Sharif Digital Repository

This overview presents a tutorial introduction to the theory of magnetic plasma confinement in toroidal confinement systems with particular emphasis on axisymmetric equilibrium geometries, and tokamaks. The discussion covers three important aspects of plasma physics: Equilibrium, Stability, and Transport. The section on equilibrium will go through an introduction to ideal magnetohydrodynamics, curvilinear system of coordinates, flux coordinates, extensions to axisymmetric equilibrium, Grad-Shafranov Equation (GSE), Green's function formalism, as well as analytical and numerical solutions to GSE. The section on stability will address topics including Lyapunov Stability in nonlinear systems,... 

We have developed a simulation system for nanoscale high-electron mobility transistors, in which the self-consistent solution of Poisson and Schrödinger equations is obtained with the finite element method. We solve the exact set of nonlinear differential equations to obtain electron wave function, electric potential distribution, electron density, Fermi surface energy and current density distribution in the whole body of the device. For more precision, local dependence of carrier mobility on the electric field distribution is considered. We furthermore compare the simulation to a recent experimental measurement and observe perfect agreement. We also propose a novel graded channel design,... 

We show a methodology for how to construct Dirac points that occur at the corners of Brillouin zone as the Photonic counterparts of graphene. We use a triangular lattice with circular holes on a silicon substrate to create a Coupled Photonic Crystal Resonator Array (CPCRA) which its cavity resonators play the role of carbon atoms in graphene. At first we draw the band structure of our CPCRA using the tight-binding method. For this purpose we first designed a cavity which its resonant frequency is approximately at the middle of the first H-polarization band gap of the basis triangular lattice. Then we obtained dipole modes and magnetic field distribution of this cavity using the Finite... 

We revisit the mathematical formulation of the famous Jaynes-Cummings-Paul Hamiltonian, which describes the interaction of a two-level atom with a single mode of an electromagnetic cavity reservoir. We rigorously show that under the condition of ultrastrong coupling between the atom and cavity in which the transition frequency is comparable to the coupling frequency, the bosonic field operators undergo non-sinusoidal time variations. As a result, the well-known solutions to the Jaynes-Cummings-Paul model are no longer valid, even when the rotating wave approximation is not used. We show how a correct mathematical solution could be found instead  

This paper establishes a simple and topological approach to track real and reactive power flow in electric transmission systems. The presented method utilizes the well-known Proportional Sharing Theorem in order to evaluate the contribution of each power source to grid elements' supplied input power. We have also put forward an approximate power tracing method for upgraded grids, using its own previously surveyed results. The main advantages of the proposed procedure, compared with conventional methods, are discussed extensively. The effectiveness of this approach has been studied and ascertained for small-scale power systems, showing prominent speed and accuracy  

In this paper, an analysis of the harmonic contents of the optical output power for an in-plane single mode laser diode is performed, and the results are described in detail. In the first step, the absolute value of power for each harmonic is obtained in terms of various laser diode parameters, and the variations of external parameters, such as modulation current, bias current and frequency, are discussed. The analysis is done by direct solution of the rate equations of an arbitrary laser diode for carrier and photon densities. It is known that the optical power has a nonlinear dependence on frequency, and the maximum optical power of each harmonic is attained in its resonance frequency. The... 

We have performed an analysis of harmonic contents of the optical output power for a diode laser and described the results in details. In the first step the absolute value of power for each harmonic is obtained in terms of various diode laser parameters, and the variations of external parameters such as modulation current, bias current and frequency are discussed. The analysis is done by direct solution of rate equations of an arbitrary diode laser for carrier and photon densities. We conclude that the maximum power occurs at isolated peaks and their loci have been investigated and shown to be predictable by theory. It is known that the optical power has a nonlinear dependence on frequency,... 

An analytical modified method is presented to investigate the clearance effects on the dynamic behavior of cantilever beams. In this work, apart from clearance, all other nonlinearities are avoided to be considered during the analytical solution. The beam is idealized using an equivalent single-degree-of-freedom structure. A tri-linear stiffness system is also adopted to simulate the beam together with the clearance. Subsequently the analytical solution is derived for a cantilever beam structure with and without considering structural damping. The experimental method is employed to verify the results from the presented analytical solutions. It is noted that the results obtained by the... 

The coaxial electrospinning for producing core-shell nanofibers due to control the release profile of drug by the shell layer has been developed. N-carboxymethyl chitosan (CMC)-polyvinyl alcohol (core)/poly(ε-caprolactone) (PCL) (shell) nanofibers were produced via coaxial electrospinning. Doxorubicin (DOX) and nickel ferrite nanoparticles were incorporated into the nanofibers for controlled release of DOX against MCF-7 breast cancer. The minimum CMC/PCL fiber diameter was found to be 300 nm by optimizing of three variables including voltage to distance ratio (1.5–2.5 kV/cm), CMC concentration (4−6 wt.%) and PCL concentration (8−12 wt.%). The synthesized core-shell fibers were characterized... 

The coaxial electrospinning for producing core-shell nanofibers due to control the release profile of drug by the shell layer has been developed. N-carboxymethyl chitosan (CMC)-polyvinyl alcohol (core)/poly(ε-caprolactone) (PCL) (shell) nanofibers were produced via coaxial electrospinning. Doxorubicin (DOX) and nickel ferrite nanoparticles were incorporated into the nanofibers for controlled release of DOX against MCF-7 breast cancer. The minimum CMC/PCL fiber diameter was found to be 300 nm by optimizing of three variables including voltage to distance ratio (1.5–2.5 kV/cm), CMC concentration (4−6 wt.%) and PCL concentration (8−12 wt.%). The synthesized core-shell fibers were characterized... 

We present an explicit solution of carrier and field distributions in abrupt PN junctions under equilibrium. An accurate logarithmic numerical method is implemented and results are compared to the analytical solutions. Analysis of results shows reasonable agreement with numerical solution as well as the depletion layer approximation. We discuss extensions to the asymmetric junctions. Approximate relations for differential capacitance C-V and current-voltage I-V characteristics are also found under non-zero external bias  

In this paper, the equivalent medium of Schwarzschild metric is discussed. The corresponding ray-tracing equations are integrated for the equivalent medium of the Schwarzschild geometry, which describes the curved space around a spherically symmetric, irrotational, and uncharged blackhole. We make comparison to the well-known expression by Einstein. While Einstein's estimate is reasonably good for large closest distances of approach to the star, it disregards the optical anisotropy of space. Instead, Virbhadra's estimate which takes the effects of anisotropy of Schwarzschild metric is shown to be more consistent with numerical simulations. Hence, a true physical anisotropy in the velocity of... 

The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The results for real-valued systems are simplified and a pair of basis functions are found. These bases are a bit less accurate than WKB solutions but much easier to work with because of their algebraic form. Furthermore, these bases exactly satisfy the initial conditions and may go over the turning points without the divergent behavior of WKB solutions. The findings of this paper allow explicit evaluation of eigenvalues of confined modes with high precision, as demonstrated by few examples  

The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that this postulation is in fact unnecessary and may be replaced by a few deeper concepts, which ultimately lead to the derivation of Poisson bracket. One would only need to use Fourier transform pairs and Kramers- Kronig identities in the complex domain. We present a definition of Hermitian time-operator and discuss some of its basic properties. © Electronic Journal of Theoretical Physics  

A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While the zeroth order linearization approximation to the operators is normally used, here, first and second order truncation perturbation schemes are proposed. These schemes employ higher-order system operators, and then approximate number operators with their corresponding mean boson numbers only where needed. Spectral densities of higher-order operators are derived, and an expression for the second-order correlation function at zero time-delay has been found, which reveals that the cavity photon occupation of an ideal laser at threshold reaches √6 - 2, in good... 

The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order interactions, do not vanish under any possible choice of canonical parameters, and lead to coupling of momentum and field. The existence of quadratic mechanical parametric interaction is then demonstrated rigorously, which has been so far assumed phenomenologically in previous studies. Corrections to the quadratic terms are particularly significant when the mechanical frequency is of the same order or larger than the electromagnetic frequency. Further discussions... 

It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli's objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time... 

A system scheme is presented, which allows non-reciprocal wave transmission or directional amplification of electromagnetic signals, using a boxed four-node method. Edges represent strong hopping interactions and diagonals stand for weak parametric interactions. Using careful optimization of values for design parameters, we are able to obtain non-reciprocity in excess of 12 and 130 dB for intrinsic and extrinsic configurations at identical input/output frequencies. For the directional amplification, an isolation as high as 40 dB is demonstrated with the forward/backward gains of ±20 dB. Cascading two such systems potentially can offer high isolations at high gains. © 1965-2012 IEEE  

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer two-dimensional (2D) transition-metal dichalcogenides (TMDCs), having the formula MX2 with M = Mo, W and X = S, Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semi-classical perturbation analysis of response functions. We numerically calculate the linear and nonlinear surface susceptibility tensors with ωΣ = ωr + ωs + ωt. Both non-degenerate and degenerate cases are studied for third-harmonic generation and nonlinear refractive index, respectively. Computational results obtained with no external fitting parameters are discussed regarding two... 

A theory is presented for the quantum radiation emitted from a single exciton in a quantum dot. We assume that the quantum dot is in strong coupling to a slab photonic crystal cavity. A dielectric function of spatial coordinates is used to explain the effects of the macroscopic medium. It has been proved that the electric field in such a medium can be described using the so-called K-function. We derive a formula for obtaining the frequency spectrum, and present an analytical result for the optical spectrum, which is dependent on the K-function. We also have considered a slab photonic crystal configuration with hexagonal structure containing a cavity to evaluate the frequency spectrum in such...