Surface solitons in quasiperiodic nonlinear photonic lattices

We study discrete surface solitons in semi-infinite, one-dimensional, nonlinear (Kerr), quasiperiodic waveguide arrays of the Fibonacci and Aubry-Andr\'e types, and explore different families of localized surface modes, as a function of optical power content (`nonlinearity') and quasiperiodic strength (`disorder'). We find a strong asymmetry in the power content of the mode as a function of the propagation constant, between the cases of focussing and defocussing nonlinearity, in both models. We also examine the dynamical evolution of a completely-localized initial excitation at the array surface. We find that in general, for a given optical power, a smaller quasiperiodic strength is required to effect localization at the surface than in the bulk. Also, for fixed quasiperiodic strength, a smaller optical power is needed to localize the excitation at the edge than inside the bulk.Comment: 8 pages, 7 figures, submitted for publicatio

Inhomogeneous superconductivity and the "pseudogap state of novel superconductors

Novel superconducting compounds such as the high Tc oxides are intrinsically inhomogeneous systems. An inhomogeneous structure is created by doping and the statistical nature of the distribution of dopants. Consequently, the critical temperature is spatially dependent: Tc = Tc (r).Comment: 63 pages text, 13 figures and 1 tabl

Two-loop renormalization-group theory for the quasi-one-dimensional Hubbard model at half filling

We derive two-loop renormalization-group equations for the half-filled one-dimensional Hubbard chains coupled by the interchain hopping. Our renormalization-group scheme for the quasi-one-dimensional electron system is a natural extension of that for the purely one-dimensional systems in the sense that transverse-momentum dependences are introduced in the g-ological coupling constants and we regard the transverse momentum as a patch index. We develop symmetry arguments for the particle-hole symmetric half-filled Hubbard model and obtain constraints on the g-ological coupling constants by which resultant renormalization equations are given in a compact form. By solving the renormalization-group equations numerically, we estimate the magnitude of excitation gaps and clarify that the charge gap is suppressed due to the interchain hopping but is always finite even for the relevant interchain hopping. To show the validity of the present analysis, we also apply this to the two-leg ladder system. By utilizing the field-theoretical bosonization and fermionization method, we derive low-energy effective theory and analyze the magnitude of all the excitation gaps in detail. It is shown that the low-energy excitations in the two-leg Hubbard ladder have SO(3) x SO(3) x U(1) symmetry when the interchain hopping exceeds the magnitude of the charge gap.Comment: 18 pages, 9 figures; Two appendices and one figure adde

Growth Kinetics in Systems with Local Symmetry

The phase transition kinetics of Ising gauge models are investigated. Despite the absence of a local order parameter, relevant topological excitations that control the ordering kinetics can be identified. Dynamical scaling holds in the approach to equilibrium, and the growth of typical length scale is characteristic of a new universality class with $L(t)\sim \left(t/\ln t\right)^{1/2}$. We suggest that the asymptotic kinetics of the 2D Ising gauge model is dual to that of the 2D annihilating random walks, a process also known as the diffusion-reaction $A+A\to \hbox{inert}$.Comment: 10 pages in Tex, 2 Postscript figures appended, NSF-ITP-93-4

Survival Probability of a Ballistic Tracer Particle in the Presence of Diffusing Traps

We calculate the survival probability P_S(t) up to time t of a tracer particle moving along a deterministic trajectory in a continuous d-dimensional space in the presence of diffusing but mutually noninteracting traps. In particular, for a tracer particle moving ballistically with a constant velocity c, we obtain an exact expression for P_S(t), valid for all t, for d<2. For d \geq 2, we obtain the leading asymptotic behavior of P_S(t) for large t. In all cases, P_S(t) decays exponentially for large t, P_S(t) \sim \exp(-\theta t). We provide an explicit exact expression for the exponent \theta in dimensions d \leq 2, and for the physically relevant case, d=3, as a function of the system parameters.Comment: RevTeX, 4 page

Superconductivity from correlated hopping

We consider a chain described by a next-nearest-neighbor hopping combined with a nearest-neighbor spin flip. In two dimensions this three-body term arises from a mapping of the three-band Hubbard model for CuO$_2$ planes to a generalized $t-J$ model and for large O-O hopping favors resonance-valence-bond superconductivity of predominantly $d$-wave symmetry. Solving the ground state and low-energy excitations by analytical and numerical methods we find that the chain is a Luther-Emery liquid with correlation exponent $K_{\rho} = (2-n)^2/2$, where $n$ is the particle density.Comment: 10 pages, RevTeX 3.0 + 2 PostScript figs. Accepted for publication in Phys.Rev.

Renormalization group analysis of the spin-gap phase in the one-dimensional t-J model

We study the spin-gap phase in the one-dimensional t-J model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also check that the universality class of the transition belongs to the $k=1$ SU(2) Wess-Zumino-Witten model.Comment: 4 pages(RevTeX), 5 figures(EPS), TITCMT-97-10, to appear in Phys. Rev. Let

Survival of Chondrocytes in Rabbit Septal Cartilage After Electromechanical Reshaping

Electromechanical reshaping (EMR) has been recently described as an alternative method for reshaping facial cartilage without the need for incisions or sutures. This study focuses on determining the short- and long-term viability of chondrocytes following EMR in cartilage grafts maintained in tissue culture. Flat rabbit nasal septal cartilage specimens were bent into semi-cylindrical shapes by an aluminum jig while a constant electric voltage was applied across the concave and convex surfaces. After EMR, specimens were maintained in culture media for 64 days. Over this time period, specimens were serially biopsied and then stained with a fluorescent live–dead assay system and imaged using laser scanning confocal microscopy. In addition, the fraction of viable chondrocytes was measured, correlated with voltage, voltage application time, electric field configuration, and examined serially. The fraction of viable chondrocytes decreased with voltage and application time. High local electric field intensity and proximity to the positive electrode also focally reduced chondrocyte viability. The density of viable chondrocytes decreased over time and reached a steady state after 2–4 weeks. Viable cells were concentrated within the central region of the specimen. Approximately 20% of original chondrocytes remained viable after reshaping with optimal voltage and application time parameters and compared favorably with conventional surgical shape change techniques such as morselization

Space-and time-resolved diffusion-limited binary reaction kinetics in capillaries: experimental observation of segregation, anomalous exponents, and depletion zone

An experimental investigation of one-dimensional, diffusion-limited A+B→C chemical reactions is reported. The persistence of reactant segregation and the formation of a depletion zone is observed and expressed in terms of the universal time exponents: α (motion of the boundary zone), β (width of instantaneous product formation zone), γ (rate of instantaneous local formation of product), δ (rate of instantaneous global formation of product), etc. There is good agreement with the recently predicted and/or simulated values: α =1/2, β =1/6, γ =2/3, δ =1/2, in contrast to classical predictions ( α =0, β =1/2, γ =0, δ =−1/2). Furthermore, classically the segregation would not be preserved and there would be no formation of a depletion zone and no motion (just dissipation) of the reaction zone. We also discuss the relations to electrode oxidation-reduction reactions, i.e., A+C→C where C is a catalyst, electrode, or “trap.”Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45162/1/10955_2005_Article_BF01049588.pd