MICROWAVE MEASUREMENTS OF STEADY-STATE AND DECAYING PLASMAS
Microwave measurements of steady-state and decaying plasma
STEADY STATE↗
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Results for “Steady state”
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Inner bremsstrahlung as a source of X-rays in the steady-state universe.
Consideration of the compatibility of matter creation in steady-state cosmology with certain X-ray observations. It is shown that, because of inner bremsstrahlung from neutron decay, the steady-state universe with neutron creation in diffuse regions is inconsistent with X-ray observations around 100 keV, unless the particle density of the universe is less than 0.1 per cu m.
Petrosian, V.↗
A hybrid multigrid technique for computing steady-state solutions to supersonic flows
Recently, Li and Sanders have introduced a class of finite difference schemes to approximate generally discontinuous solutions to hyperbolic systems of conservation laws. These equations have the form together with relevant boundary conditions. When modelling hypersonic spacecraft reentry, the differential equations above are frequently given by the compressible Euler equations coupled with a nonequilibrium chemistry model. For these applications, steady state solutions are often sought. Many tens (to hundreds) of super computer hours can be devoted to a single three space dimensional simulation. The primary difficulty is the inability to rapidly and reliably capture the steady state. In these notes, we demonstrate that a particular variant from the schemes presented can be combined with a particular multigrid approach to capture steady state solutions to the compressible Euler equations in one space dimension. We show that the rate of convergence to steady state coming from this multigrid implementation is vastly superior to the traditional approach of artificial time relaxation. Moreover, we demonstrate virtual grid independence. That is, the rate of convergence does not depend on the degree of spatial grid refinement.
Sanders, Richard↗
Analytical comparison of transient and steady state visual evoked cortical potentials
To better describe the linear-dynamic properties of the human visual-cortical response system, transient and steady state Visual Evoked Response Potentials (VERP) were observed. The stimulus presentation device provided both the evoking stimulus (flickering or pulsing lights) and a video task display. The steady state stimulus was modulated by a complex, ten frequency, sum-of-sines, wave. The transient VERP was the time-locked average of the EEG to a series of narrow light pulses (pulse width of 10 msec). The Fourier transform of the averaged pulses had properties that approximate band limited white noise, i.e., a flat spectrum over the frequency region spanned by the 10 summed sines. The Fourier transform of both the steady state and the transient evoked potentials resulted in transfer that are equivalent and therefore comparable. To investigate the effects of task loading on evoked potentials, a grammatical reasoning task was provided. Results support the relevancy of continued application of a systems engineering approach for describing neurosensory functioning.
Junker, A. M.↗
Electron density and the electric field in a steady-state F-layer Scientific report no. 263
Steady state solution for electron density equation in isothermal one-dimensional model of ionospheric F-layer
STEADY STATE↗
Steady-state boundary lubrication with formulated C-ethers to 260 C
Steady state wear and friction studies were made at boundary lubrication conditions in a pin on disk (pure iron on rotating CVM M 50 steel) sliding friction apparatus with five C ether formulated fluids (modified polyphenyl ether containing phosphrous ester, organic acid, and other additives). Conditions included 20, 150, and 260 C disk temperatures, dry air test atmosphere, 1 kilogram load, 50 rpm disk speed, and test times to 130 minutes. Results were compared with those obtained with a formulated MIL L 27502 candidate ester and the C ether base fluid. Three of the C ether formulations gave better lubrication than both reference fluids under most conditions. The other two C ether formulations yielded higher wear rates and friction coefficients than the C ether base fluid for most of the temperature range. Only one C ether formulation showed consistently higher steady state wear rates than the ester.
Loomis, W. R.↗
Steady state dynamics of large spinning net configuration structures.
Steady state dynamic properties of large spinning net-like antenna suitable for radio signal reception from space
SPIN DYNAMICS↗
Quasi-steady-state pulsed plasma thrustors.
Quasi-steady-state operation of arc thrustor obtained with pulse time of few hundred microseconds, producing continuous plasma stream
ARC DISCHARGE↗
Quasi-steady-state pulsed plasma thrusters.
Quasi-steady-state operation of arc thrustor obtained with pulse time of few hundred microseconds, producing continuous plasma stream
THRUSTOR↗
Steady-State Thermal Design of Space Radiators
Steady state thermal design of space radiators consisting of flat panel containing parallel single pass tubes
Chapman, A. J.↗
Pioneer 6 observations of a steady-state magnetosheath.
Pioneer 6 observations of steady state magnetosheath during transit of magnetopause under quiet solar wind-geomagnetic field interaction conditions
Mckibbin, D. D.↗
Effects of steady state adiabatic convection on the configuration of the near-earth plasma sheet. II
Convection in the plasma sheet is studied using two new two-dimensional, force-balanced magnetospheres that satisfy pV exp 5/3 = constant in the inner and middle plasma sheet. It is confirmed that there exists a substantial set of steady state adiabatic solutions. Like a previously obtained steady state solution, each of these models exhibit a broad minimum in equatorial magnetic field strength B(ze) tailward of the inner edge region between 10 and 20 R(E), but they possess higher values of flux tube content pV exp 5/3 and thus have more stretched tidal configurations and smaller minimum values of B(ze) than those in the original model. A steady state magnetic field model in which B(ze)/B(lobe) at 36 R(E) geocentric distance is close to the observed value has been constructed. The results indicate that the B(ze) minimum tends to form within the Alfven layers. The broader the Alfven layers, the less pronounced the minimum.
Hau, Lin-Ni↗
Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics
Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.
Yee, H. C.↗
Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations
Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.
Bailey, Harry E.↗
Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics
Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.
Yee, H. C.↗
New models for fast steady state magnetic reconnection
A new unified family of models for incompressible, steady-state magnetic reconnection in a finite region is presented. The models are obtained by expanding in powers of the Alfven Mach number and may be used to elucidate some of the puzzling properties of numerical experiments on reconnection which are not present in the classical models. The conditions imposed on the inflow boundary of the finite region determine which member of the family occurs. Petscheklien and Sonnerup like solutions are particular members. The Sonneruplike regime is a special case of a weak slow mode expansion in the inflow region, and it separates two classes of members with reversed currents. The Petscheklike regime is a singular case of a weak fast mode expansion, and it separates the hybrid regime from a regime of slow mode compressions. Care should be taken in deciding which type of reconnection is operating in a numerical experiment. Indeed, no experiment to date has used boundary conditions appropriate for demonstrating steady state Petschek reconnection.
Priest, E. R.↗
Steady state spurious errors in shock-capturing numerical schemes
The behavior of the steady state spurious error modes of the MacCormack scheme and the upwind scheme of Warming and Beam was obtained from a linearized difference equation for the steady state error. It was shown that the spurious errors can exist either as an eigensolution of the homogeneous part of this difference equation or because of excitation from large discretization errors near oblique shocks. It was found that the upwind scheme does not permit spurious oscillations on the upstream side of shocks. Examples are given for the inviscid Burgers' equation and for one and two dimensional gasdynamic flows.
Karlsen, L. K.↗
An exact solution for the steady state phase distribution in an array of oscillators coupled on a hexagonal lattice
When electronic oscillators are coupled to nearest neighbors to form an array on a hexagonal lattice, the planar phase distributions desired for excitation of a phased array antenna are not steady state solutions of the governing non-linear equations describing the system. Thus the steady state phase distribution deviates from planar. It is shown to be possible to obtain an exact solution for the steady state phase distribution and thus determine the deviation from the desired planar distribution as a function of beam steering angle.
injection locking↗