2,837 research outputs found
The Square Root Depth Wave Equations
We introduce a set of coupled equations for multilayer water waves that
removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the
presence of shear. The new well-posed equations are Hamiltonian and in the
absence of imposed background shear they retain the same travelling wave
solutions as MGN. We call the new model the Square Root Depth equations, from
the modified form of their kinetic energy of vertical motion. Our numerical
results show how the Square Root Depth equations model the effects of
multilayer wave propagation and interaction, with and without shear.Comment: 10 pages, 5 figure
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 âOctopusâ, EPSRC âReactor Core-Structure Re-location Modelling for Severe Nuclear Accidentsâ) and Horizon 2020 âIn-Vessel Melt Retentionâ. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC âMulti-Scale Exploration of Multi-phase Physics in Flowsâ. 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
From Heisenberg matrix mechanics to EBK quantization: theory and first applications
Despite the seminal connection between classical multiply-periodic motion and
Heisenberg matrix mechanics and the massive amount of work done on the
associated problem of semiclassical (EBK) quantization of bound states, we show
that there are, nevertheless, a number of previously unexploited aspects of
this relationship that bear on the quantum-classical correspondence. In
particular, we emphasize a quantum variational principle that implies the
classical variational principle for invariant tori. We also expose the more
indirect connection between commutation relations and quantization of action
variables. With the help of several standard models with one or two degrees of
freedom, we then illustrate how the methods of Heisenberg matrix mechanics
described in this paper may be used to obtain quantum solutions with a modest
increase in effort compared to semiclassical calculations. We also describe and
apply a method for obtaining leading quantum corrections to EBK results.
Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.
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
Optical discrimination between spatial decoherence and thermalization of a massive object
We propose an optical ring interferometer to observe environment-induced
spatial decoherence of massive objects. The object is held in a harmonic trap
and scatters light between degenerate modes of a ring cavity. The output signal
of the interferometer permits to monitor the spatial width of the object's wave
function. It shows oscillations that arise from coherences between energy
eigenstates and that reveal the difference between pure spatial decoherence and
that coinciding with energy transfer and heating. Our method is designed to
work with a wide variety of masses, ranging from the atomic scale to
nano-fabricated structures. We give a thorough discussion of its experimental
feasibility.Comment: 2 figure
Friedmann Equation for Brans Dicke Cosmology
In the context of Brans-Dicke scalar tensor theory of gravitation, the
cosmological Friedmann equation which relates the expansion rate of the
universe to the various fractions of energy density is analyzed rigorously. It
is shown that Brans-Dicke scalar tensor theory of gravitation brings a
negligible correction to the matter density component of Friedmann equation.
Besides, in addition to and in standard
Einstein cosmology, another density parameter, , is
expected by the theory. This implies that if is found to
be nonzero, data will favor this model instead of the standard Einstein
cosmological model with cosmological constant and will enable more accurate
predictions for the rate of change of Newtonian gravitational constant in the
future.Comment: minor reference change
An Euler Poincar\'e framework for the multilayer Green Nagdhi equations
The Green Nagdhi equations are frequently used as a model of the wave-like
behaviour of the free surface of a fluid, or the interface between two
homogeneous fluids of differing densities. Here we show that their multilayer
extension arises naturally from a framework based on the Euler Poincare theory
under an ansatz of columnar motion. The framework also extends to the
travelling wave solutions of the equations. We present numerical solutions of
the travelling wave problem in a number of flow regimes. We find that the free
surface and multilayer waves can exhibit intriguing differences compared to the
results of single layer or rigid lid models
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
Quantum interference and sub-Poissonian statistics for time-modulated driven dissipative nonlinear oscillator
We show that quantum-interference phenomena can be realized for the
dissipative nonlinear systems exhibiting hysteresis-cycle behavior and quantum
chaos. Such results are obtained for a driven dissipative nonlinear oscillator
with time-dependent parameters and take place for the regimes of long time
intervals exceeding dissipation time and for macroscopic levels of oscillatory
excitation numbers. Two schemas of time modulation: (i) periodic variation of
the strength of the {\chi}(3) nonlinearity; (ii) periodic modulation of the
amplitude of the driving force, are considered. These effects are obtained
within the framework of phase-space quantum distributions. It is demonstrated
that the Wigner functions of oscillatory mode in both bistable and chaotic
regimes acquire negative values and interference patterns in parts of
phase-space due to appropriately time-modulation of the oscillatory nonlinear
dynamics. It is also shown that the time-modulation of the oscillatory
parameters essentially improves the degree of sub-Poissonian statistics of
excitation numbers
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
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