Low-frequency linear response of a cylindrical tokamak with arbitrary cross-section to ‘helical’ perturbations

1980 ◽  
Vol 24 (2) ◽  
pp. 229-236 ◽  
Author(s):  
Torkil H. Jensen ◽  
Ming S. Chu
Keyword(s):  
Cross Section ◽  
Time Scale ◽  
Low Frequency ◽  
Arbitrary Cross Section ◽  
Fast Time ◽  
Tearing Mode ◽  
Slow Time ◽  
Slow Time Scale ◽  
Stable Plasma

Current driven, ‘helical’ (non-axisymmetric) modes of a tokamak with arbitrary cross-section are considered in the straight (cylindrical) geometry approximation. The plasma is considered surrounded by a resistive wall. The plasma may be unstable on a fast time-scale, namely the MHD or tearing mode time-scale, on a slow time-scale given by the wall properties or it may be stable. The formalism given in this paper allows determination of stability by relatively simple numerical means. In the case of instability on the slow time-scale, the formalism allows determination of growth rates and mode structures. Since the formalism is an eigenvalue formalism with orthogonal eigenfunctions, it is well suited for calculation of the effects on a stable plasma of slow error fields caused by externally driven error currents flowing predominantly in the direction of the ignorable co-ordinate.

The Dance of the Interneurons: How Inhibition Facilitates Fast Compressible and Reversible Learning in Hippocampus

2018 ◽  
Author(s):  
Wilten Nicola ◽  
Claudia Clopath
Keyword(s):  
Time Scale ◽  
State Of The Art ◽  
Fast Time ◽  
Slow Time ◽  
Fast Time Scale ◽  
Slow Time Scale ◽  
Spike Sequences ◽  
Incoming Information ◽  
Spiking Networks ◽  
Inhibitory Networks

AbstractThe hippocampus is capable of rapidly learning incoming information, even if that information is only observed once. Further, this information can be replayed in a compressed format in either forward or reversed modes during Sharp Wave Ripples (SPW-R). We leveraged state-of-the-art techniques in training recurrent spiking networks to demonstrate how primarily inhibitory networks of neurons in CA3 and CA1 can: 1) generate internal theta sequences or “time-cells” to bind externally elicited spikes in the presence of septal inhibition, 2) reversibly compress the learned representation in the form of a SPW-R when septal inhibition is removed, 3) generate and refine gamma-assemblies during SPW-R mediated compression, and 4) regulate the inter-ripple-interval timing between SPW-R’s in ripple clusters. From the fast time scale of neurons to the slow time scale of behaviors, inhibitory networks serve as the scaffolding for one-shot learning by replaying, reversing, refining, and regulating spike sequences.

scholarly journals Understanding the Overdispersed Molecular Clock

Genetics ◽  
2000 ◽  
Vol 154 (3) ◽  
pp. 1403-1417 ◽  
Author(s):  
David J Cutler
Keyword(s):  
Molecular Evolution ◽  
Molecular Clock ◽  
Time Scale ◽  
Population Parameter ◽  
Deleterious Mutations ◽  
Slow Time ◽  
Slow Time Scale ◽  
Key Population ◽  
Protein Encoding ◽  
Rates Of Molecular Evolution

Abstract Rates of molecular evolution at some protein-encoding loci are more irregular than expected under a simple neutral model of molecular evolution. This pattern of excessive irregularity in protein substitutions is often called the “overdispersed molecular clock” and is characterized by an index of dispersion, R(T) > 1. Assuming infinite sites, no recombination model of the gene R(T) is given for a general stationary model of molecular evolution. R(T) is shown to be affected by only three things: fluctuations that occur on a very slow time scale, advantageous or deleterious mutations, and interactions between mutations. In the absence of interactions, advantageous mutations are shown to lower R(T); deleterious mutations are shown to raise it. Previously described models for the overdispersed molecular clock are analyzed in terms of this work as are a few very simple new models. A model of deleterious mutations is shown to be sufficient to explain the observed values of R(T). Our current best estimates of R(T) suggest that either most mutations are deleterious or some key population parameter changes on a very slow time scale. No other interpretations seem plausible. Finally, a comment is made on how R(T) might be used to distinguish selective sweeps from background selection.

Graphical-Numerical Solution of Problems of Saint-Venant Torsion and Bending

1953 ◽  
Vol 20 (3) ◽  
pp. 321-326
Author(s):  
B. A. Boley
Keyword(s):  
Cross Section ◽  
Stress Function ◽  
Arbitrary Cross Section ◽  
Successive Approximations ◽  
Shear Stresses ◽  
Shearing Stress ◽  
First Approximation ◽  
Difference Form ◽  
Bending Of Beams

Abstract A simple successive-approximations procedure for the solution of the problems of Saint-Venant torsion and bending of beams of arbitrary cross section is presented. The shear stresses in a cross section of the beam are first calculated from the formulas valid for thin-walled sections, on the basis of an assumed set of lines of shearing stress. From these a first approximation to the stress function of either the torsion or the bending problem is found. The second approximation to the stress function is then obtained from the governing equation of the problem, expressed in finite-difference form; this in turn allows the determination of an improved set of lines of shearing stress, and hence of the shearing stress itself. The procedure can be repeated until the results of two successive steps are sufficiently close. Applications are presented for a beam cross section for which the exact solutions are known, and it is shown that no further difficulties arise in applications to more complicated shapes.

A New Model for Long-Term Stochastic Analysis and Prediction—Part I: Theoretical Background

1992 ◽  
Vol 36 (01) ◽  
pp. 1-16
Author(s):  
G. A. Athanassoulis ◽  
P. B. Vranas ◽  
T. H. Soukissian
Keyword(s):  
Time Scale ◽  
Random Function ◽  
Spectral Characteristics ◽  
Time History ◽  
Time Variable ◽  
Sea Surface ◽  
Surface Elevation ◽  
Fast Time ◽  
Slow Time

A new approach for calculating the long-term statistics of sea waves is proposed. A rational long-term stochastic model is introduced which recognizes that the wave climate at a given site in the ocean consists of a random succession of individual sea states, each sea state possessing its own duration and intensity. This model treats the sea-surface elevation as a random function of a "fast" time variable, and the time history of the spectral characteristics of the successive sea states as a random function of a "slow" time variable. By developing an appropriate conceptual framework, it becomes possible to express various probabilistic characteristics of the sea-surface elevation, which are sensible only in the fast-time scale, in terms of the statistics of sea-states duration and intensity, which is meaningful only in the slow-time scale. As an example, we study the random quantity MU(T) = "number of maxima of the sea-surface elevation lying above the level u and occurring during a long-term time period [0,T]." Exploiting the proposed framework, it is shown that, under certain clearly defined assumptions, Mu(T) can be given the structure of a renewal-reward (cumulative) process, whose interarrival times correspond to the duration of successive sea states. Thus, using renewal theory, the complete characterization of the probability structure of MU(T) is obtained. As a consequence, the long-term probability distribution function of the individual wave height is rigorously defined and calculated. The relation of the present results with corresponding ones previously obtained is thoroughly discussed. The proposed model can be extended twofold: either by replacing some of the simplifying assumptions by more realistic ones, or by extending the model for treating the corresponding problems for ship and structures responses.

Parameter Estimation in a Nonlinear Vibrating System Using an Observer for an Extended System

1999 ◽  
Author(s):  
Anindya Chatterjee ◽  
Joseph P. Cusumano
Keyword(s):  
Parameter Estimation ◽  
Time Scale ◽  
Asymptotic Methods ◽  
System Response ◽  
Parameter Estimates ◽  
Fast Time ◽  
State Variables ◽  
Slow Time ◽  
Unknown Parameters ◽  
Lipschitz Continuous

Abstract We present a new observer-based method for parameter estimation for nonlinear oscillatory mechanical systems where the unknown parameters appear linearly (they may each be multiplied by bounded and Lipschitz continuous but otherwise arbitrary, possibly nonlinear, functions of the oscillatory state variables and time). The oscillations in the system may be periodic, quasiperiodic or chaotic. The method is also applicable to systems where the parameters appear nonlinearly, provided a good initial estimate of the parameter is available. The observer requires measurements of displacements. It estimates velocities on a fast time scale, and the unknown parameters on a slow time scale. The fast and slow time scales are governed by a single small parameter ϵ. Using asymptotic methods including the method of averaging, it is shown that the observer’s estimates of the unknown parameters converge like e−ϵt where t is time, provided the system response is such that the coefficient-functions of the unknown parameters are not close to being linearly dependent. It is also shown that the method is robust in that small errors in the model cause small errors in the parameter estimates. A numerical example is provided to demonstrate the effectiveness of the method.

Sign in / Sign up

Export Citation Format

Share Document