3,657 research outputs found
Surface properties of ocean fronts
Background information on oceanic fronts is presented and the results of several models which were developed to study the dynamics of oceanic fronts and their effects on various surface properties are described. The details of the four numerical models used in these studies are given in separate appendices which contain all of the physical equations, program documentation and running instructions for the models
Recurrence in generic staircases
The straight-line flow on almost every staircase and on almost every square
tiled staircase is recurrent. For almost every square tiled staircase the set
of periodic orbits is dense in the phase space
Dimensional analysis using toric ideals: Primitive invariants
© 2014 Atherton et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units M, L, T etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer K matrix from the initial integer A matrix holding the exponents for the derived quantities. The K matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by A. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of K, is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.The third author received funding from Leverhulme Trust Emeritus Fellowship (1-SST-U445) and United Kingdom EPSRC grant: MUCM EP/D049993/1
Domain wall propagation through spin wave emission
We theoretically study field-induced domain wall (DW) motion in an
electrically insulating ferromagnet with hard- and easy-axis anisotropies. DWs
can propagate along a dissipationless wire through spin wave emission locked
into the known soliton velocity at low fields. In the presence of damping, the
mode appears before the Walker breakdown field for strong out-of-plane magnetic
anisotropy, and the usual Walker rigid-body propagation mode becomes unstable
when the field is between the maximal-DW-speed field and Walker breakdown
field.Comment: 4 pages, 4 figure
Demagnetization Borne Microscale Skyrmions
Magnetic systems are an exciting realm of study that is being explored on
smaller and smaller scales. One extremely interesting magnetic state that has
gained momentum in recent years is the skyrmionic state. It is characterized by
a vortex where the edge magnetic moments point opposite to the core. Although
skyrmions have many possible realizations, in practice, creating them in a lab
is a difficult task to accomplish. In this work, new methods for skyrmion
generation and customization are suggested. Skyrmionic behavior was numerically
observed in minimally customized simulations of spheres, hemisphere,
ellipsoids, and hemi-ellipsoids, for typ- ical Cobalt parameters, in a range
from approximately 40 nm to 120 nm in diameter simply by applying a field
Existence of vertical spin stiffness in Landau-Lifshitz-Gilbert equation in ferromagnetic semiconductors
We calculate the magnetization torque due to the spin polarization of the
itinerant electrons by deriving the kinetic spin Bloch equations based on the
- model. We find that the first-order gradient of the magnetization
inhomogeneity gives rise to the current-induced torques, which are consistent
to the previous works. At the second-order gradient, we find an effective
magnetic field perpendicular to the spin stiffness filed. This field is
proportional to the nonadiabatic parameter . We show that this vertical
spin stiffness term can significantly modify the domain-wall structure in
ferromagnetic semiconductors and hence should be included in the
Landau-Lifshitz-Gilbert equation in studying the magnetization dynamics.Comment: 7 pages, 4 figure
Ergodic directions for billiards in a strip with periodically located obstacles
We study the size of the set of ergodic directions for the directional
billiard flows on the infinite band with periodically placed
linear barriers of length . We prove that the set of ergodic
directions is always uncountable. Moreover, if is rational
the Hausdorff dimension of the set of ergodic directions is greater than 1/2.
In both cases (rational and irrational) we construct explicitly some sets of
ergodic directions.Comment: The article is complementary to arXiv:1109.458
Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
Measurements transfer information about a system to the apparatus, and then
further on -- to observers and (often inadvertently) to the environment. I show
that even imperfect copying essential in such situations restricts possible
unperturbed outcomes to an orthogonal subset of all possible states of the
system, thus breaking the unitary symmetry of its Hilbert space implied by the
quantum superposition principle. Preferred outcome states emerge as a result.
They provide framework for the ``wavepacket collapse'', designating terminal
points of quantum jumps, and defining the measured observable by specifying its
eigenstates. In quantum Darwinism, they are the progenitors of multiple copies
spread throughout the environment -- the fittest quantum states that not only
survive decoherence, but subvert it into carrying information about them --
into becoming a witness.Comment: For comments see Seth Lloyd, NATURE 450, 1167 (2007
Thomas Decomposition of Algebraic and Differential Systems
In this paper we consider disjoint decomposition of algebraic and non-linear
partial differential systems of equations and inequations into so-called simple
subsystems. We exploit Thomas decomposition ideas and develop them into a new
algorithm. For algebraic systems simplicity means triangularity, squarefreeness
and non-vanishing initials. For differential systems the algorithm provides not
only algebraic simplicity but also involutivity. The algorithm has been
implemented in Maple
Study of secondary-flow patterns in an annular cascade of turbine nozzle blades with vortex design
In order to increase understanding of the origin of losses in a turbine, the secondary-flow components in the boundary layers and the blade wakes of an annular cascade of turbine nozzle blades (vortex design) was investigated. A detailed study was made of the total-pressure contours and, particularly, of the inner-wall loss cores downstream of the blades. The inner-wall loss core associated with a blade of the turbine-nozzle cascade is largely the accumulation of low-momentum fluids originating elsewhere in the cascade. This accumulation is effected by a secondary-flow mechanism which acts to transport the low-momentum fluids across the channels on the walls and radially in the blade wakes and boundary layers. The patterns of secondary flow were determined by use of hydrogen sulfide traces, paint, flow fences, and total pressure surveys. At one flow condition investigated, the radial transport of low-momentum fluid in the blade wake and on the suction surface near the trailing edge accounted for 65 percent of the loss core; 30 percent resulted from flow in the thickened boundary layer on the suction surface and 35 percent from flow in the blade wake
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