scholarly journals The non-modal onset of the tearing instability

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
D. MacTaggart
Keyword(s):  
Initial Conditions ◽  
Linear Equations ◽  
Initial Perturbation ◽  
Transient Growth ◽  
Tearing Mode ◽  
Eigenvalue Spectrum ◽  
Tearing Instability ◽  
Set Up ◽  
Solution Behaviour ◽  
Physical Quantities

We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number$S$increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the$L_{2}$-norm, for the classical set-up of current sheets unstable to the TI, scales as$O(S^{1/4})$on time scales of$O(S^{1/4})$for$S\gg 1$. This behaviour is much faster than the time scale$O(S^{1/2})$when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.

scholarly journals On Kaufmann's theory of the impact of the pianoforte hammer

1920 ◽  
Vol 97 (682) ◽  
pp. 99-110 ◽  
Keyword(s):  
Initial Conditions ◽  
Practical Importance ◽  
Prima Facie ◽  
Point Of View ◽  
Infinite Length ◽  
Modes Of Vibration ◽  
Rigorous Treatment ◽  
The Subject ◽  
Set Up ◽  
The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

FOURTH-ORDER COMPACT SCHEME FOR OPTION PRICING UNDER THE MERTON’S AND KOU’S JUMP-DIFFUSION MODELS

2018 ◽  
Vol 21 (04) ◽  
pp. 1850027 ◽  
Author(s):  
KULDIP SINGH PATEL ◽  
MANI MEHRA
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Linear Equations ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Compact Scheme ◽  
Discrete Problem ◽  
Option Prices ◽  
Fully Discrete ◽  
Fourth Order Compact Scheme

In this paper, a compact scheme with three time levels is proposed to solve the partial integro-differential equation that governs the option prices in jump-diffusion models. In the proposed compact scheme, the second derivative approximation of the unknowns is approximated using the value of these unknowns and their first derivative approximations, thereby allowing us to obtain a tridiagonal system of linear equations for a fully discrete problem. Moreover, the consistency and stability of the proposed compact scheme are proved. Owing to the low regularity of typical initial conditions, a smoothing operator is employed to ensure the fourth-order convergence rate. Numerical illustrations concerning the pricing of European options under the Merton’s and Kou’s jump-diffusion models are presented to validate the theoretical results.

Modeling and prediction for the oxidation efficiency of magnesium sulfite in aeration tank of magnesium-based seawater exhaust gas clean system

2017 ◽  
Vol 233 (1) ◽  
pp. 164-173
Author(s):  
Quan Liu ◽  
Yimin Zhu ◽  
Tie Li ◽  
Xiaojia Tang ◽  
Weifeng Liu ◽  
...  
Keyword(s):  
Flow Field ◽  
Initial Conditions ◽  
Negative Impact ◽  
Fluid Model ◽  
Aeration Tank ◽  
Exhaust Gas ◽  
Clean System ◽  
Physics Modeling ◽  
Set Up ◽  
Oxidation Efficiency

In magnesium-based seawater exhaust gas clean system, the desulfurization by-product, magnesium sulfite (MgSO3), has a negative impact on the ecological environment, which needs to be treated to make harmless. Due to the limited space on board, the aeration oxidation method is used to convert it to magnesium sulfate. Because of the variable size, shape and flow field of aeration tank, it is difficult and expensive to design and verify the oxidation efficiency of the aeration tank by experimental method. In this work, in order to predict the oxidation efficiency accurately, RFlow, a computational fluid dynamics software, was used to analyze the flow field and MgSO3 oxidation reaction in aeration tank. The subdomain technology was adopted for physics modeling and mesh generation of the aeration tank, and the total number of meshes was 285,000. The multi-phase flow field model was set up using the multi-fluid model and dispersive k-ε turbulence model. Under the given initial conditions, the predicted oxidation efficiency was 94.2%. Compared with the results of the actual ship test, the prediction model for MgSO3 oxidation efficiency of the aeration tank is reliable.

scholarly journals Thermal-hydraulic behavior of physical quantities at critical velocities in a nuclear research reactor core channel using plate type fuel

2012 ◽  
Vol 27 (3) ◽  
pp. 229-238
Author(s):  
Ali Sidi ◽  
Zaki Boudali ◽  
Rachid Salhi
Keyword(s):  
Heat Flux ◽  
Critical Velocity ◽  
Nuclear Reactor ◽  
Reactor Core ◽  
Thermal Characteristics ◽  
Nuclear Research ◽  
Coolant Fluid ◽  
Critical Velocities ◽  
Set Up ◽  
Physical Quantities

The thermal-hydraulic study presented here relates to a channel of a nuclear reactor core. This channel is defined as being the space between two fuel plates where a coolant fluid flows. The flow velocity of this coolant should not generate vibrations in fuel plates. The aim of this study is to know the distribution of the temperature in the fuel plates, in the cladding and in the coolant fluid at the critical velocities of Miller, of Wambsganss, and of Cekirge and Ural. The velocity expressions given by these authors are function of the geometry of the fuel plate, the mechanical characteristics of the fuel plate?s material and the thermal characteristics of the coolant fluid. The thermal-hydraulic study is made under steady-state; the equation set-up of the thermal problem is made according to El Wakil and to Delhaye. Once the equation set-up is validated, the three critical velocities are calculated and then used in the calculations of the different temperature profiles. The average heat flux and the critical heat flux are evaluated for each critical velocity and their ratio reported. The recommended critical velocity to be used in nuclear channel calculations is that of Wambsganss. The mathematical model used is more precise and all the physical quantities, when using this critical velocity, stay in safe margins.

Effects of inertia and stratification in incompressible ideal fluids: pressure imbalances by rigid confinement

2013 ◽  
Vol 726 ◽  
pp. 404-438 ◽  
Author(s):  
R. Camassa ◽  
S. Chen ◽  
G. Falqui ◽  
G. Ortenzi ◽  
M. Pedroni
Keyword(s):  
Euler Equations ◽  
Initial Conditions ◽  
Numerical Algorithms ◽  
Wave Dispersion ◽  
Variable Density ◽  
Density Variation ◽  
Fluid Inertia ◽  
Time Dynamics ◽  
Long Wave ◽  
Set Up

AbstractConsequences of density stratification are studied for an ideal (Euler) incompressible fluid, confined to move under gravity between rigid lids but otherwise free to move along horizontal directions. Initial conditions that generate horizontal pressure imbalances in a laterally unbounded domain are examined. The aim is to show analytically the existence of classes of initial data for which total horizontal momentum evolves in time, even though only vertical forces act on the fluid in this set-up. A simple class of such initial conditions, leading to momentum evolution, is identified by systematic asymptotic expansions of the governing inhomogeneous Euler equations in the small-density-variation limit. These results for Euler equations are compared and confirmed with long-wave asymptotic models, which can handle arbitrary density variations and provide closed-form mathematical expressions for limiting cases. In particular, the role of wave dispersion arising from the fluid inertia is captured by the long-wave models, even for short-time dynamics emanating from initial conditions outside the models’ asymptotic range of validity. These results are compared with direct numerical simulations for variable-density Euler fluids, which further validate the numerical algorithms and the analysis.

Role of initial condition and parametric uncertainty in a severe hailstorm forecast

2021 ◽  
Author(s):  
Patrick Kuntze ◽  
Annette Miltenberger ◽  
Corinna Hoose ◽  
Michael Kunz
Keyword(s):  
Initial Conditions ◽  
Weather Prediction ◽  
Parametric Uncertainty ◽  
Radar Data ◽  
Cloud Microphysics ◽  
Initial Condition ◽  
Relative Contribution ◽  
Cloud Properties ◽  
Set Up ◽  
The Impact

<p>Forecasting high impact weather events is a major challenge for numerical weather prediction. Initial condition uncertainty plays a major role but so potentially do uncertainties arising from the representation of physical processes, e.g. cloud microphysics. In this project, we investigate the impact of these uncertainties for the forecast of cloud properties, precipitation and hail of a selected severe convective storm over South-Eastern Germany.<br>To investigate the joint impact of initial condition and parametric uncertainty a large ensemble including perturbed initial conditions and systematic variations in several cloud microphysical parameters is conducted with the ICON model (at 1 km grid-spacing). The comparison of the baseline, unperturbed simulation to satellite, radiosonde, and radar data shows that the model reproduces the key features of the storm and its evolution. In particular also substantial hail precipitation at the surface is predicted. Here, we will present first results including the simulation set-up, the evaluation of the baseline simulation, and the variability of hail forecasts from the ensemble simulation.<br>In a later stage of the project we aim to assess the relative contribution of the introduced model variations to changes in the microphysical evolution of the storm and to the fore- cast uncertainty in larger-scale meteorological conditions.</p>

Headings of UCAV Based on Nash Equilibrium

2018 ◽  
Vol 6 (3) ◽  
pp. 269-276
Author(s):  
Li Dai ◽  
Zheng Xie
Keyword(s):  
Nash Equilibrium ◽  
Linear Equations ◽  
Theoretic Model ◽  
Bounded Curvature ◽  
Smooth Path ◽  
Game Theoretic ◽  
Strategy Game ◽  
Simulation Results ◽  
Game Theoretic Model ◽  
Set Up

Abstract Given n vertices in a plane and UCAV going through each vertex once and only once and then coming back, the objective is to find the direction (heading) of motion in each vertex to minimize the smooth path of bounded curvature. This paper studies the headings of UCAV. First, the optimal headings for two vertices were given. On this basis, an n-player two-strategy game theoretic model was established. In addition, in order to obtain the mixed Nash equilibrium efficiently, n linear equations were set up. The simulation results demonstrated that the headings given in this paper are effective.

scholarly journals Parametric Study of Tsunamis Generated by Earthquakes and Landslides

2019 ◽  
Vol 7 (5) ◽  
pp. 154 ◽  
Author(s):  
Natalia Perez del Postigo Prieto ◽  
Alison Raby ◽  
Colin Whittaker ◽  
Sarah J. Boulton
Keyword(s):  
Predictive Models ◽  
Initial Conditions ◽  
Quality Data ◽  
Tsunami Generation ◽  
Fault Rupture ◽  
Physical Experiments ◽  
Dual Source ◽  
Set Up ◽  
Displacement Scale ◽  
The University

Tsunami generation and propagation mechanisms need to be clearly understood in order to inform predictive models and improve coastal community preparedness. Physical experiments, supported by mathematical models, can potentially provide valuable input data for standard predictive models of tsunami generation and propagation. A unique experimental set-up has been developed to reproduce a coupled-source tsunami generation mechanism: a two-dimensional underwater fault rupture followed by a submarine landslide. The test rig was located in a 20 m flume in the COAST laboratory at the University of Plymouth. The aim of the experiments is to provide quality data for developing a parametrisation of the initial conditions for tsunami generation processes which are triggered by a dual-source. During the test programme, the water depth and the landslide density were varied. The position of the landslide model was tracked and the free surface elevation of the water body was measured. Hence the generated wave characteristics were determined. For a coupled-source scenario, the generated wave is crest led, followed by a trough of smaller amplitude decreasing steadily as it propagates along the flume. The crest amplitude was shown to be influenced by the fault rupture displacement scale, whereas the trough was influenced by the landslide’s relative density.

scholarly journals Kinetic simulations of the coupling between current instabilities and reconnection in thin current sheets

2000 ◽  
Vol 7 (3/4) ◽  
pp. 141-150 ◽  
Author(s):  
T. Wiegelmann ◽  
J. Büchner
Keyword(s):  
Magnetic Reconnection ◽  
Current Flow ◽  
Flow Direction ◽  
Substantial Contribution ◽  
Tearing Mode ◽  
Tearing Modes ◽  
Tearing Instability ◽  
Instability Modes ◽  
Thin Current Sheet ◽  
Spatial Dimensions

Abstract. We investigate the coupling between current and tearing instability modes of a thin current sheet using the particle code GISMO. We identify pure tearing modes (kx≠ 0), instabilities in the current flow direction (ky≠ 0) and general 3D reconnection modes (kx≠ 0 and ky≠ 0). Our results give evidence that the coupling between tearing modes and current instabilities plays an important role for spontaneous magnetic reconnection. These modes give a substantial contribution to magnetic reconnection, additional to the well known 2D tearing mode. When allowing reconnection to occur in three spatial dimensions, a configuration, which was initially invariant in the current How direction, develops into a configuration with no invariant direction.

The Tearing Mode Instability in a Partially Ionized Plasma

1979 ◽  
Vol 3 (6) ◽  
pp. 367-368 ◽  
Author(s):  
N. F. Cramer ◽  
I. J. Donnelly
Keyword(s):  
Magnetic Field ◽  
Star Formation ◽  
Solar Flare ◽  
Experimental Evidence ◽  
Energy Release ◽  
Release Mechanism ◽  
Tearing Mode ◽  
Mode Instability ◽  
Laboratory Plasma ◽  
Tearing Instability

The resistive tearing mode instability is a mechanism that in some cases will render unstable a magnetohydrodynamic equilibrium of a plasma that is ideally stable, i.e. stable if no dissipative oiesses are taken into account. There is much experimental evidence that this instability is the cause of the current disruptions observed in laboratory plasma devices (von Goeler et al. 1974). In the astrophysical context, the instability has been invoked in connection with the solar flare energy release mechanism (Coppi and Friedland 1971) and the problem of the disconnection of the protostar matter from the interstellar magnetic field during star formation (Mestel 1966). In the latter problem the tearing instability gives rise to a much smaller timescale for magnetic reconnection than does ordinary resistive diffusion.

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