Capillary Forces Modeling in Micro/Nano Interactions

2007 ◽  
Author(s):  
Bo Chang ◽  
Jingrong Wang ◽  
Quan Zhou ◽  
Heikki Koivo
Keyword(s):  
Numerical Methods ◽  
Numerical Solutions ◽  
Capillary Condensation ◽  
Initial Conditions ◽  
Capillary Forces ◽  
Incline Angle ◽  
Second Derivative ◽  
System Parameters ◽  
Existence And Stability ◽  
Numerical Approaches

This paper introduces two numerical approaches to model the capillary forces under two different initial conditions: given volume of the liquid and under the capillary condensation. The paper thoroughly analyzes the solutions of both numerical methods. Due to multiple numerical solutions may exist for a given set of parameters, criteria based on the derivative and the second derivative of the solution are proposed to determine the existence and stability of those numerical solutions. The features of those numerical solutions are also carefully discussed. Moreover, the results of two numerical methods are compared in different system parameters for several configurations, including two plates with different volume of liquid between them, a plate and a cone of different incline angle, and a plate and spheres of different radius. Suggestions of the applicability of both methods are given based on the results. To allow calculation of capillary forces between arbitrary shaped objects, the paper proposes an early approach to calculate the capillary forces for discretized surfaces.

scholarly journals Numerical daemons of hydrological models are summoned by extreme precipitation

2021 ◽  
Author(s):  
Peter T. La Follette ◽  
Adriaan J. Teuling ◽  
Nans Addor ◽  
Martyn Clark ◽  
Koen Jansen ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Extreme Precipitation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Computational Cost ◽  
Numerical Error ◽  
Hydrological Models ◽  
Multiple Model ◽  
Numerical Techniques ◽  
Modeling Framework

Abstract. Hydrological models are usually systems of nonlinear differential equations for which no analytical solutions exist and thus rely on approximate numerical solutions. While some studies have investigated the relationship between numerical method choice and model error, the extent to which extreme precipitation like that observed during hurricanes Harvey and Katrina impacts numerical error of hydrological models is still unknown. This knowledge is relevant in light of climate change, where many regions will likely experience more intense precipitation events. In this experiment, a large number of hydrographs is generated with the modular modeling framework FUSE, using eight numerical techniques across a variety of forcing datasets. Multiple model structures, parameter sets, and initial conditions are incorporated for generality. The computational expense and numerical error associated with each hydrograph were recorded. It was found that numerical error (root mean square error) usually increases with precipitation intensity and decreases with event duration. Some numerical methods constrain errors much more effectively than others, sometimes by many orders of magnitude. Of the tested numerical methods, a second-order adaptive explicit method is found to be the most efficient because it has both low numerical error and low computational cost. A basic literature review indicates that many popular modeling codes use numerical techniques that were suggested by this experiment to be sub-optimal. We conclude that relatively large numerical errors might be common in current models, and because these will likely become larger as the climate changes, we advocate for the use of low cost, low error numerical methods.

scholarly journals On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Neveen G. A. Farag ◽  
Ahmed H. Eltanboly ◽  
M. S. EL-Azab ◽  
S. S. A. Obayya
Keyword(s):  
Schrödinger Equation ◽  
Fiber Optics ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Real Life ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Numerical Approaches

In this paper, four compelling numerical approaches, namely, the split-step Fourier transform (SSFT), Fourier pseudospectral method (FPSM), Crank-Nicolson method (CNM), and Hopscotch method (HSM), are exhaustively presented for solving the 1D nonlinear Schrodinger equation (NLSE). The significance of this equation is referred to its notable contribution in modeling wave propagation in a plethora of crucial real-life applications such as the fiber optics field. Although exact solutions can be obtained to solve this equation, these solutions are extremely insufficient because of their limitations to only a unique structure under some limited initial conditions. Therefore, seeking high-performance numerical techniques to manipulate this well-known equation is our fundamental purpose in this study. In this regard, extensive comparisons of the proposed numerical approaches, against the exact solution, are conducted to investigate the benefits of each of them along with their drawbacks, targeting a broad range of temporal and spatial values. Based on the obtained numerical simulations via MATLAB, we extrapolated that the SSFT invariably exhibits the topmost robust potentiality for solving this equation. However, the other suggested schemes are substantiated to be consistently accurate, but they might generate higher errors or even consume more processing time under certain conditions.

scholarly journals Numerical Modelling on the Influence of Source in the Heat Transformation: An Application in the Metal Heating for Blacksmithing

2021 ◽  
Vol 7 (2) ◽  
pp. 97-101
Author(s):  
H. P. Kandel ◽  
J. Kafle ◽  
L. P. Bagale
Keyword(s):  
Numerical Methods ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Numerical Technique ◽  
Heat Equations ◽  
Science And Engineering ◽  
Physical Problems ◽  
Different Temperatures ◽  
The One ◽  
Heat Transformation

Many physical problems, such as heat transfer and wave transfer, are modeled in the real world using partial differential equations (PDEs). When the domain of such modeled problems is irregular in shape, computing analytic solution becomes difficult, if not impossible. In such a case, numerical methods can be used to compute the solution of such PDEs. The Finite difference method (FDM) is one of the numerical methods used to compute the solutions of PDEs by discretizing the domain into a finite number of regions. We used FDMs to compute the numerical solutions of the one dimensional heat equation with different position initial conditions and multiple initial conditions. Blacksmiths fashioned different metals into the desired shape by heating the objects with different temperatures and at different position. The numerical technique applied here can be used to solve heat equations observed in the field of science and engineering.

scholarly journals Numerical solutions of fuzzy equal width models via generalized fuzzy fractional derivative operators

2021 ◽  
Vol 7 (2) ◽  
pp. 2695-2728
Author(s):  
Rehana Ashraf ◽  
◽  
Saima Rashid ◽  
Fahd Jarad ◽  
Ali Althobaiti ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Initial Conditions ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Proposed Model ◽  
Wide Range ◽  
Fractional Models ◽  
The Subject ◽  
Good Agreement ◽  
Numerical Approaches

<abstract><p>The Shehu homotopy perturbation transform method (SHPTM) via fuzziness, which combines the homotopy perturbation method and the Shehu transform, is the subject of this article. With the assistance of fuzzy fractional Caputo and Atangana-Baleanu derivatives operators, the proposed methodology is designed to illustrate the reliability by finding fuzzy fractional equal width (EW), modified equal width (MEW) and variants of modified equal width (VMEW) models with fuzzy initial conditions (ICs). In cold plasma, the proposed model is vital for generating hydro-magnetic waves. We investigated SHPTM's potential to investigate fractional nonlinear systems and demonstrated its superiority over other numerical approaches that are accessible. Another significant aspect of this research is to look at two significant fuzzy fractional models with differing nonlinearities considering fuzzy set theory. Evaluating various implementations verifies the method's impact, capabilities, and practicality. The level impacts of the parameter $ \hbar $ and fractional order are graphically and quantitatively presented, demonstrating good agreement between the fuzzy approximate upper and lower bound solutions. The findings are numerically examined to crisp solutions and those produced by other approaches, demonstrating that the proposed method is a handy and astonishingly efficient instrument for solving a wide range of physics and engineering problems.</p></abstract>

A Study on the Characteristics of a Nonlinear Oscillatory System With Dry Friction

2003 ◽  
Author(s):  
Liming Dai ◽  
Liang Xu
Keyword(s):  
Nonlinear System ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Oscillatory System ◽  
Approximate Solutions ◽  
Weakly Nonlinear ◽  
System Parameters ◽  
Weakly Nonlinear System ◽  
Highly Nonlinear ◽  
Nonlinear Oscillatory System

Nonlinear oscillatory system involved with friction is very common in nonlinear dynamics of engineering fields. This paper is to investigate the motions a nonlinear oscillatory system with involvement of dry friction. The cases of weakly and highly nonlinearity of the system are considered. Approximate and numerical solutions for the system are developed via the author’s newly developed P-T method. As demonstrated in the present work, the properties of the weakly and highly nonlinear systems exhibit great differences, though the governing equations of the two systems employ identical system parameters. The approximate solutions developed for the system are continuous everywhere on the time range considered. Under the conditions of weakly nonlinearity, the approximate solutions developed can therefore be conveniently implemented for the purpose of an analytical studying the properties of the system with numerous system parameters and various initial conditions. Taking this advantage, the behavior of motion of the weakly nonlinear system is analyzed and compared with the corresponding solutions developed with Van der Pol’s method. It is found in the present work, the system may undergo a self-excited oscillation under certain conditions. The highly nonlinear system is a physically much involved one. Its behavior is thus much complex in comparing with that of the weakly nonlinear system. Based on the approximate solutions developed for the highly nonlinear system, recurrence relations are generated for numerical calculations. For the sake of comparison with the oscillation of the weakly nonlinear system, numerical simulations for the highly nonlinear system are performed under the same initial conditions and identical system parameters. The conditions of convergence and divergence of the weakly nonlinear system are also established for application. Behavior of the oscillatory motion of the highly nonlinear system is investigated on the basis of the corresponding numerical solutions developed.

scholarly journals Plastic failure zone characteristics and stability control technology of roadway in the fault area under non-uniformly high geostress: A case study from Yuandian Coal Mine in Northern Anhui Province, China

2020 ◽  
Vol 12 (1) ◽  
pp. 406-424 ◽  
Author(s):  
Yaoguang Huang ◽  
Aining Zhao ◽  
Tianjun Zhang ◽  
Weibin Guo
Keyword(s):  
Numerical Methods ◽  
Numerical Solutions ◽  
Stress Test ◽  
Pressure Coefficient ◽  
Stability Control ◽  
Failure Zone ◽  
Plastic Failure ◽  
Comparison Results ◽  
High Geostress ◽  
The Difference

AbstractIn order to explore the effective support method for deep broken roadway, based on the in situ stress test results, the analytical and numerical solutions of the stress and the range of plastic failure zone (PFZ) in a circular roadway subjected to non-uniform loads were obtained using analytical and finite difference numerical methods based on the elastoplastic theory, respectively. Their comparison results show that the analytical and numerical methods are correct and reasonable. Furthermore, the high geostress causes the stress and range of PFZ in roadway roof and floor to increase sharply while those in roadway ribs decrease. Moreover, the greater the difference of horizontal geostress in different horizontal directions is, the larger the range of PFZ in roadway roof and floor is. The shape of PFZ in roadway varies with the ratio of horizontal lateral pressure coefficient in x-direction and y-direction. Finally, according to the distribution characteristics of PFZ and range of PFZ under the non-uniformly high geostress, this paper has proposed a combined support scheme, and refined and optimized supporting parameters. The field monitoring results prove that the roadway deformation and fracture have been effectively controlled. The research results of this paper can provide theoretical foundation as well as technical reference for the stability control of deep broken roadway under non-uniformly high geostress.

scholarly journals Feasibility Study on Oil Droplet Flow Investigations Inside Aero Engine Bearing Chambers: PDPA Techniques in Combination With Numerical Approaches

1995 ◽  
Author(s):  
A. Glahn ◽  
M. Kurreck ◽  
M. Willmann ◽  
S. Wittig
Keyword(s):  
Numerical Methods ◽  
Flow Field ◽  
Flow Analysis ◽  
Field Analysis ◽  
Oil Droplet ◽  
Droplet Flow ◽  
Aero Engine ◽  
Secondary Air ◽  
Numerical Approaches ◽  
Engine Bearing

The present paper deals with oil droplet now phenomena in aero engine bearing chambers. An experimental investigation of droplet sizes and velocities utilizing a Phase Doppler Particle Analyzer (PDPA) has been performed for the first time in bearing chamber atmospheres under real engine conditions. Influences of high rotational speeds are discussed for individual droplet size classes. Although this is an important contribution to a better understanding of the droplet flow impact on secondary air/oil system performance, an analysis of the droplet flow behaviour requires an incorporation of numerical methods because detailed measurements as performed here suffer from both strong spatial limitations with respect to the optical accessibility in real engine applications and constraints due to the extremely time consuming nature of an experimental flow field analysis. Therefore, further analysis is based on numerical methods. Droplets characterized within the experiments are exposed to the flow field of the gaseous phase predicted by use of our well-known CFD code EPOS. The droplet trajectories and velocities are calculated within a Lagrangian frame of reference by forward numerical integration of the particle momentum equation. This paper has been initiated rather to show a successful method of bearing chamber droplet flow analysis by a combination of droplet sizing techniques and numerical approaches than to present field values as a function of all operating parameters. However, a first insight into the complex droplet flow phenomena is given and specific problems in bearing chamber heat transfer are related to the droplet flow.

On New Aspects of Nested Carbon Nanotubes as Gigahertz Oscillators

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
R. Ansari ◽  
B. Motevalli
Keyword(s):  
Carbon Nanotubes ◽  
Initial Velocity ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Interaction Force ◽  
Arbitrary Length ◽  
Oscillatory Frequency ◽  
Analytical Expression ◽  
System Parameters ◽  
The Core

Nested carbon nanotubes exhibit telescopic oscillatory motion with frequencies in the gigahertz range. In this paper, our previously proposed semi-analytical expression for the interaction force between two concentric carbon nanotubes is used to solve the equation of motion. That expression also enables a new semi-analytical expression for the precise evaluation of oscillation frequency to be introduced. Alternatively, an algebraic frequency formula derived based on the simplifying assumption of constant van der Waals force is also given. Based on the given formulas, a thorough study on different aspects of operating frequencies under various system parameters is conducted, which permits fresh insight into the problem. Some notable improvements over the previously drawn conclusions are made. The strong dependence of oscillatory frequency on system parameters including the extrusion distance and initial velocity of the core as initial conditions for the motion is shown. Interestingly, our results indicate that there is a special initial velocity at which oscillatory frequency is unique for any arbitrary length of the core. A particular relationship between the escape velocity (the minimum initial velocity beyond which the core will leave the outer nanotube) and this specific initial velocity is also revealed.

Oscillatory flow past a circular cylinder in a rotating frame

1997 ◽  
Vol 345 ◽  
pp. 101-131
Author(s):  
M. D. KUNKA ◽  
M. R. FOSTER
Keyword(s):  
Circular Cylinder ◽  
Steady Flow ◽  
Stagnation Point ◽  
Oscillatory Flow ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Temporal Integration ◽  
Oncoming Flow ◽  
Flow Past ◽  
Rear Stagnation Point

Because of the importance of oscillatory components in the oncoming flow at certain oceanic topographic features, we investigate the oscillatory flow past a circular cylinder in an homogeneous rotating fluid. When the oncoming flow is non-reversing, and for relatively low-frequency oscillations, the modifications to the equivalent steady flow arise principally in the ‘quarter layer’ on the surface of the cylinder. An incipient-separation criterion is found as a limitation on the magnitude of the Rossby number, as in the steady-flow case. We present exact solutions for a number of asymptotic cases, at both large frequency and small nonlinearity. We also report numerical solutions of the nonlinear quarter-layer equation for a range of parameters, obtained by a temporal integration. Near the rear stagnation point of the cylinder, we find a generalized velocity ‘plateau’ similar to that of the steady-flow problem, in which all harmonics of the free-stream oscillation may be present. Further, we determine that, for certain initial conditions, the boundary-layer flow develops a finite-time singularity in the neighbourhood of the rear stagnation point.

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