macroscopically different states.Comment: 17 page
Estimating Granger causality from Fourier and wavelet transforms of time series data
Experiments in many fields of science and engineering yield data in the form
of time series. The Fourier and wavelet transform-based nonparametric methods
are used widely to study the spectral characteristics of these time series
data. Here, we extend the framework of nonparametric spectral methods to
include the estimation of Granger causality spectra for assessing directional
influences. We illustrate the utility of the proposed methods using synthetic
data from network models consisting of interacting dynamical systems.Comment: 6 pages, 2 figure
Signatures of chaotic and non-chaotic-like behaviour in a non-linear quantum oscillator through photon detection
The driven non-linear duffing osillator is a very good, and standard, example
of a quantum mechanical system from which classical-like orbits can be
recovered from unravellings of the master equation. In order to generated such
trajectories in the phase space of this oscillator in this paper we use a the
quantum jumps unravelling together with a suitable application of the
correspondence principle. We analyse the measured readout by considering the
power spectra of photon counts produced by the quantum jumps. Here we show that
localisation of the wave packet from the measurement of the oscillator by the
photon detector produces a concomitant structure in the power spectra of the
measured output. Furthermore, we demonstrate that this spectral analysis can be
used to distinguish between different modes of the underlying dynamics of the
oscillator.Comment: 7 pages, 6 figure
Conditions for the Quantum to Classical Transition: Trajectories vs. Phase Space Distributions
We contrast two sets of conditions that govern the transition in which
classical dynamics emerges from the evolution of a quantum system. The first
was derived by considering the trajectories seen by an observer (dubbed the
``strong'' transition) [Bhattacharya, et al., Phys. Rev. Lett. 85: 4852
(2000)], and the second by considering phase-space densities (the ``weak''
transition) [Greenbaum, et al., Chaos 15, 033302 (2005)]. On the face of it
these conditions appear rather different. We show, however, that in the
semiclassical regime, in which the action of the system is large compared to
, and the measurement noise is small, they both offer an essentially
equivalent local picture. Within this regime, the weak conditions dominate
while in the opposite regime where the action is not much larger than Planck's
constant, the strong conditions dominate.Comment: 8 pages, 2 eps figure
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