Antiferromagnetism and singlet formation in underdoped high-Tc cuprates: Implications for superconducting pairing

The extended $t-J$ 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 $\bm{k}= (\pm \pi/2, \pm \pi/2)$. 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 $d_{x^2-y^2}$ 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

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study

We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary Saffman-Taylor fingers and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed for the linear dispersion results. We show that the method may be a useful alternative to more traditional methods.Comment: 13 pages in revtex, 5 PostScript figures. changes: 1 reference added, figs. 4 and 5 rearrange

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

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a channel is developed. This is based on the global study of the phase space structure of the low-dimensional ODE's defined by the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail, and general proofs concerning properties of fixed points and existence of finite-time singularities for broad classes of solutions are given. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. The main conclusion is that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space spanning a sufficiently large set of initial conditions, are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding of them does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is discussed as the key point for a generic Dynamical Solvability Scenario which is proposed for a general context of interfacial pattern selection.Comment: 3 figures added, major rewriting of some sections, submitted to Phys. Rev.

Bistability of Slow and Fast Traveling Waves in Fluid Mixtures

The appearence of a new type of fast nonlinear traveling wave states in binary fluid convection with increasing Soret effect is elucidated and the parameter range of their bistability with the common slower ones is evaluated numerically. The bifurcation behavior and the significantly different spatiotemporal properties of the different wave states - e.g. frequency, flow structure, and concentration distribution - are determined and related to each other and to a convenient measure of their nonlinearity. This allows to derive a limit for the applicability of small amplitude expansions. Additionally an universal scaling behavior of frequencies and mixing properties is found. PACS: 47.20.-k, 47.10.+g, 47.20.KyComment: 4 pages including 5 Postscript figure

Finite size effects near the onset of the oscillatory instability

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects

Rotating Hele-Shaw cells with ferrofluids

We investigate the flow of two immiscible, viscous fluids in a rotating Hele-Shaw cell, when one of the fluids is a ferrofluid and an external magnetic field is applied. The interplay between centrifugal and magnetic forces in determining the instability of the fluid-fluid interface is analyzed. The linear stability analysis of the problem shows that a non-uniform, azimuthal magnetic field, applied tangential to the cell, tends to stabilize the interface. We verify that maximum growth rate selection of initial patterns is influenced by the applied field, which tends to decrease the number of interface ripples. We contrast these results with the situation in which a uniform magnetic field is applied normally to the plane defined by the rotating Hele-Shaw cell.Comment: 12 pages, 3 ps figures, RevTe

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