Magnetization patterns in ferromagnetic nano-elements as functions of complex variable

Assumption of certain hierarchy of soft ferromagnet energy terms, realized in small enough flat nano-elements, allows to obtain explicit expressions for their magnetization distributions. By minimising the energy terms sequentially, from most to the least important, magnetization distributions are expressed as solutions of Riemann-Hilbert boundary value problem for a function of complex variable. A number of free parameters, corresponding to positions of vortices and anti-vortices, still remain in the expression. These parameters can be found by computing and minimizing the total magnetic energy of the particle with no approximations. Thus, the presented approach is a factory of realistic Ritz functions for analytical micromagnetic calculations. These functions are so versatile, that they may even find applications on their own (e.g. for fitting magnetic microscopy images). Examples are given for multi-vortex magnetization distributions in circular cylinder, and for 2-dimensional domain walls in thin magnetic strips.Comment: 4 pages, 3 figures, 2 refs added, fixed typo

Correlations in the low-temperature phase of the two-dimensional XY model

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with fixed boundary conditions. Using a conformal mapping it is very easy to deduce the exponent eta_sigma(T) of the order parameter correlation function at any temperature in the critical phase of the model. The temperature behaviour of eta_sigma(T) is obtained numerically with a good accuracy up to the Kosterlitz-Thouless transition temperature. At very low temperatures, a good agreement is found with Berezinskii's harmonic approximation. Surprisingly, we show some evidence that there are no logarithmic corrections to the behaviour of the order parameter density profile (with symmetry breaking surface fields) at the Kosterlitz-Thouless transition temperature.Comment: 7 pages, 2 eps figure

Thermoacoustic tomography with an arbitrary elliptic operator

Thermoacoustic tomography is a term for the inverse problem of determining of one of initial conditions of a hyperbolic equation from boundary measurements. In the past publications both stability estimates and convergent numerical methods for this problem were obtained only under some restrictive conditions imposed on the principal part of the elliptic operator. In this paper logarithmic stability estimates are obatined for an arbitrary variable principal part of that operator. Convergence of the Quasi-Reversibility Method to the exact solution is also established for this case. Both complete and incomplete data collection cases are considered.Comment: 16 page

Production and characterization of micro-size pores for ion track etching applications

For many years the applications of ion track etch materials have increased considerably, like charged particles detection, molecular identification with nanopores, ion track filters, magnetic studies with nanowires and so on. Over the materials generally used as track detector, the Poly-Allyl-Diglycol Carbonate (PADC), offers many advantages, like its nearly 100 % detection efficiency for charged particle, a high resistance to harsh environment, the lowest detection threshold, a high abrasion resistance and a low production costs. All of these properties have made it particularly attractive material, even if due to its brittleness, obtaining a thin film (less than 500 μm) is still a challenge. In this work, PADC foils have been exposed to a-particles emitted by a thin radioactive source of 241Am and to C ions from the Tandetron 4130 MC accelerator. The latent tracks generated in the polymer have been developed using a standard etching procedure in 6.25 NaOH solution. The dependence of the ion tracks' geometry on the ion beam energy and fluence has been evaluated combining the information obtained through a semiautomatic computer script that selects the etched ion tracks according to their diameter and mean grey value and nanometric resolution images by atomic force microscopy

Levy stable distributions via associated integral transform

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x < \infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a distribution g_{\alpha}(x) suffices to obtain exactly g_{\alpha^{p}}(x), p=2, 3,... Similarly, from known g_{\alpha}(x) and g_{\beta}(x), 0 < \alpha, \beta < 1, we obtain g_{\alpha \beta}(x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For \alpha rational, \alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g_{l/k}(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration.Comment: 12 pages, typos removed, references adde

Integrable Hierarchies and Information Measures

In this paper we investigate integrable models from the perspective of information theory, exhibiting various connections. We begin by showing that compressible hydrodynamics for a one-dimesional isentropic fluid, with an appropriately motivated information theoretic extension, is described by a general nonlinear Schrodinger (NLS) equation. Depending on the choice of the enthalpy function, one obtains the cubic NLS or other modified NLS equations that have applications in various fields. Next, by considering the integrable hierarchy associated with the NLS model, we propose higher order information measures which include the Fisher measure as their first member. The lowest members of the hiearchy are shown to be included in the expansion of a regularized Kullback-Leibler measure while, on the other hand, a suitable combination of the NLS hierarchy leads to a Wootters type measure related to a NLS equation with a relativistic dispersion relation. Finally, through our approach, we are led to construct an integrable semi-relativistic NLS equation.Comment: 11 page

Fractional diffusion modeling of ion channel gating

An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe non-exponential, power-law like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter and Oswald [Proc. Natl. Acad. Sci. USA 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous time random walk composed of nearest neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. USA 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time-regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels

Theory of nonlinear optical properties of phenyl-substituted polyacetylenes

In this paper we present a theoretical study of the third-order nonlinear optical properties of poly(diphenyl)polyacetylene (PDPA) pertaining to the third-harmonic-generation (THG) process. We study the aforesaid process in PDPA's using both the independent electron Hueckel model, as well as correlated-electron Pariser-Parr-Pople (P-P-P) model. The P-P-P model based calculations were performed using various configuration interaction (CI) methods such as the the multi-reference-singles-doubles CI (MRSDCI), and the quadruples-CI (QCI) methods, and the both longitudinal and the transverse components of third-order susceptibilities were computed. The Hueckel model calculations were performed on oligo-PDPA's containing up to fifty repeat units, while correlated calculations were performed for oligomers containing up to ten unit cells. At all levels of theory, the material exhibits highly anisotropic nonlinear optical response, in keeping with its structural anisotropy. We argue that the aforesaid anisotropy can be divided over two natural energy scales: (a) the low-energy response is predominantly longitudinal and is qualitatively similar to that of polyenes, while (b) the high-energy response is mainly transverse, and is qualitatively similar to that of trans-stilbene.Comment: 13 pages, 7 figures (included), to appear in Physical Review B (April 15, 2004

M13 phages uptake of gold nanoparticles for radio-and thermal-therapy and contrast imaging improvement

The presented work deals with the uptake of gold nanoparticles (Au NPs) by M13 phages in solutions. In particular, the Au NPs uptake modalities and their localization in the filamentous phages are evaluated and measured. Gold spherical nanoparticles (with an average diameter of the order of 10 nm) are obtained by laser ablation in water with a sodium citrated surfactant. The interest of such application comes from the possibility to employ living biological structures to transport heavy metallic nanoparticles inside cells of tumoral tissues. Indeed, phages have the capability to introduce Au NPs in the proximity to the cell nucleus, increasing the efficiency of DNA destruction in the tumoral cells by employing low doses of ionizing radiation during radiotherapy and hyperthermia treatments. Several analyses and microscopy characterizations of the prepared phages samples embedding gold nanoparticles are presented, demonstrating that the presence of Au NPs increases the phages imaging contrast

Static Solitons of the Sine-Gordon Equation and Equilibrium Vortex Structure in Josephson Junctions

The problem of vortex structure in a single Josephson junction in an external magnetic field, in the absence of transport currents, is reconsidered from a new mathematical point of view. In particular, we derive a complete set of exact analytical solutions representing all the stationary points (minima and saddle-points) of the relevant Gibbs free-energy functional. The type of these solutions is determined by explicit evaluation of the second variation of the Gibbs free-energy functional. The stable (physical) solutions minimizing the Gibbs free-energy functional form an infinite set and are labelled by a topological number Nv=0,1,2,... Mathematically, they can be interpreted as nontrivial ''vacuum'' (Nv=0) and static topological solitons (Nv=1,2,...) of the sine-Gordon equation for the phase difference in a finite spatial interval: solutions of this kind were not considered in previous literature. Physically, they represent the Meissner state (Nv=0) and Josephson vortices (Nv=1,2,...). Major properties of the new physical solutions are thoroughly discussed. An exact, closed-form analytical expression for the Gibbs free energy is derived and analyzed numerically. Unstable (saddle-point) solutions are also classified and discussed.Comment: 17 pages, 4 Postscript figure