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Full-Text Articles in Physical Sciences and Mathematics

Treatment Of A Ring With Periodic Atomic Placement Through Differential Geometry, Gregory Karjala, Lok Lew Yan Voon Dec 2012

Treatment Of A Ring With Periodic Atomic Placement Through Differential Geometry, Gregory Karjala, Lok Lew Yan Voon

Explorations – The Journal of Undergraduate Research, Scholarship and Creativity at Wright State

Most treatments of Bloch’s Theorem have relied on group theory or other mathematical methods for its proof. In this paper we give a derivation of the quantum number first proposed by Y.C Lee and Wei Z. Lee for the Benzene ring through the use of differential geometry. We also develop a Bloch style relationship relation for the benzene ring with an additional quantum number. Through this treatment we show the usefulness of differential geometry in the theorist’s toolkit when it comes to solid-state problems.


Stretching A Surface Having A Layer Of Porous Medium In A Viscous Fluid, M. Sajid, Z. Abbas, N. Ali, T. Javed Dec 2012

Stretching A Surface Having A Layer Of Porous Medium In A Viscous Fluid, M. Sajid, Z. Abbas, N. Ali, T. Javed

Applications and Applied Mathematics: An International Journal (AAM)

The present analysis deals with the steady, incompressible flow of a viscous fluid over a stretching sheet having a layer of porous medium of uniform thickness. The two-dimensional flow equations are derived in a Cartesian coordinate system. The semi-infinite region filled with a viscous fluid is divided into two regions namely, a clear fluid region and a region having a uniform pores. Darcy's law has been used for the flow of fluid in the porous medium region. An exact similar solution of the problem is obtained. The obtained solution is constrained by a relation between the porosity parameter and the …


On The Geometrıc Interpretatıons Of The Kleın-Gordon Equatıon And Solution Of The Equation By Homotopy Perturbation Method, Hasan Bulut, H. M. Başkonuş Dec 2012

On The Geometrıc Interpretatıons Of The Kleın-Gordon Equatıon And Solution Of The Equation By Homotopy Perturbation Method, Hasan Bulut, H. M. Başkonuş

Applications and Applied Mathematics: An International Journal (AAM)

This paper is organized in the following ways: In the first part, we obtained the Klein Gordon Equation (KGE) in the Galilean space. In the second part, we applied Homotopy Perturbation Method (HPM) to this differential equation. In the third part, we gave two examples for the Klein Gordon equation. Finally, We compared the numerical results of this differential equation with their exact results. We also showed that approach used is easy and highly accurate.


54th Rocky Mountain Conference On Analytical Chemistry Jul 2012

54th Rocky Mountain Conference On Analytical Chemistry

Rocky Mountain Conference on Magnetic Resonance

Final program, abstracts, and information about the 54th annual meeting of the Rocky Mountain Conference on Analytical Chemistry, co-endorsed by the Colorado Section of the American Chemical Society and the Society for Applied Spectroscopy. Held in Copper Mountain, Colorado, July 15-19, 2012.


Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv Jun 2012

Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv

Applications and Applied Mathematics: An International Journal (AAM)

Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.


Hydromagnetic Instability Of Streaming Viscoelastic Fluids Through Porous Media, Pardeep Kumar, Hari Mohan Jun 2012

Hydromagnetic Instability Of Streaming Viscoelastic Fluids Through Porous Media, Pardeep Kumar, Hari Mohan

Applications and Applied Mathematics: An International Journal (AAM)

The hydromagnetic instability of the plane interface between two uniform, superposed and streaming Rivlin-Ericksen viscoelastic fluids through porous medium is considered. The case of two uniform streaming fluids separated by a horizontal boundary is studied. It is observed, for the special case where perturbations in the direction and transverse direction of streaming are ignored, that the system is stable for stable configuration and unstable for unstable configuration. If the perturbations in the direction of streaming only one ignored, then the system is stable for stable configuration. However, the magnetic field succeeds in stabilizing certain wave-number range, which is otherwise potentially …


A Macroscopic Two-Phase Blood Flow Through A Bell Shaped Stenosis In An Artery With Permeable Wall, V. P. Srivastava, Mala Tandon, Rupesh K. Srivastav Jun 2012

A Macroscopic Two-Phase Blood Flow Through A Bell Shaped Stenosis In An Artery With Permeable Wall, V. P. Srivastava, Mala Tandon, Rupesh K. Srivastav

Applications and Applied Mathematics: An International Journal (AAM)

The present work concerns the effects of the hematocrit and the permeability of the wall on blood flow characteristics due to the presence of a bell shaped stenosis in an artery. In this analysis, the flowing blood is represented by a macroscopic two-phase model, as a suspension of erythrocytes in plasma. The analytical expressions for the flow characteristics, namely, the flow resistance (impedance), the wall shear stress distribution in the stenotic region and the shearing stress at the stenosis throat have been derived. Results for the effects of permeability as well as of hematocrit on these flow characteristics are shown …


Mhd Mixed Convective Flow Of Viscoelastic And Viscous Fluids In A Vertical Porous Channel, R. Sivaraj, B. R. Kumar, J. Prakash Jun 2012

Mhd Mixed Convective Flow Of Viscoelastic And Viscous Fluids In A Vertical Porous Channel, R. Sivaraj, B. R. Kumar, J. Prakash

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we analyze the problem of steady, mixed convective, laminar flow of two incompressible, electrically conducting and heat absorbing immiscible fluids in a vertical porous channel filled with viscoelastic fluid in one region and viscous fluid in the other region. A uniform magnetic field is applied in the transverse direction, the fluids rise in the channel driven by thermal buoyancy forces associated with thermal radiation. The equations are modeled using the fully developed flow conditions. An exact solution is obtained for the velocity, temperature, skin friction and Nusselt number distributions. The physical interpretation to these expressions is examined …


New Explicit Solutions For Homogeneous Kdv Equations Of Third Order By Trigonometric And Hyperbolic Function Methods, Marwan Alquran, Roba Al-Omary, Qutaibeh Katatbeh Jun 2012

New Explicit Solutions For Homogeneous Kdv Equations Of Third Order By Trigonometric And Hyperbolic Function Methods, Marwan Alquran, Roba Al-Omary, Qutaibeh Katatbeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study two-component evolutionary systems of the homogeneous KdV equation of the third order types (I) and (II). Trigonometric and hyperbolic function methods such as the sine-cosine method, the rational sine-cosine method, the rational sinh-cosh method, sech-csch method and rational tanh-coth method are used for analytical treatment of these systems. These methods, have the advantage of reducing the nonlinear problem to a system of algebraic equations that can be solved by computerized packages.


Boundary Stabilization Of Torsional Vibrations Of A Solar Panel, Prasanta K. Nandi, Ganesh C. Gorain, Samarjit Kar Jun 2012

Boundary Stabilization Of Torsional Vibrations Of A Solar Panel, Prasanta K. Nandi, Ganesh C. Gorain, Samarjit Kar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study a boundary stabilization of the torsional vibrations of a solar panel. The panel is held by a rigid hub at one end and is totally free at the other. The dynamics of the overall system leads to hybrid system of equations. It is set to a certain initial vibrations with a control torque as a stabilizer at the hub end only. Taking a non-linear damping as boundary stabilizer, a uniform exponential energy decay rate is obtained directly. Thus an explicit form of uniform stabilization of the system is achieved by means of the exponential energy …


Thermal Instability Of Rivlin-Ericksen Elastico-Viscous Rotating Fluid In Porous Medium In Hydromagnetics, S. K. Kango, Vikram Singh Jun 2012

Thermal Instability Of Rivlin-Ericksen Elastico-Viscous Rotating Fluid In Porous Medium In Hydromagnetics, S. K. Kango, Vikram Singh

Applications and Applied Mathematics: An International Journal (AAM)

The thermal instability of a layer of Rivlin-Ericksen elastico-viscous rotating fluid in a porous medium in hydromagnetics is considered. For stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like an ordinary (Newtonian) fluid. The magnetic field is found to have a stabilizing effect on the thermal instability of a layer of Rivlin-Ericksen fluid in the absence of rotation whereas the medium permeability has a destabilizing effect on thermal instability of Rivlin-Ericksen fluid in the absence of rotation. Rotation always has a stabilizing effect. The magnetic field, medium permeability and rotation introduce oscillatory modes in the system, which were non-existent in their …


Section Abstracts: Astronomy, Mathematics And Physics With Materials Science Apr 2012

Section Abstracts: Astronomy, Mathematics And Physics With Materials Science

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics, and Physics with Material Science Section for the 90th Annual Meeting of the Virginia Academy of Science, May 23-25, 2012, Norfolk State University, Norfolk, Virginia


A Dialogue Between Contemporary Perspectives And Ellen White On Divine Action And Quantum Physics, Michael F. Younker Jan 2012

A Dialogue Between Contemporary Perspectives And Ellen White On Divine Action And Quantum Physics, Michael F. Younker

Journal of the Adventist Theological Society

No abstract provided.


Multimessenger Astronomy: Modeling Gravitational And Electromagnetic Radiations From A Stellar Binary System, Kevin Kern Jan 2012

Multimessenger Astronomy: Modeling Gravitational And Electromagnetic Radiations From A Stellar Binary System, Kevin Kern

Bridges: A Journal of Student Research

Our Sun is one of roughly 100 billion other stars that make up the Milky Way Galaxy. Two-thirds of all stars are paired off, with a gravitational bond between the two stars. Such systems are known as stellar binaries. Although these binaries are very common in the galaxy, there is much yet to be learned about their formation, evolution, and interactions. The approach taken in this thesis is to produce simulated data representing the expected measurements that an observational astronomer would collect. We attempt to simulate three different stellar binary star systems: an eclipsing binary, a spectroscopic binary, and a …


Morphological And Optical Properties Of Vacuum Evaporated Zno Thin Films, Farzana Chowdhury, S. M. Firoz Hasan, M. Sahabul Alam Jan 2012

Morphological And Optical Properties Of Vacuum Evaporated Zno Thin Films, Farzana Chowdhury, S. M. Firoz Hasan, M. Sahabul Alam

Turkish Journal of Physics

ZnO thin films were deposited onto chemically and ultrasonically cleaned glass substrates by thermal evaporation in vacuum (\sim 10^{-6} mbar). The thickness of the films was measured by frequency shift of quartz crystal. The optical properties of the films have been ascertained by UV-VIS-NIR spectrophotometry in the photon wavelength range of 300--2500 nm. The effect of substrate temperature on the optical properties of the films has been investigated, where all film thickness was kept fixed at 100 \pm 10 nm. The optical transmittance spectra reveal a maximum transmittance of 88% at room temperature around photon wavelength of 2350 nm. Band …


The Composition Dependence Of The Optical Band Gap In Ge Doped Se-Te Glassy Alloy, Mainika Kapoor, Nagesh Thakur Jan 2012

The Composition Dependence Of The Optical Band Gap In Ge Doped Se-Te Glassy Alloy, Mainika Kapoor, Nagesh Thakur

Turkish Journal of Physics

Bulk glasses with the chemical composition (Se_{80}Te_{20})_{100-x}Ge_x (x = 0, 2, 4, 6) have been prepared from high purity constituent elements. Fragments of the bulk glasses are used to deposit thin films by vacuum thermal evaporation and compositional dependence of the optical and physical properties have been studied. It has been found that optical absorption is due to indirect transition and the optical band gap E_g increases with increasing Ge content in Se-Te glassy alloy. The relationship between the E_g and chemical composition is discussed in terms of cohesive energy and co-ordination number.


Slab Waveguide Sensor Based On Amplified Phase Change Due To Multiple Total Internal Reflections, Sofyan A. Taya, Taher M. El-Agez Jan 2012

Slab Waveguide Sensor Based On Amplified Phase Change Due To Multiple Total Internal Reflections, Sofyan A. Taya, Taher M. El-Agez

Turkish Journal of Physics

We present theoretically an optical slab waveguide sensor based on amplified phase change due to multiple total internal reflections (TIRs). Compared with the conventional waveguide sensors, the proposed approach provides higher sensitivity. In this sensor, we adopt the change in the ellipsometric total phase change \Delta as the measuring probe of changes in the refractive index (RI) of the cladding. The change in \Delta is calculated for large number of alternating total reflections. Numerical calculations show that \Delta is strongly dependent on the RI variations of the cladding. Moreover, theoretical simulations show that the resolution of this sensor is predicted …


Resonant Electron Transfer And L-Shell Excitation For _{26}Fe^{19+} And _{30}Zn^{23+} Ions, Hassan Ramadan Jan 2012

Resonant Electron Transfer And L-Shell Excitation For _{26}Fe^{19+} And _{30}Zn^{23+} Ions, Hassan Ramadan

Turkish Journal of Physics

Resonant transfer and excitation (RTE) involving simultaneous electron capture and projectile L-shell excitation has been calculated for Fe^{19+} and Zn^{23+} ions, in charge states ranging from nitrogen-like to oxygen-like incident on molecular hydrogen over an energy range 0--250 MeV. By the same way the calculations have been performed with helium over an energy range 0--300 MeV. The calculations are carried out using the angular momentum average (AMA) scheme in the isolated resonance approximation (IRA). This method was previously used to calculate RTE cross sections for N-like P^{8+} and Ca^{13+}, where the results are found to agree with the present calculations. …


Bianchi-V Cosmological Models With Viscous Fluid And Constant Deceleration Parameter In General Relativity, Sharad Kandalkar, Pramod Khade, Mohini Gaikwad Jan 2012

Bianchi-V Cosmological Models With Viscous Fluid And Constant Deceleration Parameter In General Relativity, Sharad Kandalkar, Pramod Khade, Mohini Gaikwad

Turkish Journal of Physics

In this paper we discuss the variation law for Hubble's parameter, average scale factor in spatially homogenous anisotropic Bianchi Type V space-time that yields a constant value deceleration parameter. Using the law of variation for Hubble's parameter, exact solutions of Einstein's field equations are obtained for Bianchi-V space time filled with viscous fluid in two different cases where the universe exhibits power law and exponential expansion. We investigate a number of solutions with constant and time varying cosmological constant together with variable and constant bulk viscosity. We find that the constant value of deceleration parameter is reasonable for the present …


Symmetry And The Order Of Events In Time. The Asymmetrical Order Of Events In Time In A Reversible Energy Converter, Ben-Zion Ginzburg, Randy Wayne Jan 2012

Symmetry And The Order Of Events In Time. The Asymmetrical Order Of Events In Time In A Reversible Energy Converter, Ben-Zion Ginzburg, Randy Wayne

Turkish Journal of Physics

The positive increase of entropy that occurs in irreversible processes has always served as a criterion for distinguishing the past from the future. The unerring ability of the Second Law of Thermodynamics to predict the order of events in time based on a change of entropy in macroscopic systems has led to the concept of the thermodynamical arrow of time. In this paper we analyze a cyclical reversible energy converter, in which thermal energy is converted into useful work without any net change of entropy. While it is usually assumed that time is an outsider in the equations of reversible …


Symmetry And The Order Of Events In Time. A Proposed Identity Of Negative Mass With Antimatter, Randy Wayne Jan 2012

Symmetry And The Order Of Events In Time. A Proposed Identity Of Negative Mass With Antimatter, Randy Wayne

Turkish Journal of Physics

In another paper in this series, we developed a symmetrical theory of mass which describes how systems of positive mass and negative mass will respond to an input of thermal energy. A system composed of positive mass or negative mass will respond to an input of thermal energy in opposite ways. For example, if a system composed of positive mass expands in response to radiation from a hot body, a system composed of negative mass will contract. Likewise, if the system composed of positive mass contracts when brought in communication with a cold body, a system composed of negative mass …


Thermodynamics Of Liquid Alkali Metals Using Pseudopotential Perturbation Scheme, Jagendra Kamalsinh Baria, Ashvinkumar Ramaniklal Jani Jan 2012

Thermodynamics Of Liquid Alkali Metals Using Pseudopotential Perturbation Scheme, Jagendra Kamalsinh Baria, Ashvinkumar Ramaniklal Jani

Turkish Journal of Physics

Recently proposed model potential of Baria and Jani is used with the exchange and correlation effect of Sarkar et al. to calculate internal energy (Enthalpy), Entropy and Helmholtz free energy of liquid Na, K, Rb and Cs at various temperatures with the variational approach. The parameter of the potential is determined with the standard zero pressure condition. The structure factor derived by Percus-Yevick solution for hard sphere fluids which is characterized by hard sphere diameter \sigma is used. A good agreement between theoretical investigations and experimental findings has confirmed the ability of the model potential to the liquid alkali metals.


Exactly Solvable Potentials From Decemvirate Power Potential, Nilamoni Saikia Jan 2012

Exactly Solvable Potentials From Decemvirate Power Potential, Nilamoni Saikia

Turkish Journal of Physics

A transformation method is presented which consist of a coordinate transformation and a functional transformation that allow generation of exact analytic bound state solutions of the Schrodinger Green's function equation. The method proposed here, which involves the generation of an exact analytic solution from solvable decemvirate power potential within the framework of Green's functions technique, makes it possible to generate a number of solved quantum systems for original quantum systems with multi-term potentials. The generated quantum systems are in general energy dependent with a single normalized eigenstate. A method has been devised to convert a subset of the generated quantum …


The Influence Of Confinements On The Photon Flux Spectra In Amorphous Silicon Quantum Dots, Moafak Cadim Abdulrida, Nidhal Moosa Abdul-Ameer, Shatha Mohammad Abdul-Hakeem Jan 2012

The Influence Of Confinements On The Photon Flux Spectra In Amorphous Silicon Quantum Dots, Moafak Cadim Abdulrida, Nidhal Moosa Abdul-Ameer, Shatha Mohammad Abdul-Hakeem

Turkish Journal of Physics

We have theoretically calculated the photon flux of radiative recombination in amorphous silicon quantum dots (a-SiQDs) at room temperature. These quantum dots have been ranged in their diameter 1 to 4 nm. The convolution of probability density function of deepest energy states of conduction P_C(E) and valence P_V(E) bands within the capture volume was adopted. The behavior of this function can be classified into four regions according to the quantum dot size. The effect of spatial and quantum confinements on the peak value of photon flux must be taken into account. We found that a blue shift is classified by …


Te Surface Waves In Dielectric Slab Sandwiched Between Lhm Slabs, Ass'ad I. Ass'ad, Hassan S. Ashour Jan 2012

Te Surface Waves In Dielectric Slab Sandwiched Between Lhm Slabs, Ass'ad I. Ass'ad, Hassan S. Ashour

Turkish Journal of Physics

In this work, the dispersion relation for TE surface waves has been derived for a slab waveguide constructed from a dielectric material slab sandwiched between two thick layers of left-handed material (LHM). The dispersion relation and the power flow were numerically solved for a given set of parameters: the structural factor, dielectric slab thickness, and the operating frequency on the effective refractive index and power flow. We found that the wave effective refractive index decreases with thickness increase as well as increase in frequency. We found that the effective refractive index increases slightly with increase of structural factor. Also, the …


Prediction Of Some Mechanical And Vibrational Properties Of Gax (X = P, As, Sb) Semiconductor Compounds, Anil Ratilal Jivani, Ashvinkumar Ramniklal Jani Jan 2012

Prediction Of Some Mechanical And Vibrational Properties Of Gax (X = P, As, Sb) Semiconductor Compounds, Anil Ratilal Jivani, Ashvinkumar Ramniklal Jani

Turkish Journal of Physics

The static elastic constants (C_{11}, C_{12} and C_{44}), pressure derivative of elastic constants, pressure derivative of bulk modulus, propagation velocities of longitudinal and transverse waves in [100], [110] and [111] directions and Young modulus are investigated through computations using the higher-order perturbation theory based on pseudopotential formalism, in which we have applied our own proposed model potential for GaP, GaAs and GaSb semiconductor compounds. In the present calculations, two local-field correction functions are employed to consider exchange and correlation effects. The numerical values of the aforesaid properties are found to be sensitive to the selection of the local-field correction function …


Dynamics And Noise Of Fiber-Grating Semiconductor Lasers Affected By The Line-Width Enhancement Factor, Salah Abdulrhmann Jan 2012

Dynamics And Noise Of Fiber-Grating Semiconductor Lasers Affected By The Line-Width Enhancement Factor, Salah Abdulrhmann

Turkish Journal of Physics

This paper numerically investigates the effect of the line-width enhancement factor on the dynamics and the intensity noise of InGaAs/InP lasers pumping in the wavelength of 980 nm at the strong optical feedback limit. The investigation is performed based on an improved time-delay rate equation model of a single-mode laser. The analyses are performed in terms of the temporal trajectory of the laser intensity, bifurcation diagram, relative intensity noise and injection current. The simulation results indicate that the laser, under strong optical feedback, mainly operates in CW, pulsation or chaos operation depending on the line-width enhancement factor and injection current …


Determination Of Barrier Height Temperature Coefficient By Norde's Method In Ideal Co/N-Gaas Schottky Contacts, Abdulmeci̇t Turut Jan 2012

Determination Of Barrier Height Temperature Coefficient By Norde's Method In Ideal Co/N-Gaas Schottky Contacts, Abdulmeci̇t Turut

Turkish Journal of Physics

We have formed the ideal Co/n-GaAs Schottky barrier diodes (SBDs) by magnetron DC sputtering. The experimental current-voltage data of the Co/n-GaAs SBD are almost independent of the sample temperature and quite well obey the thermionic emission model from 100 K to 320 K. We have showed that the temperature coefficient of the barrier height can be determined using Norde's method instead of the temperature-dependent capacitance-voltage measurements or the flat-band barrier height values because the thermionic emission current dominates in the ideal SBDs. We have obtained a barrier height temperature coefficient value of \alpha = 0.41 meV/K for Co/n-GaAs SBDs used …


Structure And Electrical Properties Of Lanthanum Doped Bi_2sr_2ca_{2-X}La_Xcu_3o_{10+ \Delta} Superconductor, Kareem Jasim Jan 2012

Structure And Electrical Properties Of Lanthanum Doped Bi_2sr_2ca_{2-X}La_Xcu_3o_{10+ \Delta} Superconductor, Kareem Jasim

Turkish Journal of Physics

In this work we studied the effect of La-doping on phase purity, crystal structure and electrical resistivity of Bi_2Sr_2Ca_2Cu_3O_{10+\delta} superconductor, synthesized by usual solid state reaction method. The X-ray florescence (XRF) show the stoichiometry of samples and X-ray diffraction (XRD) analysis showed the change of structure from orthorhombic to tetragonal by increasing La doping. It was found that the change of lanthanum concentrations of all our samples produce a change in the oxygen content, the ratio of lattice parameters c/a and mass density \rho_m. Electrical resistivity, using the four-probe technique, was used to find the critical temperature T_c and to …


Behavior Of Temperature Dependence Of Permeability Curves At Different Stages Of Crystallizations Of Nanocrystalline Fe_{70.5}Cr_3cu_1nb_3si_{13.5}B_9, Saadni Islam, Kazi Hanium Maria, Shamima Choudhury, Mohammad Abdul Hakim, Dilip Kumar Saha Jan 2012

Behavior Of Temperature Dependence Of Permeability Curves At Different Stages Of Crystallizations Of Nanocrystalline Fe_{70.5}Cr_3cu_1nb_3si_{13.5}B_9, Saadni Islam, Kazi Hanium Maria, Shamima Choudhury, Mohammad Abdul Hakim, Dilip Kumar Saha

Turkish Journal of Physics

Nanocrystalline amorphous ribbons of composition Fe_{70.5}Cr_3Cu_1Nb_3Si_{13.5}B_9 prepared by rapid solidification technique have been studied in the present work. Amorphicity of the ribbons has been confirmed by X-ray diffraction. Crystallization temperatures were identified by X-ray diffraction and crystallization products were analyzed by XRD. When annealed below the crystallization temperature, i.e. when the sample is in amorphous state, temperature dependence of permeability curves were characterized by sharp increase of permeability and subsequent fall to lower value near ferro-paramagnetic transition temperature, which is typical Hopkinson effect for soft ferromagnetic single phase material. Under devitrification, when the sample is in a two phase state, …