Search results for: quantum master equation

Authors: Fuziyah Ishak, Siti Norazura Ahmad

Abstract:

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Delele Worku Ayele, Bing-Joe Hwang

Abstract:

A method that does not employ hot injection techniques has been developed for the size-tunable synthesis of high-quality CdSe quantum dots (QDs) with a zinc blende structure. In this environmentally benign synthetic route, which uses relatively less toxic precursors, solvents, and capping ligands, CdSe QDs that absorb visible light are obtained. The size of the as-prepared CdSe QDs and, thus, their optical properties can be manipulated by changing the microwave reaction conditions. The QDs are characterized by XRD, TEM, UV-vis, FTIR, time-resolved fluorescence spectroscopy, and fluorescence spectrophotometry. In this approach, the reaction is conducted in open air and at a much lower temperature than in hot injection techniques. The use of microwaves in this process allows for a highly reproducible and effective synthesis protocol that is fully adaptable for mass production and can be easily employed to synthesize a variety of semiconductor QDs with the desired properties. The possible application of the as-prepared CdSe QDs has been also assessed using deposition on TiO2 films.

Keywords: average life time, CdSe QDs, microwave (MW), mass production oleic acid, Na2SeSO3

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Authors: Akanksha Singh, Mahesh Kumar, Shailesh N. Sharma

Abstract:

Semiconductor quantum dots (QDs) such as CdSe, CdS, InP, etc. have gained significant interest in the recent years due to its application in various fields such as LEDs, solar cells, lasers, biological markers, etc. The interesting feature of the QDs is their tunable band gap. The size of the QDs can be easily varied by varying the synthesis parameters which change the band gap. One of the limitations with II-VI semiconductor QDs is their biological application. The use of cadmium makes them unsuitable for biological applications. III-V QD such as InP overcomes this problem as they are structurally robust because of the covalent bonds which do not allow the ions to leak. Also, InP QDs has large Bohr radii which increase the window for the quantum confinement effect. The synthesis of InP QDs is difficult and time consuming. Authors have synthesized InP using a novel, quick synthesis method which utilizes trioctylphosphine as a source of phosphorus. In this work, authors have made InP composites with P3HT(Poly(3-hexylthiophene-2,5-diyl))polymer(organic-inorganic hybrid material) and gold nanoparticles(metal-semiconductor composites). InP-P3HT shows FRET phenomenon whereas InP-Au shows charge transfer mechanism. The synthesized InP QDs has an absorption band at 397 nm and PL peak position at 491 nm. The band gap of the InP QDs is 2.46 eV as compared to the bulk band gap of InP i.e. 1.35 eV. The average size of the QDs is around 3-4 nm. In order to protect the InP core, a shell of wide band gap material i.e. ZnS is coated on the top of InP core. InP-P3HT composites were made in order to study the charge transfer/energy transfer phenomenon between them. On adding aliquots of P3HT to InP QDs solution, the P3HT PL increases which can be attributed to the dominance of Förster energy transfer between InP QDs (donor) P3HT polymer (acceptor). There is a significant spectral overlap between the PL spectra of InP QDs and absorbance spectra of P3HT. But in the case of InP-Au nanocomposites, significant charge transfer was seen from InP QDs to Au NPs. When aliquots of Au NPs were added to InP QDs, a decrease in the PL of the InP QDs was observed. This is due to the charge transfer from the InP QDs to the Au NPs. In the case of metal semiconductor composites, the enhancement and quenching of QDs depend on the size of the QD and the distance between the QD and the metal NP. These two composites have different phenomenon between donor and acceptor and hence can be utilized for two different applications. The InP-P3HT composite can be utilized for LED devices due to enhancement in the PL emission (FRET). The InP-Au can be utilized efficiently for photovoltaic application owing to the successful charge transfer between InP-Au NPs.

Keywords: charge transfer, FRET, gold nanoparticles, InP quantum dots

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Authors: A. Banerjee, C. Grazon, B. Nadal, T. Pons, Y. Krishnan, B. Dubertret

Abstract:

Quantum Dots (QDs) have emerged as novel fluorescent probes for biomedical applications. The photophysical properties of QDs such as broad absorption, narrow emission spectrum, reduced blinking, and enhanced photostability make them advantageous over organic fluorophores. However, for some biological applications, QDs need to be first targeted to specific intracellular locations. It parallel, base pairing properties and biocompatibility of DNA has been extensively used for biosensing, targetting and intracellular delivery of numerous bioactive agents. The combination of the photophysical properties of QDs and targettability of DNA has yielded fluorescent, stable and targetable nanosensors. QD-DNA conjugates have used in drug delivery, siRNA, intracellular pH sensing and several other applications; and continue to be an active area of research. In this project, a novel method to synthesise QD-DNA conjugates and their applications in bioimaging are investigated. QDs are first solubilized in water using a thiol based amphiphilic co-polymer and, then conjugated to amine functionalized DNA using a heterobifunctional linker. The conjugates are purified by size exclusion chromatography and characterized by UV-Vis absorption and fluorescence spectroscopy, electrophoresis and microscopy. Parameters that influence the conjugation yield such as reducing agents, the excess of salt and pH have been investigated in detail. In optimized reaction conditions, up to 12 single-stranded DNA (15 mer length) can be conjugated per QD. After conjugation, the QDs retain their colloidal stability and high quantum yield; and the DNA is available for hybridization. The reaction has also been successfully tested on QDs emitting different colors and on Gold nanoparticles and therefore highly generalizable. After extensive characterization and robust synthesis of QD-DNA conjugates in vitro, the physical properties of these conjugates in cellular milieu are being invistigated. Modification of QD surface with DNA appears to remarkably alter the fate of QD inside cells and can have potential implications in therapeutic applications.

Keywords: bioimaging, cellular targeting, drug delivery, photostability

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Authors: Siu-Siu Guo, Qingxuan Shi

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In this paper, single-degree-of-freedom (SDOF) systems to white noise and colored noise excitations are investigated. By expressing colored noise excitation as a second-order filtered white noise process and introducing colored noise as an additional state variable, the equation of motion for SDOF system under colored noise is then transferred artificially to multi-degree-of-freedom (MDOF) system under white noise excitations. As a consequence, corresponding Fokker-Planck-Kolmogorov (FPK) equation governing the joint probabilistic density function (PDF) of state variables increases to 4-dimension (4-D). Solution procedure and computer programme become much more sophisticated. The exponential-polynomial closure (EPC) method, widely applied for cases of SDOF systems under white noise excitations, is developed and improved for cases of systems under colored noise excitations and for solving the complex 4-D FPK equation. On the other hand, Monte Carlo simulation (MCS) method is performed to test the approximate EPC solutions. Two examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Corresponding band-limited power spectral densities (PSDs) for colored noise excitations are separately given. Numerical studies show that the developed EPC method provides relatively accurate estimates of the stationary probabilistic solutions. Moreover, statistical parameter of mean-up crossing rate (MCR) is taken into account, which is important for reliability and failure analysis.

Keywords: filtered noise, narrow-banded noise, nonlinear dynamic, random vibration

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Authors: Merouane Salhi, Mohamed Roudane, Abdelkader Kirad

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In this work, we present a new form of characteristics method, which is a technique for solving partial differential equations. Typically, it applies to first-order equations; the aim of this method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data. This latter developed under the real gas theory, because when the thermal and the caloric imperfections of a gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with the gas parameters. The gas doesn’t stay perfect. Its state equation change and it becomes for a real gas. The presented equations of the characteristics remain valid whatever area or field of study. Here we need have inserted the developed Prandtl Meyer function in the mathematical system to find a new model when the effect of stagnation pressure is taken into account. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation, the thermodynamic parameters and the value of Prandtl Meyer function. However, with the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analyzing the supersonic flow for thermally and calorically imperfect gas. The supersonic parameters depend directly on the stagnation parameters of the combustion chamber. The resolution has been made by the finite differences method using the corrector predictor algorithm. As results, the developed mathematical model used to design 2D minimum length nozzles under effect of the stagnation parameters of fluid flow. A comparison for air with the perfect gas PG and high temperature models on the one hand and our results by the real gas theory on the other of nozzles shapes and characteristics are made.

Keywords: numerical methods, nozzles design, real gas, stagnation parameters, supersonic expansion, the characteristics method

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Keltoum Bouherine, Olivier Leroy

Abstract:

The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.

Keywords: electron density, electric field, microwave plasma reactor, gas velocity, non-equilibrium plasma

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

Abstract:

This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Afiqah Shafify Amran, Siti Aisyah Shamsudin, Nurul Yuziana Mohd Yusof

Abstract:

Cadmium Sulphide (CdS) from group II-IV quantum dots with good optical properties was successfully synthesized by using the simple colloidal method. Capping them with ligand Polyethylinamine (PEI) alters the surface defect of CdS while, thioglycolic acid (TGA) was added to the reaction as a stabilizer. Due to their cytotoxicity, we decided to conjugate them with the protein cage nanoparticles. In this research, we used capsid of Cowpea Chlorotic Mottle Virus (CCMV) to package the CdS because they have the potential to serve in drug delivery, cell targeting and imaging. Adding Sodium Hydroxide (NaOH) changes the pH of the systems hence the isoelectric charge is adjusted. We have characterized and studied the morphology and the optical properties of CdS and CdS-CCMV by transmitted electron microscopic (TEM), UV-Vis spectroscopy, photoluminescence spectroscopy, UV lamp and Fourier transform infrared spectroscopy (FTIR), respectively. The results obtained suggest that the protein cage nanoparticles do not affect the optical properties of CdS.

Keywords: cadmium sulphide, cowpea chlorotic mottle virus, protein cage nanoparticles, quantum dots

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Authors: Sylwia Krawiec, Joanna Cabaj, Karol Malecha

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Nowadays, progress in the field of the analytical methods is of great interest for reliable biological research and medical diagnostics. Classical techniques of chemical analysis, despite many advantages, do not permit to obtain immediate results or automatization of measurements. Chemical sensors have displaced the conventional analytical methods - sensors combine precision, sensitivity, fast response and the possibility of continuous-monitoring. Biosensor is a chemical sensor, which except of conventer also possess a biologically active material, which is the basis for the detection of specific chemicals in the sample. Each biosensor device mainly consists of two elements: a sensitive element, where is recognition of receptor-analyte, and a transducer element which receives the signal and converts it into a measurable signal. Through these two elements biosensors can be divided in two categories: due to the recognition element (e.g immunosensor) and due to the transducer (e.g optical sensor). Working of optical sensor is based on measurements of quantitative changes of parameters characterizing light radiation. The most often analyzed parameters include: amplitude (intensity), frequency or polarization. Changes in the optical properties one of the compound which reacts with biological material coated on the sensor is analyzed by a direct method, in an indirect method indicators are used, which changes the optical properties due to the transformation of the testing species. The most commonly used dyes in this method are: small molecules with an aromatic ring, like rhodamine, fluorescent proteins, for example green fluorescent protein (GFP), or nanoparticles such as quantum dots (QDs). Quantum dots have, in comparison with organic dyes, much better photoluminescent properties, better bioavailability and chemical inertness. These are semiconductor nanocrystals size of 2-10 nm. This very limited number of atoms and the ‘nano’-size gives QDs these highly fluorescent properties. Rapid and sensitive detection of dopamine is extremely important in modern medicine. Dopamine is very important neurotransmitter, which mainly occurs in the brain and central nervous system of mammals. Dopamine is responsible for the transmission information of moving through the nervous system and plays an important role in processes of learning or memory. Detection of dopamine is significant for diseases associated with the central nervous system such as Parkinson or schizophrenia. In developed optical biosensor for detection of dopamine, are used graphene quantum dots (GQDs). In such sensor dopamine molecules coats the GQD surface - in result occurs quenching of fluorescence due to Resonance Energy Transfer (FRET). Changes in fluorescence correspond to specific concentrations of the neurotransmitter in tested sample, so it is possible to accurately determine the concentration of dopamine in the sample.

Keywords: biosensor, dopamine, fluorescence, quantum dots

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

Abstract:

In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma

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Authors: Justin Zhengjie Tan, Yang Zhao

Abstract:

Adiabatic Rapid Passage, a popular method of achieving population inversion, is studied in a Rabi dimer model in the presence of noise which acts as a dissipative environment. The integration of the multi-Davydov D2 Ansatz into the time-dependent variational framework enables us to model the intricate quantum system accurately. By influencing the system with a driving field strength resonant with the energy spacing, the probability of adiabatic rapid passage, which is modelled after the Landau Zener model, can be derived along with several other observables, such as the photon population. The effects of a dissipative environment can be reproduced by coupling the system to a common phonon mode. By manipulating the strength and frequency of the driving field, along with the coupling strength of the phonon mode to the qubits, we are able to control the qubits and photon dynamics and subsequently increase the probability of Adiabatic Rapid Passage happening.

Keywords: quantum electrodynamics, adiabatic rapid passage, Landau-Zener transitions, dissipative environment

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Authors: Delele Worku Ayele, Bing-Joe Hwang

Abstract:

A method that does not employ hot injection techniques has been developed for the size-tunable synthesis of high-quality CdSe quantum dots (QDs) with a zinc blende structure. In this environmentally benign synthetic route, which uses relatively less toxic precursors, solvents, and capping ligands, CdSe QDs that absorb visible light are obtained. The size of the as-prepared CdSe QDs and, thus, their optical properties can be manipulated by changing the microwave reaction conditions. The QDs are characterized by XRD, TEM, UV-vis, FTIR, time-resolved fluorescence spectroscopy, and fluorescence spectrophotometry. In this approach, the reaction is conducted in open air and at a much lower temperature than in hot injection techniques. The use of microwaves in this process allows for a highly reproducible and effective synthesis protocol that is fully adaptable for mass production and can be easily employed to synthesize a variety of semiconductor QDs with the desired properties. The possible application of the as-prepared CdSe QDs has been also assessed using deposition on TiO2 films.

Keywords: CdSe QDs, Na2SeSO3, microwave (MW), oleic acid, mass production, average life time

Procedia PDF Downloads 709

Authors: Nana Adjoah Mbroh, Suares Clovis Oukouomi Noutchie

Abstract:

Singularly perturbed problems are parameter dependent problems, and they play major roles in the modelling of real-life situational problems in applied sciences. Thus, designing efficient numerical schemes to solve these problems is of much interest since the exact solutions of such problems may not even exist. Generally, singularly perturbed problems are identified by a small parameter multiplying at least the highest derivative in the equation. The presence of this parameter causes the solution of these problems to be characterized by rapid oscillations. This unique feature renders classical numerical schemes inefficient since they are unable to capture the behaviour of the exact solution in the part of the domain where the rapid oscillations are present. In this paper, a numerical scheme is proposed to solve a singularly perturbed Volterra Integro-differential equation. The scheme is based on the midpoint rule and employs the non-standard finite difference scheme to solve the differential part whilst the composite trapezoidal rule is used for the integral part. A fully fledged error estimate is performed, and Richardson extrapolation is applied to accelerate the convergence of the scheme. Numerical simulations are conducted to confirm the theoretical findings before and after extrapolation.

Keywords: midpoint rule, non-standard finite difference schemes, Richardson extrapolation, singularly perturbed problems, trapezoidal rule, uniform convergence

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Authors: Divij Gupta

Abstract:

Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: Irna Malganova

Abstract:

The paper assessed the effectiveness of the use of urban functional zoning using the method of M.A. Kramer by the example of Kazan city (Republic of Tatarstan, Russian Federation) using geoinformation technologies. On the basis of the data obtained, the calculations were carried out to obtain data on population density, overcoming geographic determinism, as well as the effectiveness of the formation of urban frameworks. The authors proposed recommendations for the effectiveness of municipal frameworks in the period from 2018 to 2021: economic, social, environmental and social. The study of effective territorial planning in a given period allows to display of the dynamics of planning changes, as well as assessment of changes in the formation of urban frameworks. Based on the incoming data obtained from the master plan of the municipal formation of Kazan, in the period from 2018 to 2021, there was an increase in population by 13841 people or 1.1% of the values of 2018. In addition, the area of Kazan increased by 2419.6 hectares. In the structure of the distribution of areas of functional zones, there was an increase in such zones of the municipality as zones of residential and public purpose. Changes in functional zoning, as well as territories requiring reorganization, are presented using geoinformation technologies in open-source software Quantum Geographic Information System (QGIS 3.32). According to the calculations based on the method of functional zoning efficiency by M.A. Kreimer, the territorial-planning structure of Kazan City is quite effective. However, in the development of spatial planning concepts, it is possible to emphasize the weakened interest of the population in the development of territorial planning documents. Thus, the approach to spatial planning of Kazan differs from foreign methods and approaches based on the joint development of planning directions and development of territories of municipalities between the developers of the planning structure, business representatives and the population. The population plays the role of the target audience on which territorial planning is oriented. It follows that there is a need to satisfy the opinions and demands of the population.

Keywords: spatial development, metamorphosis, Kazan city, spatial planning, efficiency, geographic determinism., GIS, QGIS

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Authors: H. Naderpour, R. C. Barros, S. M. Khatami

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Seismic excitation is naturally caused large horizontal relative displacements, which is able to provide collisions between two adjacent buildings due to insufficient separation distance and severe damages are occurred due to impact especially in tall buildings. In this paper, an impact is numerically simulated and two needed parameters are calculated, including impact force and energy absorption. In order to calculate mentioned parameters, mathematical study needs to model an unreal link element, which is logically assumed to be spring and dashpot to determine lateral displacement and damping ratio of impact. For the determination of dynamic response of impact, a new equation of motion is theoretically suggested to evaluate impact force and energy dissipation. In order to confirm the rendered equation, a series of parametric study are performed and the accuracy of formula is confirmed.

Keywords: pounding, impact, dissipated energy, coefficient of restitution

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

Abstract:

As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

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Authors: Wedad Albalawi

Abstract:

The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of hardy, inequality of coposon, steklov operator

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Clarinda Vitorino Nhangumbe, Fredericks Ebrahim, Betuel Canhanga

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The price of an option weather derivatives can be approximated as a solution of the two-dimensional convection-diffusion dominant partial differential equation derived from the Ornstein-Uhlenbeck process, where one variable represents the weather dynamics and the other variable represent the underlying weather index. With appropriate financial boundary conditions, the solution of the pricing equation is approximated using a nonstandard finite difference method. It is shown that the proposed numerical scheme preserves positivity as well as stability and consistency. In order to illustrate the accuracy of the method, the numerical results are compared with other methods. The model is tested for real weather data.

Keywords: nonstandard finite differences, Ornstein-Uhlenbeck process, partial differential equations approach, weather derivatives

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Authors: Punit Kumar, Niraj Kumar

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The influence of transverse surface roughness on EHL characteristics has been investigated numerically using an extensive set of full EHL line contact simulations for shear-thinning lubricants under pure sliding condition. The shear-thinning behavior of lubricant is modeled using Carreau viscosity equation along with Doolittle-Tait equation for lubricant compressibility. The surface roughness is assumed to be sinusoidal and it is present on the stationary surface. It is found that surface roughness causes sharp pressure peaks along with reduction in central and minimum film thickness. With increasing amplitude of surface roughness, the minimum film thickness decreases much more rapidly as compared to the central film thickness.

Keywords: EHL, Carreau, shear-thinning, surface roughness, amplitude, wavelength

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Authors: S. P. Raut, S. K. Soni, A. W. Kolhatkar

Abstract:

Denim is widely used by every age of people all over the world. As the use of denim is increasing progressively, till now the handle properties of denim fabric not reported at significant level. In the present study, five commercial denim fabric samples were used. Denim samples, weighing from 8.5oz/sq yds to 14.5 oz/sq yds, were processed as per standard commercial procedure for denim finishing. These finished denim samples were tested on Kawabata Evaluation System(KES) for low stress mechanical properties. The results of KES values are used for calculation of Total Hand value(THV) using equation for summer suit. The obtained result for THV using equation for summer suit for denim samples is in the range from 1.62 to 3.30. These values of low stress mechanical properties values given by KES, can be used to engineer the denim fabric for bottom wear.

Keywords: denim, handle value, Kawabata evaluation system, objective evaluation

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Authors: Arunroong Wongkungwan

Abstract:

This study aimed to investigate the influence of selected antecedents, which were tourists’ satisfaction towards attractions in Bangkok, perceived value of the attractions, feelings of engagement with the attractions, acquaintance with the attractions, push factors, pull factors and motivation to seek novelty, on foreign tourist’s loyalty towards tourist attractions in Bangkok. By using multi stage sampling technique, 400 international tourists were sampled. After that, Semi Structural Equation Model was utilized in the analysis stage by LISREL. The Semi Structural Equation Model of the selected antecedents of tourist’s loyalty attractions had a correlation with the empirical data through the following statistical descriptions: Chi- square = 3.43, df = 4, P- value = 0.48893; RMSEA = 0.000; CFI = 1.00; CN = 1539.75; RMR = 0.0022; GFI = 1.00 and AGFI = 0.98. The findings indicated that all antecedents were able together to predict the loyalty of the foreign tourists who visited Bangkok at 73 percent.

Keywords: antecedent, Bangkok, foreign tourists, loyalty, tourist attractions

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Authors: Stephen Kirkup

Abstract:

This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: boundary element method, Laplace’s equation, vector calculus, simulation, education

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Authors: L. A. Ostrovsky, Yu. A. Stepanyants

Abstract:

Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described.

Keywords: Earth rotation, internal waves, nonlinear waves, solitons

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Authors: E. L. Albuquerque, U. L. Fulco, G. S. Ourique

Abstract:

The focus of this work is on the numerical investigation of the charge transport properties of the de novo-designed alpha3 polypeptide, as well as in its variants, all of them probed by gene engineering. The theoretical framework makes use of a tight-binding model Hamiltonian, together with ab-initio calculations within quantum chemistry simulation. The alpha3 polypeptide is a 21-residue with three repeats of the seven-residue amino acid sequence Leu-Glu-Thr-Leu-Ala-Lys-Ala, forming an alpha–helical bundle structure. Its variants are obtained by Ala→Gln substitution at the e (5th) and g (7th) position, respectively, of the alpha3 polypeptide amino acid sequence. Using transmission electron microscopy and atomic force microscopy, it was observed that the alpha3 polypeptide and one of its variant do have the ability to form fibrous assemblies, while the other does not. Our main aim is to investigate whether or not the biased alpha3 polypeptide and its variants can be also identified by quantum charge transport measurements through current-voltage (IxV) curves as a pattern to characterize their fibrous assemblies. It was observed that each peptide has a characteristic current pattern, which may be distinguished by charge transport measurements, suggesting that it might be a useful tool for the development of biosensors.

Keywords: charge transport properties, electronic transmittance, current-voltage characteristics, biological sensor

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Authors: Dara Singh, Keikhosrow Firouzbakhsh, Mohammad Taghi Ahmadian

Abstract:

In this paper, conventional laser Keratoplasty surgeries in the human eye are studied. For this purpose, a validated 3D finite volume model of the human eye is introduced. In this model the fluid flow has also been considered. The discretized domain of the human eye incorporates a bio-heat transfer equation coupled with a Boussinesq equation. Both continuous and pulsed lasers have been modeled and the results are compared. Moreover, two different conventional surgical positions that are upright and recumbent are compared for these laser therapies. The simulation results show that in these conventional surgeries, the temperature rises above the critical values at the laser insertion areas. However, due to the short duration and the localized nature, the potential damages are restricted to very small regions and can be ignored. The conclusion is that the present day lasers are acceptably safe to the human eye.

Keywords: eye, heat-transfer, keratoplasty laser, surgery

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Authors: Innocent O. Arukalam, Emeka E. Oguzie

Abstract:

Interest in the development of eco-friendly anti-corrosion coatings using bio-based renewable materials is gaining momentum recently. To this effect, chitin biopolymer, which is non-toxic, biodegradable, and inherently possesses anti-microbial property, was successfully synthesized from snail shells and used as a filler in the preparation of epoxy coating. The chitin particles were characterized with contact angle goniometer, scanning electron microscope (SEM), Fourier transform infrared (FTIR) spectrophotometer, and X-ray diffractometer (XRD). The performance of the coatings was evaluated by immersion and electrochemical impedance spectroscopy (EIS) tests. Electronic structure properties of the coating ingredients and molecular level interaction of the corrodent and coated Q235 steel were appraised by quantum chemical computations (QCC) and molecular dynamics (MD) simulation techniques, respectively. The water contact angle (WCA) measurement of chitin particles was found to be 129.3o while that of chitin particles modified with amino trimethoxy silane (ATMS) was 149.6o, suggesting it is highly hydrophobic. Immersion and EIS analyses revealed that epoxy coating containing silane-modified chitin exhibited lowest water absorption and highest barrier as well as anti-corrosion performances. The QCC showed that quantum parameters for the coating containing silane-modified chitin are optimum and therefore corresponds to high corrosion protection. The high negative value of adsorption energies (Eads) for the coating containing silane-modified chitin indicates the coating molecules interacted and adsorbed strongly on the steel surface. The observed results have shown that silane-modified epoxy-chitin coating would perform satisfactorily for surface protection of metal structures in saline environment.

Keywords: chitin, EIS, epoxy coating, hydrophobic, molecular dynamics simulation, quantum chemical computation

Procedia PDF Downloads 99