Search results for: one and two-dimensional Schrodinger equation

Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

Abstract:

In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

Procedia PDF Downloads 82

Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

Abstract:

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

Procedia PDF Downloads 238

Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

Procedia PDF Downloads 497

Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

Abstract:

In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

Procedia PDF Downloads 505

Authors: Nadaniela Egidi, Pierluigi Maponi

Abstract:

The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

Procedia PDF Downloads 70

Authors: Ih-Ching Hsu

Abstract:

Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

Procedia PDF Downloads 191

Authors: Olukunle C. Olawole, Dilip Kumar De

Abstract:

We have modified Richardson-Dushman equation considering thermal expansion of lattice and change of chemical potential with temperature in material. The corresponding modified Richardson-Dushman (MRDE) equation fits quite well the experimental data of thermoelectronic current density (J) vs T from carbon nanotubes. It provides a unique technique for accurate determination of W0 Fermi energy, EF0 at 0 K and linear thermal expansion coefficient of carbon nano-tube in good agreement with experiment. From the value of EF0 we obtain the charge carrier density in excellent agreement with experiment. We describe application of the equations for the evaluation of performance of concentrated solar thermionic energy converter (STEC) with emitter made of carbon nanotube for future applications.

Keywords: carbon nanotube, modified Richardson-Dushman equation, fermi energy at 0 K, charge carrier density

Procedia PDF Downloads 341

Authors: Sharmin Sultana, Reinhard Schlickeiser

Abstract:

A degenerate relativistic quantum plasma (DRQP) system (containing relativistically degenerate electrons, degenerate/non-degenerate light nuclei, and non-degenerate heavy nuclei) is considered to investigate the propagation characteristics of electrostatic solitary waves (in the ionic scale length) theoretically and numerically. The ion-acoustic solitons are found to be associated with the modified ion-acoustic waves (MIAWs) in which inertia (restoring force) is provided by mass density of the light or heavy nuclei (degenerate pressure of the cold electrons). A mechanical-motion analog (Sagdeev-type) pseudo-potential approach is adopted to study the properties of large amplitude solitary waves. The basic properties of the large amplitude MIAWs and their existence domain in terms of soliton speed (Mach number) are examined. On the other hand, a multi-scale perturbation approach, leading to an evolution equation for the envelope dynamics, is adopted to derive the cubic nonlinear Schrödinger equation (NLSE). The criteria for the occurrence of modulational instability (MI) of the MIAWs are analyzed via the nonlinear dispersion relation of the NLSE. The possibility for the formation of highly energetic localized modes (e.g. peregrine solitons, rogue waves, etc.) is predicted in such DRQP medium. Peregrine solitons or rogue waves with amplitudes of several times of the background are observed to form in DRQP. The basic features of these modulated waves (e.g. envelope solitons, peregrine solitons, and rogue waves), which are found to form in DRQP, and their MI criteria (on the basis of different intrinsic plasma parameters), are investigated. It is emphasized that our results should be useful in understanding the propagation characteristics of localized disturbances and the modulation dynamics of envelope solitons, and their instability criteria in astrophysical DRQP system (e.g. white dwarfs, neutron stars, etc., where matters under extreme conditions are assumed to exist) and also in ultra-high density experimental plasmas.

Keywords: degenerate plasma, envelope solitons, modified ion-acoustic waves, modulational instability, rogue waves

Procedia PDF Downloads 171

Authors: Sabrina Ladjama, Aicha Rizi, Azzedine Abbaci

Abstract:

In this work, we use the crossover model to formulate a comprehensive fundamental equation of state for the thermodynamic properties for several n-alkanes in the critical region that extends to the classical region. This equation of state is constructed on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity. The model can be applied in a wide range of temperatures and densities around the critical point for n-heptane. It is found that the developed model represents most of the reliable experimental data accurately.

Keywords: crossover model, critical region, fundamental equation, n-heptane

Procedia PDF Downloads 439

Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

Abstract:

We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

Procedia PDF Downloads 401

Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

Abstract:

Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

Procedia PDF Downloads 368

Authors: A. A. Soliman

Abstract:

The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

Procedia PDF Downloads 269

Authors: Proficiency Munsaka, Peter Baricholo, Erich Rohwer

Abstract:

Pulse evolutions along the 5 cm long, 6.0 ×4.2 μm² cross-section silicon germanium (SiGe) photonic waveguides were simulated and compared with experiments. Simulations were carried out by solving a generalized nonlinear Schrodinger equation (GNLSE) for an optical pulse evolution along the length of the SiGe photonic waveguides by the split-step Fourier method (SSFM). The solution obtained from the SSFM gave the pulse envelope in both time and spectral domain calculated at each distance step along the propagation direction. The SiGe photonic waveguides were pumped in an anomalous group velocity dispersion (GVD) regime using a 4.7 μm, 210 fs femtosecond laser to produce a significant supercontinuum (SC). The simulated propagation of ultrafast pulse along the SiGe photonic waveguides produced an SC covering the atmospheric window (2.5-8.5 μm) containing the molecular fingerprints for important gases. Thus, the mid-infrared supercontinuum generation in SiGe photonic waveguides system can be commercialized for gas spectroscopy for detecting gases that include CO₂, CH₄, H₂O, SO₂, SO₃, NO₂, H₂S, CO, and NO at trace level using absorption spectroscopy technique. The simulated profile evolutions are spectrally and temporally similar to those obtained by other researchers. Obtained evolution profiles are characterized by pulse compression, Soliton fission, dispersive wave generation, stimulated Raman Scattering, and Four Wave mixing.

Keywords: silicon germanium photonic waveguide, supercontinuum generation, spectroscopy, mid infrared

Procedia PDF Downloads 96

Authors: Hamid Hamli Benzahar

Abstract:

The main goal of this research is to study the deflection of a composite beam CB taking into account the effect of shear deformation. The structure is made up of two beams of different sections, joined together by thin adhesive, subjected to end moments and a distributed load. The fundamental differential equation of CB can be obtained from the total energy equation while considering the shear deformation. The differential equation found will be compared with those found in CB, where the shear deformation is zero. The CB system is numerically modeled by the finite element method, where the numerical results of deflection will be compared with those found theoretically.

Keywords: composite beam, shear deformation, moments, finites elements

Procedia PDF Downloads 37

Authors: Khaled Moaddy

Abstract:

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

Procedia PDF Downloads 101

Authors: Jiya Mohammed, Ibrahim Ismail Giwa

Abstract:

Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.

Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow

Procedia PDF Downloads 436

Authors: Alok Shiomurti Tripathi, Ajay Kumar Timiri, Papiya Mitra Mazumder, Anil Chandewar

Abstract:

The present study evaluates the possible drug interaction between glimepiride (GLIM) and sildenafil citrate (SIL) in streptozotocin (STZ) induced in diabetic nephropathic (DN) animals and also postulates the possible mechanism of interaction by molecular modeling studies. Diabetic nephropathy was induced by single dose of STZ (60 mg/kg, ip) and confirms it by assessing the blood and urine biochemical parameters on 28th day of its induction. Selected DN animals were used for the drug interaction between GLIM (0.5mg/kg, p.o.) and SIL (2.5 mg/kg, p.o.) after 29th and 70th day of protocol. Drug interaction were assessed by evaluating the plasma drug concentration using HPLC-UV and also determine the change in the biochemical parameter in blood and urine. Mechanism of the interaction was postulated by molecular modeling study using Maestro module of Schrodinger software. DN was confirmed as there was significant alteration in the blood and urine biochemical parameter in STZ treated groups. The concentration of SIL increased significantly (p<0.001) in rat plasma when co administered with GLIM after 70th day of protocol. Molecular modelling study revealed few important interactions with rat serum albumin and CYP2C9.GLIM has strong hydrophobic interaction with binding site residues of rat serum albumin compared to SIL. Whereas, for CYP2C9, GLIM has strong hydrogen bond with polar contacts and hydrophobic interactions than SIL. Present study concludes that bioavailability of SIL increases when co-administered chronically with GLIM in the management of DN animals and mechanism has been supported by molecular modeling studies.

Keywords: diabetic nephropathy, glimepiride, sildenafil citrate, pharmacokinetics, homology modeling, schrodinger

Procedia PDF Downloads 337

Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled

Abstract:

This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility

Procedia PDF Downloads 174

Authors: E. V. Krishnan

Abstract:

In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.

Keywords: travelling wave solutions, Jacobi elliptic functions, solitary wave solutions, Korteweg-de Vries equation

Procedia PDF Downloads 299

Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

Abstract:

In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

Procedia PDF Downloads 67

Authors: Tai-Ping Chang

Abstract:

In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

Procedia PDF Downloads 289

Authors: P. Srinivas, P. V. N. Prasad

Abstract:

Since torque ripple is the main cause of noise and vibrations, the performance of Switched Reluctance Motor (SRM) can be improved by minimizing its torque ripple using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands. The DTC of SRM is analysed by two methods. In one of the methods, the actual torque is computed by conducting Finite Element Analysis (FEA) on the design specifications of the motor. In the other method, the torque is computed by Simplified Torque Equation. The variation of peak current, average current, torque ripple and speed settling time with Simplified Torque Equation model is compared with FEA based model.

Keywords: direct toque control, simplified torque equation, finite element analysis, torque ripple

Procedia PDF Downloads 452

Authors: Abdel-Maksoud Abdel-Kader Soliman

Abstract:

The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

Procedia PDF Downloads 460

Authors: Elisha Kyirem

Abstract:

Undoubtedly, climate change is a major global challenge that could threaten the very foundation upon which life on earth is anchored, with its impacts on human mobility attracting the attention of policy makers and researchers. There is an increasing body of literature and case studies suggesting that migration could be a way through which the vulnerable move away from areas exposed to climate extreme events to improve their lives and that of their families. This presents migration as a way through which people voluntarily move to seek opportunities that could help reduce their exposure and avoid danger from climate events. Thus, migration is seen as a proactive adaptation strategy aimed at building resilience and improving livelihoods to enable people to adapt to future changing events. However, there has not been any mathematical equation linking migration and climate change adaptation. Drawing from literature in development studies, this paper develops an equation that seeks to link the relationship between migration and climate change adaptation. The mathematical equation establishes the linkages between migration, resilience, poverty reduction and vulnerability, and these the paper maintains, are the key variables for conceptualizing the migration-climate change adaptation nexus. The paper then tests the validity of the equation using the sustainable livelihood framework and publicly available data on migration and tourism in Ghana.

Keywords: migration, adaptation, climate change, adaptation, poverty reduction

Procedia PDF Downloads 352

Authors: Satyanarayana Engu, Ahmed Mohd, V. Murugan

Abstract:

We study the large time asymptotics of solutions to the Cauchy problem for a forced Burgers equation (FBE) with the initial data, which is continuous and summable on R. For which, we first derive explicit solutions of FBE assuming a different class of initial data in terms of Hermite polynomials. Later, by violating this assumption we prove the existence of a solution to the considered Cauchy problem. Finally, we give an asymptotic approximate solution and establish that the error will be of order O(t^(-1/2)) with respect to L^p -norm, where 1≤p≤∞, for large time.

Keywords: Burgers equation, Cole-Hopf transformation, Hermite polynomials, large time asymptotics

Procedia PDF Downloads 290

Authors: Saeed Ghali, Hoda El-Faramawy, Mamdouh Eissa, Michael Mishreky

Abstract:

Scale-resistant austenitic stainless steel, X45CrNiW 18-9, has been developed, and modified steels produced through partial and total nickel replacement by nitrogen. These modified steels were produced in a 10 kg induction furnace under different nitrogen pressures and were cast into ingots. The produced modified stainless steels were forged, followed by air cooling. The phases of modified stainless steels have been investigated using the Schaeffler diagram, dilatometer, and microstructure observations. Both partial and total replacement of nickel using 0.33-0.50% nitrogen are effective in producing fully austenitic stainless steels. The nitrogen contents were determined and compared with those calculated using the Institute of Metal Science (IMS) equation. The results showed great deviations between the actual nitrogen contents and predicted values through IMS equation. So, an equation has been derived based on chemical composition, pressure, and temperature at 1600oC. [N%] = 0.0078 + 0.0406*X, where X is a function of chemical composition and nitrogen pressure. The derived equation has been used to calculate the nitrogen content of different steels using published data. The results reveal the difficulty of deriving a general equation for the prediction of nitrogen content covering different steel compositions. So, it is necessary to use a narrow composition range.

Keywords: solubility, nitrogen, stainless steel, Schaeffler

Procedia PDF Downloads 201

Authors: Amit Bhunia, Mohit Kumar Singh, Maryam Al Huwayz, Mohamed Henini, Shouvik Datta

Abstract:

We report [https://arxiv.org/abs/2107.13518] experimental detection and control of Schrodinger’s Cat like macroscopically large, quantum coherent state of a two-component Bose-Einstein condensate of spatially indirect electron-hole pairs or excitons using a resonant tunneling diode of III-V Semiconductors. This provides access to millions of excitons as qubits to allow efficient, fault-tolerant quantum computation. In this work, we measure phase-coherent periodic oscillations in photo-generated capacitance as a function of an applied voltage bias and light intensity over a macroscopically large area. Periodic presence and absence of splitting of excitonic peaks in the optical spectra measured by photocapacitance point towards tunneling induced variations in capacitive coupling between the quantum well and quantum dots. Observation of negative ‘quantum capacitance’ due to a screening of charge carriers by the quantum well indicates Coulomb correlations of interacting excitons in the plane of the sample. We also establish that coherent resonant tunneling in this well-dot heterostructure restricts the available momentum space of the charge carriers within this quantum well. Consequently, the electric polarization vector of the associated indirect excitons collective orients along the direction of applied bias and these excitons undergo Bose-Einstein condensation below ~100 K. Generation of interference beats in photocapacitance oscillation even with incoherent white light further confirm the presence of stable, long-range spatial correlation among these indirect excitons. We finally demonstrate collective Rabi oscillations of these macroscopically large, ‘multipartite’, two-level, coupled and uncoupled quantum states of excitonic condensate as qubits. Therefore, our study not only brings the physics and technology of Bose-Einstein condensation within the reaches of semiconductor chips but also opens up experimental investigations of the fundamentals of quantum physics using similar techniques. Operational temperatures of such two-component excitonic BEC can be raised further with a more densely packed, ordered array of QDs and/or using materials having larger excitonic binding energies. However, fabrications of single crystals of 0D-2D heterostructures using 2D materials (e.g. transition metal di-chalcogenides, oxides, perovskites etc.) having higher excitonic binding energies are still an open challenge for semiconductor optoelectronics. As of now, these 0D-2D heterostructures can already be scaled up for mass production of miniaturized, portable quantum optoelectronic devices using the existing III-V and/or Nitride based semiconductor fabrication technologies.

Keywords: exciton, Bose-Einstein condensation, quantum computation, heterostructures, semiconductor Physics, quantum fluids, Schrodinger's Cat

Procedia PDF Downloads 154

Authors: Azad A. Mohammed, Dunyazad K. Assi, Alan S. Abdulrahman

Abstract:

Current ACI 318 Code provides two limits for minimum steel ratio for concrete beams. When concrete compressive strength be larger than 31 MPa the limit of √(fc')/4fy usually governs. In this paper shortcomings related to using this limit was fairly discussed and showed that the limit is based on 90% safety factor and was derived based on modulus of rupture equation suitable for concretes of compressive strength lower than 31 MPa. Accordingly, the limit is nor suitable and critical for concretes of higher compressive strength. An alternative equation was proposed for minimum steel ratio of rectangular beams and was found that the proposed limit is accurate for beams of wide range of concrete compressive strength. Shortcomings of the current ACI 318 Code equation and accuracy of the proposed equation were supported by test data obtained from testing six reinforced concrete beams.

Keywords: concrete beam, compressive strength, minimum steel ratio, modulus of rupture

Procedia PDF Downloads 512

Authors: Guesh Simretab Gebremedhin, Saumya Rajan Jena

Abstract:

In this work, a septic B-spline scheme has been used to simplify the process of solving an approximate solution of the generalized Rosenau-regularized long-wave equation (GR-RLWE) with initial boundary conditions. The resulting system of first-order ODEs has dealt with Butcher’s fifth order Runge-Kutta (BFRK) approach without using finite difference techniques for discretizing the time-dependent variables at each time level. Here, no transformation or any kind of linearization technique is employed to tackle the nonlinearity of the equation. Two test problems have been selected for numerical justifications and comparisons with other researchers on the basis of efficiency, accuracy, and results of the two invariants Mᵢ (mass) and Eᵢ (energy) of some motion that has been used to test the conservative properties of the proposed scheme.

Keywords: septic B-spline scheme, Butcher's fifth order Runge-Kutta approach, error norms, generalized Rosenau-RLW equation

Procedia PDF Downloads 27

Authors: Jian-Ping Yu, Wen-Xiu Ma, Yong-Li Sun, Chaudry Masood Khalique

Abstract:

In this paper, a 2d Toda equation is studied, which is a classical integrable system and plays a vital role in mathematics, physics and other areas. New lump-type solution is constructed by using the Hirota bilinear method. One interesting feature of this research is that this lump-type solutions possesses two types of multiple-lump-type waves, which are one- and two-lump-type waves. Moreover, the corresponding 3d plots, density plots and contour plots are given to show the dynamical features of the obtained multiple-lump-type solutions.

Keywords: 2d Toda equation, Hirota bilinear method, Lump-type solution, multiple-lump-type solution

Procedia PDF Downloads 189