Papers by Keyword: Hamiltonian

Abstract: In this paper, we present the photovoltaic characteristics of nanoscale Schottky junction solar cell consisting of graphene and GaAs using numerical simulation based on non-equilibrium Green’s function formalism. In our model, light-matter interaction is formulated by the coupling and scattering self-energy matrices whereas heterostructure is designed with a Hamiltonian matrix. An efficiency of 2.36% is obtained for monolayer graphene on GaAs; the efficiency is later enhanced to 5.40% by increasing both the number of graphene layers and the doping concentration of GaAs. The parameters to calculate power conversion efficiency, series and shunt resistances are extracted from the J-V characteristic. The I-V characteristic is also numerically simulated to extract reverse saturation current, ideality factor, and rectification ratio. Moreover, the power density is calculated for the optimized structure; the maximum power density of 7.46 mW/cm² is obtained for four layers of graphene and a doping concentration of 10¹⁷/cm³ in GaAs.

Abstract: The WK-recursive network has received much attention due to its many attractive properties. In this paper, we consider the one-to-one disjoint path covers properties of the WK-recursive network. We use K(d, t) to denote the WK-recursive network of level t, each of which basic modules is a d-vertex complete graph, where d > 1 and t ≥ 1. We prove that for any two distinct vertices u and v, there exist d-1 node-disjoint paths whose union covers all vertices of K(d, t) for d ≥ 3 and t ≥ 1. The results is optimal for vertices in different K_j(d, t − 1) for t ≥ 2, since each K_j(d, t − 1) with 1 ≤ j ≤ d has d − 1 open edges.

Abstract: The symplectic method is applied to study analytically the deflection field of bi-directional functionally graded piezoelectric materials in this paper. And the material properties varies exponentially both along the axial and transverse coordinates.The dual equations were presented by variation principle and introducing separation of variables used. Then in the symplectic space which consists of the original variables and their dual variables, the problem can be solved via symplectic expansion. This comparisons with experimental data were carried out to verify the validity of the symplectic method.

Abstract: This paper presents symplectic method for the derivation of exact solutions of functionally graded piezoelectric beam with the material properties varying exponentially both along the axial and transverse coordinates. In the approach, the related equations and formulas are developed in terms of dual equations, which can be solved by variables separation and symplectic expansion in Hamiltonian system. To verify advantages of the method, numerical examples of bi-directional functionally piezoelectric beam are discussed.

Abstract: Hamiltonian of the solid body with a crack inside in field of tensile stresses was derived. Hamiltonian equations describe process of crack propagation. A crack propagation was considered in heterogeneous material when in ground matrix present inclusions with work-of-fracture per unit surface significantly greater than in the matrix. Condition of cracks arrest in such system was found and length of path, passed until crack’s stop, was calculated.

Abstract: In this paper, we developed a high-fidelity model to handle large overall motion of multi-flexible bodies. As a demonstration, the model is applied to a planar flexible beam system. An explicit expression of the kinetic energy is derived for the planar beams. The elastic strain energy is described via an accurate beam finite element formulation. The Hamilton equations are integrated by a symplectic integration scheme for enhanced accuracy and guaranteed numerical stability. The Hamilton and the corresponding Hamilton’s equations of beam vibration problems are formulated. It appears that the proposed symplectic finite elements are capable of providing accurate and robust simulation in the dynamic modeling of multi-flexible bodies systems with large overall motions.

Abstract: Shrinking the size of a solid down to nanometer scale is indeed fascinating, which makes all the otherwise constant physical quantities to be tunable such as the Young’s modulus, dielectric constant, melting point, etc. The variation of size also generates novel properties that can hardly be seen in the bulk such as the conductor-insulator and nonmagnetic-magnetic transition of noble metals at the nanoscale. Although the physics of materials at the nanoscale has been extensively investigated, the laws governing the energetic and dynamic behavior of electrons at such a scale and their consequences on the tunable physical properties of nanostructures have not been well understood [C. Q. Sun, Prog Solid State Chem 35, 1-159 (2007); Prog Mater Sci 54, 179-307 (2009)]. The objective of the contribution is to update the recent progress in dealing with the coordination-resolved energetic and dynamic behavior of bonds in the low-dimensional systems with consideration of the joint effect of temperature and pressure. It is shown that the broken-bond-induced local strain and the associated charge and energy quantum trapping at the defect sites perturbs the atomic cohesive energy, electroaffinity, the Hamiltonian and the associated properties of entities ranging from point defects, surfaces, nanocavities and nanostructures. Application of the theories to observations has led to consistent understanding of the behavior of nanometer-sized materials and the interdependence of these entities as well as the means of determining the bond energy through the temperature-dependent measurements.

Abstract: The Quantum well structures have exhibited significant utility in the fabrication of advanced laser devices. The Gallium nitride semiconductor and its alloy particularly AlGaN based quantum structures are having important applications in optical data storage systems and the visible displays. Due to tailoring of wide band gap energy the spectrum obtained is from visible to ultraviolet wavelength range. We had thoroughly investigated the influence of Aluminum mole fraction variation in AlxGa1-xN under a biased condition for GaN/AlGaN based quantum heterostructure optical properties. Here, we had used 6X6 Hamiltonian to realize these properties. The 6X6 Hamiltonian has been chosen to include the many body effect in the calculation and to enhance the accuracy of the optimized results. The paper is focused to reveal the Aluminum mole fraction dependence of near and far filed intensities, peak optical gain, carrier concentration, and optical confinement factor. The effective index method has been used in determination of the optical field intensity in the near and far regimes. The variation in Aluminum mole fraction produces disparity in carrier concentration; hence, we have obtained the spontaneous emission and optical gain as a function of photon energy for different carrier density. The piezoelectric effect on GaN quantum well due to AlGaN barriers has been included through Poisson equation. This Poisson equation has been solved in a self-consistent manner along with Schrödinger and subsequently carrier concentrations have been deduced with a high accuracy using our simulation tools developed in MATLAB.

Abstract: Investigation of the properties of peptide plane in protein chain from both classical and quantum approach is presented. We calculated interatomic force constants for peptide plane and hydrogen bonds between peptide planes in protein chain. On the basis of force constants, displacements of each atom in peptide plane, and time of action we found that the value of the peptide plane action is close to the Planck constant. This indicates that peptide plane from the energy viewpoint possesses synergetic classical/quantum properties. Consideration of peptide planes in protein chain from information viewpoint also shows that protein chain possesses classical and quantum properties. So, it appears that protein chain behaves as a triple dual system: (1) structural - amino acids and peptide planes, (2) energy - classical and quantum state, and (3) information - classical and quantum coding. Based on experimental facts of protein chain, we proposed from the structure-energy-information viewpoint its synergetic code system.