Lyapunov Exponent and Density of States of a One-Dimensional Non-Hermitian Schrödinger Equation

We calculate, using numerical methods, the Lyapunov exponent (E) and the density of states (E) at energy E of a one-dimensional non-Hermitian Schrödinger equation with off-diagonal disorder. For the particular case we consider, both (E) and (E) depend only on the modulus of E. We find a pronounced maximum of (|E|) at energy E=2/ , which seems to be linked to the fixed point structure of an associated random map. We show how the density of states (E) can be expanded in powers of E. We find (|E|)=(1/ ²)+(4/3 ³) |E|²+. This expansion, which seems to be asymptotic, can be carried out to an arbitrarily high order.     

Effective chiral magnetic currents, topological magnetic charges, and microwave vortices in a cavity with an enclosed ferrite disk

In microwaves, a TE-polarized rectangular-waveguide resonator with an inserted thin ferrite disk gives an example of a nonintegrable system. The interplay of reflection and transmission at the disk interfaces together with the material gyrotropy effect gives rise to whirlpool-like electromagnetic vortices in the proximity of the ferromagnetic resonance. Based on numerical simulation, we show that a character of microwave vortices in a cavity can be analyzed by means of consideration of equivalent magnetic currents. Maxwell equations allows introduction of a magnetic current as a source of the electromagnetic field. Specifically, we found that in such nonintegrable structures, magnetic gyrotropy and geometrical factors leads to the effect of symmetry breaking resulting in effective chiral magnetic currents and topological magnetic charges. As an intriguing fact, one can observe precessing behavior of the electric-dipole polarization inside a ferrite disk.     

Continuum Dynamics on Manifolds: Application to Elasticity of Residually-Stressed Bodies

This paper is concerned with the dynamics of continua on differentiable manifolds. We present a covariant derivation of the equations of motion, viewing motion as a curve in an infinite-dimensional Banach manifold of embeddings of a body manifold in a space manifold. Our main application is the motion of residually-stressed elastic bodies, where the residual stresses result from a geometric incompatibility between body and space manifolds. We then study a particular example of elastic vibrations of a two-dimensional curved annulus embedded in a sphere.     

Analysis of wave fluctuation phenomena in random media in presence of a reflecting boundary

Modelling of wave propagation for modern high-frequency radio links must take into account the fluctuation phenomena caused by random changes of the medium's parameters. There are two factors that cause signals from transmitter to receiver to arrive via multiple random paths. The first is a result of scattering by boundaries and various obstacles, while the second is related to random changes in the refractive index of the medium. Similar phenomena are observed in underwater acoustic propagation. In this work the influence of both factors is demonstrated in a simple example when the propagation takes place above a perfectly reflecting surface in the presence of a randomly fluctuating medium.     

Percolation theory and fragmentation measures in social networks

We study the statistical properties of a recently proposed social networks measure of fragmentation F after removal of a fraction q of nodes or links from the network. The measure F   is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network. We compare this measure with the one traditionally used in percolation theory, _P∞$P_{\infty }$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods, we study Erd?s–Rényi (ER) and scale-free (SF) networks under various node removal strategies. We find that for a network obtained after removal of a fraction q   of nodes above criticality, _P∞≈(1-F)^1/2$P_{\infty }\approx (1-F{)}^{1/2}$. For fixed _P∞$P_{\infty }$ and close to criticality, we show that 1-F$1-F$ better reflects the actual fragmentation. For a given _P∞$P_{\infty }$, 1-F$1-F$ has a broad distribution and thus one can improve significantly the fragmentation of the network. We also study and compare the fragmentation measure F   and the percolation measure _P∞$P_{\infty }$ for a real national social network of workplaces linked by the households of the employees and find similar results.     

Limits for superfocusing with finite evanescent wave amplification

Perfect lensing using negative refractive index materials and radiationless electromagnetic interference both provides extreme subwavelength focusing by "amplifying" evanescent wave components that are usually lost. This Letter provides a relation between the achievable focus spot size, the amplification available, and the focal length. This may be considered as a revised version of Abbe's diffraction limit for focusing systems that have evanescent wave amplification. It is useful in comparing the amplification achieved in various subwavelength focusing implementations as well as determining when it is better to use existing near-field techniques, such as simple diffraction from an aperture or slit, than to attempt complicated superfocusing.     

Origin of intense magnetic fields near black holes due to non-minimal gravitational-electromagnetic coupling

The origin of magnetic fields in astrophysical objects is a challenging problem in astrophysics. Throughout the years, many scientists have suggested that non-minimal gravitational-electromagnetic coupling (NMGEC) could be the origin of the ubiquitous astrophysical magnetic fields. We investigate the possible origin of intense magnetic fields by NMGEC near rotating black holes, connected with quasars and gamma-ray bursts. Whereas these intense magnetic fields are difficult to explain astrophysically, we find that they are easily explained by NMGEC.     

Locally convex functions and the Schwarzian derivative

In this paper we study various classes of locally convex analytic functions in the unit disc, which are invariant under the group of M?bius automorphisms of the unit disc. Bounds for the Schwarzian derivative of functions in these classes are achieved and used to obtain estimates for the uniform hyperbolic radius of univalence in these classes.     

The Geometry of Cauchy's Fluxes

A formulation of the Cauchy theory for balance laws of scalar valued quantities is considered from a general geometric point of view. It is assumed only that the ambient space is an orientable m-dimensional manifold. The analog of the usual flux vector field is an (m−1)-differential form. Both the Cauchy theorem and differential version of the balance laws are formulated in this context. Accepted December 9, 1999?Published online July 12, 2000     

A new look at the linear-modulated optically stimulated luminescence (LM-OSL) as a tool for dating and dosimetry

Optically stimulated luminescence (OSL) has been in use for dosimetry and dating in the last two decades. Since the OSL dependence on time is a featureless decaying function, a linear-modulation of the stimulating-light intensity has been suggested [Bulur, E., 1996. An alternative technique for optically stimulated luminescence. Radiat. Meas. 26, 701–709.], which resulted in a peak-shaped curve. The properties of this curve have been studied, assuming first-, second- and general-order kinetics. In a recent paper we have shown [Chen, R., Pagonis, V., 2008. A unified presentation of thermoluminescence (TL), phosphorescence and linear-modulated OSL (LM-OSL). J. Phys. D: Appl. Phys. 41, 035102 (1–6).] that for general-order curves, the peak maximum cannot be expected to depend linearly on the dose of excitation. A new presentation of the LM-OSL has been suggested, in which the peak maximum is linear with the filling of trapping states, which, in turn, may be expected to be linear with the dose under appropriate conditions. In the present work, we report on results of numerical simulation of the LM-OSL using the one trap-one recombination center (OTOR) model, dealing with the traffic of carriers between one trapping state, one kind of recombination center and the conduction and valence bands during excitation and read-out, and without making any simplifying assumptions. The process during optical read-out has been followed in the simulation that consisted of the numerical solution of the relevant sets of coupled differential equations, and also by analytical treatment. Sets of parameters leading to approximately first- and second-order kinetics, and to intermediate cases, have been used and the results presented in the original and the new ways are shown. The consequences concerning dating and dosimetry are discussed.