Editor(s)
Prof. Abbas Mohammed
Fellow IET, Senior Member IEEE, Professor, Senior Consultant ExAudio AB, Sweden.

ISBN 978-81-19761-64-7 (Print)
ISBN 978-81-19761-81-4 (eBook)
DOI: 10.9734/bpi/cppsr/v1

This book covers key areas of physical science. The contributions by the authors include full potential linearized augmented plane wave, density functional theory,  generalized gradient approximation, valence band maxima, Fermi level, quantum dots,  semiconductors, alkali metals and alkaline earth metals, impulse response function, fractional derivative, fractional integration, mittag-leffler function, stretched exponential function, quantitative susceptibility mapping, specific heat, green's function, density of states, model hamiltonian, high resolution spectroscopy, tunneling spectroscopy, quantum field, Wigner’s analysis, special relativity, Schrödinger equation, Romanovski polynomials, Euclidean space,  boiling heat transfer, Monte Carlo Method, flow boiling, heat transfer coefficient, Trefftz functions,thermodynamics, thermodynamic equilibrium, equilibrium temperature, Loschmidt's number, kinetic theory of gases, Boltzmann’s distribution. This book contains various materials suitable for students, researchers and academicians in the field of physical science.

 

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Chapters


The present work has covered the basic properties of Ca0.875Ba0.125Te alloy. The full potential linearized augmented plane wave (FP-LAPW) scheme, which is based on density functional theory in the framework of generalized gradient approximation (GGA), has been used to study the ground-state properties as well as the optical, mechanical, elastic, and thermal properties of the Ca0.875Ba0.125Te alloy. In order to model Ca1-xBaxTe alloy, 16-atoms supercell of the type 2 x 2 x 2 is employed. The lattice structure of Ca0.875Ba0.125Te alloy is obtained by replacing one Ca atom by one Ba atom in the crystal lattice of CaTe. The charge density plot, electronic structure and density of states plots are made and discussed for the alloy. The lower valence band maxima (VBM) and the upper conduction band minima (CBM) of Ca0.875Ba0.125Te alloy is located at \(\Gamma\) point, ensuing in a direct band gap, whereas in case of parent element CaTe the nature of the band gap is indirect. The characteristic properties of Ca0.875Ba0.125Te alloy is dominated by Te 5p electrons (below the Fermi level) and Ba 4d and Ca 3d electrons (above the Fermi level). The highest sigma and maximum Energy loss of Ca0.875Ba0.125Te happen at lower and higher photon energies, respectively. As a result, Ca0.875Ba0.125Te predicted electrical and optical characteristics demonstrate that it is an appropriate material for use in solar cells and optical devices.

We will study the formation of constituent expressions of various physical laws with impulse response function or memory kernel h(t) as delta function, singular power-law decay function, non-singular power law decay function, Mittag-Leffler function, pure exponential function and stretched exponential function. The motivation to have this chapter is to discuss, issues about using singular and non-singular functions as basic impulse response function or memory kernels; in basic evolution equation in several process dynamics-and its implications to obtain constituent equations for various systems. This gives a generalization of system studies. We will restrict our analysis to simple constitutive equations of few common physical laws that we deal in everyday studies. We will study two types of system with evolution equation defined as convolution i.e. y(t) = h(t)*x(t) (from Causality Principle). The physical laws that we discuss with various types of memory kernel are capacitor or dielectric relaxation/force/stress strain rate equations, population growth/radioactive decay equations, diffusion equations and wave equations. First considering the cause (input) x(t) is proportional to rate of change of some other physical quantity, i.e. x(t\(\propto\) f(1) (t) and second is a system where output response i.e. y(t) is proportional to rate of change of cause (input) x(t) i.e. y(t) \(\propto\) x(1) (t). We note the first type of system is like ‘response current’ to a change in applied voltage observed in dielectric relaxations and capacitor or force to rate of change of momentum or stress and strain rate equations.  The second one corresponds to population growth or radioactive decay type system.  The corollary to second type of system we study where cause X is replaced by L [x] ; where L denotes a ‘Linear operator’ and y(t) \(\propto\) x(1) (t). With L as Laplacian operator L \(\equiv\) \(\nabla\)2, we see that we will be getting various types of diffusion equations.  Extending further making effect as y(t) \(\propto\) x(2) (t), we will write various types of wave-equations. We will derive formation of these basic constitutive equations with zero-memory case where the memory-kernel or impulse response function is a delta-function and memorized relaxation cases with singular and non-singular memory kernels or impulse response functions that decays with time. These decaying functions used as memory kernel gives a reality in which memory fades as time grows. However, the question arises is the memory kernel be of singular or non-singular function? We will see that for the zero-memory case where the memory kernel is a delta function (singular in nature) returns classical constitutive equations for system that we know and use in every day physics but with the case where memory kernel is other than delta function we get constitutive equations with fractional derivatives and fractional integrations, different from what we know classically. We will note that singular function that we use for time-decaying memory kernel gives rise to conjugation to classical constitutive equations where its fractional counterpart replaces integer-order (classical) derivative or integral operation. We will see that non-singular memory kernel gives rise to more complicated constitutive equations as weighted infinite series sum of repeated integrations or weighted series sum of fractional integrations.

The objective of the study is to measure the optical properties of gray matter in the cerebral cortex in a spectral range of 400–1100 nm, including attenuation coefficients, scattering coefficients, scattering efficiency, and estimates of the penetration depth for optical imaging. The study aims to identify absorption peaks and investigate structural properties, such as neuron density, using Beer's law and the Mie model. The findings contribute to developing noninvasive diagnostic imaging techniques and therapies in the near-infrared (NIR) range for the cerebral cortex in the human brain. Gray matter in the outermost layer of the cerebral cortex plays a significant role in information processes, such as reasoning and planning, in addition to influencing intelligence, emotion, memory, and language. In this paper, measurements of the optical properties, such as the attenuation coefficients, scattering coefficients, scattering efficiency, and the penetration depth of gray matter in the cerebral cortex were measured in the fresh brain tissue of a healthy human male at a spectral range of 400–1100 nm. Determining the optical properties of gray matter is important for developing NIR noninvasive diagnostic imaging techniques and therapies. The absorption spectra of the gray matter tissues obtained here showed clear peaks at 550 and 580 nm due to oxyhemoglobin (HbO2) and at 970 nm due to water. The possible NIR optical imaging depth was roughly 3.8 mm at 800 nm, determined by the theoretical limit resulting from ballistic and snake photons. Using Beer’s law and the Mie model, structural properties (e.g., neuron density) in the gray matter of human brain tissue were investigated for the first time. The density of neurons in the examined gray matter tissue sample was estimated as roughly 40,000 neurons/mg. In addition, an extensive investigation is performed and a summary of optical properties, including scattering coefficients and transport length, for both gray and white matter in the human cerebral cortex, is outlined based on existing literature. The study will particularly emphasize examining the maximum distance light can traverse and the depth at which it can effectively penetrate, which facilitates noninvasive imaging of neurons in deep tissue regions. Recent techniques from the literature are explored that highlight structural changes in the normal brain, aging, and neurodegenerative diseases.

Specific Heat and Density of MgB2 Superconductor in Two Band Models: A Theoretical Study

Anuj Nuwal , Pradeep Chaudhary , S. C. Tiwari

Current Perspective to Physical Science Research Vol. 1, 20 September 2023, Page 94-113
https://doi.org/10.9734/bpi/cppsr/v1/10834F

The goal of this work is to compare the results of theory qualitatively with the existing data from experiments while examining the fundamental properties of MgBsuperconductive properties, such as specific heat, density of states, and temperature. MgBwith \(\mathit{T}\)c \(\approx\) 40K, is a record-breaking compound among the s-p metals and alloys. This substance seems to be a unique illustration of dual band electrical frameworks that are only loosely coupled to one another. The superconductivity in this simple compound is mostly due to the boron sub-lattice conduction band, as demonstrated by experimental evidence. There are two superconductivity gaps, according to investigations like tunneling spectroscopy, specific heat measurements, and high resolution spectroscopy. Considering a canonical two band BCS Hamiltonian containing a Fermi Surface of \(\pi\) - and \(\sigma\)- bands and following Green's function technique and equation of motion method, we have shown that MgBpossess two superconducting gaps. The system permits a precursor period for Cooper pair droplets, which transitions into a locked state at a threshold temperature below the mean field solution, it is also noted. Additionally, a study of specific heat and state densities is offered. For particular heat, the consistency between theory and experimental findings is quite convincing. Introduction, Model Hamiltonian, Physical Properties, Numerical Calculations, Discussion, and Conclusions are the five components that make up the study.

Mathematical Structures of Different Categories of Quantum Fields

E. Comay

Current Perspective to Physical Science Research Vol. 1, 20 September 2023, Page 114-132
https://doi.org/10.9734/bpi/cppsr/v1/6262B

Quantum field theory is a covering quantum theory that applies to high-energy processes where particles are created and destroyed. Properties of a quantum field that represents an elementary particle and a quantum field that mediates interaction between particles are analyzed. This analysis relies on fundamental physical principles. The mathematical structure of these fields proves that they are completely different physical objects. A further analysis proves that a quantum field that represents an elementary massive particle and a quantum field that represents a massless particle have a completely different mathematical structure. The results are used in an examination of free spin-1/2 elementary massive particles and other free elementary particles that have an integral spin. Inherent inconsistencies are found for elementary massive particles that have an integral spin and for the Majorana neutrino. The analysis also proves that interaction mediating fields do not represent a genuine particle. In particular, the electroweak theory of the W \(\pm\) and the Z particles has no coherent basis.

Construction of Exactly Solvable Potentials from Romanovski Polynomials

Nabaratna Bhagawati

Current Perspective to Physical Science Research Vol. 1, 20 September 2023, Page 133-141
https://doi.org/10.9734/bpi/cppsr/v1/6492C

We apply Extended transformation method to construct exactly solvable potentials of stationary state Schrodinger equation in any arbitrary dimensional Euclidean space. The normalized wave functions of the constructed potentials are obtained in terms of Romanovski polynomials. We show that there are six choices of coordinate transformation each leading to a potential for which Schrodinger equation is exactly solvable in terms of Romanovski polynomials. With analytical calculations we report that out of these six potentials only two are independent.

Investigations on Boiling Heat Transfer during Flow in Mini-Channels: Error Analysis with the Use of Monte Carlo Method

Magdalena Piasecka , Beata Maciejewska , Artur Piasecki

Current Perspective to Physical Science Research Vol. 1, 20 September 2023, Page 142-173
https://doi.org/10.9734/bpi/cppsr/v1/7307A

Numerous applications for compact mini-channel heat exchangers have been broadened in recent years, especially in applications with phase change. The advantages of using such devices are that they allow one to remove large heat fluxes, retaining small dimensions of the heat exchange system and provide effectiveness of cooling or thermoregulation. The authors of this chapter described current research which aims to establish heat transfer calculations of flow boiling in mini-channels. The model mini-channel heat exchanger was proposed as the test section with five parallel mini-channels 1 mm deep, asymmetrically heated. The working fluid was Fluorinert FC-770 that laminarly flowed in the circulation loop. The temperature of the common heated wall of the mini-channels was measured by infrared thermography while fluid temperature at the inlet and outlet to the test section was controlled due to K-type thermoelements. Investigations of heat transfer related to the subcooled boiling region. The main objective was to determine local heat transfer coefficients on the contact surface between the working fluid and the heated wall from the Robin boundary condition. The mathematical model described by the heat equation in the mini-channel wall and by the Fourier-Kirchhoff equation in a flowing fluid leads to an inverse heat transfer problem. This problem was solved using the FEM with the Trefftz-type basis functions. As temperature measurement is crucial during heat transfer research, an additional experiment was conducted for the estimation of the temperature measurement uncertainty. During such an experiment, temperature measurement was performed with the use of K-type thermoelements and an infrared camera in two mini-channels simultaneously. Since the uncertainty components are not approximately the same magnitude, the Monte Carlo method was indicated to estimate the uncertainty of the surface temperature measurement. The results obtained from this simulation method were compared with the results of the computation related to the uncertainty propagation method. Both methods of temperature were found to be consistent. The estimate of the temperature uncertainty measurements included in the final results of the heat transfer coefficient.

Was Loschmidt Correct in Asserting that the Entropy of a Closed System can be Decreased?

Andreas Trupp

Current Perspective to Physical Science Research Vol. 1, 20 September 2023, Page 174-221
https://doi.org/10.9734/bpi/cppsr/v1/19818D

The laws of thermodynamics are a set of scientific principles that define a set of physical properties that describe thermodynamic systems in thermodynamic equilibrium, including temperature, energy, and entropy. J.C. Maxwell demonstrated in 1868 that if the equilibrium temperature in a vertical column of gas subject to gravity was a function of height, a perpetual motion machine of the second sort would be achievable. Maxwell, on the other hand, maintained that the temperature must be the same at all locations down the column. Boltzmann felt the same way. Loschmidt was their opponent. He asserted that the equilibrium temperature decreased with height and that a perpetual motion machine of the second sort running through such a column was compatible with his interpretation of the second law of thermodynamics. As a result, he was confident he had discovered an infinite supply of useful energy for humanity. Later, E. Mach, too, did not consider the development of a second-generation perpetual motion machine to be impossible, although he did not cite Loschmidt's notion. In this article, new arguments (based on statistical mechanics) are provided for the hypothesis that an insulated column of gas subject to gravity does not take on a homogenous temperature: Since Boltzmann’s distribution of energies leads to the general gas law even in case the molecules are supposed to be extended objects, it follows that Boltzmann’s distribution cannot be strictly valid if experience requires to replace the general gas law pV=NkT by p(V-b) = NkT. But such a modification of the general gas law is undoubtedly required. With a modification of the general gas law and hence a deviation from Boltzmann’s distribution of energies thus being indispensable, it further follows that a homogeneous temperature cannot be achieved in an insulated column if gas subject to gravity.