**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**796

# World Academy of Science, Engineering and Technology

## [Physical and Mathematical Sciences]

### Online ISSN : 1307-6892

##### 796 Biography of the Earth in the Light of the Laws of Classical Physics

**Authors:**
I. V. Kuzminov

**Abstract:**

The proposed article is an analytical review of previously published articles in the series "Physics of Gravity", "The Picture of the World by Second Law of Thermodynamics" and others. The article shows the key role of the forces of gravity and the action of the second law of thermodynamics in shaping the picture of the world. In other words, the second law of thermodynamics can be called the law of matter cooling. The action in the compartment of the inverse temperature dependence of the forces of gravity and the second law of thermodynamics is carried out by the processes of separation, condensation, phase transitions, and transformation of matter. On the basis of the proposed concept, along the way, completely new versions of the development of events in the biography of the Earth are put forward. For example, new versions of the origin of planets, the origin of continents and others are being put forward. This article contains a list of articles and videos that are somehow related to the proposed topic. Articles and videos are presented in English and Russian.

**Keywords:**
Gravity,
the second law of thermodynamics,
electron rotation,
inverse temperature dependence,
inertia forces,
centrifugal forces.

##### 795 Investigation of the Surface Features of the Jupiter’s Galilean Moons

**Authors:**
Revaz Chigladze

**Abstract:**

The purpose of the research is to investigate the surfaces of Jupiter's Galilean moons (satellites), namely to identify which moon has the most uniform surface among them, what is the difference between the front (in the direction of motion) and the back sides of each moon's surface, as well as the temporal variations of the moons. Since 1981, the E. Kharadze Georgian National Astrophysical Observatory has been conducting polarimetric (P) and photometric (M) observations of Jupiter's Galilean moons with telescopes of different diameters (40-cm and 125-cm), as well as polarimeter Automatic Scanning Electron Polarimeter (ASEP)-78, the latest generation photometer with polarimeter and modern light receiver Santana Barbara Instrument Group (SBIG). As it turns out from the analysis of the observed material, parameters P and M depend on: α, the phase angle of the moon (satellite); L, the orbital latitude of the moon (satellite); λ, the wavelength, and t, the period of observation, i.e., P = P (α, L, λ, t), and similarly: M = M (α, L, λ, t). Based on the analysis of the obtained results, we get: The magnitude of the degree of polarization of Jupiter's Galilean moons near the opposition significantly differs from zero. Europa appears to have the most uniform surface, and Callisto has the least. Time variations are most characteristic of Io, which confirms the presence of volcanic activity on its surface. Based on the observed materials, it can be seen that the intensity of light reflected from the front hemisphere of the first three moons: Io, Europa, and Ganymede, is less than the intensity of light reflected from the rear hemisphere, while the picture with Callisto is opposite. The paper provides an explanation of this fact.

**Keywords:**
Galilean moons,
polarization,
degree of polarization,
photometry,
front and rear hemispheres.

##### 794 Fixed Point of Lipschitz Quasi Nonexpansive Mappings

**Authors:**
M. Moosavi,
H. Khatibzadeh

**Abstract:**

In this article, we study demiclosed and strongly quasi-nonexpansive of a sequence generated by the proximal point algorithm for a finite family of quasi-nonexpansive mappings in Hadamard spaces. Δ-convergence of iterations for the sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them to a common fixed point of sequence are also established. Our results generalize and improve several previously known results of the existing literature.

**Keywords:**
Fixed point,
Hadamard space,
proximal point algorithm,
quasi-nonexpansive sequence of mappings,
resolvent.

##### 793 Ultrafast Transistor Laser Containing Graded Index Separate Confinement Heterostructure

**Authors:**
Mohammad Hosseini

**Abstract:**

Ultrafast transistor laser investigated here has the graded index separate confinement heterostructure (GRIN-SCH) in its base region. Resonance-free optical frequency response with -3 dB bandwidth of more than 26 GHz has been achieved for a single quantum well transistor laser by using graded index layers of AlξGa1-ξAs (ξ: 0.1→0) in the left side of quantum well and AlξGa1-ξAs (ξ: 0.05→0) in the right side of quantum well. All required parameters, including quantum well and base transit time, optical confinement factor and spontaneous recombination lifetime, have been calculated using a self-consistent charge control model.

**Keywords:**
Transistor laser,
ultrafast,
GRIN-SCH,
-3db optical bandwidth,
AlξGa1-ξAs.

##### 792 Driver of Tectonic Plate Fracture and Movement

**Authors:**
Xuguang Leng

**Abstract:**

The theory of tectonic plate asteroid driver provides that comet and asteroid collisions have ample energy to fracture, move, and deform tectonic plate. The enormous kinetic energy of an asteroid collision is dissipated through the fracture and violent movement of the tectonic plates, and stored in the plate deformations. The stored energy will be released in the future through plate slow movement. The reflection of plate edge upwards upon collision impact causes the plate to sit on top of adjacent plate and creates the subduction plate. Higher probability and higher energy of asteroid collision in the equator area provides the net energy to drive heavier land plates to higher latitudes, offsetting the tidal and self spin forces, creating a more random land plates distribution. The trend of asteroid collisions is less frequency and intensity as loose objects are merging into the planets and Jupiter is taking ever larger shares of collisions. As overall energy input from asteroid collision decreases, plate movement is slowing down and eventually land plates will congregate towards equator area. The current trajectory of plate movements is the cumulative effect of past asteroid collisions, and can be altered, new plates be created, by future collisions.

**Keywords:**
Tectonic plate,
Earth,
asteroid,
comet.

##### 791 Creation and Annihilation of Spacetime Elements

**Authors:**
Dnyanesh P. Mathur,
Gregory L. Slater

**Abstract:**

Gravitation and the expansion of the universe at a large scale are generally regarded as two completely distinct phenomena. Yet, in General theory of Relativity (GR), they both manifest as 'curvature' of spacetime. We propose a hypothesis which treats these two 'curvature-producing' phenomena as aspects of an underlying process. This process treats spacetime itself as composed of discrete units (Plancktons) and is 'dynamic' in the sense that these elements of spacetime are continually being both created and annihilated. It is these two complementary processes of Planckton creation and Planckton annihilation which manifest themselves as - 'cosmic expansion' on the one hand and as 'gravitational attraction’ on the other. The Planckton hypothesis treats spacetime as a perfect fluid in the same manner as the co-moving frame of reference of Friedman equations and the Gullstrand-Painleve metric; i.e., Planckton hypothesis replaces 'curvature' of spacetime by the 'flow' of Plancktons (spacetime). Here we discuss how this perspective may allow a unified description of both cosmological and gravitational acceleration as well as providing a mechanism for inducing an irreducible action at every point associated with the creation and annihilation of Plancktons, which could be identified as the zero point energy.

**Keywords:**
Discrete spacetime,
spacetime flow,
zero point energy,
dark energy.

##### 790 The Physics of Gravity: A Hypothesis Based on Classical Physics

**Authors:**
I. V. Kuzminov

**Abstract:**

The alternative hypothesis of the physics of gravitation is put forward in this paper. The hypothesis is constructed on the laws of classical physics. The process of expansion of the Universe explains the physics of gravity. The expansion of the Universe induces the resistance of gyroscopic forces of electron’s rotation. The second component of gravity forces is the resistance arising from the second derivative of linear expansion. This hypothesis does not reject the existing foundation of settlement, particularly as it is empirically constructed. The forces of gravitation and inertia share a common nature, which has been recognized before. The presented hypothesis does not criticize existing theories of gravitation; rather, it explores a separate theme. It is important to acknowledge that the expansion of the Universe exhibits isotropic characteristics. The proposed hypothesis provides a fundamental direction for further research. It is worth noting that this article does not aim to encompass all possible aspects of future investigations.

**Keywords:**
Gyroscopic forces,
the unity of the micro- and macrocosm,
the expansion of the universe,
the second derivative of expansion.

##### 789 Quantum-Like Approach for Deriving a Theory Describing the Concept of Interpretation

**Authors:**
Yehuda Roth

**Abstract:**

In quantum theory, a system’s time evolution is predictable unless an observer performs measurement, as the measurement process can randomize the system. This randomness appears when the measuring device does not accurately describe the measured item, i.e., when the states characterizing the measuring device appear as a superposition of those being measured. When such a mismatch occurs, the measured data randomly collapse into a single eigenstate of the measuring device. This scenario resembles the interpretation process in which the observer does not experience an objective reality but interprets it based on preliminary descriptions initially ingrained into his/her mind. This distinction is the motivation for the present study in which the collapse scenario is regarded as part of the interpretation process of the observer. By adopting the formalism of the quantum theory, we present a complete mathematical approach that describes the interpretation process. We demonstrate this process by applying the proposed interpretation formalism to the ambiguous image "My wife and mother-in-law" to identify whether a woman in the picture is young or old.

**Keywords:**
Interpretation,
ambiguous images,
data reception,
state
matching,
classification,
determination.

##### 788 Explicit Solution of an Investment Plan for a DC Pension Scheme with Voluntary Contributions and Return Clause under Logarithm Utility

**Authors:**
Promise A. Azor,
Avievie Igodo,
Esabai M. Ase

**Abstract:**

The paper merged the return of premium clause and voluntary contributions to investigate retirees’ investment plan in a defined contributory (DC) pension scheme with a portfolio comprising of a risk-free asset and a risky asset whose price process is described by geometric Brownian motion (GBM). The paper considers additional voluntary contributions paid by members, charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause. To achieve this, the Weilbull mortality force function is used to establish the mortality rate of members during accumulation phase. Furthermore, an optimization problem from the Hamilton Jacobi Bellman (HJB) equation is obtained using dynamic programming approach. Also, the Legendre transformation method is used to transform the HJB equation which is a nonlinear partial differential equation to a linear partial differential equation and solves the resultant equation for the value function and the optimal distribution plan under logarithm utility function. Finally, numerical simulations of the impact of some important parameters on the optimal distribution plan were obtained and it was observed that the optimal distribution plan is inversely proportional to the initial fund size, predetermined interest rate, additional voluntary contributions, charge on balance and instantaneous volatility.

**Keywords:**
Legendre transform,
logarithm utility,
optimal distribution plan,
return clause of premium,
charge on balance,
Weibull mortality function.

##### 787 Mode-Locked Fiber Laser Using Charcoal and Graphene Saturable Absorbers to Generate 20-GHz and 50-GHz Pulse Trains, Respectively

**Authors:**
Ashiq Rahman,
Sunil Thapa,
Shunyao Fan,
Niloy K. Dutta

**Abstract:**

A 20-GHz and a 50-GHz pulse train are generated using a fiber ring laser setup that incorporates rational harmonic mode-locking (RHML). Two separate experiments were carried out using charcoal nanoparticles and graphene nanoparticles acting as saturable absorbers to reduce the pulse width generated from RHML. Autocorrelator trace shows that the pulse width is reduced from 5.6 ps to 3.2 ps using charcoal at 20 GHz, and to 2.7 ps using graphene at 50-GHz repetition rates, which agrees with the simulation findings. Numerical simulations have been carried out to study the effect of varying the linear and nonlinear absorbance parameters of both absorbers on output pulse widths. Experiments closely agree with the simulations.

**Keywords:**
Fiber optics,
fiber lasers,
mode locking,
saturable absorbers.

##### 786 Localising Gauss's Law and the Electric Charge Induction on a Conducting Sphere

**Authors:**
Sirapat Lookrak,
Anol Paisal

**Abstract:**

Space debris has numerous manifestations including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane so the Gaussian surface is a very small cylinder and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless manoeuvring space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.

**Keywords:**
Near-field approximation,
far-field approximation,
localized Gauss’s law,
electric charge density.

##### 785 Approximated Solutions of Two-Point Nonlinear Boundary Problem by a Combination of Taylor Series Expansion and Newton Raphson Method

**Authors:**
Chinwendu. B. Eleje,
Udechukwu P. Egbuhuzor

**Abstract:**

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

**Keywords:**
Newton Raphson method,
non-linear boundary value problem,
Taylor series approximation,
Michaelis-Menten equation.

##### 784 Appraisal of Relativistic Effects on GNSS Receiver Positioning

**Authors:**
I. Yakubu,
Y. Y. Ziggah,
E. A. Gyamera

**Abstract:**

The Global Navigation Satellite System (GNSS) started with the launch of the United State Department of Defense Global Positioning System (GPS). GNSS systems has grown over the years to include: GLONASS (Russia); Galileo (European Union); BeiDou (China). Any GNSS architecture consists of three major segments: Space, Control and User Segments. Errors such as; multipath, ionospheric and tropospheric effects, satellite clocks, receiver noise and orbit errors (relativity effect) have significant effects on GNSS positioning. To obtain centimeter level accuracy, the impacts of the relative motion of the satellites and earth need to be taken into account. This paper discusses the relevance of the theory of relativity as a source of error for GNSS receivers for position fix based on available relevant literature. Review of relevant literature reveals that due to relativity; Time dilation, Gravitational frequency shift and Sagnac effect cause significant influence on the use of GNSS receivers for positioning by an error range of ± 2.5 m based on pseudo-range computation.

**Keywords:**
GNSS,
relativistic effects,
pseudo-range,
accuracy.

##### 783 Investigation of the Effect of Pressure Changes on the Gas Proportional Detector

**Authors:**
S. M. Golgoun,
S. M. Taheri

**Abstract:**

Investigation of radioactive contamination of personnel working in radiation centers to identify radioactive materials and then measure the potential contamination and eliminate it has always been considered. Various ways have been proposed to detect radiation so far and different detectors have been designed. A gas sealed proportional counter is one of these detectors which has special working conditions. In this research, a gas sealed detector of proportional counter type was made and then its various parameters were investigated. Some parameters are influential on their working conditions and one of these most important parameters is the internal pressure of the proportional gas-filled detector. In this experimental research, we produced software for examination and altering high voltage, registering data, and calculating efficiency of the detector. By this, we investigated different gas pressure effects on detector efficiency and proposed optimizing working conditions of this detector. After reviewing the results, we suggested a range between 20-30 mbar pressure for this gas sealed detector.

**Keywords:**
Gas sealed detector,
proportional detector,
gas pressure measurement,
counter.

##### 782 Simulation of the Asphaltene Deposition Rate in a Wellbore Blockage via Computational Fluid Dynamics

**Authors:**
Xiaodong Gao,
Pingchuan Dong,
Qichao Gao

**Abstract:**

This work attempts to predict the deposition rate of asphaltene particles in blockage tube through CFD simulation. The Euler-Lagrange equation has been applied during the flow of crude oil and asphaltene particles. The net gravitational force, virtual mass, pressure gradient, Saffman lift, and drag forces are incorporated in the simulations process. Validation of CFD simulation results is compared to the benchmark experiments from the previous literature. Furthermore, the effects of blockage location, blockage length, and blockage thickness on deposition rate are also analyzed. The simulation results indicate that the maximum deposition rate of asphaltene occurs in the blocked tube section, and the greater the deposition thickness, the greater the deposition rate. Moreover, the deposition amount and maximum deposition rate along the length of the tube have the same trend. Results of this study are in the ability to better understand the deposition of asphaltene particles in production and help achieve to deal with the asphaltene challenges.

**Keywords:**
Asphaltene deposition rate,
blockage length,
blockage thickness,
blockage diameter,
transient condition.

##### 781 Dynamic Fast Tracing and Smoothing Technique for Geiger-Muller Dosimeter

**Authors:**
M. Ebrahimi Shohani,
S. M. Taheri,
S. M. Golgoun

**Abstract:**

Environmental radiation dosimeter is a kind of detector that measures the dose of the radiation area. Dosimeter registers the radiation and converts it to the dose according to the calibration parameters. The limit of a dose is different at each radiation area and this limit should be notified and reported to the user and health physics department. The stochastic nature of radiation is the reason for the fluctuation of any gamma detector dosimetry. In this research we investigated Geiger-Muller type of dosimeter and tried to improve the dose measurement. Geiger-Muller dosimeter is a counter that converts registered radiation to the dose. Therefore, for better data analysis, it is necessary to apply an algorithm to smooth statistical variations of registered radiation. We proposed a method to smooth these fluctuations much more and also proposed a dynamic way to trace rapid changes of radiations. Results show that our method is fast and reliable method in comparison the traditional method.

**Keywords:**
Geiger-Muller,
radiation detection,
smoothing algorithms,
dosimeter,
dose calculation.

##### 780 Calibration of 2D and 3D Optical Measuring Instruments in Industrial Environments at Submillimeter Range

**Authors:**
A. Mínguez-Martínez,
J. de Vicente

**Abstract:**

Modern manufacturing processes have led to the miniaturization of systems and, as a result, parts at the micro and nanoscale are produced. This trend seems to become increasingly important in the near future. Besides, as a requirement of Industry 4.0, the digitalization of the models of production and processes makes it very important to ensure that the dimensions of newly manufactured parts meet the specifications of the models. Therefore, it is possible to reduce the scrap and the cost of non-conformities, ensuring the stability of the production at the same time. To ensure the quality of manufactured parts, it becomes necessary to carry out traceable measurements at scales lower than one millimeter. Providing adequate traceability to the SI unit of length (the meter) to 2D and 3D measurements at this scale is a problem that does not have a unique solution in industrial environments. Researchers in the field of dimensional metrology all around the world are working on this issue. A solution for industrial environments, even if it is not complete, will enable working with some traceability. At this point, we believe that the study of the surfaces could provide us with a first approximation to a solution. In this paper, we propose a calibration procedure for the scales of optical measuring instruments, particularizing for a confocal microscope, using material standards easy to find and calibrate in metrology and quality laboratories in industrial environments. Confocal microscopes are measuring instruments capable of filtering the out-of-focus reflected light so that when it reaches the detector, it is possible to take pictures of the part of the surface that is focused. Varying and taking pictures at different Z levels of the focus, a specialized software interpolates between the different planes, and it could reconstruct the surface geometry into a 3D model. As it is easy to deduce, it is necessary to give traceability to each axis. As a complementary result, the roughness Ra parameter will be traced to the reference. Although the solution is designed for a confocal microscope, it may be used for the calibration of other optical measuring instruments, by applying minor changes.

**Keywords:**
Industrial environment,
confocal microscope,
optical measuring instrument,
traceability.

##### 779 Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model

**Authors:**
Amadi Ugwulo Chinyere,
Lewis D. Gbarayorks,
Emem N. H. Inamete

**Abstract:**

In this paper, the mandatory contribution, additional voluntary contribution (AVC) and administrative charges are merged together to determine the optimal investment strategy (OIS) for a pension plan member (PPM) in a defined contribution (DC) pension scheme under the modified constant elasticity of variance (M-CEV) model. We assume that the voluntary contribution is a stochastic process and a portfolio consisting of one risk free asset and one risky asset modeled by the M-CEV model is considered. Also, a stochastic differential equation consisting of PPM’s monthly contributions, voluntary contributions and administrative charges is obtained. More so, an optimization problem in the form of Hamilton Jacobi Bellman equation which is a nonlinear partial differential equation is obtained. Using power transformation and change of variables method, an explicit solution of the OIS and the value function are obtained under constant absolute risk averse (CARA). Furthermore, numerical simulations on the impact of some sensitive parameters on OIS were discussed extensively. Finally, our result generalizes some existing result in the literature.

**Keywords:**
DC pension fund,
modified constant elasticity of variance,
optimal investment strategies,
voluntary contribution,
administrative charges.

##### 778 An Axisymmetric Finite Element Method for Compressible Swirling Flow

**Authors:**
Raphael Zanella,
Todd A. Oliver,
Karl W. Schulz

**Abstract:**

This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

**Keywords:**
Axisymmetric problem,
compressible Navier-
Stokes equations,
continuous finite elements,
swirling flow.

##### 777 Finite Element Approximation of the Heat Equation under Axisymmetry Assumption

**Authors:**
Raphael Zanella

**Abstract:**

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit time marching. The code is verified by space and time convergence tests using a manufactured solution. An example problem is solved with an axisymmetric formulation and with a 3D formulation. Both formulations lead to the same result but the code based on the axisymmetric formulation is mush faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest of using an axisymmetric formulation when it is possible.

**Keywords:**
Axisymmetric problem,
continuous finite elements,
heat equation,
weak formulation.

##### 776 The Proof of Analogous Results for Martingales and Partial Differential Equations Options Price Valuation Formulas Using Stochastic Differential Equation Models in Finance

**Authors:**
H. D. Ibrahim,
H. C. Chinwenyi,
A. H. Usman

**Abstract:**

Valuing derivatives (options, futures, swaps, forwards, etc.) is one uneasy task in financial mathematics. The two ways this problem can be effectively resolved in finance is by the use of two methods (Martingales and Partial Differential Equations (PDEs)) to obtain their respective options price valuation formulas. This research paper examined two different stochastic financial models which are Constant Elasticity of Variance (CEV) model and Black-Karasinski term structure model. Assuming their respective option price valuation formulas, we proved the analogous of the Martingales and PDEs options price valuation formulas for the two different Stochastic Differential Equation (SDE) models. This was accomplished by using the applications of Girsanov theorem for defining an Equivalent Martingale Measure (EMM) and the Feynman-Kac theorem. The results obtained show the systematic proof for analogous of the two (Martingales and PDEs) options price valuation formulas beginning with the Martingales option price formula and arriving back at the Black-Scholes parabolic PDEs and vice versa.

**Keywords:**
Option price valuation,
Martingales,
Partial Differential Equations,
PDEs,
Equivalent Martingale Measure,
Girsanov Theorem,
Feyman-Kac Theorem,
European Put Option.

##### 775 Effect of the Tidal Charge Parameter on Temperature Anisotropies of the Cosmic Microwave Background Radiation

**Authors:**
Evariste Norbert Boj,
Jan Schee

**Abstract:**

We present the calculations of the temperature anisotropy of the cosmic microwave background radiation (CMBR) caused by an inhomogeneous region (the clump) within the Friedmann-Lemaitre-Robertson-Walker (FLRW) model of the Universe build in the framework of the Randall-Sundrum one brane model. We present two spherically symmetrical and statical models of the clump, the braneworld Reissner-Nordstrom black hole (bRNBH) and the perfect fluid sphere of uniform density matched to the FLRW spacetime via an external bRNBH. The boundary of the vacuum region expands, which induces an additional frequency shift to a photon of the CMBR passing through this inhomogeneity in comparison to the case of a photon propagating through a pure FLRW spacetime. This frequency shift is associated with an effective change of temperature of the CMBR in the corresponding direction. We give estimates on the changes of the effective temperature of the CMBR’s photon with the change of parameters describing the brane and the induced tidal forces from the bulk.

**Keywords:**
Braneworld,
CMBR,
Randall-Sundrum model,
Rees-Sciama effect,
Reissner-Nordstrom black hole.

##### 774 JEWEL: A Cosmological Model Due to the Geometrical Displacement of Galactic Object Like Black, White and Worm Holes

**Authors:**
Francesco Pia

**Abstract:**

Stellar objects such as black, white and worm holes can be the subject of speculative reasoning if represented in a simplified and geometric form in order to be able to move them; and the cosmological model is one of the most important contents in relation to speculations that can then open the way to other aspects that are not strictly speculative but practical, precisely in the Universe represented by us. In this work, thanks to the hypothesis of a very large number of black, white and worm holes present in our Universe, we imagine that they can be moved; it was therefore thought to align them on a plane and following a redistribution, and the boundaries of this plane were ideally joined, giving rise to a sphere that has the stellar objects examined radially distributed. Thanks to geometrical displacements of these stellar objects that do not make each one of them lose their functionality in the region in which they are located, at the end of the speculative process it is possible to highlight a spherical layer that allows a flow from the outside and inside this spherical shell allowing to relate to other external and internal spherical layers; this aspect that seems useful to describe the universe we live in, for example inside one of the spherical shells just described. The name "Jewel" was chosen because, imagining the speculative process present in this work at the end of steps, the cosmological model tends to be "luminous". This cosmological model includes, for each internal part of a generic layer, different and numerous moments of our universe thanks to an eternal flow inward. There are many aspects to explore, one of these is the connection between the outermost and the inside of the spherical layers.

**Keywords:**
Black hole,
cosmological model,
cosmology,
white hole.

##### 773 Development of Nondestructive Imaging Analysis Method Using Muonic X-Ray with a Double-Sided Silicon Strip Detector

**Authors:**
I-Huan Chiu,
Kazuhiko Ninomiya,
Shin’ichiro Takeda,
Meito Kajino,
Miho Katsuragawa,
Shunsaku Nagasawa,
Atsushi Shinohara,
Tadayuki Takahashi,
Ryota Tomaru,
Shin Watanabe,
Goro Yabu

**Abstract:**

In recent years, a nondestructive elemental analysis method based on muonic X-ray measurements has been developed and applied for various samples. Muonic X-rays are emitted after the formation of a muonic atom, which occurs when a negatively charged muon is captured in a muon atomic orbit around the nucleus. Because muonic X-rays have a higher energy than electronic X-rays due to the muon mass, they can be measured without being absorbed by a material. Thus, estimating the two-dimensional (2D) elemental distribution of a sample became possible using an X-ray imaging detector. In this work, we report a non-destructive imaging experiment using muonic X-rays at Japan Proton Accelerator Research Complex. The irradiated target consisted of a polypropylene material, and a double-sided silicon strip detector, which was developed as an imaging detector for astronomical obervation, was employed. A peak corresponding to muonic X-rays from the carbon atoms in the target was clearly observed in the energy spectrum at an energy of 14 keV, and 2D visualizations were successfully reconstructed to reveal the projection image from the target. This result demonstrates the potential of the nondestructive elemental imaging method that is based on muonic X-ray measurement. To obtain a higher position resolution for imaging a smaller target, a new detector system will be developed to improve the statistical analysis in further research.

**Keywords:**
DSSD,
muon,
muonic X-ray,
imaging,
non-destructive analysis

##### 772 Bound State Solutions of the Schrödinger Equation for Hulthen-Yukawa Potential in D-Dimensions

**Authors:**
I. Otete,
A. I. Ejere,
I. S. Okunzuwa

**Abstract:**

In this work, we used the Hulthen-Yukawa potential to obtain the bound state energy eigenvalues of the Schrödinger equation in D-dimensions within the frame work of the Nikiforov-Uvarov (NU) method. We demonstrated the graphical behaviour of the Hulthen and the Yukawa potential and investigated how the screening parameter and the potential depth affected the structure and the nature of the bound state eigenvalues. The results we obtained showed that increasing the screening parameter lowers the energy eigenvalues. Also, the eigenvalues acted as an inverse function of the potential depth. That is, increasing the potential depth reduces the energy eigenvalues.

**Keywords:**
Schrödinger's equation,
bound state,
Hulthen-Yukawa potential,
Nikiforov-Uvarov,
D-dimensions

##### 771 Strongly Coupled Finite Element Formulation of Electromechanical Systems with Integrated Mesh Morphing using Radial Basis Functions

**Authors:**
D. Kriebel,
J. E. Mehner

**Abstract:**

The paper introduces a method to efficiently simulate nonlinear changing electrostatic fields occurring in micro-electromechanical systems (MEMS). Large deflections of the capacitor electrodes usually introduce nonlinear electromechanical forces on the mechanical system. Traditional finite element methods require a time-consuming remeshing process to capture exact results for this physical domain interaction. In order to accelerate the simulation process and eliminate the remeshing process, a formulation of a strongly coupled electromechanical transducer element will be introduced which uses a combination of finite-element with an advanced mesh morphing technique using radial basis functions (RBF). The RBF allows large geometrical changes of the electric field domain while retain high element quality of the deformed mesh. Coupling effects between mechanical and electrical domains are directly included within the element formulation. Fringing field effects are described accurate by using traditional arbitrary shape functions.

**Keywords:**
electromechanical,
electric field,
transducer,
simulation,
modeling,
finite-element,
mesh morphing,
radial basis function

##### 770 De Broglie Wavelength Defined by the Rest Energy E0 and Its Velocity

**Authors:**
K. Orozović,
B. Balon

**Abstract:**

In this paper, we take a different approach to de Broglie wavelength, as we relate it to relativistic physics. The quantum energy of the photon radiated by a body with de Broglie wavelength, as it moves with velocity v, can be defined within relativistic physics by rest energy E₀. In this way, we can show the connection between the quantum of radiation energy of the body and the rest of energy E₀ and thus combine what has been incompatible so far, namely relativistic and quantum physics. So, here we discuss the unification of relativistic and quantum physics by introducing the factor k that is analog to the Lorentz factor in Einstein's theory of relativity.

**Keywords:**
de Brogli wavelength,
relativistic physics,
rest energy,
quantum physics.

##### 769 Multiple Approaches for Ultrasonic Cavitation Monitoring of Oxygen-Loaded Nanodroplets

**Authors:**
Simone Galati,
Adriano Troia

**Abstract:**

**Keywords:**
Cavitation,
Drug Delivery,
Nanodroplets,
Ultrasound.

##### 768 Pension Plan Member’s Investment Strategies with Transaction Cost and Couple Risky Assets Modelled by the O-U Process

**Authors:**
Udeme O. Ini,
Edikan E. Akpanibah

**Abstract:**

This paper studies the optimal investment strategies for a plan member (PM) in a defined contribution (DC) pension scheme with transaction cost, taxes on invested funds and couple risky assets (stocks) under the Ornstein-Uhlenbeck (O-U) process. The PM’s portfolio is assumed to consist of a risk-free asset and two risky assets where the two risky assets are driven by the O-U process. The Legendre transformation and dual theory is use to transform the resultant optimal control problem which is a nonlinear partial differential equation (PDE) into linear PDE and the resultant linear PDE is then solved for the explicit solutions of the optimal investment strategies for PM exhibiting constant absolute risk aversion (CARA) using change of variable technique. Furthermore, theoretical analysis is used to study the influences of some sensitive parameters on the optimal investment strategies with observations that the optimal investment strategies for the two risky assets increase with increase in the dividend and decreases with increase in tax on the invested funds, risk averse coefficient, initial fund size and the transaction cost.

**Keywords:**
Ornstein-Uhlenbeck process,
portfolio management,
Legendre transforms,
CARA utility.

##### 767 Application of Differential Transformation Method for Solving Dynamical Transmission of Lassa Fever Model

**Authors:**
M. A. Omoloye,
M. I. Yusuff,
O. K. S. Emiola

**Abstract:**

The use of mathematical models for solving biological problems varies from simple to complex analyses, depending on the nature of the research problems and applicability of the models. The method is more common nowadays. Many complex models become impractical when transmitted analytically. However, alternative approach such as numerical method can be employed. It appropriateness in solving linear and non-linear model equation in Differential Transformation Method (DTM) which depends on Taylor series make it applicable. Hence this study investigates the application of DTM to solve dynamic transmission of Lassa fever model in a population. The mathematical model was formulated using first order differential equation. Firstly, existence and uniqueness of the solution was determined to establish that the model is mathematically well posed for the application of DTM. Numerically, simulations were conducted to compare the results obtained by DTM and that of fourth-order Runge-Kutta method. As shown, DTM is very effective in predicting the solution of epidemics of Lassa fever model.

**Keywords:**
Differential Transform Method,
Existence and uniqueness,
Lassa fever,
Runge-Kutta Method.