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Positive Field Cooled Susceptibility in Multiply Connected Type I Superconductors

Positive Field Cooled Susceptibility in Multiply Connected Type I Superconductors

Expulsion of magnetic field from the inner region of simply connected type-I superconductors was first ob- served by Walther Meissner and Robert Ochsenfeld in 1933, 22 years after the discovery of superconductivity [1]. The two German scientists showed that these super- conducting systems, when cooled below the correspond- ing critical temperature T c in the presence of low mag-

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The Classical Hall Effect in Multiply Connected Plane Regions Part I: Topologies with Stream Function

The Classical Hall Effect in Multiply Connected Plane Regions Part I: Topologies with Stream Function

DOI: 10.4236/jamp.2019.79136 1969 Journal of Applied Mathematics and Physics at large magnetic field [1] [2], for contacts of finite size [3], and in the absence of symmetries [4]. There are also several formulae for devices with small output contacts at weak magnetic field [5] [6] [7] [8]. An early mention of bounded Hall plates with a single hole is [9], where the author computed the impedance matrix of symmetric circular rings with large symmetric contacts with the me- thod of conformal mapping. This was a by-product of a calculation of the power delivered by an infinitely long magneto-hydrodynamic generator. It was also proven in a strict mathematical way that these devices give no Hall voltage on the inner sense contacts placed on the x-axis when current is sent through outer supply contacts centered on the y-axis. However, the author did not elaborate on the question, if this effect is due to symmetry only. Moreover it was proven that there is no Hall voltage between any contacts in any symmetric or asymmetric multiply connected conductive region if all its boundaries are conducting—we will pick up this thread in a follow-up paper part II. The Hall effect in double boundary geometries with small contacts was studied in [10] with the goal of reducing the zero point error (offset) of Hall plates. The authors called their rec- tangular ring “anti-Hall bar within a Hall bar” (see Figure 1) and focused on the fact that current flowing through points on the outer boundary gives no Hall signal on the inner boundary, and vice versa, whereas the offsets measured on both boundaries are affected by both currents. Multiply-connected Hall-plates with contacts of arbitrary size on the boundaries of holes are investigated in [11] on an advanced mathematical level. Another aspect of Hall plates with ring to- pology is the reversal of the Hall voltage when sense and supply contacts are on the inner boundaries in contrast to being on the outer boundaries. If a material consists of a huge number of such rings the sign of the macroscopic Hall con- stant depends on the electrical coupling of the rings. This was predicted theoret- ically in [12] and verified experimentally in [13]. The funny result is that see- mingly in contrast to introductory text books the sign of the Hall voltage does not correctly reveal the sign of the majority charge carriers, unless one takes into account the exact complicated topology of such chainmail-like meta-materials. The same effect was observed in finite-element analyses of van der Pauw-Hall measurements on samples with inhomogeneities [14].
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The Classical Hall Effect in Multiply Connected Plane Regions Part II: Spiral Current Streamlines

The Classical Hall Effect in Multiply Connected Plane Regions Part II: Spiral Current Streamlines

Multiply-connected Hall plates show different phenomena than singly con- nected Hall plates. In part I (published in Journal of Applied Physics and Mathematics), we discussed topologies where a stream function can be defined, with special reference to Hall/Anti-Hall bar configurations. In part II, we focus on topologies where no conventional stream function can be defined, like Cor- bino disks. If current is injected and extracted at different boundaries of a mul- tiply-connected conductive region, the current density shows spiral streamlines at strong magnetic field. Spiral streamlines also appear in simply-connected Hall plates when current contacts are located in their interior instead of their boundary, particularly if the contacts are very small. Spiral streamlines and cir- culating current are studied for two complementary planar device geometries: either all boundaries are conducting or all boundaries are insulating. The latter case means point current contacts and it can be treated similarly to singly con- nected Hall plates with peripheral contacts through the definition of a so-called loop stream function. This function also establishes a relation between Hall plates with complementary boundary conditions. The theory is explained by examples.
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Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions

Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions

Chapter 3 explains some results that will be used for solving Dirichlet problem with discontinuous coefficients in bounded simply connected region. First, some preliminaries for solving Dirichlet problem with discontinuous coefficients will be reviewed. Next, the integral equations will be derived and applied to solve this problem. Finally, there will be some numerical examples to prove the accuracy of the suggested method. Neumann problem with discontinuous coefficients will also be discussed in this chapter.

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The Inverse Problem for Elliptic Equations from Dirichlet to Neumann Map in Multiply Connected Domains

The Inverse Problem for Elliptic Equations from Dirichlet to Neumann Map in Multiply Connected Domains

The present paper deals with the inverse problem for linear elliptic equations of second order from Dirichlet to Neumann map in multiply connected domains. Firstly the formulation and the complex form of the problem for the equations are given, and then the existence and global uniqueness of solutions for the above problem are proved by the complex

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Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions

Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions

Nasser (2007) has developed a new method for solving the Dirichlet problem on bounded and unbounded simply connected regions with smooth boundaries. His method is based on two uniquely Fredholm integral equations of the second kind with the generalized Neumann kernel. Alagele (2012) used Nasser’s method for computing Green’s function on bounded simply connected region by getting a unique solution of interior Dirichlet problem using integral equation approach with the generalized Neumann kernel. Nezhad (2013) computed the Green’s function on unbounded simply connected region by getting a unique solution of the exterior
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A probabilistic examplar based model

A probabilistic examplar based model

algorithms Although, the proposed model in this thesis usesa multiply connected Bayesian determine best the to network exemplars, the probability propagation method in... is it facilitat[r]

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Numerical conformal mapping of unbounded multiply connected regions onto circular slit regions

Numerical conformal mapping of unbounded multiply connected regions onto circular slit regions

This paper presents a boundary integral equation method for conformal mapping of unbounded multiply connected regions onto circular slit regions. Three linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. The integral equations are uniquely solvable. The kernels involved in these integral equations are the classical and the adjoint generalized Neumann kernels. Several numerical examples are presented.

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Fast numerical conformal mapping of bounded multiply connected regions via integral equations

Fast numerical conformal mapping of bounded multiply connected regions via integral equations

The integral equations derived in Sangawi (2014a), Sangawi (2014b), Sangawi and Murid (2013) and Sangawi et al. (2013) are solved numerically using MATLAB solver that requires explicitly defined coefficient matrix. The operation for this approach are O((m + 1) 2 n 2 ), where m + 1 is the number of connectivity of the region and n is number of node for each boundary. It is not suitable for higher connectivity and more challenging region problems. Some improvements need to be done for reducing the operations and memory requirement for numerical conformal mapping in order to apply in real problem.
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Bandwidth Enhancement Techniques using Stacked Microstrip Patch Antennas

Bandwidth Enhancement Techniques using Stacked Microstrip Patch Antennas

A Microstrip patch antenna (MPA) consists of a radiating patch on one side of a dielectric substrate which has a ground plane on the other side is shown in Figure 2. The patch is generally made of a conducting material such as copper or gold and can take any available shape. Radiating patch and the feed lines is usually photo etched on the dielectric substrate.

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Boundary integral equations approach for numerical conformal mapping of multiply connected regions

Boundary integral equations approach for numerical conformal mapping of multiply connected regions

In Chapter 4, we apply the result of Chapter 3 to derive a new boundary integral equation related to conformal mapping f (z) of multiply connected region onto an annulus with circular slits. We discretized the integral equation and imposed some normalizing conditions different from Murid and Mohamed (2007), and Mohamed and Murid (2007b) for the case doubly connected region via the Kerzman-Stein and the Neumann kernels. We also extend the construction of the boundary integral equation in Chapter 3 to a triply connected regions. The boundary values of f (z) is completely determined from the boundary values of f (z) through a boundary relationship. Discretization of the integral equation leads to a system of non-linear equations. Together with some normalizing conditions, we show how a unique solution to the system can be computed by means of an optimization method. We report our numerical results and give comparisons with existing method for some test regions.
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Investigations in the dynamics of three different classes of meromorphic functions

Investigations in the dynamics of three different classes of meromorphic functions

We may now lift these results to the Baker domain U for the function f{ t) = t-\- e“ * by noting th a t z = e“ * maps U to G so we have th a t dU contains the lines L"*", L ~ . Indeed e~* is univalent in the region between L'*', L ~ , which includes C7, so th a t the prime ends of U and G correspond under the mapping. Thus, corresponding to On we have cross cuts C'^ : x = — log —9n < y < 9n of U which cut off domains D!^ in U such th a t = Dn- The prime end of U defined by (C^) is denoted by Q and has impression L+ U U {oo}. For any z > 0, [z, oo) is an end cut of U which converges to
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Many-path interference and topologically suppressed tunneling

Many-path interference and topologically suppressed tunneling

tuned if the particle interacts with a magnetic field penetrating the loop. This topological mechanism allows one to suppress the tunneling of a charged particle [2] if a gauge field is present. Tunneling of a spin can be modified similarly if its classical equilibrium positions are connected by two paths in phase space instead of only one path [3].

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Boundary integral equations with the generalized Neumann kernel for laplace's equations in multiply connected regions

Boundary integral equations with the generalized Neumann kernel for laplace's equations in multiply connected regions

Since the integral equations (26), (59) and (60) are uniquely solvable, then for sufficiently large number of collocation points on each boundary component, the linear system (78) is also uniquely solvable [3]. The linear system (78) is solved using the Gauss elimination method. The computational details are similar to previous works [17,18] in connection with numerical conformal mapping of multiply connected regions. See [20] for some ideas on how to handle regions with corners to achieve good accuracy.

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Theoretical scheme on numerical conformal mapping of unbounded multiply connected domain by fundamental solutions method

Theoretical scheme on numerical conformal mapping of unbounded multiply connected domain by fundamental solutions method

Now, we consider the case when D is a bounded multiply connected domain con- taining 0 and ∞ in its interior and exterior, respectively. Using the transformation z → 1/z, we propose the new scheme (to be called “dual”) corresponding to (2.15) as follows:

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An integral equation method for solving neumann problems on simply and multiply connected regions with smooth boundaries

An integral equation method for solving neumann problems on simply and multiply connected regions with smooth boundaries

This research presents several new boundary integral equations for the solution of Laplace’s equation with the Neumann boundary condition on both bounded and unbounded multiply connected regions. The integral equations are uniquely solvable Fredholm integral equations of the second kind with the generalized Neumann kernel. The complete discussion of the solvability of the integral equations is also presented. Numerical results obtained show the efficiency of the proposed method when the boundaries of the regions are sufficiently smooth.
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Evolutionary equation of inertial waves in 3 D multiply connected domain with Dirichlet boundary condition

Evolutionary equation of inertial waves in 3 D multiply connected domain with Dirichlet boundary condition

Abstract. We study initial-boundary value problem for an equation of composite type in 3-D multiply connected domain. This equation governs nonsteady inertial waves in rotating fluids. The solution of the problem is obtained in the form of dynamicpotentials, which density obeys the uniquely solvable integral equation. Thereby the existence theorem is proved. Besides, the uniqueness of the solution is studied. All results hold for interior domains and for exterior domains with appropriate conditions at infinity.

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Hollow quasi Fatou components of quasiregular maps

Hollow quasi Fatou components of quasiregular maps

We prove two results, which concern the cases that a hollow quasi-Fatou compo- nent is either bounded or unbounded. The first shows that quasi-Fatou components of quasiregular maps of transcendental type that are both bounded and hollow have properties very similar to those of multiply connected Fatou components of tran- scendental entire functions. In order to state this result we need to give a number of definitions, all of which are familiar from complex dynamics.

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General Boundary Value Problems for Nonlinear Uniformly Elliptic Equations in Multiply Connected Infinite Domains

General Boundary Value Problems for Nonlinear Uniformly Elliptic Equations in Multiply Connected Infinite Domains

multiply connected infinite domain D with the boundary  . The above boundary value problem is called Problem G. Problem G extends the work [8] in which the equation (0.1) includes a nonlinear lower term and the boundary condition (0.2) is more general. If the complex equation (0.1) and the boundary condition (0.2) meet certain assumptions, some solvability results for Problem G can be obtained. By using reduction to absurdity, we first discuss a priori estimates of solutions and solvability for a modified problem. Then we present results on solvability of Problem G.

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Integral representations for solutions of some BVPs for the Lamé system in multiply connected domains

Integral representations for solutions of some BVPs for the Lamé system in multiply connected domains

Section 6 is devoted to the traction problem. It turns out that the solution of this problem does exist in the form of a double layer potential if, and only if, the given forces are balanced on each connected component of the boundary. While in a simply connected domain the solution of the traction problem can be always represented by means of a double layer potential (provided that, of course, the given forces are balanced on the boundary), this is not true in a multiply connected domain. Therefore the presence or absence of “ holes ” makes a difference.

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