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At least 505 records · Page 28

Stochastic stability and instability of model ecosystems

In this work, we initiate a stability study of multispecies communities in stochastic environment by using Ito's differential equations as community models. By applying the direct method of Liapunov, we obtain sufficient conditions for stability and instability in the mean of the equilibrium populations. The conditions are expressed in terms of the dominant diagonal property of community matrices, which is a suitable mechanism for resolving the central problem of 'complexity vs stability' in model ecosystems. As a by-product of this analysis we exhibit important structural properties of the stochastic density-dependent models, and establish tolerance of community stability to a broad class of nonlinear time-varying perturbations.

Ladde, G. S.↗

Stability of laser heated flows

A local stability analysis is utilized to determine the stability of disturbances generated at each point along a nozzle of variable area ratio for a one-dimensional flow heated by laser radiation entering from the upstream direction. The governing equations for the quasi-one-dimensional flow without viscous dissipation, diffusion, and thermal conduction but including radiative heat transfer are given. The governing equations are combined to yield a relationship which governs the Mach number variation through the nozzle. The complete steady-state solution can be calculated from knowledge of the Mach number profile, the inlet conditions, and the laser power. The local stability analysis permits obtaining contour (or contours) of neutral stability. Solutions have been obtained for various nozzle configurations, but only one set of example calculations is presented. The results obtained indicate that the analysis serves as an important indicator as to where potential absorption wave phenomena may be initiated.

Wu, P. K. S.↗

Stability and control of maneuvering high-performance aircraft

The stability and control of a high-performance aircraft was analyzed, and a design methodology for a departure prevention stability augmentation system (DPSAS) was developed. A general linear aircraft model was derived which includes maneuvering flight effects and trim calculation procedures for investigating highly dynamic trajectories. The stability and control analysis systematically explored the effects of flight condition and angular motion, as well as the stability of typical air combat trajectories. The effects of configuration variation also were examined.

Stengel, R. F.↗

A theoretical analysis of airplane longitudinal stability and control as affected by wind shear

The longitudinal equations of motion with wind shear terms were used to analyze the stability and motions of a jet transport. A positive wind shear gives a decreasing head wind or changes a head wind into a tail wind. A negative wind shear gives a decreasing tail wind or changes a tail wind into a head wind. It was found that wind shear had very little effect on the short period mode and that negative wind shear, although it affected the phugoid, did not cause stability problems. On the other hand, it was found that positive wind shear can cause the phugoid to become aperiodic and unstable. In this case, a stability boundary for the phugoid was found that is valid for most aircraft at all flight speeds. Calculations of aircraft motions confirmed the results of the stability analysis. It was found that a flight path control automatic pilot and an airspeed control system provide good control in all types of wind shear. Appendixes give equations of motion that include the effects of downdrafts and updrafts and extend the longitudinal equations of motion for shear to six degrees of freedom.

Sherman, W. L.↗

Current status of longitudinal stability, 24 May 1948

The problems of static and dynamic longitudinal stability both at high speeds and at low speeds are discussed and data are presented which indicate progress made in the solution of these problems. It is shown that the incorporation of large amounts of sweepback on both the wing and the horizontal tail can significantly increase the Mach number at which critical trim changes and stability changes occur and can greatly reduce the trim changes and stability changes encountered at supercritical speeds. Data are also presented which demonstrate the possibility of obtaining satisfactory longitudinal stability in the landing configuration for wings with sweepback of the order of 45 deg utilizing various stall control devices. Optimum arrangements for such devices, however, should be determined experimentally.

Donlan, C. J.↗

Solar seismology. I - The stability of the solar p-modes

The stability of the radial p-modes of the sun is investigated by computing nonadiabatic eigenvalues and eigenfunctions for a solar envelope model which extends from an inner radius of about 0.3 solar radius out to an optical depth of about 0.0003. The calculations take into account in a crude fashion the response of the convective flux to the oscillation. The dynamical effect of turbulence in the convection zone is parametrized in terms of a turbulent shear viscosity. The results show that if damping by turbulent viscosity is neglected, all modes with periods longer than 6 minutes are unstable. The familiar kappa-mechanism, which operates in the H ionization-H(-) opacity region, is the dominant source of driving of the oscillations. Modes with periods shorter than 6 minutes are stabilized by radiative damping in the solar atmosphere. When turbulent dissipation of pulsational energy is included, all modes are predicted to be stable. However, the margin of stability is very small. In view of the large uncertainty that must be assigned to the estimate of turbulent damping, it is concluded that theoretical calculations cannot unequivocally resolve the question of the stability of the solar p-modes.

Goldreich, P.↗

Armalcolite stability as a function of pressure and oxygen fugacity

High-pressure experiments in a piston-cylinder apparatus with silver-palladium containers were conducted to study the stability of synthetic armalcolite, (Fe,Mg)Ti2O5, as a function of pressures up to 15 kbar at 1000, 1100, and 1200 C. Three armalcolite compositions were used, each with an initial Fe/(Fe + Mg) ratio of 0.5. Composition I contained no zirconium, whereas compositions II and III were prepared with 4% and 10% by weight ZrO2. Difference in stability due to the presence or absence of Zr in these synthetic armalcolites is discussed. 4 wt% ZrO2 appears to saturate armalcolite at 1200 C and 1 atm. Zirconium is found to reduce armalcolite stability, but this effect is not great. The stability of armalcolite as a function of oxygen fugacity is determined thermogravimetrically at 1200 C and 1 atm. Knowledge of the range of oxygen fugacity at which armalcolite is stable and of the equilibrium oxide mineral assemblages outside this range provides important information about lunar cooling histories in terms of oxygen fugacity.

Friel, J. J.↗

Stability analysis of a reinforced carbon carbon shell

This paper presents the development of a stability analysis for the nose cap of the NASA Space Shuttle Orbiter. Stability is evaluated by the differential stiffness analysis of the NASTRAN finite-element computer code, addressing those nonstandard characteristics in the nose cap such as nonuniform curvature, asymmetrical and nonuniform loads, support fixity, and various combinations of membrane and bending stresses. A full-sized nose cap, thinner than production, was statically tested and stability analyzed. The failing load level correlated to within 30%. The region and mode of buckling that occurred during test was accurately predicted by analysis. The criterion for predicting instability is based on the behavior of the nonlinear deflections. The deflections are nonlinear elastic in that the stresses are well within the elastic range of the material, but the geometry-load relationship produces nonlinear deflections. The load-deflection relationship is well defined by differential stiffness analysis up to the zero-slope portion of the curve, the point of neutral stability or where the shell 'snaps through' just prior to general instability.

Agan, W. E.↗

Effect of winglets on a first-generation jet transport wing. 5: Stability characteristics of a full-span wing with a generalized fuselage at high subsonic speeds

The effects of winglets on the static aerodynamic stability characteristics of a KC-135A jet transport model at high subsonic speeds are presented. The investigation was conducted in the Langley 8 foot transonic pressure tunnel using 0.035-scale wing panels mounted on a generalized research fuselage. Data were taken over a Mach number range from 0.50 to 0.95 at angles of attack ranging from -12 deg to 20 deg and sideslip angles of 0 deg, 5 deg, and -5 deg. The model was tested at two Reynolds number ranges to achieve a wide angle of attack range and to determine the effect of Reynolds number on stability. Results indicate that adding the winglets to the basic wing configuration produces small increases in both lateral and longitudinal aerodynamic stability and that the model stability increases slightly with Reynolds number. The winglets do increase the wing bending moments slightly, but the buffet onset characteristics of the model are not affected by the winglets.

Jacobs, P. F.↗

Stability of constant gain systems with vector feedback

The state space, the controllability, and the observability concepts are discussed in connection with the proposed stability analysis which permits drastic dimensional reductions for a vector feedback problem. Any constant gain system's stability can thus be analyzed in the frequency domain with a single Nyquist plot. The analysis considers the total system with all loops closed, a disturbance vector as input, and the feedback vector as output. All constant gain systems are shown to be decomposable into stable subsystems where the degree of the decomposition determines the dimensions. The maximum decomposition results in the state-space approach which is the limit case. The method is demonstrated with the stability analysis of the pogo phenomenon, an oscillatory interaction between the propulsion and the structure of a space vehicle. This problem, with eigenvalues over a hundred, was drastically but rigorously reduced to a stability analysis of a 4x4 matrix.

Vonpragenau, G. L.↗

Flap-lag-torsion aeroelastic stability of circulation-controlled rotors in hover

The results of a theoretical investigation of the flap-lag-torsion stability of circulation controlled rotors in hover are presented. Stability boundaries are presented as a function of thrust and lag frequency, at several levels of blowing coefficient, for flap frequencies of 1.1/rev and 1.8/ rev. The effects of several parameters on the blade flap-lag stability are examined, including structural damping, structural coupling, pitch-lag and pitch-flap coupling, and the blade feathering motion. The trailing edge blowing can have a major impact on the blade aeroelastic stability, which should be considered in the rotor design. The implications of these results for the current CCR and X-Wing rotorcraft designs are considered.

Chopra, I.↗

Influence of a magnetic field on the pulsational stability of stars

Under certain simplifying assumptions the influence of a magnetic field on the pulsational stability of stars has been investigated, with a particular application to the problem of the stability of upper-main-sequence stars. It has been found that, if the magnetic field averaged over a spherical shell is either constant at all layers or distributed such that nu, the ratio of magnetic to thermodynamic pressure, is constant at all layers, the critical mass for stability against nuclear-energized pulsations is virtually unaffected by the presence of the field. On the other hand, if the field is strong in the envelope but weak in the core of the star, the critical mass is considerably increased; when nu exceeds about 0.1 in the envelope, stability is attained at all masses.

Strothers, R.↗

Stability analysis for laminar flow control, part 2

Topics covered include: (1) optimization of the numerics of the SALLY stability analysis code; (2) relation between temporal and spatial stability theory; (3) compressible flow stability calculations; (4) spectral methods for the boundary layer equations; and (5) numerical study of nonlinear, nonparallel stability of incompressible flows.

Orszag, S. A.↗

Retrieval techniques: LVLH and inertially stabilized payloads

Procedures and techniques are discussed for retrieving payloads that are inertially or local vertical/local horizontal (LVLH) stabilized. Selection of the retrieval profile to be used depends on several factors: (1) control authority of the payload, (2) payload sensitivity to primary reaction control system (PRCS) plumes, (3) whether the payload is inertially or LVLH stabilized, (4) location of the grapple fixture, and (5) orbiter propellant consumption. The general retrieval profiles recommended are a V-bar approach for payloads that are LVLH or gravity-gradient stabilized, and the V-bar approach with one or two phase flyaround for inertially stabilized payloads. Once the general type of profile has been selected, the detailed retrieval profile and timeline should consider the various guidelines, groundrules, and constraints associated with a particular payload or flight. Reaction control system (RCS) propellant requirements for the recommended profiles range from 200 to 1500 pounds, depending on such factors as braking techniques, flyaround maneuvers (if necessary), and stationkeeping operations. The time required to perform a retrieval (starting from 1000 feet) varies from 20 to 130 minutes, depending on the complexity of the profile. The goals of this project are to develop a profile which ensures mission success; to make the retrieval profiles simple; and to keep the pilot workload to a minimum by making use of the automatic features of the orbiter flight software whenever possible.

Yglesias, J. A.↗

Attitude stability of spinning satellites

Some problems of attitude stability of spinning satellites are treated in a rigorous manner. With certain restrictions, linearized stability analysis correctly predicts the attitude stability of spinning satellites, even in the critical cases of the Liapunov-Poincare stability theory.

Caughey, T. K.↗

Examination of the flap-lag stability of rigid articulated rotor blades

A critical examination of flap-lag stability of a centrally hinged, spring-restrained rigid blade in both hover and forward flight is presented. Several differences in the equations of motion for blade flap-lag stability in the existing literature are identified. A rigorous and systematic development of these equations for a rigid articulated blade in forward flight shows the existence of some linear aerodynamic coupling terms associated with blade steady-state flapping and lagging in the perturbation equations. The differences identified are shown to be associated with whether or not the lag hinge flaps with the blade. The implications of these differences on stability are examined, and it is shown that the pitch-lag coupling terms associated with a hinge arrangement in which the lag hinge flaps with the blade have a marked influence on flap-lag stability, depending on the system parameters.

Kaza, K. R. V.↗

Advanced stability analysis for laminar flow control

Five classes of problems are addressed: (1) the extension of the SALLY stability analysis code to the full eighth order compressible stability equations for three dimensional boundary layer; (2) a comparison of methods for prediction of transition using SALLY for incompressible flows; (3) a study of instability and transition in rotating disk flows in which the effects of Coriolis forces and streamline curvature are included; (4) a new linear three dimensional instability mechanism that predicts Reynolds numbers for transition to turbulence in planar shear flows in good agreement with experiment; and (5) a study of the stability of finite amplitude disturbances in axisymmetric pipe flow showing the stability of this flow to all nonlinear axisymmetric disturbances.

Orszag, S. A.↗

Station stability measurement

Methods and instrumentation are being developed to determine the frequency stability of Deep Space Stations. The efforts are presently focused on the verification of the stability of the X-band uplink and other RF and microwave subsystems which contribute to the overall stability of the system. The measurement methodology is presented as well as frequency stability data generated with the development measurement system. The system characteristics are highlighted and the potential areas where improvements could be made are discussed.

Sosa, E. N.↗