One-Dimensional Nonlinear Parametric Instability of Inhomogeneous Plasma: Time Domain Problem

2021 ◽  
Vol 24 (3) ◽  
pp. 272-279
Author(s):  
N. V. Gerasimenko ◽  
F. M. Trukhachev ◽  
E. Z. Gusakov ◽  
L. V. Simonchik ◽  
A. V. Tomov
Keyword(s):  
Initial Conditions ◽  
Inhomogeneous Plasma ◽  
Parametric Instability ◽  
Analytical Models ◽  
Dimensional Model ◽  
One Dimensional ◽  
Proposed Model ◽  
Wide Range ◽  
Spatial And Temporal Characteristics ◽  
Good Agreement

A numerical one-dimensional model of convective parametric instability of inhomogeneous plasma is developed. By using this model, a numerical solution describing spatial and temporal characteristics of interacting waves is obtained. The results obtained are in a good agreement with known analytical models and substantially generalize them. In particular, an important advantage of the proposed model is the possibility of varying initial conditions, analyzing behavior of the system in the presence of incident wave fluctuations that is important for the future study of the absolute instability mode. The model is also provides possibility to simulate absolute parametric instability with a wide range of controllable parameters, as well as to study interacting wave transients.

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>

scholarly journals EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

1996 ◽  
Vol 10 (25) ◽  
pp. 3451-3459 ◽  
Author(s):  
ANTÓNIO M.R. CADILHE ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Exact Solution ◽  
Domain Wall ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Zero Temperature ◽  
Dimensional Model ◽  
One Dimensional ◽  
Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

Optimization of synthetic jet actuation by analytical modeling

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Max Huber ◽  
Andreas Zienert ◽  
Perez Weigel ◽  
Martin Schüller ◽  
Hans-Reinhard Berger ◽  
...  
Keyword(s):  
High Performance ◽  
Synthetic Jet ◽  
Parameter Study ◽  
Content Type ◽  
One Dimensional ◽  
Wide Range ◽  
Jet Actuators ◽  
Different Dimensions ◽  
Oscillation Correction ◽  
Good Agreement

Purpose The purpose of this paper is to analyze and optimize synthetic jet actuators (SJAs) by means of a literature-known one-dimensional analytical model. Design/methodology/approach The model was fit to a wide range of experimental data from in-house built SJAs with different dimensions. A comprehensive parameter study was performed to identify coupling between parameters of the model and to find optimal dimensions of SJAs. Findings The coupling of two important parameters, the diaphragm resonance frequency and the cavity volume, can be described by a power law. Optimal orifice length and diameter can be calculated from cavity height in good agreement with literature. A transient oscillation correction is required to get correct simulation outcomes. Originality/value Based on these findings, SJA devices can be optimized for maximum jet velocity and, therefore, high performance.

scholarly journals Rare temperature histories and cirrus ice number density in a parcel and a one-dimensional model

2014 ◽  
Vol 14 (23) ◽  
pp. 13013-13022 ◽  
Author(s):  
D. M. Murphy
Keyword(s):  
Temperature Dependence ◽  
Low Temperatures ◽  
Ice Crystals ◽  
Strong Increase ◽  
Number Density ◽  
Dimensional Model ◽  
One Dimensional ◽  
Slow Growth Rate ◽  
Wide Range ◽  
The One

Abstract. A parcel and a one-dimensional model are used to investigate the temperature dependence of ice crystal number density. The number of ice crystals initially formed in a cold cirrus cloud is very sensitive to the nucleation mechanism and the detailed history of cooling rates during nucleation. A possible small spread in the homogeneous freezing threshold due to varying particle composition is identified as a sensitive nucleation parameter. In a parcel model, the slow growth rate of ice crystals at low temperatures inherently leads to a strong increase in ice number density at low temperatures. This temperature dependence is not observed. The model temperature dependence occurs for a wide range of assumptions and for either homogeneous or, less strongly, heterogeneous freezing. However, the parcel model also shows that random temperature fluctuations result in an extremely wide range of ice number densities. A one-dimensional model is used to show that the rare temperature trajectories resulting in the lowest number densities are disproportionately important. Low number density ice crystals sediment and influence a large volume of air. When such fall streaks are included, the ice number becomes less sensitive to the details of nucleation than it is in a parcel model. The one-dimensional simulations have a more realistic temperature dependence than the parcel mode. The one-dimensional model also produces layers with vertical dimensions of meters even if the temperature forcing has a much broader vertical wavelength. Unlike warm clouds, cirrus clouds are frequently surrounded by supersaturated air. Sedimentation through supersaturated air increases the importance of any process that produces small numbers of ice crystals. This paper emphasizes the relatively rare temperature trajectories that produce the fewest crystals. Other processes are heterogeneous nucleation, sedimentation from the very bottom of clouds, annealing of disordered to hexagonal ice, and entrainment.

A predictive combustion model for one-dimensional gasoline engine simulation

2020 ◽  
pp. 146808742094590
Author(s):  
Yoshihiro Nomura ◽  
Seiji Yamamoto ◽  
Makoto Nagaoka ◽  
Stephan Diel ◽  
Kenta Kurihara ◽  
...  
Keyword(s):  
Gasoline Engine ◽  
Early Stage ◽  
Burning Velocity ◽  
Turbulent Flame ◽  
Operating Conditions ◽  
Combustion Model ◽  
One Dimensional ◽  
Turbulent Reynolds Number ◽  
Proposed Model ◽  
Wide Range

A new predictive combustion model for a one-dimensional computational fluid dynamics tool in the multibody dynamics processes of gasoline engines was developed and validated. The model consists of (1) a turbulent burning velocity model featuring a flame radius–based transitional function, steady burning velocity that considers local quenching using the Karlovitz number and laminarization by turbulent Reynolds number, as well as turbulent flame thickness and its quenching model near the liner wall, and (2) a knock model featuring auto-ignition by the Livengood–Wu integration and ignition delay time obtained using a full-kinetic model. The proposed model and previous models were verified under a wide range of operating conditions using engines with widely different specifications. Good agreement was only obtained for combustion characteristics by the proposed model without requiring individual calibration of model constants. The model was also evaluated for utilization after prototyping. Improved accuracy, especially of ignition timing, was obtained after further calibration using a small amount of engine data. It was confirmed that the proposed model is highly accurate at the early stage of the engine development process, and is also applicable for engine calibration models that require higher accuracy.

Mathematical Modeling of Ultra-High-Pressure Waterjet Peening

2005 ◽  
Vol 127 (2) ◽  
pp. 186-191 ◽  
Author(s):  
S. Kunaporn ◽  
M. Ramulu ◽  
M. Hashish
Keyword(s):  
Mathematical Modeling ◽  
High Pressure ◽  
High Cycle Fatigue ◽  
Fatigue Tests ◽  
Analytical Models ◽  
Test Results ◽  
Ultra High Pressure ◽  
Proposed Model ◽  
Compressive Residual Stresses ◽  
Good Agreement

Waterjet peening is a recent promising method in surface treatment. It has the potential to induce compressive residual stresses that benefit the fatigue life of materials similar to the conventional shot peening process. However, there are no analytical models that incorporate process parameters (i.e., supply pressure, jet exposure time, and nozzle traverse rate, etc) to allow predicting the optimized peening process. Mathematical modeling of high-pressure waterjet peening was developed in this study to describe the relation between the waterjet peening parameters and the resulting material modifications. Results showed the possibility of using the proposed mathematical model to predict an initial range for effective waterjet peening under the variation of waterjet peening conditions. The high cycle fatigue tests were performed to validate the proposed model and fatigue test results showed good agreement with the predictions.

Steady Compressible Flow through a Single Row of Radial Holes in the Wall of a Pipeline

1970 ◽  
Vol 12 (4) ◽  
pp. 248-258 ◽  
Author(s):  
G. H. Trengrouse
Keyword(s):  
Discharge Coefficient ◽  
Pressure Change ◽  
Single Row ◽  
One Dimensional ◽  
Discharge Coefficients ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Flow Through ◽  
Flow Theories ◽  
Good Agreement

Measured values of discharge coefficient for air flow through a single row of radial holes in the wall of a pipeline are reported, together with the values of pipe Mach numbers in the immediate vicinity of the holes. A wide range of pressure and area ratios are considered, the flow through the holes being either into or out of the pipe. It is shown that the effects on the measured values of both the pressure level at discharge from the holes and the air temperature are negligible. The agreement between the pressure change in the pipeline due to the holes, obtained experimentally, and that predicted by simple, one-dimensional flow theories is generally unsatisfactory. However, theoretical predictions of the jet efflux angles based on two-dimensional, incompressible, non-viscous flow arguments are in good agreement with those measured, but discrepancies do arise in the prediction of discharge coefficients.

A One-Dimensional Model of Simultaneous Hemodialysis and Ultrafiltration With Highly Permeable Membranes

1981 ◽  
Vol 103 (4) ◽  
pp. 261-266 ◽  
Author(s):  
M. Y. Jaffrin ◽  
B. B. Gupta ◽  
J. M. Malbrancq
Keyword(s):  
Protein Concentration ◽  
Flux Distribution ◽  
Transmembrane Pressure ◽  
Dimensional Model ◽  
One Dimensional ◽  
Diffusive Mass Transfer ◽  
Model Predictions ◽  
Polyacrylonitrile Membrane ◽  
Good Agreement

A one-dimensional model of combined convective and diffusive mass transfer in a hemodialyser is presented. Solutions and results are given for two regimes of ultrafiltration (UF): at low transmembrane pressures when UF flow is proportional to transmembrane pressure and in the limit of large transmembrane pressures when UF is limited by protein concentration polarization. It is found that the overall clearance is always less than the sum of dialytic and UF clearances due to interaction between convective and diffusive transfers. For a given UF flow the clearance is not sensitive to UF flux distribution along the membrane. Model predictions of urea clearance are in good agreement with measurements obtained in vitro with saline on hemodialysers equipped with a polyacrylonitrile membrane.

scholarly journals Kompiuterinis biojutiklių su perforuota ir selektyvia membrana modeliavimas vienmačiu keturių sluoksnių modeliu

2009 ◽  
Vol 50 ◽  
pp. 328-333
Author(s):  
Karolis Petrauskas
Keyword(s):  
Numerical Experiments ◽  
Enzymatic Reaction ◽  
Diffusion Reaction ◽  
Homogeneous Layer ◽  
Dimensional Model ◽  
One Dimensional ◽  
Proposed Model ◽  
The One ◽  
Menten Kinetic ◽  
Reaction Equations

Straipsnyje pateikiamas vienmatis biojutiklio su perforuota ir selektyvia membrana modelis. Šis modelis sudarytas pakeičiant perforuotą membraną dviem homogeniškais sluoksniais atitinkamai membranos dalims, kur skylutės yra užpildytos fermento ir kur fermento nėra. Pasiūlytas modelis buvo ištirtas vykdant skaitinius eksperimentus, kad būtų nustatytos sąlygos, kuriomis jis gali būti taikomas tiksliam biojutiklio veiksmo modeliavimui. Šio modelio tikslumas buvo vertinamas lyginant juo gaunamus rezultatus su dvimačio modelio rezultatais. Pasiūlyto modelio rezultatai taip pat buvo palyginti su vienmačio modelio, kuriame perforuota membrana pakeičiama vienu homogenišku sluoksniu, rezultatais. Biojutiklis buvo modeliuojamas reakcijos-difuzijos lygtimis su netiesiniu nariu, aprašančiu fermentinės reakcijos Michaelio–Menteno kinetiką. Modelio lygčių sistema buvo sprendžiama skaitiškai, naudojant baigtinių skirtumų metodą.Computer-Aided Modeling of a Biosensor with Selective and Perforated Membranes Using a Four-Layered One-Dimensional ModelKarolis Petrauskas SummaryThis article presents a one-dimensional model for a biosensor with perforated and selective membranes. This model is constructed by replacing the perforated membrane with two homogeneous layers. These layers are used to model parts of the perforated membrane, where holes are fi lled with an enzyme and where is no enzyme in the holes, separately. The proposed model was investigated by performing numerical experiments in order to determine conditions, under which the proposed model can be used to simulate an operation of a biosensor with an outer perforated membrane precisely. A preciseness of the model was measured by comparing its results with results of the corresponding two-dimensional model. Beside the measurement of the preciseness, results of the proposed model were compared to the results of the one-dimensional model, constructed by replacing the perforated membrane with one homogeneous layer. A biosensor was modeled using diffusion-reaction equations with a nonlinear member representing the Michaelis-Menten kinetic of an enzymatic reaction. These equations were solved numerically, using the method of fi nite differences.: 18px;"> 

High Pressure Diesel Engine Modeling

2003 ◽  
Author(s):  
Riccardo Baudille ◽  
Gino Bella ◽  
Rossella Rotondi
Keyword(s):  
Liquid Fuel ◽  
Initial Conditions ◽  
Injection Velocity ◽  
Dimensional Model ◽  
Flow Conditions ◽  
One Dimensional ◽  
Engine Modeling ◽  
Fuel Jet ◽  
Initial Drop ◽  
The One

In multi hole Diesel injectors, cavitation can offer advantages in the development on the fuel spray, because the primary atomization of the liquid fuel jet can be improved due to the enhanced turbulence. Several multi dimensional models of cavitating nozzle flow have been developed in order to provide information about the flow at the exit of a cavitating orifice. In this paper an analytical one-dimensional model, by Sarre et al. [1], to predict the flow conditions at the exit of a cavitating nozzle, is analyzed. The results obtained are compared with the ones obtained using the multi dimensional code Fluent in order to investigate the predictive capability of the one-dimensional code. The model provides initial conditions for multidimensional spray modeling: the effective injection velocity and the initial drop or injected liquid ‘blob’ size. The simulations were performed using an improved version of the KIVA3V code, in which an hybrid break up model, developed by the authors, is used and the results in terms of penetrations and global SMD are compared with the experimental ones. The one dimensional model predicts reasonable discharge coefficient for sharp injector geometry. Where the r/d ratio increases and the cavitation effects appear not clearly marked there are same discrepancies between the one dimensional and the multidimensional approach.

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