# A New Look at Formulation of Charge Storage in Capacitors and Application to Classical Capacitor and Fractional Capacitor Theory | Chapter 14 | Advances and Trends in Physical Science Research Vol. 2

In this study, we revisit the concept of classical capacitor theory-and derive a possible new explanation of the definition charge stored in a capacitor. We introduce a ‘capacity function’ with respect to time to describe the charge storage in a classical capacitor and for a fractional capacitor. The observation regarding capacitor breakdown is very interesting. This study practically described for DC link capacitors (in power supply circuits), that the capacitor breaks down even it were never exceeded its maximum voltage limit. Here we will describe that the charge stored at any time in a capacitor as a ‘convolution integral’ of defined capacity function of a capacitor and voltage stress across it which comes from the causality principle. This approach, however, is different from the conventional method, where we multiply the capacity and the voltage functions to obtain charge stored. This new concept is in line with the observation of that charge stored as a step function and the relaxation current in form of impulse function for ‘ideal geometrical capacitor’ of constant capacity; when an uncharged capacitor is impressed with a constant voltage stress. Also this new formulation is valid for a power-law decay current that is given by ‘universal dielectric relaxation law’ called as ‘Curie von-Schweidler law’, when an uncharged capacitor is impressed with a constant voltage stress. This universal dielectric relaxation law gives rise to fractional derivative relating voltage stress and relaxation current that is formulation of ‘fractional capacitor’. A ‘fractional capacitor’ we will discuss with this new concept of redefining the charge store definition i.e. via this ‘convolution integral’ approach, and obtain the loss tangent value. We will also show how for a ‘fractional capacitor’ by use of ‘fractional integration’ we can convert the fractional capacity a constant that is in terms of fractional units (Farads per sec to the power of fractional number); to normal units of Farads. From the defined capacity function, we will also derive integrated capacity of capacitor. We will also give a possible physical explanation by taking example of porous and non-porous pitchers of constant volume holding water and thus, explaining the various interesting aspects of a classical capacitor and a fractional capacitor that we arrive with this new formulation; and also relates to a capacitor breakdown theory-due to electrostatic forces. Study investigates the charge stored in a capacitor, as a function of time is not the usual multiplication operation of capacity and voltage; instead, the charge is convolution integral of these two functions, derived from causality principles. With this formulation, we showed for a fractional capacitor, the charge goes to infinity for large times, when the fractional capacitor is placed on a constant voltage; and is in line with earlier fractional order models and observations.  With this formulation of convolution integral, this study also showed that the relaxation current is in the form of impulse function for ideal geometrical capacitor of constant capacity, when stressed by a constant voltage and for fractional capacitor with power-law decay current that is given by universal dielectric relaxation law called as Curie von-Schweidler law. Practically, this new ‘generalized- formulation’ has use while getting the charge stored in a capacitor which is a function of time with time-varying voltage stress across it, and to convert the fractional capacity units to usual capacity units in Farads.

## Biography of author(s)

Shantanu Das
Reactor Control System Design Section (E & I Group), BARC, Mumbai-400085, India.
Department of Physics, Condensed Matter Physics Research Centre – CMPRC, Jadavpur University, Kolkata-700032, West Bengal, India.

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# Plasma Sprayed Red Mud-Fly Ash Composite Coatings on Mild Steel: A Comprehensive Outline | Chapter 13 | Advances and Trends in Physical Science Research Vol. 2

The present investigation aims at evaluating the effect of fly ash addition on coating characteristics of pure red mud. Plasma sprayed coatings composed of red mud and a varying percentage of fly ash on mild steel were considered for the study. Coating technologies have already gained a promising momentum for the creation of emerging materials in the last few decades. Plasma spraying technique was used with varying levels of power namely 6, 9, 12 and 15 kW. Plasma spray is one of the most widely used techniques involved in surface modification by improvement of wear resistance, which may affirm the great versatility and its application to a wide spectrum of materials. Investigations of the coatings focused on tribological properties like sliding wear behaviour, wear morphology, wear mechanism and frictional force. Different coating characteristics like surface morphology, hardness, porosity, thickness and new phase formation are studied. The sustainability of these coatings towards high temperature at air environment up to 1000°C is evaluated by finding their adhesion strength.  DSC and TGA techniques are implemented to observe the coating behaviour to heat. The coatings show remarkable resistance towards high temperature by virtue of adhesion strength compensation. It is feasible to use these coatings limiting < 800°C otherwise dislodging of coating from metal. Fly ash with 10, 20 and 50% by weight was mixed with red mud and sliding wear test performed using a pin on disc wear test machine. The wear test was performed for sliding distance up to 942 m with track diameter of 100 mm and at a sliding speed of 100 rpm (0.523 m/s); applying a normal load of 10 N for a maximum duration of 30 minutes. The variation of wear rate and frictional force with that of sliding distance and time has been presented. The addition of fly ash with red mud reduces the wear rate by enhancing the coating property. But the optimum percentages of fly ash required for better coating material still impact a question mark for the researchers. It is observed that for the early stage the wear rate increases slowly and then rises drastically with sliding distance for all coating type and finally becomes stagnant. Operating power level proved to be the remarkable variable for different coating property. In our observation the coatings wear resistance (reverse of wear rate) decreases until an optimum value at 12 kW, afterwards indicating some other dominating parameters. Significant wear resistance was visible with the addition of fly ash due to an increase in bond strength and dense film at the interface. Wear rate decreases with operating power up to 12 kW, thereafter increases with initiating other dominating parameters. The present study concludes that, red mud coatings possess acceptable thermal properties. Fly ash is a beneficiary reinforcing agent for red mud, and the composite can be coat able with favoring surface properties. These coatings can be operated at high temperature. It is observed that, these composite coatings can also be employed for suitable trbological applications. Plasma generating power, adversely affect the coating morphology. Our work is a portfolio for researcher to discover many other aspects of red mud and its composite coatings. Study of corrosion wear behaviour may be implemented by future investigators to find its distinct application areas.

## Biography of author(s)

Harekrushna Sutar
Department of Chemical Engineering, Indira Gandhi Institute of Technology, Sarang, India and Department of Chemical Engineering, Jadavpur University, Kolkata, India and Department of Metallurgical and Materials Engineering, National Institute of Technology, Rourkela, India.

Rabiranjan Murmu
Department of Chemical Engineering, Indira Gandhi Institute of Technology, Sarang, India.

Debashis Roy
Department of Chemical Engineering, Jadavpur University, Kolkata, India.

Subash Chandra Mishra
Department of Metallurgical and Materials Engineering, National Institute of Technology, Rourkela, India.

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# Characterisation of Worst Month Statistics for Satellite-Earth Links Performance in Tropical Locations | Chapter 12 | Advances and Trends in Physical Science Research Vol. 2

The study presents the results of experimental data showing seasonal variability of rainfall intensities at two locations in Nigeria. The increasing development in satellite technology has brought about several novel mobile satellite services and applications. Consequently, there is a pressing demand for seamless data transfer and accessibility to satellite-earth microwave links in SHF/EHF frequency bands. Mobile platforms available via satellite include e-defence, Tele-banking, Skype, e-learning and so on. Consumers continue to press for ubiquitous coverage, internet traffic by-pass, scalability and improved quality of service of communication systems. However, rain has been the major degradation parameter for the availability of satellite signals especially at frequencies greater than 10 GHz. This paper presents some statistical analysis of rainfall in two tropical locations in Nigeria – Akure (7°17’N, 5°18’E, 358 m) in the Southwest, and Jos Plateau (9°57’N, 8°58’E, 1192 m) in the north central. Rainfall intensities of one-minute integration time were measured for 19 months (June 2013 to December 2014). The degrading effect of rainfall intensities was highlighted in the statistics of the worst month and monthly variations in rain rates along Ku-band signal paths in the study locations.  Predicted results showed that rain induced attenuation values above 30 dB occurred during the worst months, while clear sky values are below 2 dB. The worst month statistics obtained were largely different from those proposed by the ITU. Thus, for optimum link budgeting, the modified values of Q and ß should be adapted in these regions. The worst month statistics derived would serve as an essential planning tool for the system link designer for fade analysis and site diversity implementation; and eventually, result in better availability of radio-communication systems in the region. The results will facilitate improved radio-communication planning in the region. More investigation on beacon measurements of rain-induced attenuation is required to corroborate these results. The paper has revealed crucial considerations that affect the quality objectives of telecommunication systems. The results show that AY and AWM can be safely estimated from measured data of one minute integration time, and modelled with ITU-R recommended values. However, it is recommended that the worst-month design criteria of 178 mm/h and 150 mm/h for Akure and Jos, be considered as the actual design goal. Also, the relationship between the worst-month and average year has been given by β and Q1 parameters, as 0.372 and 1.060 for Akure, and 0.207 and 2.042 for Jos. Rain fade levels in worst month in both study locations are about 50% higher than levels in the average year, which suggests the need for alternative methods of mitigating rain fade such as adaptive power control schemes.

## Biography of author(s)

Moses Oludare Ajewole
Department of Physics, Federal University of Technology, Akure, Nigeria.

Joseph S. Ojo
Department of Physics, Federal University of Technology, Akure, Nigeria.

Omotayo May Durodola
Department of Physics, University of Jos, Nigeria.

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# Superluminal Motion of Free Spin-half Particles in a Fiber Bundle Formalism | Chapter 11 | Advances and Trends in Physical Science Research Vol. 2

The hypothesis of the spin of an electron, leading to its angular momentum, is no longer an open question, in science. Experimental evidence like the hydrogen fine structure and the Stern-Gerlach experiment in the 1920s and, recently, Nuclear Magnetic Resonance (NMR) have for long paved the way to definitely end this debate. Equipped with this mathematical machinery potent enough to handle the theories which are of interest to us, the expectation value of the overall relative linear velocity component of a fermion field was investigated in a previous paper, found quantized, and exceeding the speed of light. In the present article, we aim to review and describe this result in the framework of a fiber bundle theory.  Using a method developed in the 1980s by Zimmer for Dynamical-System theory, we explicate the feasibility of the superluminal free electron and neutrino result in bundle language.

## Biography of author(s)

Emmanuel D. K. Gazoya
National Nuclear Research Institute / ARC, Ghana Atomic Energy Commission, Accra, Box LG 80, Ghana.

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# Degradation Monitoring of Hindered Amine Light Stabilizer Doped Polymers | Chapter 10 | Advances and Trends in Physical Science Research Vol. 2

Polycarbonate (PC) is the most widely used aromatic polymer in various industrial applications. It is a condensation polymer in which benzene rings plus quaternary carbon atoms form bulky stiff molecules that promote rigidity and strength. The bulky chains crystallize with great difficulty, so the polymer is normally amorphous with excellent characteristics such as optical clarity, heat stability and mechanical resistance. The fluorescence and fluorescence excitation spectra of pure and doped PC depending on hindered-amine light stabilizers (HALS: Tinuvin 770 and Tinuvin 123) concentration and different processing conditions have been studied. Non-processed PC has no emission band in the visible range but processed PC with additives show visible fluorescence bands between 400–470 nm. It suggested that PC undergoes a kind of degradation process which lead to the fluorescence emission caused by the transitions from the new distortion-related localized states (defect states) created by processing and the additives. Such defects lead also to the emergence of a new band in the excitation and emission spectra at lower energies, where the symmetry of the bands break near. The intensity of these bands drastically depends on the sample treatment where the luminescence intensity quantitatively characterizes the concentration of defect radicals. An increase in screw speed resulted in an increase in specific mechanical energy (SME), higher SME led to a remarkable macromolecular degradation. The fluorescence spectroscopy of pure and doped polycarbonate (PC) depending on hindered-amine light stabilizers (HALS: Tinuvin 770 and Tinuvin 123) concentration and different processing conditions have been shown that pure non-processed PC has no emission band in the visible range but have an absorption band at 290 nm. Processing under excessive conditions is most likely to produce chains and general degradation which leads to a fluorescence emission. Processed PC with additives shows visible fluorescence bands between 400–470 nm. The intensity of these bands drastically depends on the sample treatment where the luminescence intensity quantitatively characterizes the concentration of defect radicals. PC becomes considerably yellow discolored with higher concentration of Tinuvin 770 or Tinuvin 123 and the PC gets more brittle (higher degradation grade).

## Biography of author(s)

Roushdey Salh
Department of physics, Umeå University, 901 87 Umeå, Sweden.

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# Application of Xylopia aethiopica Seed Extract as Aluminium Alloy Corrosion Inhibitor in 0.75 M KOH Alkaline Solution | Chapter 9 | Advances and Trends in Physical Science Research Vol. 2

Corrosion  phenomena,  control  and  prevention  are  unavoidable  scientific  issues  that  should  be addressed due to increase of technological development. Aluminium (Al) is one of the most abundant elements found in the earth’s crust. The applications site of Almakes it to yield corrosion attack despite its corrosion resistance. The aim of alloying is to enhance the desired properties possessed by the Al. Plant extracts are rich source of naturally synthesised chemical compounds that can be extracted by simple procedure. The present study investigated the corrosion inhibition of Al alloy in 0.75 M  KOH  solution  at  room  temperature  using Xylopia  aethiopicaseed  extract.  The gravimetric technique was employed in the study. It was revealed that the presence of the spice extract in the test solution retards the corrosion rate.  The calculated inhibition efficiency from the inhibitor surface coverage was observed to increase linearly with the inhibitor concentration. The consideration of the Langmuir adsorption isotherm indicated that the mechanism of adsorption is Physisorption. Temkin isotherm models explained that there were lateral attractions of the inhibitor molecules on the Al alloy surface. Flory-Huggins isotherm model confirms that there is bulky displacement of water molecules on  the  metal  surface  due  to  the  presence  of  the  inhibitor  molecules.  This depicts that the  spice constituents clustered on the Al alloy surface preventing contact with the corrosive environment.

## Biography of author(s)

O. F. Nwosu
Department of Physics/Electronics, Abia State Polytechnic, PMB 7166 Aba, Abia State, Nigeria.
Department of Physics, University of Port Harcourt, PMB 5323 Choba, Rivers State, Nigeria

E. Osarolube
Department of Physics, University of Port Harcourt, PMB 5323 Choba, Rivers State, Nigeria

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# Cosmic Vacuum Energy Determining the Space-Time Geometry of the Empty Universe | Chapter 8 | Advances and Trends in Physical Science Research Vol. 2

Different from energies constituted by baryons or photons both of which are expressed as energiesper particle, vacuum energy by its nature represents a ”volume energy”, i.e. an energy represented bythe sheer space volume, however, not simply reacting to the temporal change of this space volume,but rather in a non-evident way which we here try to fix using thermodynamic principles. Vacuumenergy is interpreted as a phenomenon of a polarization of empty space by real cosmic matter withthe consequence that the prevailing vacuum energy should depend on the cosmic matter density. Wetry to interpret vacuum energy as a form of a heat capacity of cosmic volumes and study by the use ofthermodynamical principles how the heat content of cosmic volumes should change with the changeof the volumes themselves. In the present days of modern cosmology, it is assumed that the mainingredient to cosmic energy presently is vacuum energy with an energy densityεvacthat is constantover the cosmic evolution. This paper shows that this assumption of constant vacuum energy densityis unphysical, since it conflicts with the requirements of cosmic thermodynamics. The study startsfrom the total vacuum energy including the negatively valued gravitational binding energy and showsthat cosmic thermodynamics then requires the cosmic vacuum energy density which can only varywith cosmic scaleR=R(t)according toεvac∼Rwith only two values ofνbeing allowed, namelyν1= 2andν2= 5/2. The study then discusses these two remaining solutions and find, whenrequiring a universe with a constant total energy, that the only allowed power index isν1= 2. Theconsequences of this scaling ofεvacare discussed and the results for a cosmic scale evolution of aquasi-empty universe are presented.

## Biography of author(s)

Michael Heyl
Deutsches Zentrum f ̈ur Luft und Raumfahrt (DLR), K ̈onigswinterer Str.  522 – 524, 53227 Bonn,Germany.

FAHR, Hans-Jrg Helmuth
Argelander Institute for Astronomy, Section Astrophysics, University of Bonn, Germany.

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# Paleoenvironmental Analysis and Its Significance in Sedimentology: Case Study of the Conglomerate Facies of the Awi Formation, Calabar Flank, Southeast Nigeria | Chapter 7 | Advances and Trends in Physical Science Research Vol. 2

Pebble morphometry of unbroken quartz pebbles collected from the basal section of Awi Formation exposed around Ewen area, southeastern Nigeria was studied for paleoenvironmental reconstruction. Paleoenvironmental analysis refers to the study or use of ancient geological materials (rocks) to infer the depositional environment or setting within which they were deposited. Pebble morphometric analysis has aided the determination of paleoenvironment during the deposition of Awi Formation. The depositional processes responsible for shaping the pebbles and the environment that prevailed during past geological times was characterised. This involved the measurement of the three orthogonal axes (long, intermediate and short), determination of their corresponding roundness, flatness indices and elongation indices for no less than 200 pebbles. The pebbles were selected from 20 points across four exposed sections of the Awi Formation around Ewen village. The roundness was determined using the standard roundness chart. The results show that the pebbles are sub-rounded to sub-angular and predominantly compact-bladed. The mean values for the following morphometric parameters: Flatness index, elongation ratio, maximum projection sphericity index and oblate-prolate (OP) index are 0.57, 0.78, 0.74 and 15.65 respectively. These values are in agreement with those of modern fluvial pebbles. This result was integrated with the deductions from bivariate plots of roundness against elongation ratio and sphericity against OP index, and they all inferred the deposition of the conglomeratic sandstones in a fluvial setting with subordinate transitional setting. Fluviatile process with some overlapping littoral influence has been shown to be responsible for the variation in clast morphology of the paraconglomerates (matrix-supported) of Awi Formation. Integrating all observations viz; the sediment stratification and grading style (fining upwards successions) and the dominant unidirectional nature of the crudely imbricate pebbles, a typical fluvial setting is inferred. It is possible that the jointing, faulting, sheeting and/or exfoliation of the rocks of the Oban Massif, which is believed to be the principal source of the sediments (provenance), also accounts for the abundance of vein quartz in the area which was eventually adapted for this study. Within sedimentary settings as this one with paraconglomerates associated with high energy flux during deposition and other typical channel lag deposits are locations of good economic deposits (placer deposits) and in some cases hydrocarbon accumulation. Therefore, besides the significance for pebble morphometry in deciphering paleoenvironments, it also gives clues for potential sites of ore bodies and/or characteristics of some targets for hydrocarbon pools. There are obviously several methods for paleoenvironmental reconstruction using sediments as earlier mentioned, grain morphology is one. However, care must be taken when reconstructing paleoenvironment because the shape of grains is a result of so many other factors and for effective utilisation, a careful study and integration of all other parameters are recommended.

## Biography of author(s)

Emmanuel Etim Okon
Department of Geology, University of Calabar, P.M.B. 1115, Calabar, Nigeria.

Romeo Akombi Ojong
Department of Geology, University of Calabar, P.M.B. 1115, Calabar, Nigeria.

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# A Simulation Study of Artificial Heating of the Ionosphere by Powerful High Frequency Radio Waves | Chapter 6 | Advances and Trends in Physical Science Research Vol. 2

Results of numerical modeling of the behavior of the F-layer ionospheric plasma during the periods of action of powerful high frequency radio waves, utilized for artificial heating experiments and pumped into the ionosphere by ground-based ionospheric heaters, are presented and discussed. For obtaining the presented simulation results, two distinct mathematical models were applied. The first mathematical model is based on a numerical solution of the system of transport equations for ionospheric plasma. This mathematical model allows us to simulate large-scale disturbances of the spatial structure of the F-region ionosphere, caused by the absorbed energy of powerful high frequency radio waves. The second mathematical model is based on a numerical solution of the system of kinetic equations for ion and electron gases in the ionosphere. The latter mathematical model allows us to investigate numerically kinetic processes in ionospheric plasma, in particular, the behavior of magnetic field aligned super-small-scale irregularities in the concentration of charged particles. Moreover, this model has allowed us to establish new details of the mechanism responsible for artificial heating of ionospheric plasma by powerful high frequency radio waves, pumped into the ionosphere by ground-based ionospheric heaters. These new details of the heating mechanism will be presented and discussed in this study.

The results indicated that the presence of a standing high-power HF radio wave ought to influence significantly on the behavior of the bulk flow velocities of electrons and positively charged ions. At the levels of the loops of the wave, the vectors of the bulk flow velocities of the positive ions and electrons rotate with the frequency equal to the frequency of the disturbing HF radio wave. It turned out that considerable differences between modules of bulk flow velocities of electrons and positive ions take place at the levels of the wave’s loops, whereas, mentioned velocities are equal and negligible at the levels of the nodal points. As a consequence, intensive heating of the F-layer ionospheric plasma ought to arise at the levels of the loops of a wave. On the contrary, at the levels of the nodal points, the ionospheric plasma ought to stay undisturbed. The present study, revealed new details of the mechanism responsible for artificial heating of ionospheric plasma by powerful HF radio waves, pumped into the ionosphere by ground-based ionospheric heaters, have been submitted.

## Biography of author(s)

Oleg V. Mingalev

Polar Geophysical Institute, Russian Academy of Sciences, Academgorodok Str. 26a,  Apatity 184209, Murmansk Region, Russia.

Mikhail N. Melnik

Polar Geophysical Institute, Russian Academy of Sciences, Academgorodok Str. 26a,  Apatity 184209, Murmansk Region, Russia.

Victor S. Mingalev

Polar Geophysical Institute, Russian Academy of Sciences, Academgorodok Str. 26a,  Apatity 184209, Murmansk Region, Russia.