Exact trace formulae for a class of one-dimensional ray-splitting systems

Based on quantum graph theory we establish that the ray-splitting trace formula proposed by Couchman {\it et al.} (Phys. Rev. A {\bf 46}, 6193 (1992)) is exact for a class of one-dimensional ray-splitting systems. Important applications in combinatorics are suggested.Comment: 14 pages, 3 figure

Novel criticality in a model with absorbing states

We study a one-dimensional model which undergoes a transition between an active and an absorbing phase. Monte Carlo simulations supported by some additional arguments prompted as to predict the exact location of the critical point and critical exponents in this model. The exponents $\delta=0.5$ and $z=2$ follows from random-walk-type arguments. The exponents $\beta = \nu_{\perp}$ are found to be non-universal and encoded in the singular part of reactivation probability, as recently discussed by H. Hinrichsen (cond-mat/0008179). A related model with quenched randomness is also studied.Comment: 5 pages, 5 figures, generalized version with the continuously changing exponent bet

Critical depinning force and vortex lattice order in disordered superconductors

We simulate the ordering of vortices and its effects on the critical current in superconductors with varied vortex-vortex interaction strength and varied pinning strengths for a two-dimensional system. For strong pinning the vortex lattice is always disordered and the critical depinning force only weakly increases with decreasing vortex-vortex interactions. For weak pinning the vortex lattice is defect free until the vortex-vortex interactions have been reduced to a low value, when defects begin to appear with a simultaneous rapid increase in the critical depinning force. In each case the depinning force shows a maximum for non-interacting vortices. The relative height of the peak increases and the peak width decreases for decreasing pinning strength in excellent agreement with experimental trends associated with the peak effect. We show that scaling relations exist between the distance between defects in the vortex lattice and the critical depinning force.Comment: 5 pages, 6 figure

Equipment design for biosorption studies with microorganisms

Two laboratory devices have been designed for experimental use in biosorption studies involving the uptake and controlled release of elements from encapsulated living cells of microorganisms. The first device is an alginate bead maker capable of producing uniform (1.5 mm diameter) sodium alginate beads with encapsulated microorganisms. The second device is a flow-cell that can subject the encapsulated microorganisms to changing fluids, streaming gaseous microaerophyllic conditions, and which also allows for samples of fluid and beads to be extracted at any time during changing experimental conditions. Both devices are novel and simple in their design, and enable improved accuracy and precise handling of encapsulated specimens with minimal labour and expenditure

Transverse depinning in strongly driven vortex lattices with disorder

Using numerical simulations we investigate the transverse depinning of moving vortex lattices interacting with random disorder. We observe a finite transverse depinning barrier for vortex lattices that are driven with high longitudinal drives, when the vortex lattice is defect free and moving in correlated 1D channels. The transverse barrier is reduced as the longitudinal drive is decreased and defects appear in the vortex lattice, and the barrier disappears in the plastic flow regime. At the transverse depinning transition, the vortex lattice moves in a staircase pattern with a clear transverse narrow-band voltage noise signature.Comment: 4 pages, 4 figure

Critical Currents and Vortex States at Fractional Matching Fields in Superconductors with Periodic Pinning

We study vortex states and dynamics in 2D superconductors with periodic pinning at fractional sub-matching fields using numerical simulations. For square pinning arrays we show that ordered states form at 1/1, 1/2, and 1/4 filling fractions while only partially ordered states form at other filling fractions, such as 1/3 and 1/5, in agreement with recent imaging experiments. For triangular pinning arrays we observe matching effects at filling fractions of 1/1, 6/7, 2/3, 1/3, 1/4, 1/6, and 1/7. For both square and triangular pinning arrays we also find that, for certian sub-matching fillings, vortex configurations depend on pinning strength. For weak pinning, ordering in which a portion of the vortices are positioned between pinning sites can occur. Depinning of the vortices at the matching fields, where the vortices are ordered, is elastic while at the incommensurate fields the motion is plastic. At the incommensurate fields, as the applied driving force is increased, there can be a transition to elastic flow where the vortices move along the pinning sites in 1D channels and a reordering transition to a triangular or distorted triangular lattice. We also discuss the current-voltage curves and how they relate to the vortex ordering at commensurate and incommensurate fields.Comment: 14 figure

Dynamic Vortex Phases and Pinning in Superconductors with Twin Boundaries

We investigate the pinning and driven dynamics of vortices interacting with twin boundaries using large scale molecular dynamics simulations on samples with near one million pinning sites. For low applied driving forces, the vortex lattice orients itself parallel to the twin boundary and we observe the creation of a flux gradient and vortex free region near the edges of the twin boundary. For increasing drive, we find evidence for several distinct dynamical flow phases which we characterize by the density of defects in the vortex lattice, the microscopic vortex flow patterns, and orientation of the vortex lattice. We show that these different dynamical phases can be directly related to microscopically measurable voltage - current V(I) curves and voltage noise. By conducting a series of simulations for various twin boundary parameters we derive several vortex dynamic phase diagrams.Comment: 5 figures, to appear in Phys. Rev.

Collagen 11a1 is Indirectly Activated by Lymphocyte Enhancer-Binding Factor 1 (Lef1) and Negatively Regulates Osteoblast Maturation

Alpha 1 (XI) collagen (Col11a1) is essential for normal skeletal development. Mutations in Col11a1 cause Marshall and Stickler syndromes, characterized by craniofacial abnormalities, nearsightedness and hearing abnormalities. Despite its link to human diseases, few studies have characterized the factors that control Col11a1 transcription. We previously identified Col11a1 as a differentially expressed gene in Lef1-suppressed MC3T3 preosteoblasts. Here we report that Lef1 activates the Col11a1 promoter. This activation is dependent upon the DNA binding domain of Lef1, but does not require the ß-catenin interaction domain, suggesting that it is not responsive to Wnt signals. Targeted deletion of Col11a1 with an antisense morpholino accelerated osteoblastic differentiation and mineralization in C2C12 cells, similar to what was observed in Lef1-suppressed MC3T3 cells. Moreover incubation with a purified Col11a1 N-terminal fragment, V1B, prevented alkaline phosphatase expression in MC3T3 and C2C12 cells. These results suggest that Lef1 is an activator of the Col11a1 promoter and that Col11a1 suppresses terminal osteoblast differentiation