668 research outputs found
Antiferromagnetism and singlet formation in underdoped high-Tc cuprates: Implications for superconducting pairing
The extended model is theoretically studied, in the context of hole
underdoped cuprates. Based on results obtained by recent numerical studies, we
identify the mean field state having both the antiferromagnetic and staggered
flux resonating valence bond orders. The random-phase approximation is employed
to analyze all the possible collective modes in this mean field state. In the
static (Bardeen Cooper Schrieffer) limit justified in the weak coupling regime,
we obtain the effective superconducting interaction between the doped holes at
the small pockets located around . In contrast
to the spin-bag theory, which takes into acccount only the antiferromagnetic
order, this effective force is pair breaking for the pairing without the nodes
in each of the small hole pocket, and is canceled out to be very small for the
pairing with nodes which is realized in the real cuprates.
Therefore we conclude that no superconducting instability can occur when only
the magnetic mechanism is considered. The relations of our work with other
approaches are also discussed.Comment: 20 pages, 7 figures, REVTeX; final version accepted for publicatio
A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation
We present a new class of exact solutions for the so-called {\it Laplacian
Growth Equation} describing the zero-surface-tension limit of a variety of 2D
pattern formation problems. Contrary to common belief, we prove that these
solutions are free of finite-time singularities (cusps) for quite general
initial conditions and may well describe real fingering instabilities. At long
times the interface consists of N separated moving Saffman-Taylor fingers, with
``stagnation points'' in between, in agreement with numerous observations. This
evolution resembles the N-soliton solution of classical integrable PDE's.Comment: LaTeX, uuencoded postscript file
Gravity-driven instability in a spherical Hele-Shaw cell
A pair of concentric spheres separated by a small gap form a spherical
Hele-Shaw cell. In this cell an interfacial instability arises when two
immiscible fluids flow. We derive the equation of motion for the interface
perturbation amplitudes, including both pressure and gravity drivings, using a
mode coupling approach. Linear stability analysis shows that mode growth rates
depend upon interface perimeter and gravitational force. Mode coupling analysis
reveals the formation of fingering structures presenting a tendency toward
finger tip-sharpening.Comment: 13 pages, 4 ps figures, RevTex, to appear in Physical Review
Multidimensional Pattern Formation Has an Infinite Number of Constants of Motion
Extending our previous work on 2D growth for the Laplace equation we study
here {\it multidimensional} growth for {\it arbitrary elliptic} equations,
describing inhomogeneous and anisotropic pattern formations processes. We find
that these nonlinear processes are governed by an infinite number of
conservation laws. Moreover, in many cases {\it all dynamics of the interface
can be reduced to the linear time--dependence of only one ``moment" }
which corresponds to the changing volume while {\it all higher moments, ,
are constant in time. These moments have a purely geometrical nature}, and thus
carry information about the moving shape. These conserved quantities (eqs.~(7)
and (8) of this article) are interpreted as coefficients of the multipole
expansion of the Newtonian potential created by the mass uniformly occupying
the domain enclosing the moving interface. Thus the question of how to recover
the moving shape using these conserved quantities is reduced to the classical
inverse potential problem of reconstructing the shape of a body from its
exterior gravitational potential. Our results also suggest the possibility of
controlling a moving interface by appropriate varying the location and strength
of sources and sinks.Comment: CYCLER Paper 93feb00
Microscopic Selection of Fluid Fingering Pattern
We study the issue of the selection of viscous fingering patterns in the
limit of small surface tension. Through detailed simulations of anisotropic
fingering, we demonstrate conclusively that no selection independent of the
small-scale cutoff (macroscopic selection) occurs in this system. Rather, the
small-scale cutoff completely controls the pattern, even on short time scales,
in accord with the theory of microscopic solvability. We demonstrate that
ordered patterns are dynamically selected only for not too small surface
tensions. For extremely small surface tensions, the system exhibits chaotic
behavior and no regular pattern is realized.Comment: 6 pages, 5 figure
Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell
We report analytical results for the development of the viscous fingering
instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We
derive a generalized version of Darcy's law in such cylindrical background, and
find it recovers the usual Darcy's law for flow in flat, rectangular cells,
with corrections of higher order in b/a. We focus our interest on the influence
of cell's radius of curvature on the instability characteristics. Linear and
slightly nonlinear flow regimes are studied through a mode-coupling analysis.
Our analytical results reveal that linear growth rates and finger competition
are inhibited for increasingly larger radius of curvature. The absence of
tip-splitting events in cylindrical cells is also discussed.Comment: 14 pages, 3 ps figures, Revte
Scaling Relations of Viscous Fingers in Anisotropic Hele-Shaw Cells
Viscous fingers in a channel with surface tension anisotropy are numerically
studied. Scaling relations between the tip velocity v, the tip radius and the
pressure gradient are investigated for two kinds of boundary conditions of
pressure, when v is sufficiently large. The power-law relations for the
anisotropic viscous fingers are compared with two-dimensional dendritic growth.
The exponents of the power-law relations are theoretically evaluated.Comment: 5 pages, 4 figure
Universal Power Law in the Noise from a Crumpled Elastic Sheet
Using high-resolution digital recordings, we study the crackling sound
emitted from crumpled sheets of mylar as they are strained. These sheets
possess many of the qualitative features of traditional disordered systems
including frustration and discrete memory. The sound can be resolved into
discrete clicks, emitted during rapid changes in the rough conformation of the
sheet. Observed click energies range over six orders of magnitude. The measured
energy autocorrelation function for the sound is consistent with a stretched
exponential C(t) ~ exp(-(t/T)^{b}) with b = .35. The probability distribution
of click energies has a power law regime p(E) ~ E^{-a} where a = 1. We find the
same power law for a variety of sheet sizes and materials, suggesting that this
p(E) is universal.Comment: 5 pages (revtex), 10 uuencoded postscript figures appended, html
version at http://rainbow.uchicago.edu/~krame
Parallel flow in Hele-Shaw cells with ferrofluids
Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow
with relative velocity parallel to the interface between them. The interface is
unstable due to a Kelvin-Helmholtz type of instability in which fluid flow
couples with inertial effects to cause an initial small perturbation to grow.
Large amplitude disturbances form stable solitons. We consider the effects of
applied magnetic fields when one of the two fluids is a ferrofluid. The
dispersion relation governing mode growth is modified so that the magnetic
field can destabilize the interface even in the absence of inertial effects.
However, the magnetic field does not affect the speed of wave propagation for a
given wavenumber. We note that the magnetic field creates an effective
interaction between the solitons.Comment: 12 pages, Revtex, 2 figures, revised version (minor changes
Fluctuations in viscous fingering
Our experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels
reveal finger width fluctuations that were not observed in previous
experiments, which had lower aspect ratios and higher capillary numbers Ca.
These fluctuations intermittently narrow the finger from its expected width.
The magnitude of these fluctuations is described by a power law, Ca^{-0.64},
which holds for all aspect ratios studied up to the onset of tip instabilities.
Further, for large aspect ratios, the mean finger width exhibits a maximum as
Ca is decreased instead of the predicted monotonic increase.Comment: Revised introduction, smoothed transitions in paper body, and added a
few additional minor results. (Figures unchanged.) 4 pages, 3 figures.
Submitted to PRE Rapi
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