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Results for “INVARIANCE PRINCIPLES”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Generalized invariance principles and the theory of stability.

Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.

Lasalle, J. P.↗
DOE OSTI2018

Non-stationary Almost Sure Invariance Principle for Hyperbolic Systems with Singularities

We investigate a wide class of two-dimensional hyperbolic systems with singularities, and prove the almost sure invariance principle (ASIP) for the random process generated by sequences of dynamically Hölder observables. The observables could be unbounded, and the process may be non-stationary and need not have linearly growing variances. Our results apply to Anosov diffeomorphisms, Sinai dispersing billiards and their perturbations. The random processes under consideration are related to the fluctuation of Lyapunov exponents, the shrinking target problem, etc.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Contact Hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior

This paper describes the connections between the notions of Hamiltonian system, contact Hamiltonian system and nonholonomic system from the perspective of differential equations and dynamical systems. It shows that action minimizing curves of nonholonomic system satisfy the dissipative Lagrange system, which is equivalent to the contact Hamiltonian system under some generic conditions. As the initial research of contact Hamiltonian dynamics in this direction, we investigate the dynamics of contact Hamiltonian systems in some special cases including invariants, completeness of phase flows and periodic behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2011

Spectral Invariance Principles Observed in Spectral Radiation Measurements of the Transition Zone

The main theme for our research is the understanding and closure of the surface spectral shortwave radiation problem in fully 3D cloud situations by combining the new ARM scanning radars, shortwave spectrometers, and microwave radiometers with the arsenal of radiative transfer tools developed by our group. In particular, we define first a large number of cloudy test cases spanning all 3D possibilities not just the customary uniform-overcast ones. Second, for each case, we define a "Best Estimate of Clouds That Affect Shortwave Radiation" using all relevant ARM instruments, notably the new scanning radars, and contribute this to the ARM Archive. Third, we test the ASR-signature radiative transfer model RRTMG_SW for those cases, focusing on the near-IR because of long-standing problems in this spectral region, and work with the developers to improve RRTMG_SW in order to increase its penetration into the modeling community.

Marshak, Alexander↗
NASA NTRS1992

Symmetry as Bias: Rediscovering Special Relativity

This paper describes a rational reconstruction of Einstein's discovery of special relativity, validated through an implementation: the Erlanger program. Einstein's discovery of special relativity revolutionized both the content of physics and the research strategy used by theoretical physicists. This research strategy entails a mutual bootstrapping process between a hypothesis space for biases, defined through different postulated symmetries of the universe, and a hypothesis space for physical theories. The invariance principle mutually constrains these two spaces. The invariance principle enables detecting when an evolving physical theory becomes inconsistent with its bias, and also when the biases for theories describing different phenomena are inconsistent. Structural properties of the invariance principle facilitate generating a new bias when an inconsistency is detected. After a new bias is generated. this principle facilitates reformulating the old, inconsistent theory by treating the latter as a limiting approximation. The structural properties of the invariance principle can be suitably generalized to other types of biases to enable primal-dual learning.

Lowry, Michael R.↗
DOE OSTI2014

Heisenberg picture approach to the stability of quantum Markov systems

Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

The application of the principles of invariance to the radiative transfer equation in plant canopies

Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.

Ganapol, B. D.↗
NASA NTRS1993

A survey of propfan noise propagation at cruise

Acoustic measurements collected during the Propfan Test Assessment (PTA) program in 1989 had demonstrated that cruising Propfans have undesirably high far-field noise level. This study attempts to investigate the source of these noise disturbances generated by a single-rotating propeller with supersonic tip speed. Various atmospheric and propagation effects responsible for shaping the far-field acoustics will be examined. A methodology for analyzing Propfan propagation noise is proposed based on the theory of geometrical acoustics. This approach allows acoustic rays to be traced into the far-field via Snell's law. Amplitude variation along the rays are evaluated by applying the Blokhintzev energy invariant principle. Additional terms are appended to the energy invariant principle to account for propagation and atmospheric effects. A FORTRAN program is written to analyze the rays emitted from a helicoidal source path traced by supersonic helical speed blade tip. Earlier papers by Myers and Farassat have demonstrated the presence of Mach envelopes that lead to formation of caustics. Linear geometric acoustics is used to ascertain the existence of these nonlinear caustics in the far-field. The importance of caustics to Propfan noise generation is then studied.

Sim, Ben WEL-C.↗
DOE OSTI2015

Relativistic mean-field model with energy dependent self-energies

Conventional relativistic mean-field theory is extended with the introduction of higher-order derivative couplings of nucleons with the meson fields. The Euler-Lagrange equations follow from the principle of stationary action. From invariance principles of the Lagrangian density the most general expressions for the conserved current and energy-momentum tensor are derived. The nucleon self-energies show the explicit dependence on the meson fields. They contain additional regulator functions which describe the energy dependence. The density dependence of meson-nucleon couplings causes the apperance of additional rearrangement contributions in the self-energies. The equation of state of infinite nuclear matter is obtained and the thermodynamical consistency of the model is demonstrated. This model is applied to the description of spherical, non-rotating stars in β-equilibrium. Stellar structure is calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations. The results for neutron stars are shown in terms of mass-radius relations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗