scholarly journals Residual conductance of correlated one-dimensional nanosystems: A numerical approach

2004 ◽  
Vol 39 (1) ◽  
pp. 107-120 ◽  
Author(s):  
R. A. Molina ◽  
P. Schmitteckert ◽  
D. Weinmann ◽  
R. A. Jalabert ◽  
G.-L. Ingold ◽  
...  
Keyword(s):  
Numerical Approach ◽  
One Dimensional ◽  
Residual Conductance

scholarly journals A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 453 ◽  
Author(s):  
Mukhtar ◽  
Sohaib ◽  
Ahmad
Keyword(s):  
Numerical Approximation ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Moment Generating Function ◽  
Numerical Approach ◽  
Test Problems ◽  
Batch Crystallization ◽  
One Dimensional ◽  
Engineering Sciences ◽  
The Moment

In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the efficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.

Electron Transmission Through Modified Schottky Barriers

2001 ◽  
Vol 685 ◽  
Author(s):  
Kevin L. Jensen
Keyword(s):  
Schottky Barrier ◽  
Conduction Band ◽  
Current Density ◽  
Transport Mechanism ◽  
Airy Function ◽  
Numerical Approach ◽  
Schottky Barriers ◽  
Present Treatment ◽  
One Dimensional ◽  
Electron Transmission

AbstractThe effects of a Coulomb-like potential in the Schottky barrier existing between a material-diamond interface is analyzed. The inclusion is intended to mimic the effects of an ionized trap within the barrier, and therefore to account for charge injection into the conduction band of diamond via a Poole-Frenkel transport mechanism. The present treatment is to provide a qualitative account of the increase in current density near the inclusion, which can be substantial. The model is first reduced to an analytically tractable one-dimensional tunneling problem addressable by an Airy Function approach in order to investigate the nature of the effect. A more comprehensive numerical approach is then applied. Finally, statistical arguments are used to estimate emission site densities using the results of the aforementioned analysis.

Investigations on the Rotordynamic Coefficients of Pocket Damper Seals Using the Multifrequency, One-Dimensional, Whirling Orbit Model and RANS Solutions

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Jun Li ◽  
Zhigang Li ◽  
Zhenping Feng
Keyword(s):  
Numerical Approach ◽  
Single Frequency ◽  
Response Force ◽  
Vibration Frequencies ◽  
Deformation Method ◽  
One Dimensional ◽  
Rotordynamic Coefficients ◽  
Motion Signal ◽  
Multiple Frequencies ◽  
Orbit Model

The numerical approach using the multifrequency one-dimensional whirling orbit model and Reynolds-averaged Navier-Stokes (RANS) solution was proposed for prediction of rotordynamic coefficients of pocket damper seal (PDS). By conducting the multiple frequencies one-dimensional whirling orbit for rotor center as the excitation signal, the unsteady RANS solutions combined with mesh deformation method were utilized to calculate the transient response forces on the PDS rotor surface. Unlike the single frequency whirling orbit models which require a separate computation for each frequency, the multifrequency whirling orbit model yields results for multiple frequencies and therefore requires only one computation for different frequencies. The rotor motion signal and response force signal were transformed to the frequency domain using the fast fourier transform, then the eight rotordynamic coefficients of the PDS were determined at fourteen different vibration frequencies 20–300 Hz. The numerical results of rotordynamic coefficients of the PDS were in good agreement with experimental data. The accuracy and availability of the proposed method was demonstrated. The effects of vibration frequencies and pressure ratios on the rotordynamic coefficients of PDS were also investigated using the presented numerical method. The multifrequency one-dimensional whirling orbit model is a promising method for prediction of the rotordynamic coefficients of the PDS.

Two-Dimensional Numerical Modelling of Hydrogen Diffusion in Metals Assisted by Both Stress and Strain

2010 ◽  
Vol 138 ◽  
pp. 117-126 ◽  
Author(s):  
Jesús Toribio ◽  
Viktor Kharin ◽  
Diego Vergara ◽  
Miguel Lorenzo
Keyword(s):  
Concentration Distribution ◽  
Hydrogen Diffusion ◽  
Numerical Approach ◽  
Stress And Strain ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Weighted Residual Method ◽  
One Dimensional ◽  
Triangular Elements ◽  
The One

The present work is based on previous research on the one-dimensional (1D) analysis of the hydrogen diffusion process, and proposes a numerical approach of the same phenomenon in two-dimensional (2D) situations, e.g. notches. The weighted residual method was used to solve numerically the differential equations set out when the geometry was discretized through the application of the finite element method. Three-node triangular elements were used in the discretization, due to its simplicity, and a numerical algorithm was numerically implemented to obtain the hydrogen concentration distribution in the material at different time increments. The model is a powerful tool to analyze hydrogen embrittlement phenomena in structural materials.

Ad- and Desorption of Oxygen at Metal-Oxide Interfaces: Numerical Approach for Concentration-Dependent Diffusion Coefficient

2006 ◽  
Vol 258-260 ◽  
pp. 360-365
Author(s):  
M. Stasiek ◽  
Andreas Öchsner
Keyword(s):  
Diffusion Coefficients ◽  
Atomic Oxygen ◽  
Coupled System ◽  
Numerical Approach ◽  
Time Dependent ◽  
General Boundary Conditions ◽  
Oxide Interfaces ◽  
One Dimensional ◽  
Concentration Dependency ◽  
Constant Coefficients

A numerical approach for the segregation of atomic oxygen at Ag/MgO interfaces is presented. A general segregation kinetics is considered and the coupled system of differ- ential equations is solved due to a one-dimensional finite difference scheme which accounts for concentration-dependent diffusion coefficients. Based on a model oxide distribution, the influence of the concentration-dependency is numerically investigated and compared with the solution for constant coefficients. In addition, the numerical approach allows for the consider- ation of general boundary conditions, specimen sizes and time-dependent material and process parameters.

scholarly journals Existence, uniqueness and numerical solution of a fractional PDE with integral conditions

2019 ◽  
Vol 24 (3) ◽  
pp. 368-386
Author(s):  
Jesus Martín-Vaquero ◽  
Ahcene Merad
Keyword(s):  
Existence And Uniqueness ◽  
Recent Literature ◽  
Numerical Approach ◽  
Integral Conditions ◽  
Fractional Partial Differential Equation ◽  
One Dimensional ◽  
Fractional Pde ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Conditions ◽  
Hereditary Properties

This paper is devoted to the solution of one-dimensional Fractional Partial Differential Equation (FPDE) with nonlocal integral conditions. These FPDEs have been of considerable interest in the recent literature because fractional-order derivatives and integrals enable the description of the memory and hereditary properties of different substances. Existence and uniqueness of the solution of this FPDE are demonstrated. As for the numerical approach, a Galerkin method based on least squares is considered. The numerical examples illustrate the fast convergence of this technique and show the efficiency of the proposed method.

A New Approach to Compute Natural Frequencies and Mode Shapes of One-Dimensional Continuous Structures With Arbitrary Nonuniformities

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Linear Time ◽  
Longitudinal Vibration ◽  
Numerical Approach ◽  
Mode Shapes ◽  
Cross Sectional ◽  
One Dimensional ◽  
Dirac Delta ◽  
Mass Distributions ◽  
Jump Discontinuities

Abstract One-dimensional continuous structures include longitudinal vibration of bars, torsional vibration of circular shafts, and transverse vibration of beams. Using the linear time-varying system theory, algorithms are developed in this paper to compute natural frequencies and mode shapes of these structures with nonuniform spatial parameters (mass distributions, material properties and cross-sectional areas) which can have jump discontinuities. A general numerical approach has been presented to include Dirac-delta functions and their spatial derivatives due to jump discontinuities. Numerical results are presented to illustrate the application of these techniques to the solution of different types of spatial variations of parameters and boundary conditions.

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