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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Invariant Forms of Dissolution Fingers

Dissolution of fractured and porous media introduces a positive feedback between fluid flow and reactant transport, leading to the emergence of pronounced, fingerlike channels. We investigate the formation of these structures using a microfluidic Hele-Shaw cell with a soluble bottom. Our experiments show that the shape of dissolution fingers is invariant and reveals itself over time as the fingers extend into the system. Here, by combining reactive-transport theory and conformal mapping techniques we derive these invariant forms. We relate these results to natural dissolution fingers in karst landscapes, and illustrate how to determine the groundwater flow rate responsible for their formation based on the finger shape.

Flows in porous media↗
DOE OSTI2024

Experimental measurements for extracting nonlinear invariants

Nonlinear integrable optics are a promising alternative approach to lattice design. The integrable optics test accelerator (IOTA) at Fermilab has been constructed for dedicated studies of magnetostatic elliptical elements as described by Danilov and Nagaitsev. The most compelling verification of correct implementation of the NIO lattice is direct observation of the analytically expected invariants. This report outlines the experimental and analytical methods for extracting the nonlinear invariants of motion from data gathered in the last IOTA run.

43 PARTICLE ACCELERATORS↗
NASA NTRS1972

Lorentz-invariant formulation of Cherenkov radiation by tachyons

Previous treatments of Cherenkov radiation, electromagnetic and gravitational, by tachyons were in error because the prescription employed to cut off the divergent integral over frequency is not a Lorentz invariant procedure. The resulting equation of motion for the tachyon is therefore not covariant. The proper procedure requires an extended, deformable distribution of charge or mass and yields a particularly simple form for the tachyon's world line, one that could be deduced from simple invariance considerations. It is shown that Cherenkov radiation by tachyons implys their ultimate annihilation with an antitachyon and demonstrates a disturbing property of tachyons, namely the impossibility of specifying arbitrary Cauchy data even in a purely classical theory.

Jones, F. C.↗
NASA NTRS1972

Invariant poles feedback control of flexible, highly variable spacecraft.

This paper describes a technique for single-axis control of a model of a highly flexible Space Station. Active damping of lower frequency flexibility modes is employed. In the control technique, referred to as invariant poles feedback control (IPFC), feedback gains are adjusted so that the closed-loop system's characteristic equation is matched to that of a reference model; hence, closed-loop system's poles will not move - they will be invariant (provided bending frequencies and parameters can be identified accurately). This is accomplished by obtaining the system's characteristic equation in closed form; equating respective coefficients between terms of like powers in s in the system and reference model characteristic equations; and, solving for the feedback gains. The feedback gains are explicit functions of system plant parameters and the coefficients of the reference model's characteristic equation, and are easily programmed for the digital computer.

Mendel, J. M.↗
NASA NTRS1973

The development and preliminary application of an invariant coupled diffusion and chemistry model

In many real-world pollution chemical reaction problems, the rate of reaction problems, the rate of reaction may be greatly affected by unmixedness. An approximate closure scheme for a chemical kinetic submodel which conforms to the principles of invariant modeling and which accounts for the effects of inhomogeneous mixing over a wide range of conditions has been developed. This submodel has been coupled successfully with invariant turbulence and diffusion models, permitting calculation of two-dimensional diffusion of two reacting (isothermally) chemical species. The initial calculations indicate the ozone reactions in the wake of stratospheric aircraft will be substantially affected by the rate of diffusion of ozone into the wake, and in the early wake, by unmixedness.

Hilst, G. R.↗
NASA NTRS1972

A graphical test for checking the stability of a linear time-invariant feedback system.

A continuous-time scalar linear time-invariant feedback system is considered for the purpose of checking Willems' (1969, 1970) graphical test for a scalar linear time-invariant feedback system with constant feedback. Heavy reliance is placed on the theory of almost periodic functions. Following definition of the problem and layout of notation, attention is given to solution of the problem, considering only the almost periodic part of the open-loop transfer function.

Callier, F. M.↗
NASA NTRS1972

Invariant poles feedback control of flexible highly variable spacecraft.

Description of a technique for single-axis control of a model of a highly flexible space station. Active damping of lower frequency flexibility modes is employed. In the control technique, referred to as invariant poles feedback control, feedback gains are adjusted so that the closed-loop system characteristic equation is matched to that of a reference model. Hence closed-loop system poles will not move; they will be invariant (provided that bending frequencies and parameters can be identified accurately). This is accomplished by obtaining the system characteristic equation in closed form; equating respective coefficients between terms of like powers in s in the system and reference model characteristic equations; and solving for the feedback gains. The feedback gains are explicit functions of system plant parameters and the coefficients of the reference model characteristic equation, and are easily programmed for the digital computer.

Mendel, J. M.↗
NASA NTRS1972

Invariance and stability for bounded uncertain systems.

The positive limit sets of the solutions of a contingent differential equation are shown to possess an invariance property. In this connection the 'invariance principle' in the theory of Lyapunov stability is extended to systems with unknown, bounded, time-varying parameters, and thus to a large and important class of nonautonomous systems. Asymptotic stability criteria are obtained and applied to guaranteed cost control problems.

Peng, T. K. C.↗
NASA NTRS1974

Optimal compensator structure for linear time-invariant plant with inaccessible states

The problem is considered of designing an optimal linear time-invariant dynamic compensator for the regulation of an n-th order linear time-invariant plant with m independent outputs. The initial plant state is characterized by its first and second moments, and the cost is usual quadratic infinite-time penalty on the state and control, averaged over the initial plant and compensator states. The compensator is based on a minimal-order Luenberger observer and consequently has fixed dimension n-m. Necessary and sufficient conditions are derived for optimality of the compensator gains. The optimal compensator is shown to be unique if the plant has a particular canonical form, and, in general, for any arbitrary plant, the class of all optimal compensators is precisely determined.

Blanvillain, P. J. P.↗
NASA NTRS1974

Application of an invariant second-order closure model to compressible turbulent shear layers

A second-order closure model for two-dimensional, compressible shear flows is investigated using the invariant modeling technique developed by Donaldson. The invariant model parameters were originally selected by comparison of model predictions with critical experimental data on basic incompressible flows. Additional modeling for compressible flows has been introduced. A number of different shear flows such as the free shear layer, flat plate boundary layer and a simulation of the mixing region of a chemical laser are computed. The model is consistent with first-order closure turbulence models for equilibrium flows and is further capable of predicting nonequilibrium flows that cannot be correctly solved by eddy viscosity models. The results are in generally good agreement with experimental measurements but suggest the need for inclusion of a Mach number dependent model of the pressure diffusion terms in order to adequately represent high speed compressible flows.

Varma, A. K.↗
NASA NTRS1974

Secular-invariant relationships among internal geomagnetic field coefficients

Some features of the secular variation of the geomagnetic field are examined. Contours encircling constant magnetic flux (third adiabatic invariant), corresponding to a shell of field lines in secular motion, reveal a general westward drift that is longitude and latitude dependent (with minima in the north Pacific and south Atlantic areas). Some invariant relationships appear among the field coefficients in the tilted, centered dipole (geomagnetic) coordinate system.

Roederer, J. G.↗
NASA NTRS1975

Adiabatic invariants and phase equilibria for first-order orbital resonances

In the planar circular restricted three-body problem, the evolution of near-commensurable orbits is studied under change in the mass ratio, mu. The evolution involves preservation of two adiabatic invariants. Transition from circulation to libration may occur; such transitions are of two types. Type I transition occurs when the evolutionary track in phase space passes through near-zero eccentricity; as in the ordinary case (no transition), pre- and post-evolutionary states are linked by solution of a two-point boundary-value problem. Type II transition occurs when the evolutionary track encounters an unstable phase equilibrium or periodic orbit. There is then a discontinuous change in one adiabatic invariant, and pre- and post-evolutionary states are linked by solution of a three-point boundary-value problem. No evolutionary track can encounter a stable phase equilibrium, but the class of all stable phase equilibria is mapped into itself under mu change.

Heppenheimer, T. A.↗
NASA NTRS1975

Some estimation formulae for continuous time-invariant linear systems

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Bierman, G. J.↗
NASA NTRS1977

A fast invariant imbedding method for multiple scattering calculations and an application to equivalent widths of CO2 lines on Venus

The invariant imbedding method considered is based on an equation which describes the change in the reflected radiation when an optically thin layer is added to the top of the atmosphere. The equation is used to treat the problem of reflection from a planetary atmosphere as an initial value problem. A fast method is discussed for the solution of the invariant imbedding equation. The speed and accuracy of the new method are illustrated by comparing it with the doubling program published by Hansen and Travis (1974). Computations are performed of the equivalent widths of carbon dioxide absorption lines in solar radiation reflected by Venus for several models of the planetary atmosphere.

Sato, M.↗
NASA NTRS1977

Linear systems with structure group and their feedback invariants

A general method described by Hermann and Martin (1976) for the study of the feedback invariants of linear systems is considered. It is shown that this method, which makes use of ideas of topology and algebraic geometry, is very useful in the investigation of feedback problems for which the classical methods are not suitable. The transfer function as a curve in the Grassmanian is examined. The general concepts studied in the context of specific systems and applications are organized in terms of the theory of Lie groups and algebraic geometry. Attention is given to linear systems which have a structure group, linear mechanical systems, and feedback invariants. The investigation shows that Lie group techniques are powerful and useful tools for analysis of the feedback structure of linear systems.

Martin, C.↗
NASA NTRS1979

Feedback invariants for nonlinear systems

The effect of nonlinear feedback on nonlinear systems is discussed for problems where the controls are entered linearly. The invariance of certain quantities under feedback are established, and it is shown that these quantities contain enough information to determine if the system can be linearized using feedback and change of coordinates. Attention is given to scalar input systems emphasizing a new F-invariant property.

Brockett, R. W.↗
NASA NTRS1981

On the conservation of the first adiabatic invariant in perpendicular shocks

The conservation of the first adiabatic invariant of particle motion, the particle magnetic moment, at the front of perpendicular magnetosonic fast-mode shock waves is considered. Results of numerical simulations are presented which show that preshock and postshock values of the magnetic moment are on the average equal for particles transmitted by infinitesimally thin perpendicular magnetosonic fast-mode shocks, in contrast to extrapolations from adiabatic theory, which suggest that the first invariant is least likely to be conserved in this situation. The observed conservation is thus attributed to the continuity of the flux of total particle and field angular momentum across the shock front as a result of angular momentum conservation.

Pesses, M. E.↗
NASA NTRS1984

Development and testing of stable, invariant, isoparametric curvilinear 2- and 3-D hybrid-stress elements

Linear and quadratic Serendipity hybrid-stress elements are examined in respect of stability, coordinate invariance, and optimality. A formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements. The resulting least-order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles. A distortion sensitivity study for two- and three-dimensional elements provides favorable numerical comparisons with the assumed displacement method.

Punch, E. F.↗