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

Reactualisation of Triadology in Polemics with Postmetaphysics

Received 30 July 2021. Accepted 16 December 2021. Published online 30 December 2021.Review of Oleg Davydov (2020). Revelation of Love: Trinitarian Truth of Being. St. Andrew’s Biblical Theological Institute

Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

A Theology of History: In Search of a Method

Received 8 August 2022. Published online 10 October 2022.Review of the book by Priest M. V. Legeyev (2021). Bogoslovie istorii kak nauka. Metod. [Theology of history as a science. Method]. Sankt-Peterburgskaia Dukhovnaia Akademiia

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

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

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

Instrumentation for study of nanomaterials in NPI REZ (New laboratory for material study in Nuclear Physics Institute in REZ)

Nano-sized materials become irreplaceable component of a number of devices for every aspect of human life. The development of new materials and deepening of the current knowledge require a set of specialized techniques-deposition methods for preparation/modification of the materials and analytical tools for proper understanding of their properties. A thoroughly equipped research centers become the requirement for the advance and development not only in nano-sized field. The Center of Accelerators and Nuclear Analytical Methods (CANAM) in the Nuclear Physics Institute (NPI) comprises a unique set of techniques for the synthesis or modification of nanostructured materials and systems, and their characterization using ion beam, neutron beam and microscopy imaging techniques. The methods are used for investigation of a broad range of nano-sized materials and structures based on metal oxides, nitrides, carbides, carbon-based materials (polymers, fullerenes, graphenes, etc.) and nano-laminate composites (MAX phases). These materials can be prepared at NPI using ion beam sputtering, physical vapor deposition and molecular beam epitaxy. Based on the deposition method and parameters, the samples can be tuned to possess specific properties, e.g., composition, thickness (nm-μm), surface roughness, optical and electrical properties, etc. Various nuclear analytical methods are applied for the sample characterization. RBS, RBS-channeling, PIXE, PIGE, micro-beam analyses and Transmission Spectroscopy are accomplished at the Tandetron 4130MC accelerator, and additionally the Neutron Depth Profiling (NDP) and Prompt Gamma Neutron Activation (PGNA) analyses are performed at an external neutron beam from the LVR-15 research reactor. The multimode AFM facility provides further surface related information, magnetic/electrical properties with nano-metric precision, nano-indentation, etc