Numerical methods for integral equations of Mellin type

We present a survey of numerical methods (based on piecewise polynomial approximation) for integral equations of Mellin type, including examples arising in boundary integral methods for partial differential equations on polygonal domains

Shielding efficiency and E(J) characteristics measured on large melt cast Bi-2212 hollow cylinders in axial magnetic fields

We show that tubes of melt cast Bi-2212 used as current leads for LTS magnets can also act as efficient magnetic shields. The magnetic screening properties under an axial DC magnetic field are characterized at several temperatures below the liquid nitrogen temperature (77 K). Two main shielding properties are studied and compared with those of Bi-2223, a material that has been considered in the past for bulk magnetic shields. The first property is related to the maximum magnetic flux density that can be screened, Blim; it is defined as the applied magnetic flux density below which the field attenuation measured at the centre of the shield exceeds 1000. For a cylinder of Bi-2212 with a wall thickness of 5 mm and a large ratio of length over radius, Blim is evaluated to 1 T at T = 10 K. This value largely exceeds the Blim value measured at the same temperature on similar tubes of Bi-2223. The second shielding property that is characterized is the dependence of Blim with respect to variations of the sweep rate of the applied field, dBapp/dt. This dependence is interpreted in terms of the power law E = Ec(J/Jc)^n and allows us to determine the exponent n of this E(J) characteristics for Bi-2212. The characterization of the magnetic field relaxation involves very small values of the electric field. This gives us the opportunity to experimentally determine the E(J) law in an unexplored region of small electric fields. Combining these results with transport and AC shielding measurements, we construct a piecewise E(J) law that spans over 8 orders of magnitude of the electric field.Comment: 16 pages, 7 figure

An optimal order collocation method for first kind boundary integral equations on polygons.

This paper discusses the convergence of the collocation method using splines of any order k for first kind integral equations with logarithmic kernels on closed polygonal boundaries in ℝ2. Before discretization the equation is transformed to an equivalent equation over [-π,π] using a nonlinear parametrization of the polygon which varies more slowly than arc-length near each corner. This has the effect of producing a transformed equation with a solution which is smooth on [-π,π]. This latter integral equation is shown to be well-posed in appropriate Sobolev spaces. The structure of the integral operator is described in detail, and can be written in terms of certain non-standard Mellin convolution operators. Using this information we are able to show that the collocation method using splines of order k (degree k-1) converges with optimal order O(hk). (The collocation points are the midpoints of subintervals when k is odd and the break-points when k is even, and stability is shown under the assumption that the method may be modified slightly.) Using the numerical solutions to the transformed equation we construct numerical solutions of the original equation which converge optimally in a certain weighted norm. Finally the method is shown to produce superconvergent approximations to interior potentials such as those used to solve harmonic boundary value problems by the boundary integral method. The convergence results are illustrated with some numerical examples

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

Conjugated Polymers in Bioelectronics.

The emerging field of organic bioelectronics bridges the electronic world of organic-semiconductor-based devices with the soft, predominantly ionic world of biology. This crosstalk can occur in both directions. For example, a biochemical reaction may change the doping state of an organic material, generating an electronic readout. Conversely, an electronic signal from a device may stimulate a biological event. Cutting-edge research in this field results in the development of a broad variety of meaningful applications, from biosensors and drug delivery systems to health monitoring devices and brain-machine interfaces. Conjugated polymers share similarities in chemical "nature" with biological molecules and can be engineered on various forms, including hydrogels that have Young's moduli similar to those of soft tissues and are ionically conducting. The structure of organic materials can be tuned through synthetic chemistry, and their biological properties can be controlled using a variety of functionalization strategies. Finally, organic electronic materials can be integrated with a variety of mechanical supports, giving rise to devices with form factors that enable integration with biological systems. While these developments are innovative and promising, it is important to note that the field is still in its infancy, with many unknowns and immense scope for exploration and highly collaborative research. The first part of this Account details the unique properties that render conjugated polymers excellent biointerfacing materials. We then offer an overview of the most common conjugated polymers that have been used as active layers in various organic bioelectronics devices, highlighting the importance of developing new materials. These materials are the most popular ethylenedioxythiophene derivatives as well as conjugated polyelectrolytes and ion-free organic semiconductors functionalized for the biological interface. We then discuss several applications and operation principles of state-of-the-art bioelectronics devices. These devices include electrodes applied to sense/trigger electrophysiological activity of cells as well as electrolyte-gated field-effect and electrochemical transistors used for sensing of biochemical markers. Another prime application example of conjugated polymers is cell actuators. External modulation of the redox state of the underlying conjugated polymer films controls the adhesion behavior and viability of cells. These smart surfaces can be also designed in the form of three-dimensional architectures because of the processability of conjugated polymers. As such, cell-loaded scaffolds based on electroactive polymers enable integrated sensing or stimulation within the engineered tissue itself. A last application example is organic neuromorphic devices, an alternative computing architecture that takes inspiration from biology and, in particular, from the way the brain works. Leveraging ion redistribution inside a conjugated polymer upon application of an electrical field and its coupling with electronic charges, conjugated polymers can be engineered to act as artificial neurons or synapses with complex, history-dependent behavior. We conclude this Account by highlighting main factors that need to be considered for the design of a conjugated polymer for applications in bioelectronics-although there can be various figures of merit given the broad range of applications, as emphasized in this Account

Inhomogeneity of the intrinsic magnetic field in superconducting YBa2Cu3OX compounds as revealed by rare-earth EPR-probe

X-band electron paramagnetic resonance on doped Er3+ and Yb3+ ions in Y0.99(Yb,Er)0.01Ba2Cu3OX compounds with different oxygen contents in the wide temperature range (4-120)K have been made. In the superconducting species, the strong dependencies of the linewidth and resonance line position from the sweep direction of the applied magnetic field are revealed at the temperatures significantly below TC. The possible origins of the observed hysteresis are analyzed. Applicability of the presented EPR approach to extract information about the dynamics of the flux-line lattice and critical state parameters (critical current density, magnetic penetration depth, and characteristic spatial scale of the inhomogeneity) is discussedComment: 17 pages, 5 Figures. Renewed versio

Temperature dependence of the EPR linewidth of Yb3+ - ions in Y0.99Yb0.01Ba2Cu3OX compounds: Evidence for an anomaly near TC

Electron paramagnetic resonance experiments on doped Yb3+ ions in YBaCuO compounds with different oxygen contents have been made. We have observed the strong temperature dependence of the EPR linewidth in the all investigated samples caused by the Raman processes of spin-lattice relaxation. The spin-lattice relaxation rate anomaly revealed near TC in the superconducting species can be assigned to the phonon density spectrum changesComment: 10 pages, 4 figures Renewed versio

Normal-superconducting transition induced by high current densities in YBa2Cu3O7-d melt-textured samples and thin films: Similarities and differences

Current-voltage characteristics of top seeded melt-textured YBa2Cu3O7-d are presented. The samples were cut out of centimetric monoliths. Films characteristics were also measured on microbridges patterned on thin films grown by dc sputtering. For both types of samples, a quasi-discontinuity or quenching was observed for a current density J* several times the critical current density Jc. Though films and bulks much differ in their magnitude of both Jc and J*, a proposal is made as to a common intrinsic origin of the quenching phenomenon. The unique temperature dependence observed for the ratio J*/Jc, as well as the explanation of the pre-quenching regime in terms of a single dissipation model lend support to our proposal.Comment: 10 pages, 10 figures, submitted to Physical Review

A limit model for thermoelectric equations

We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck-Peltier-Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular nonsmooth domains. Two existence results are studied under different assumptions on the electrical conductivity. Their proofs are based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. The second purpose is to show the existence of a limit model illustrating the asymptotic situation.Comment: 20 page