Electrochemistry of Symmetrical Ion Channel: Three-Dimensional Nernst-Planck-Poisson Model

2015 ◽  
Vol 363 ◽  
pp. 68-78
Author(s):  
Bogusław Bożek ◽  
H. Leszczyński ◽  
Katarzyna Tkacz-Śmiech ◽  
Marek Danielewski
Keyword(s):  
Time Evolution ◽  
Stationary State ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Poisson Model ◽  
Ionic Transport ◽  
Equation System ◽  
Local Concentration

The paper provides a physical description of ionic transport through the rigid symmetrical channel. A three-dimensional mathematical model, in which the ionic transport is treated as the electrodiffusion of ions, is presented. The model bases on the solution of the 3D Nernst-Planck-Poisson system for cylindrical geometry. The total flux includes drift (convection) and diffusion terms. It allows simulating the transport characteristics at the steady-state and time evolution of the system. The numerical solutions of the coupled differential diffusion equation system are obtained by finite element method. Examples are presented in which the flow characteristics at the stationary state and during time evolution are compared. It is shown that the stationary state is achieved after about 2×10 -8 s since the process beginning. Various initial conditions (channel charging and dimensions) are considered as the key parameters controlling the selectivity of the channel. The model allows determining the flow characteristic, calculating the local concentration and potential across the channel. The model can be extended to simulate transport in polymer membranes and nanopores which might be useful in designing biosensors and nanodevices.

Performance Analysis of Grease-Lubricated Journal Bearings Including Thermal Effects

1997 ◽  
Vol 119 (4) ◽  
pp. 859-868 ◽  
Author(s):  
J. Y. Jang ◽  
M. M. Khonsari
Keyword(s):  
Performance Analysis ◽  
Thermal Effects ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Journal Bearings ◽  
Computational Results ◽  
Governing Equations ◽  
Bingham Plastic ◽  
The Ideal

A detailed analysis of the flow characteristics and lubrication effectiveness of grease in journal bearings is presented. Based on the ideal Bingham plastic model, the appropriate governing equations are developed which effectively handle the formation of a floating core as well as a core which may attach itself to either the shaft or the stationary bushing. The formulation and numerical solutions presented pertain to three-dimensional flows in finite journal bearings. Moreover, an extensive amount of computational results are presented, which take thermal effects into account according to the thermohydrodynamic theory.

scholarly journals Anelastic and Compressible Simulation of Moist Deep Convection

2014 ◽  
Vol 71 (10) ◽  
pp. 3767-3787 ◽  
Author(s):  
Marcin J. Kurowski ◽  
Wojciech W. Grabowski ◽  
Piotr K. Smolarkiewicz
Keyword(s):  
Initial Conditions ◽  
Deep Convection ◽  
Three Dimensional ◽  
Pressure Profile ◽  
Equation System ◽  
Acoustic Mode ◽  
Nonhydrostatic Pressure ◽  
Scale Turbulence ◽  
Short Time ◽  
Benchmark Solutions

Abstract Anelastic and compressible solutions are compared for two moist deep convection benchmarks, a two-dimensional thermal rising in a saturated moist-neutral deep atmosphere, and a three-dimensional supercell formation. In the anelastic model, the pressure applied in the moist thermodynamics comes from either the environmental hydrostatically balanced pressure profile in the standard anelastic model or is combined with nonhydrostatic perturbations from the elliptic pressure solver in the generalized anelastic model. The compressible model applies either an explicit acoustic-mode-resolving scheme requiring short time steps or a novel implicit scheme allowing time steps as large as those used in the anelastic model. The consistency of the unified numerical framework facilitates direct comparisons of results obtained with anelastic and compressible models. The anelastic and compressible rising thermal solutions agree not only with each other but also with the previously published compressible benchmark solution based on the comprehensive representation of moist dynamics and thermodynamics. In contrast to earlier works focusing on the formulation of moist thermodynamics, the compatibility of the initial conditions is emphasized and its impact on the benchmark solutions is documented. The anelastic and compressible supercell solutions agree well for various versions of anelastic and compressible models even for cloud updrafts reaching 15% of the speed of sound. The nonhydrostatic pressure perturbations turn out to have a negligible impact on the moist dynamics. Numerical and physical details of the simulations, such as the advection scheme, spatial and temporal resolution, or parameters of the subgrid-scale turbulence, have a more significant effect on the solutions than the particular equation system applied.

scholarly journals Projective Synchronization of a 3D Chaotic System with Quadratic and Quartic Nonlinearities

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Babatunde Idowu ◽  
Kehinde Oyeleke ◽  
Cornelius Ogabi ◽  
Olasunkanmi Olusola
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Dimensional System

Introduction: In this work, the projective synchronization of two identical three dimensional chaotic system with quadratic and quartic non linearities was considered as well as the equilibrium and stability analysis of the system. The projective synchronization with same and different scaling factor was carried out for this category of system to show its feasibility in order to establish that no matter the type and number of nonlinearities, projective synchronization can be achieved. Numerical simulations was done to verify the above. In all kinds of chaos synchronization, projective synchronization (PS), characterized by a scaling factor that two systems synchronize proportionally, is one of the most interesting problems. It was first reported by Mainieri et al [1] , where it was stated that the two identical systems (master and slave) could be synchronized up to a scaling factor, . They further stated that the scaling factor was dependent on the chaotic evolution and initial conditions so that the ultimate state of projective synchronization was unpredictable. Aims: Is to achieve projective synchronization of two identical three Dimensional chaotic system with quadratic and quartic nonlinearities synchronizing to a scaling factor and also present the equilibrium and stability analysis of the system. This is to establish that projective synchronization can be achieved for varied systems with varied nonlinearities. Materials and Methods: We employed the adaptive synchronization technique to achieve projective synchronization of the system (master and slave) with different scaling factors, and the fourth order RungeKutta algorithm is used for numerical solutions. Results: In this work, the projective synchronization of two identical three dimensional systems with quadratic and quartic nonlinearities was achieved with the same and different scaling factor, . The equilibrium and stability analysis of the system was also presented. Numerical simulations was done to verify the above. Conclusion: The investigated projective synchronization behaviour of two identical three-dimensional system with two nonlinearities (quadratic and quartic) was achieved for cases where the scaling factor is the same and when different. This shows that projective synchronization can be achieved for systems with varying nonlinearities even when the scaling factor is different and this suggests its use in communication using chaotic wave forms as carriers, perhaps with a view to securing communication.

Stochastic numerical investigations for nonlinear three-species food chain system

2021 ◽  
Author(s):  
Zulqurnain Sabir
Keyword(s):  
Food Chain ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Interior Point Algorithm ◽  
Top Predator ◽  
Chain System ◽  
Comparison Of The Results ◽  
Global And Local ◽  
Algorithm Scheme

In this work, three-dimensional nonlinear food chain system is numerically treated using the computational heuristic framework of artificial neural networks (ANNs) together with the proficiencies of global and local search approaches based on genetic algorithm (GA) and interior-point algorithm scheme (IPAS), i.e. ANN–GA–IPAS. The three-dimensional food chain system consists of prey populations, specialist predator and top-predator. The formulation of an objective function using the differential system of three-species food chain and its initial conditions is presented and the optimization is performed by using the hybrid computing efficiency of GA–IPAS. The achieved numerical solutions through ANN–GA–IPAS to solve the nonlinear three-species food chain system are compared with the Adams method to validate the exactness of the designed ANN–GA–IPAS. The comparison of the results is presented to authenticate the correctness of the designed ANN–GA–IPAS for solving the nonlinear three-species food chain system. Moreover, statistical representations for 40 independent trials and 30 variables validate the efficacy, constancy and reliability of ANN–GA–IPAS.

Numerical Simulations of Three-Dimensional Flows in a Cubic Cavity With an Oscillating Lid

1993 ◽  
Vol 115 (4) ◽  
pp. 680-686 ◽  
Author(s):  
Reima Iwatsu ◽  
Jae Min Hyun ◽  
Kunio Kuwahara
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Sinusoidal Oscillations ◽  
Dependent Flow

Numerical studies are made of three-dimensional flow of a viscous fluid in a cubical container. The flow is driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions are acquired by solving the time-dependent, three-dimensional incompressible Navier-Stokes equations by employing very fine meshes. Results are presented for wide ranges of two principal physical parameters, i.e., the Reynolds number, Re ≤ 2000 and the frequency parameter of the lid oscillation, ω′ ≤ 10.0. Comprehensive details of the flow structure are analyzed. Attention is focused on the three-dimensionality of the flow field. Extensive numerical flow visualizations have been performed. These yield sequential plots of the main flows as well as the secondary flow patterns. It is found that the previous two-dimensional computational results are adequate in describing the main flow characteristics in the bulk of interior when ω′ is reasonably high. For the cases of high-Re flows, however, the three-dimensional motions exhibit additional complexities especially when ω′ is low. It is asserted that, thanks to the recent development of the supercomputers, calculation of three-dimensional, time-dependent flow problems appears to be feasible at least over limited ranges of Re.

scholarly journals A Quantum Model for the Dynamics of Cold Dark Matter

2019 ◽  
Vol 4 (4) ◽  
pp. 89
Author(s):  
Tim Zimmermann ◽  
Massimo Pietroni ◽  
Javier Madroñero ◽  
Luca Amendola ◽  
Sandro Wimberger
Keyword(s):  
Dark Matter ◽  
Numerical Scheme ◽  
Cold Dark Matter ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Equation System ◽  
Numerical Approach ◽  
Quantum Model ◽  
Numerical Examples ◽  
Key Features

A model for cold dark matter is given by the solution of a coupled Schrödinger–Poisson equation system. We present a numerical scheme for integrating these equations, discussing the problems arising from their nonlinear and nonlocal character. After introducing and testing our numerical approach, we illustrate key features of the system by numerical examples in 1 + 1 dimensions. In particular, we study the properties of asymptotic states to which the numerical solutions converge for artificial initial conditions.

Effect of initial conditions on mean flow characteristics of a three dimensional turbulent wall jet

2021 ◽  
pp. 095440622110149
Author(s):  
Sarvesh Kumar ◽  
Amitesh Kumar
Keyword(s):  
Reynolds Number ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Wall Jet ◽  
Mean Flow ◽  
Mean Velocity ◽  
Nozzle Length ◽  
Number Formula ◽  
Local Reynolds Number

The effect of initial conditions in a [Formula: see text] sidewall enclosure on the mean flow characteristics of a three dimensional turbulent square wall jet has been studied experimentally. The initial conditions are varied by varying the length of the nozzle; it is varied as l/ h = 10, 50, and 90, where l and h indicates the nozzle length and the side of the square nozzle, respectively. The effect of nozzle length on initial velocity profiles, velocity distribution in lateral and wall normal directions, spread rate, decay of maximum mean velocity, local Reynolds number and similarity behaviour has been studied. The wall normal spread width is higher for the nozzle length l/h = 10 in the near field [Formula: see text] but this trend completely changed after [Formula: see text]. The spread rate is found independent of the initial condition of the nozzles in the fully developed region. The decay rate of maximum mean velocity is found higher for l/ h = 10 in the region of ([Formula: see text], whereas decay rate becomes independent of the initial conditions in the fully developed region [Formula: see text]. The local Reynolds number variation is also estimated along the downstream directions for present case and found that the local Reynolds number [Formula: see text] reaches approximately 56% of the jet exit Reynolds number [Formula: see text] at [Formula: see text] for nozzle length l/ h = 10, while it is 57% and 59% of Rejet for the nozzles [Formula: see text] and [Formula: see text] respectively at the same location. The nozzle l/ h = 10 attained self similar behaviour more quickly as compared to the other nozzles. The sidewall played a significant role which pushed the fluid more towards the center resulting in a lower jet half width in the wall normal direction as compared to the corresponding case, without a sidewall. The decay rates of the maximum mean velocity for all the nozzles are estimated to be 1.08 which is in the accepted range found in the literature.

scholarly journals Interactions between Tandem Cylinders in an Open Channel: Impact on Mean and Turbulent Flow Characteristics

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1718
Author(s):  
Hasan Zobeyer ◽  
Abul B. M. Baki ◽  
Saika Nowshin Nowrin
Keyword(s):  
Turbulent Flow ◽  
Open Channel ◽  
Recirculation Zone ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Flow Recirculation ◽  
Tandem Cylinders ◽  
Flow Development ◽  
The Mean ◽  
Recirculation Length

The flow hydrodynamics around a single cylinder differ significantly from the flow fields around two cylinders in a tandem or side-by-side arrangement. In this study, the experimental results on the mean and turbulence characteristics of flow generated by a pair of cylinders placed in tandem in an open-channel flume are presented. An acoustic Doppler velocimeter (ADV) was used to measure the instantaneous three-dimensional velocity components. This study investigated the effect of cylinder spacing at 3D, 6D, and 9D (center to center) distances on the mean and turbulent flow profiles and the distribution of near-bed shear stress behind the tandem cylinders in the plane of symmetry, where D is the cylinder diameter. The results revealed that the downstream cylinder influenced the flow development between cylinders (i.e., midstream) with 3D, 6D, and 9D spacing. However, the downstream cylinder controlled the flow recirculation length midstream for the 3D distance and showed zero interruption in the 6D and 9D distances. The peak of the turbulent metrics generally occurred near the end of the recirculation zone in all scenarios.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

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