scholarly journals Braginskii viscosity on an unstructured, moving mesh accelerated with super-time-stepping

2019 ◽  
Vol 491 (2) ◽  
pp. 2919-2938 ◽  
Author(s):  
Thomas Berlok ◽  
Rüdiger Pakmor ◽  
Christoph Pfrommer
Keyword(s):  
Large Scale ◽  
Moving Mesh ◽  
Time Step ◽  
Time Stepping ◽  
Linearly Polarized ◽  
Anisotropic Transport ◽  
Cluster Mergers ◽  
The Stability ◽  
Large Scale Simulations ◽  
The Magnetic Field

ABSTRACT We present a method for efficiently modelling Braginskii viscosity on an unstructured, moving mesh. Braginskii viscosity, i.e. anisotropic transport of momentum with respect to the direction of the magnetic field, is thought to be of prime importance for studies of the weakly collisional plasma that comprises the intracluster medium (ICM) of galaxy clusters. Here, anisotropic transport of heat and momentum has been shown to have profound consequences for the stability properties of the ICM. Our new method for modelling Braginskii viscosity has been implemented in the moving mesh code arepo. We present a number of examples that serve to test the implementation and illustrate the modified dynamics found when including Braginskii viscosity in simulations. These include (but are not limited to) damping of fast magnetosonic waves, interruption of linearly polarized Alfvén waves by the firehose instability, and the inhibition of the Kelvin–Helmholtz instability by Braginskii viscosity. An explicit update of Braginskii viscosity is associated with a severe time-step constraint that scales with (Δx)2, where Δx is the grid size. In our implementation, this restrictive time-step constraint is alleviated by employing second-order accurate Runge–Kutta–Legendre super-time-stepping. We envision including Braginskii viscosity in future large-scale simulations of Kelvin–Helmholtz unstable cold fronts in cluster mergers and AGN-generated bubbles in central cluster regions.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

Methods for Performance Improvement of Kademlia-based Overlay Networks (Methoden zur Leistungsverbesserung eines Kademlia-basierten Overlay-Netzes)

2007 ◽  
Vol 49 (5) ◽  
Author(s):  
Andreas Binzenhöfer ◽  
Phuoc Tran-Gia ◽  
Holger Schnabel
Keyword(s):  
Performance Improvement ◽  
Large Scale ◽  
Overlay Networks ◽  
P2p Networks ◽  
P2p Systems ◽  
Business Applications ◽  
Open Questions ◽  
The Stability ◽  
Large Scale Simulations ◽  
Unstable States

SummaryStructured peer-to-peer (p2p) networks are highly distributed systems with a potential to support business applications. There are numerous different suggestions on how to implement such systems. However, before legal p2p systems can become mainstream they need to offer improved efficiency, robustness, and stability. While Chord is the most researched and best understood mechanism, the Kademlia algorithm is widely-used in deployed applications. There are still many open questions concerning the performance of the latter. In this paper we identify the main problems of Kademlia by large scale simulations and present modifications which help to avoid those problems. This way, we are able to significantly improve the performance and robustness of Kademlia-based applications, especially in times of churn and in unstable states. In particular, we show how to increase the stability of the overlay, make searches more efficient, and adapt the maintenance traffic to the current churn rate in a self-organizing way.

scholarly journals Super-Time-Stepping Scheme for Option Pricing

2020 ◽  
Vol 13 (13) ◽  
pp. 51-54
Author(s):  
Kedar Nath Uprety ◽  
Harithar Khanal ◽  
Ananta Upreti
Keyword(s):  
Option Pricing ◽  
Euler Method ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Time Stepping ◽  
Black Scholes ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Explicit Finite Difference Method

We solve the Black - Scholes equation for option pricing numerically using an Explicit finite difference method. To overcome the stability restriction of the explicit scheme for parabolic partial differential equations in the time step size Courant-Friedrichs-Lewy (CFL) condition, we employ a Super Time Stepping (STS) strategy based on modified Chebyshev polynomial. The numerical results show that the STS scheme boasts of large efficiency gains compared to the standard explicit Euler method.

Efficient Event-Driven Simulation of Large Networks of Spiking Neurons and Dynamical Synapses

2000 ◽  
Vol 12 (10) ◽  
pp. 2305-2329 ◽  
Author(s):  
Maurizio Mattia ◽  
Paolo Del Giudice
Keyword(s):  
Large Scale ◽  
Spiking Neurons ◽  
New Approach ◽  
Computational Load ◽  
Synaptic Structure ◽  
Event Driven ◽  
Synaptic Dynamics ◽  
And Performance ◽  
The Stability ◽  
Large Scale Simulations

A simulation procedure is described for making feasible large-scale simulations of recurrent neural networks of spiking neurons and plastic synapses. The procedure is applicable if the dynamic variables of both neurons and synapses evolve deterministically between any two successive spikes. Spikes introduce jumps in these variables, and since spike trains are typically noisy, spikes introduce stochasticity into both dynamics. Since all events in the simulation are guided by the arrival of spikes, at neurons or synapses, we name this procedure event-driven. The procedure is described in detail, and its logic and performance are compared with conventional (synchronous) simulations. The main impact of the new approach is a drastic reduction of the computational load incurred upon introduction of dynamic synaptic efficacies, which vary organically as a function of the activities of the pre- and postsynaptic neurons. In fact, the computational load per neuron in the presence of the synaptic dynamics grows linearly with the number of neurons and is only about 6% more than the load with fixed synapses. Even the latter is handled quite efficiently by the algorithm. We illustrate the operation of the algorithm in a specific case with integrate-and-fire neurons and specific spike-driven synaptic dynamics. Both dynamical elements have been found to be naturally implementable in VLSI. This network is simulated to show the effects on the synaptic structure of the presentation of stimuli, as well as the stability of the generated matrix to the neural activity it induces.

scholarly journals A Time-Stepping DPG Scheme for the Heat Equation

2017 ◽  
Vol 17 (2) ◽  
pp. 237-252 ◽  
Author(s):  
Thomas Führer ◽  
Norbert Heuer ◽  
Jhuma Sen Gupta
Keyword(s):  
Heat Equation ◽  
Order Approximation ◽  
Test Functions ◽  
Optimal Test ◽  
Time Step ◽  
Time Stepping ◽  
Backward Euler ◽  
The Stability ◽  
Convergence Orders ◽  
Theoretical Results

AbstractWe introduce and analyze a discontinuous Petrov–Galerkin method with optimal test functions for the heat equation. The scheme is based on the backward Euler time stepping and uses an ultra-weak variational formulation at each time step. We prove the stability of the method for the field variables (the original unknown and its gradient weighted by the square root of the time step) and derive a Céa-type error estimate. For low-order approximation spaces this implies certain convergence orders when time steps are not too small in comparison with mesh sizes. Some numerical experiments are reported to support our theoretical results.

On a Large Time-Stepping Method for the Swift-Hohenberg Equation

2016 ◽  
Vol 8 (6) ◽  
pp. 992-1003 ◽  
Author(s):  
Zhengru Zhang ◽  
Yuanzi Ma
Keyword(s):  
Steady State ◽  
Numerical Experiments ◽  
Stability Property ◽  
Large Time ◽  
Time Step ◽  
Time Stepping ◽  
Time Simulation ◽  
Large Time Step ◽  
Step Algorithm ◽  
The Stability

AbstractThe main purpose of this work is to contrast and analyze a large time-stepping numerical method for the Swift-Hohenberg (SH) equation. This model requires very large time simulation to reach steady state, so developing a large time step algorithm becomes necessary to improve the computational efficiency. In this paper, a semi-implicit Euler schemes in time is adopted. An extra artificial term is added to the discretized system in order to preserve the energy stability unconditionally. The stability property is proved rigorously based on an energy approach. Numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches by comparing with the classical scheme.

scholarly journals Parallel magnetic field suppresses dissipation in superconducting nanostrips

2017 ◽  
Vol 114 (48) ◽  
pp. E10274-E10280 ◽  
Author(s):  
Yong-Lei Wang ◽  
Andreas Glatz ◽  
Gregory J. Kimmel ◽  
Igor S. Aranson ◽  
Laxman R. Thoutam ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Vortex Motion ◽  
Experimental Studies ◽  
Resistive State ◽  
Parallel Magnetic Field ◽  
Ginzburg Landau ◽  
Type Ii Superconductors ◽  
Large Scale Simulations ◽  
The Magnetic Field

The motion of Abrikosov vortices in type-II superconductors results in a finite resistance in the presence of an applied electric current. Elimination or reduction of the resistance via immobilization of vortices is the “holy grail” of superconductivity research. Common wisdom dictates that an increase in the magnetic field escalates the loss of energy since the number of vortices increases. Here we show that this is no longer true if the magnetic field and the current are applied parallel to each other. Our experimental studies on the resistive behavior of a superconducting Mo0.79Ge0.21 nanostrip reveal the emergence of a dissipative state with increasing magnetic field, followed by a pronounced resistance drop, signifying a reentrance to the superconducting state. Large-scale simulations of the 3D time-dependent Ginzburg–Landau model indicate that the intermediate resistive state is due to an unwinding of twisted vortices. When the magnetic field increases, this instability is suppressed due to a better accommodation of the vortex lattice to the pinning configuration. Our findings show that magnetic field and geometrical confinement can suppress the dissipation induced by vortex motion and thus radically improve the performance of superconducting materials.

scholarly journals Stability Analysis of Decoupled Time-stepping Schemes for the Specialized Conduction System/myocardium Coupled Problem in Cardiology

2017 ◽  
Vol 12 (5) ◽  
pp. 208-239 ◽  
Author(s):  
S. Mani Aouadi ◽  
W. Mbarki ◽  
N. Zemzemi
Keyword(s):  
Time Discretization ◽  
Conduction System ◽  
Splitting Schemes ◽  
Time Step ◽  
Time Stepping ◽  
Time Splitting ◽  
Coupling Terms ◽  
The Stability ◽  
Fully Coupled ◽  
Purkinje Network

The Purkinje network is the rapid conduction system in the heart. It ensures the physiological spread of the electrical wave in the ventricles. In this work, we consider a problem that models the coupling between the Purkinje network and the myocardium. We first prove the stability of the space semi-discretized problem. Then we present four different strategies for solving the Purkinje/ myocardium coupling. The strategies are based on different time discretization of the coupling terms. The first scheme is fully coupled, where the coupling terms are considered implicit. The second and the third schemes are based on Gauss-Seidel time-splitting schemes where one coupling term is considered explicit and the other is implicit. The last is a Jacobi-like time-splitting scheme where both coupling terms are considered explicit. Our main result is the proof of the stability of the three considered schemes under the same restriction on the time step. Moreover, we show that the energy of the problem is slightly affected by the time-splitting schemes. We illustrate the theoretical result by different numerical simulations in 2D. We also conduct 3D simulations using physiologically detailed ionic models.

scholarly journals Transition from eruptive to confined flares in the same active region

2017 ◽  
Vol 601 ◽  
pp. A26 ◽  
Author(s):  
F. P. Zuccarello ◽  
R. Chandra ◽  
B. Schmieder ◽  
G. Aulanier ◽  
R. Joshi
Keyword(s):  
Magnetic Field ◽  
Active Region ◽  
Solar Atmosphere ◽  
Large Scale ◽  
Magnetic Energy ◽  
Direct Result ◽  
Magnetic Field Model ◽  
Large Scale Field ◽  
The Stability ◽  
The Magnetic Field

Context. Solar flares are sudden and violent releases of magnetic energy in the solar atmosphere that can be divided into two classes: eruptive flares, where plasma is ejected from the solar atmosphere resulting in a coronal mass ejection (CME), and confined flares, where no CME is associated with the flare. Aims. We present a case study showing the evolution of key topological structures, such as spines and fans, which may determine the eruptive versus non-eruptive behavior of the series of eruptive flares followed by confined flares, which all originate from the same site. Methods. To study the connectivity of the different flux domains and their evolution, we compute a potential magnetic field model of the active region. Quasi-separatrix layers are retrieved from the magnetic field extrapolation. Results. The change in behavior of the flares from one day to the next – from eruptive to confined – can be attributed to the change in orientation of the magnetic field below the fan with respect to the orientation of the overlaying spine rather than an overall change in the stability of the large-scale field. Conclusions. Flares tend to be more confined when the field that supports the filament and the overlying field gradually becomes less anti-parallel as a direct result of changes in the photospheric flux distribution, being themselves driven by continuous shearing motions of the different magnetic flux concentrations.

Evolution of Large-Scale Coronal Structures

1994 ◽  
Vol 144 ◽  
pp. 29-33
Author(s):  
P. Ambrož
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Large Scale ◽  
Coronal Magnetic Field ◽  
Source Surface ◽  
Solar Cycles ◽  
Characteristic Relationship ◽  
The Magnetic Field ◽  
Coronal Structures

AbstractThe large-scale coronal structures observed during the sporadically visible solar eclipses were compared with the numerically extrapolated field-line structures of coronal magnetic field. A characteristic relationship between the observed structures of coronal plasma and the magnetic field line configurations was determined. The long-term evolution of large scale coronal structures inferred from photospheric magnetic observations in the course of 11- and 22-year solar cycles is described.Some known parameters, such as the source surface radius, or coronal rotation rate are discussed and actually interpreted. A relation between the large-scale photospheric magnetic field evolution and the coronal structure rearrangement is demonstrated.

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