Numerical Simulation and Stability Analysis of Thin Flexible Micro Film for Thermotunneling Application

2012 ◽  
Author(s):  
Eniko T. Enikov ◽  
Mahdi Ganji
Keyword(s):  
Numerical Simulation ◽  
Contact Area ◽  
Numerical Solutions ◽  
Thermionic Emission ◽  
Hot Electrons ◽  
Beam Equation ◽  
Practical Implementation ◽  
Beam Model ◽  
Small Current ◽  
Thermo Electric

Combined thermionic emission and tunneling of hot electrons (thermo-tunneling) has emerged as a potential new solidstate cooling technology. Practical implementation of thermo-tunneling, however, requires the formation of a nanometer-sized gap spanning macroscopically significant surfaces. Thermo-tunneling is a term used to describe combined emission of hot electrons (thermionic emission) and tunneling of electrons through a narrow potential barrier between two surfaces (field emission). Thermo-tunneling of hot electrons across a few-nanometer gap has application to vacuum electronics, flat panel displays, and holds great potential in thermo-electric cooling and energy generation. Development of new thermo-tunneling applications requires creation of a stable nanometer gap between two surfaces. This presentation is focused on our effort to investigate the stability of the the thin flexible structure under electrostatic and lorenz forces opposing each other. In this presentation, we report the result of numerical simulation with some mathematical simplifications. The mathematical model used for the numerical simulation is well studied in the literature. Using forth-order partial differential beam equation, we studied the steady state solutions of the thermo-tunneling beam model using Galerkin method. Essential output parameters of the model include a central contact area measured by its length (delta) and the thermo-tunneling current. Both parameters are determined as a function of the externally applied external potential and magnetic field. Numerical solutions of the model show two possible operating modes: (1) symmetric deformation with negligibly small current; and (2) asymmetric mode where the B-field controls the current and contact area. Under practical values for the externally applied magnetic and electric fields, it has been shown that the second mode is only possible for electrode with very low work functions, e.g. below 0.5 eV. Therefore, novel materials such as Diamond-like carbon films are likely to be essential in thermo-tunneling applications.

Flexible Electrode Structures for Thermo-Tunneling Applications

2011 ◽  
Author(s):  
Eniko T. Enikov ◽  
Carlos Gamez ◽  
Shezaan Kanjiyani ◽  
Mahdi Ganji ◽  
Joshua Gill
Keyword(s):  
Magnetic Field ◽  
Contact Area ◽  
Numerical Solutions ◽  
Flexible Structures ◽  
Tunneling Current ◽  
Hot Electrons ◽  
Practical Implementation ◽  
Small Current ◽  
Thermo Electric ◽  
Asymmetric Mode

Combined thermionic emission and tunneling of hot electrons (thermo-tunneling) has emerged as a potential new solid-state cooling technology. Practical implementation of thermo-tunneling, however, requires the formation of a nanometer-sized gap spanning macroscopically significant surfaces. Thermo-tunneling of hot electrons across a few-nanometer gap has application to vacuum electronics, flat panel displays, and holds great potential in thermo-electric cooling and energy generation. Development of new thermo-tunneling applications requires creation of a stable nanometer gap between two surfaces. This presentation is focused on our effort to investigate the feasibility of creating such gaps using distributed electro-magnetic forces arising in thin-film flexible structures. Early efforts based on rigid electrodes showed that the effective tunneling approaches 400 square-micrometers, which albeit small, could lead to useful practical systems. In this presentation, we report a theoretical and experimental investigation of a thin-electrode system which could lead to further increase on the effective tunneling area. The device under study consists of a thin membrane collector electrode (anode) suspended over the emitting electrode (cathode). The structure is placed in a vacuum enclosure with an externally generated magnetic field perpendicular to the current flow in the membrane. The resulting Lorentz force is then directed upwards, separating the two surfaces. A mathematical model of the steady-state operation of the device is presented along with predictions of the contact area and tunneling current. Essential output parameters of the model include a central contact area measured by its length (delta) and the thermo-tunneling current. Both parameters are determined as a function of the externally applied external potential and magnetic field. Numerical solutions of the model show two possible operating modes: (1) symmetric deformation with negligibly small current; and (2) asymmetric mode where the B-field controls the current and contact area.

Preliminary results of numerical simulation of submarine landslide-generated waves

2021 ◽  
Author(s):  
Ramtin Sabeti ◽  
Mohammad Heidarzadeh
Keyword(s):  
Numerical Simulation ◽  
Numerical Modelling ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Source Region ◽  
Three Dimensional ◽  
Terminal Velocity ◽  
Sensitivity Analyses ◽  
Physical Experiments ◽  
Set Up

<p>Landslide-generated waves have been major threats to coastal areas and have led to destruction and casualties. Their importance is undisputed, most recently demonstrated by the 2018 Anak Krakatau tsunami, causing several hundred fatalities. The accurate prediction of the maximum initial amplitude of landslide waves (<em>η<sub>max</sub></em>) around the source region is a vital hazard indicator for coastal impact assessment. Laboratory experiments, analytical solutions and numerical modelling are three major methods to investigate the (<em>η<sub>max</sub></em>). However, the numerical modelling approach provides a more flexible and cost- and time-efficient tool. This research presents a numerical simulation of tsunamis due to rigid landslides with consideration of submerged conditions. In particular, this simulation focuses on studying the effect of landslide parameters on <em>η<sub>max</sub>.</em> Results of simulations are compared with our conducted physical experiments at the Brunel University London (UK) to validate the numerical model.</p><p>We employ the fully three-dimensional computational fluid dynamics package, FLOW-3D Hydro for modelling the landslide-generated waves. This software benefit from the Volume of Fluid Method (VOF) as the numerical technique for tracking and locating the free surface. The geometry of the simulation is set up according to the wave tank of physical experiments (i.e. 0.26 m wide, 0.50 m deep and 4.0 m). In order to calibrate the simulation model based on the laboratory measurements, the friction coefficient between solid block and incline is changed to 0.41; likewise, the terminal velocity of the landslide is set to 0.87 m/s. Good agreement between the numerical solutions and the experimental results is found. Sensitivity analyses of landslide parameters (e.g. slide volume, water depth, etc.) on <em>η<sub>max </sub></em>are performed. Dimensionless parameters are employed to study the sensitivity of the initial landslide waves to various landslide parameters.</p>

A Universal Predictor-corrector Algorithm for Numerical Simulation of Generalized Fractional Differential Equations

2021 ◽  
Author(s):  
Zaid Odibat
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Differential Operators ◽  
Numerical Solutions ◽  
Fractional Operators ◽  
Initial Value ◽  
Generalized Fractional Integral ◽  
Fractional Differential ◽  
Predictor Corrector

Abstract This study introduces some remarks on generalized fractional integral and differential operators, that generalize some familiar fractional integral and derivative operators, with respect to a given function. We briefly explain how to formulate representations of generalized fractional operators. Then, mainly, we propose a predictor-corrector algorithm for the numerical simulation of initial value problems involving generalized Caputo-type fractional derivatives with respect to another function. Numerical solutions of some generalized Caputo-type fractional derivative models have been introduced to demonstrate the applicability and efficiency of the presented algorithm. The proposed algorithm is expected to be widely used and utilized in the field of simulating fractional-order models.

Numerical Simulation of Digital Microfluidics Based on Electro-Dynamic Model

2012 ◽  
Vol 2 (3) ◽  
pp. 14-23
Author(s):  
Liguo Chen ◽  
Mingxiang Ling ◽  
Deli Liu
Keyword(s):  
Numerical Simulation ◽  
Simulation Model ◽  
Contact Line ◽  
Contact Area ◽  
Digital Microfluidics ◽  
Phase Contact ◽  
Electrowetting On Dielectric ◽  
Three Phase ◽  
Internal Mechanism ◽  
Contact Domain

Aiming at the doubt and divarication about the internal mechanism of electrowetting on dielectric (EWOD) in digital microfluidics, the authors attempted to explain the internal mechanism of EWOD through electro-dynamic-based numerical simulation model. First, the boundary conditions for the governing equation were found. Then the influence of mesh number on simulation results was analyzed and feasibility of the simulation model was verified by comparing numerical results with theoretical ratiocination. Finally, they compared the electro-dynamic actuation force acting on the surface of droplet on three digital microfluidic structures, which have the same three-phase contact line but different area of contact domain. Analytical results showed that electro-dynamic force generated solely by the accumulation of induced charges in contact domain was three times larger than that generated by three-phase contact line. Induced charges accumulated on both three-phase contact line and contact area of droplet gave the contribution to EWOD, but contact area played a major role in the change of contact angle of droplet.

scholarly journals Numerical Simulation of the Fractal-Fractional Ebola Virus

2020 ◽  
Vol 4 (4) ◽  
pp. 49 ◽  
Author(s):  
H. M. Srivastava ◽  
Khaled M. Saad
Keyword(s):  
Numerical Simulation ◽  
Ebola Virus ◽  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Polynomial Functions ◽  
Fractional Differentiation ◽  
Lagrange Polynomial ◽  
New Models ◽  
Difference Methods ◽  
Two Parameters

In this work we present three new models of the fractal-fractional Ebola virus. We investigate the numerical solutions of the fractal-fractional Ebola virus in the sense of three different kernels based on the power law, the exponential decay and the generalized Mittag-Leffler function by using the concepts of the fractal differentiation and fractional differentiation. These operators have two parameters: The first parameter ρ is considered as the fractal dimension and the second parameter k is the fractional order. We evaluate the numerical solutions of the fractal-fractional Ebola virus for these operators with the theory of fractional calculus and the help of the Lagrange polynomial functions. In the case of ρ=k=1, all of the numerical solutions based on the power kernel, the exponential kernel and the generalized Mittag-Leffler kernel are found to be close to each other and, therefore, one of the kernels is compared with such numerical methods as the finite difference methods. This has led to an excellent agreement. For the effect of fractal-fractional on the behavior, we study the numerical solutions for different values of ρ and k. All calculations in this work are accomplished by using the Mathematica package.

Numerical simulation of time-fractional partial differential equations arising in fluid flows via reproducing Kernel method

2019 ◽  
Vol 30 (11) ◽  
pp. 4711-4733 ◽  
Author(s):  
Omar Abu Arqub
Keyword(s):  
Numerical Simulation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Multiphase Flows ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Kernel Method ◽  
Fractional Partial Differential Equations ◽  
Reproducing Kernel Method ◽  
Content Type

Purpose The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this paper is to present results on the numerical simulation for time-fractional partial differential equations arising in transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types. Design/methodology/approach Those resulting mathematical models are solved by using the reproducing kernel method, which provide appropriate solutions in term of infinite series formula. Convergence analysis, error estimations and error bounds under some hypotheses, which provide the theoretical basis of the proposed method are also discussed. Findings The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the prospects of the gained results and the method are discussed through academic validations. Originality/value In this paper and for the first time: the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows. The authors applied the reproducing kernel method systematically for the numerical solutions of time-fractional Tricomi and Keldysh equations subject to Robin functions types.

scholarly journals An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination

2014 ◽  
Vol 24 (3) ◽  
pp. 635-646 ◽  
Author(s):  
Deqiong Ding ◽  
Qiang Ma ◽  
Xiaohua Ding
Keyword(s):  
Numerical Simulation ◽  
Global Stability ◽  
Difference Equations ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Numerical Solutions ◽  
Time Step ◽  
The Stability ◽  
Nsfd Scheme ◽  
Nonstandard Finite Difference

Abstract In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our proof of global stability utilizes the method of Lyapunov functions. Numerical simulation illustrates the effectiveness of our results

Numerical Simulation on Fracture Formation on Surfaces of Bi-Layered Materials

2007 ◽  
Vol 353-358 ◽  
pp. 993-996
Author(s):  
Tian Hui Ma ◽  
Ju Ying Yang ◽  
Zheng Zhao Liang ◽  
Yong Bin Zhang ◽  
Tao Xu
Keyword(s):  
Numerical Simulation ◽  
Numerical Solutions ◽  
Process Analysis ◽  
Failure Process ◽  
Layered Materials ◽  
Numerical Code ◽  
Material Layer ◽  
Fracture Formation ◽  
Constant State ◽  
The Individual

Fracture formation on surfaces of bi-layered materials is studied numerically. A simplified two-layered materials model like growing tree trunk is present. This work is focused on patterns of fractures and fracture saturation. We consider the formation of crack pattern in bark as an example of pattern formation due to expansion of one material layer with respect to another. As a result of this expansion, the bark stretches until it reaches its limit of deformation and cracks. A novel numerical code, 3D Realistic Failure Process Analysis code (abbreviated as RFPA3D) is used to obtain numerical solutions. In this numerical code, the heterogeneity of materials is taken into account by assigning different properties to the individual elements according to statistical distribution function. Elastic-brittle constitutive relation with residual strength for elements and a Mohr-Coulomb criterion with a tensile cut-off are adopted so that the elements may fail either in shear or in tension. The discontinuity feature of the initiated crack is automatically induced by using degraded stiffness approach when the tensile strain of the failed elements reaching a certain value. The different patterns are obtained by varying simulation parameters, the thickness of the material layer. Numerical simulation clearly demonstrates that the stress state transition precludes further infilling of fractures and the fracture spacing reaches constant state,i.e. the socalled fracture saturation. It also indicates that RFPA code is a viable tool for modeling fracture formation and studying fracture patterns.

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