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Microstructure And Geotechnical Properties Of St. Peter Sandstone In Clayton, Iowa, Amir Hossein Bagherieh
Microstructure And Geotechnical Properties Of St. Peter Sandstone In Clayton, Iowa, Amir Hossein Bagherieh
Doctoral Dissertations
"The St. Peter Sandstone is significantly different from the minerals and rocks which have been studied extensively in mining. It is brittle and characterized by an unusually high friction angle. On the other hand it is friable, and it is nearly cohesionless. The scarcity of the ground control techniques for this particular mining environment has created many difficulties for mine operators. This research aims to establish a fundamental understanding of the basic mechanical and strength properties of the St. Peter Sandstone for engineering design and scientific research. The specific objectives are 1) characterizing the strength of the St. Peter Sandstone, …
Distributed State Verification In The Smart Grid Using Physical Attestation, Thomas Patrick Roth
Distributed State Verification In The Smart Grid Using Physical Attestation, Thomas Patrick Roth
Doctoral Dissertations
"A cyber process in a distributed system can fabricate its internal state in its communications with its peers. These state fabrications can cause other processes in the distributed system to make incorrect control decisions. Cyber-physical systems have a unique advantage in the detection of falsified states because processes typically have observable effects on a shared physical infrastructure. This physical infrastructure acts as a high-integrity message channel that broadcasts changes in individual process states. The objective of this research is to demonstrate that there are cases where physical feedback from the shared infrastructure can be used to detect state fabrications. To …
2015 Spring Commencement, Georgia Southern University
2015 Spring Commencement, Georgia Southern University
Commencement Programs
No abstract provided.
2015 Fall Commencement, Georgia Southern University
2015 Fall Commencement, Georgia Southern University
Commencement Programs
No abstract provided.
Gurc Program [2015], Gurc
Evaluation Of Rock Fall Hazards Using Lidar Technology, Norbert H. Maerz, Travis Kassebaum, Kenneth J. Boyko, James Otoo
Evaluation Of Rock Fall Hazards Using Lidar Technology, Norbert H. Maerz, Travis Kassebaum, Kenneth J. Boyko, James Otoo
Geosciences and Geological and Petroleum Engineering Faculty Research & Creative Works
Lidar (light detection and ranging) is a relatively new technology that is being used in many aspects of geology and engineering, including researching the potential for rock falls on highway rock cuts. At Missouri University of Science and Technology, we are developing methods for measuring joint orientations remotely and quantifying the raveling process. Measuring joint orientations remotely along highways is safer, more accurate and can result in larger and more accurate data sets, including measurements from otherwise inaccessible areas. Measuring the nature of rock raveling will provide the data needed to begin the process of modeling the rock raveling process. …
Georgia Southern Magazine, Georgia Southern University
Georgia Southern Magazine, Georgia Southern University
Georgia Southern Magazine
- Eagles in Love
- Taste of Excitement
- "I Just Want to be a Good Guy"
- Outstanding Service
- Another Leap Forward
An Approach To Extract The Parameters Of Solar Cells From Their Illuminated I-V Curves Using The Lambert W Function, Ahmed A. El Tayyan
An Approach To Extract The Parameters Of Solar Cells From Their Illuminated I-V Curves Using The Lambert W Function, Ahmed A. El Tayyan
Turkish Journal of Physics
In this article an approach based on the Lambert W function is applied to analysis of various types solar cells and solar modules at a given insolation level and temperature; it can be used to extract accurate values of the parameters of a solar cell/module using experimental data or information available from the datasheet. These parameters are the photocurrent I_{ph}, the reverse saturation current I_o, the diode ideality factor a, the series resistance R_s, and the shunt resistance R_{sh}. The parameters I_o, a, R_s, and R_{sh} are calculated with the aid of 4 equations that can be solved simultaneously while …
Electric And Magnetic Field Induced Geometric Phases For The 2d Harmonic Oscillator In Noncommutative Phase Space, Mai-Lin Liang, Li-Fang Xu
Electric And Magnetic Field Induced Geometric Phases For The 2d Harmonic Oscillator In Noncommutative Phase Space, Mai-Lin Liang, Li-Fang Xu
Turkish Journal of Physics
In this work, we point out the phenomenon whereby the noncommutative corrections to the geometric phases induced by an electric field and a magnetic field have different orders in terms of the noncommutative parameters. The first order correction is zero for the electric field induced geometric phase and it is nonzero for the magnetic field induced geometric phase. In our calculation, the system is in coherent states when the electric field is applied, so the corresponding geometric phase calculated is that of the coherent states. Considering that the noncommutative parameters are very small, it is better to use the magnetic …
Dye-Sensitized Solar Cells Based On Dyes Extracted From Dried Plant Leaves, Sofyan A. Taya, Taher M. El-Agez, Kamal S. Elrefi, Monzir S. Abdel-Latif
Dye-Sensitized Solar Cells Based On Dyes Extracted From Dried Plant Leaves, Sofyan A. Taya, Taher M. El-Agez, Kamal S. Elrefi, Monzir S. Abdel-Latif
Turkish Journal of Physics
In this work, natural dyes were extracted from dried plant leaves of plant cream, apricot, figs, apples, sage, thyme, mint, Ziziphus jujuba, orange, shade tree, basil, berry, Mirabelle plum, Victoria plum, peach, mango, pomegranate, banana, guava, and fluoridation-treated plant. The extracts were used as photosensitizers for dye-sensitized solar cells (DSSCs). The cells were assembled using nanostructured TiO_2 films. The best performance was observed for the DSSC sensitized with Ziziphus jujuba with an efficiency of 1.077%. The impedance spectroscopy of 3 cells was carried out and the equivalent circuits were found.
Schrödinger Equation With Modified Smorodinsky-Winternitz Potential, Akpan Ndem Ikot, Hassan Hassanabadi, Elham Maghsoodi, Saber Zarrinkamar
Schrödinger Equation With Modified Smorodinsky-Winternitz Potential, Akpan Ndem Ikot, Hassan Hassanabadi, Elham Maghsoodi, Saber Zarrinkamar
Turkish Journal of Physics
We present solutions of the Schrödinger equation for the modified Smorodinsky-Winternitz potential in an exact analytical manner. The considered potential is of noncentral nature and includes the Pöschl-Teller potential in the radial as the radial term and includes both azimuthal and polar angle-dependent terms. The problem, after separation of variables, is solved via the Nikiforov-Uvarov method and the solutions are reported.
Higher-Dimensional Bianchi Type-Iii Universe With Strange Quark Matter Attached To String Cloud In General Relativity, Pradyumn Kumar Sahoo, Bivudutta Mishra
Higher-Dimensional Bianchi Type-Iii Universe With Strange Quark Matter Attached To String Cloud In General Relativity, Pradyumn Kumar Sahoo, Bivudutta Mishra
Turkish Journal of Physics
In this paper, our intention is to construct 5-dimensional Bianchi type-III cosmological models for quark matter attached to a string cloud in general relativity. Different cases for the metric potentials are considered and studied. The physical and kinematical behaviors of all the models are discussed. It is observed that most of the models admit initial singularity.
Cosmological Models Filled With A Perfect Fluid Source In The F(R,T) Theory Of Gravity, Dnyaneshwar Dadaji Pawar, Yadao Solanke
Cosmological Models Filled With A Perfect Fluid Source In The F(R,T) Theory Of Gravity, Dnyaneshwar Dadaji Pawar, Yadao Solanke
Turkish Journal of Physics
We investigated the physical behavior of an LRS Bianchi type I cosmological model in the framework of the f(R,T) theory of gravity in the presence of a perfect fluid, where R is the Ricci scalar and T is the trace of the stress energy tensor of the matter. In order to obtain a deterministic solution of the field equations we assumed the special law of variation of the Hubble parameter proposed by Berman that yields the constant deceleration parameter. Some physical properties of the models are discussed.
Extension Of The Class Of Exactly Solvable Nonstationary Quantum Mechanics Problems, Rana Gazanfar Aghayeva
Extension Of The Class Of Exactly Solvable Nonstationary Quantum Mechanics Problems, Rana Gazanfar Aghayeva
Turkish Journal of Physics
A modified factorization method for a charged particle in a time-dependent magnetic field has been developed by virtue of motion quantum integrals. Application of this method to the considered system helps to find exact solutions for a range of nonstationary potentials.
A Theoretical Way To Determine Gamma-Ray Mass Attenuation Coefficients Of Materials, Eli̇f Ebru Ermi̇ş, Ercan Pi̇li̇çer, Cüneyt Çeli̇ktaş
A Theoretical Way To Determine Gamma-Ray Mass Attenuation Coefficients Of Materials, Eli̇f Ebru Ermi̇ş, Ercan Pi̇li̇çer, Cüneyt Çeli̇ktaş
Turkish Journal of Physics
The gamma-ray mass attenuation coefficients of various absorber materials such as Ag, Al, Au, Bakelite, Cu, Fe, Pb, Plexiglas, Si, Sn, water, and Zn were determined theoretically at different gamma-ray energies and different absorber thicknesses in order to investigate how the number of gamma photons and their energies affect the calculation of mass attenuation coefficients of the absorbers since no study such a comprehensive work here was encountered. For this purpose, the FLUKA Monte Carlo (MC) and XCOM programs were used. Calculated coefficients were compared to the literature values and found to agree well with them. The FLUKA MC program …
Polaron Effects On The Second-Harmonic Generation In Asymmetrical Semiexponential Quantum Wells, Bo Xiao, Kangxian Guo, Sen Mou, Zhongmin Zhang
Polaron Effects On The Second-Harmonic Generation In Asymmetrical Semiexponential Quantum Wells, Bo Xiao, Kangxian Guo, Sen Mou, Zhongmin Zhang
Turkish Journal of Physics
Polaron effects on the second-harmonic generation (SHG) in asymmetrical semiexponential quantum wells (ASEQWs) are investigated theoretically. By using the framework of the compact-density-matrix approach and iterative method, the analytical expression of the SHG coefficients in ASEQWs is presented. Numerical results are illustrated for a typical GaAs/AlGaAs. By considering the electron--LO--phonon interaction (ELOPI), the energy levels and the wave functions of an electron confined in ASEQWs are obtained. It is found that whether we consider the ELOPI or not, the incident photon frequency $\omega$ and parameters $U_0$ and $\sigma$ also affect the SHG coefficient obviously.
On The Capacitance Of Crystalline Silicon Solar Cells In Steady State, Fabe Idrissa Barro, Moustapha Sane, Bernard Zouma
On The Capacitance Of Crystalline Silicon Solar Cells In Steady State, Fabe Idrissa Barro, Moustapha Sane, Bernard Zouma
Turkish Journal of Physics
In this work, an analytical approach is presented for modeling the capacitance of crystalline silicon solar cells. Based on a one-dimensional modeling of the cell, the excess minority carrier density, the photovoltage, and the capacitance are calculated. The motivation of this work are two-fold: to show base doping density and illumination effects on the capacitance of silicon solar cells, and to propose a determination technique for both dark capacitance and base doping density from C-V characteristics.
A Computational Study On The Interaction Between O$_{2}$ And Pristine And Ge-Doped Aluminum Phosphide Nanotubes, Mahdi Rezaei Sameti, Alireza Kazemi
A Computational Study On The Interaction Between O$_{2}$ And Pristine And Ge-Doped Aluminum Phosphide Nanotubes, Mahdi Rezaei Sameti, Alireza Kazemi
Turkish Journal of Physics
In this research the interaction between oxygen molecules and the outside and inside surfaces of pristine and Ge-doped (4,4) armchair and (6,0) zigzag models of aluminum phosphide nanotubes (AlPNTs) was systematically investigated using density function theory. Structural parameters, adsorption energy, quantum parameters, HOMO/LUMO orbitals, and nuclear quadrupole resonance (NQR) parameters were calculated for all models of AlPNTs. The aim of this work was to investigate the effects of Ge doping and O$_{2}$ adsorption on the electrical and structural parameters of (4,4) armchair and (8,0) zigzag models of AlPNTs. The results revealed that adsorption energies for all models were negative with …
Search For Mixed-Symmetry State In Even-Even $^{130-138}$Ce Isotopes Within The Interacting Boson Model-2, Ali Mahdi Abdul Hussain, Falih Hussain Al-Khudair, Abdul Ridha Hussain Subber
Search For Mixed-Symmetry State In Even-Even $^{130-138}$Ce Isotopes Within The Interacting Boson Model-2, Ali Mahdi Abdul Hussain, Falih Hussain Al-Khudair, Abdul Ridha Hussain Subber
Turkish Journal of Physics
The energy levels and reduced transition probabilities B(M1) and B(E2) of the even-even $^{130-138}$Ce isotopes were calculated by using the interacting boson model-2. We have analyzed the F-spin values and produced the symmetry labeling of the states. The calculated results were compared with the available experimental data. It was proved that the proton--neutron interacting boson model is a reasonable model for calculating low-lying spectra in the set of Ce isotopes and the quality of fit presented in this work is acceptable.
Adiabatic Loading Of Rotating Bosons Into 1d Optical Lattice, Shemi S. M. Soliman, Yehya Elsharkawy
Adiabatic Loading Of Rotating Bosons Into 1d Optical Lattice, Shemi S. M. Soliman, Yehya Elsharkawy
Turkish Journal of Physics
In this paper, the entropy-temperature curves are investigated for rotating boson gases in a 1D optical lattice with transverse harmonic confinement. Regimes at which the atomic sample can be significantly heated or cooled by adiabatically changing the lattice depth and the rotation rate are demonstrated. The suggested approach, which is the semiclassical approximation, includes the correction due to the finite size effect. The obtained results show that the entropy--temperature curves have a monotonically increasing nature for this system, in agreement with the standard thermodynamic arguments. For fixed temperature, entropy always increases with the increasing of the rotation rate or optical …
Survey Of Muon Stripping In The Muon-Catalyzed $D-D$ Fusion Cycle In Pure Deuterium, Seyed Mohammad Motevalli, Maedeh Mohammdapourfard
Survey Of Muon Stripping In The Muon-Catalyzed $D-D$ Fusion Cycle In Pure Deuterium, Seyed Mohammad Motevalli, Maedeh Mohammdapourfard
Turkish Journal of Physics
Muon-catalyzed fusion is a very efficient nuclear fusion method to which a wide variety of experimental and theoretical studies have been devoted in recent years. The mixtures of hydrogen isotopes are the most appropriate particles to do this kind of fusion. The efficiency of muon-catalyzed fusion in mixtures of pure deuterium is due to the abundance of this isotope as compared to other hydrogen isotopes. The most important issue of reducing the efficiency of the muon-catalyzed fusion chain in pure deuterium mixtures is the probability of muons sticking to the helium-3 particle produced after the $d-d$ nuclear fusion reaction. In …
Description Of The Yrast Superdeformed Bands In Even-Even Nuclei In A $\Sim$ 190 Region Using The Nuclear Softness Model, Ali Khalaf, Karima Abdelmageed, Manal Sirag
Description Of The Yrast Superdeformed Bands In Even-Even Nuclei In A $\Sim$ 190 Region Using The Nuclear Softness Model, Ali Khalaf, Karima Abdelmageed, Manal Sirag
Turkish Journal of Physics
A two-parameter nuclear softness (NS2) model for the transition energies is proposed by treating the variation of the moment of inertia with spin. The model has been applied to the yrast superdeformed (SD) bands in even-even nuclei in the mass region A $\sim $ 190. The model parameters have been determined from the fitting procedure in order to minimize the relative root mean square deviation between the experimental E2 transition $\gamma $-ray energies and the calculated ones. The basic experimental data on SD bands are given in the form of a series of $\gamma $-ray transitional energies and the spins …
Synthesis And Properties Of A Spinel Cathode Material For Lithium Ion Battery With Flat Potential Plateau, Ahmed Abdulrahman Ahmed Al-Tabbakh, Norlida Kamarulzaman, Aseel Al-Zubaidi
Synthesis And Properties Of A Spinel Cathode Material For Lithium Ion Battery With Flat Potential Plateau, Ahmed Abdulrahman Ahmed Al-Tabbakh, Norlida Kamarulzaman, Aseel Al-Zubaidi
Turkish Journal of Physics
A potential cathode material for lithium ion battery was synthesised by combustion reaction. The thermal behaviour of the as-synthesised precursor was measured using a thermogravimetric analyser and the range of calcination temperature from 500 $^{\circ}$C to 800 $^{\circ}$C was determined. X-ray diffraction analysis showed that all calcined powders crystallised in the cubic spinel structure of the $Fd\bar{3}m$ space group. The particle size distributions and morphologies of the powders were obtained using a particle size analyser and scanning electron microscope. The effect of calcination temperature on the electrochemical performance was investigated using galvanostatic charge/discharge measurements. The potential profiles of charge and …
A Full Relativistic Treatment In Analyzing $\Alpha $-$^{12}$C And $\Alpha $-$^{40,42,44,48}$Ca Elastic Scattering Data At 1.37 Gev, Zuhair Fayyad Mahmoud Shehadeh
A Full Relativistic Treatment In Analyzing $\Alpha $-$^{12}$C And $\Alpha $-$^{40,42,44,48}$Ca Elastic Scattering Data At 1.37 Gev, Zuhair Fayyad Mahmoud Shehadeh
Turkish Journal of Physics
A simple optical potential of Woods-Saxon form is used within the framework of the Klein-Gordon equation, for the first time, to analyze the elastic differential cross sections for 1.37 GeV (lab) incident $\alpha $-particles on $^{12}$C and calcium isotopes $^{40,42,44,48}$Ca. The relativistic energy-momentum relation assures the need for relativistic calculations. As such, the previously determined parameters of all optical potential forms, used in the nonrelativistic Schrödinger equation and successfully analyzing the $\alpha $-$^{12}$C and $\alpha $-$^{40,42,44,48}$Ca data at 1.37 GeV, are to be revised. In the presence of Coulomb potential, as in the cases under consideration, the asymptotic solution of …
Symmetry And The Order Of Events In Time: The Thermodynamics Of Blackbodies Composed Of Positive Or Negative Masssymmetry And The Order Of Events In Time: The Thermodynamics Of Blackbodies Composed Of Positive Or Negative Mass, Randy Wayne
Turkish Journal of Physics
I have previously proposed a discrete symmetry called CPM (charge-parity-mass) symmetry that defines matter as having positive mass and antimatter as having negative mass-both being involved in processes that proceed forward in time. I have generalized the second law of thermodynamics to describe and predict the order of events in time that take place in reversible thermodynamic systems composed of positive or negative mass. Here I extend the CPM symmetry to irreversible thermo-optical radiation systems characterized by the Stefan-Boltzmann law, Planck's blackbody radiation law, and Einstein's law of specific heat. The laws of radiation analyzed in terms of CPM symmetry …
Crystal Dynamics Of Zinc Chalcogenides I: An Application To Znscrystal Dynamics Of Zinc Chalcogenides I: An Application To Zns, Jay Prakash Dubey, Raj Kishor Tiwari, Kripa Shankar Upadhyaya, Pramod Kumar Pandey
Crystal Dynamics Of Zinc Chalcogenides I: An Application To Znscrystal Dynamics Of Zinc Chalcogenides I: An Application To Zns, Jay Prakash Dubey, Raj Kishor Tiwari, Kripa Shankar Upadhyaya, Pramod Kumar Pandey
Turkish Journal of Physics
A van der Waals three body force rigid shell model (VTRSM) developed earlier for NaCl and CsCl structure was expanded by us for zinc blende structure (ZBS). This model includes the effect of three body interactions and van der Waals interactions in the rigid shell model where short-range interactions were considered up to the second neighbor. Our model thus developed was applied to study the phonon dispersion curves, Debye temperature variation, two phonon Raman/IR spectra, and anharmonic elastic properties of ZnS. Our results are in good agreement with the measured data wherever available.
Multiwave Solutions Of Fractional 4th And 5th Order Burgers Equationsmultiwave Solutions Of Fractional 4th And 5th Order Burgers Equations, Emad A-B. Abdel-Salam, Gamal Fargahly Hassan
Multiwave Solutions Of Fractional 4th And 5th Order Burgers Equationsmultiwave Solutions Of Fractional 4th And 5th Order Burgers Equations, Emad A-B. Abdel-Salam, Gamal Fargahly Hassan
Turkish Journal of Physics
Fractional 4th and 5th order Burgers equations were studied by improving the generalized Exp-function method. The chief aim here was to discuss single-wave, double-wave, three-wave, and four-wave solutions for the space-time fractional (STF), time-fractional (TF), and space-fractional (SF) 4th and 5th order Burgers equations. The arbitrariness of the fractional orders allows much richer structures. It was observed that the wave amplitude of STF and SF Burgers equations is directly proportional to the noninteger derivative order, but the wave amplitude of TF Burgers equations is inversely proportional to the noninteger derivative order. From the graphical study of the obtained solution, a …
Solution Processable Graphene Oxide Hole Transport Layers And Their Application In P3ht:Hhper Active Layer Based Bhjscsolution Processable Graphene Oxide Hole Transport Layers And Their Application In P3ht:Hhper Active Layer Based Bhjsc, Görkem Memi̇şoğlu, Hali̇de Di̇ker, Canan Varlikli
Solution Processable Graphene Oxide Hole Transport Layers And Their Application In P3ht:Hhper Active Layer Based Bhjscsolution Processable Graphene Oxide Hole Transport Layers And Their Application In P3ht:Hhper Active Layer Based Bhjsc, Görkem Memi̇şoğlu, Hali̇de Di̇ker, Canan Varlikli
Turkish Journal of Physics
Graphene oxide (GO) material was synthesized by an improved Hummers method and characterized by FT-IR, XPS, XRD, AFM, SEM, and UV-VIS analyses. The thickness of the GO layer was measured as 1.5 nm. Solution processed bulk heterojunction solar cells comprising poly(3-hexylthiophene) (P3HT) as the electron donor and N,N'-bis-2-(1-hydoxyhexyl)-3,4,9,10-perylenebis(dicarboximide) (HHPER) as the electron acceptor component of the active layer were produced with and without the GO doped PEDOT-PSS hole transport layers. The optical investigations of the active layer were performed by ground state absorption and photoluminescence measurements. Optimized blend w/w was determined as P3HT:HHPER, 3:1. It was found that the presence …
Evaluation Of The Global Solar Irradiance In The Vhembe District Of Limpopo Province, South Africa, Using Different Theoretical Modelsevaluation Of The Global Solar Irradiance In The Vhembe District Of Limpopo Province, South Africa, Using Different Theoretical Models, Tshimangadzo Sophie Mulaudzi, Nnditshedzeni Eric Maluta, Vaith Sankaran
Evaluation Of The Global Solar Irradiance In The Vhembe District Of Limpopo Province, South Africa, Using Different Theoretical Modelsevaluation Of The Global Solar Irradiance In The Vhembe District Of Limpopo Province, South Africa, Using Different Theoretical Models, Tshimangadzo Sophie Mulaudzi, Nnditshedzeni Eric Maluta, Vaith Sankaran
Turkish Journal of Physics
An attempt has been made to employ three different theoretical models for the determination of global solar radiation for the climate conditions of the Vhembe district of Limpopo Province in South Africa. The models are: 1) the Angstrom linear-based model, 2) the Hargreaves and Samani (temperature-based) model, and 3) the Garcia model. These models require the following meteorological data inputs: temperature, sunshine hours, and global solar irradiance on the horizontal surface. The regression coefficients from our previous study were also employed in the calculations. A 4-year (2007--2010) global solar irradiance and temperature data set from the Agricultural Research Council and …
A Comparative Study: Synthetic Dyes As Photosensitizers For Dye-Sensitized \\Solar Cellsa Comparative Study: Synthetic Dyes As Photosensitizers For Dye-Sensitized \\Solar Cells, Amal M. Al-Kahlout, Hatem S. El-Ghamri, Naji Al Dahoudi, Taher M. El-Agez, Sofyan A. Taya, Monzir S. Abdel-Latif
A Comparative Study: Synthetic Dyes As Photosensitizers For Dye-Sensitized \\Solar Cellsa Comparative Study: Synthetic Dyes As Photosensitizers For Dye-Sensitized \\Solar Cells, Amal M. Al-Kahlout, Hatem S. El-Ghamri, Naji Al Dahoudi, Taher M. El-Agez, Sofyan A. Taya, Monzir S. Abdel-Latif
Turkish Journal of Physics
In this paper, dye-sensitized solar cells (DSSCs) were fabricated using a zinc oxide (ZnO) semiconducting layer and different synthetic dyes. Eight different synthetic dyes were used to fabricate the DSSCs. Nanocrystalline ZnO powder was coated on transparent conducting fluorine-doped tin oxide glass using the doctor blade method to form a thin layer. The absorption spectra of the synthetic dyes were investigated. DSSCs were characterized with $J$-$V$ characteristic curves. The parameters reflecting the cell performance were calculated. The results revealed that eosin Y dye corresponds to the highest conversion efficiency. The dependence of the sintering temperature and the thicknesses of the …