Fundamental Research and Application of Physical Science Vol. 9

The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. The quantization of the forced harmonic oscillator is studied with the quantum variable (\(\mathit{x}\) , \(\hat{v}\)) , with the commutation relation [\(\mathit{x}\) , \(\hat{v}\)] = \(\mathit{i}\hbar\)/\(\mathit{m}\) , and using a Schrödinger’s like equation on these variable, and associating a linear operator to a constant of motion \(\mathit{K}\)(\(\mathit{x, v, t}\)) of the classical system, The comparison with the quantization in the space (\(\mathit{x, p}\)) is done with the usual Schrödinger’s equation for the Hamiltonian \(\mathit{H}\)(\(\mathit{x, p, t}\)), and with the commutation relation [\(\mathit{x}\) , \(\hat{p}\)] = \(\mathit{i}\hbar\). It is found that for the non-resonant case, both forms of quantization bring about the same result. The difference means that the H-approach case brings about more complex behavior in the quantum dynamics than the K-approach case, and that the H-approach case losses more information than the K-approach case.However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (\(\mathit{x}\) , \(\hat{v}\)) quantization has fewer oscillations than the (\(\mathit{x}\) , \(\hat{p}\)) quantization, the average energy of the system is higher in (\(\mathit{x}\) , \(\hat{p}\)) quantization than on the (\(\mathit{x}\) , \(\hat{v}\)) quantization, and the Boltzmann- Shannon entropy on the (\(\mathit{x}\) , \(\hat{p}\)) quantization is higher than on the (\(\mathit{x}\) , \(\hat{v}\)) quantization. The parameter does not appear to be suitable for experimental measurement because the variation in the average value of the energy is quite modest. Entropy is a nice parameter to investigate experimentally because it differs significantly.

This chapter discuss about statistic Methods for Assessments of Risks and Damages at Nuclear Power Plants. Given the rapid expansion of risk assessment on many fronts, one may ask whether risk assessment really offers something new as a scientific response to new demands created by technology, or whether it is only a short-term fad, something old in a new guise which will soon disappear. The associated treats under NPP exploitation are also growing as a result of many man-made and natural circumstances, including serving as targets for potential targeted terrorist assaults. For any NPP, accurate evaluations of the associated risks and damages are required at all times, including during the planning, construction, and operation phases of its intricately integrated emergency management system. Here we try to analyze some possible methods of NPP risk assessments. Early we predicted the irradiation doses and corresponded risks for population under implementation of Russian Federal Program:" Delineation of a change management process institutionalizes the actions of members of NPP professional staff in making organizational changes that impact the various sources of risk. Development of Russian atomic energy industrial complex on 2007-2020 years at 10 homeland NPP, that operated in normal non disasters regimes during two last decades. But such data are absent for NPP, that have been or will be under non prognostic emergencies. Only after NPP disasters can the necessary information, in part or in full, be gathered. When NPP are placed in some risky conflict zones with high levels of potential terrorism threats, they are subject to intensely negative natural reactions (earthquakes, tsunamis, etc.) as well as artificial ones. Here the using of classic methods of expertise risk NPP assessments are not correct and often impossible at all. Some needed thematic data may be obtained from primary virtual computer tests of individual NPP with imitation of possible disasters. It allows to plan the actions for NPP operators and special services under serious NPP disasters or may be to prevent them at all. Utilization of mixed oxides of uranium and plutonium (MOX fuel) in specially design reactors is considered one of the promising directions for further development of nuclear industry, let alone the challenge of peaceful utilization of the stock of military plutonium.

Aim: The aim of this study is to explain how to multiply the mild Solar electrical energy for use on planet Earth.

‘Live Better Electrically’ is a component of my ‘Message from the SUN’ article and explains the use with amplification of the mild Solar electrical energy in micro-amperes or low milli-amperes reaching the Earth with the ‘Coil Effect’.

The Northern and Southern Lights are caused by the Solar IMF¹. ‘Gill’s Electronic Theory of Magnetism 1964’ shows how the solar IMF on approaching the magnetosphere of the Earth splits into its negative and positive electric energy components which head for the opposite magnetic poles of the Earth to cause the equally bright Aurora Borealis and Aurora Australis.

Some applications to harness this solar electrical energy reaching the Earth are presented and dot product equations are presented to support these applications without any need of Henrik Lorentz’s 1893 cross products.

Line diagrams will explain how to amplify the mild solar electrical energy reaching the Earth as required.

‘Gill’s electronic theory of magnetism 1964’ explains better and should replace ‘Maxwell’s dipole theory of magnetism 1873’.

The purpose of the study is the mechanical characteristics of a living body. The article examines the specifics of the impact of acoustic waves on the organisms of living beings. It is commonly known that vibrations and acoustic oscillations can cause both negative and positive influence on living organisms. The most harmful effect is caused by the tone acoustic oscillations when the tone frequency coincides with the resonance frequency of the whole body or individual organs. It is understood that such resonance frequencies of human organs fall between 0.5 and 20 Hz. Only in this situation, when a person is in an acoustic field with a frequency that is not the same as their resonance frequency, can the human body be shielded from harmful acoustic waves. On the contrary, we can use the effect of acoustic fields on the organisms of plant pests with a frequency corresponding to the resonant frequency of the pest's body. Then the acoustic field will have a destructive effect on the plant pest. The death of the Colorado beetle under the influence of vibrations and acoustic vibrations was discovered in the laboratory. It is necessary to note slackness of the beetles subjected to acoustic influence in a mode of radiation of monochromatic waves. Any influence of acoustic waves on a potato at direct survey, and also after time till the harvesting moment had not been revealed. The method and device for its implementation are developed and described below. The author registered in the Patent Office of Ukraine "Acoustic solution of the Colorado beetle and device for implementation" No. 25548 A 01 M 1/04, 1/18 October 30, 1998. Destruction of the Colorado beetle by affecting its body with acoustic vibrations. in accordance with the reduction of labor intensity of the operation with increased toxicity. The results of this work are of great importance in the study of the relationship between the processes in the atmosphere of the Earth and the biosphere through acoustic vibrations.

The objective of this work is to design highly anisotropic 2D photonic crystals (PhCs) with near-zero refractive indices (NZRIs). We demonstrate that PhCs, composed of dielectric rods and organized in rectangular lattices can support unidirectional wave propagation with NZRIs along short sides of unit cells. Divergent waves that are incident are collimated as a result of complete suppression of wave propagation along the orthogonal direction. We used MPB and COMSOL software packages for simulating the dispersion diagrams, S21 transmission spectra, and wave patterns. The results show that the observed collimation effect is correlated with flat equi-frequency contours (EFCs) of PhCs, while operating frequency corresponds to the lower edge of the 2^nd transmission band of the crystal. We have recorded wave patterns beyond PhC fragment designed for operation in the microwave range as experimental confirmation of the computational results. Fabricated samples were irradiated by divergent TM polarized electromagnetic waves and were made up of ceramic dielectric rods with mm-size diameters. Obtained results extend perspectives of low-loss artificial anisotropic media with NZRI properties for microwave and photonic applications. Collimators can have many potential applications in electromagnetics and photonics, such as enhancing the gain and directionality of antennas’ radiation patterns and connecting waveguides with different widths.

In this chapter, the principles of non-Hermitian quantum mechanics are applied to the time independent perturbation theory and compared with the Zeeman effect. In recent years, non-Hermitian quantum physics has gained a great deal of popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. Here, we have also shown the condition under which the Zeeman Effect results will still be true even though the Hamiltonian taken into consideration is non-Hermitian.

The study is split into two categories under the research's objective: theoretical and experimental. Some of the alleged miracles performed by modern and ancient magicians-often referred to as "psychics"-are as follows: 1) the selective action on distant objects (especially "contagious magic"); 2) the discovery of hidden cavity structures (underground water reservoirs, buried treasures, etc.); 3) the structuring of space around a psychic (the so-called magic rings or charmed rings, allegedly protecting against malicious influence); 4) the alteration of a person's own weight (particularly levitation); and 5) the capacity to become invisible. These miracles might emerge from phenomena occurring in the physical vacuum, which characterized by intrinsic angular momentum: A quantum entity produces a pair of oppositely charged virtual particles with spin (virtual photon) in this vacuum. Because the virtual photon has precessing spin, it can be categorized as a spin vortex. Spin vortices in this vacuum can interact through spin supercurrent, the value of which is determined by the mutual orientation of spins of interacting spin vortices. From a physical perspective, a person's capacity to perform a miracle depends on their capacity to control the properties of spins (orientation, precession frequency, etc.) of spin vortices produced in the vortex-type physical vacuum by quantum entities that make up their organism.

One model of electro-gravimagnetic (EGM) field and electro-gravimagnetic charges and currents has been developed based on the biquaternionic generalization of Maxwell and Dirac equations. The connection between them is described by one biquaternionic wave (biwave) equation. Fundamental and regular solutions of this equation are constructed for known charges of currents, as well as in their absence. Using the theory of generalized functions shock EGM waves are considered and the conditions on the fronts of shock waves are obtained.

In particular, solutions describing gravitational waves and longitudinal electromagnetic waves are presented. It is shown that the presence of the longitudinal component of EM waves is associated with the density of the EGM field, which is described by the scalar component of the intensity biquaternion.

The law of inertia is postulated for free charge-currents in the absence of external EGM fields in the biquaternionic form. The mutual bigradient of such chargescurrents is equal to zero. Its consequence is the well-known laws of conservation of charge and mass. Solutions of this equation are constructed, which describe the objects of dimension N=3,2,1 (particles, body, tissue, fibers).

Taken together, these two biwave equations are a closed system for determining the EGM field and the movement of the EGM charges-currents generated by it.

It is known that the control volume method is widely used in numerical analysis for solving boundary value problems. Using this approach allows obtaining an approximate-analytical method for obtaining a solution to boundary value problems. A method for averaging boundary value problems over the volume being moved is proposed. The control volume is unique and movable in the area under consideration. The solution of the problem is obtained by averaging the differential equation over the volume being moved. For two-dimensional boundary value problems, it is also recommended to average over one variable. On the basis of which an ordinary differential is obtained and the solution of which gives a better solution to the problem. Examples are given.

Nanopowders can be defined as powdered materials with individual particles in nanometer scale or materials with crystalline in nanometer scale. Nanoparticles (NPs) are made up of a large amount of atoms or molecules bonded with each other with a total size varying from 1 nm to around 100 nm. Due to their very small sizes, NPs possess an extraordinarily high surface area-to-volume ratio, which changes their physical-chemical properties compared to their macroscale counterparts. Nano sized powders of TiO₂ (titanium dioxide) and Nb₂O₅ (Niobium (V) oxide) were used to fabricate TiO₂/Nb₂O₅ composites thin films by EPD (electrophoretic deposition) technique. In an EPD cell, pellets of magnesium nitrate hexahydrate and metal oxide powders were suspended in propan-2-ol. 1.2 cm apart, the electrodes were submerged in the suspension with a DC potential supplied across them. Through visual examination and analysis of UV-Vis-NIR spectrophotometer spectra, key EPD process parameters, including as the applied DC electric field, deposition duration, and solid concentration in suspension, were improved. The films with deposition times of 90 s, powder concentrations of 0.01 g/40 mL, and direct current (DC) voltage of 35 V had the maximum transmittance (55%) of all the samples. XRD micrographs confirmed that TiO₂ and Nb₂O₅ particles were presented in the composite film. SEM (scanning electron microscope) micrographs of the composite electrode thin films showed that porous films of high quality with well controlled morphology were deposited by using the EPD technique.

The objective of this work is to develop a thin and efficient transmission cloak for hiding objects larger than the wavelengths of incident radiation by using multi-layer coating composed of ordinary dielectrics, instead of meta- and plasmonic materials. The genetic algorithm-based optimization process is used to determine the parameters of the cloak layers, and the fitness function is the reciprocal of the total scattering cross-width of the cloaked target, which is obtained from the solution of the Helmholtz equation. The proposed cloak demonstrates better cloaking efficiency than does a similarly sized metamaterial cloak designed by using the transformation optics relations.

We study accretion of matter as well as X-ray emission spectra of low-mass black hole binaries in massive Brans-Dicke gravity assuming that the gravitational field generated by the stellar-mass black hole in the binary is the Schwarzschild-de Sitter space-time, which is the analogue of the Schwarzschild geometry of Einstein’s theory in massive Brans-Dicke gravity. In the first part of the computation we compute the accretion disk surrounding the stellar mass black hole adopting the well-known non-relativistic Shakura-Sunyaev model for an optically thick, cool, and geometrically thin disk. The most relevant quantities of interest are computed, i.e., i) the fluid radial velocity, ii) the energy and surface density, and iii) the pressure as a function of the radial coordinate. Next, in the second part of the computation we compute the soft spectral component of the X-ray emission expected from the disk. Finally, we investigate in detail the impact of the mass of the scalar field on the properties of the binary, and we make a comparison to the usual Schwarzschild solution as well.

This chapter is dealing with the detection and investigation of such and similar peculiarities of radiation effects in Mg0:Mn²+ crystals. Magnesium oxide has long been of interest for various important phenomena, including such as; defect induced magnetism, spin electron reflectivity, broad laser emission, thermoluminescent dosimetry etc [1-5]. Moreover, nanostructures of this material exhibited suitability for different kinds of applications ranging from wastewater treatment to spintronics depending upon their shape and size.  In that work the thermally stimulated luminescence and IR absorption spectra of Mg0:Mn²+ crystals irradiated in different reactors have been studied. The steady increase of peaks at 450 K (curve 2) and at 550 K (curve 1) is observed up to the dose of [10]¹⁵ n/cm^2 and not until relatively high fluencies their complicated non-steady behavior is registered. The trend of these changes in the same fluence range (10¹⁴ - 10¹⁷n/cm²) depends both on the initial state of the crystal and on the irradiation source, which may be explained by the "small dose effect". Such trend of the processes in the irradiated MgO: Mn⁽²⁺⁾ crystal i.e. destruction of hole-type trapping centers at the starting stage of the irradiation, is confirmed by dependence of the absorption coefficient peak of IR bands at 3290,3370 and 1600 cm] ^-1 on the neutron fluence