Magnetic flux pinning in superconductors with hyperbolic-tesselation arrays of pinning sites

We study magnetic flux interacting with arrays of pinning sites (APS) placed on vertices of hyperbolic tesselations (HT). We show that, due to the gradient in the density of pinning sites, HT APS are capable of trapping vortices for a broad range of applied magnetic fluxes. Thus, the penetration of magnetic field in HT APS is essentially different from the usual scenario predicted by the Bean model. We demonstrate that, due to the enhanced asymmetry of the surface barrier for vortex entry and exit, this HT APS could be used as a "capacitor" to store magnetic flux.Comment: 7 pages, 5 figure

Critical currents in superconductors with quasiperiodic pinning arrays: One-dimensional chains and two-dimensional Penrose lattices

We study the critical depinning current J_c, as a function of the applied magnetic flux Phi, for quasiperiodic (QP) pinning arrays, including one-dimensional (1D) chains and two-dimensional (2D) arrays of pinning centers placed on the nodes of a five-fold Penrose lattice. In 1D QP chains of pinning sites, the peaks in J_c(Phi) are shown to be determined by a sequence of harmonics of long and short periods of the chain. This sequence includes as a subset the sequence of successive Fibonacci numbers. We also analyze the evolution of J_c(Phi) while a continuous transition occurs from a periodic lattice of pinning centers to a QP one; the continuous transition is achieved by varying the ratio gamma = a_S/a_L of lengths of the short a_S and the long a_L segments, starting from gamma = 1 for a periodic sequence. We find that the peaks related to the Fibonacci sequence are most pronounced when gamma is equal to the "golden mean". The critical current J_c(Phi) in QP lattice has a remarkable self-similarity. This effect is demonstrated both in real space and in reciprocal k-space. In 2D QP pinning arrays (e.g., Penrose lattices), the pinning of vortices is related to matching conditions between the vortex lattice and the QP lattice of pinning centers. Although more subtle to analyze than in 1D pinning chains, the structure in J_c(Phi) is determined by the presence of two different kinds of elements forming the 2D QP lattice. Indeed, we predict analytically and numerically the main features of J_c(Phi) for Penrose lattices. Comparing the J_c's for QP (Penrose), periodic (triangular) and random arrays of pinning sites, we have found that the QP lattice provides an unusually broad critical current J_c(Phi), that could be useful for practical applications demanding high J_c's over a wide range of fields.Comment: 18 pages, 15 figures (figures 7, 9, 10, 13, 15 in separate "png" files

Mitofusin 2 Regulated Transport of Mitochondria is Necessary for Axonal Integrity

The ubiquitous finding of axonal degeneration in a number of the most prevalent neuropathologies marks the importance of understanding axonal biology and the axonal self-destruct mechanism. Though our understanding of axonal degeneration remains largely incomplete, several down-steam steps of the molecular cascade have been elucidated. While this insight has emerged from models of axon degeneration following physical injury or toxic insult, a more comprehensive understanding of the upstream events may be gained from studying primary axonopathies with defined genetic causes. This dissertation aims to elucidate a molecular mechanism underlying the loss of axons in Charcot-Marie-Tooth Disease type 2A, which is caused by mutations in the mitofusin 2: MFN2) gene. Utilizing an in vitro culture system, we find that CMT2A associated MFN2 mutants disrupt the transport of axonal mitochondria in DRG neurons. Though MFN2 has a previously defined role in facilitating mitochondrial fusion, we propose a direct role for MFN2 in mediating transport based on its interaction with key components of the mitochondrial transport apparatus and perturbation of transport in MFN2 null DRG neurons. MFN2 does not provide a direct link between mitochondria and microtubule based motors, but is poised to mediate transport by a still undefined mechanism. The ability of MFN2 to mediate transport is separate from its ability to mediate fusion as MFN2 disease mutants, that have been shown to retain their ability to fuse mitochondria, cannot rescue the transport deficit in MFN2 null neurons. Additionally, loss of mitochondrial fusion by knockdown of opa-1 is not sufficient to disrupt mitochondrial transport despite reduced mitochondrial function. These findings may explain why mutations in or haplo-insufficiency of opa-1 leads to Dominant Optic Atrophy: DOA) but not degeneration of long peripheral axons, highlighting the potential importance of mitochondrial transport for axon integrity. To further test our hypothesis that mitochondrial transport is critical for the integrity of axons, we expressed MFN2 mutants in cultured DRG neurons and looked for signs of degenerating axons. High levels of Ca2+€€ or reactive oxygen species: ROS) delineated a population of degenerating axons that we not observed in opa-1 knock down cultures. Mitochondria in MFN2 mutant expressing cells showed little change in membrane potential compared to a significant change in the mitochondrial membrane potential of opa-1 silenced cells; however, both groups of cultured neurons upregulated glycolysis and were sensitive to treatment with 2DG. We hypothesize that these changes in the MFN2 mutant expressing cells could be explained by lack of mitochondrial flux across segments of axon which must resort to use of glycolysis. The absence of mitochondria could cause segments of axon to become vulnerable to local perturbations in energy or Ca2+ levels and explain the axonal degeneration observed in culture. In this way, disrupted redistribution of mitochondria in CMT2A patients would put the longest axons at the highest risk due to the probability of incurring at least one insult along its length for which mitochondria could not compensate. Finally we attempted to study an animal model of CMT2A to see if our in vitro findings we recapitulated in vivo. To this end we obtained a mouse line in which the R94Q mutation had been knocked in to the endogenous allele. To accurately mirror conditions in CMT2A patients we chose to analyze heterozygous mice. Though homozygous mice die by the third postnatal week, heterozygous mice are phenotypically normal showing no signs of axon loss or muscle denervation. Differential expression of the MFN2 homologue MFN1, absolute length of axons or absolute time to disease may account for the discrepancy between the mouse model and human patients. Hopefully this work will help elucidate the molecular mechanisms underlying CMT2A and contribute toward a more general understanding of why axons degenerate

Electron-hole symmetry and solutions of Richardson pairing model

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.Comment: 9 pages, 1 figure; accepted for publication in Eur. Phys. J.

Dynamics of self-organized driven particles with competing range interaction

Non-equilibrium self-organized patterns formed by particles interacting through competing range interaction are driven over a substrate by an external force. We show that, with increasing driving force, the pre-existed static patterns evolve into dynamic patterns either via disordered phase or depinned patterns, or via the formation of non-equilibrium stripes. Strikingly, the stripes are formed either in the direction of the driving force or in the transverse direction, depending on the pinning strength. The revealed dynamical patterns are summarized in a dynamical phase diagram.Comment: 8 pages, 11 figure