scholarly journals Mildly relativistic magnetized shocks in electron-ion plasmas I. Electromagnetic shock structure

2020 ◽  
Author(s):  
Arianna Ligorini ◽  
Jacek Niemiec ◽  
Oleh Kobzar ◽  
Masanori Iwamoto ◽  
Artem Bohdan ◽  
...  
Keyword(s):  
Electromagnetic Waves ◽  
Large Scale ◽  
Scale Effects ◽  
Mean Field ◽  
Wave Amplification ◽  
Particle In Cell ◽  
Relativistic Shocks ◽  
Theoretical Predictions ◽  
The Mean ◽  
Effective Wave

Abstract Mildly relativistic shocks in magnetized electron-ion plasmas are investigated with 2D kinetic particle-in-cell simulations of unprecedentedly high resolution and large scale for conditions that may be found at internal shocks in blazar cores. Ion-scale effects cause corrugations along the shock surface whose properties somewhat depend on the configuration of the mean perpendicular magnetic field, that is either in or out of the simulation plane. We show that the synchrotron maser instability persists to operate in mildly relativistic shocks in agreement with theoretical predictions and produces coherent emission of upstream-propagating electromagnetic waves. Shock front ripples are excited in both mean-field configurations and they engender effective wave amplification. The interaction of these waves with upstream plasma generates electrostatic wakefields.

scholarly journals Derivation and precision of mean field electrodynamics with mesoscale fluctuations

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
Hongzhe Zhou ◽  
Eric G. Blackman ◽  
Luke Chamandy
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Scale Separation ◽  
Precision Error ◽  
Theoretical Predictions ◽  
Wide Scale ◽  
The Mean ◽  
Scale Properties ◽  
Galactic Dynamos ◽  
Correction Terms

Mean field electrodynamics (MFE) facilitates practical modelling of secular, large scale properties of astrophysical or laboratory systems with fluctuations. Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages. Often however, real systems do not exhibit such scale separation. This raises two questions: (I) What are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (II) How precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a filtering contribution from differences in the way observations and theory are projected through the measurement kernel. Minimizing the sum of these contributions can produce an optimal scale of averaging that makes the theory maximally precise. The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work.

scholarly journals The mean tilt of sunspot bipolar regions: theory, simulations and comparison with observations

2020 ◽  
Vol 495 (1) ◽  
pp. 238-248
Author(s):  
N Kleeorin ◽  
N Safiullin ◽  
K Kuzanyan ◽  
I Rogachevskii ◽  
A Tlatov ◽  
...  
Keyword(s):  
Coriolis Force ◽  
Large Scale ◽  
Mean Field ◽  
Wolf Number ◽  
Additional Contribution ◽  
Solar Cycles ◽  
Dynamo Theory ◽  
Large Scale Magnetic Field ◽  
Budget Equation ◽  
The Mean

ABSTRACT A theory of the mean tilt of sunspot bipolar regions (the angle between a line connecting the leading and following sunspots and the solar equator) is developed. A mechanism of formation of the mean tilt is related to the effect of the Coriolis force on meso-scale motions of super-granular convection and large-scale meridional circulation. The balance between the Coriolis force and the Lorentz force (the magnetic tension) determines an additional contribution caused by the large-scale magnetic field to the mean tilt of the sunspot bipolar regions at low latitudes. The latitudinal dependence of the solar differential rotation affects the mean tilt, which can explain deviations from Joy’s law for the sunspot bipolar regions at high latitudes. The theoretical results obtained and the results from numerical simulations based on the non-linear mean-field dynamo theory, which takes into account conservation of the total magnetic helicity and the budget equation for the evolution of the Wolf number density, are in agreement with observational data of the mean tilt of sunspot bipolar regions over individual solar cycles 15–24.

scholarly journals Characterizing the dynamo in a radiatively inefficient accretion flow

2020 ◽  
Vol 494 (4) ◽  
pp. 4854-4866 ◽  
Author(s):  
Prasun Dhang ◽  
Abhijit Bendre ◽  
Prateek Sharma ◽  
Kandaswamy Subramanian
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Compact Object ◽  
Rotational Instability ◽  
Test Field ◽  
Poloidal Magnetic Field ◽  
Accretion Flow ◽  
The Mean ◽  
Value Decomposition

ABSTRACT We explore the magneto-rotational instability (MRI)-driven dynamo in a radiatively inefficient accretion flow (RIAF) using the mean field dynamo paradigm. Using singular value decomposition (SVD) we obtain the least-squares fitting dynamo coefficients α and γ by comparing the time series of the turbulent electromotive force and the mean magnetic field. Our study is the first one to show the poloidal distribution of these dynamo coefficients in global accretion flow simulations. Surprisingly, we obtain a high value of the turbulent pumping coefficient γ, which transports the mean magnetic flux radially outwards. This would have implications for the launching of magnetized jets that are produced efficiently in presence a large-scale poloidal magnetic field close to the compact object. We present a scenario of a truncated disc beyond the RIAF where a large-scale dynamo-generated poloidal magnetic field can aid jet launching close to the black hole. Magnitude of all the calculated coefficients decreases with radius. Meridional variations of αϕϕ, responsible for toroidal to poloidal field conversion, is very similar to that found in shearing box simulations using the ‘test field’ (TF) method. By estimating the relative importance of α-effect and shear, we conclude that the MRI-driven large-scale dynamo, which operates at high latitudes beyond a disc scale height, is essentially of the α − Ω type.

scholarly journals Mean Waiting Time in Large-Scale and Critically Loaded Power of d Load Balancing Systems

2021 ◽  
Vol 5 (2) ◽  
pp. 1-34
Author(s):  
Tim Hellemans ◽  
Benny Van Houdt
Keyword(s):  
Load Balancing ◽  
Waiting Time ◽  
Large Scale ◽  
Mean Field ◽  
Arrival Rate ◽  
Mean Field Limit ◽  
Mean Waiting Time ◽  
Constant Rate ◽  
Finite Set ◽  
The Mean

Mean field models are a popular tool used to analyse load balancing policies. In some exceptional cases the waiting time distribution of the mean field limit has an explicit form. In other cases it can be computed as the solution of a set of differential equations. In this paper we study the limit of the mean waiting time E[Wλ] as the arrival rate λ approaches 1 for a number of load balancing policies in a large-scale system of homogeneous servers which finish work at a constant rate equal to one and exponential job sizes with mean 1 (i.e. when the system gets close to instability). As E[Wλ] diverges to infinity, we scale with -log(1-λ) and present a method to compute the limit limλ-> 1- -E[Wλ]/l(1-λ). We show that this limit has a surprisingly simple form for the load balancing algorithms considered. More specifically, we present a general result that holds for any policy for which the associated differential equation satisfies a list of assumptions. For the well-known LL(d) policy which assigns an incoming job to a server with the least work left among d randomly selected servers these assumptions are trivially verified. For this policy we prove the limit is given by 1/d-1. We further show that the LL(d,K) policy, which assigns batches of K jobs to the K least loaded servers among d randomly selected servers, satisfies the assumptions and the limit is equal to K/d-K. For a policy which applies LL(di) with probability pi, we show that the limit is given by 1/ ∑i pi di - 1. We further indicate that our main result can also be used for load balancers with redundancy or memory. In addition, we propose an alternate scaling -l(pλ) instead of -l(1-λ), where pλ is adapted to the policy at hand, such that limλ-> 1- -E[Wλ]/l(1-λ)=limλ-> 1- -E[Wλ]/l(pλ), where the limit limλ-> 0+ -E[Wλ]/l(pλ) is well defined and non-zero (contrary to limλ-> 0+ -E[Wλ]/l(1-λ)). This allows to obtain relatively flat curves for -E[Wλ]/l(pλ) for λ ∈ [0,1] which indicates that the low and high load limits can be used as an approximation when λ is close to one or zero. Our results rely on the earlier proven ansatz which asserts that for certain load balancing policies the workload distribution of any finite set of queues becomes independent of one another as the number of servers tends to infinity.

scholarly journals Fluctuations in an Equilibrium Convective Ensemble. Part I: Theoretical Formulation

2006 ◽  
Vol 63 (8) ◽  
pp. 1996-2004 ◽  
Author(s):  
George C. Craig ◽  
Brenda G. Cohen
Keyword(s):  
Large Scale ◽  
Companion Paper ◽  
Cumulus Clouds ◽  
Theoretical Formulation ◽  
Mass Fluxes ◽  
Theoretical Predictions ◽  
Cloud Resolving Model ◽  
Total Mass Flux ◽  
The Mean ◽  
Convective Cells

Abstract To provide a theoretical basis for stochastic parameterization of cumulus convection, the equilibrium fluctuations of a field of cumulus clouds under homogeneous large-scale forcing are derived statistically, using the Gibbs canonical ensemble from statistical mechanics. In the limit of noninteracting convective cells, the statistics of these convective fluctuations can be written in terms of the large-scale, externally constrained properties of the system. Using this framework, the probability density function of individual cloud mass fluxes is shown to be exponential. An analytical expression for the distribution function of total mass flux over a region of given size is also derived, and the variance of this distribution is found to be inversely related to the mean number of clouds in the ensemble. In a companion paper, these theoretical predictions are tested against cloud resolving model data.

scholarly journals Analysis of the temperature component of the combined standard uncertainty of the refractive index according to the test data of the control system for meteorological parameters developed for the Lyptsi geodetic polygon

2021 ◽  
pp. 34-38
Author(s):  
Pavel Neyezhmakov ◽  
Alexander Prokopov ◽  
Tatiana Panasenko ◽  
Andrii Shloma
Keyword(s):  
Refractive Index ◽  
Electromagnetic Waves ◽  
Large Scale ◽  
Meteorological Parameters ◽  
Accurate Determination ◽  
Practical Implementation ◽  
Main Task ◽  
Accuracy Of Measurements ◽  
Length Measurements ◽  
The Mean

The National Scientific Centre “Institute of Metrology” is actively involved in the implementation of a number of international projects under the EMPIR programme. One of such joint projects is the EMPIR 18SIB01 GeoMetre research project “Large-scale dimensional measurements for geodesy”. The overall goal of the project is to ensure traceability of length measurements – from the measurement standard of the unit of length to long distances typical for geodetic measurements. As a result of the project, it is necessary to provide length measurements of at least 5 km with an expanded uncertainty of no more than 1 mm. The main task of the NSC “Institute of Metrology” within this project is the development, research and practical implementation of methods and means of accounting for the influence of the earth’s atmosphere on the results of measurements of long distances in geodesy, carried out using electromagnetic waves in the optical range. When performing the section Task 1.4 of the project, new methods of highly accurate determination of the mean integral refractive index of air, used as a correction taking into account the influence of the atmosphere on the measurement results, are justified. Requirements for the accuracy of measurements of meteorological parameters at discrete points of the baseline are formulated, which are necessary to determine the mean integral refractive index. That is, the requirements for the metrological characteristics of temperature, pressure and humidity sensors are determined. The article discusses the results of the development, manufacture and testing of the sensors for temperature measurement. It is shown that the created sensors meet the requirements of the GeoMetre project.

scholarly journals A state-dependent mean-field formalism to model different activity states in conductance based networks of spiking neurons

2019 ◽  
Author(s):  
Cristiano Capone ◽  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Maurizio Mattia ◽  
Alain Destexhe
Keyword(s):  
Population Dynamics ◽  
High Performance ◽  
Large Scale ◽  
Mean Field ◽  
Analytic Solutions ◽  
Slow Oscillations ◽  
State Dependent ◽  
The Mean ◽  
Field Formalism ◽  
High Performance Computers

AbstractHigher and higher interest has been shown in the recent years to large scale spiking simulations of cerebral neuronal networks, coming both from the presence of high performance computers and increasing details in the experimental observations. In this context it is important to understand how population dynamics are generated by the designed parameters of the networks, that is the question addressed by mean field theories. Despite analytic solutions for the mean field dynamics has already been proposed generally for current based neurons (CUBA), the same for more realistic neural properties, such as conductance based (COBA) network of adaptive exponential neurons (AdEx), a complete analytic model has not been achieved yet. Here, we propose a novel principled approach to map a COBA on a CUBA. Such approach provides a state-dependent approximation capable to reliably predict the firing rate properties of an AdEx neuron with non-instantaneous COBA integration. We also applied our theory to population dynamics, predicting the dynamical properties of the network in very different regimes, such as asynchronous irregular (AI) and synchronous irregular (SI) (slow oscillations, SO).This results show that a state-dependent approximation can be successfully introduced in order to take into account the subtle effects of COBA integration and to deal with a theory capable to correctly predicts the activity in regimes of alternating states like slow oscillations.

scholarly journals Biologically realistic mean-field models of conductancebased networks of spiking neurons with adaptation

2018 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

AbstractAccurate population models are needed to build very large scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of Adaptive exponential Integrate and fire excitatory and inhibitory neurons. Using a Master Equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable to correctly predict the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high and low activity states alternate (UP-DOWN state dynamics), leading to slow oscillations. We conclude that such mean-field models are “biologically realistic” in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large scale models involving multiple brain areas.

scholarly journals Magnetic Field Amplification by a Plasma Cavitation Instability in Relativistic Shock Precursors

2022 ◽  
Vol 924 (1) ◽  
pp. L12
Author(s):  
J. R. Peterson ◽  
S. Glenzer ◽  
F. Fiuza
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Gamma Ray ◽  
Beam Current ◽  
Particle In Cell ◽  
Field Amplification ◽  
Relativistic Shocks ◽  
Wide Range ◽  
Cavitation Instability ◽  
Shock Precursor

Abstract Plasma streaming instabilities play an important role in magnetic field amplification and particle acceleration in relativistic shocks and their environments. However, in the far shock precursor region where accelerated particles constitute a highly relativistic and dilute beam, streaming instabilities typically become inefficient and operate at very small scales when compared to the gyroradii of the beam particles. We report on a plasma cavitation instability that is driven by dilute relativistic beams and can increase both the magnetic field strength and coherence scale by orders of magnitude to reach near-equipartition values with the beam energy density. This instability grows after the development of the Weibel instability and is associated with the asymmetric response of background leptons and ions to the beam current. The resulting net inductive electric field drives a strong energy asymmetry between positively and negatively charged beam species. Large-scale particle-in-cell simulations are used to verify analytical predictions for the growth and saturation level of the instability and indicate that it is robust over a wide range of conditions, including those associated with pair-loaded plasmas. These results can have important implications for the magnetization and structure of shocks in gamma-ray bursts, and more generally for magnetic field amplification and asymmetric scattering of relativistic charged particles in plasma astrophysical environments.

Performance Analysis of Work Stealing in Large-scale Multithreaded Computing

2021 ◽  
Vol 6 (2) ◽  
pp. 1-28
Author(s):  
Nikki Sonenberg ◽  
Grzegorz Kielanski ◽  
Benny Van Houdt
Keyword(s):  
Fixed Point ◽  
Large Scale ◽  
Field Model ◽  
Unique Fixed Point ◽  
Mean Field ◽  
Response Time Distribution ◽  
Mean Field Model ◽  
Work Stealing ◽  
Poisson Arrivals ◽  
The Mean

Randomized work stealing is used in distributed systems to increase performance and improve resource utilization. In this article, we consider randomized work stealing in a large system of homogeneous processors where parent jobs spawn child jobs that can feasibly be executed in parallel with the parent job. We analyse the performance of two work stealing strategies: one where only child jobs can be transferred across servers and the other where parent jobs are transferred. We define a mean-field model to derive the response time distribution in a large-scale system with Poisson arrivals and exponential parent and child job durations. We prove that the model has a unique fixed point that corresponds to the steady state of a structured Markov chain, allowing us to use matrix analytic methods to compute the unique fixed point. The accuracy of the mean-field model is validated using simulation. Using numerical examples, we illustrate the effect of different probe rates, load, and different child job size distributions on performance with respect to the two stealing strategies, individually, and compared to each other.

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