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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 91 records · Page 5

Modal dynamics of high-frequency transverse combustion instabilities

This paper investigates the modal dynamics of self-excited high frequency transverse instabilities in a multi-nozzle, swirl-stabilized can combustor. It utilizes results from multiple pressure sensors to decompose the disturbance into clockwise (CW) and counter-clockwise (CCW) waves, enabling a reconstruction of the pressure amplitude, phase, anti-nodal line location, and spin ratio. While these types of decompositions have been demonstrated on small scale combustors, particularly annular combustors, this is the first study to analyze these results for a high power, multi-nozzle can combustor. Its particular focus is in characterizing the system evolution in phase space and the nature of the system attractors under linearly unstable conditions; results are presented in spin ratio-phase difference space, so that limit cycle oscillations appear as fixed points. Results are shown for conditions where three different attractors dominate (standing, CW, and CCW) but are taken for very long time periods (~50,000 cycles) so that the system's interaction with these attractors can be observed. For the standing mode-dominated case, the phase portrait shows spiral trajectories converging to a single fixed point. For the spinning mode dominated cases, however, multiple fixed points and saddle points were observed, and the trajectories showed a more complicated structure. It was also shown that even though the CW mode is dominant, this mode intermittently switches to standing or CCW modes for short period. These results suggest that the strength of each attractor depends on test conditions and that random noise stochastically perturbs the system so that large regions of the phase space are explored. Lastly, one interesting observation is that the angular velocity of the anti-nodal line linearly varies with the spin ratio under standing-mode dominant conditions.

42 ENGINEERING↗

Random interactions in higher order neural networks

Recurrent networks of polynomial threshold elements with random symmetric interactions are studied. Precise asymptotic estimates are derived for the expected number of fixed points as a function of the margin of stability. In particular, it is shown that there is a critical range of margins of stability (depending on the degree of polynomial interaction) such that the expected number of fixed points with margins below the critical range grows exponentially with the number of nodes in the network, while the expected number of fixed points with margins above the critical range decreases exponentially with the number of nodes in the network. The random energy model is also briefly examined and links with higher order neural networks and higher order spin glass models made explicit.

Baldi, Pierre↗

Apparent Transition Behavior of Widely-Used Turbulence Models

The Spalart-Allmaras and the Menter SST kappa-omega turbulence models are shown to have the undesirable characteristic that, for fully turbulent computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart-Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause nonuniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a higher freestream turbulence level or by making a simple change to one of the model constants. Two-equation kappa-omega models, including the SST model, exhibit strong sensitivity to numerical resolution near the area where turbulence initiates. Thus, inconsistent apparent transition behavior with grid refinement in this case does not appear to stem from the presence of a degenerate fixed point. Rather, it is a fundamental property of the kappa-omega model itself, and is not easily remedied.

Rumsey, Christopher L.↗

Apparent Transition Behavior of Widely-Used Turbulence Models

The Spalart-Allmaras and the Menter SST k-omega turbulence models are shown to have the undesirable characteristic that, for fully turbulent computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart-Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause non-uniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a higher freestream turbulence level or by making a simple change to one of the model constants. Two-equation k-omega models, including the SST model, exhibit strong sensitivity to numerical resolution near the area where turbulence initiates. Thus, inconsistent apparent transition behavior with grid refinement in this case does not appear to stem from the presence of a degenerate fixed point. Rather, it is a fundamental property of the k-omega model itself, and is not easily remedied.

Rumsey, Christopher L.↗

Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low-rank approximation of the dielectric matrix

We present an efficient preconditioning technique for accelerating the fixed-point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low-rank approximation of the dielectric matrix (LRDM) based on Gâteaux derivatives of the residual of fixed-point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these Gâteaux derivatives in conjunction with the Chebyshev filtered subspace iteration procedure, an approach widely used in large-scale Kohn-Sham DFT calculations. Further, we propose a variant of LRDM preconditioner based on adaptive accumulation of low-rank approximations from previous self-consistent field iterations, and also extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We demonstrate the robustness and efficiency of the LRDM preconditioner against other widely used preconditioners on a range of benchmark systems with sizes ranging from ~100 to 1100 atoms (~500–20,000 electrons). The benchmark systems include various combinations of metal-insulating-semiconducting heterogeneous material systems, nanoparticles with localized d orbitals near the Fermi energy, nanofilm with metal dopants, and magnetic systems. In all benchmark systems, the LRDM preconditioner converges robustly within 20–30 iterations. In contrast, other widely used preconditioners show slow convergence in many cases, as well as divergence of the fixed-point iteration in some cases. Lastly, we demonstrate the computational efficiency afforded by the LRDM method, with up to 3.4-fold reduction in computational cost for the total ground-state calculation compared to other preconditioners.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.

Serrallés, José Cruz [Weill Cornell Med. Coll.]↗

Non-Wilsonian ultraviolet completion via transseries

We study some of the implications for the perturbative renormalization program when augmented with the Borel–Ecalle resummation. We show the emergence of a new kind of nonperturbative fixed point for the scalar [Formula: see text] model, representing an ultraviolet self-completion by transseries. We argue that this completion is purely non-Wilsonian and it depends on one arbitrary constant stemming from the transseries solution of the renormalization group equation. On the other hand, if no fixed points are demanded through the adjustment of this arbitrary constant, we end up with an effective theory in which the scalar mass is quadratically-sensitive to the cutoff, even working in dimensional regularization. Complete decoupling of the scalar mass to this energy scale can be used to determine a physical prescription for the Borel–Laplace resummation of the renormalons in nonasymptotically free models. We also comment on possible orthogonal scenarios available in the literature that might play a role when no fixed points exist.

Physics↗

Experimental determination of material damping using vibration analyzer

Structural damping is an important dynamic characteristic of engineering materials that helps to damp vibrations by reducing their amplitudes. In this investigation, an experimental method is illustrated to determine the damping characteristics of engineering materials using a dual channel Fast Fourier Transform (FFT) analyzer. A portable Compaq III computer which houses the analyzer, is used to collect the dynamic responses of three metal rods. Time-domain information is analyzed to obtain the logarithmic decrement of their damping. The damping coefficients are then compared to determine the variation of damping from material to material. The variations of damping from one point to another of the same material, due to a fixed point excitation, and the variable damping at a fixed point due to excitation at different points, are also demonstrated.

Chowdhury, Mostafiz R.↗

Dynamics and control of coherent structures in the turbulent wall layer: An overview

We expand the velocity field in the vicinity of the wall in empirical eigenfunctions obtained from experiment. Truncating our system and using Galerkin projection, we obtain a closed set of non-linear ordinary differential equations with ten degrees of freedom. We find a rich dynamical behavior, including in particular a heteroclinic attracting orbit giving rise to intermittency. The intermittent jump from one attracting point to the other resembles in many respects the bursts observed in experiments. Specifically, the time between jumps and the duration of the jumps, is approximately that observed in a burst; the jump begins with the formation of a narrowed and intensified updraft, like the ejection phase of a burst, and is followed by a gentle, diffuse downdraft like the sweep phase of a burst. The magnitude of the Reynolds stress spike produced during a burst is limited by our truncation. The behavior is quite robust, much of it being due to the symmetries present (Aubry's group has examined dimensions up to 128 with persistence of the global behavior). We have examined eigenvalues and coefficients obtained from experiment, and from exact simulation, which differ in magnitude. Similar behavior is obtained in both cases; in the latter case, the heteroclinic orbits connect limit cycles instead of fixed points, corresponding to cross-stream waving of the streamwise rolls. The bifurcation diagram remains structurally similar, but somewhat distorted. The role of the pressure term is made clear - it triggers the intermittent jumps, which otherwise would occur at longer and longer intervals, as the system trajectory is attracted closer and closer to the heteroclinic cycle. The pressure term results in the jumps occurring at essentially random times, and the magnitude of the signal determines the average timing. Stretching of the wall region shows that the model is consistent with observations of polymer drag reduction. Change of the third order coefficients, corresponding to acceleration or deceleration of the mean flow, changes the heteroclinic cycles from attracting to repelling, increasing or decreasing the stability, in agreement with observations. The existence of fixed points is an artifact introduced by the projection; however, a decoupled model still displays the rich dynamics. Numerous assumptions made in Aubry et al. (1988) can now be proved exactly. Feeding back eigenfuncitons with the proper phase can delay the bursting, (the heteroclinic jump to the other fixed point), decreasing the drag. It is also possible to speed up the bursting, increasing mixing to control separation. Our approach is optimal for short time tracking in control.

Berkooz, Gal↗

A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. Here, we prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.

97 MATHEMATICS AND COMPUTING↗

Some results on contractive mappings as related to pattern recognition

Several of the techniques used in pattern recognition are reformulated as the problem of determining fixed points of a function. If x sub 0 is a fixed point of f and if f is contractive at x sub 0, then, for any y belonging to a sufficiently small neighborhood of x sub 0 the orbit of y will converge to x sub 0. Several general results regarding contractive mappings are developed with emphasis on functions.

Brown, D. R.↗

Anderson acceleration with approximate calculations: Applications to scientific computing

Here we provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least-squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed-point iterations arising from the Richardson's scheme to solve linear systems with open-source benchmark matrices with various preconditioners and (ii) non-linear deterministic fixed-point iterations arising from non-linear time-dependent Boltzmann equations.

97 MATHEMATICS AND COMPUTING↗

Effects of motion of the equatorial plane on the orbital elements of an earth satellite.

Exact differential equations relating the perturbations to satellite orbital elements by the motion of the earth's equatorial plane are derived, and they are solved to second order in precession. The system proposed in a previous paper (Kozai, 1960), in which the inclination and the argument of perigee are referred to the equator of date and the longitude of the ascending node is measured from a fixed point along a fixed plane and then along the equator of date, can still be recommended for precise studies of satellite motion even when the second-order perturbations are taken into account.

Kozai, Y.↗

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.↗

Cloud Ozone Dust Imager (CODI): Investigation and Technical Plan - Volume 1

The Cloud Ozone Dust Imager (CODI) is proposed to investigate the current climatic balance of the Mars atmosphere, with particular emphasis on the important but poorly understood roles which dust and water ice aerosols play in this balance. The large atmospheric heating (20-50 K) resulting from global dust storms around Mars perihelion is well recognized. However, groundbased observations of Mars atmospheric temperatures, water vapor, and clouds since the Viking missions have identified a much colder, cloudier atmosphere around Mars aphelion that may prove as important as global dust storms in determining the interannual and long-term behavior of the Mars climate. The key climate issues CODI is designed to investigate are: 1) the degree to which non-linear interactions between atmospheric dust heating, water vapor saturation, and cloud nucleation influence the seasonal and interannual variability of the Mars atmosphere, and 2) whether the strong orbital forcing of atmospheric dust loading, temperatures and water vapor saturation determines the long-term balance of Mars water, as reflected in the north-south hemispheric asymmetries of atmospheric water vapor and polar water ice abundances. The CODI experiment will measure the daily, seasonal and (potentially) interannual variability of atmospheric dust and cloud opacities, and the key physical properties of these aerosols which determine their role in the climate cycles of Mars. CODI is a small (1.2 kg), fixed pointing camera, in which four wide-angle (+/- 70 deg) lenses illuminate fixed filters and CCD arrays. Simultaneous sky/surface imaging of Mars is obtained at an angular resolution of 0.28 deg/pixel for wavelengths of 255, 336, 502, and 673 nm (similar to Hubble Space Telescope filters). These wavelengths serve to measure atmospheric ozone (255 and 336 nm), discriminate ice and dust aerosols (336 and 673 nm), and construct color images (336, 502, and 673 nm). The CODI images are detected on four 512 x 512 pixel arrays, as partitioned on two 1024 x 1024 CCD's operated in frame transfer mode. The center of the CODI field-of-view is canted 40 deg from the zenith direction to obtain sky brightness measurements and a 20 deg surface field-of-view. Daily image observations will be conducted when the Sun is greater than or equal to 5 deg outside the edge of the CODI field-of-view, and twilight and nighttime imaging will obtained on a weekly basis. The 673 nm channel includes a polarizer wheel to obtain sky/surface polarimetry. A dust cover protects the entire lens assemblies of all four CODI channels. This opaque dust cover, which is normally opened for CODI imaging, includes a small fixed mirror and transparent window positioned above the 673 nm lens, to redirect the 673 nm field-of-view to the surface for descent imaging. Fixed pointing, internal data buffering, low operating power (2-4 W for less than or equal to 30 seconds), selective data transmission, and simple operational characteristics of the CODI experiment place minimum resource and operational demands on the Mars Surveyor 1998 lander. The CODI science goals are optimized for, but not restricted to, a low-latitude landing site (20 deg S-30 deg N). The primary CODI measurement objectives are the opacities, wave forms, particle properties (size, shape, and alignment), and heights of clouds; the opacities, particle properties, and vertical distribution of dust; and the opacity and vertical distribution of ozone. The variability of cloud, ozone, and dust opacities will be determined on diurnal, daily, and seasonal timescales. Wind velocities will be determined from cloud motions and wave characteristics; and the temporal variability of atmospheric water vapor, with limited altitude information, will be inferred from the CODI ozone observations. Secondary measurement objectives include limited descent imaging capability, surface uv-visible photometry and polarimetry, photochemistry, and meteorite infall rates.

Clancy, R. Todd↗

Projective embedding of dynamical systems: Uniform mean field equations

Herein we study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the original system dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of rank-1 projector operator, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. We prove a variety of results on the relationship between the spectrum of the Jacobian for fixed points in the original and in the embedded system. Direct applications of PEDS can be non-convex optimization and machine learning.

97 MATHEMATICS AND COMPUTING↗

Implementing system simulation of C3 systems using autonomous objects

The basis of all conflict recognition in simulation is a common frame of reference. Synchronous discrete-event simulation relies on the fixed points in time as the basic frame of reference. Asynchronous discrete-event simulation relies on fixed-points in the model space as the basic frame of reference. Neither approach provides sufficient support for autonomous objects. The use of a spatial template as a frame of reference is proposed to address these insufficiencies. The concept of a spatial template is defined and an implementation approach offered. Discussed are the uses of this approach to analyze the integration of sensor data associated with Command, Control, and Communication systems.

Rogers, Ralph V.↗

Reconfigurable Advanced Receiver Design and Implementation

While the demand for real-time broadband information access has grown and continues to grow at a rapid Pace, the need for a reconfigurable receiver system has increased. To achieve the goal to communicate with multiple shuttles at a time, a filter bank in polyphase structure is introduced. This paper presents the design and implementation for high-speed, high-performance, and fixed-point polyphase filter banks. The polyphase filter structure is designed such that the use of a fixed-point system has minimum impact on the performance of the filter. The final hardware implementation is done on a Xilinx FPGA chip.

Xu, Jianjing↗