Approximate 3-Dimensional Electrical Impedance Imaging

We discuss a new approach to three-dimensional electrical impedance imaging based on a reduction of the information to be demanded from a reconstruction algorithm. Images are obtained from a single measurement by suitably simplifying the geometry of the measuring chamber and by restricting the nature of the object to be imaged and the information required from the image. In particular we seek to establish the existence or non-existence of a single object (or a small number of objects) in a homogeneous background and the location of the former in the (x,y)-plane defined by the measuring electrodes. Given in addition the conductivity of the object rough estimates of its position along the z-axis may be obtained. The approach may have practical applications.Comment: 12 pages, 4 figures, LaTeX, Appendix added and other minor change

Analysis of Traveling and Standing Waves in the DNA Model by Peyrard-Bishop-Dauxois

The model by Peyrard - Bishop - Dauxois (the PBD model), which describes the DNA molecule nonlinear dynamics, is considered. This model represents two chains of rigid disks connected by nonlinear springs. An interaction between opposite disks of different chains is modeled by the Morse potential. Solutions of equations of motion are obtained analytically in two approximations of the small parameter method for two limit cases. The first one is the long-wavelength limit of traveling waves, when frequencies of vibrations are small. Dispersion relations are obtained also for the long-wavelength limit by the small parameter method. The second case is a limit of high frequency standing waves in the form of out-of-phase vibration modes. Two such out-of-phase modes are obtained; it is selected one of them, which has the larger frequency. In both cases systems of nonlinear ODEs are obtained. Nonlinear terms are presented by the Tailor series expansion, where terms up to third degree by displacement are saved. The analytical solutions are compared with checking numerical simulation obtained by the Runge - Kutta method of the 4-th order. The comparison shows a good exactness of these approximate analytical solutions. Stability of the standing localized modes is analyzed by the numerical-analytical approach, which is connected with the Lyapunov definition of stability

Resonance Behavior of the Forced Dissipative Spring-Pendulum System

Dynamics of the dissipative spring-pendulum system under periodic external excitation in the vicinity of external resonance and simultaneous external and internal resonances is studied. Analysis of the system resonance behaviour is made on the base of the concept of nonlinear normal vibration modes (NNMs), which is generalized for systems with small dissipation. The multiple scales method and subsequent transformation to the reduced system with respect to the system energy, an arctangent of the amplitudes ratio and a difference of phases of required solutions are applied. Equilibrium positions of the reduced system correspond to nonlinear normal modes. So-called Transient nonlinear normal modes (TNNMs), which exist only for some certain levels of the system energy are selected. In the vicinity of values of time, corresponding to these energy levels, these TNNMs temporarily attract other system motions. Interaction of nonlinear vibration modes under resonance conditions is also analysed. Reliability of obtained analytical results is confirmed by numerical and numerical-analytical simulation

Universality of Brezin and Zee's Spectral Correlator

The smoothed correlation function for the eigenvalues of large hermitian matrices, derived recently by Brezin and Zee [Nucl. Phys. B402 (1993) 613], is generalized to all random-matrix ensembles of Wigner-Dyson type. Submitted to Nuclear Physics B[FS].Comment: 6 pages, REVTeX-3.0, INLO-PUB-93100

Numerical solution and spectrum of boundary-domain integral equation for the Neumann BVP with variable coefficient

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 Taylor & Francis.In this paper, a numerical implementation of a direct united boundary-domain integral equation (BDIE) related to the Neumann boundary value problem for a scalar elliptic partial differential equation with a variable coefficient is discussed. The BDIE is reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretization of the BDIEs with quadrilateral domain elements leads to a system of linear algebraic equations (discretized BDIE). Then, the system is solved by LU decomposition and Neumann iterations. Convergence of the iterative method is discussed in relation to the distribution of eigenvalues of the corresponding discrete operators calculated numerically.The work was supported by the grant EP/H020497/1 "Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients" of the EPSRC, UK

Formal analytical solutions for the Gross-Pitaevskii equation

Considering the Gross-Pitaevskii integral equation we are able to formally obtain an analytical solution for the order parameter $\Phi (x)$ and for the chemical potential $\mu$ as a function of a unique dimensionless non-linear parameter $\Lambda$. We report solutions for different range of values for the repulsive and the attractive non-linear interactions in the condensate. Also, we study a bright soliton-like variational solution for the order parameter for positive and negative values of $\Lambda$. Introducing an accumulated error function we have performed a quantitative analysis with other well-established methods as: the perturbation theory, the Thomas-Fermi approximation, and the numerical solution. This study gives a very useful result establishing the universal range of the $\Lambda$-values where each solution can be easily implemented. In particular we showed that for $\Lambda <-9$, the bright soliton function reproduces the exact solution of GPE wave function.Comment: 8 figure

Plasmon Resonances in Nanoparticles, Their Applications to Magnetics and Relation to the Riemann Hypothesis

The review of the mathematical treatment of plasmon resonances as an eigenvalue problem for specific boundary integral equations is presented and general properties of plasmon spectrum are outlined. Promising applications of plasmon resonances to magnetics are described. Interesting relation of eigenvalue treatment of plasmon resonances to the Riemann hypothesis is discussed.Comment: 10 pages; misprints corrected, some explanations added. Physica B (2011

Bose-Einstein condensation in an optical lattice: A perturbation approach

We derive closed analytical expressions for the order parameter $\Phi (x)$ and for the chemical potential $\mu$ of a Bose-Einstein Condensate loaded into a harmonically confined, one dimensional optical lattice, for sufficiently weak, repulsive or attractive interaction, and not too strong laser intensities. Our results are compared with exact numerical calculations in order to map out the range of validity of the perturbative analytical approach. We identify parameter values where the optical lattice compensates the interaction-induced nonlinearity, such that the condensate ground state coincides with a simple, single particle harmonic oscillator wave function

Self-Induced Quasistationary Magnetic Fields

The interaction of electromagnetic radiation with temporally dispersive magnetic solids of small dimensions may show very special resonant behaviors. The internal fields of such samples are characterized by magnetostatic-potential scalar wave functions. The oscillating modes have the energy orthogonality properties and unusual pseudo-electric (gauge) fields. Because of a phase factor, that makes the states single valued, a persistent magnetic current exists. This leads to appearance of an eigen-electric moment of a small disk sample. One of the intriguing features of the mode fields is dynamical symmetry breaking

Distribution of the sheet current in a magnetically shielded superconducting filament

The distribution of the transport current in a superconducting filament aligned parallel to the flat surface of a semi-infinite bulk magnet is studied theoretically. An integral equation governing the current distribution in the Meissner state of the filament is derived and solved numerically for various filament-magnet distances and different relative permeabilities. This reveals that the current is depressed on the side of the filament adjacent to the surface of the magnet and enhanced on the averted side. Substantial current redistributions in the filament can already occur for low values of the relative permeability of the magnet, when the distance between the filament and the magnet is short, with evidence of saturation at moderately high values of this quantity, similar to the findings for magnetically shielded strips.Comment: 11 pages, 5 figures; submitted to Physica