51,255 research outputs found
Fluctuation-induced interactions between dielectrics in general geometries
We study thermal Casimir and quantum non-retarded Lifshitz interactions
between dielectrics in general geometries. We map the calculation of the
classical partition function onto a determinant which we discretize and
evaluate with the help of Cholesky factorization. The quantum partition
function is treated by path integral quantization of a set of interacting
dipoles and reduces to a product of determinants. We compare the approximations
of pairwise additivity and proximity force with our numerical methods. We
propose a ``factorization approximation'' which gives rather good numerical
results in the geometries that we study
Shear dispersion along circular pipes is affected by bends, but the torsion of the pipe is negligible
The flow of a viscous fluid along a curving pipe of fixed radius is driven by
a pressure gradient. For a generally curving pipe it is the fluid flux which is
constant along the pipe and so I correct fluid flow solutions of Dean (1928)
and Topakoglu (1967) which assume constant pressure gradient. When the pipe is
straight, the fluid adopts the parabolic velocity profile of Poiseuille flow;
the spread of any contaminant along the pipe is then described by the shear
dispersion model of Taylor (1954) and its refinements by Mercer, Watt et al
(1994,1996). However, two conflicting effects occur in a generally curving
pipe: viscosity skews the velocity profile which enhances the shear dispersion;
whereas in faster flow centrifugal effects establish secondary flows that
reduce the shear dispersion. The two opposing effects cancel at a Reynolds
number of about 15. Interestingly, the torsion of the pipe seems to have very
little effect upon the flow or the dispersion, the curvature is by far the
dominant influence. Lastly, curvature and torsion in the fluid flow
significantly enhance the upstream tails of concentration profiles in
qualitative agreement with observations of dispersion in river flow
Study of Quark Propagator Solutions to the Dyson--Schwinger Equation in a Confining Model
We solve the Dyson--Schwinger equation for the quark propagator in a model
with singular infrared behavior for the gluon propagator. We require that the
solutions, easily found in configuration space, be tempered distributions and
thus have Fourier transforms. This severely limits the boundary conditions that
the solutions may satisify. The sign of the dimensionful parameter that
characterizes the model gluon propagator can be either positive or negative. If
the sign is negative, we find a unique solution. It is singular at the origin
in momentum space, falls off like as , and it
is truly nonperturbative in that it is singular in the limit that the
gluon--quark interaction approaches zero. If the sign of the gluon propagator
coefficient is positive, we find solutions that are, in a sense that we
exhibit, unconstrained linear combinations of advanced and retarded
propagators. These solutions are singular at the origin in momentum space, fall
off like asympotically, exhibit ``resonant--like" behavior at the
position of the bare mass of the quark when the mass is large compared to the
dimensionful interaction parameter in the gluon propagator model, and smoothly
approach a linear combination of free--quark, advanced and retarded two--point
functions in the limit that the interaction approaches zero. In this sense,
these solutions behave in an increasingly ``particle--like" manner as the quark
becomes heavy. The Feynman propagator and the Wightman function are not
tempered distributions and therefore are not acceptable solutions to the
Schwinger--Dyson equation in our model. On this basis we advance several
arguments to show that the Fourier--transformable solutions we find are
consistent with quark confinement, even though they have singularities on th
Angular dependence of domain wall resistivity in artificial magnetic domain structures
We exploit the ability to precisely control the magnetic domain structure of
perpendicularly magnetized Pt/Co/Pt trilayers to fabricate artificial domain
wall arrays and study their transport properties. The scaling behaviour of this
model system confirms the intrinsic domain wall origin of the
magnetoresistance, and systematic studies using domains patterned at various
angles to the current flow are excellently described by an angular-dependent
resistivity tensor containing perpendicular and parallel domain wall
resistivities. We find that the latter are fully consistent with Levy-Zhang
theory, which allows us to estimate the ratio of minority to majority spin
carrier resistivities, rho-down/rho-up~5.5, in good agreement with thin film
band structure calculations.Comment: 14 pages, 3 figure
Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry
A sphere containing electrically conducting fluid can generate a magnetic field by dynamo action, provided the flow is sufficiently complicated and vigorous. The dynamo mechanism is thought to sustain magnetic fields in planets and stars. The kinematic dynamo problem tests steady flows for magnetic instability, but rather few dynamos have been found so far because of severe numerical difficulties. Dynamo action might, therefore, be quite unusual, at least for large-scale steady flows. We address this question by testing a two-parameter class of flows for dynamo generation of magnetic fields containing an axial dipole. The class of flows includes two completely different types of known dynamos, one dominated by differential rotation (D) and one with none. We find that 36% of the flows in seven distinct zones in parameter space act as dynamos, while the remaining 64% either fail to generate this type of magnetic field or generate fields that are too small in scale to be resolved by our numerical method. The two previously known dynamo types lie in the same zone, and it is therefore possible to change the flow continuously from one to the other without losing dynamo action. Differential rotation is found to promote large-scale axisymmetric toroidal magnetic fields, while meridional circulation (M) promotes large-scale axisymmetric poloidal fields concentrated at high latitudes near the axis. Magnetic fields resembling that of the Earth are generated by D > 0, corresponding to westward flow at the surface, and M of either sign but not zero. Very few oscillatory solutions are 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
The analytic structure of heavy quark propagators
The renormalised quark Dyson-Schwinger equation is studied in the limit of
the renormalised current heavy quark mass m_R --> infinity. We are particularly
interested in the analytic pole structure of the heavy quark propagator in the
complex momentum plane. Approximations in which the quark-gluon vertex is
modelled by either the bare vertex or the Ball-Chiu Ansatz, and the Landau
gauge gluon propagator takes either a gaussian form or a gaussian form with an
ultraviolet asymptotic tail are used.Comment: 21 pages Latex and 5 postscript figures. The original version of this
paper has been considerably extended to include a formalism dealing with the
renormalised heavy quark Dyson-Schwinger equation and uses a more realistic
Ansatz for the gluon propagator
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