720 research outputs found
Stretching an heteropolymer
We study the influence of some quenched disorder in the sequence of monomers
on the entropic elasticity of long polymeric chains. Starting from the
Kratky-Porod model, we show numerically that some randomness in the favoured
angles between successive segments induces a change in the elongation versus
force characteristics, and this change can be well described by a simple
renormalisation of the elastic constant. The effective coupling constant is
computed by an analytic study of the low force regime.Comment: Latex, 7 pages, 3 postscript figur
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
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
Characteristic Angles in the Wetting of an Angular Region: Deposit Growth
As was shown in an earlier paper [1], solids dispersed in a drying drop
migrate to the (pinned) contact line. This migration is caused by outward flows
driven by the loss of the solvent due to evaporation and by geometrical
constraint that the drop maintains an equilibrium surface shape with a fixed
boundary. Here, in continuation of our earlier paper [2], we theoretically
investigate the evaporation rate, the flow field and the rate of growth of the
deposit patterns in a drop over an angular sector on a plane substrate.
Asymptotic power laws near the vertex (as distance to the vertex goes to zero)
are obtained. A hydrodynamic model of fluid flow near the singularity of the
vertex is developed and the velocity field is obtained. The rate of the deposit
growth near the contact line is found in two time regimes. The deposited mass
falls off as a weak power Gamma of distance close to the vertex and as a
stronger power Beta of distance further from the vertex. The power Gamma
depends only slightly on the opening angle Alpha and stays between roughly -1/3
and 0. The power Beta varies from -1 to 0 as the opening angle increases from 0
to 180 degrees. At a given distance from the vertex, the deposited mass grows
faster and faster with time, with the greatest increase in the growth rate
occurring at the early stages of the drying process.Comment: v1: 36 pages, 21 figures, LaTeX; submitted to Physical Review E; v2:
minor additions to Abstract and Introductio
A note on the extension of the polar decomposition for the multidimensional Burgers equation
It is shown that the generalizations to more than one space dimension of the
pole decomposition for the Burgers equation with finite viscosity and no force
are of the form u = -2 viscosity grad log P, where the P's are explicitly known
algebraic (or trigonometric) polynomials in the space variables with polynomial
(or exponential) dependence on time. Such solutions have polar singularities on
complex algebraic varieties.Comment: 3 pages; minor formatting and typos corrected. Submitted to Phys.
Rev. E (Rapid Comm.
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
Two-finger selection theory in the Saffman-Taylor problem
We find that solvability theory selects a set of stationary solutions of the
Saffman-Taylor problem with coexistence of two \it unequal \rm fingers
advancing with the same velocity but with different relative widths
and and different tip positions. For vanishingly small
dimensionless surface tension , an infinite discrete set of values of the
total filling fraction and of the relative
individual finger width are selected out of a
two-parameter continuous degeneracy. They scale as
and . The selected values of differ from
those of the single finger case. Explicit approximate expressions for both
spectra are given.Comment: 4 pages, 3 figure
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