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At least 91 records · Page 5

Nonlinear dynamics in cardiac conduction

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

NASA Discipline Cardiopulmonary↗

General analytic results for nonlinear waves and solitons in molecular clouds

We study nonlinear wave phenomena in self-gravitating fluid systems, with a particular emphasis on applications to molecular clouds. This paper presents analytical results for one spatial dimension. We show that a large class of physical systems can be described by theories with a 'charge density' q(rho); this quantity replaces the density on the right-hand side of the Poisson equation for the gravitational potential. We use this formulation to prove general results about nonlinear wave motions in self-gravitating systems. We show that in order for stationary waves to exist, the total charge (the integral of the charge density over the wave profile) must vanish. This 'no-charge' property for solitary waves is related to the capability of a system to be stable to gravitational perturbations for arbitrarily long wavelengths. We find necessary and sufficient conditions on the charge density for the existence of solitary waves and stationary waves. We study nonlinear wave motions for Jeans-type theories (where q(rho) = rho-rho(sub 0)) and find that nonlinear waves of large amplitude are confined to a rather narrow range of wavelengths. We also study wave motions for molecular clouds threaded by magnetic fields and show how the allowed range of wavelengths is affected by the field strength. Since the gravitational force in one spatial dimension does not fall off with distance, we consider two classes of models with more realistic gravity: Yukawa potentials and a pseudo two-dimensional treatment. We study the allowed types of wave behavior for these models. Finally, we discuss the implications of this work for molecular cloud structure. We argue that molecular clouds can support a wide variety of wave motions and suggest that stationary waves (such as those considered in this paper) may have already been observed.

Adams, Fred C.↗

Paneling methods with vorticity effects and corrections for nonlinear compressibility

Supersonic panel methods and axisymmetric body-modeling singularity methods are presently combined with corrections for nonlinear flow phenomena to a complete missile, its airbreathing inlets, and wing-body combinations. The computer code LRCDM2 is used as an illustrative example of the methods in question. Attention is given to a preliminary method which employs panels to estimate additive drag and lift acting on supersonic rectangular inlets, as well as to the method used to correct off-body flowfields for the presence of a shock. Examples of missile applications of these methods with the appropriate nonlinear corrections are presented.

Dillenius, Marnix F. E.↗

Some remarks on waves in the solar wind

Waves are significant to the solar wind in two ways as modifiers of the particle distribution functions, and as diagnostics. In addition, the solar wind serves as an important laboratory for the study of plasma wave processes, as it is possible to make detailed measurements of phenomena which are too small to be easily measured by laboratory sized sensors. There are two areas where waves (we include discontinuities under this heading) must make important modifications of the distribution functions: in accelerating the alpha particles to higher speeds than the protons (Marsch et al.) and in accelerating the solar wind itself. A third area is possibly in maintaining the relative isotropy of the solar wind ion distribution in the solar wind rest frame. As the solar wind is nearly collisionless, the ions should conserve magnetic moment in rushing out from the sun, and therefore Tperp/B should be relatively constant, but it is obviously not. This has not received much attention. The waves, both electromagnetic and electrostatic, which are pan of the solar Type 111 burst phenomenon, have been extensively studied as examples of nonlinear plasma phenomena, and also used as remote sensors to trace the solar magnetic field. The observations made by Ulysses show that the field can be traced in this way out to perhaps a little more than an A.U., but then the electromagnetic pan of the type 111 burst fades out. Nevertheless, sometimes Langmuir waves appear at Ulysses at an appropriate extrapolated time. This seems to support the picture in which the electromagnetic waves at the fundamental plasma frequency are trapped in density fluctuations. Langmuir waves in the solar wind are usually in quasi-thermal equilibrium quasi because the solar wind itself is not isothermal. The Observatory of Paris group (Steinberg. Meyer-Vernet, Hoang) has exploited this with an experiment on WIND which is capable of providing density and temperature on a faster time scale than hitherto. Recently it has been found that Langmuir waves are associated with magnetic holes. This may help to elucidate the nature of magnetic holes. Nonlinear processes are important in the transformation of wave energy to panicle energy. Some recent examples from WIND data will be shown.

Kellogg, Paul J.↗

Theory of the unmagnetized plasma.

The Vlasov mathematical model of a plasma, which has come to be thought more useful than any other in describing the dynamical behavior of the majority of plasmas of interest, is first examined. Macroscopic variables and moment equations; linear electrostatics solutions; plasma oscillations, ion acoustic waves, and linear instabilities are treated, as well as external fields, 'test' charges, and nonlinear Vlasov phenomena. Plasmas are statistically described, and attention is given to the kinetic theory of the stable, uniform plasma and the Balescu-Lenard equation; two-time ensemble averages and fluctuation spectra in stable plasmas; the kinetic theory of the unstable plasma; and ensembles of Vlasov plasmas. Some illustrative experiments are described. Four appendixes deal with the electrostatic approximation and transverse waves; solution of the linearized Vlasov equation in a magnetic field; estimates of correlation functions from thermal equilibrium; and equivalence of spatially uniform BBGKY and Klimontovich correlations.

Montgomery, D. C.↗

A study and evaluation of image analysis techniques applied to remotely sensed data

An analysis of phenomena causing nonlinearities in the transformation from Landsat multispectral scanner coordinates to ground coordinates is presented. Experimental results comparing rms errors at ground control points indicated a slight improvement when a nonlinear (8-parameter) transformation was used instead of an affine (6-parameter) transformation. Using a preliminary ground truth map of a test site in Alabama covering the Mobile Bay area and six Landsat images of the same scene, several classification methods were assessed. A methodology was developed for automatic change detection using classification/cluster maps. A coding scheme was employed for generation of change depiction maps indicating specific types of changes. Inter- and intraseasonal data of the Mobile Bay test area were compared to illustrate the method. A beginning was made in the study of data compression by applying a Karhunen-Loeve transform technique to a small section of the test data set. The second part of the report provides a formal documentation of the several programs developed for the analysis and assessments presented.

Atkinson, R. J.↗

The linear and non-linear aerodynamics of three-surface aircraft concepts

It is noted that most modern fighter aircraft rely on vortex interaction to provide lift enhancement at maneuvering angles of attack. It is shown that the close-coupled horizontal canard in a three-surface configuration provides a control surface which in addition to its other control functions, can be used to optimize this vortex interaction. Attention is given to a study intended to provide a detailed understanding of the aerodynamics of this type of configuration. The discussion examines the results of this investigation and hypotheses are presented to explain the linear and nonlinear aerodynamic phenomena observed.

Agnew, J. W.↗

A Constitutive Model for the Inelastic Multiaxial Cyclic Response of a Nickel Base Superalloy Rene 80

The objective was to develop unified constitutive equations which can model a variety of nonlinear material phenomena observed in Rene 80 at elevated temperatures. A constitutive model was developed based on back stress and drag stress. The tensorial back stress was used to model directional effects; whereas, the scalar drag stress was used to model isotropic effects and cyclic hardening or softening. A flow equation and evolution equations for the state variables were developed in multiaxial form. Procedures were developed to generate the material parameters. The model predicted very well the monotonic tensile, cyclic, creep, and stress relaxation behavior of Rene 80 at 982 C. The model was then extended to 871, 760, and 538 C. It was shown that strain rate dependent behavior at high temperatures and strain rate independent behavior at the lower temperatures could be predicted very well. A large number of monotonic tensile, creep, stress relation, and cyclic experiments were predicted. The multiaxial capabilities of the model were verified extensively for combined tension/torsion experiments. The prediction of the model agreed very well for proportional, nonproportional, and pure shear cyclic loading conditions at 982 and 871 C.

Ramaswamy, V. G.↗

Paneling methods with vorticity effects and corrections for nonlinear compressibility

The prediction of missile aerodynamic characteristics is presently undertaken through the application of supersonic paneling methods and nonlinear corrections to the prediction of missile aerodynamic characteristics. Attention is given to supersonic panel methods and line-singularity methods for the modeling of axisymmetric bodies, in combination with corrections for nonlinear flow phenomena, which are applied to complete missile, inlets, and wing-body combinations. The LRCDM2 computer program is used as an example of the methods presented.

Dillenius, Marnix F. E.↗

An initial investigation into methods of computing transonic aerodynamics sensitivity coefficients

Based upon the program outlined in the modified proposal, the initial effort has concentrated on developing the quasi-analytical approach for determining aerodynamic influence coefficients. In addition, in order to keep these initial efforts computationally efficient and straightforward, it was decided to first consider only two-dimensional flow and to model the problem using the transonic small perturbation equation with surface boundary conditions applied along the slit. The small perturbation equation was selected instead of the full potential equation because it permits the capturing of important nonlinear physical phenomena while being by comparison easy to handle from a coding standpoint. Consequently, the initial objectives were: (1) investigate the feasibility of using the quasi-analytical approach for determining aerodynamic sensitivity coefficients in the transonic regime; (2) determine the accuracy of the quasi-analytical approach by comparing results to those computed using finite difference techniques; and (3) investigate efficient methods for solving the large set of equations associated with the quasi-analytical approach.

Carlson, Leland A.↗

Program For Elastoplastic Analyses Of Plane Frames

PLAN2D is FORTRAN computer program for plastic analysis of planar frame structures. Given structure and loading pattern as input, calculates ultimate load that structure sustains before collapse. Element moments and plastic hinge rotations calculated for ultimate load. Locations of hinges required for collapse mechanisms to form also determined. Nonlinear collapse phenomena simulated by iterative linear analyses.

Lawrence, C.↗

An overview of selected NASP aeroelastic studies at the NASA Langley Research Center

Following an initial discussion of the NASP flight environment, the results of recent aeroelastic testing of NASP-type highly swept delta-wing models in Langley's Transonic Dynamics Tunnel (TDT) are summarized. Subsonic and transonic flutter characteristics of a variety of these models are described, and several analytical codes used to predict flutter of these models are evaluated. These codes generally provide good, but conservative predictions of subsonic and transonic flutter. Also, test results are presented on a nonlinear transonic phenomena known as aileron buzz which occurred in the wind tunnel on highly swept delta wings with full-span ailerons. An analytical procedure which assesses the effects of hypersonic heating on aeroelastic instabilities (aerothermoelasticity) is also described. This procedure accurately predicted flutter of a heated aluminum wing on which experimental data exists. Results are presented on the application of this method to calculate the flutter characteristics of a fine-element model of a generic NASP configuration. Finally, it is demonstrated analytically that active controls can be employed to improve the aeroelastic stability and ride quality of a generic NASP vehicle flying at hypersonic speeds.

Spain, Charles V.↗

Lattice Boltzmann model for simulation of magnetohydrodynamics

A numerical method, based on a discrete Boltzmann equation, is presented for solving the equations of magnetohydrodynamics (MHD). The algorithm provides advantages similar to the cellular automaton method in that it is local and easily adapted to parallel computing environments. Because of much lower noise levels and less stringent requirements on lattice size, the method appears to be more competitive with traditional solution methods. Examples show that the model accurately reproduces both linear and nonlinear MHD phenomena.

Chen, Shiyi↗

Role of shock dynamics in transonic flutter

A computational study of the influence of shock motion on flutter and divergence in transonic flow is presented. The numerical scheme models the entire fluid-structure system as a single continuum dynamics problem, by using a mixed Eulerian-Lagrangian formulation. No assumptions of small displacements are made, but the effect of viscosity is neglected. The results from this study indicate that the shock dynamics gives rise to limit cycles and highly nonlinear aeroelastic phenomena, such as weak divergence and flutter-divergence interactions. Although the shocks typically are destabilizing at the linear flutter boundary, they often have a strongly stabilizing effect for moderate-amplitude motions. The shocks are thus capable of quenching an emerging bending-torsion flutter motion and turning it into limit cycle flutter. The usefulness of classical flutter and divergence boundary diagrams is severely limited in transonic flow, because much of the global dynamic stability information is lost in such a presentation.

Bendiksen, Oddvar O.↗

Some recent applications of Navier-Stokes codes to rotorcraft

Many operational limitations of helicopters and other rotary-wing aircraft are due to nonlinear aerodynamic phenomena incuding unsteady, three-dimensional transonic and separated flow near the surfaces and highly vortical flow in the wakes of rotating blades. Modern computational fluid dynamics (CFD) technology offers new tools to study and simulate these complex flows. However, existing Euler and Navier-Stokes codes have to be modified significantly for rotorcraft applications, and the enormous computational requirements presently limit their use in routine design applications. Nevertheless, the Euler/Navier-Stokes technology is progressing in anticipation of future supercomputers that will enable meaningful calculations to be made for complete rotorcraft configurations.

Mccroskey, W. J.↗

Fast neural solution of a nonlinear wave equation

A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.

Toomarian, Nikzad↗

Modelling chaotic vibrations using NASTRAN

Due to the unavailability and, later, prohibitive cost of the computational power required, many phenomena in nonlinear dynamic systems have in the past been addressed in terms of linear systems. Linear systems respond to periodic inputs with periodic outputs, and may be characterized in the time domain or in the frequency domain as convenient. Reduction to the frequency domain is frequently desireable to reduce the amount of computation required for solution. Nonlinear systems are only soluble in the time domain, and may exhibit a time history which is extremely sensitive to initial conditions. Such systems are termed chaotic. Dynamic buckling, aeroelasticity, fatigue analysis, control systems and electromechanical actuators are among the areas where chaotic vibrations have been observed. Direct transient analysis over a long time period presents a ready means of simulating the behavior of self-excited or externally excited nonlinear systems for a range of experimental parameters, either to characterize chaotic behavior for development of load spectra, or to define its envelope and preclude its occurrence.

Sheerer, T. J.↗