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The mathematical complexity of the B_J(x) Brillouin function makes it unsuitable for most calculations and its application difficult for computer programming in magnetism. Here, its approximation with the tanh function is proposed to ease the mathematical operations for most cases. The approximation works with good accuracy, acceptable in practical calculations. This approximation has already formed the foundation of the “hyperbolic model” in magnetism for the study of hysteretic phenomena. The reversal of the Brillouin function is an important but difficult mathematical problem for practical purposes. Here, a proposal has been put forward for an easy approximation using an analytical expression. This provides a good workable solution for the B_J(x)⁻¹ function dependent on J, the angular momentum quantum number of the material used. The proposed approximation is applicable within the working range of practical applications. The paper aims to discuss these issues.

The multi-variant Brillouin function is closely approximated by the tanh function to ease calculations. Its mathematically unsolved reversed function is approximated by a simple analytical expression with a good working accuracy.

The Brillouin function and its reversal can be approximated for practical users mostly for professionals working in Magnetism.

Most if not all practical problems in Magnetism can be solved within the limitations of the two approximations.

Both proposed functions can ease the mathematical problems faced by researchers and other users in Magnetism.

Ease the frustration of most users working in the field of Magnetism.

The application of the tanh function for replacing the Brillouin function led to the creation of the hyperbolic model of hysteresis. To the author's knowledge, the reverse function was mathematically only solved in 2015 with a vastly complicated mathematics, and is hardly suitable for practical calculations in Magnetism. The proposed simple expression can be very useful for theorists and experimental scientists.

Using the Jefimenko generalization of the Biot‐Savart law and the Laplace transform we analyse the electromagnetic radiation of a vertical dipole antenna fed with a pulsed current. We get the magnetic field from the vector potential directly while the electric field is obtained through Maxwell’s equations. We write explicitly the expressions of the electromagnetic field for an exponentially decaying pulse and for a truncated harmonic pulse in vacuum and in a dispersive dielectric of the ionosphere type.

Future developments of computer systems will be handicapped not by the limitations of hardware, but by our lack of understanding of the human reasoning processes. The development of three‐dimensional chips, cryogenic superconducting, or optical systems — and in due course, biological computers — presages the emergence of generations of super information processors whose power will dwarf the present generation of devices as they, in turn, have dwarfed the capacity of the computers of the pre‐transistor age. The effective application of such powerful future computers will be limited by the lack of an adequate theoretical basis for the processing of information. Gordon Scarrott has championed the need for a ‘science of information’ which should investigate the ‘natural properties of information such as function, structure, dynamic behaviour and statistical features…’ Such an effort should ‘… lead to a conceptual framework to guide systems design.’

Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops.

A physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process.

The implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops.

The physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.

This work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.

The resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.

The description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.

The original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

Notes that Scalar digital plane waves are made of a finite or infinite sequence of discrete pulses which are solutions of a wave equation. Discusses the 1D and 2D wave equations and shows how the 1D and 2D Laplace transforms may be used in connection with digital signals. Gives some examples of digital plane waves and, as an illustration, gives three different applications of this technique.

The purpose of this paper is to analyze various properties of anatase titanium dioxide (TiO₂) nanoparticles. Further, it proposes to implement Linear Combinations of Atomic Orbitals (LCAO) basis set under the framework of density functional theory and outline how LCAO is able to provide improved results in terms of various mechanical properties rather than plane wave and other theoretical results.

This paper provides an exploratory study on anatase TiO₂ by implementing OLCAO–DFT–LDA–LBFGS–EOS–PZ algorithms to find out various ground-level properties. The data so obtained are complemented by various analysis using mathematical expressions, description of internal processes occurred and comparison to others’ analytical results.

The paper provides some empirical insights on how mechanical properties of anatase TiO₂ improved by implementing LCAO methodology. From the analysis of electronic properties, it is seen that the anatase TiO₂ supports the inter band indirect transition from O-2p in valence region to Ti-3d in the conduction region.

Most of the electronic properties are underestimated because a single exchange-correlation potential is not continuous across the gap. This gap can be enhanced by implementing Green’s function in place of DFT and the other way is to implement self-interaction correction.

The use of anatase TiO₂ is primarily used for catalytic applications. This is also used to enhance the quality of paper in the paper industry. Additionally, this is used as a prime ingredient in cosmetic industry.

This paper fulfills an identified need to study how LCAO, another basis set, plays an important role in improving material properties.

The purpose of this paper is to investigate an alternative to established hysteresis models.

Different mathematical representations of the magnetic hysteresis are compared and some differences are briefly discussed. After this, the application of the T(x) function is presented and an inductor model is developed. Implementation details of the used transient circuit simulator code are further discussed. From real measurement results, parameters for the model are extracted. The results of the final simulation are finally discussed and compared to measurements.

The T(x) function possesses a fast mathematical formulation with very good accuracy. It is shown that this formulation is very well suited for an implementation in transient circuit simulator codes. Simulation results using the developed model are in very good agreement with measurements.

For the purpose of this paper, only soft magnetic materials were considered. However, literature suggests, that the T(x) function can be extended to hard magnetic materials. Investigations on this topic are considered as future work.

While the mathematical background of the T(x) function is very well presented in the referenced papers, the application in a model of a real device is not very well discussed yet. The presented paper is directly applicable to typical problems in the field of power electronics.

The paper sets out to formulate the intermolecular forces leading to Barkhausen instability. In the approach the known concept of effective field is used within the framework of the T(x) model. The aim is to provide a mathematical tool to theoreticians and applied scientists in magnetism that is easier to use than those of other models. At the same time to demonstrate the easy applicability of the T(x) model to hysteretic phenomena.

With the combination of the effective and the external field the model is applied to hysteresis loops as well as to the anhysteretic state showing in both cases the local development of unstable conditions at beyond a critical point, leading to local hysteresis loops.

The paper formulates the critical conditions for the hysteretic and the anhysteretic process and calculates the susceptibility as the functions of magnetisation and the applied field.

Experimental verification will be required to prove the applicability to the various magnetic materials and to the accuracy of the model.

The paper provides an easy mathematical and visual method to show the conditions before and after the Barkhausen instability sets in during the magnetisation process.

The paper provides an easy mathematical tool for theoreticians and experimental scientists with a visual presentation of processes leading to Barkhausen instability and magnetic behaviour beyond that by using the T(x) model.

Investigates the enigmatic phenomenon of information from the two major perspectives of modern cybernetics: the negentropic and the evolutionary. Discusses the meaning of this phenomenon, considering it, ultimately, as the means of combating entropy within cybernetic or control systems which create or receive, process, stock, and use information, eventually with the purpose of regulating their matter‐energy fluxes necessary for struggling against inner entropy. Discusses the sense of information as relating to thermodynamical entropy in a philosophical manner and not in some formal (mathematical) language.