Some nonlinear space decomposition algorithms
Tai, Xue-Cheng; Espedal, M.
1996-12-31
Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.
Nonlinear vibrating system identification via Hilbert decomposition
NASA Astrophysics Data System (ADS)
Feldman, Michael; Braun, Simon
2017-02-01
This paper deals with the identification of nonlinear vibration systems, based on measured signals for free and forced vibration regimes. Two categories of time domain signal are analyzed, one of a fast inter-modulation signal and a second as composed of several mono-components. To some extent, this attempts to imitate analytic studies of such systems, with its two major analysis groups - the perturbation and the harmonic balance methods. Two appropriate signal processing methods are then investigated, one based on demodulation and the other on signal decomposition. The Hilbert Transform (HT) has been shown to enable effective and simple methods of analysis. We show that precise identification of the nonlinear parameters can be obtained, contrary to other average HT based methods where only approximation parameters are obtained. The effectiveness of the proposed methods is demonstrated for the precise nonlinear system identification, using both the signal demodulation and the signal decomposition methods. Following the exposition of the tools used, both the signal demodulation as well as decomposition are applied to classical examples of nonlinear systems. Cases of nonlinear stiffness and damping forces are analyzed. These include, among other, an asymmetric Helmholtz oscillator, a backlash with nonlinear turbulent square friction, and a Duffing oscillator with dry friction.
Nonlinear mode decomposition: A noise-robust, adaptive decomposition method
NASA Astrophysics Data System (ADS)
Iatsenko, Dmytro; McClintock, Peter V. E.; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool—nonlinear mode decomposition (NMD)—which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques—which, together with the adaptive choice of their parameters, make it extremely noise robust—and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Nonlinear mode decomposition: a noise-robust, adaptive decomposition method.
Iatsenko, Dmytro; McClintock, Peter V E; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques-which, together with the adaptive choice of their parameters, make it extremely noise robust-and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Regular Decompositions for H(div) Spaces
Kolev, Tzanio; Vassilevski, Panayot
2012-01-01
We study regular decompositions for H(div) spaces. In particular, we show that such regular decompositions are closely related to a previously studied “inf-sup” condition for parameter-dependent Stokes problems, for which we provide an alternative, more direct, proof.
Decomposition theorem in ideal topological spaces
NASA Astrophysics Data System (ADS)
AL-omeri, W.; Noorani, Mohd. Salmi; AL-Omari, A.
2014-06-01
We introduce new classes of sets called a* -I -open,A-β-I-open sets, A-pre* -I-open sets, strongly T-I -sets, A-β-T-I-sets, strongly BA -I -sets, BA -I -sets, and δβA -I -open sets in ideal topological spaces. Using these sets, to obtain decompositions of continuity in an ideal topological space.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
Nonlinear Oscillators in Space Physics
NASA Technical Reports Server (NTRS)
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
Nonlinear Elasticity in a Deforming Ambient Space
NASA Astrophysics Data System (ADS)
Yavari, Arash; Ozakin, Arkadas; Sadik, Souhayl
2016-12-01
In this paper, we formulate a nonlinear elasticity theory in which the ambient space is evolving. For a continuum moving in an evolving ambient space, we model time dependency of the metric by a time-dependent embedding of the ambient space in a larger manifold with a fixed background metric. We derive both the tangential and the normal governing equations. We then reduce the standard energy balance written in the larger ambient space to that in the evolving ambient space. We consider quasi-static deformations of the ambient space and show that a quasi-static deformation of the ambient space results in stresses, in general. We linearize the nonlinear theory about a reference motion and show that variation of the spatial metric corresponds to an effective field of body forces.
Nonlinear E -mode clustering in Lagrangian space
NASA Astrophysics Data System (ADS)
Yu, Hao-Ran; Pen, Ue-Li; Zhu, Hong-Ming
2017-02-01
We study the nonlinear E -mode clustering in Lagrangian space by using large scale structure N -body simulations and use the displacement field information in Lagrangian space to recover the primordial linear density field. We find that, compared to Eulerian nonlinear density fields, the E -mode displacement fields in Lagrangian space improves the cross-correlation scale k with initial density field by a factor of 6-7, containing 2 orders of magnitude more primordial information. This illustrates ability of potential density reconstruction algorithms, to improve the baryonic acoustic oscillation measurements from current and future large scale structure surveys.
Decomposition of fuzzy soft sets with finite value spaces.
Feng, Feng; Fujita, Hamido; Jun, Young Bae; Khan, Madad
2014-01-01
The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter.
NASA Astrophysics Data System (ADS)
Feigin, Alexander; Gavrilov, Andrey; Loskutov, Evgeny; Mukhin, Dmitry
2015-04-01
Proper decomposition of the complex system into well separated "modes" is a way to reveal and understand the mechanisms governing the system behaviour as well as discover essential feedbacks and nonlinearities. The decomposition is also natural procedure that provides to construct adequate and concurrently simplest models of both corresponding sub-systems, and of the system in whole. In recent works two new methods of decomposition of the Earth's climate system into well separated modes were discussed. The first method [1-3] is based on the MSSA (Multichannel Singular Spectral Analysis) [4] for linear expanding vector (space-distributed) time series and makes allowance delayed correlations of the processes recorded in spatially separated points. The second one [5-7] allows to construct nonlinear dynamic modes, but neglects delay of correlations. It was demonstrated [1-3] that first method provides effective separation of different time scales, but prevent from correct reduction of data dimension: slope of variance spectrum of spatio-temporal empirical orthogonal functions that are "structural material" for linear spatio-temporal modes, is too flat. The second method overcomes this problem: variance spectrum of nonlinear modes falls essentially sharply [5-7]. However neglecting time-lag correlations brings error of mode selection that is uncontrolled and increases with growth of mode time scale. In the report we combine these two methods in such a way that the developed algorithm allows constructing nonlinear spatio-temporal modes. The algorithm is applied for decomposition of (i) multi hundreds years globally distributed data generated by the INM RAS Coupled Climate Model [8], and (ii) 156 years time series of SST anomalies distributed over the globe [9]. We compare efficiency of different methods of decomposition and discuss the abilities of nonlinear spatio-temporal modes for construction of adequate and concurrently simplest ("optimal") models of climate systems
Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition.
Mauguière, Frédéric A L; Collins, Peter; Kramer, Zeb C; Carpenter, Barry K; Ezra, Gregory S; Farantos, Stavros C; Wiggins, Stephen
2015-10-15
We re-examine the prototypical roaming reaction--hydrogen atom roaming in formaldehyde decomposition--from a phase space perspective. Specifically, we address the question "why do trajectories roam, rather than dissociate through the radical channel?" We describe and compute the phase space structures that define and control all possible reactive events for this reaction, as well as provide a dynamically exact description of the roaming region in phase space. Using these phase space constructs, we show that in the roaming region, there is an unstable periodic orbit whose stable and unstable manifolds define a conduit that both encompasses all roaming trajectories exiting the formaldehyde well and shepherds them toward the H2···CO well.
Efficient variants of the vertex space domain decomposition algorithm
Chan, T.F.; Shao, J.P. . Dept. of Mathematics); Mathew, T.P. . Dept. of Mathematics)
1994-11-01
Several variants of the vertex space algorithm of Smith for two-dimensional elliptic problems are described. The vertex space algorithm is a domain decomposition method based on nonoverlapping subregions, in which the reduced Schur complement system on the interface is solved using a generalized block Jacobi-type preconditioner, with the blocks corresponding to the vertex space, edges, and a coarse grid. Two kinds of approximations are considered for the edge and vertex space subblocks, one based on Fourier approximation, and another based on an algebraic probing technique in which sparse approximations to these subblocks are computed. The motivation is to improve the efficiency of the algorithm without sacrificing the optimal convergence rate. Numerical and theoretical results on the performance of these algorithms, including variants of an algorithm of Bramble, Pasciak, and Schatz are presented.
A comparison between the propagators method and the decomposition method for nonlinear equations
Azmy, Y.Y.; Protopopescu, V. ); Cacuci, D.G. . Dept. of Chemical and Nuclear Engineering)
1990-01-01
Recently, a new formalism for solving nonlinear problems has been formulated. The formalism is based on the construction of advanced and retarded propagators that generalize the customary Green's functions in linear theory. One of the main advantages of this formalism is the possibility of transforming nonlinear differential equations into nonlinear integral equations that are usually easier to handle theoretically and computationally. The aim of this paper is to compare, on an example, the performances of the propagator method with other methods used for nonlinear equations, in particular, the decomposition method. The propagator method is stable, accurate, and efficient for all initial values and time intervals considered, while the decomposition method is unstable at large time intervals, even for very conveniently chosen initial conditions. 5 refs., 4 tabs.
Nonextensivity, Complexity and Nonlinearity in Space Plasmas
NASA Astrophysics Data System (ADS)
Pavlos, G. P.
2017-01-01
Experimental time series, extracted from many and different space plasma systems corresponding to, solar wind, magnetospheric and other space plasma systems reveal common dynamical, geometrical, or statistical characteristics. Such characteristics are the low dimensionality, the typical intermittent turbulence multifractality, the temporal or spatial multiscale correlations and power laws scale invariance, non Gaoussianity and others. This universal aspect of experimental time series profiles was understood in the past as the chaos or SOC universality. However, after two or three decades of theoretical development in understanding of the nonlinearity and complexity, we can give a more compact theoretical description of the underline universal physical processes that produce the experimental time series complexity. Finally, in this study, we present and explain the modern complex set of theoretical concepts from the point of view of physics as the unification theory of nonlinear theory of non-equilibrium plasma systems as well as the presupposed theoretical framework of time series analysis of space plasma charachteristics.
Nonlinear color-image decomposition for image processing of a digital color camera
NASA Astrophysics Data System (ADS)
Saito, Takahiro; Aizawa, Haruya; Yamada, Daisuke; Komatsu, Takashi
2009-01-01
This paper extends the BV (Bounded Variation) - G and/or the BV-L1 variational nonlinear image-decomposition approaches, which are considered to be useful for image processing of a digital color camera, to genuine color-image decomposition approaches. For utilizing inter-channel color cross-correlations, this paper first introduces TV (Total Variation) norms of color differences and TV norms of color sums into the BV-G and/or BV-L1 energy functionals, and then derives denoising-type decomposition-algorithms with an over-complete wavelet transform, through applying the Besov-norm approximation to the variational problems. Our methods decompose a noisy color image without producing undesirable low-frequency colored artifacts in its separated BV-component, and they achieve desirable high-quality color-image decomposition, which is very robust against colored random noise.
NASA Technical Reports Server (NTRS)
Huang, Norden E.; Zukor, Dorothy J. (Technical Monitor)
2001-01-01
A new method for analyzing nonlinear and nonstationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Classical nonlinear system models are used to illustrate the roles played by the nonlinear and nonstationary effects in the energy-frequency-time distribution.
Chirped nonlinear resonance dynamics in phase space
NASA Astrophysics Data System (ADS)
Friedland, Lazar; Armon, Tsafrir
2016-10-01
Passage through and capture into resonance in systems with slowly varying parameters is one of the outstanding problems of nonlinear dynamics. Examples include resonant capture in planetary dynamics , resonant excitation of nonlinear waves, adiabatic resonant transitions in atomic and molecular systems and more. In the most common setting the problem involves a nonlinear oscillator driven by an oscillating perturbation with a slowly varying frequency, which passes through the resonance with the unperturbed oscillator. The process of resonant capture in this case involves crossing of separatrix and, therefore, the adiabatic theorem cannot be used in studying this problem no matter how slow is the variation of the driving frequency. It will be shown that if instead of analyzing complicated single orbit dynamics in passage through resonance, one considers the evolution of a distribution of initial conditions in phase space, simple adiabaticity and phase space incompressibility arguments yield a solution to the resonant capture probability problem. The approach will be illustrated in the case of a beam of charged particles driven by a chirped frequency wave passing through the Cherenkov resonance with the velocity distribution of the particles. Supported by Israel Science Foundation Grant 30/14.
NASA Astrophysics Data System (ADS)
Georgiou, K.; Tang, J.; Riley, W. J.; Torn, M. S.
2014-12-01
Soil organic matter (SOM) decomposition is regulated by biotic and abiotic processes. Feedback interactions between such processes may act to dampen oscillatory responses to perturbations from equilibrium. Indeed, although biological oscillations have been observed in small-scale laboratory incubations, the overlying behavior at the plot-scale exhibits a relatively stable response to disturbances in input rates and temperature. Recent studies have demonstrated the ability of microbial models to capture nonlinear feedbacks in SOM decomposition that linear Century-type models are unable to reproduce, such as soil priming in response to increased carbon input. However, these microbial models often exhibit strong oscillatory behavior that is deemed unrealistic. The inherently nonlinear dynamics of SOM decomposition have important implications for global climate-carbon and carbon-concentration feedbacks. It is therefore imperative to represent these dynamics in Earth System Models (ESMs) by introducing sub-models that accurately represent microbial and abiotic processes. In the present study we explore, both analytically and numerically, four microbe-enabled model structures of varying levels of complexity. The most complex model combines microbial physiology, a non-linear mineral sorption isotherm, and enzyme dynamics. Based on detailed stability analysis of the nonlinear dynamics, we calculate the system modes as functions of model parameters. This dependence provides insight into the source of state oscillations. We find that feedback mechanisms that emerge from careful representation of enzyme and mineral interactions, with parameter values in a prescribed range, are critical for both maintaining system stability and capturing realistic responses to disturbances. Corroborating and expanding upon the results of recent studies, we explain the emergence of oscillatory responses and discuss the appropriate microbe-enabled model structure for inclusion in ESMs.
Huang, Shaoguang; Tian, Lan; Ma, Xiaojie; Wei, Ying
2016-04-01
Hearing impaired people have their own hearing loss characteristics and listening preferences. Therefore hearing aid system should become more natural, humanized and personalized, which requires the filterbank in hearing aids provides flexible sound wave decomposition schemes, so that patients are likely to use the most suitable scheme for their own hearing compensation strategy. In this paper, a reconfigurable sound wave decomposition filterbank is proposed. The prototype filter is first cosine modulated to generate uniform subbands. Then by non-linear transformation the uniform subbands are mapped to nonuniform subbands. By changing the control parameters, the nonlinear transformation changes which leads to different subbands allocations. It provides four different sound wave decomposition schemes without changing the structure of the filterbank. The performance of the proposed reconfigurable filterbank was compared with that of fixed filerbanks, fully customizable filterbanks and other existing reconfigurable filterbanks. It is shown that the proposed filterbank provides satisfactory matching performance as well as low complexity and delay, which make it suitable for real hearing aid applications.
Middleton, Beth A.
2014-01-01
A cornerstone of ecosystem ecology, decomposition was recognized as a fundamental process driving the exchange of energy in ecosystems by early ecologists such as Lindeman 1942 and Odum 1960). In the history of ecology, studies of decomposition were incorporated into the International Biological Program in the 1960s to compare the nature of organic matter breakdown in various ecosystem types. Such studies still have an important role in ecological studies of today. More recent refinements have brought debates on the relative role microbes, invertebrates and environment in the breakdown and release of carbon into the atmosphere, as well as how nutrient cycling, production and other ecosystem processes regulated by decomposition may shift with climate change. Therefore, this bibliography examines the primary literature related to organic matter breakdown, but it also explores topics in which decomposition plays a key supporting role including vegetation composition, latitudinal gradients, altered ecosystems, anthropogenic impacts, carbon storage, and climate change models. Knowledge of these topics is relevant to both the study of ecosystem ecology as well projections of future conditions for human societies.
Bao, Fei; Li, Chen; Wang, Xinlong; Wang, Qingfu; Du, Shuanping
2010-07-01
Classification for ship-radiated underwater sound is one of the most important and challenging subjects in underwater acoustical signal processing. An approach to ship classification is proposed in this work based on analysis of ship-radiated acoustical noise in subspaces of intrinsic mode functions attained via the ensemble empirical mode decomposition. It is shown that detection and acquisition of stable and reliable nonlinear features become practically feasible by nonlinear analysis of the time series of individual decomposed components, each of which is simple enough and well represents an oscillatory mode of ship dynamics. Surrogate and nonlinear predictability analysis are conducted to probe and measure the nonlinearity and regularity. The results of both methods, which verify each other, substantiate that ship-radiated noises contain components with deterministic nonlinear features well serving for efficient classification of ships. The approach perhaps opens an alternative avenue in the direction toward object classification and identification. It may also import a new view of signals as complex as ship-radiated sound.
Nonlinear whistler wave scattering in space plasmas
Yukhimuk, V.; Roussel-Dupre, R.
1997-04-01
In this paper the evolution of nonlinear scattering of whistler mode waves by kinetic Alfven waves (KAW) in time and two spatial dimensions is studied analytically. The authors suggest this nonlinear process as a mechanism of kinetic Alfven wave generation in space plasmas. This mechanism can explain the dependence of Alfven wave generation on whistler waves observed in magnetospheric and ionospheric plasmas. The observational data show a dependence for the generation of long periodic pulsations Pc5 on whistler wave excitation in the auroral and subauroral zone of the magnetosphere. This dependence was first observed by Ondoh T.I. For 79 cases of VLF wave excitation registered by Ondoh at College Observatory (L=64.6 N), 52 of them were followed by Pc5 geomagnetic pulsation generation. Similar results were obtained at the Loparskaia Observatory (L=64 N) for auroral and subauroral zone of the magnetosphere. Thus, in 95% of the cases when VLF wave excitation occurred the generation of long periodic geomagnetic pulsations Pc5 were observed. The observations also show that geomagnetic pulsations Pc5 are excited simultaneously or insignificantly later than VLF waves. In fact these two phenomena are associated genetically: the excitation of VLF waves leads to the generation of geomagnetic pulsations Pc5. The observations show intensive generation of geomagnetic pulsations during thunderstorms. Using an electromagnetic noise monitoring system covering the ULF range (0.01-10 Hz) A.S. Fraser-Smith observed intensive ULF electromagnetic wave during a large thunderstorm near the San-Francisco Bay area on September 23, 1990. According to this data the most significant amplification in ULF wave activity was observed for waves with a frequency of 0.01 Hz and it is entirely possible that stronger enhancements would have been measured at lower frequencies.
Unconditional Schauder decompositions and stopping times in the Lebesgue-Bochner spaces
NASA Astrophysics Data System (ADS)
Cullender, Stuart F.; Labuschagne, Coenraad C. A.
2007-12-01
We extend Troitsky's study of martingales in Banach lattices to include stopping times. Results from the theory of unconditional Schauder decompositions and multipliers are used to derive an optional stopping theorem for unbounded stopping times. We also apply these techniques to convergent nets of stopped processes, as well as to unconditional Schauder decompositions in vector-valued Lp-spaces (1
Valuation of financial models with non-linear state spaces
NASA Astrophysics Data System (ADS)
Webber, Nick
2001-02-01
A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.
NASA Astrophysics Data System (ADS)
Jiang, Fan; Zhu, Zhencai; Li, Wei; Zhou, Gongbo; Chen, Guoan
2014-07-01
Accurately identifying faults in rotor-bearing systems by analyzing vibration signals, which are nonlinear and nonstationary, is challenging. To address this issue, a new approach based on ensemble empirical mode decomposition (EEMD) and self-zero space projection analysis is proposed in this paper. This method seeks to identify faults appearing in a rotor-bearing system using simple algebraic calculations and projection analyses. First, EEMD is applied to decompose the collected vibration signals into a set of intrinsic mode functions (IMFs) for features. Second, these extracted features under various mechanical health conditions are used to design a self-zero space matrix according to space projection analysis. Finally, the so-called projection indicators are calculated to identify the rotor-bearing system's faults with simple decision logic. Experiments are implemented to test the reliability and effectiveness of the proposed approach. The results show that this approach can accurately identify faults in rotor-bearing systems.
Nonlinear regime-switching state-space (RSSS) models.
Chow, Sy-Miin; Zhang, Guangjian
2013-10-01
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
High Speed Nonlinear Interferometric Vibrational Analysis of Lipids by Spectral Decomposition
Chowdary, Praveen D.; Benalcazar, Wladimir A.; Jiang, Zhi; Marks, Daniel M.
2010-01-01
Unlike other CARS-based spectroscopy techniques, nonlinear interferometric vibrational spectroscopy (NIVS) is linear in analyte concentration and has a Raman lineshape free of non-resonant background distortions. We use spontaneous Raman scattering as a high accuracy benchmark for NIVS. As a challenging comparison, we examine spectra in the CH stretching region of 6 lipid samples. Singular value decomposition and reference to an independent chemical assay are used to directly compare NIVS and spontaneous Raman scattering. We demonstrate that NIVS can determine the relative degree of unsaturation in six different lipid samples as accurately as spontaneous Raman spectroscopy, but 200 times faster. A skin tissue sample is mapped out to demonstrate quantitative lipid-protein differentiation with spatial resolution. PMID:20373786
Bahri, A.; Bendersky, M.; Cohen, F. R.; Gitler, S.
2009-01-01
This article gives a natural decomposition of the suspension of a generalized moment-angle complex or partial product space which arises as the polyhedral product functor described below. The introduction and application of the smash product moment-angle complex provides a precise identification of the stable homotopy type of the values of the polyhedral product functor. One direct consequence is an analysis of the associated cohomology. For the special case of the complements of certain subspace arrangements, the geometrical decomposition implies the homological decomposition in earlier work of others as described below. Because the splitting is geometric, an analogous homological decomposition for a generalized moment-angle complex applies for any homology theory. Implied, therefore, is a decomposition for the Stanley–Reisner ring of a finite simplicial complex, and natural generalizations. PMID:19620727
A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems
NASA Astrophysics Data System (ADS)
Taverniers, Søren; Tartakovsky, Daniel M.
2017-02-01
Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton-Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.
Spinodal Decomposition for theCahn-Hilliard Equation in Higher Dimensions:Nonlinear Dynamics
NASA Astrophysics Data System (ADS)
Maier-Paape, Stanislaus; Wanner, Thomas
This paper addresses the phenomenon of spinodal decomposition for the Cahn-Hilliard equation
NASA Astrophysics Data System (ADS)
Amabili, M.; Sarkar, A.; Païdoussis, M. P.
2003-09-01
The nonlinear (large-amplitude) response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of their lowest natural frequencies is investigated. The shell is assumed to be completely filled with an incompressible and inviscid fluid at rest. Donnell's nonlinear shallow-shell theory is used, and the solution is obtained by the Galerkin method. The proper orthogonal decomposition (POD) method is used to extract proper orthogonal modes that describe the system behaviour from time-series response data. These time series have been obtained via the conventional Galerkin approach (using normal modes as a projection basis) with an accurate model involving 16 degrees of freedom, validated in previous studies. The POD method, in conjunction with the Galerkin approach, permits a lower-dimensional model as compared to those obtainable via the conventional Galerkin approach. Different proper orthogonal modes computed from time series at different excitation frequencies are used and solutions are compared. Some of these sets of modes are capable of describing the system behaviour over the whole frequency range around the fundamental resonance with good accuracy and with only 3 degrees of freedom. They allow a drastic reduction in the computational effort, as compared to using the 16 degree-of-freedom model necessary when the conventional Galerkin approach is used.
The geometry of the light-cone cell decomposition of moduli space
Garner, David Ramgoolam, Sanjaye
2015-11-15
The moduli space of Riemann surfaces with at least two punctures can be decomposed into a cell complex by using a particular family of ribbon graphs called Nakamura graphs. We distinguish the moduli space with all punctures labelled from that with a single labelled puncture. In both cases, we describe a cell decomposition where the cells are parametrised by graphs or equivalence classes of finite sequences (tuples) of permutations. Each cell is a convex polytope defined by a system of linear equations and inequalities relating light-cone string parameters, quotiented by the automorphism group of the graph. We give explicit examples of the cell decomposition at low genus with few punctures.
Ma, Matthew Huei-Ming
2016-01-01
Good quality cardiopulmonary resuscitation (CPR) is the mainstay of treatment for managing patients with out-of-hospital cardiac arrest (OHCA). Assessment of the quality of the CPR delivered is now possible through the electrocardiography (ECG) signal that can be collected by an automated external defibrillator (AED). This study evaluates a nonlinear approximation of the CPR given to the asystole patients. The raw ECG signal is filtered using ensemble empirical mode decomposition (EEMD), and the CPR-related intrinsic mode functions (IMF) are chosen to be evaluated. In addition, sample entropy (SE), complexity index (CI), and detrended fluctuation algorithm (DFA) are collated and statistical analysis is performed using ANOVA. The primary outcome measure assessed is the patient survival rate after two hours. CPR pattern of 951 asystole patients was analyzed for quality of CPR delivered. There was no significant difference observed in the CPR-related IMFs peak-to-peak interval analysis for patients who are younger or older than 60 years of age, similarly to the amplitude difference evaluation for SE and DFA. However, there is a difference noted for the CI (p < 0.05). The results show that patients group younger than 60 years have higher survival rate with high complexity of the CPR-IMFs amplitude differences. PMID:27529068
Performance of Scattering Matrix Decomposition and Color Spaces for Synthetic Aperture Radar Imagery
NASA Astrophysics Data System (ADS)
Terzuoli, Andrew; Arriagada, Manuel; Saville, Michael
Polarimetrc Synthetic Aperture Radar (SAR) has been shown to be a powerful tool in re-mote sensing because uses up to four simultaneous measurements giving additional degrees of freedom for processing. Typically, polarization decomposition techniques are applied to the polarization-dependent data to form colorful imagery that is easy for operators systems to interpret. Yet, the presumption is that the SAR system operates with maximum bandwidth which requires extensive processing for near-or real-time application. In this research, color space selection is investigated when processing sparse polarimetric SAR data as in the case of the publicly available Volumetric SAR Data Set, Version 1:0". To improve information quality in resultant color imagery, three scattering matrix decompositions were investigated (linear, Pauli and Krogager) using two common color spaces (RGB, CMY) to deter-mine the best combination for accurate feature extraction. A mathematical model is presented for each de-composition technique and color space to the Cramer-Rao lower bound (CRLB) and quantify the performance bounds from an estimation perspective for given SAR system and processing parameters. After a deep literature review in color science, the mathematical model for color spaces was not able to be computed together with the mathematical model for decomposition techniques. The color spaces used for this research were functions of variables that are out of the scope of electrical engineering research and include factors such as the way humans sense color, envi-ronment inuences in the color stimulus and device technical characteristics used to display the SAR image. Hence, SAR imagery was computed for speci c combinations of decomposition technique and color space and allow the reader to gain an abstract view of the performance differences. The views expressed in this article are those of the authors and do not reflect the official policy of the U.S. Air Force, U.S. Department of Defense
A modified descriptor for blob detection in nonlinear scale space
NASA Astrophysics Data System (ADS)
Zhao, Liangjin; Ding, Yan; Xu, Hong
2017-01-01
In this paper, we present a novel binary descriptor with orientation, which called Intensity-Centroid LDB (IC-LDB). This descriptor resolves the problems that the current non-binary descriptors are too compute-expensive to achieve real-time performance in the nonlinear scale space and that the original Local Difference Binary (LDB) descriptors do not have an orientation component to keep rotation invariant. Experimental results demonstrate that IC-LDB proposed in this paper was faster than previously non-binary descriptors which were used in nonlinear scale space, while performing as well in many situations.
Using Space as a Nonlinear Plasma Laboratory
NASA Astrophysics Data System (ADS)
Papadopoulos, Konstantinos
2008-11-01
Ionospheric heaters have been an important tool of plasma physics investigations. The extent that non-linear plasma phenomena can be triggered and observed depends critically on the heater power, its Effective Radiative Power (ERP) and its scanning capability. Increasing these parameters allows us to reach thresholds associated with effects that were not previously observed. The latest entry to ionospheric heating, the HF transmitter associated with the High Frequency Active Ionospheric Research Program (HAARP) was completed in June 2007. The transmitter consists of 180 antenna elements spanning 30.6 acres and can radiate 3.6 MW of HF power (a factor of almost 4 higher than any previous heater) in the 2.8-10.0 MHz range. With increasing frequency the beam-width varies from 15-5 degrees, corresponding to 20-30 dB gain and resulting in ERP between 1-5 GW. The antenna can point to any direction in a cone 30 degrees from the vertical, with reposition time of 15 microseconds resulting in superluminal scanning speeds. The transmitter can synthesize essentially any waveform and transmit any polarization. These capabilities far exceed those of any previous heater and allow for new frontier research in non-linear plasma physics. The presentation will focus first on the relationship of the new capabilities of the facility with thresholds of physical processes that had not been achieved previously. It will then present new spectacular results that have been achieved during the last year. They include whistler injection and amplification, injection of shear and magnetosonic waves in the magnetosphere, Langmuir turbulence, upper hybrid waves and thermal instabilities, electron acceleration, optical emissions and formation of artificial ducts for whistler propagation. The presentation will also discuss future experiments made possible for the first time by the new transmitter capabilities, large bandwidth and high ERP.
NASA Astrophysics Data System (ADS)
Atangana, Abdon
2013-10-01
We exploit a relatively new analytical technique, the Homotopy Decomposition Method (HDM), for solving nonlinear fractional partial differential equations arising in prey-predator biological population dynamics system. Numerical solutions are provided and they have certain properties which exhibit biologically significant dependence on the parameter values. The fractional derivatives are described in the Caputo sense. The HDM is reliable and reduces the number of computations. This gives the HDM a wider applicability. In addition, the method is very easy to use.
Reliability evaluation of nonlinear design space in pharmaceutical product development.
Hayashi, Yoshihiro; Kikuchi, Shingo; Onuki, Yoshinori; Takayama, Kozo
2012-01-01
Formulation design space of indomethacin tablets was investigated using a nonlinear response surface method incorporating multivariate spline interpolation (RSM-S). In this study, a resampling method with replacement was applied to evaluate the reliability of border on the design space estimated by RSM-S. The quantities of lactose, cornstarch, and microcrystalline cellulose were chosen as the formulation factors. Response surfaces were estimated using RSM-S, and the nonlinear design space was defined under the restriction of more than 3 kgf hardness and more than 70% dissolution 30 min before and after an accelerated test. The accuracy of the resampling method was elucidated and high correlation coefficients were produced. However, the distribution of the border on the design space generated by the resampling method was far from normal, and the confidence interval of the border was estimated using a nonparametric percentile technique. Consequently, the reliability of the design space was decreased by approaching the edge of the experimental design. RSM-S and this resampling method might be useful for estimating the reliability of nonlinear design space.
Domain decomposition methods for nonconforming finite element spaces of Lagrange-type
NASA Technical Reports Server (NTRS)
Cowsar, Lawrence C.
1993-01-01
In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.
Nonlinear Analysis of the Space Shuttle Superlightweight External Fuel Tank
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Britt, Vicki O.; Collins, Timothy J.; Starnes, James H., Jr.
1996-01-01
Results of buckling and nonlinear analyses of the Space Shuttle external tank superlightweight liquid-oxygen (LO2) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests that were conducted on the original external tank. The results illustrate three distinctly different types of nonlinear response for thin-walled shells subjected to combined mechanical and thermal loads. The nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of non- linear behavior generally require a large-scale, high-fidelity finite-element model. Results are also presented that show that a fluid-filled launch-vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full-scale structural tests of the original standard-weight external tank suggest that the finite-element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the superlightweight LO2 tank.
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.; Vassilevski, Panayot S.
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
An investigation of the use of temporal decomposition in space mission scheduling
NASA Technical Reports Server (NTRS)
Bullington, Stanley E.; Narayanan, Venkat
1994-01-01
This research involves an examination of techniques for solving scheduling problems in long-duration space missions. The mission timeline is broken up into several time segments, which are then scheduled incrementally. Three methods are presented for identifying the activities that are to be attempted within these segments. The first method is a mathematical model, which is presented primarily to illustrate the structure of the temporal decomposition problem. Since the mathematical model is bound to be computationally prohibitive for realistic problems, two heuristic assignment procedures are also presented. The first heuristic method is based on dispatching rules for activity selection, and the second heuristic assigns performances of a model evenly over timeline segments. These heuristics are tested using a sample Space Station mission and a Spacelab mission. The results are compared with those obtained by scheduling the missions without any problem decomposition. The applicability of this approach to large-scale mission scheduling problems is also discussed.
Nonlinear shell analyses of the space shuttle solid rocket boosters
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr.; Gillian, Ronnie E.; Nemeth, Michael P.
1989-01-01
A variety of structural analyses have been performed on the Solid Rocket Boosters (SRB's) to provide information that would contribute to the understanding of the failure which destroyed the Space Shuttle Challenger. This paper describes nonlinear shell analyses that were performed to characterize the behavior of an overall SRB structure and a segment of the SRB in the vicinity of the External Tank Attachment (ETA) ring. Shell finite element models were used that would accurately reflect the global load transfer in an SRB in a manner such that nonlinear shell collapse and ovalization could be assessed. The purpose of these analyses was to calculate the overall deflection and stress distributions for these SRB models when subjected to mechanical loads corresponding to critical times during the launch sequence. Static analyses of these SRB models were performed using a snapshot picture of the loads. Analytical results obtained using these models show no evidence of nonlinear shell collapse for the pre-liftoff loading cases considered.
A nonlinear filtering process diagnostic system for the Space Station
NASA Technical Reports Server (NTRS)
Yoel, Raymond R.; Buchner, M.; Loparo, K.; Cubukcu, Arif
1988-01-01
A nonlinear filtering process diagnostic system, terrestrial simulation and real time implementation studies is presented. Possible applications to Space Station subsystem elements are discussed. A process diagnostic system using model based nonlinear filtering for systems with random structure was shown to provide improvements in stability, robustness, and overall performance in comparison to linear filter based systems. A suboptimal version of the nonlinear filter (zero order approximation filter, or ZOA filter) was used in simulation studies, initially, with a pressurized water reactor model and then with water/steam heat exchanger models. Finally, a real time implementation for leak detection in a water/steam heat exchanger was conducted using the ZOA filter and heat exchanger models.
A nonlinear state-space approach to hysteresis identification
NASA Astrophysics Data System (ADS)
Noël, J. P.; Esfahani, A. F.; Kerschen, G.; Schoukens, J.
2017-02-01
Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinear state-space models to identify hysteresis dynamics. This approach is shown to provide a general framework to hysteresis identification, featuring flexibility and parsimony of representation. Nonlinear model terms are constructed as a multivariate polynomial in the state variables, and parameter estimation is performed by minimising weighted least-squares cost functions. Technical issues, including the selection of the model order and the polynomial degree, are discussed, and model validation is achieved in both broadband and sine conditions. The study is carried out numerically by exploiting synthetic data generated via the Bouc-Wen equations.
NASA Astrophysics Data System (ADS)
Rafiq Abuturab, Muhammad
2016-06-01
A new multiple color-image authentication system based on HSI (Hue-Saturation-Intensity) color space and QR decomposition in gyrator domains is proposed. In this scheme, original color images are converted from RGB (Red-Green-Blue) color spaces to HSI color spaces, divided into their H, S, and I components, and then obtained corresponding phase-encoded components. All the phase-encoded H, S, and I components are individually multiplied, and then modulated by random phase functions. The modulated H, S, and I components are convoluted into a single gray image with asymmetric cryptosystem. The resulting image is segregated into Q and R parts by QR decomposition. Finally, they are independently gyrator transformed to get their encoded parts. The encoded Q and R parts should be gathered without missing anyone for decryption. The angles of gyrator transform afford sensitive keys. The protocol based on QR decomposition of encoded matrix and getting back decoded matrix after multiplying matrices Q and R, enhances the security level. The random phase keys, individual phase keys, and asymmetric phase keys provide high robustness to the cryptosystem. Numerical simulation results demonstrate that this scheme is the superior than the existing techniques.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
NASA Technical Reports Server (NTRS)
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Space vehicle pose estimation via optical correlation and nonlinear estimation
NASA Astrophysics Data System (ADS)
Rakoczy, John M.; Herren, Kenneth A.
2008-03-01
A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.
Space Vehicle Pose Estimation via Optical Correlation and Nonlinear Estimation
NASA Technical Reports Server (NTRS)
Rakoczy, John; Herren, Kenneth
2007-01-01
A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.
Space Vehicle Pose Estimation via Optical Correlation and Nonlinear Estimation
NASA Technical Reports Server (NTRS)
Rakoczy, John M.; Herren, Kenneth A.
2008-01-01
A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.
Parker, Shane M.; Shiozaki, Toru
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
NASA Astrophysics Data System (ADS)
Hofmann, M.; Rudolph, G.; Schmidt, M.
2013-08-01
We consider a system with symmetries whose configuration space is a compact Lie group, acted upon by inner automorphisms. The classical reduced phase space of this system decomposes into connected components of orbit type subsets. To investigate hypothetical quantum effects of this decomposition one has to construct the associated costratification of the Hilbert space of the quantum system in the sense of Huebschmann. In the present paper, instead of the decomposition by orbit types, we consider the related decomposition by reflection types (conjugacy classes of reflection subgroups). These two decompositions turn out to coincide, e.g., for the classical groups SU(n) and Sp(n). We derive defining relations for reflection type subsets in terms of irreducible characters and discuss how to obtain from that the corresponding costratification of the Hilbert space of the system. To illustrate the method, we give explicit results for some low rank classical groups.
Hierarchical approximate policy iteration with binary-tree state space decomposition.
Xu, Xin; Liu, Chunming; Yang, Simon X; Hu, Dewen
2011-12-01
In recent years, approximate policy iteration (API) has attracted increasing attention in reinforcement learning (RL), e.g., least-squares policy iteration (LSPI) and its kernelized version, the kernel-based LSPI algorithm. However, it remains difficult for API algorithms to obtain near-optimal policies for Markov decision processes (MDPs) with large or continuous state spaces. To address this problem, this paper presents a hierarchical API (HAPI) method with binary-tree state space decomposition for RL in a class of absorbing MDPs, which can be formulated as time-optimal learning control tasks. In the proposed method, after collecting samples adaptively in the state space of the original MDP, a learning-based decomposition strategy of sample sets was designed to implement the binary-tree state space decomposition process. Then, API algorithms were used on the sample subsets to approximate local optimal policies of sub-MDPs. The original MDP was decomposed into a binary-tree structure of absorbing sub-MDPs, constructed during the learning process, thus, local near-optimal policies were approximated by API algorithms with reduced complexity and higher precision. Furthermore, because of the improved quality of local policies, the combined global policy performed better than the near-optimal policy obtained by a single API algorithm in the original MDP. Three learning control problems, including path-tracking control of a real mobile robot, were studied to evaluate the performance of the HAPI method. With the same setting for basis function selection and sample collection, the proposed HAPI obtained better near-optimal policies than previous API methods such as LSPI and KLSPI.
On time-space of nonlinear phenomena with Gompertzian dynamics.
Waliszewski, Przemyslaw; Konarski, Jerzy
2005-04-01
This paper describes a universal relationship between time and space for a nonlinear process with Gompertzian dynamics, such as growth. Gompertzian dynamics implicates a coupling between time and space. Those two categories are related to each other through a linear function of their logarithms. Moreover, we demonstrate that the spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium of regular states, that is, states with dynamics that are predictable for any time-point (e.g., sinusoidal glycolytic oscillations) and chaotic states, that is, states with dynamics that are unpredictable in time, but are characterized by certain regularities (e.g., the existence of strange attractor for any biochemical reaction). We conclude that both this equilibrium and volume of the available complementary Euclidean space determine temporal and spatial expansion of a process with Gompertzian dynamics.
Nonlinear system identification with applications to space weather prediction
NASA Astrophysics Data System (ADS)
Palanthandalam-Madapusi, Harish J.
2007-02-01
System identification is the process of constructing empirical mathematical models of dynamcal systems using measured data. Since data represents a key link between mathematical principles and physical processes, system identification is an important research area that can benefit all disciplines. In this dissertation, we develop identification methods for Hammerstein-Wiener models, which are model structures based on the interconnection of linear dynamics and static nonlinearities. These identification methods identify models in state-space form and use known basis functions to represent the unknown nonlinear maps. Next, we use these methods to identify periodically- switching Hammerstein-Wiener models for predicting magnetic-field fluctuation on the surface of the Earth, 30 to 90 minutes into the future. These magnetic- field fluctuations caused by the solar wind (ejections of charged plasma from the surface of the Sun) can damage critical systems aboard satellites and drive currents in power grids that can overwhelm and damage transformers. By predicting magnetic-field fluctuations on the Earth, we obtain advance warning of future disturbances. Furthermore, to predict solar wind conditions 27 days in advance, we use solar wind measurements and image measurements to construct nonlinear time-series models. We propose a class of radial basis functions to represent the nonlinear maps, which have fewer parameters that need to be tuned by the user. Additionally, we develop an identification algorithm that simultaneously identifies the state space matrices of an unknown model and reconstructs the unknown input, using output measurements and known inputs. For this purpose, we formulate the concept of input and state observability, that is, conditions under which both the unknown input and initial state of a known model can be determined from output measurements. We provide necessary and sufficient conditions for input and state observability in discrete-time systems.
Spatiotemporal Domain Decomposition for Massive Parallel Computation of Space-Time Kernel Density
NASA Astrophysics Data System (ADS)
Hohl, A.; Delmelle, E. M.; Tang, W.
2015-07-01
Accelerated processing capabilities are deemed critical when conducting analysis on spatiotemporal datasets of increasing size, diversity and availability. High-performance parallel computing offers the capacity to solve computationally demanding problems in a limited timeframe, but likewise poses the challenge of preventing processing inefficiency due to workload imbalance between computing resources. Therefore, when designing new algorithms capable of implementing parallel strategies, careful spatiotemporal domain decomposition is necessary to account for heterogeneity in the data. In this study, we perform octtree-based adaptive decomposition of the spatiotemporal domain for parallel computation of space-time kernel density. In order to avoid edge effects near subdomain boundaries, we establish spatiotemporal buffers to include adjacent data-points that are within the spatial and temporal kernel bandwidths. Then, we quantify computational intensity of each subdomain to balance workloads among processors. We illustrate the benefits of our methodology using a space-time epidemiological dataset of Dengue fever, an infectious vector-borne disease that poses a severe threat to communities in tropical climates. Our parallel implementation of kernel density reaches substantial speedup compared to sequential processing, and achieves high levels of workload balance among processors due to great accuracy in quantifying computational intensity. Our approach is portable of other space-time analytical tests.
An ISAR imaging algorithm for the space satellite based on empirical mode decomposition theory
NASA Astrophysics Data System (ADS)
Zhao, Tao; Dong, Chun-zhu
2014-11-01
Currently, high resolution imaging of the space satellite is a popular topic in the field of radar technology. In contrast with regular targets, the satellite target often moves along with its trajectory and simultaneously its solar panel substrate changes the direction toward the sun to obtain energy. Aiming at the imaging problem, a signal separating and imaging approach based on the empirical mode decomposition (EMD) theory is proposed, and the approach can realize separating the signal of two parts in the satellite target, the main body and the solar panel substrate and imaging for the target. The simulation experimentation can demonstrate the validity of the proposed method.
Longitudinal emittance growth due to nonlinear space charge effect
NASA Astrophysics Data System (ADS)
Lau, Y. Y.; Yu, Simon S.; Barnard, John J.; Seidl, Peter A.
2012-03-01
Emittance posts limits on the key requirements of final pulse length and spot size on target in heavy ion fusion drivers. In this paper, we show studies on the effect of nonlinear space charge on longitudinal emittance growth in the drift compression section. We perform simulations, using the 3D PIC code WARP, for a high current beam under conditions of bends and longitudinal compression. The linear growth rate for longitudinal emittance turns out to depend only on the peak line charge density, and is independent of pulse length, velocity tilt, and/or the pipe and beam size. This surprisingly simple result is confirmed by simulations and analytic calculations.
Nonlinear rotordynamics analysis. [Space Shuttle Main Engine turbopumps
NASA Technical Reports Server (NTRS)
Noah, Sherif T.
1991-01-01
Effective analysis tools were developed for predicting the nonlinear rotordynamic behavior of the Space Shuttle Main Engine (SSME) turbopumps under steady and transient operating conditions. Using these methods, preliminary parametric studies were conducted on both generic and actual HPOTP (high pressure oxygen turbopump) models. In particular, a novel modified harmonic balance/alternating Fourier transform (HB/AFT) method was developed and used to conduct a preliminary study of the effects of fluid, bearing and seal forces on the unbalanced response of a multi-disk rotor in the presence of bearing clearances. The method makes it possible to determine periodic, sub-, super-synchronous and chaotic responses of a rotor system. The method also yields information about the stability of the obtained response, thus allowing bifurcation analyses. This provides a more effective capability for predicting the response under transient conditions by searching in proximity of resonance peaks. Preliminary results were also obtained for the nonlinear transient response of an actual HPOTP model using an efficient, newly developed numerical method based on convolution integration. Currently, the HB/AFT is being extended for determining the aperiodic response of nonlinear systems. Initial results show the method to be promising.
Non-linear stochastic growth rates and redshift space distortions
Jennings, Elise; Jennings, David
2015-04-09
The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a non-linear, stochastic relation between θ = ∇ ∙ v(x,t)/aH and δ. This provides a new phenomenological approach that examines the conditional mean <θ|δ>, together with the fluctuations of θ around this mean. We also measure these stochastic components using N-body simulations and find they are non-negative and increase with decreasing scale from ~10 per cent at k < 0.2 h Mpc-1 to 25 per cent at kmore » ~ 0.45 h Mpc-1 at z = 0. Both the stochastic relation and non-linearity are more pronounced for haloes, M ≤ 5 × 1012 M⊙ h-1, compared to the dark matter at z = 0 and 1. Non-linear growth effects manifest themselves as a rotation of the mean <θ|δ> away from the linear theory prediction -fLTδ, where fLT is the linear growth rate. This rotation increases with wavenumber, k, and we show that it can be well-described by second-order Lagrangian perturbation theory (2LPT) fork < 0.1 h Mpc-1. Furthermore, the stochasticity in the θ – δ relation is not so simply described by 2LPT, and we discuss its impact on measurements of fLT from two-point statistics in redshift space. Furthermore, given that the relationship between δ and θ is stochastic and non-linear, this will have implications for the interpretation and precision of fLT extracted using models which assume a linear, deterministic expression.« less
Non-linear stochastic growth rates and redshift space distortions
Jennings, Elise; Jennings, David
2015-04-09
The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a non-linear, stochastic relation between θ = ∇ ∙ v(x,t)/aH and δ. This provides a new phenomenological approach that examines the conditional mean <θ|δ>, together with the fluctuations of θ around this mean. We also measure these stochastic components using N-body simulations and find they are non-negative and increase with decreasing scale from ~10 per cent at k < 0.2 h Mpc^{-1} to 25 per cent at k ~ 0.45 h Mpc^{-1} at z = 0. Both the stochastic relation and non-linearity are more pronounced for haloes, M ≤ 5 × 10^{12} M_{⊙} h^{-1}, compared to the dark matter at z = 0 and 1. Non-linear growth effects manifest themselves as a rotation of the mean <θ|δ> away from the linear theory prediction -f_{LT}δ, where f_{LT }is the linear growth rate. This rotation increases with wavenumber, k, and we show that it can be well-described by second-order Lagrangian perturbation theory (2LPT) fork < 0.1 h Mpc^{-1}. Furthermore, the stochasticity in the θ – δ relation is not so simply described by 2LPT, and we discuss its impact on measurements of f_{LT} from two-point statistics in redshift space. Furthermore, given that the relationship between δ and θ is stochastic and non-linear, this will have implications for the interpretation and precision of f_{LT} extracted using models which assume a linear, deterministic expression.
A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott
Garland, Howard; Raghunathan, M. S.
1975-01-01
We give a new proof of Bott's result, that the loop space of a compact, simply connected, simple Lie group has a cellular decomposition of a certain type. In particular, one obtains the Poincaré polynomial for the loop space and Bott periodicity for the unitary group. PMID:16592292
Decomposition theorem in ideal topological spaces via a*-I-open sets and Asemi*-I-open sets
NASA Astrophysics Data System (ADS)
AL-Omeri, W.; Noorani, Mohd. Salmi.; AL-Omari, A.
2014-09-01
In this paper, we investigate some properties of a*-I-open set [3] and Asemi*-I-open sets defined in [3] in ideal topological space. The relationships of other related classes of sets are investigated. Also, a new decomposition of continuous functions is obtained by using δβA-I-open and SA*-set functions in an ideal topological space.
Nonlinear sigma models with compact hyperbolic target spaces
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James
2016-06-23
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. In conclusion, the diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Nonlinear sigma models with compact hyperbolic target spaces
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; ...
2016-06-23
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in themore » O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. In conclusion, the diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.« less
Nonlinear sigma models with compact hyperbolic target spaces
NASA Astrophysics Data System (ADS)
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James
2016-06-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Cai, X.C.
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces
Lieu, Linh H. Vese, Luminita A.
2008-10-15
We propose a new class of models for image restoration and decomposition by functional minimization. Following ideas of Y. Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, our model decomposes a given (degraded or textured) image u{sub 0} into a sum u+v. Here u element of BV is a function of bounded variation (a cartoon component), while the noisy (or textured) component v is modeled by tempered distributions belonging to the negative Hilbert-Sobolev space H{sup -s}. The proposed models can be seen as generalizations of a model proposed by S. Osher, A. Sole, L. Vese and have been also motivated by D. Mumford and B. Gidas. We present existence, uniqueness and two characterizations of minimizers using duality and the notion of convex functions of measures with linear growth, following I. Ekeland and R. Temam, F. Demengel and R. Temam. We also give a numerical algorithm for solving the minimization problem, and we present numerical results of denoising, deblurring, and decompositions of both synthetic and real images.
Hessian estimates in weighted Lebesgue spaces for fully nonlinear elliptic equations
NASA Astrophysics Data System (ADS)
Byun, Sun-Sig; Lee, Mikyoung; Palagachev, Dian K.
2016-03-01
We prove global regularity in weighted Lebesgue spaces for the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equations. As a consequence, regularity in Morrey spaces of the Hessian is derived as well.
Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming
2016-01-01
The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning. PMID:27403634
Parallel computation of a highly nonlinear Boussinesq equation model through domain decomposition
NASA Astrophysics Data System (ADS)
Sitanggang, Khairil Irfan; Lynett, Patrick
2005-09-01
Implementations of the Boussinesq wave model to calculate free surface wave evolution in large basins are, in general, computationally very expensive, requiring huge amounts of CPU time and memory. For large scale problems, it is either not affordable or practical to run on a single PC. To facilitate such extensive computations, a parallel Boussinesq wave model is developed using the domain decomposition technique in conjunction with the message passing interface (MPI). The published and well-tested numerical scheme used by the serial model, a high-order finite difference method, is identical to that employed in the parallel model. Parallelization of the tridiagonal matrix systems included in the serial scheme is the most challenging aspect of the work, and is accomplished using a parallel matrix solver combined with an efficient data transfer scheme. Numerical tests on a distributed-memory super-computer show that the performance of the current parallel model in simulating wave evolution is very satisfactory. A linear speedup is gained as the number of processors increases. These tests showed that the CPU time efficiency of the model is about 75-90%.
Brodsky, Ethan K; Holmes, James H; Yu, Huanzhou; Reeder, Scott B
2008-05-01
Chemical-shift artifacts associated with non-Cartesian imaging are more complex to model and less clinically acceptable than the bulk fat shift that occurs with conventional spin-warp Cartesian imaging. A novel k-space based iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) approach is introduced that decomposes multiple species while simultaneously correcting distortion of off-resonant species. The new signal model accounts for the additional phase accumulated by off-resonant spins at each point in the k-space acquisition trajectory. This phase can then be corrected by adjusting the decomposition matrix for each k-space point during the final IDEAL processing step with little increase in reconstruction time. The technique is demonstrated with water-fat decomposition using projection reconstruction (PR)/radial, spiral, and Cartesian spin-warp imaging of phantoms and human subjects, in each case achieving substantial correction of chemical-shift artifacts. Simulations of the point-spread-function (PSF) for off-resonant spins are examined to show the nature of the chemical-shift distortion for each acquisition. Also introduced is an approach to improve the signal model for species which have multiple resonant peaks. Many chemical species, including fat, have multiple resonant peaks, although such species are often approximated as a single peak. The improved multipeak decomposition is demonstrated with water-fat imaging, showing a substantial improvement in water-fat separation.
Application of 2D-Nonlinear Shallow Water Model of Tsunami by using Adomian Decomposition Method
Waewcharoen, Sribudh; Boonyapibanwong, Supachai; Koonprasert, Sanoe
2008-09-01
One of the most important questions in tsunami modeling is the estimation of tsunami run-up heights at different points along a coastline. Methods for numerical simulation of tsunami wave propagation in deep and shallow seas are well developed and have been widely used by many scientists (2001-2008). In this paper, we consider a two-dimensional nonlinear shallow water model of tsunami given by Tivon Jacobson is work [1]. u{sub t}+uu{sub x}+{nu}u{sub y} -c{sup 2}(h{sub x}+(h{sub b}){sub x}) {nu}{sub t}+u{nu}{sub x}+{nu}{nu}{sub y} = -c{sup 2}(h{sub y}+(h{sub b}){sub y}) h{sub t}+(hu){sub x}+(h{nu}){sub y} = 0 g-shore, h is surface elevation and s, t is time, u is velocity of cross-shore, {nu} is velocity of along-shore, h is surface elevation and h{sub b} is function of shore. This is a nondimensionalized model with the gravity g and constant reference depth H factored into c = {radical}(gH). We apply the Adomian Decompostion Method (ADM) to solve the tsunami model. This powerful method has been used to obtain explicit and numerical solutions of three types of diffusion-convection-reaction (DECR) equations. The ADM results for the tsunami model yield analytical solutions in terms of a rapidly convergent infinite power series. Symbolic computation, numerical results and graphs of solutions are obtained by Maple program.
Jean C. Ragusa; Vijay Mahadevan; Vincent A. Mousseau
2009-05-01
High-fidelity modeling of nuclear reactors requires the solution of a nonlinear coupled multi-physics stiff problem with widely varying time and length scales that need to be resolved correctly. A numerical method that converges the implicit nonlinear terms to a small tolerance is often referred to as nonlinearly consistent (or tightly coupled). This nonlinear consistency is still lacking in the vast majority of coupling techniques today. We present a tightly coupled multiphysics framework that tackles this issue and present code-verification and convergence analyses in space and time for several models of nonlinear coupled physics.
NASA Astrophysics Data System (ADS)
Shiraishi, Maresuke; Sugiyama, Naonori S.; Okumura, Teppei
2017-03-01
We propose an efficient way to test rotational invariance in the cosmological perturbations by use of galaxy correlation functions. In symmetry-breaking cases, the galaxy power spectrum can have extra angular dependence in addition to the usual one due to the redshift-space distortion, k ^ .n ^ . We confirm that, via the decomposition into not the usual Legendre basis Lℓ(k ^.n ^) but the bipolar spherical harmonic one {Yℓ(k ^)⊗Yℓ'(n ^)}LM, the symmetry-breaking signal can be completely distinguished from the usual isotropic one since the former yields nonvanishing L ≥1 modes but the latter is confined to the L =0 one. As a demonstration, we analyze the signatures due to primordial-origin symmetry breakings such as the well-known quadrupolar-type and dipolar-type power asymmetries and find nonzero L =2 and 1 modes, respectively. Fisher matrix forecasts of their constraints indicate that the Planck-level sensitivity could be achieved by the SDSS or BOSS-CMASS data, and an order-of-magnitude improvement is expected in a near future survey as PFS or Euclid by virtue of an increase in accessible Fourier mode. Our methodology is model-independent and hence applicable to the searches for various types of statistically anisotropic fluctuations.
Nonlinear effects associated with oblique whistler waves in space plasmas
NASA Astrophysics Data System (ADS)
Sharma, R. P.; Nandal, P.; Yadav, N.; Uma, R.
2016-10-01
In the present work, we have examined the nonlinear interaction of pump whistler wave and low frequency kinetic Alfvén wave (KAW) in three regions viz., solar wind, earth's radiation belt, and magnetopause. The modification in the background density leads to the introduction of nonlinearity. The nonlinear ponderomotive force is responsible for this change in density. Low frequency kinetic Alfvén wave is excited by the nonlinear ponderomotive force of pump whistler wave. A set of dimensionless equations characterizing the dynamics of whistler wave and low frequency KAW perturbed by whistler wave were developed. The coupled equations were then simulated numerically. The nonlinear effects related with the whistler wave were studied. The resulting localized structures and the magnetic turbulent spectra in various regions have been investigated.
NASA Astrophysics Data System (ADS)
Yao, Ruo-Xia; Wang, Wei; Chen, Ting-Hua
2014-11-01
Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.
Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Konotop, Vladimir V.
2008-04-25
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schroedinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.
NASA Astrophysics Data System (ADS)
Canoglu, Ahmet; Güldogan, Bahri; Salihoglu, Selâmi
We obtain new integrable coupled nonlinear partial differential equations by assuming the soliton connection having values in orthogonal-symplectic Lie superalgebras [B(m, n), C(n), D(m, n)]. These equations are coupled Nonlinear Schrödinger equations on various super symmetric spaces.
Nonlinear Approximation and the Space BV(R2)
1997-01-01
processing Techniques for ndingminimizers g for Uf t based on variational calculus and nonlinear partial di erential equations have been put forward by...operators and statistical estimation as well as in digital image processing Techniques for nding minimizers g for Uf t based on variational calculus and...techniques based on variational calculus and nonlinear partial dierential equations see eg DMS LOR MS CL especially to the problems of noise
Chen, Jin; He, Simin; Huang, Bing; Wu, Peng; Qiao, Zhiqiang; Wang, Jun; Zhang, Liyuan; Yang, Guangcheng; Huang, Hui
2017-03-29
High energy and low signature properties are the future trend of solid propellant development. As a new and promising oxidizer, hexanitrohexaazaisowurtzitane (CL-20) is expected to replace the conventional oxidizer ammonium perchlorate to reach above goals. However, the high pressure exponent of CL-20 hinders its application in solid propellants so that the development of effective catalysts to improve the thermal decomposition properties of CL-20 still remains challenging. Here, 3D hierarchically ordered porous carbon (3D HOPC) is presented as a catalyst for the thermal decomposition of CL-20 via synthesizing a series of nanostructured CL-20/HOPC composites. In these nanocomposites, CL-20 is homogeneously space-confined into the 3D HOPC scaffold as nanocrystals 9.2-26.5 nm in diameter. The effect of the pore textural parameters and surface modification of 3D HOPC as well as CL-20 loading amount on the thermal decomposition of CL-20 is discussed. A significant improvement of the thermal decomposition properties of CL-20 is achieved with remarkable decrease in decomposition peak temperature (from 247.0 to 174.8 °C) and activation energy (from 165.5 to 115.3 kJ/mol). The exceptional performance of 3D HOPC could be attributed to its well-connected 3D hierarchically ordered porous structure, high surface area, and the confined CL-20 nanocrystals. This work clearly demonstrates that 3D HOPC is a superior catalyst for CL-20 thermal decomposition and opens new potential for further applications of CL-20 in solid propellants.
Wang Dengshan; Hu Xinghua; Liu, W. M.
2010-08-15
We investigate the localized nonlinear matter waves in the two-component Bose-Einstein condensates with time- and space-modulated nonlinearities analytically and numerically. The similarity transformations are developed to solve the coupled Gross-Pitaevskii equations and two families of explicitly exact solutions are derived. Our results show that not only the attractive spatiotemporal inhomogeneous interactions but the repulsive ones support novel localized nonlinear matter waves in two-component Bose-Einstein condensates. The dynamics of these matter waves, including the breathing solitons, quasibreathing solitons, resonant solitons, and moving solitons, is discussed. We confirm the stability of the exact solutions by adding various initial stochastic noise and study the general cases of the interaction parameters numerically. We also provide the experimental parameters to produce these phenomena in future experiments.
Keith, Jeff; Westbury, Chris; Goldman, James
2015-09-01
Corpus-based semantic space models, which primarily rely on lexical co-occurrence statistics, have proven effective in modeling and predicting human behavior in a number of experimental paradigms that explore semantic memory representation. The most widely studied extant models, however, are strongly influenced by orthographic word frequency (e.g., Shaoul & Westbury, Behavior Research Methods, 38, 190-195, 2006). This has the implication that high-frequency closed-class words can potentially bias co-occurrence statistics. Because these closed-class words are purported to carry primarily syntactic, rather than semantic, information, the performance of corpus-based semantic space models may be improved by excluding closed-class words (using stop lists) from co-occurrence statistics, while retaining their syntactic information through other means (e.g., part-of-speech tagging and/or affixes from inflected word forms). Additionally, very little work has been done to explore the effect of employing morphological decomposition on the inflected forms of words in corpora prior to compiling co-occurrence statistics, despite (controversial) evidence that humans perform early morphological decomposition in semantic processing. In this study, we explored the impact of these factors on corpus-based semantic space models. From this study, morphological decomposition appears to significantly improve performance in word-word co-occurrence semantic space models, providing some support for the claim that sublexical information-specifically, word morphology-plays a role in lexical semantic processing. An overall decrease in performance was observed in models employing stop lists (e.g., excluding closed-class words). Furthermore, we found some evidence that weakens the claim that closed-class words supply primarily syntactic information in word-word co-occurrence semantic space models.
Yokoyama, Naoto; Takaoka, Masanori
2014-12-01
A single-wave-number representation of a nonlinear energy spectrum, i.e., a stretching-energy spectrum, is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wave-number space and analytical expressions of detailed energy budgets in the nonlinear interactions. We numerically solved the FvK equation and observed the following facts. Kinetic energy and bending energy are comparable with each other at large wave numbers as the weak turbulence theory suggests. On the other hand, stretching energy is larger than the bending energy at small wave numbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a(k) and its companion mode a(-k) is observed at the small wave numbers. The energy is input into the wave field through stretching-energy transfer at the small wave numbers, and dissipated through the quartic part of kinetic-energy transfer at the large wave numbers. Total-energy flux consistent with energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.
The effects of nonlinear loading upon the Space Station Freedom 20 kHz power system
NASA Technical Reports Server (NTRS)
Leskovich, R. Thomas; Hansen, Irving G.
1989-01-01
The Space Station Freedom power distribution system, which consists of dual redundant 20-kHz, 440-V RMS, single-phase power systems, is discussed. The effect of a typical space station nonlinear load on the measurement of RMS current and voltage at various points in the space station power system has been investigated using the Electromagnetic Transients Program (EMTP). The load current distortion at the user interface, its effect on the distribution system, and its relationship to power factor have been studied. Modeling results are compared to test data. The differences under nonlinear loading are evaluated and presented as a measure of distribution voltage distortion and current measurement accuracy.
Dynamic control of robot arms in tasks space using nonlinear feedback
NASA Technical Reports Server (NTRS)
Bejczy, A. K.; Tarn, T. J.
1988-01-01
Differential geometric system and control theory is used to develop a new dynamic system feedback technique for robot task space commands. The nonlinear robot arm system is feedback-linearized and simultaneously is output-decoupled by an appropriate nonlinear feedback and nonlinear coordinate transformation. On the joint space level, the scheme only commands drive forces or torques or their equivalent quantities addressed to the joint drives. An important property of the technique is that the planned and commanded task space trajectory together with its time derivatives directly drive the robot arm through a linear system model. A method for task space motion planning matching the requirements of the new scheme is briefly presented. The implications of the new technique for second and third order model robot arms with and without force feedback measuremnts and for two or more dynamically cooperating robot arms are discussed.
Space formations and nonlinear properties of noncentrosymmetric germanates
Korotkov, Anton Sergeevich
2014-10-15
Space formations of Ge-O polyhedra have been analyzed for 114 noncentrosymmetric germanates. The type of Ge-O polyhedra space formations is dependent on the stoichiometric ratio SR=n(O)/n(Ge), where n(O) is the number of oxygen and n(Ge) is the number of germanium atoms in formal composition of the compound. Individual (Ge-O) polyhedra are found for SR≥3 chains of the polyhedra that exist in the range of SR=3–5. Only framework formations are possible at SR≤2.7. - graphical abstract: Examples of space formations of polyhedra. - Highlights: • Space formations of Ge-O polyhedra have been analyzed. • The dependence of the type of Ge-O polyhedra space formations on the stoichiometric ratio SR=n(O)/n(Ge) was established. • Set of experimental SHG data of noncentrosymmetric germanates was presented.
Nonlinear resonances in the case of asymmetric space vehicles' free-fall in the atmosphere
NASA Astrophysics Data System (ADS)
Aslanov, V. S.
1992-10-01
The uncontrolled motion around the mass center of a space vehicle with small dynamic and aerodynamic asymmetry during descent in the atmosphere is considered in a nonlinear formulation. The spatial motion is divided into quick and slow motions. Two fast variables are identified: the phase angle of attack and the roll angle relative to the wind. A general scheme for reducing the equations of motion to the standard two-frequency system is proposed. New nonlinear resonances are identified.
Visualization of high-density 3D graphs using nonlinear visual space transformations
NASA Astrophysics Data System (ADS)
Hao, Ming C.; Dayal, Umeshwar; Garg, Pankaj; Machiraju, Vijay
2002-03-01
The real world data distribution is seldom uniform. Clutter and sparsity commonly occur in visualization. Often, clutter results in overplotting, in which certain data items are not visible because other data items occlude them. Sparsity results in the inefficient use of the available display space. Common mechanisms to overcome this include reducing the amount of information displayed or using multiple representations with a varying amount of detail. This paper describes out experiments on Non-Linear Visual Space Transformations (NLVST). NLVST encompasses several innovative techniques: (1) employing a histogram for calculating the density of data distribution; (2) mapping the raw data values to a non-linear scale for stretching a high-density area; (3) tightening the sparse area to save the display space; (4) employing different color ranges of values on a non-linear scale according to the local density. We have applied NLVST to several web applications: market basket analysis, transactions observation, and IT search behavior analysis.
McCullagh, Nuala; Szalay, Alexander S.
2015-01-10
Baryon acoustic oscillations (BAO) are a powerful probe of the expansion history of the universe, which can tell us about the nature of dark energy. In order to accurately characterize the dark energy equation of state using BAO, we must understand the effects of both nonlinearities and redshift space distortions on the location and shape of the acoustic peak. In a previous paper, we introduced a novel approach to second order perturbation theory in configuration space using the Zel'dovich approximation, and presented a simple result for the first nonlinear term of the correlation function. In this paper, we extend this approach to redshift space. We show how to perform the computation and present the analytic result for the first nonlinear term in the correlation function. Finally, we validate our result through comparison with numerical simulations.
Task decomposition for multilimbed robots to work in the reachable-but-unorientable space
NASA Technical Reports Server (NTRS)
Su, Chao; Zheng, Yuan F.
1990-01-01
Multilimbed industrial robots that have at least one arm and two or more legs are suggested for enlarging robot workspace in industrial automation. To plan the motion of a multilimbed robot, the arm-leg motion-coordination problem is raised and task decomposition is proposed to solve the problem; that is, a given task described by the destination position and orientation of the end-effector is decomposed into subtasks for arm manipulation and for leg locomotion, respectively. The former is defined as the end-effector position and orientation with respect to the legged main body, and the latter as the main-body position and orientation in the world coordinates. Three approaches are proposed for the task decomposition. The approaches are further evaluated in terms of energy consumption, from which an optimal approach can be selected.
Task decomposition for a multilimbed robot to work in reachable but unorientable space
NASA Technical Reports Server (NTRS)
Su, Chau; Zheng, Yuan F.
1991-01-01
Robot manipulators installed on legged mobile platforms are suggested for enlarging robot workspace. To plan the motion of such a system, the arm-platform motion coordination problem is raised, and a task decomposition is proposed to solve the problem. A given task described by the destination position and orientation of the end effector is decomposed into subtasks for arm manipulation and for platform configuration, respectively. The former is defined as the end-effector position and orientation with respect to the platform, and the latter as the platform position and orientation in the base coordinates. Three approaches are proposed for the task decomposition. The approaches are also evaluated in terms of the displacements, from which an optimal approach can be selected.
A Model for Nonlinear Photoexcitation of Molecular Hydrogen in Space
NASA Astrophysics Data System (ADS)
Glownia, J. H.; Sorokin, P. P.
2000-05-01
A model for nonlinear photoexcitation of H2 molecules in tenuous clouds near bright stars (e.g. PDRs or PNe) is presented. In the model, H atoms and H2 molecules coexist in a cold neutral cloud surrounding an H II region represented by a conventional Strömgren sphere. An intense band of Ly-α radiation is produced by H++ e- recombination and frequency redistribution occuring in the H II region. Due to elastic scattering by H atoms, the Ly-α radiation slowly diffuses outward through the neutral cloud, its photon density becoming enormously enhanced in the process. This provides the basic pumping field required for the nonlinear effects to be described. Via resonant inverse Raman scattering (IRS), the intense Ly-α radiation field induces strong nonlinear absorption of VUV continuum starlight by orthohydrogen molecules in X0, J''=1 around three ''primary'' frequencies (B9-0P1, B6-0P1, and B3-0R1), the primary IRS terminal levels (X5, J''=1), (X4, J''=1), and (X3, J''=1) simultaneously becoming strongly populated. (Parahydrogen absorbs via IRS on B3-0R0.) Via either Ly-α -pumped, spontaneous resonant Raman scattering, or secondary IRS processes, molecules in the primary IRS terminal levels are selectively redistributed into higher-lying X-state levels such as (X10, J''=5), (X13, J''=5), and (X14, J''=1). A thin shell (thickness ~ 10,000 km) of H2 molecules populating select vibrationally excited X-state levels thus surrounds the Strömgren sphere. >From a handful of the populated high-lying X-state levels, there occur strong resonances with Ly-α . Intense Ly-α radiation can thus induce broadband stimulated Raman scattering (SRS) to occur on these transitions, generating broadband IR Stokes-wave light on strong transitions to EF-state levels. An SRS process would occur as part of a 2n-wave parametric oscillation (SRS-PO) process, with light at additional frequencies being generated on strong transitions ultimately returning molecules to the X-state level from
Image enhancement by non-linear extrapolation in frequency space
NASA Technical Reports Server (NTRS)
Anderson, Charles H. (Inventor); Greenspan, Hayit K. (Inventor)
1998-01-01
An input image is enhanced to include spatial frequency components having frequencies higher than those in an input image. To this end, an edge map is generated from the input image using a high band pass filtering technique. An enhancing map is subsequently generated from the edge map, with the enhanced map having spatial frequencies exceeding an initial maximum spatial frequency of the input image. The enhanced map is generated by applying a non-linear operator to the edge map in a manner which preserves the phase transitions of the edges of the input image. The enhanced map is added to the input image to achieve a resulting image having spatial frequencies greater than those in the input image. Simplicity of computations and ease of implementation allow for image sharpening after enlargement and for real-time applications such as videophones, advanced definition television, zooming, and restoration of old motion pictures.
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
NASA Astrophysics Data System (ADS)
Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.
2017-02-01
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.
Wharton, A. M.; Sekar Iyengar, A. N.; Janaki, M. S.
2013-02-15
Hilbert Huang transform (HHT) based time series analysis was carried out on nonlinear floating potential fluctuations obtained from hollow cathode glow discharge plasma in the presence of anode glow. HHT was used to obtain contour plots and the presence of nonlinearity was studied. Frequency shift with time, which is a typical nonlinear behaviour, was detected from the contour plots. Various plasma parameters were measured and the concepts of correlation coefficients and the physical contribution of each intrinsic mode function have been discussed. Physically important quantities such as instantaneous energy and their uses in studying physical phenomena such as intermittency and non-stationary data have also been discussed.
Suppression of Space Charge Induced Beam Halo in Nonlinear Focusing Channel
Batygin, Yuri Konstantinovich; Scheinker, Alexander; Kurennoy, Sergey; Li, Chao
2016-01-29
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. We discuss a new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.
Suppression of Space Charge Induced Beam Halo in Nonlinear Focusing Channel
Batygin, Yuri Konstantinovich; Scheinker, Alexander; Kurennoy, Sergey; ...
2016-01-29
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. We discuss a new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry. The resulting solution is applied to the problemmore » of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.« less
Sonnad, Kiran G.; Cary, John R.
2015-04-15
A procedure to obtain a near equilibrium phase space distribution function has been derived for beams with space charge effects in a generalized periodic focusing transport channel. The method utilizes the Lie transform perturbation theory to canonically transform to slowly oscillating phase space coordinates. The procedure results in transforming the periodic focusing system to a constant focusing one, where equilibrium distributions can be found. Transforming back to the original phase space coordinates yields an equilibrium distribution function corresponding to a constant focusing system along with perturbations resulting from the periodicity in the focusing. Examples used here include linear and nonlinear alternating gradient focusing systems. It is shown that the nonlinear focusing components can be chosen such that the system is close to integrability. The equilibrium distribution functions are numerically calculated, and their properties associated with the corresponding focusing system are discussed.
On the analytical modeling of the nonlinear vibrations of pretensioned space structures
NASA Technical Reports Server (NTRS)
Housner, J. M.; Belvin, W. K.
1983-01-01
Pretensioned structures are receiving considerable attention as candidate large space structures. A typical example is a hoop-column antenna. The large number of preloaded members requires efficient analytical methods for concept validation and design. Validation through analyses is especially important since ground testing may be limited due to gravity effects and structural size. The present investigation has the objective to present an examination of the analytical modeling of pretensioned members undergoing nonlinear vibrations. Two approximate nonlinear analysis are developed to model general structural arrangements which include beam-columns and pretensioned cables attached to a common nucleus, such as may occur at a joint of a pretensioned structure. Attention is given to structures undergoing nonlinear steady-state oscillations due to sinusoidal excitation forces. Three analyses, linear, quasi-linear, and nonlinear are conducted and applied to study the response of a relatively simple cable stiffened structure.
Nonlinear Analysis of the Space Shuttle Super-Lightweight External Fuel Tank
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Britt, Vicki O.; Collins, Timothy J.; Starnes, James H., Jr.
1996-01-01
The results of buckling and nonlinear analyses of the Space Shuttle External Tank super-lightweight liquid oxygen (LOX) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests conducted on the original external tank. These results illustrate three distinctly different types of nonlinear responses for thin-walled shells subjected to combined mechanical and thermal loads. These nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of nonlinear behavior generally require a large scale high-fidelity finite element model. Results are also presented that show that a fluid filled launch vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full scale structural tests of the original standard weight external tank suggest that the finite element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the super lightweight LOX tank.
NASA Technical Reports Server (NTRS)
Abdeldayem, Hossin A.; Dowdye, Edward; Jamison, Tracee; Canham, John
2005-01-01
NASA is striving to develop a scientific understanding of the universe and the Earth-Sun System and its response to natural or human-induced changes. Space lasers are vital tools for NASA's missions to advance our understanding of space research and improving our prediction capability for climate, weather, and natural hazards. Unfortunately, several past space missions that utilized lasers proved to be short-lived and unreliable. In this paper, we are reporting the results of our investigations on several nonlinear optical crystals, which are vital components in space lasers. Examples of these investigations are: The correlation of the phase diagrams of nonlinear crystals and its durability, the effect of radiating these crystals by high-energy beams of protons and gamma on their second harmonic efficiency, and measurements of the high-energy and low-energy thresholds for each crystal before and after irradiation. A set of proper criteria for these crystals will be presented. We will also discuss the possible causes of failures in a space laser and propose a solution to a contamination problem in all future space lasers.
Nonlinear longitudinal space charge oscillations in relativistic electron beams.
Musumeci, P; Li, R K; Marinelli, A
2011-05-06
In this Letter we study the evolution of an initial periodic modulation in the temporal profile of a relativistic electron beam under the effect of longitudinal space-charge forces. Linear theory predicts a periodic exchange of the modulation between the density and the energy profiles at the beam plasma frequency. For large enough initial modulations, wave breaking occurs after 1/2 period of plasma oscillation leading to the formation of short current spikes. We confirm this effect by direct measurements on a ps-modulated electron beam from an rf photoinjector. These results are useful for the generation of intense electron pulse trains for advanced accelerator applications.
Nonlinear Longitudinal Space Charge Oscillations in Relativistic Electron Beams
Musumeci, P.; Li, R. K.; Marinelli, A.
2011-05-06
In this Letter we study the evolution of an initial periodic modulation in the temporal profile of a relativistic electron beam under the effect of longitudinal space-charge forces. Linear theory predicts a periodic exchange of the modulation between the density and the energy profiles at the beam plasma frequency. For large enough initial modulations, wave breaking occurs after 1/2 period of plasma oscillation leading to the formation of short current spikes. We confirm this effect by direct measurements on a ps-modulated electron beam from an rf photoinjector. These results are useful for the generation of intense electron pulse trains for advanced accelerator applications.
NASA Astrophysics Data System (ADS)
Nourazar, Salman; Nazari-Golshan, Akbar; Yıldırım, Ahmet; Nourazar, Maryam
2012-07-01
The physical science importance of the Cauchy problem of the reaction-diffusion equation appears in the modelling of a wide variety of nonlinear systems in physics, chemistry, ecology, biology, and engineering. A hybrid of Fourier transform and Adomian decomposition method (FTADM) is developed for solving the nonlinear non-homogeneous partial differential equations of the Cauchy problem of reaction-diffusion. The results of the FTADM and the ADM are compared with the exact solution. The comparison reveals that for the same components of the recursive sequences, the errors associated with the FTADM are much lesser than those of the ADM. We show that as time increases the results of the FTADM approaches 1 with only six recursive terms. This is in agreement with the physical property of the density-dependent nonlinear diffusion of the Cauchy problem which is also in agreement with the exact solution. The monotonic and very rapid convergence of the results of the FTADM towards the exact solution is shown to be much faster than that of the ADM
Similarity solution to fractional nonlinear space-time diffusion-wave equation
NASA Astrophysics Data System (ADS)
Costa, F. Silva; Marão, J. A. P. F.; Soares, J. C. Alves; de Oliveira, E. Capelas
2015-03-01
In this article, the so-called fractional nonlinear space-time wave-diffusion equation is presented and discussed. This equation is solved by the similarity method using fractional derivatives in the Caputo, Riesz-Feller, and Riesz senses. Some particular cases are presented and the corresponding solutions are shown by means of 2-D and 3-D plots.
NASA Astrophysics Data System (ADS)
Kuruoǧlu, Zeki C.
2016-11-01
Direct numerical solution of the coordinate-space integral-equation version of the two-particle Lippmann-Schwinger (LS) equation is considered without invoking the traditional partial-wave decomposition. The singular kernel of the three-dimensional LS equation in coordinate space is regularized by a subtraction technique. The resulting nonsingular integral equation is then solved via the Nystrom method employing a direct-product quadrature rule for three variables. To reduce the computational burden of discretizing three variables, advantage is taken of the fact that, for central potentials, the azimuthal angle can be integrated out, leaving a two-variable reduced integral equation. A regularization method for the kernel of the two-variable integral equation is derived from the treatment of the singularity in the three-dimensional equation. A quadrature rule constructed as the direct product of single-variable quadrature rules for radial distance and polar angle is used to discretize the two-variable integral equation. These two- and three-variable methods are tested on the Hartree potential. The results show that the Nystrom method for the coordinate-space LS equation compares favorably in terms of its ease of implementation and effectiveness with the Nystrom method for the momentum-space version of the LS equation.
Fast transport in phase space due to nonlinear wave-particle interaction in the radiation belts.
NASA Astrophysics Data System (ADS)
Artemyev, Anton; Vasiliev, Alexii; Mourenas, Didier; Agapitov, Oleksiy; Krasnoselskikh, Vladimir; Boscher, Daniel; Rolland, Guy
2014-05-01
We present an analytical, simplified formulation accounting for the fast transport of particles in phase space, in the presence of nonlinear wave-particle resonant interactions in an inhomogeneous magnetic field representative of the radiation belts. We show that the general approach for the description of the evolution of the particle velocity distribution based on the Fokker-Plank equation can be modified to consider the process of nonlinear wave-particle interaction, including particle trapping. Such a modification consists in one additional operator describing fast particle jumps in phase space. The proposed approach is illustrated by considering the acceleration of relativistic electrons by strongly oblique whistler waves. We determine the typical variation of electron phase-density due to nonlinear wave-particle interaction and compare this variation with pitch-angle/energy diffusion due to quasi-linear electron scattering. We show that relation between nonlinear and quasi-linear effects is controlled by the distribution of wave-amplitudes. When this distribution has a heavy tail, nonlinear effects can become dominant in the formation of the electron energy distribution.
NASA Astrophysics Data System (ADS)
Liu, Peipei; Sohn, Hoon; Park, Byeongjin
2015-06-01
Damage often causes a structural system to exhibit severe nonlinear behaviors, and the resulting nonlinear features are often much more sensitive to the damage than their linear counterparts. This study develops a laser nonlinear wave modulation spectroscopy (LNWMS) so that certain types of damage can be detected without any sensor placement. The proposed LNWMS utilizes a pulse laser to generate ultrasonic waves and a laser vibrometer for ultrasonic measurement. Under the broadband excitation of the pulse laser, a nonlinear source generates modulations at various frequency values due to interactions among various input frequency components. State space attractors are reconstructed from the ultrasonic responses measured by LNWMS, and a damage feature called Bhattacharyya distance (BD) is computed from the state space attractors to quantify the degree of damage-induced nonlinearity. By computing the BD values over the entire target surface using laser scanning, damage can be localized and visualized without relying on the baseline data obtained from the pristine condition of a target structure. The proposed technique has been successfully used for visualizing fatigue crack in an aluminum plate and delamination and debonding in a glass fiber reinforced polymer wind turbine blade.
Disentangling Redshift-Space Distortions and Nonlinear Bias using the 2D Power Spectrum
Jennings, Elise; Wechsler, Risa H.
2015-08-07
We present the nonlinear 2D galaxy power spectrum, P(k, µ), in redshift space, measured from the Dark Sky simulations, using galaxy catalogs constructed with both halo occupation distribution and subhalo abundance matching methods, chosen to represent an intermediate redshift sample of luminous red galaxies. We find that the information content in individual µ (cosine of the angle to the line of sight) bins is substantially richer then multipole moments, and show that this can be used to isolate the impact of nonlinear growth and redshift space distortion (RSD) effects. Using the µ < 0.2 simulation data, which we show is not impacted by RSD effects, we can successfully measure the nonlinear bias to an accuracy of ~ 5% at k < 0.6hMpc-1 . This use of individual µ bins to extract the nonlinear bias successfully removes a large parameter degeneracy when constraining the linear growth rate of structure. We carry out a joint parameter estimation, using the low µ simulation data to constrain the nonlinear bias, and µ > 0.2 to constrain the growth rate and show that f can be constrained to ~ 26(22)% to a kmax < 0.4(0.6)hMpc-1 from clustering alone using a simple dispersion model, for a range of galaxy models. Our analysis of individual µ bins also reveals interesting physical effects which arise simply from different methods of populating halos with galaxies. We also find a prominent turnaround scale, at which RSD damping effects are greater then the nonlinear growth, which differs not only for each µ bin but also for each galaxy model. These features may provide unique signatures which could be used to shed light on the galaxy–dark matter connection. Furthermore, the idea of separating nonlinear growth and RSD effects making use of the full information in the 2D galaxy power spectrum yields significant improvements in constraining cosmological parameters and may be a promising probe of galaxy formation models.
Zhang, Zuxing; Wu, Jian; Xu, Kun; Hong, Xiaobin; Lin, Jintong
2009-09-14
A tunable multiwavelength fiber laser with ultra-narrow wavelength spacing and large wavelength number using a semiconductor optical amplifier (SOA) has been demonstrated. Intensity-dependent transmission induced by nonlinear polarization rotation in the SOA accounts for stable multiwavelength operation with wavelength spacing less than the homogenous broadening linewidth of the SOA. Stable multiwavelength lasing with wavelength spacing as small as 0.08 nm and wavelength number up to 126 is achieved at room temperature. Moreover, wavelength tuning of 20.2 nm is implemented via polarization tuning.
Guo, Bin; Chen, Zhongsheng; Guo, Jinyun; Liu, Feng; Chen, Chuanfa; Liu, Kangli
2016-01-01
Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960–2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD). Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years) and inter-decadal scale (quasi-12 and quasi-23 years). Moreover, the 2–3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements. PMID:27007388
Guo, Bin; Chen, Zhongsheng; Guo, Jinyun; Liu, Feng; Chen, Chuanfa; Liu, Kangli
2016-03-21
Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960-2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD). Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years) and inter-decadal scale (quasi-12 and quasi-23 years). Moreover, the 2-3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements.
Demonstration of decomposition and optimization in the design of experimental space systems
NASA Technical Reports Server (NTRS)
Padula, Sharon; Sandridge, Chris A.; Haftka, Raphael T.; Walsh, Joanne L.
1989-01-01
Effective design strategies for a class of systems which may be termed Experimental Space Systems (ESS) are needed. These systems, which include large space antenna and observatories, space platforms, earth satellites and deep space explorers, have special characteristics which make them particularly difficult to design. It is argued here that these same characteristics encourage the use of advanced computer-aided optimization and planning techniques. The broad goal of this research is to develop optimization strategies for the design of ESS. These strategics would account for the possibly conflicting requirements of mission life, safety, scientific payoffs, initial system cost, launch limitations and maintenance costs. The strategies must also preserve the coupling between disciplines or between subsystems. Here, the specific purpose is to describe a computer-aided planning and scheduling technique. This technique provides the designer with a way to map the flow of data between multidisciplinary analyses. The technique is important because it enables the designer to decompose the system design problem into a number of smaller subproblems. The planning and scheduling technique is demonstrated by its application to a specific preliminary design problem.
NASA Astrophysics Data System (ADS)
Mozaffarilegha, Marjan; Esteki, Ali; Ahadi, Mohsen; Nazeri, Ahmadreza
The speech-evoked auditory brainstem response (sABR) shows how complex sounds such as speech and music are processed in the auditory system. Speech-ABR could be used to evaluate particular impairments and improvements in auditory processing system. Many researchers used linear approaches for characterizing different components of sABR signal, whereas nonlinear techniques are not applied so commonly. The primary aim of the present study is to examine the underlying dynamics of normal sABR signals. The secondary goal is to evaluate whether some chaotic features exist in this signal. We have presented a methodology for determining various components of sABR signals, by performing Ensemble Empirical Mode Decomposition (EEMD) to get the intrinsic mode functions (IMFs). Then, composite multiscale entropy (CMSE), the largest Lyapunov exponent (LLE) and deterministic nonlinear prediction are computed for each extracted IMF. EEMD decomposes sABR signal into five modes and a residue. The CMSE results of sABR signals obtained from 40 healthy people showed that 1st, and 2nd IMFs were similar to the white noise, IMF-3 with synthetic chaotic time series and 4th, and 5th IMFs with sine waveform. LLE analysis showed positive values for 3rd IMFs. Moreover, 1st, and 2nd IMFs showed overlaps with surrogate data and 3rd, 4th and 5th IMFs showed no overlap with corresponding surrogate data. Results showed the presence of noisy, chaotic and deterministic components in the signal which respectively corresponded to 1st, and 2nd IMFs, IMF-3, and 4th and 5th IMFs. While these findings provide supportive evidence of the chaos conjecture for the 3rd IMF, they do not confirm any such claims. However, they provide a first step towards an understanding of nonlinear behavior of auditory system dynamics in brainstem level.
Some exact solutions of a system of nonlinear Schroedinger equations in three-dimensional space
Moskalyuk, S.S.
1988-02-01
Interactions that break the symmetry of systems of nonrelativistic Schroedinger equations but preserve their symmetry with respect to one-parameter subgroups of the Schroedinger group are described. Ansatzes for invariant solutions and the corresponding systems of reduced equations in invariant variables for Galileo-invariant Schroedinger equations are found. Exact solutions for the system of nonlinear Schroedinger equations in three-dimensional space for the generalized Hubbard model are obtained.
A robust nonlinear attitude control law for space stations with flexible structural components
NASA Technical Reports Server (NTRS)
Wang, P. K. C.
1985-01-01
In this paper, a nonlinear attitude control law for space stations with flexible structural components is derived using a rigid-body model. This control law, depending on the Cayley-Rodriguez parameters, globally stabilizes the equilibrium of the rigid-body model. The effect of elastic deformations of the flexible structural components on the resulting feedback system dynamics is analyzed. It is found that the system's stability property is highly robust with respect to structural vibrations and inertial variations. The time-domain behavior of the feedback system is studied numerically using a model of a typical space station with flexible solar panels.
Contamination and Radiation Effects on Nonlinear Crystals for Space Laser Systems
NASA Technical Reports Server (NTRS)
Abdeldayem, Hossain A.; Dowdye, Edward; Jamison, Tracee; Canham, John; Jaeger, Todd
2005-01-01
Space Lasers are vital tools for NASA s space missions and military applications. Although, lasers are highly reliable on the ground, several past space laser missions proved to be short-lived and unreliable. In this communication, we are shedding more light on the contamination and radiation issues, which are the most common causes for optical damages and laser failures in space. At first, we will present results based on the study of liquids and subsequently correlate these results to the particulates of the laser system environment. We present a model explaining how the laser beam traps contaminants against the optical surfaces and cause optical damages and the role of gravity in the process. We also report the results of the second harmonic generation efficiency for nonlinear optical crystals irradiated with high-energy beams of protons. In addition, we are proposing to employ the technique of adsorption to minimize the presence of adsorbing molecules present in the laser compartment.
Ebrahimi, Farideh; Setarehdan, Seyed-Kamaledin; Ayala-Moyeda, Jose; Nazeran, Homer
2013-10-01
The conventional method for sleep staging is to analyze polysomnograms (PSGs) recorded in a sleep lab. The electroencephalogram (EEG) is one of the most important signals in PSGs but recording and analysis of this signal presents a number of technical challenges, especially at home. Instead, electrocardiograms (ECGs) are much easier to record and may offer an attractive alternative for home sleep monitoring. The heart rate variability (HRV) signal proves suitable for automatic sleep staging. Thirty PSGs from the Sleep Heart Health Study (SHHS) database were used. Three feature sets were extracted from 5- and 0.5-min HRV segments: time-domain features, nonlinear-dynamics features and time-frequency features. The latter was achieved by using empirical mode decomposition (EMD) and discrete wavelet transform (DWT) methods. Normalized energies in important frequency bands of HRV signals were computed using time-frequency methods. ANOVA and t-test were used for statistical evaluations. Automatic sleep staging was based on HRV signal features. The ANOVA followed by a post hoc Bonferroni was used for individual feature assessment. Most features were beneficial for sleep staging. A t-test was used to compare the means of extracted features in 5- and 0.5-min HRV segments. The results showed that the extracted features means were statistically similar for a small number of features. A separability measure showed that time-frequency features, especially EMD features, had larger separation than others. There was not a sizable difference in separability of linear features between 5- and 0.5-min HRV segments but separability of nonlinear features, especially EMD features, decreased in 0.5-min HRV segments. HRV signal features were classified by linear discriminant (LD) and quadratic discriminant (QD) methods. Classification results based on features from 5-min segments surpassed those obtained from 0.5-min segments. The best result was obtained from features using 5-min HRV
Disentangling Redshift-Space Distortions and Nonlinear Bias using the 2D Power Spectrum
Jennings, Elise; Wechsler, Risa H.
2015-08-07
We present the nonlinear 2D galaxy power spectrum, P(k, µ), in redshift space, measured from the Dark Sky simulations, using galaxy catalogs constructed with both halo occupation distribution and subhalo abundance matching methods, chosen to represent an intermediate redshift sample of luminous red galaxies. We find that the information content in individual µ (cosine of the angle to the line of sight) bins is substantially richer then multipole moments, and show that this can be used to isolate the impact of nonlinear growth and redshift space distortion (RSD) effects. Using the µ < 0.2 simulation data, which we show ismore » not impacted by RSD effects, we can successfully measure the nonlinear bias to an accuracy of ~ 5% at k < 0.6hMpc-1 . This use of individual µ bins to extract the nonlinear bias successfully removes a large parameter degeneracy when constraining the linear growth rate of structure. We carry out a joint parameter estimation, using the low µ simulation data to constrain the nonlinear bias, and µ > 0.2 to constrain the growth rate and show that f can be constrained to ~ 26(22)% to a kmax < 0.4(0.6)hMpc-1 from clustering alone using a simple dispersion model, for a range of galaxy models. Our analysis of individual µ bins also reveals interesting physical effects which arise simply from different methods of populating halos with galaxies. We also find a prominent turnaround scale, at which RSD damping effects are greater then the nonlinear growth, which differs not only for each µ bin but also for each galaxy model. These features may provide unique signatures which could be used to shed light on the galaxy–dark matter connection. Furthermore, the idea of separating nonlinear growth and RSD effects making use of the full information in the 2D galaxy power spectrum yields significant improvements in constraining cosmological parameters and may be a promising probe of galaxy formation models.« less
Seljak, Uroš
2012-03-01
On large scales a nonlinear transformation of matter density field can be viewed as a biased tracer of the density field itself. A nonlinear transformation also modifies the redshift space distortions in the same limit, giving rise to a velocity bias. In models with primordial nongaussianity a nonlinear transformation generates a scale dependent bias on large scales. We derive analytic expressions for the large scale bias, the velocity bias and the redshift space distortion (RSD) parameter β, as well as the scale dependent bias from primordial nongaussianity for a general nonlinear transformation. These biases can be expressed entirely in terms of the one point distribution function (PDF) of the final field and the parameters of the transformation. The analysis shows that one can view the large scale bias different from unity and primordial nongaussianity bias as a consequence of converting higher order correlations in density into 2-point correlations of its nonlinear transform. Our analysis allows one to devise nonlinear transformations with nearly arbitrary bias properties, which can be used to increase the signal in the large scale clustering limit. We apply the results to the ionizing equilibrium model of Lyman-α forest, in which Lyman-α flux F is related to the density perturbation δ via a nonlinear transformation. Velocity bias can be expressed as an average over the Lyman-α flux PDF. At z = 2.4 we predict the velocity bias of -0.1, compared to the observed value of −0.13±0.03. Bias and primordial nongaussianity bias depend on the parameters of the transformation. Measurements of bias can thus be used to constrain these parameters, and for reasonable values of the ionizing background intensity we can match the predictions to observations. Matching to the observed values we predict the ratio of primordial nongaussianity bias to bias to have the opposite sign and lower magnitude than the corresponding values for the highly biased galaxies, but this
Study of outgassing and decomposition of space shuttle heat protection tiles, fillers and adhesive
NASA Technical Reports Server (NTRS)
Proctor, B. L.; Hoffman, J. H.
1982-01-01
The purpose of this project was to determine the chemicals desorbing from the space shuttle heat protection tiles. The original protocol for this project involved direct insertion probe mass spectrometry (DIPMS) analysis of the outgassing products from the tiles. However, this method proved unsatisfactory due to the large number of compounds desorbing from the tiles. A purge and trap technique was then employed to collect and separate the chemicals desorbing from the tiles. The maximum temperature in this analysis was 180 C which is the gas chromatograph fused silica capillary column's temperature limit. The desorption was also carried out at atmospheric pressure with helium as the purge gas. A description of the modified protocol is given. All compounds are tentatively identified.
NASA Astrophysics Data System (ADS)
Tovbis, Alexander; Venakides, Stephanos
2010-04-01
The initial value problem for an integrable system, such as the Nonlinear Schrödinger equation, is solved by subjecting the linear eigenvalue problem arising from its Lax pair to inverse scattering, and, thus, transforming it to a matrix Riemann-Hilbert problem (RHP) in the spectral variable. In the semiclassical limit, the method of nonlinear steepest descent ([4,5]), supplemented by the g-function mechanism ([3]), is applied to this RHP to produce explicit asymptotic solution formulae for the integrable system. These formule are based on a hyperelliptic Riemann surface {mathcal {R} = mathcal {R}(x,t)} in the spectral variable, where the space-time variables ( x, t) play the role of external parameters. The curves in the x, t plane, separating regions of different genuses of {mathcal {R}(x,t)}, are called breaking curves or nonlinear caustics. The genus of {mathcal {R}(x,t)} is related to the number of oscillatory phases in the asymptotic solution of the integrable system at the point x, t. The evolution theorem ([10]) guarantees continuous evolution of the asymptotic solution in the space-time away from the breaking curves. In the case of the analytic scattering data f( z; x, t) (in the NLS case, f is a normalized logarithm of the reflection coefficient with time evolution included), the primary role in the breaking mechanism is played by a phase function {{Im h(z;x,t)}}, which is closely related to the g function. Namely, a break can be caused ([10]) either through the change of topology of zero level curves of {Im h(z;x,t)} (regular break), or through the interaction of zero level curves of {{Im h(z;x,t)}} with singularities of f (singular break). Every time a breaking curve in the x, t plane is reached, one has to prove the validity of the nonlinear steepest descent asymptotics in the region across the curve. In this paper we prove that in the case of a regular break, the nonlinear steepest descent asymptotics can be “automatically” continued through the
Computer-assisted bladder cancer grading: α-shapes for color space decomposition
NASA Astrophysics Data System (ADS)
Niazi, M. K. K.; Parwani, Anil V.; Gurcan, Metin N.
2016-03-01
According to American Cancer Society, around 74,000 new cases of bladder cancer are expected during 2015 in the US. To facilitate the bladder cancer diagnosis, we present an automatic method to differentiate carcinoma in situ (CIS) from normal/reactive cases that will work on hematoxylin and eosin (H and E) stained images of bladder. The method automatically determines the color deconvolution matrix by utilizing the α-shapes of the color distribution in the RGB color space. Then, variations in the boundary of transitional epithelium are quantified, and sizes of nuclei in the transitional epithelium are measured. We also approximate the "nuclear to cytoplasmic ratio" by computing the ratio of the average shortest distance between transitional epithelium and nuclei to average nuclei size. Nuclei homogeneity is measured by computing the kurtosis of the nuclei size histogram. The results show that 30 out of 34 (88.2%) images were correctly classified by the proposed method, indicating that these novel features are viable markers to differentiate CIS from normal/reactive bladder.
A comparative study of new non-linear uncertainty propagation methods for space surveillance
NASA Astrophysics Data System (ADS)
Horwood, Joshua T.; Aristoff, Jeffrey M.; Singh, Navraj; Poore, Aubrey B.
2014-06-01
We propose a unified testing framework for assessing uncertainty realism during non-linear uncertainty propagation under the perturbed two-body problem of celestial mechanics, with an accompanying suite of metrics and benchmark test cases on which to validate different methods. We subsequently apply the testing framework to different combinations of uncertainty propagation techniques and coordinate systems for representing the uncertainty. In particular, we recommend the use of a newly-derived system of orbital element coordinates that mitigate the non-linearities in uncertainty propagation and the recently-developed Gauss von Mises filter which, when used in tandem, provide uncertainty realism over much longer periods of time compared to Gaussian representations of uncertainty in Cartesian spaces, at roughly the same computational cost.
Steady-state analysis of a nonlinear rotor-housing system. [Space Shuttle Main Engine
NASA Technical Reports Server (NTRS)
Noah, S. T.; Kim, Y. B.
1990-01-01
The periodic steady state response of a high pressure oxygen turbopump (HBOTP) of a Space Shuttle main engine (SSME), involving a clearance between the bearing and housing carrier, is sought. A harmonic balance method utilizig Fast Fourier Transform (FFT) algorithm is developed for the analysis. An impedance method is used to reduce the number of degrees of freedom to the displacements at the bearing clearance. Harmonic and subharmonic responses to imbalance for various system parameters are studied. The results show that the computational technique developed in this study is an effective and flexible method for determining the stable and unstable periodic response of complex rotor-housing systems with clearance type nonlinearity.
New Space Weather and Nonlinear Waves and Processes Prize announced for 2013
NASA Astrophysics Data System (ADS)
Thompson, Victoria
2012-01-01
At the 2011 Fall Meeting in San Francisco, Calif., AGU announced the creation of a new award: the Space Weather and Nonlinear Waves and Processes Prize. The prize, which is being made possible by a generous contribution from longtime AGU members and NASA Jet Propulsion Laboratory (JPL), California Institute of Technology, scientists Bruce Tsurutani and Olga Verkhoglyadova, will recognize an AGU member scientist and will come with a $10,000 award. Tsurutani has served as a researcher with JPL since 1972 and is currently a senior research scientist. He was also the president of AGU's Space Physics and Aeronomy section from 1990 to 1992 and is a recipient of AGU's John Adam Fleming Medal, given “for original research and technical leadership in geomagnetism, atmospheric electricity, aeronomy, space physics, and related sciences.” Verkhoglyadova served as a professor of space physics in the Department of Astrophysics and Space Physics at Taras Shevchenko National University of Kyiv, in the Ukraine, prior to coming to the United States. Their leadership and dedication to AGU and to their field are apparent in their passion for this prize.
Interferometric and nonlinear-optical spectral-imaging techniques for outer space and live cells
NASA Astrophysics Data System (ADS)
Itoh, Kazuyoshi
2015-12-01
Multidimensional signals such as the spectral images allow us to have deeper insights into the natures of objects. In this paper the spectral imaging techniques that are based on optical interferometry and nonlinear optics are presented. The interferometric imaging technique is based on the unified theory of Van Cittert-Zernike and Wiener-Khintchine theorems and allows us to retrieve a spectral image of an object in the far zone from the 3D spatial coherence function. The retrieval principle is explained using a very simple object. The promising applications to space interferometers for astronomy that are currently in progress will also be briefly touched on. An interesting extension of interferometric spectral imaging is a 3D and spectral imaging technique that records 4D information of objects where the 3D and spectral information is retrieved from the cross-spectral density function of optical field. The 3D imaging is realized via the numerical inverse propagation of the cross-spectral density. A few techniques suggested recently are introduced. The nonlinear optical technique that utilizes stimulated Raman scattering (SRS) for spectral imaging of biomedical targets is presented lastly. The strong signals of SRS permit us to get vibrational information of molecules in the live cell or tissue in real time. The vibrational information of unstained or unlabeled molecules is crucial especially for medical applications. The 3D information due to the optical nonlinearity is also the attractive feature of SRS spectral microscopy.
Nonlinear model of space manipulator joint considering time-variant stiffness and backlash
NASA Astrophysics Data System (ADS)
Yang, Tianfu; Yan, Shaoze; Han, Zengyao
2015-04-01
Modeling of space manipulator joints has been studied for years but accurate positioning control is still unsatisfactory. One of the primary reasons is that, in the past researches, effects of the high-ratio reducers in the joints have usually been neglected. In this paper, a nonlinear dynamic model of the manipulator joint with planetary gear train transmission is developed by considering time-variant joint stiffness, backlash and reduction ratio. Based on the gear parameters and meshing phase relationship, the stiffness of the joint model is presented, in which the time-variant stiffness of 2K-H planetary gear train and the backlash are taken into consideration. The backlash effect is modeled as an alternate engagement mechanism, and the transmitted torque is defined as a dead zone function. This model is simulated on a two-link space manipulator system. The results show that the time-variant stiffness effect can be simplified as a constant value in most cases when other shafting parts are flexible, while if the total stiffness is approximate to the nonlinear stiffness, the positioning accuracy is reduced if neglecting the time-variant part. On the other hand, the backlash is the main source of positioning error and impact. Minimizing backlash is the most effective way to improve positioning accuracy and avoid the impact in the gearing system.
Efremova, L S
2013-11-30
We use the notions of the Ω-function and functions suitable to it, to give a detailed proof of a decomposition theorem for the space of C{sup 1}-smooth skew products of interval maps whose quotient maps have complicated dynamics and satisfy the additional condition of Ω-stability with respect to the C{sup 1}-norm. In our theorem, the space of C{sup 1}-smooth skew products is decomposed into a union of four nonempty, pairwise disjoint subspaces. We give examples of maps contained in each of the four subspaces. Bibliography: 46 titles.
Non-Linear Cosmological Power Spectra in Real and Redshift Space
NASA Technical Reports Server (NTRS)
Taylor, A. N.; Hamilton, A. J. S.
1996-01-01
We present an expression for the non-linear evolution of the cosmological power spectrum based on Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self-gravitating fields. Some exact solutions are found for power-law initial spectra. We have extended this analysis into red-shift space and found a solution for the non-linear, anisotropic redshift-space power spectrum in the limit of plane-parallel redshift distortions. The quadrupole-to-monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, beta. The point of zero-crossing of the quadrupole, kappa(sub o), is found to obey a simple scaling relation and we calculate this scale in the Zel'dovich approximation. This model is found to be in good agreement with a series of N-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole-to-monopole ratio found in the merged QDOT plus 1.2-Jy-IRAS redshift survey. Using a likelihood technique we have estimated that the distortion parameter is constrained to be beta greater than 0.5 at the 95 percent level. Our results are fairly insensitive to the local primordial spectral slope, but the likelihood analysis suggests n = -2 un the translinear regime. The zero-crossing scale of the quadrupole is k(sub 0) = 0.5 +/- 0.1 h Mpc(exp -1) and from this we infer that the amplitude of clustering is sigma(sub 8) = 0.7 +/- 0.05. We suggest that the success of this model is due to non-linear redshift-space effects arising from infall on to caustic and is not dominated by virialized cluster cores
A non-linear model predictive controller with obstacle avoidance for a space robot
NASA Astrophysics Data System (ADS)
Wang, Mingming; Luo, Jianjun; Walter, Ulrich
2016-04-01
This study investigates the use of the non-linear model predictive control (NMPC) strategy for a kinematically redundant space robot to approach an un-cooperative target in complex space environment. Collision avoidance, traditionally treated as a high level planning problem, can be effectively translated into control constraints as part of the NMPC. The objective of this paper is to evaluate the performance of the predictive controller in a constrained workspace and to investigate the feasibility of imposing additional constraints into the NMPC. In this paper, we reformulated the issue of the space robot motion control by using NMPC with predefined objectives under input, output and obstacle constraints over a receding horizon. An on-line quadratic programming (QP) procedure is employed to obtain the constrained optimal control decisions in real-time. This study has been implemented for a 7 degree-of-freedom (DOF) kinematically redundant manipulator mounted on a 6 DOF free-floating spacecraft via simulation studies. Real-time trajectory tracking and collision avoidance particularly demonstrate the effectiveness and potential of the proposed NMPC strategy for the space robot.
Dynamic analysis of space-related linear and non-linear structures
NASA Technical Reports Server (NTRS)
Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.
1990-01-01
In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.
Dynamic analysis of space-related linear and non-linear structures
NASA Technical Reports Server (NTRS)
Bosela, Paul A.; Shaker, Francis J.; Fertis, Demeter G.
1990-01-01
In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photo-voltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic control system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.
The Non-linear Schrödinger Equation and the Conformal Properties of Non-relativistic Space-Time
NASA Astrophysics Data System (ADS)
Horváthy, P. A.; Yera, J.-C.
2009-08-01
The cubic non-linear Schrödinger equation where the coefficient of the nonlinear term is a function F(t,x) only passes the Painlevé test of Weiss, Tabor, and Carnevale only for F=(a+bt)-1, where a and b are constants. This is explained by transforming the time-dependent system into the constant-coefficient NLS by means of a time-dependent non-linear transformation, related to the conformal properties of non-relativistic space-time. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background.
NASA Technical Reports Server (NTRS)
Tsurutani, Bruce T.
1995-01-01
As the lead-off presentation for the topic of nonlinear waves and their evolution, we will illustrate some prominent examples of waves in space plasmas. We will describe recent observations detected within planetary foreshocks, near comets and in interplanetary space. It is believed that the nonlinear LF plasma wave features discussed here are part of and may be basic to the development of plasma turbulence. In this sense, this is one area of space plasma physics that is fundamental, with applications to fusion physics and astrophysics as well. It is hoped that the reader(s) will be stimulated to study nonlinear wave development themselves, if he/she is not already involved.
Experiments in Nonlinear Adaptive Control of Multi-Manipulator, Free-Flying Space Robots
NASA Technical Reports Server (NTRS)
Chen, Vincent Wei-Kang
1992-01-01
Sophisticated robots can greatly enhance the role of humans in space by relieving astronauts of low level, tedious assembly and maintenance chores and allowing them to concentrate on higher level tasks. Robots and astronauts can work together efficiently, as a team; but the robot must be capable of accomplishing complex operations and yet be easy to use. Multiple cooperating manipulators are essential to dexterity and can broaden greatly the types of activities the robot can achieve; adding adaptive control can ease greatly robot usage by allowing the robot to change its own controller actions, without human intervention, in response to changes in its environment. Previous work in the Aerospace Robotics Laboratory (ARL) have shown the usefulness of a space robot with cooperating manipulators. The research presented in this dissertation extends that work by adding adaptive control. To help achieve this high level of robot sophistication, this research made several advances to the field of nonlinear adaptive control of robotic systems. A nonlinear adaptive control algorithm developed originally for control of robots, but requiring joint positions as inputs, was extended here to handle the much more general case of manipulator endpoint-position commands. A new system modelling technique, called system concatenation was developed to simplify the generation of a system model for complicated systems, such as a free-flying multiple-manipulator robot system. Finally, the task-space concept was introduced wherein the operator's inputs specify only the robot's task. The robot's subsequent autonomous performance of each task still involves, of course, endpoint positions and joint configurations as subsets. The combination of these developments resulted in a new adaptive control framework that is capable of continuously providing full adaptation capability to the complex space-robot system in all modes of operation. The new adaptive control algorithm easily handles free
NASA Astrophysics Data System (ADS)
Aitouche, A.; Yang, Q.; Ould Bouamama, B.
2011-05-01
This paper presents a procedure dealing with the issue of fault detection and isolation (FDI) using nonlinear analytical redundancy (NLAR) technique applied in a proton exchange membrane (PEM) fuel cell system based on its mathematic model. The model is proposed and simplified into a five orders state space representation. The transient phenomena captured in the model include the compressor dynamics, the flow characteristics, mass and energy conservation and manifold fluidic mechanics. Nonlinear analytical residuals are generated based on the elimination of the unknown variables of the system by an extended parity space approach to detect and isolate actuator and sensor faults. Finally, numerical simulation results are given corresponding to a faults signature matrix.
Modal test/analysis correlation of Space Station structures using nonlinear sensitivity
NASA Technical Reports Server (NTRS)
Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan
1992-01-01
The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlations. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.
Modal Test/Analysis Correlation of Space Station Structures Using Nonlinear Sensitivity
NASA Technical Reports Server (NTRS)
Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan
1992-01-01
The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlation. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.
On the nonlinear dynamics of a space platform based mobile flexible manipulator
NASA Astrophysics Data System (ADS)
Modi, V. J.; Mah, H. W.; Misra, A. K.
1993-10-01
A relatively general formulation is developed for studying the dynamics of an orbiting arbitrary chain of translating, slewing flexible bodies. The formulation accounts for transverse, axial, and torsional deformation of beams. The model takes into account joint flexibility in three dimensions as well as specified and generalized coordinates at the joints, with freedom to transverse over a flexible platform free to librate and carrying a flexible payload. The model can also analyze a cluster of flexible bodies at joints forming 'flower petal-type' configurations, rigid central-body-based geometry applicable to a large class of scientific and communications satellites. The versatility of the formulation permits dynamical analysis and nonlinear control of a wide class of space- and ground-based manipulators.
Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method
NASA Technical Reports Server (NTRS)
Loh, Ching Y.
2003-01-01
The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.
NASA Astrophysics Data System (ADS)
Bhrawy, A. H.
2016-01-01
This paper reports a new spectral collocation technique for solving time-space modified anomalous subdiffusion equation with a nonlinear source term subject to Dirichlet and Neumann boundary conditions. This model equation governs the evolution for the probability density function that describes anomalously diffusing particles. Anomalous diffusion is ubiquitous in physical and biological systems where trapping and binding of particles can occur. A space-time Jacobi collocation scheme is investigated for solving such problem. The main advantage of the proposed scheme is that, the shifted Jacobi Gauss-Lobatto collocation and shifted Jacobi Gauss-Radau collocation approximations are employed for spatial and temporal discretizations, respectively. Thereby, the problem is successfully reduced to a system of algebraic equations. The numerical results obtained by this algorithm have been compared with various numerical methods in order to demonstrate the high accuracy and efficiency of the proposed method. Indeed, for relatively limited number of Gauss-Lobatto and Gauss-Radau collocation nodes imposed, the absolute error in our numerical solutions is sufficiently small. The results have been compared with other techniques in order to demonstrate the high accuracy and efficiency of the proposed method.
New Facts on the Nature of Gravitational Force And Nonlinear Oscillations of Space
NASA Astrophysics Data System (ADS)
Kursunoglu, Behram N.
2002-07-01
This paper discusses the letters received by this author from Albert Einstein, Erwin Schrodinger, and Paul Adrian Maurice Dirac, about fifty years ago which comment on my nonsymmetrical generalization of Einstein's general relativistic theory of gravitation. The writing of this paper, because of the dates of the letters, seems to have been delayed by half a century. Of the three versions of the nonsymmetrical theory (Einstein, Schrodinger and Kursunoglu Theories) my own paper contains results obtained as solutions of Generalized Theory of Gravitation field equations. In this paper it is shown that the field equations yield space nonlinear oscillations; a quartet of gravitational forces, quintessence, and replace Einstein's Cosmological Constant by two invariant parameters r0 and q related according to r02 q2 = c4/2G, where r0 is a length varying between zero and infinity and where q2 has the dimensions of energy density. These parameters govern the expansion of the universe with increasing acceleration and their existence yield four different solutions at each space-time point.
NASA Astrophysics Data System (ADS)
Wu, Huilan; Yao, Yuqin
2017-01-01
The time- and space-modulated nonlinearity is the important character of the Bose-Einstein condensates (BECs). Many works have been done on atomic BECs with spatially modulated nonlinearity, but there is little work on atomic-molecular BECs. In this paper, we construct one family of explicitly exact solutions of the atomic-molecular BECs with time- and space-modulated nonlinearities and trapping potential by similarity transformations. We discuss the dynamics of matter waves including breathing solitons, quasi-breathing solitons, resonant solitons and moving solitons. We analyze the linear stability of the solutions by adding various initial stochastic noise. We also provide the experimental parameters to produce these phenomena in future experiments.
NASA Astrophysics Data System (ADS)
Zheng, Yi; Zhang, Pengjie; Jing, Yipeng; Lin, Weipeng; Pan, Jun
2013-11-01
Massive spectroscopic redshift surveys open a promising window to accurately measure peculiar velocity at cosmological distances through redshift space distortion (RSD). In Paper I Zhang et al. [Phys. Rev. D 87, 063526 (2013)] of this series of work, we proposed decomposing peculiar velocity into three eigenmodes (vδ, vS, and vB) in order to facilitate the RSD modeling and peculiar velocity reconstruction. In the current paper we measure the dark matter RSD-related statistics of the velocity eigenmodes through a set of N-body simulations. These statistics include the velocity power spectra, correlation functions, one-point probability distribution functions, cumulants, and the damping functions describing the Finger of God effect. We have carried out a number of tests to quantify possible numerical artifacts in these measurements and have confirmed that these numerical artifacts are under control. Our major findings are as follows: (1) The power spectrum measurement shows that these velocity components have distinctly different spatial distribution and redshift evolution, consistent with predictions in Paper I. In particular, we measure the window function W˜(k,z). W˜ describes the impact of nonlinear evolution on the vδ-density relation. We confirm that the approximation W˜=1 can induce a significant systematic error of O(10%) in RSD cosmology. We demonstrate that W˜ can be accurately described by a simple fitting formula with one or two free parameters. (2) The correlation function measurement shows that the correlation length is O(100), O(10), and O(1)Mpc for vδ, vS, and vB, respectively. These correlation lengths determine where we can treat the velocity fields as spatially uncorrelated. Hence, they are important properties in RSD modeling. (3) The velocity probability distribution functions and cumulants quantify non-Gaussianities of the velocity fields. We confirm speculation in Paper I that vδ is largely Gaussian, but with non-negligible non
Nonlinear dust-acoustic structures in space plasmas with superthermal electrons, positrons, and ions
NASA Astrophysics Data System (ADS)
Saberian, E.; Esfandyari-Kalejahi, A.; Afsari-Ghazi, M.
2017-01-01
Some features of nonlinear dust-acoustic (DA) structures are investigated in a space plasma consisting of superthermal electrons, positrons, and positive ions in the presence of negatively charged dust grains with finite-temperature by employing a pseudo-potential technique in a hydrodynamic model. For this purpose, it is assumed that the electrons, positrons, and ions obey a kappa-like (κ) distribution in the background of adiabatic dust population. In the linear analysis, it is found that the dispersion relation yield two positive DA branches, i.e., the slow and fast DA waves. The upper branch (fast DA waves) corresponds to the case in which both (negatively charged) dust particles and (positively charged) ion species oscillate in phase with electrons and positrons. On the other hand, the lower branch (slow DA waves) corresponds to the case in which only dust particles oscillate in phase with electrons and positrons, while ion species are in antiphase with them. On the other hand, the fully nonlinear analysis shows that the existence domain of solitons and their characteristics depend strongly on the dust charge, ion charge, dust temperature, and the spectral index κ. It is found that the minimum/maximum Mach number increases as the spectral index κ increases. Also, it is found that only solitons with negative polarity can propagate and that their amplitudes increase as the parameter κ increases. Furthermore, the domain of Mach number shifts to the lower values, when the value of the dust charge Z d increases. Moreover, it is found that the Mach number increases with an increase in the dust temperature. Our analysis confirms that, in space plasmas with highly charged dusts, the presence of superthermal particles (electrons, positrons, and ions) may facilitate the formation of DA solitary waves. Particularly, in two cases of hydrogen ions H+ ( Z i = 1) and doubly ionized Helium atoms He2+ ( Z i = 2), the mentioned results are the same. Additionally, the
Tavakoli, Rouhollah
2016-01-01
An unconditionally energy stable time stepping scheme is introduced to solve Cahn–Morral-like equations in the present study. It is constructed based on the combination of David Eyre's time stepping scheme and Schur complement approach. Although the presented method is general and independent of the choice of homogeneous free energy density function term, logarithmic and polynomial energy functions are specifically considered in this paper. The method is applied to study the spinodal decomposition in multi-component systems and optimal space tiling problems. A penalization strategy is developed, in the case of later problem, to avoid trivial solutions. Extensive numerical experiments demonstrate the success and performance of the presented method. According to the numerical results, the method is convergent and energy stable, independent of the choice of time stepsize. Its MATLAB implementation is included in the appendix for the numerical evaluation of algorithm and reproduction of the presented results. -- Highlights: •Extension of Eyre's convex–concave splitting scheme to multiphase systems. •Efficient solution of spinodal decomposition in multi-component systems. •Efficient solution of least perimeter periodic space partitioning problem. •Developing a penalization strategy to avoid trivial solutions. •Presentation of MATLAB implementation of the introduced algorithm.
Lee, Kang Il
2016-12-01
The speed of sound (SOS), the normalized broadband ultrasound attenuation (nBUA), and the nonlinear parameter (B/A) were measured in 18 trabecular-bone-mimicking phantoms consisting of water-saturated aluminum foams. The strong slow wave and the very weak fast wave were consistently observed in the signals transmitted through all of the phantoms. It was found that the SOS increased as the porosity and the trabecular spacing increased. In contrast, both the nBUA and the B/A showed opposite dependences on the porosity and the trabecular spacing. All three ultrasound parameters exhibited high correlation coefficients with the porosity and the trabecular spacing.
Negassa, Wakene C.; Guber, Andrey K.; Kravchenko, Alexandra N.; Marsh, Terence L.; Hildebrandt, Britton; Rivers, Mark L.
2015-01-01
Physical protection of soil carbon (C) is one of the important components of C storage. However, its exact mechanisms are still not sufficiently lucid. The goal of this study was to explore the influence of soil structure, that is, soil pore spatial arrangements, with and without presence of plant residue on (i) decomposition of added plant residue, (ii) CO2 emission from soil, and (iii) structure of soil bacterial communities. The study consisted of several soil incubation experiments with samples of contrasting pore characteristics with/without plant residue, accompanied by X-ray micro-tomographic analyses of soil pores and by microbial community analysis of amplified 16S–18S rRNA genes via pyrosequencing. We observed that in the samples with substantial presence of air-filled well-connected large (>30 µm) pores, 75–80% of the added plant residue was decomposed, cumulative CO2 emission constituted 1,200 µm C g-1 soil, and movement of C from decomposing plant residue into adjacent soil was insignificant. In the samples with greater abundance of water-filled small pores, 60% of the added plant residue was decomposed, cumulative CO2 emission constituted 2,000 µm C g-1 soil, and the movement of residue C into adjacent soil was substantial. In the absence of plant residue the influence of pore characteristics on CO2 emission, that is on decomposition of the native soil organic C, was negligible. The microbial communities on the plant residue in the samples with large pores had more microbial groups known to be cellulose decomposers, that is, Bacteroidetes, Proteobacteria, Actinobacteria, and Firmicutes, while a number of oligotrophic Acidobacteria groups were more abundant on the plant residue from the samples with small pores. This study provides the first experimental evidence that characteristics of soil pores and their air/water flow status determine the phylogenetic composition of the local microbial community and directions and magnitudes of soil C
Negassa, Wakene C; Guber, Andrey K; Kravchenko, Alexandra N; Marsh, Terence L; Hildebrandt, Britton; Rivers, Mark L
2015-01-01
Physical protection of soil carbon (C) is one of the important components of C storage. However, its exact mechanisms are still not sufficiently lucid. The goal of this study was to explore the influence of soil structure, that is, soil pore spatial arrangements, with and without presence of plant residue on (i) decomposition of added plant residue, (ii) CO2 emission from soil, and (iii) structure of soil bacterial communities. The study consisted of several soil incubation experiments with samples of contrasting pore characteristics with/without plant residue, accompanied by X-ray micro-tomographic analyses of soil pores and by microbial community analysis of amplified 16S-18S rRNA genes via pyrosequencing. We observed that in the samples with substantial presence of air-filled well-connected large (>30 µm) pores, 75-80% of the added plant residue was decomposed, cumulative CO2 emission constituted 1,200 µm C g(-1) soil, and movement of C from decomposing plant residue into adjacent soil was insignificant. In the samples with greater abundance of water-filled small pores, 60% of the added plant residue was decomposed, cumulative CO2 emission constituted 2,000 µm C g(-1) soil, and the movement of residue C into adjacent soil was substantial. In the absence of plant residue the influence of pore characteristics on CO2 emission, that is on decomposition of the native soil organic C, was negligible. The microbial communities on the plant residue in the samples with large pores had more microbial groups known to be cellulose decomposers, that is, Bacteroidetes, Proteobacteria, Actinobacteria, and Firmicutes, while a number of oligotrophic Acidobacteria groups were more abundant on the plant residue from the samples with small pores. This study provides the first experimental evidence that characteristics of soil pores and their air/water flow status determine the phylogenetic composition of the local microbial community and directions and magnitudes of soil C
Negassa, Wakene C.; Guber, Andrey K.; Kravchenko, Alexandra N.; Marsh, Terence L.; Hildebrandt, Britton; Rivers, Mark L.
2015-07-01
Physical protection of soil carbon (C) is one of the important components of C storage. However, its exact mechanisms are still not sufficiently lucid. The goal of this study was to explore the influence of soil structure, that is, soil pore spatial arrangements, with and without presence of plant residue on (i) decomposition of added plant residue, (ii) CO₂ emission from soil, and (iii) structure of soil bacterial communities. The study consisted of several soil incubation experiments with samples of contrasting pore characteristics with/without plant residue, accompanied by X-ray micro-tomographic analyses of soil pores and by microbial community analysis of amplified 16S–18S rRNA genes via pyrosequencing. We observed that in the samples with substantial presence of air-filled well-connected large (>30 µm) pores, 75–80% of the added plant residue was decomposed, cumulative CO₂ emission constituted 1,200 µm C g⁻¹ soil, and movement of C from decomposing plant residue into adjacent soil was insignificant. In the samples with greater abundance of water-filled small pores, 60% of the added plant residue was decomposed, cumulative CO₂ emission constituted 2,000 µm C g⁻¹ soil, and the movement of residue C into adjacent soil was substantial. In the absence of plant residue the influence of pore characteristics on CO₂ emission, that is on decomposition of the native soil organic C, was negligible. The microbial communities on the plant residue in the samples with large pores had more microbial groups known to be cellulose decomposers, that is, Bacteroidetes, Proteobacteria, Actinobacteria, and Firmicutes, while a number of oligotrophic Acidobacteria groups were more abundant on the plant residue from the samples with small pores. This study provides the first experimental evidence that characteristics of soil pores and their air/water flow status determine the phylogenetic composition of the local microbial community and directions and magnitudes of
Nonlinear optical frequency conversion with KTP and BiBO crystals for lasers in space
NASA Astrophysics Data System (ADS)
Potreck, Arne; Schröder, Helmut; Lammers, Melanie; Tzeremes, Georgios; Riede, Wolfgang
2014-09-01
Within ESA's ADM-Aeolus and EarthCARE missions Doppler-wind Lidar systems will be operated in the Earth's orbit to measure global wind profiles. The active instrument will be based on a Nd:YAG laser, frequency tripled by nonlinear optical crystals. Different crystals are therefore to compare and qualify in regard of their space acceptability. A dedicated set-up to measure the maximum conversion efficiencies and its stability during longterm operation for KTP crystals (SHG) and BiBO crystals (SHG and THG) is presented in this work. In order to detect gray-tracking and its influence on thermal lensing in situ, measurements with a Shack-Hartmann sensor and a co-aligned HeNe laser were performed. Conversion efficiencies were 76+/-3 % at SHG for KTP and BiBO crystals and 48+/-2 % at THG with a combination of two BiBO crystals. During longterm experiments of 60 million laser pulses, conversion efficiencies were demonstrated to be stable over time (+/-1 % at SHG with KTP and +/-2 % at THG with BiBO). The occurrence of gray-tracking was detected in the KTP crystal and the resulting thermal lensing with an exponential saturation over time was observed in situ.
Negassa, Wakene C.; Guber, Andrey K.; Kravchenko, Alexandra N.; ...
2015-07-01
Physical protection of soil carbon (C) is one of the important components of C storage. However, its exact mechanisms are still not sufficiently lucid. The goal of this study was to explore the influence of soil structure, that is, soil pore spatial arrangements, with and without presence of plant residue on (i) decomposition of added plant residue, (ii) CO₂ emission from soil, and (iii) structure of soil bacterial communities. The study consisted of several soil incubation experiments with samples of contrasting pore characteristics with/without plant residue, accompanied by X-ray micro-tomographic analyses of soil pores and by microbial community analysis ofmore » amplified 16S–18S rRNA genes via pyrosequencing. We observed that in the samples with substantial presence of air-filled well-connected large (>30 µm) pores, 75–80% of the added plant residue was decomposed, cumulative CO₂ emission constituted 1,200 µm C g⁻¹ soil, and movement of C from decomposing plant residue into adjacent soil was insignificant. In the samples with greater abundance of water-filled small pores, 60% of the added plant residue was decomposed, cumulative CO₂ emission constituted 2,000 µm C g⁻¹ soil, and the movement of residue C into adjacent soil was substantial. In the absence of plant residue the influence of pore characteristics on CO₂ emission, that is on decomposition of the native soil organic C, was negligible. The microbial communities on the plant residue in the samples with large pores had more microbial groups known to be cellulose decomposers, that is, Bacteroidetes, Proteobacteria, Actinobacteria, and Firmicutes, while a number of oligotrophic Acidobacteria groups were more abundant on the plant residue from the samples with small pores. This study provides the first experimental evidence that characteristics of soil pores and their air/water flow status determine the phylogenetic composition of the local microbial community and directions and
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H., Jr.
2002-01-01
The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.
Bernardini, A. E.; Rocha, R. da
2007-03-15
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.
An Inhomogeneous Space-Time Patching Model Based on a Nonlocal and Nonlinear Schrödinger Equation
NASA Astrophysics Data System (ADS)
Dantas, Christine C.
2016-10-01
We consider an integrable, nonlocal and nonlinear, Schrödinger equation (NNSE) as a model for building space-time patchings in inhomogeneous loop quantum cosmology (LQC). We briefly review exact solutions of the NNSE, specially those obtained through "geometric equivalence" methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.
Optical ranked-order filtering using threshold decomposition
Allebach, J.P.; Ochoa, E.; Sweeney, D.W.
1987-10-09
A hybrid optical/electronic system performs median filtering and related ranked-order operations using threshold decomposition to encode the image. Threshold decomposition transforms the nonlinear neighborhood ranking operation into a linear space-invariant filtering step followed by a point-to-point threshold comparison step. Spatial multiplexing allows parallel processing of all the threshold components as well as recombination by a second linear, space-invariant filtering step. An incoherent optical correlation system performs the linear filtering, using a magneto-optic spatial light modulator as the input device and a computer-generated hologram in the filter plane. Thresholding is done electronically. By adjusting the value of the threshold, the same architecture is used to perform median, minimum, and maximum filtering of images. A totally optical system is also disclosed. 3 figs.
Optical ranked-order filtering using threshold decomposition
Allebach, Jan P.; Ochoa, Ellen; Sweeney, Donald W.
1990-01-01
A hybrid optical/electronic system performs median filtering and related ranked-order operations using threshold decomposition to encode the image. Threshold decomposition transforms the nonlinear neighborhood ranking operation into a linear space-invariant filtering step followed by a point-to-point threshold comparison step. Spatial multiplexing allows parallel processing of all the threshold components as well as recombination by a second linear, space-invariant filtering step. An incoherent optical correlation system performs the linear filtering, using a magneto-optic spatial light modulator as the input device and a computer-generated hologram in the filter plane. Thresholding is done electronically. By adjusting the value of the threshold, the same architecture is used to perform median, minimum, and maximum filtering of images. A totally optical system is also disclosed.
Batakliev, Todor; Georgiev, Vladimir; Anachkov, Metody; Rakovsky, Slavcho; Zaikov, Gennadi E
2014-06-01
Catalytic ozone decomposition is of great significance because ozone is a toxic substance commonly found or generated in human environments (aircraft cabins, offices with photocopiers, laser printers, sterilizers). Considerable work has been done on ozone decomposition reported in the literature. This review provides a comprehensive summary of the literature, concentrating on analysis of the physico-chemical properties, synthesis and catalytic decomposition of ozone. This is supplemented by a review on kinetics and catalyst characterization which ties together the previously reported results. Noble metals and oxides of transition metals have been found to be the most active substances for ozone decomposition. The high price of precious metals stimulated the use of metal oxide catalysts and particularly the catalysts based on manganese oxide. It has been determined that the kinetics of ozone decomposition is of first order importance. A mechanism of the reaction of catalytic ozone decomposition is discussed, based on detailed spectroscopic investigations of the catalytic surface, showing the existence of peroxide and superoxide surface intermediates.
Batakliev, Todor; Georgiev, Vladimir; Anachkov, Metody; Rakovsky, Slavcho
2014-01-01
Catalytic ozone decomposition is of great significance because ozone is a toxic substance commonly found or generated in human environments (aircraft cabins, offices with photocopiers, laser printers, sterilizers). Considerable work has been done on ozone decomposition reported in the literature. This review provides a comprehensive summary of the literature, concentrating on analysis of the physico-chemical properties, synthesis and catalytic decomposition of ozone. This is supplemented by a review on kinetics and catalyst characterization which ties together the previously reported results. Noble metals and oxides of transition metals have been found to be the most active substances for ozone decomposition. The high price of precious metals stimulated the use of metal oxide catalysts and particularly the catalysts based on manganese oxide. It has been determined that the kinetics of ozone decomposition is of first order importance. A mechanism of the reaction of catalytic ozone decomposition is discussed, based on detailed spectroscopic investigations of the catalytic surface, showing the existence of peroxide and superoxide surface intermediates. PMID:26109880
NASA Astrophysics Data System (ADS)
Gonçalves, P. B.; Silva, F. M. A.; Del Prado, Z. J. G. N.
2008-08-01
In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application, and models of reduced complexity are attractive in many cases where time-consuming numerical procedures are required. This paper discusses the derivation of discrete low-dimensional models for the nonlinear vibration analysis of thin cylindrical shells. In order to understand the peculiarities inherent to this class of structural problems, the nonlinear vibrations and dynamic stability of a circular cylindrical shell subjected to static and dynamic loads are analyzed. This choice is based on the fact that cylindrical shells exhibit a highly nonlinear behavior under both static and dynamic loads. Geometric nonlinearities due to finite-amplitude shell motions are considered by using Donnell's nonlinear shallow-shell theory. A perturbation procedure, validated in previous studies, is used to derive a general expression for the nonlinear vibration modes and the discretized equations of motion are obtained by the Galerkin method using modal expansions for the displacements that satisfy all the relevant boundary and symmetry conditions. Next, the model is analyzed via the Karhunen-Loève expansion to investigate the relative importance of each mode obtained by the perturbation solution on the nonlinear response and total energy of the system. The responses of several low-dimensional models are compared. It is shown that rather low-dimensional but properly selected models can describe with good accuracy the response of the shell up to very large vibration amplitudes.
Infectious diseases in space and time: noise and nonlinearity in epidemiological dynamics
NASA Astrophysics Data System (ADS)
Grenfell, Bryan
2005-03-01
I illustrate the impact of noise and nonlinearity on the spatio-temporal dynamics and evolution of epidemics using mathematical models and analyses of detailed epidemiological data from childhood infections, such as measles.
Chao, T.T.; Sanzolone, R.F.
1992-01-01
Sample decomposition is a fundamental and integral step in the procedure of geochemical analysis. It is often the limiting factor to sample throughput, especially with the recent application of the fast and modern multi-element measurement instrumentation. The complexity of geological materials makes it necessary to choose the sample decomposition technique that is compatible with the specific objective of the analysis. When selecting a decomposition technique, consideration should be given to the chemical and mineralogical characteristics of the sample, elements to be determined, precision and accuracy requirements, sample throughput, technical capability of personnel, and time constraints. This paper addresses these concerns and discusses the attributes and limitations of many techniques of sample decomposition along with examples of their application to geochemical analysis. The chemical properties of reagents as to their function as decomposition agents are also reviewed. The section on acid dissolution techniques addresses the various inorganic acids that are used individually or in combination in both open and closed systems. Fluxes used in sample fusion are discussed. The promising microwave-oven technology and the emerging field of automation are also examined. A section on applications highlights the use of decomposition techniques for the determination of Au, platinum group elements (PGEs), Hg, U, hydride-forming elements, rare earth elements (REEs), and multi-elements in geological materials. Partial dissolution techniques used for geochemical exploration which have been treated in detail elsewhere are not discussed here; nor are fire-assaying for noble metals and decomposition techniques for X-ray fluorescence or nuclear methods be discussed. ?? 1992.
Morozovska, Anna N.; Morozovsky, Nicholas V.; Eliseev, Eugene A.; Varenyk, Olexandr V.; Kim, Yunseok; Strelcov, Evgheni; Tselev, Alexander; Kalinin, Sergei V.
2014-08-14
We performed self-consistent modelling of nonlinear electrotransport and electromechanical response of thin films of mixed ionic-electronic conductors (MIEC) allowing for steric effects of mobile charged defects (ions, protons, or vacancies), electron degeneration, and Vegard stresses. We establish correlations between the features of the nonlinear space-charge dynamics, current-voltage, and bending-voltage curves for different types of the film electrodes. A pronounced ferroelectric-like hysteresis of the bending-voltage loops and current maxima on the double hysteresis current-voltage loops appear for the electron-transport electrodes. The double hysteresis loop with pronounced humps indicates a memristor-type resistive switching. The switching occurs due to the strong nonlinear coupling between the electronic and ionic subsystems. A sharp meta-stable maximum of the electron density appears near one open electrode and moves to another one during the periodic change of applied voltage. Our results can explain the nonlinear nature and correlation of electrical and mechanical memory effects in thin MIEC films. The analytical expression proving that the electrically induced bending of MIEC films can be detected by interferometric methods is derived.
Development, analysis, and testing of robust nonlinear guidance algorithms for space applications
NASA Astrophysics Data System (ADS)
Wibben, Daniel R.
This work focuses on the analysis and application of various nonlinear, autonomous guidance algorithms that utilize sliding mode control to guarantee system stability and robustness. While the basis for the algorithms has previously been proposed, past efforts barely scratched the surface of the theoretical details and implications of these algorithms. Of the three algorithms that are the subject of this research, two are directly derived from optimal control theory and augmented using sliding mode control. Analysis of the derivation of these algorithms has shown that they are two different representations of the same result, one of which uses a simple error state model (Delta r/Deltav) and the other uses definitions of the zero-effort miss and zero-effort velocity (ZEM/ZEV) values. By investigating the dynamics of the defined sliding surfaces and their impact on the overall system, many implications have been deduced regarding the behavior of these systems which are noted to feature time-varying sliding modes. A formal finite time stability analysis has also been performed to theoretically demonstrate that the algorithms globally stabilize the system in finite time in the presence of perturbations and unmodeled dynamics. The third algorithm that has been subject to analysis is derived from a direct application of higher-order sliding mode control and Lyapunov stability analysis without consideration of optimal control theory and has been named the Multiple Sliding Surface Guidance (MSSG). Via use of reinforcement learning methods an optimal set of gains has been found that make the guidance perform similarly to an open-loop optimal solution. Careful side-by-side inspection of the MSSG and Optimal Sliding Guidance (OSG) algorithms has shown some striking similarities. A detailed comparison of the algorithms has demonstrated that though they are nearly indistinguishable at first glance, there are some key differences between the two algorithms and they are indeed
NASA Astrophysics Data System (ADS)
Chang, Der-Chen; Markina, Irina; Wang, Wei
2016-09-01
The k-Cauchy-Fueter operator D0(k) on one dimensional quaternionic space H is the Euclidean version of spin k / 2 massless field operator on the Minkowski space in physics. The k-Cauchy-Fueter equation for k ≥ 2 is overdetermined and its compatibility condition is given by the k-Cauchy-Fueter complex. In quaternionic analysis, these complexes play the role of Dolbeault complex in several complex variables. We prove that a natural boundary value problem associated to this complex is regular. Then by using the theory of regular boundary value problems, we show the Hodge-type orthogonal decomposition, and the fact that the non-homogeneous k-Cauchy-Fueter equation D0(k) u = f on a smooth domain Ω in H is solvable if and only if f satisfies the compatibility condition and is orthogonal to the set ℋ(k)1 (Ω) of Hodge-type elements. This set is isomorphic to the first cohomology group of the k-Cauchy-Fueter complex over Ω, which is finite dimensional, while the second cohomology group is always trivial.
NASA Astrophysics Data System (ADS)
Pilling, Sergio; Nair, Binu G.; Escobar, Antonio; Fraser, Helen; Mason, Nigel
2014-03-01
Glycine is the simplest proteinaceous amino acid that has been extensively detected in carbonaceous meteorites and was recently observed in the cometary samples returned to Earth by NASA's Stardust spacecraft. In space, such species is exposed to several radiation fields at different temperatures. In aqueous solutions, this species appears mainly as zwitterionic glycine (+NH3CH2COO-) however, in solid phase, it may be found in amorphous or crystalline forms. Here, we present an experimental study on the destruction of two zwitterionic glycine crystals ( α- and β-form) at two different temperatures (300 K and 14 K) by 2 keV electrons in an attempt to test the behavior and stability of this molecular species in different space environments. The samples were analyzed in situ by Fourier transform infrared spectrometry at electron fluences. The experiments were carried out under ultra-high vacuum conditions at the Molecular Physics Laboratory at the Open University at Milton Keynes, UK. The dissociation cross section of glycine is approximately 5 times higher for the 14 K samples when compared to the 300 K samples. In contrast, no significant differences emerged between the dissociation cross sections of α- and β-forms of glycine for fixed temperature experiments. We therefore conclude that the destruction cross section is more heavily dependent on temperature than the phase of the condensed glycine material. This may be associated with the opening of additional reaction routes in the frozen samples involving the trapped daughter species (e.g. CO2 and CO). The half-life of studied samples extrapolated to space conditions shows that glycine molecules on the surface of interstellar grains has less survivability and they are highly sensitive to ambient radiations, however, they can survive extended period of time in the solar system like environments. Survivability increases by a factor of 5 if the samples are at 300 K when compared to low temperature experiments at 14
A fundamental approach to the problem of domain decomposition in structured grid generation
NASA Astrophysics Data System (ADS)
Piperni, Pasquale
2003-10-01
A new approach is presented for the automation of structured grid generation in multiply-connected domains. In this approach, the domain decomposition problem is cast as a classical boundary value problem in which the mesh topology is defined through the imposition of appropriate boundary conditions on the domain boundaries. The automation of the domain decomposition process is achieved by transferring it from the physical space to the topological space, where it is amenable to a rigorous solution. Once the domain is decomposed in the topological space, the mesh is generated in the physical space via the solution of a non-linear elliptic partial differential operator which takes into account the curvature of the physical space. The forms of the decomposition surfaces are obtained as part of the solution of the differential operator. The latter is solved iteratively in a system of overlapping sub-domains in which the decomposition surfaces are left floating, and in which only the shape of the domain boundaries and the point distribution thereon influence the form of the final mesh. It is shown that the proper representation of domain curvature is an essential element to the success of the domain decomposition strategy. In any curved space, the curvature of the decomposition surfaces must closely mirror the curvature of the space in order to yield a high quality mesh. Since the decomposition of the multiply-connected domain is done in the topological space, the curvature of the physical space must be re-injected into the system through the solution of an appropriate differential operator. A new mathematical formulation is derived for this purpose and takes the form of a new forcing function in the elliptic grid generation equations. This new Curvature term is completely general and can be applied to both two- and three-dimensional domains of arbitrary shape. The combination of the new grid generation equations and the domain decomposition strategy provides a
NASA Technical Reports Server (NTRS)
Sable, Dan M.; Cho, Bo H.; Lee, Fred C.
1990-01-01
A detailed comparison of a boost converter, a voltage-fed, autotransformer converter, and a multimodule boost converter, designed specifically for the space platform battery discharger, is performed. Computer-based nonlinear optimization techniques are used to facilitate an objective comparison. The multimodule boost converter is shown to be the optimum topology at all efficiencies. The margin is greatest at 97 percent efficiency. The multimodule, multiphase boost converter combines the advantages of high efficiency, light weight, and ample margin on the component stresses, thus ensuring high reliability.
ERIC Educational Resources Information Center
Napier, J.
1988-01-01
Outlines the role of the main organisms involved in woodland decomposition and discusses some of the variables affecting the rate of nutrient cycling. Suggests practical work that may be of value to high school students either as standard practice or long-term projects. (CW)
NASA Astrophysics Data System (ADS)
Poiata, N.; Satriano, C.; Vilotte, J. P.; Bernard, P.; Obara, K.
2015-12-01
Seismic radiation associated with transient deformations along the faults and subduction interfaces encompasses a variety of events, i.e., tectonic tremors, low-frequency earthquakes (LFE), very low-frequency earthquakes (VLFs), and slow-slip events (SSE), with a wide range of seismic moment and characteristic durations. Characterizing in space and time the complex sources of these slow earthquakes, and their relationship with background seismicity and large earthquakes generation, is of great importance for understanding the physics and mechanics of the processes of active deformations along the plate interfaces. We present here first developments towards a methodology for: (1) extracting the different frequency and scale components of observed tectonic tremor signal, using advanced time-frequency and time-scale signal representation such as Gabor transform scheme based on, e.g. Wilson bases or Modified Discrete Cosine Transform (MDCT) bases; (2) reconstructing their corresponding potential sources in space and time, using the array method of Poiata et al. (2015). The methodology is assessed using a dataset of tectonic tremor episodes from Shikoku, Japan, recorded by the Hi-net seismic network operated by NIED. We illustrate its performance and potential in providing activity maps - associated to different scale-components of tectonic tremors - that can be analyzed statistically to improve our understanding of tremor sources and scaling, as well as their relation with the background seismicity.
Nonlinear wave structures on NO+ions in active plasma-jet space experiment ``North-Star''.
NASA Astrophysics Data System (ADS)
Kovaleva, Irina; Gavrilov, Boris; Zetzer, Julius; Pfaff, Robert; Poklad, Yuriy; Erlandson, Robert
Ionospheric density irregularities cause scintillations of GPS signals. Their nature and generation mechanisms are subject of many investigations. Model of nonlinear gradient-drift ion-cyclotron structures is proposed in [1,2]. In accordance with the model density humps or holes are formed by one ion species of ionosphere plasma and accompanied by short-wave-length oscillations on their trailing edge. The nonlinear structures are excited on transversal to geomagnetic field concentration gradient of ion species. Experimental registrations of the irregularities do not sufficiently attend to this properties. Experimental data of active ionospheric experiment “North Star” (plasma-jet space experiment)[3] are revised in relaxation phase of plasma-jet injections. The mentioned above nonlinear structures on NO+ ion species are identified. The generation mechanism is considered. [1]Kovaleva I.Kh.//Phys plasmas, 19, 102905, doi: 10.1063/1.4763561,2012 [2]Kovaleva I.Kh.//Plasma Phys Reports 39, 3, pp226-235, 2013 [3]Erlandson R.E.,MengC.I., Y.,Zetzer J,I.//J. Spacecraft and rockets V.41, N.4,pp481-482
Zeng, Nianyin; Wang, Zidong; Li, Yurong; Du, Min; Liu, Xiaohui
2011-07-01
In this paper, a mathematical model for sandwich-type lateral flow immunoassay is developed via short available time series. A nonlinear dynamic stochastic model is considered that consists of the biochemical reaction system equations and the observation equation. After specifying the model structure, we apply the extended Kalman filter (EKF) algorithm for identifying both the states and parameters of the nonlinear state-space model. It is shown that the EKF algorithm can accurately identify the parameters and also predict the system states in the nonlinear dynamic stochastic model through an iterative procedure by using a small number of observations. The identified mathematical model provides a powerful tool for testing the system hypotheses and also for inspecting the effects from various design parameters in both rapid and inexpensive way. Furthermore, by means of the established model, the dynamic changes in the concentration of antigens and antibodies can be predicted, thereby making it possible for us to analyze, optimize, and design the properties of lateral flow immunoassay devices.
NASA Astrophysics Data System (ADS)
El-Hanbaly, A. M.; Sallah, M.; El-Shewy, E. K.; Darweesh, H. F.
2015-10-01
Linear and nonlinear dust-acoustic (DA) waves are studied in a collisionless, unmagnetized and dissipative dusty plasma consisting of negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal ions. The normal mode analysis is used to obtain a linear dispersion relation illustrating the dependence of the wave damping rate on the carrier wave number, the dust viscosity coefficient, the ratio of the ion temperature to the electron temperatures, and the nonthermal parameter. The plasma system is analyzed nonlinearly via the reductive perturbation method that gives the KdV-Burgers equation. Some interesting physical solutions are obtained to study the nonlinear waves. These solutions are related to soliton, a combination between a shock and a soliton, and monotonic and oscillatory shock waves. Their behaviors are illustrated and shown graphically. The characteristics of the DA solitary and shock waves are significantly modified by the presence of nonthermal (fast) ions, the ratio of the ion temperature to the electron temperature, and the dust kinematic viscosity. The topology of the phase portrait and the potential diagram of the KdV-Burgers equation is illustrated, whose advantage is the ability to predict different classes of traveling wave solutions according to different phase orbits. The energy of the soliton wave and the electric field are calculated. The results in this paper can be generalized to analyze the nature of plasma waves in both space and laboratory plasma systems.
El-Hanbaly, A. M.; Sallah, M.; El-Shewy, E. K.; Darweesh, H. F.
2015-10-15
Linear and nonlinear dust-acoustic (DA) waves are studied in a collisionless, unmagnetized and dissipative dusty plasma consisting of negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal ions. The normal mode analysis is used to obtain a linear dispersion relation illustrating the dependence of the wave damping rate on the carrier wave number, the dust viscosity coefficient, the ratio of the ion temperature to the electron temperatures, and the nonthermal parameter. The plasma system is analyzed nonlinearly via the reductive perturbation method that gives the KdV-Burgers equation. Some interesting physical solutions are obtained to study the nonlinear waves. These solutions are related to soliton, a combination between a shock and a soliton, and monotonic and oscillatory shock waves. Their behaviors are illustrated and shown graphically. The characteristics of the DA solitary and shock waves are significantly modified by the presence of nonthermal (fast) ions, the ratio of the ion temperature to the electron temperature, and the dust kinematic viscosity. The topology of the phase portrait and the potential diagram of the KdV-Burgers equation is illustrated, whose advantage is the ability to predict different classes of traveling wave solutions according to different phase orbits. The energy of the soliton wave and the electric field are calculated. The results in this paper can be generalized to analyze the nature of plasma waves in both space and laboratory plasma systems.
NASA Technical Reports Server (NTRS)
Young, Richard D.; Nemeth, Michael P.; Collins, Timothy J.; Starnes, James H., Jr.
1998-01-01
Results of linear bifurcation and nonlinear analyses of the Space Shuttle superlightweight (SLWT) external liquid-oxygen (LO2) tank for an important early booster ascent loading condition are presented. These results for thin-walled linear elastic shells that are subjected to combined mechanical and thermal loads illustrate an important type of response mode that may be encountered in the design of other liquid-fuel launch vehicles. Linear bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the forward ogive section of the LO2 tank. In contrast, the nonlinear response phenomenon is shown to consist of short-wavelength bending deformations in the forward ogive and barrel sections of the LO2 tank that growing amplitude in a stable manner increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the forward ogive section. For the linear bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shield generally require a large-scale, high-fidelity finite-element model. Results are also presented that show that the SLWT LO2 tank can support loads in excess of approximately 2.6 times the values of the operational loads considered.
Effect of joint damping and joint nonlinearity on the dynamics of space structures
NASA Technical Reports Server (NTRS)
Bowden, Mary; Dugundji, John
1988-01-01
Analyses of the effect of linear joint characteristics on the vibrations of a free-free, three-joint beam model show that increasing joint damping increases resonant frequencies and increases modal damping but only to the point where the joint gets 'locked up' by damping. This behavior is different from that predicted by modeling joint damping as proportional damping. Nonlinear analyses of the three-joint model with cubic springs at the joints show all the classical single DOF nonlinear response behavior at each resonance of the multiple DOF system: nondoubling of response for a doubling of forcing amplitude, multiple solutions, jump behavior, and resonant frequency shifts. These properties can be concisely quantified by characteristic backbone curves, which show the locus of resonant peaks for increasing forcing amplitude.
1991-05-01
Office of Scientific Research under Grant F49620-87-C-0074. References 1. S. Rajasekaran and D. W . Murray , Incremental finite element matrices, J...2081-2105, 1968. 3. D. W . Murray , Finite element nonlinear analysis of plates, Ph. D. Dissertation, Dept. of Civil Engineering, University of...Air Force Office of Scientific Research (AFOSR) TABLE OF CONTENTS SUMMARY fENCLOSED PhD THESES AND PAPERS W . K. Belvin Simulation and Interdisciplinary
Mixing of two collinear Rayleigh waves in an isotropic nonlinear elastic half-space
Morlock, Merlin B.; Kim, Jin-Yeon; Jacobs, Laurence J.; Qu, Jianmin
2014-02-18
Nonlinear mixing of two collinear, initially monochromatic, Rayleigh waves propagating in the same direction in an isotropic, nonlinear elastic solid is investigated analytically. A system of coupled ordinary differential equations is derived based on the Lagrange equations of the second kind to predict the evolution of the higher harmonic and combination frequency components of the fundamentals waves. Numerical results show that the energy transfer is larger for higher frequencies, and that the oscillation of the energy between the different frequency components depends on the amplitudes and frequencies of the fundamental waves. Furthermore, it is illustrated that the horizontal velocity component can form a shock wave while the vertical velocity component can form a pulse. The occurrence of these effects is independent of the specific fundamental frequencies and amplitudes that are mixed. However, the nonlinear interaction is more efficient when the mixing frequencies are close to each other which increases both effects. The analytical model is then extended by implementing diffraction effects in the parabolic approximation.
Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces
NASA Astrophysics Data System (ADS)
Mabdaoui, M.; Moussa, H.; Rhoudaf, M.
2017-03-01
We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem ... where A is a Leray-Lions operator having a growth not necessarily of polynomial type. The lower order term Φ :Ω × (0,T)× R→ R^N is a Carathéodory function, for a.e. (x,t)in Q_T and for all sin R, satisfying only a growth condition and the right hand side f belongs to L^1(Q_T).
A State-Space Approach to Parametrization of Stabilizing Controllers for Nonlinear Systems
1994-05-12
Diaz-Bobillo (1993), Control of Uncertain Systems: A Linear Program- ming Approach, A Monograph to be Published. [7] Desoer , C.A. and C.A. Lin (1984...Nonlinear Unity-Feedback Systems and &-Parametrization, Int. J. Control, Vo1.40, pp.37-51. [8] Desoer , C.A. and R.W. Liu (1982), Global...Parametrization of Feedback Systems with Nonlin- ear Plants, Systems and Control Letts., Vol. 1, pp.249-251. [9] Desoer ,C.A., R.W.Liu, J.Murray and R.Saeks
Numerical approximations to nonlinear conservation laws with locally varying time and space grids
NASA Technical Reports Server (NTRS)
Osher, S.; Sanders, R.
1983-01-01
Numerical approximations to the initial value problem for nonlinear systems of conservation laws are considered. The considered system is said to be hyperbolic when all eigenvalues of every real linear combination of the Jacobian matrices are real. Solutions may develop discontinuities in finite time, even when the initial data are smooth. In the investigation, explicit finite difference methods which use locally varying time grids are considered. The global CFL restriction is replaced by a local restriction. The numerical flux function is studied from a finite volume viewpoint, and a differencing technique is developed at interface points between regions of distinct time increments.
Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces
NASA Astrophysics Data System (ADS)
Mabdaoui, M.; Moussa, H.; Rhoudaf, M.
2016-03-01
We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem [Equation not available: see fulltext.]where A is a Leray-Lions operator having a growth not necessarily of polynomial type. The lower order term Φ :Ω × (0,T)× {R}→ {R}^N is a Carathéodory function, for a.e. (x,t)in Q_T and for all sin R , satisfying only a growth condition and the right hand side f belongs to L^1(Q_T).
On Asymptotic Stability in Energy Space of Ground States for Nonlinear Schrödinger Equations
NASA Astrophysics Data System (ADS)
Cuccagna, Scipio; Mizumachi, Tetsu
2008-11-01
We consider nonlinear Schrödinger equations iu_t +Δ u +β (|u|^2)u=0 , text{for} (t,x)in mathbb{R}× mathbb{R}^d, where d ≥ 3 and β is smooth. We prove that symmetric finite energy solutions close to orbitally stable ground states converge to a sum of a ground state and a dispersive wave as t → ∞ assuming the so called the Fermi Golden Rule (FGR) hypothesis. We improve the “sign condition” required in a recent paper by Gang Zhou and I.M.Sigal.
NASA Astrophysics Data System (ADS)
El-Hanbaly, A. M.; El-Shewy, E. K.; Sallah, M.; Darweesh, H. F.
2015-05-01
The propagation of linear and nonlinear dust acoustic waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negative dust grains has been investigated. The Boltzmann distribution is suggested for electrons whereas vortex-like distribution for ions. In the linear analysis, the dispersion relation is obtained, and the dependence of damping rate of the waves on the carrier wave number , the dust kinematic viscosity coefficient and the ratio of the ions to the electrons temperatures is discussed. In the nonlinear analysis, the modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation is derived via the reductive perturbation method. Bifurcation analysis is discussed for non-dissipative system in the absence of Burgers term. In the case of dissipative system, the tangent hyperbolic method is used to solve mKdV-Burgers equation, and yield the shock wave solution. The obtained results may be helpful in better understanding of waves propagation in the astrophysical plasmas as well as in inertial confinement fusion laboratory plasmas.
On Schubert decompositions of quiver Grassmannians
NASA Astrophysics Data System (ADS)
Lorscheid, Oliver
2014-02-01
In this paper, we introduce Schubert decompositions for quiver Grassmannians and investigate certain classes of quiver Grassmannians with a Schubert decomposition into affine spaces. The main theorem puts the cells of a Schubert decomposition into relation to the cells of a certain simpler quiver Grassmannian. This allows us to extend known examples of Schubert decompositions into affine spaces to a larger class of quiver Grassmannians. This includes exceptional representations of the Kronecker quiver as well as representations of forests with block matrices of the form (0100). Finally, we draw conclusions on the Euler characteristics and the cohomology of quiver Grassmannians.
NASA Astrophysics Data System (ADS)
Yothers, Mitchell P.; Browder, Aaron E.; Bumm, Lloyd A.
2017-01-01
We have developed a real-space method to correct distortion due to thermal drift and piezoelectric actuator nonlinearities on scanning tunneling microscope images using Matlab. The method uses the known structures typically present in high-resolution atomic and molecularly resolved images as an internal standard. Each image feature (atom or molecule) is first identified in the image. The locations of each feature's nearest neighbors are used to measure the local distortion at that location. The local distortion map across the image is simultaneously fit to our distortion model, which includes thermal drift in addition to piezoelectric actuator hysteresis and creep. The image coordinates of the features and image pixels are corrected using an inverse transform from the distortion model. We call this technique the thermal-drift, hysteresis, and creep transform. Performing the correction in real space allows defects, domain boundaries, and step edges to be excluded with a spatial mask. Additional real-space image analyses are now possible with these corrected images. Using graphite(0001) as a model system, we show lattice fitting to the corrected image, averaged unit cell images, and symmetry-averaged unit cell images. Statistical analysis of the distribution of the image features around their best-fit lattice sites measures the aggregate noise in the image, which can be expressed as feature confidence ellipsoids.
Linear and nonlinear analysis of orbital telescope/space shuttle dynamics and control
NASA Technical Reports Server (NTRS)
Roberts, A. S., Jr.; Joshi, S. M.
1976-01-01
Work completed on the design and study of an annular suspension and pointing (ASP) system for the space shuttle was presented. This system makes use of a magnetically suspended vernier pointing assembly. The following objectives were pursued in this study: (1) development of a detailed mathematical model of the Space Shuttle/ASP system, (2) design of control laws in order to obtain the desired pointing performance, and (3) prediction of the statistical pointing accuracies in the presence of stochastic disturbances such as crew-motion, and sensor and actuator noise. The first two of these objectives are documented in this report.
NASA Astrophysics Data System (ADS)
El-Hanbaly, A. M.; El-Shewy, E. K.; Sallah, M.; Darweesh, H. F.
2016-05-01
The nonlinear characteristics of the dust acoustic (DA) waves are studied in a homogeneous, collisionless, unmagnetized, and dissipative dusty plasma composed of negatively charged dusty grains, superthermal electrons, and nonextensive ions. Sagdeev pseudopotential technique has been employed to study the large amplitude DA waves. It (Sagdeev pseudopotential) has an evidence for the existence of compressive and rarefractive solitons. The global features of the phase portrait are investigated to understand the possible types of solutions of the Sagdeev form. On the other hand, the reductive perturbation technique has been used to study small amplitude DA waves and yields the Korteweg-de Vries-Burgers (KdV-Burgers) equation that exhibits both soliton and shock waves. The behavior of the obtained results of both large and small amplitude is investigated graphically in terms of the plasma parameters like dust kinematic viscosity, superthermal and nonextensive parameters.
NASA Technical Reports Server (NTRS)
Karimbadi, H.; Krauss-Varban, D.
1992-01-01
A novel diffusion formalism that takes into account the finite width of resonances is presented. The resonance diagram technique is shown to reproduce the details of the particle orbits very accurately, and can be used to determine the acceleration/scattering in the presence of a given wave spectrum. Ways in which the nonlinear orbits can be incorporated into the diffusion equation are shown. The resulting diffusion equation is an extension of the Q-L theory to cases where the waves have large amplitudes and/or are coherent. This new equation does not have a gap at 90 deg in cases where the individual orbits can cross the gap. The conditions under which the resonance gap at 90-deg pitch angle exits are also examined.
NASA Astrophysics Data System (ADS)
Palo, M.; Cusano, P.
2013-01-01
We analyse the seismic noise recorded at the Colima Volcano (Mexico) in the period December 2005-May 2006 by four broadband three-component seismic stations. Specifically, we characterize the spectral content of the signal and follow its time evolution along all the data set. Moreover, we infer the properties of the attractor in the phase space by false nearest neighbours analysis and Grassberger-Procaccia algorithm, and adopt a time-domain decomposition method (independent component analysis) to find the basic constituents (independent components) of the system. Constraints on the seismic wavefield are inferred by the polarization analysis. We find two states of the background seismicity visible in different time-intervals that are Phase A and Phase B. Phase A has a spectrum with two peaks at 0.15 Hz and 0.3 Hz, with the latter dominating, an attractor of correlation dimension close to 3, three quasi-monochromatic independent components, and a relevant fraction of crater-pointing polarization solutions in the near-field. In Phase B, the spectrum is preserved but with the highest peak at 0.15 Hz, the attractor has a correlation dimension close to 2, two independent components are extracted, and the polarization solutions are dominated by Rayleigh waves incoming from the southwest direction. We depict two sources acting on the background seismicity that are the microseismic noise loading on the Pacific coastline and a low-energy volcanic tremor. A change in the amplitude of the microseismic noise can induce the switching from a state of the system to the other.
Chen, W; Holm, S
2004-04-01
Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation. In this study, a linear integro-differential equation wave model was developed for the anomalous attenuation by using the space-fractional Laplacian operation, and the strategy is then extended to the nonlinear Burgers equation. A new definition of the fractional Laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional Laplacian. Under the Szabo's smallness approximation, where attenuation is assumed to be much smaller than the wave number, the linear model is found consistent with arbitrary frequency power-law dependency.
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr.; Song, Kyongchan; Elliott, Kenny B.; Raju, Ivatury S.; Warren, Jerry E.
2012-01-01
Elastic-plastic, large-deflection nonlinear stress analyses are performed for the external hat-shaped stringers (or stiffeners) on the intertank portion of the Space Shuttle s external tank. These stringers are subjected to assembly strains when the stringers are initially installed on an intertank panel. Four different stringer-feet configurations including the baseline flat-feet, the heels-up, the diving-board, and the toes-up configurations are considered. The assembly procedure is analytically simulated for each of these stringer configurations. The location, size, and amplitude of the strain field associated with the stringer assembly are sensitive to the assumed geometry and assembly procedure. The von Mises stress distributions from these simulations indicate that localized plasticity will develop around the first eight fasteners for each stringer-feet configuration examined. However, only the toes-up configuration resulted in high assembly hoop strains.
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr.; Warren, Jerry E.; Elliott, Kenny B.; Song, Kyongchan; Raju, Ivatury S.
2012-01-01
Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.
Space-time evolution of the nonlinear two-stream instability
Lemons, D.S.; Jones, M.E.; Lee, H.
1983-01-01
A cold electron beam penetrating a cold plasma is electrostatically unstable. The instability produces a growing electric field that saturates when the beam electrons are suddenly trapped by a single wave. During trapping a significant amount of energy is transferred from the beam to the field and ultimately to the plasma. At Los Alamos experiments are being performed that demonstrate this anomalous beam-driven plasma heating. The heating efficiency is a function of the phase velocity of the trapping wave. According to our generalization of a previous calculation, the instability is absolute and its wave form evolves in both space and time. Modifying trapping theory to account for the space and time evolution of the two-stream instability, we find that the heating efficiency should change in time. This prediction is in agreement with results from one-dimensional PIC simulations.
NASA Astrophysics Data System (ADS)
Mohamad, Mustafa A.; Cousins, Will; Sapsis, Themistoklis P.
2016-10-01
We consider the problem of the probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities. Systems with these properties can be found in a variety of areas including mechanics, fluids, and waves. Here we develop a computational method, a probabilistic decomposition-synthesis technique, that takes into account the nature of internal instabilities to inexpensively determine the non-Gaussian probability density function for any arbitrary quantity of interest. Our approach relies on the decomposition of the statistics into a 'non-extreme core', typically Gaussian, and a heavy-tailed component. This decomposition is in full correspondence with a partition of the phase space into a 'stable' region where we have no internal instabilities, and a region where non-linear instabilities lead to rare transitions with high probability. We quantify the statistics in the stable region using a Gaussian approximation approach, while the non-Gaussian distribution associated with the intermittently unstable regions of phase space is inexpensively computed through order-reduction methods that take into account the strongly nonlinear character of the dynamics. The probabilistic information in the two domains is analytically synthesized through a total probability argument. The proposed approach allows for the accurate quantification of non-Gaussian tails at more than 10 standard deviations, at a fraction of the cost associated with the direct Monte-Carlo simulations. We demonstrate the probabilistic decomposition-synthesis method for rare events for two dynamical systems exhibiting extreme events: a two-degree-of-freedom system of nonlinearly coupled oscillators, and in a nonlinear envelope equation characterizing the propagation of unidirectional water waves.
Nonlinear propagation of positron-acoustic waves in a four component space plasma
NASA Astrophysics Data System (ADS)
Shah, M. G.; Hossen, M. R.; Mamun, A. A.
2015-10-01
> The nonlinear propagation of positron-acoustic waves (PAWs) in an unmagnetized, collisionless, four component, dense plasma system (containing non-relativistic inertial cold positrons, relativistic degenerate electron and hot positron fluids as well as positively charged immobile ions) has been investigated theoretically. The Korteweg-de Vries (K-dV), modified K-dV (mK-dV) and further mK-dV (fmK-dV) equations have been derived by using reductive perturbation technique. Their solitary wave solutions have been numerically analysed in order to understand the localized electrostatic disturbances. It is observed that the relativistic effect plays a pivotal role on the propagation of positron-acoustic solitary waves (PASW). It is also observed that the effects of degenerate pressure and the number density of inertial cold positrons, hot positrons, electrons and positively charged static ions significantly modify the fundamental features of PASW. The basic features and the underlying physics of PASW, which are relevant to some astrophysical compact objects (such as white dwarfs, neutron stars etc.), are concisely discussed.
The Vector Decomposition Problem
NASA Astrophysics Data System (ADS)
Yoshida, Maki; Mitsunari, Shigeo; Fujiwara, Toru
This paper introduces a new computational problem on a two-dimensional vector space, called the vector decomposition problem (VDP), which is mainly defined for designing cryptosystems using pairings on elliptic curves. We first show a relation between the VDP and the computational Diffie-Hellman problem (CDH). Specifically, we present a sufficient condition for the VDP on a two-dimensional vector space to be at least as hard as the CDH on a one-dimensional subspace. We also present a sufficient condition for the VDP with a fixed basis to have a trapdoor. We then give an example of vector spaces which satisfy both sufficient conditions and on which the CDH is assumed to be hard in previous work. In this sense, the intractability of the VDP is a reasonable assumption as that of the CDH.
NASA Astrophysics Data System (ADS)
Tan, Heping; Yu, Qizheng; Zhang, Jizhou
In this paper, the transient combined heat transfer in the silicon glass porthole of Space Shuttle is studied by control volume method, ray tracing method and spectral band model. The temperature field in the silicon glass and heat flux entering the space cabin are given under the 3rd kind nonlinear boundary condition. The computational results show, if the radiation in the silicon glass is omitted, the errors for temperature fields are not too evident, but for heat flux are quite large.
Nonlinear research of an image motion stabilization system embedded in a space land-survey telescope
NASA Astrophysics Data System (ADS)
Somov, Yevgeny; Butyrin, Sergey; Siguerdidjane, Houria
2017-01-01
We consider an image motion stabilization system embedded into a space telescope for a scanning optoelectronic observation of terrestrial targets. Developed model of this system is presented taking into account physical hysteresis of piezo-ceramic driver and a time delay at a forming of digital control. We have presented elaborated algorithms for discrete filtering and digital control, obtained results on analysis of the image motion velocity oscillations in the telescope focal plane, and also methods for terrestrial and in-flight verification of the system.
Nonlinear Attitude Control of Planar Structures in Space Using Only Internal Controls
NASA Technical Reports Server (NTRS)
Reyhanoglu, Mahmut; Mcclamroch, N. Harris
1993-01-01
An attitude control strategy for maneuvers of an interconnection of planar bodies in space is developed. It is assumed that there are no exogeneous torques and that torques generated by joint motors are used as means of control so that the total angular momentum of the multibody system is a constant, assumed to be zero. The control strategy utilizes the nonintegrability of the expression for the angular momentum. Large angle maneuvers can be designed to achieve an arbitrary reorientation of the multibody system with respect to an inertial frame. The theoretical background for carrying out the required maneuvers is summarized.
Zhang, Zhen; Yan, Lixin; Du, Yingchao; Zhou, Zheng; Su, Xiaolu; Zheng, Lianmin; Wang, Dong; Tian, Qili; Wang, Wei; Shi, Jiaru; Chen, Huaibi; Huang, Wenhui; Gai, Wei; Tang, Chuanxiang
2016-05-05
High-intensity trains of electron bunches with tunable picosecond spacing are produced and measured experimentally with the goal of generating terahertz (THz) radiation. By imposing an initial density modulation on a relativistic electron beam and controlling the charge density over the beam propagation, density spikes of several-hundred-ampere peak current in the temporal profile, which are several times higher than the initial amplitudes, have been observed for the first time. We also demonstrate that the periodic spacing of the bunch train can be varied continuously either by tuning launching phase of a radiofrequency gun or by tuning the compression of a downstream magnetic chicane. Narrow-band coherent THz radiation from the bunch train was also measured with μJ-level energies and tunable central frequency of the spectrum in the range of ~0.5 to 1.6 THz. Our results pave the way towards generating mJ-level narrow-band coherent THz radiation and driving high-gradient wakefield-based acceleration.
Zhang, Zhen; Yan, Lixin; Du, Yingchao; Zhou, Zheng; Su, Xiaolu; Zheng, Lianmin; Wang, Dong; Tian, Qili; Wang, Wei; Shi, Jiaru; Chen, Huaibi; Huang, Wenhui; Gai, Wei; Tang, Chuanxiang
2016-05-06
High-intensity trains of electron bunches with tunable picosecond spacing are produced and measured experimentally with the goal of generating terahertz (THz) radiation. By imposing an initial density modulation on a relativistic electron beam and controlling the charge density over the beam propagation, density spikes of several-hundred-ampere peak current in the temporal profile, which are several times higher than the initial amplitudes, have been observed for the first time. We also demonstrate that the periodic spacing of the bunch train can be varied continuously either by tuning launching phase of a radio-frequency gun or by tuning the compression of a downstream magnetic chicane. Narrow-band coherent THz radiation from the bunch train was also measured with μJ-level energies and tunable central frequency of the spectrum in the range of ∼0.5 to 1.6 THz. Our results pave the way towards generating mJ-level narrow-band coherent THz radiation and driving high-gradient wakefield-based acceleration.
NASA Astrophysics Data System (ADS)
Zhang, Zhen; Yan, Lixin; Du, Yingchao; Zhou, Zheng; Su, Xiaolu; Zheng, Lianmin; Wang, Dong; Tian, Qili; Wang, Wei; Shi, Jiaru; Chen, Huaibi; Huang, Wenhui; Gai, Wei; Tang, Chuanxiang
2016-05-01
High-intensity trains of electron bunches with tunable picosecond spacing are produced and measured experimentally with the goal of generating terahertz (THz) radiation. By imposing an initial density modulation on a relativistic electron beam and controlling the charge density over the beam propagation, density spikes of several-hundred-ampere peak current in the temporal profile, which are several times higher than the initial amplitudes, have been observed for the first time. We also demonstrate that the periodic spacing of the bunch train can be varied continuously either by tuning launching phase of a radio-frequency gun or by tuning the compression of a downstream magnetic chicane. Narrow-band coherent THz radiation from the bunch train was also measured with μ J -level energies and tunable central frequency of the spectrum in the range of ˜0.5 to 1.6 THz. Our results pave the way towards generating mJ-level narrow-band coherent THz radiation and driving high-gradient wakefield-based acceleration.
NASA Astrophysics Data System (ADS)
LeFloch, Philippe G.; Ma, Yue
2016-09-01
The Hyperboloidal Foliation Method (introduced by the authors in 2014) is extended here and applied to the Einstein equations of general relativity. Specifically, we establish the nonlinear stability of Minkowski spacetime for self-gravitating massive scalar fields, while existing methods only apply to massless scalar fields. First of all, by analyzing the structure of the Einstein equations in wave coordinates, we exhibit a nonlinear wave-Klein-Gordon model defined on a curved background, which is the focus of the present paper. For this model, we prove here the existence of global-in-time solutions to the Cauchy problem, when the initial data have sufficiently small Sobolev norms. A major difficulty comes from the fact that the class of conformal Killing fields of Minkowski space is significantly reduced in the presence of a massive scalar field, since the scaling vector field is not conformal Killing for the Klein-Gordon operator. Our method relies on the foliation (of the interior of the light cone) of Minkowski spacetime by hyperboloidal hypersurfaces and uses Lorentz-invariant energy norms. We introduce a frame of vector fields adapted to the hyperboloidal foliation and we establish several key properties: Sobolev and Hardy-type inequalities on hyperboloids, as well as sup-norm estimates, which correspond to the sharp time decay for the wave and the Klein-Gordon equations. These estimates allow us to control interaction terms associated with the curved geometry and the massive field by distinguishing between two levels of regularity and energy growth and by a successive use of our key estimates in order to close a bootstrap argument.
NASA Astrophysics Data System (ADS)
de la Torre, Sylvain; Guzzo, Luigi
2012-11-01
We investigate the ability of state-of-the-art redshift-space distortion models for the galaxy anisotropic two-point correlation function, ξ(r⊥, r∥), to recover precise and unbiased estimates of the linear growth rate of structure f, when applied to catalogues of galaxies characterized by a realistic bias relation. To this aim, we make use of a set of simulated catalogues at z = 0.1 and 1 with different luminosity thresholds, obtained by populating dark matter haloes from a large N-body simulation using halo occupation prescriptions. We examine the most recent developments in redshift-space distortion modelling, which account for non-linearities on both small and intermediate scales produced, respectively, by randomized motions in virialized structures and non-linear coupling between the density and velocity fields. We consider the possibility of including the linear component of galaxy bias as a free parameter and directly estimate the growth rate of structure f. Results are compared to those obtained using the standard dispersion model, over different ranges of scales. We find that the model of Taruya et al., the most sophisticated one considered in this analysis, provides in general the most unbiased estimates of the growth rate of structure, with systematic errors within ±4 per cent over a wide range of galaxy populations spanning luminosities between L > L* and L > 3L*. The scale dependence of galaxy bias plays a role on recovering unbiased estimates of f when fitting quasi-non-linear scales. Its effect is particularly severe for most luminous galaxies, for which systematic effects in the modelling might be more difficult to mitigate and have to be further investigated. Finally, we also test the impact of neglecting the presence of non-negligible velocity bias with respect to mass in the galaxy catalogues. This can produce an additional systematic error of the order of 1-3 per cent depending on the redshift, comparable to the statistical errors the we
On symmetric decompositions of positive operators
NASA Astrophysics Data System (ADS)
Anastasia Jivulescu, Maria; Nechita, Ion; Găvruţa, Paşc
2017-04-01
We present results concerning decompositions of positive operators acting on finite-dimensional Hilbert spaces. Our motivation is the study of a generalized version of the SIC–POVM problem, which has applications to Quantum Information Theory. We relax some of the conditions in the SIC–POVM setting (the elements sum up to the identity, resp. the elements have unit rank), and we focus on equiangular decompositions (the elements of the decomposition should have the same length, and pairs of distinct elements should have constant angles). We characterize all such decompositions, comparing our results with the case of SIC–POVMs. We also generalize some existing Welch-type inequalities.
A nonlinear optimization approach for disturbance rejection in flexible space structures
NASA Technical Reports Server (NTRS)
Parlos, Alexander G.; Sunkel, John W.
1990-01-01
In this paper the design of an active control law for the rejection of persistent disturbances in large space structures is presented. The control system design approach is based on a deterministic model of the disturbances, with a model-based-compensator (MBC) structure, optimizing the magnitude of the disturbance that the structure can tolerate without violating certain predetermined constraints. In addition to closed-loop stability, the explicit treatment of state, control and control rate constraints, such as structural displacement, control actuator effort, and compensator time guarantees that the final design will exhibit desired performance characteristics. The technique is applied for the vibration damping of a simple two bay truss structure which is subjected to persistent disturbances, such as shuttle docking. Preliminary results indicate that the proposed control system can reject considerable persistent disturbances by utilizing most of the available control, while limiting the structural displacements to within desired tolerances. Further work, however, for incorporating additional design criteria, such as compensator robustness to be traded-off against performance specifications, is warranted.
NASA Astrophysics Data System (ADS)
Owolabi, Kolade M.; Atangana, Abdon
2016-09-01
In this paper, dynamics of time-dependent fractional-in-space nonlinear Schrödinger equation with harmonic potential V(x),x in R in one, two and three dimensions have been considered. We approximate the Riesz fractional derivative with the Fourier pseudo-spectral method and advance the resulting equation in time with both Strang splitting and exponential time-differencing methods. The Riesz derivative introduced in this paper is found to be so convenient to be applied in models that are connected with applied science, physics, and engineering. We must also report that the Riesz derivative introduced in this work will serve as a complementary operator to the commonly used Caputo or Riemann-Liouville derivatives in the higher-dimensional case. In the numerical experiments, one expects the travelling wave to evolve from such an initial function on an infinite computational domain (-∞, &infty); , which we truncate at some large, but finite values L. It is important that the value of L is chosen large enough to give enough room for the wave function to propagate. We observe a different distribution of complex wave functions for the focusing and defocusing cases.
Ngeo, Jimson; Tamei, Tomoya; Ikeda, Kazushi; Shibata, Tomohiro
2015-01-01
Accurate proportional myoelectric control of the hand is important in replicating dexterous manipulation in robot prostheses and orthoses. However, this is still difficult to achieve due to the complex and high degree-of-freedom (DOF) nature present in the governing musculoskeletal system. To address this problem, we suggest using a low dimensional encoding based on nonlinear synergies to represent both the high-DOF finger joint kinematics and the coordination of muscle activities taken from surface electromyographic (EMG) signals. Generating smooth multi-finger movements using EMG inputs is then done by using a shared Gaussian Process latent variable model that learns a dynamical model between both the kinematic and EMG data represented in a shared latent space. The experimental results show that the method is able to synthesize continuous movements of a full five-finger hand model, with total dimensions as large as 69 (although highly redundant and correlated). Finally, by comparing the estimation performances when the number of EMG latent dimensions are varied, we show that these synergistic features can capture the variance, shared and specific to the observed kinematics.
Yongjun, Wang; Qinghua, Tian; Zhi, Wang; Xiaoqing, Zhu; Chen, Wu; Chao, Shang; Xin, Xiangjun
2016-03-10
In this paper, we establish a simple model to analyze the semiconductor optical amplifier's (SOA) nonlinear polarization rotation (NPR) and acquire the variable curves of phase difference between TE and TM modes with bias current, pump power, probe power, and linewidth enhancement factor (LEF). The results indicate that the optical switch based on the SOA's NPR can be realized by changing the pump's optical power and the main operating parameters, such as bias current and hold beam power, and then the pump power can be determined. On this basis, a time-space-time (T-S-T) optical packet switching node is proposed, in which the SOA's NPR switch is the basic element. Then, the T-S and S-T experimental systems are set up, and the experimental results demonstrate that the proposed switch scheme can implement the optical switching function in accordance with the routing requirement. The signal-to-noise ratio (SNR) exceeds 20 dB, and the extinction ratio (ER) is more than 10 dB after being delayed and switched in the node.
Uncertainty propagation in orbital mechanics via tensor decomposition
NASA Astrophysics Data System (ADS)
Sun, Yifei; Kumar, Mrinal
2016-03-01
Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker-Planck equation (FPE) is defined on a relatively high dimensional (6-D) state-space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the x-y-z subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors' knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral ("super-fast") convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.
Analyzing spinodal decomposition of an anisotropic fluid mixture
NASA Astrophysics Data System (ADS)
Gruhn, Thomas; Pogorelov, Evgeny; Seiferling, Felix; Emmerich, Heike
2017-02-01
Spinodal decomposition leads to spontaneous fluctuations of the local concentration. In the early stage, the resulting pattern provides explicit information about the material properties of the mixture. In the case of two isotropic fluids, the static structure factor shows the characteristic ring shape. If one component is a liquid crystal, the pattern is typically anisotropic and the structure factor is more complex. Using numerical methods, we investigate how structure factors can be used to extract information about material properties like the diffusion constant or the isotropic and the anisotropic contributions to the interfacial tension. The method is based on momenta taken from structure factors in the early stage of the spinodal demixing. We perform phase field calculations for an isotropic and an anisotropic spinodal decomposition. A comparison of the extracted results with analytic values is made. The calculations show that linear modes dominate in the beginning of the growth process, while non-linear modes grow monotonously in the region of the k-space for which damping is predicted by the linearized theory. As long as non-linear modes are small enough, linearized theory can be applied to extract material properties from the structure factor.
Ławryńczuk, Maciej
2017-03-01
This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearised on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimisation problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimisation repeated at each sampling instant.
NASA Astrophysics Data System (ADS)
El-Tantawy, S. A.
2016-05-01
We examine the likelihood of the ion-acoustic rogue waves propagation in a non-Maxwellian electronegative plasma in the framework of the family of the Korteweg-de Vries (KdV) equations (KdV/modified KdV/Extended KdV equation). For this purpose, we use the reductive perturbation technique to carry out this study. It is known that the family of the KdV equations have solutions of distinct structures such as solitons, shocks, kinks, cnoidal waves, etc. However, the dynamics of the nonlinear rogue waves is governed by the nonlinear Schrödinger equation (NLSE). Thus, the family of the KdV equations is transformed to their corresponding NLSE developing a weakly nonlinear wave packets. We show the possible region for the existence of the rogue waves and define it precisely for typical parameters of space plasmas. We investigate numerically the effects of relevant physical parameters, namely, the negative ion relative concentration, the nonthermal parameter, and the mass ratio on the propagation of the rogue waves profile. The present study should be helpful in understanding the salient features of the nonlinear structures such as, ion-acoustic solitary waves, shock waves, and rogue waves in space and in laboratory plasma where two distinct groups of ions, i.e. positive and negative ions, and non-Maxwellian (nonthermal) electrons are present.
Morphological Decomposition in Reading Hebrew Homographs
ERIC Educational Resources Information Center
Miller, Paul; Liran-Hazan, Batel; Vaknin, Vered
2016-01-01
The present work investigates whether and how morphological decomposition processes bias the reading of Hebrew heterophonic homographs, i.e., unique orthographic patterns that are associated with two separate phonological, semantic entities depicted by means of two morphological structures (linear and nonlinear). In order to reveal the nature of…
ERIC Educational Resources Information Center
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Charles R. Tolle; Mark Pengitore
2009-08-01
This paper explores the overlaps between the Control community’s work on System Identification (SysID) and the Physics, Mathematics, Chaos, and Complexity communities’ work on phase-space reconstruction via time-delay embedding. There are numerous overlaps between the goals of each community. Nevertheless, the Controls community can gain new insight as well as some new very powerful tools for SysID from the latest developments within the Physics, Mathematics, Chaos, and Complexity communities. These insights are gained via the work on phase-space reconstruction of non-linear dynamics. New methods for discovering non-linear differential based equations that evolved from embedding operations can shed new light on hybrid-systems theory, Nyquest-Shannon’s Theories, and network based control theory. This paper strives to guide the Controls community towards a closer inspection of the tools and additional insights being developed within the Physics, Mathematics, Chaos, and Complexity communities for discovery of system dynamics, the first step in control system development. The paper introduces the concepts of phase-space reconstruction via time-delay embedding (made famous byWhitney, Takens, and Sauer’s Thoreoms), intergrate-and-fire embedding, and non-linear differential equation discovery based on Perona’s method.
Smalyuk, V.A.; Sadot, O.; Delettrez, J.A.; Meyerhofer, D.D.; Regan, S.P.; Sangster, T.C.
2005-12-05
Nonlinear growth of 3-D broadband nonuniformities was measured near saturation levels using x-ray radiography in planar foils accelerated by laser light. The initial target modulations were seeded by laser nonuniformities and later amplified during acceleration by Rayleigh-Taylor instability. The nonlinear saturation velocities are measured for the first time and are found to be in excellent agreement with Haan predictions. The measured growth of long-wavelength modes is consistent with enhanced, nonlinear, long-wavelength generation in ablatively driven targets.
Tse, Peter W.; Wang, Dong
2017-01-01
Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions. PMID:28216586
Tse, Peter W; Wang, Dong
2017-02-14
Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions.
Cai, Jun-Hao; Chen, He; Chen, Sheng-Ping; Hou, Jing
2017-02-20
We present the results of numerical simulations of dissipative soliton generation using nonlinear Schrödinger equations in an all-normal-dispersion (ANDi) mode-locked fiber laser based on a nonlinear optical loop mirror (NOLM). Firstly, systematic and computationally intensive analysis of the pulse state distributions in two-dimensional parameter spaces of an ANDi fiber laser was conducted. In addition, we determined that unstable non-vanishing regions including pulsation and noise-like pulses are directly related to the saturable absorptions of NOLMs and that two critical filter bandwidths separate those regions from stable ones. Finally, we found that the multi-pulsing power threshold can be maximized by using an optimal optical filter bandwidth.
NASA Astrophysics Data System (ADS)
Antoine, Xavier; Tang, Qinglin; Zhang, Yong
2016-11-01
In this paper, we propose some efficient and robust numerical methods to compute the ground states and dynamics of Fractional Schrödinger Equation (FSE) with a rotation term and nonlocal nonlinear interactions. In particular, a newly developed Gaussian-sum (GauSum) solver is used for the nonlocal interaction evaluation [31]. To compute the ground states, we integrate the preconditioned Krylov subspace pseudo-spectral method [4] and the GauSum solver. For the dynamics simulation, using the rotating Lagrangian coordinates transform [14], we first reformulate the FSE into a new equation without rotation. Then, a time-splitting pseudo-spectral scheme incorporated with the GauSum solver is proposed to simulate the new FSE. In parallel to the numerical schemes, we also prove some existence and nonexistence results for the ground states. Dynamical laws of some standard quantities, including the mass, energy, angular momentum and the center of mass, are stated. The ground states properties with respect to the fractional order and/or rotating frequencies, dynamics involving decoherence and turbulence together with some interesting phenomena are reported.
Niang, Oumar; Thioune, Abdoulaye; El Gueirea, Mouhamed Cheikh; Deléchelle, Eric; Lemoine, Jacques
2012-09-01
The major problem with the empirical mode decomposition (EMD) algorithm is its lack of a theoretical framework. So, it is difficult to characterize and evaluate this approach. In this paper, we propose, in the 2-D case, the use of an alternative implementation to the algorithmic definition of the so-called "sifting process" used in the original Huang's EMD method. This approach, especially based on partial differential equations (PDEs), was presented by Niang in previous works, in 2005 and 2007, and relies on a nonlinear diffusion-based filtering process to solve the mean envelope estimation problem. In the 1-D case, the efficiency of the PDE-based method, compared to the original EMD algorithmic version, was also illustrated in a recent paper. Recently, several 2-D extensions of the EMD method have been proposed. Despite some effort, 2-D versions for EMD appear poorly performing and are very time consuming. So in this paper, an extension to the 2-D space of the PDE-based approach is extensively described. This approach has been applied in cases of both signal and image decomposition. The obtained results confirm the usefulness of the new PDE-based sifting process for the decomposition of various kinds of data. Some results have been provided in the case of image decomposition. The effectiveness of the approach encourages its use in a number of signal and image applications such as denoising, detrending, or texture analysis.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
NASA Technical Reports Server (NTRS)
Cai, Wei; Wang, Jian-Zhong
1993-01-01
We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
Effect of motor dynamics on nonlinear feedback robot arm control
NASA Technical Reports Server (NTRS)
Tarn, Tzyh-Jong; Li, Zuofeng; Bejczy, Antal K.; Yun, Xiaoping
1991-01-01
A nonlinear feedback robot controller that incorporates the robot manipulator dynamics and the robot joint motor dynamics is proposed. The manipulator dynamics and the motor dynamics are coupled to obtain a third-order-dynamic model, and differential geometric control theory is applied to produce a linearized and decoupled robot controller. The derived robot controller operates in the robot task space, thus eliminating the need for decomposition of motion commands into robot joint space commands. Computer simulations are performed to verify the feasibility of the proposed robot controller. The controller is further experimentally evaluated on the PUMA 560 robot arm. The experiments show that the proposed controller produces good trajectory tracking performances and is robust in the presence of model inaccuracies. Compared with a nonlinear feedback robot controller based on the manipulator dynamics only, the proposed robot controller yields conspicuously improved performance.
Nonlinear amplitude approximation for bilinear systems
NASA Astrophysics Data System (ADS)
Jung, Chulwoo; D'Souza, Kiran; Epureanu, Bogdan I.
2014-06-01
An efficient method to predict vibration amplitudes at the resonant frequencies of dynamical systems with piecewise-linear nonlinearity is developed. This technique is referred to as bilinear amplitude approximation (BAA). BAA constructs a single vibration cycle at each resonant frequency to approximate the periodic steady-state response of the system. It is postulated that the steady-state response is piece-wise linear and can be approximated by analyzing the response over two time intervals during which the system behaves linearly. Overall the dynamics is nonlinear, but the system is in a distinct linear state during each of the two time intervals. Thus, the approximated vibration cycle is constructed using linear analyses. The equation of motion for analyzing the vibration of each state is projected along the overlapping space spanned by the linear mode shapes active in each of the states. This overlapping space is where the vibratory energy is transferred from one state to the other when the system switches from one state to the other. The overlapping space can be obtained using singular value decomposition. The space where the energy is transferred is used together with transition conditions of displacement and velocity compatibility to construct a single vibration cycle and to compute the amplitude of the dynamics. Since the BAA method does not require numerical integration of nonlinear models, computational costs are very low. In this paper, the BAA method is first applied to a single-degree-of-freedom system. Then, a three-degree-of-freedom system is introduced to demonstrate a more general application of BAA. Finally, the BAA method is applied to a full bladed disk with a crack. Results comparing numerical solutions from full-order nonlinear analysis and results obtained using BAA are presented for all systems.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H.,Jr.
1998-01-01
Results of linear bifurcation and nonlinear analyses of the Space Shuttle super lightweight (SLWT) external liquid-oxygen (LO2) tank are presented for an important end-of-flight loading condition. These results illustrate an important type of response mode for thin-walled shells, that are subjected to combined mechanical and thermal loads, that may be encountered in the design of other liquid-fuel launch vehicles. Linear bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the aft dome of the LO2 tank. In contrast, the nonlinear response phenomenon is shown to consist of a short-wavelength bending deformation in the aft elliptical dome of the LO2 tank that grows in amplitude in a stable manner with increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the aft dome. For the linear bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shell generally require a large-scale, high fidelity finite-element model. Results are also presented that show that the SLWT LO2 tank can support loads in excess of approximately 1.9 times the values of the operational loads considered.
Liu, Shuo; Yan, Fengping; Feng, Ting; Wu, Beilei; Dong, Ze; Chang, Gee-Kung
2014-08-20
A kind of switchable and spacing-tunable dual-wavelength thulium-doped silica fiber laser based on a nonlinear amplifier loop mirror is presented and experimentally demonstrated. By adjusting the polarization controllers (PCs), stable dual-wavelength operation is obtained at the 2 μm band. The optical signal-to-noise ratio (OSNR) is better than 56 dB. The wavelength tuning is performed by applying static strain into the fiber Bragg grating. A tuning range from 0 to 5.14 nm is achieved for the dual-wavelength spacing. By adjusting the PCs properly, the fiber laser can also operate in single-wavelength state with the OSNR for each wavelength more than 50 dB.
Smolinska, Agnieszka; Blanchet, Lionel; Coulier, Leon; Ampt, Kirsten A. M.; Luider, Theo; Hintzen, Rogier Q.; Wijmenga, Sybren S.; Buydens, Lutgarde M. C.
2012-01-01
Background In the last decade data fusion has become widespread in the field of metabolomics. Linear data fusion is performed most commonly. However, many data display non-linear parameter dependences. The linear methods are bound to fail in such situations. We used proton Nuclear Magnetic Resonance and Gas Chromatography-Mass Spectrometry, two well established techniques, to generate metabolic profiles of Cerebrospinal fluid of Multiple Sclerosis (MScl) individuals. These datasets represent non-linearly separable groups. Thus, to extract relevant information and to combine them a special framework for data fusion is required. Methodology The main aim is to demonstrate a novel approach for data fusion for classification; the approach is applied to metabolomics datasets coming from patients suffering from MScl at a different stage of the disease. The approach involves data fusion in kernel space and consists of four main steps. The first one is to extract the significant information per data source using Support Vector Machine Recursive Feature Elimination. This method allows one to select a set of relevant variables. In the next step the optimized kernel matrices are merged by linear combination. In step 3 the merged datasets are analyzed with a classification technique, namely Kernel Partial Least Square Discriminant Analysis. In the final step, the variables in kernel space are visualized and their significance established. Conclusions We find that fusion in kernel space allows for efficient and reliable discrimination of classes (MScl and early stage). This data fusion approach achieves better class prediction accuracy than analysis of individual datasets and the commonly used mid-level fusion. The prediction accuracy on an independent test set (8 samples) reaches 100%. Additionally, the classification model obtained on fused kernels is simpler in terms of complexity, i.e. just one latent variable was sufficient. Finally, visualization of variables importance in
Decomposition of Sodium Tetraphenylborate
Barnes, M.J.
1998-11-20
The chemical decomposition of aqueous alkaline solutions of sodium tetraphenylborate (NaTPB) has been investigated. The focus of the investigation is on the determination of additives and/or variables which influence NaTBP decomposition. This document describes work aimed at providing better understanding into the relationship of copper (II), solution temperature, and solution pH to NaTPB stability.
Avoiding spurious submovement decompositions : a globally optimal algorithm.
Rohrer, Brandon Robinson; Hogan, Neville
2003-07-01
Evidence for the existence of discrete submovements underlying continuous human movement has motivated many attempts to extract them. Although they produce visually convincing results, all of the methodologies that have been employed are prone to produce spurious decompositions. Examples of potential failures are given. A branch-and-bound algorithm for submovement extraction, capable of global nonlinear minimization (and hence capable of avoiding spurious decompositions), is developed and demonstrated.
Hilbert complexes of nonlinear elasticity
NASA Astrophysics Data System (ADS)
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
NASA Astrophysics Data System (ADS)
Mišković, Olivera; Olea, Rodrigo
2011-01-01
Motivated by possible applications within the framework of anti-de Sitter gravity/conformal field theory correspondence, charged black holes with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D dimensions, and whose electric field is described by nonlinear electrodynamics are studied. For a topological static black hole ansatz, the field equations are exactly solved in terms of the electromagnetic stress tensor for an arbitrary nonlinear electrodynamic Lagrangian in any dimension D and for arbitrary positive values of Gauss-Bonnet coupling. In particular, this procedure reproduces the black hole metric in Born-Infeld and conformally invariant electrodynamics previously found in the literature. Altogether, it extends to D>4 the four-dimensional solution obtained by Soleng in logarithmic electrodynamics, which comes from vacuum polarization effects. Falloff conditions for the electromagnetic field that ensure the finiteness of the electric charge are also discussed. The black hole mass and vacuum energy as conserved quantities associated to an asymptotic timelike Killing vector are computed using a background-independent regularization of the gravitational action based on the addition of counterterms which are a given polynomial in the intrinsic and extrinsic curvatures.
Analysis of nonlinear dynamics by square matrix method
NASA Astrophysics Data System (ADS)
Yu, Li Hua
2017-03-01
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. We show that because of the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculations to a low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The Jordan decomposition leads to a transformation to a new variable, which is an accurate action-angle variable, in good agreement with trajectories and tune obtained from tracking. More importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and tune fluctuation. Thus the square matrix theory shows a good potential in theoretical understanding of a complicated dynamical system to guide the optimization of dynamical apertures. The method is illustrated by many examples of comparison between theory and numerical simulation. In particular, we show that the square matrix method can be used for fast optimization to reduce the nonlinearity of a system.
NASA Astrophysics Data System (ADS)
Do, K. D.
2017-02-01
Equations of motion of extensible and shearable slender beams with large translational and rotational motions under external loads in three-dimensional space are first derived in a vector form. Boundary feedback controllers are then designed to ensure that the beams are practically K∞-exponentially stable at the equilibrium. The control design, well-posedness, and stability analysis are based on two Lyapunov-type theorems developed for a class of evolution systems in Hilbert space. Numerical simulations on a slender beam immersed in sea water are included to illustrate the effectiveness of the proposed control design.
A decomposition of irreversible diffusion processes without detailed balance
NASA Astrophysics Data System (ADS)
Qian, Hong
2013-05-01
As a generalization of deterministic, nonlinear conservative dynamical systems, a notion of canonical conservative dynamics with respect to a positive, differentiable stationary density ρ(x) is introduced: dot{x}=j(x) in which ∇.(ρ(x)j(x)) = 0. Such systems have a conserved "generalized free energy function" F[u] = ∫u(x, t)ln (u(x, t)/ρ(x))dx in phase space with a density flow u(x, t) satisfying ∂ut = -∇.(ju). Any general stochastic diffusion process without detailed balance, in terms of its Fokker-Planck equation, can be decomposed into a reversible diffusion process with detailed balance and a canonical conservative dynamics. This decomposition can be rigorously established in a function space with inner product defined as ⟨ϕ, ψ⟩ = ∫ρ-1(x)ϕ(x)ψ(x)dx. Furthermore, a law for balancing F[u] can be obtained: The non-positive dF[u(x, t)]/dt = Ein(t) - ep(t) where the "source" Ein(t) ⩾ 0 and the "sink" ep(t) ⩾ 0 are known as house-keeping heat and entropy production, respectively. A reversible diffusion has Ein(t) = 0. For a linear (Ornstein-Uhlenbeck) diffusion process, our decomposition is equivalent to the previous approaches developed by Graham and Ao, as well as the theory of large deviations. In terms of two different formulations of time reversal for a same stochastic process, the meanings of dissipative and conservative stationary dynamics are discussed.
Matsumoto, N.; Kitagawa, G.; Roeloffs, E.A.
2003-01-01
For the groundwater level observed at the Haibara well, Shizuoka Prefecture, central Japan, time series analysis using state-space modelling is applied to extract hydrological anomalies related to earthquakes. This method can decompose observed groundwater level time series into five components: atmospheric pressure, tidal, and precipitation responses, observation noise, and residual water level. The decomposed responses to atmospheric pressure and precipitation are independently determined and are consistent with the expected response to surface loading. In the groundwater level at the Haibara well, 28 coseismic changes can be discerned during the period from 1981 April to 1997 December. There is a threshold in the relationship between earthquake magnitude and the well-hypocentre distance, above which earthquakes cause coseismic changes in the residual water level. All of the coseismic water level changes at the Haibara well are decreases, although 33 per cent of the estimated coseismic volumetric strain steps are contraction, which would be expected to cause water level increases. The coseismic changes in groundwater level are more closely proportional to the estimated ground motion than to coseismic volumetric strain steps, suggesting that ground motion due to earthquakes is the major cause of the coseismic water level drops and that the contribution from static strain is rather small. Possible pre- or inter-earthquake water level changes have occurred at the Haibara well and may have been caused by local aseismic crustal deformation.
Dominant modal decomposition method
NASA Astrophysics Data System (ADS)
Dombovari, Zoltan
2017-03-01
The paper deals with the automatic decomposition of experimental frequency response functions (FRF's) of mechanical structures. The decomposition of FRF's is based on the Green function representation of free vibratory systems. After the determination of the impulse dynamic subspace, the system matrix is formulated and the poles are calculated directly. By means of the corresponding eigenvectors, the contribution of each element of the impulse dynamic subspace is determined and the sufficient decomposition of the corresponding FRF is carried out. With the presented dominant modal decomposition (DMD) method, the mode shapes, the modal participation vectors and the modal scaling factors are identified using the decomposed FRF's. Analytical example is presented along with experimental case studies taken from machine tool industry.
Delcey, Mickaël G.; Freitag, Leon; González, Leticia; Pedersen, Thomas Bondo; Aquilante, Francesco; Lindh, Roland
2014-05-07
We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032 Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 Å for S{sub 0} and 0.11 Å for T{sub 1}, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry.
Analysis of Nonlinear Dynamics by Square Matrix Method
Yu, Li Hua
2016-07-25
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.
NASA Technical Reports Server (NTRS)
Periaux, J.
1979-01-01
The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.
Nonlinear ordinary difference equations
NASA Technical Reports Server (NTRS)
Caughey, T. K.
1979-01-01
Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.
A benders decomposition approach to multiarea stochastic distributed utility planning
NASA Astrophysics Data System (ADS)
McCusker, Susan Ann
Until recently, small, modular generation and storage options---distributed resources (DRs)---have been installed principally in areas too remote for economic power grid connection and sensitive applications requiring backup capacity. Recent regulatory changes and DR advances, however, have lead utilities to reconsider the role of DRs. To a utility facing distribution capacity bottlenecks or uncertain load growth, DRs can be particularly valuable since they can be dispersed throughout the system and constructed relatively quickly. DR value is determined by comparing its costs to avoided central generation expenses (i.e., marginal costs) and distribution investments. This requires a comprehensive central and local planning and production model, since central system marginal costs result from system interactions over space and time. This dissertation develops and applies an iterative generalized Benders decomposition approach to coordinate models for optimal DR evaluation. Three coordinated models exchange investment, net power demand, and avoided cost information to minimize overall expansion costs. Local investment and production decisions are made by a local mixed integer linear program. Central system investment decisions are made by a LP, and production costs are estimated by a stochastic multi-area production costing model with Kirchhoff's Voltage and Current Law constraints. The nested decomposition is a new and unique method for distributed utility planning that partitions the variables twice to separate local and central investment and production variables, and provides upper and lower bounds on expected expansion costs. Kirchhoff's Voltage Law imposes nonlinear, nonconvex constraints that preclude use of LP if transmission capacity is available in a looped transmission system. This dissertation develops KVL constraint approximations that permit the nested decomposition to consider new transmission resources, while maintaining linearity in the three
NASA Astrophysics Data System (ADS)
Kakad, Bharati; Kakad, Amar; Omura, Yoshiharu
2014-07-01
Spacecraft observations revealed the presence of electrostatic solitary waves (ESWs) in various regions of the Earth's magnetosphere. Over the years, many researchers have attempted to model these observations in terms of electron/ion acoustic solitary waves by using nonlinear fluid theory/simulations. The ESW structures predicted by fluid models can be inadequate due to its inability in handling kinetic effects. To provide clear view on the application of the fluid and kinetic treatments in modeling the ESWs, we perform both fluid and particle-in-cell (PIC) simulations of ion acoustic solitary waves (IASWs) and estimate the quantitative differences in their characteristics like speed, amplitude, and width. We find that the number of trapped electrons in the wave potential is higher for the IASW, which are generated by large-amplitude initial density perturbation (IDP). The present fluid and PIC simulation results are in close agreement for small amplitude IDPs, whereas for large IDPs they show discrepancy in the amplitude, width, and speed of the IASW, which is attributed to negligence of kinetic effects in the former approach. The speed of IASW in the fluid simulations increases with the increase of IASW amplitude, while the reverse tendency is seen in the PIC simulation. The present study suggests that the fluid treatment is appropriate when the magnitude of phase velocity of IASW is less than the ion acoustic (IA) speed obtained from their linear dispersion relation, whereas when it exceeds IA speed, it is necessary to include the kinetic effects in the model.
A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
NASA Astrophysics Data System (ADS)
Williams, Matthew O.; Kevrekidis, Ioannis G.; Rowley, Clarence W.
2015-12-01
The Koopman operator is a linear but infinite-dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a data-driven method for approximating the leading eigenvalues, eigenfunctions, and modes of the Koopman operator. The method requires a data set of snapshot pairs and a dictionary of scalar observables, but does not require explicit governing equations or interaction with a "black box" integrator. We will show that this approach is, in effect, an extension of dynamic mode decomposition (DMD), which has been used to approximate the Koopman eigenvalues and modes. Furthermore, if the data provided to the method are generated by a Markov process instead of a deterministic dynamical system, the algorithm approximates the eigenfunctions of the Kolmogorov backward equation, which could be considered as the "stochastic Koopman operator" (Mezic in Nonlinear Dynamics 41(1-3): 309-325, 2005). Finally, four illustrative examples are presented: two that highlight the quantitative performance of the method when presented with either deterministic or stochastic data and two that show potential applications of the Koopman eigenfunctions.
NASA Astrophysics Data System (ADS)
Rudraraju, Shiva; van der Ven, Anton; Garikipati, Krishna
2016-06-01
We present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes diffusional phase transformations that are accompanied by symmetry-breaking structural changes of the crystal unit cell and reveals the importance of a mechanochemical spinodal, defined as the region in strain-composition space, where the free-energy density function is non-convex. The approach is relevant to phase transformations wherein the structural order parameters can be expressed as linear combinations of strains relative to a high-symmetry reference crystal. The governing equations describing mechanochemical spinodal decomposition are variationally derived from a free-energy density function that accounts for interfacial energy via gradients of the rapidly varying strain and composition fields. A robust computational framework for treating the coupled, higher-order diffusion and nonlinear strain gradient elasticity problems is presented. Because the local strains in an inhomogeneous, transforming microstructure can be finite, the elasticity problem must account for geometric nonlinearity. An evaluation of available experimental phase diagrams and first-principles free energies suggests that mechanochemical spinodal decomposition should occur in metal hydrides such as ZrH2-2c. The rich physics that ensues is explored in several numerical examples in two and three dimensions, and the relevance of the mechanism is discussed in the context of important electrode materials for Li-ion batteries and high-temperature ceramics.
NASA Astrophysics Data System (ADS)
Satija, Aaditya; Caers, Jef
2015-03-01
Inverse modeling is widely used to assist with forecasting problems in the subsurface. However, full inverse modeling can be time-consuming requiring iteration over a high dimensional parameter space with computationally expensive forward models and complex spatial priors. In this paper, we investigate a prediction-focused approach (PFA) that aims at building a statistical relationship between data variables and forecast variables, avoiding the inversion of model parameters altogether. The statistical relationship is built by first applying the forward model related to the data variables and the forward model related to the prediction variables on a limited set of spatial prior models realizations, typically generated through geostatistical methods. The relationship observed between data and prediction is highly non-linear for many forecasting problems in the subsurface. In this paper we propose a Canonical Functional Component Analysis (CFCA) to map the data and forecast variables into a low-dimensional space where, if successful, the relationship is linear. CFCA consists of (1) functional principal component analysis (FPCA) for dimension reduction of time-series data and (2) canonical correlation analysis (CCA); the latter aiming to establish a linear relationship between data and forecast components. If such mapping is successful, then we illustrate with several cases that (1) simple regression techniques with a multi-Gaussian framework can be used to directly quantify uncertainty on the forecast without any model inversion and that (2) such uncertainty is a good approximation of uncertainty obtained from full posterior sampling with rejection sampling.
Application of decomposition techniques to the preliminary design of a transport aircraft
NASA Technical Reports Server (NTRS)
Rogan, J. E.; Kolb, M. A.
1987-01-01
A nonlinear constrained optimization problem describing the preliminary design process for a transport aircraft has been formulated. A multifaceted decomposition of the optimization problem has been made. Flight dynamics, flexible aircraft loads and deformations, and preliminary structural design subproblems appear prominently in the decomposition. The use of design process decomposition for scheduling design projects, a new system integration approach to configuration control, and the application of object-centered programming to a new generation of design tools are discussed.
NASA Technical Reports Server (NTRS)
Goldstein, M. L.
1977-01-01
In a study of cosmic ray propagation in interstellar and interplanetary space, a perturbed orbit resonant scattering theory for pitch angle diffusion in a slab model of magnetostatic turbulence is slightly generalized and used to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field. This diffusion coefficient has been useful for describing the solar modulation of the galactic cosmic rays, and for explaining the diffusive phase in solar flares in which the initial anisotropy of the particle distribution decays to isotropy.
The inner structure of empirical mode decomposition
NASA Astrophysics Data System (ADS)
Wang, Yung-Hung; Young, Hsu-Wen Vincent; Lo, Men-Tzung
2016-11-01
The empirical mode decomposition (EMD) is a nonlinear method that is truly adaptive with good localization property in the time domain for analyzing non-stationary complex data. The EMD has been proven useful in a wide range of applications. However, due to the nonlinear and complex nature of the sifting process, the most essential step of the EMD, a firm mathematical foundation or a transparent physical description are still lacked for EMD. Here, we embark on constructing a mathematical theory of the sifting operator. We first show that the sifting operator can be expressed as the data plus the sum of the responses to the impulses (multiplied by the data value) at the extrema. Such an expression of the sifting operator is then used to investigate the adaptive nature and the localizing effect of the EMD. Alternatively, the sifting operator can also be represented by a sifting matrix, which depends nonlinearly on the extrema distribution. Based on the eigen-decomposition of the sifting matrix, the transfer function of the sifting process is analyzed. Finally we answer what an intrinsic mode function (IMF) is from the wave perspective by exploring the physical basis of the IMFs.
A nonlinear quality-related fault detection approach based on modified kernel partial least squares.
Jiao, Jianfang; Zhao, Ning; Wang, Guang; Yin, Shen
2017-01-01
In this paper, a new nonlinear quality-related fault detection method is proposed based on kernel partial least squares (KPLS) model. To deal with the nonlinear characteristics among process variables, the proposed method maps these original variables into feature space in which the linear relationship between kernel matrix and output matrix is realized by means of KPLS. Then the kernel matrix is decomposed into two orthogonal parts by singular value decomposition (SVD) and the statistics for each part are determined appropriately for the purpose of quality-related fault detection. Compared with relevant existing nonlinear approaches, the proposed method has the advantages of simple diagnosis logic and stable performance. A widely used literature example and an industrial process are used for the performance evaluation for the proposed method.
Decomposing Nekrasov decomposition
NASA Astrophysics Data System (ADS)
Morozov, A.; Zenkevich, Y.
2016-02-01
AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions — this is immediately seen when conformal block is represented in the form of a matrix model. However, the q-deformation of the same block has a deeper decomposition — into a sum over a quadruple of Young diagrams of a product of four topological vertices. We analyze the interplay between these two decompositions, their properties and their generalization to multi-point conformal blocks. In the latter case we explain how Dotsenko-Fateev all-with-all (star) pair "interaction" is reduced to the quiver model nearest-neighbor (chain) one. We give new identities for q-Selberg averages of pairs of generalized Macdonald polynomials. We also translate the slicing invariance of refined topological strings into the language of conformal blocks and interpret it as abelianization of generalized Macdonald polynomials.
The generalized triangular decomposition
NASA Astrophysics Data System (ADS)
Jiang, Yi; Hager, William W.; Li, Jian
2008-06-01
Given a complex matrix mathbf{H} , we consider the decomposition mathbf{H} = mathbf{QRP}^* , where mathbf{R} is upper triangular and mathbf{Q} and mathbf{P} have orthonormal columns. Special instances of this decomposition include the singular value decomposition (SVD) and the Schur decomposition where mathbf{R} is an upper triangular matrix with the eigenvalues of mathbf{H} on the diagonal. We show that any diagonal for mathbf{R} can be achieved that satisfies Weyl's multiplicative majorization conditions: prod_{iD1}^k \\vert r_{i}\\vert le prod_{iD1}^k sigma_i, ; ; 1 le k < K, quad prod_{iD1}^K \\vert r_{i}\\vert = prod_{iD1}^K sigma_i, where K is the rank of mathbf{H} , sigma_i is the i -th largest singular value of mathbf{H} , and r_{i} is the i -th largest (in magnitude) diagonal element of mathbf{R} . Given a vector mathbf{r} which satisfies Weyl's conditions, we call the decomposition mathbf{H} = mathbf{QRP}^* , where mathbf{R} is upper triangular with prescribed diagonal mathbf{r} , the generalized triangular decomposition (GTD). A direct (nonrecursive) algorithm is developed for computing the GTD. This algorithm starts with the SVD and applies a series of permutations and Givens rotations to obtain the GTD. The numerical stability of the GTD update step is established. The GTD can be used to optimize the power utilization of a communication channel, while taking into account quality of service requirements for subchannels. Another application of the GTD is to inverse eigenvalue problems where the goal is to construct matrices with prescribed eigenvalues and singular values.
Nonlinear Image Denoising Methodologies
2002-05-01
53 5.3 A Multiscale Approach to Scale-Space Analysis . . . . . . . . . . . . . . . . 53 5.4...etc. In this thesis, Our approach to denoising is first based on a controlled nonlinear stochastic random walk to achieve a scale space analysis ( as in... stochastic treatment or interpretation of the diffusion. In addition, unless a specific stopping time is known to be adequate, the resulting evolution
Optimal domain decomposition strategies
NASA Technical Reports Server (NTRS)
Yoon, Yonghyun; Soni, Bharat K.
1995-01-01
The primary interest of the authors is in the area of grid generation, in particular, optimal domain decomposition about realistic configurations. A grid generation procedure with optimal blocking strategies has been developed to generate multi-block grids for a circular-to-rectangular transition duct. The focus of this study is the domain decomposition which optimizes solution algorithm/block compatibility based on geometrical complexities as well as the physical characteristics of flow field. The progress realized in this study is summarized in this paper.
NASA Astrophysics Data System (ADS)
Sanjuán, J.; Lobo, A.; Ramos-Castro, J.
2009-11-01
Low-noise temperature measurements at frequencies in the millihertz range are required in the laser interferometer space antenna (LISA) and LISA PathFinder missions. The required temperature stability for LISA is around 10 μK Hz-1/2 at frequencies down to 0.1 mHz. In this paper we focus on the identification and reduction in a source of excess noise detected when measuring time-varying temperature signals. This is shown to be due to nonidealities in the analog-to-digital converter (ADC) transfer curve, and degrades the measurement by about one order of magnitude in the measurement bandwidth when the measured temperature drifts by a few ~μK s-1. In a suitable measuring system for the LISA mission, this noise needs to be reduced. Two different methods based on the same technique have been implemented, both consisting in the addition of dither signals out of band to mitigate the ADC nonideality errors. Excess noise of this nature has been satisfactorily reduced by using these methods when measuring temperature ramps up to 10 μK s-1.
NASA Technical Reports Server (NTRS)
Goldstein, M. L.
1976-01-01
The propagation of charged particles through interstellar and interplanetary space has often been described as a random process in which the particles are scattered by ambient electromagnetic turbulence. In general, this changes both the magnitude and direction of the particles' momentum. Some situations for which scattering in direction (pitch angle) is of primary interest were studied. A perturbed orbit, resonant scattering theory for pitch-angle diffusion in magnetostatic turbulence was slightly generalized and then utilized to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field, Kappa. All divergences inherent in the quasilinear formalism when the power spectrum of the fluctuation field falls off as K to the minus Q power (Q less than 2) were removed. Various methods of computing Kappa were compared and limits on the validity of the theory discussed. For Q less than 1 or 2, the various methods give roughly comparable values of Kappa, but use of perturbed orbits systematically results in a somewhat smaller Kappa than can be obtained from quasilinear theory.
Sanjuán, J; Lobo, A; Ramos-Castro, J
2009-11-01
Low-noise temperature measurements at frequencies in the millihertz range are required in the laser interferometer space antenna (LISA) and LISA PathFinder missions. The required temperature stability for LISA is around 10 microK Hz(-1/2) at frequencies down to 0.1 mHz. In this paper we focus on the identification and reduction in a source of excess noise detected when measuring time-varying temperature signals. This is shown to be due to nonidealities in the analog-to-digital converter (ADC) transfer curve, and degrades the measurement by about one order of magnitude in the measurement bandwidth when the measured temperature drifts by a few approximately microK s(-1). In a suitable measuring system for the LISA mission, this noise needs to be reduced. Two different methods based on the same technique have been implemented, both consisting in the addition of dither signals out of band to mitigate the ADC nonideality errors. Excess noise of this nature has been satisfactorily reduced by using these methods when measuring temperature ramps up to 10 microK s(-1).
Empirical mode decomposition for analyzing acoustical signals
NASA Technical Reports Server (NTRS)
Huang, Norden E. (Inventor)
2005-01-01
The present invention discloses a computer implemented signal analysis method through the Hilbert-Huang Transformation (HHT) for analyzing acoustical signals, which are assumed to be nonlinear and nonstationary. The Empirical Decomposition Method (EMD) and the Hilbert Spectral Analysis (HSA) are used to obtain the HHT. Essentially, the acoustical signal will be decomposed into the Intrinsic Mode Function Components (IMFs). Once the invention decomposes the acoustic signal into its constituting components, all operations such as analyzing, identifying, and removing unwanted signals can be performed on these components. Upon transforming the IMFs into Hilbert spectrum, the acoustical signal may be compared with other acoustical signals.
Nonlinear damping identification from transient data
NASA Astrophysics Data System (ADS)
Smith, Clifford B.; Wereley, Norman M.
1999-06-01
To study new damping augmentation methods for helicopter rotor systems, accurate and reliable nonlinear damping identification techniques are needed. For example, current studies on applications of magnetorheological (MR) dampers for rotor stability augmentation suggest that a strong Coulomb damping characteristic will be manifested as the field applied to the MR fluid is maximized. Therefore, in this work, a single degree of freedom (SDOF) system having either nonlinear Coulomb or quadratic damping is considered. This paper evaluates three analyses for identifying damping from transient test data; an FFT-based moving block analysis, an analysis based on a periodic Fourier series decomposition, and a Hilbert transform based technique. Analytical studies are used to determine the effects of block length, noise, and error in identified modal frequency on the accuracy of the identified damping level. The FFT-based moving block has unacceptable performance for systems with nonlinear damping. These problems were remedied in the Fourier series based analysis and acceptable performance is obtained for nonlinear damping identification from both this technique and the Hilbert transform based method. To more closely simulate a helicopter rotor system test, these techniques were then applied to a signal composed of two closely spaced modes. This data was developed to simulate a response containing the first lag and 1/rev modes. The primary mode of interest (simulated lag mode) had either Coulomb or quadratic damping, and the close mode (1/rev) was either undamped or had a specified viscous damping level. A comprehensive evaluation of the effects of close mode amplitude, frequency, and damping level was performed. A classifier was also developed to identify the dominant damping mechanism in a signal of 'unknown' composition. This classifier is based on the LMS error of a fit of the analytical envelope expression to the experimentally identified envelope signal. In most
Colosi, John A
2008-09-01
While many results have been intuited from numerical simulation studies, the precise connections between shallow-water acoustic variability and the space-time scales of nonlinear internal waves (NLIWs) as well as the background environmental conditions have not been clearly established analytically. Two-dimensional coupled mode propagation through NLIWs is examined using a perturbation series solution in which each order n is associated with nth-order multiple scattering. Importantly, the perturbation solution gives resonance conditions that pick out specific NLIW scales that cause coupling, and seabed attenuation is demonstrated to broaden these resonances, fundamentally changing the coupling behavior at low frequency. Sound-speed inhomogeneities caused by internal solitary waves (ISWs) are primarily considered and the dependence of mode coupling on ISW amplitude, range width, depth structure, location relative to the source, and packet characteristics are delineated as a function of acoustic frequency. In addition, it is seen that significant energy transfer to modes with initially low or zero energy involves at least a second order scattering process. Under moderate scattering conditions, comparisons of first order, single scattering theoretical predictions to direct numerical simulation demonstrate the accuracy of the approach for acoustic frequencies upto 400 Hz and for single as well as multiple ISW wave packets.
Kolesik, M; Wright, E M; Andreasen, J; Brown, J M; Carlson, D R; Jones, R J
2012-07-02
We introduce a new computational approach for femtosecond pulse propagation in the transparency region of gases that permits full resolution in three space dimensions plus time while fully incorporating quantum coherent effects such as high-harmonic generation and strong-field ionization in a holistic fashion. This is achieved by utilizing a one-dimensional model atom with a delta-function potential which allows for a closed-form solution for the nonlinear optical response due to ground-state to continuum transitions. It side-steps evaluation of the wave function, and offers more than one hundred-fold reduction in computation time in comparison to direct solution of the atomic Schrödinger equation. To illustrate the capability of our new computational approach, we apply it to the example of near-threshold harmonic generation in Xenon, and we also present a qualitative comparison between our model and results from an in-house experiment on extreme ultraviolet generation in a femtosecond enhancement cavity.
Hydrazine decomposition and other reactions
NASA Technical Reports Server (NTRS)
Armstrong, Warren E. (Inventor); La France, Donald S. (Inventor); Voge, Hervey H. (Inventor)
1978-01-01
This invention relates to the catalytic decomposition of hydrazine, catalysts useful for this decomposition and other reactions, and to reactions in hydrogen atmospheres generally using carbon-containing catalysts.
Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra
NASA Astrophysics Data System (ADS)
Hatch, D. R.; Jenko, F.; Bañón Navarro, A.; Bratanov, V.; Terry, P. W.; Pueschel, M. J.
2016-07-01
A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest in the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a non-modal treatment is necessary to understand key features of the turbulence.
Domain decomposition for aerodynamic and aeroacoustic analyses, and optimization
NASA Technical Reports Server (NTRS)
Baysal, Oktay
1995-01-01
The overarching theme was the domain decomposition, which intended to improve the numerical solution technique for the partial differential equations at hand; in the present study, those that governed either the fluid flow, or the aeroacoustic wave propagation, or the sensitivity analysis for a gradient-based optimization. The role of the domain decomposition extended beyond the original impetus of discretizing geometrical complex regions or writing modular software for distributed-hardware computers. It induced function-space decompositions and operator decompositions that offered the valuable property of near independence of operator evaluation tasks. The objectives have gravitated about the extensions and implementations of either the previously developed or concurrently being developed methodologies: (1) aerodynamic sensitivity analysis with domain decomposition (SADD); (2) computational aeroacoustics of cavities; and (3) dynamic, multibody computational fluid dynamics using unstructured meshes.
Perturbed nonlinear differential equations
NASA Technical Reports Server (NTRS)
Proctor, T. G.
1974-01-01
For perturbed nonlinear systems, a norm, other than the supremum norm, is introduced on some spaces of continuous functions. This makes possible the study of new types of behavior. A study is presented on a perturbed nonlinear differential equation defined on a half line, and the existence of a family of solutions with special boundedness properties is established. The ideas developed are applied to the study of integral manifolds, and examples are given.
Debye decomposition of time-lapse spectral induced polarisation data
NASA Astrophysics Data System (ADS)
Weigand, M.; Kemna, A.
2016-01-01
Spectral induced polarisation (SIP) measurements capture the low-frequency electrical properties of soils and rocks and provide a non-invasive means to access lithological, hydrogeological, and geochemical properties of the subsurface. The Debye decomposition (DD) approach is now increasingly being used to analyse SIP signatures in terms of relaxation time distributions due to its flexibility regarding the shape of the spectra. Imaging and time-lapse (monitoring) SIP measurements, capturing SIP variations in space and time, respectively, are now more and more conducted and lead to a drastic increase in the number of spectra considered, which prompts the need for robust and reliable DD tools to extract quantitative parameters from such data. We here present an implementation of the DD method for the analysis of a series of SIP data sets which are expected to only smoothly change in terms of spectral behaviour, such as encountered in many time-lapse applications where measurement geometry does not change. The routine is based on a non-linear least-squares inversion scheme with smoothness constraints on the spectral variation and in addition from one spectrum of the series to the next to deal with the inherent ill-posedness and non-uniqueness of the problem. By means of synthetic examples with typical SIP characteristics we elucidate the influence of the number and range of considered relaxation times on the inversion results. The source code of the presented routines is provided under an open source licence as a basis for further applications and developments.
Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory
NASA Technical Reports Server (NTRS)
Lucia, David J.; Beran, Philip S.; Silva, Walter A.
2003-01-01
This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.
Domain decomposition: A bridge between nature and parallel computers
NASA Technical Reports Server (NTRS)
Keyes, David E.
1992-01-01
Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.
NASA Technical Reports Server (NTRS)
Sheen, Jyh-Jong; Bishop, Robert H.
1992-01-01
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Minimax eigenvector decomposition for data hiding
NASA Astrophysics Data System (ADS)
Davidson, Jennifer
2005-09-01
Steganography is the study of hiding information within a covert channel in order to transmit a secret message. Any public media such as image data, audio data, or even file packets, can be used as a covert channel. This paper presents an embedding algorithm that hides a message in an image using a technique based on a nonlinear matrix transform called the minimax eigenvector decomposition (MED). The MED is a minimax algebra version of the well-known singular value decomposition (SVD). Minimax algebra is a matrix algebra based on the algebraic operations of maximum and addition, developed initially for use in operations research and extended later to represent a class of nonlinear image processing operations. The discrete mathematical morphology operations of dilation and erosion, for example, are contained within minimax algebra. The MED is much quicker to compute than the SVD and avoids the numerical computational issues of the SVD because the operations involved only integer addition, subtraction, and compare. We present the algorithm to embed data using the MED, show examples applied to image data, and discuss limitations and advantages as compared with another similar algorithm.
Irreducible Decompositions and Stationary States of Quantum Channels
NASA Astrophysics Data System (ADS)
Carbone, Raffaella; Pautrat, Yan
2016-06-01
For a quantum channel (completely positive, trace-preserving map), we prove a generalization to the infinite-dimensional case of a result by Baumgartner and Narnhofer [3]: this result is, in a probabilistic language, a decomposition of a general quantum channel into its irreducible recurrent components. More precisely, we prove that the positive recurrent subspace (i.e. the space supporting the invariant states) can be decomposed as the direct sum of supports of extremal invariant states; this decomposition is not unique, in general, but we can determine all the possible decompositions. This allows us to describe the full structure of invariant states.
Multicriteria approximation through decomposition
Burch, C.; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E.
1998-06-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of their technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. Their method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) the authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing; (2) they also show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
Multicriteria approximation through decomposition
Burch, C. |; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E. |
1997-12-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
A Thin Codimension-One Decomposition of the Hilbert Cube
ERIC Educational Resources Information Center
Phon-On, Aniruth
2010-01-01
For cell-like upper semicontinuous (usc) decompositions "G" of finite dimensional manifolds "M", the decomposition space "M/G" turns out to be an ANR provided "M/G" is finite dimensional ([Dav07], page 129). Furthermore, if "M/G" is finite dimensional and has the Disjoint Disks Property (DDP), then "M/G" is homeomorphic to "M" ([Dav07], page 181).…
Nondyadic decomposition algorithm with Meyer's wavelet packets: an application to EEG signal
NASA Astrophysics Data System (ADS)
Carre, Philippe; Richard, Noel; Fernandez-Maloigne, Christine; Paquereau, Joel
1999-10-01
In this paper, we propose an original decomposition scheme based on Meyer's wavelets. In opposition to a classical technique of wavelet packet analysis, the decomposition is an adaptative segmentation of the frequential axis which does not use a filters bank. This permits a higher flexibility in the band frequency definition. The decomposition computes all possible partitions from a sequential space: it does not only compute those that come from a dyadic decomposition. Our technique is applied on the electroencephalogram signal; here the purpose is to extract a best basis of frequential decomposition. This study is part of a multimodal functional cerebral imagery project.
NASA Astrophysics Data System (ADS)
Jaber, Abobaker M.
2014-12-01
Two nonparametric methods for prediction and modeling of financial time series signals are proposed. The proposed techniques are designed to handle non-stationary and non-linearity behave and to extract meaningful signals for reliable prediction. Due to Fourier Transform (FT), the methods select significant decomposed signals that will be employed for signal prediction. The proposed techniques developed by coupling Holt-winter method with Empirical Mode Decomposition (EMD) and it is Extending the scope of empirical mode decomposition by smoothing (SEMD). To show performance of proposed techniques, we analyze daily closed price of Kuala Lumpur stock market index.
NASA Astrophysics Data System (ADS)
Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David
2015-03-01
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.
Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David
2015-03-15
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.
1989-06-15
following surprising situation. Namely associated with the integrable nonlinear Schrodinger equations are standard numerical schemes which exhibit at...36. An Initial Boundary Value Problem for the Nonlinear Schrodinger Equations , A.S. Fokas, Physica D March 1989. 37. Evolution Theory, Periodic... gravity waves and wave excitation phenomena related to moving pressure distributions; numerical approximation and computation; nonlinear optics; and
Izumi, Yudai; Nakagawa, Kazumichi
2011-08-01
One of the leading hypotheses regarding the origin of prebiotic molecules on primitive Earth is that they formed from inorganic molecules in extraterrestrial environments and were delivered by meteorites, space dust and comets. To evaluate the availability of extraterrestrial amino acids, it is necessary to examine their decomposition and oligomerization rates as induced by extraterrestrial energy sources, such as vacuum ultraviolet (VUV) and X-ray photons and high energy particles. This paper reports the quantum yields of decomposition ((8.2 ± 0.7) × 10(-2) photon(-1)) and homo-dimerization ((1.2 ± 0.3) × 10(-3) photon(-1)) and decomposition of the dimer (0.24 ± 0.06 photon(-1)) of solid L-alanine (Ala) induced by VUV light with an energy of 7.2 eV. Using these quantum yields, the half-life of L-Ala on the surface of a space object in the present earth orbit was estimated to be about 52 days, even when only photons with an energy of 7.2 eV emitted from the present Sun were considered. The actual half-life of solid L-Ala on the surface of a space object orbit around the present day Earth would certainly be much shorter than our estimate, because of the added effect of photons and particles of other energies. Thus, we propose that L-Ala needs to be shielded from solar VUV in protected environments, such as the interior of a meteorite, within a time scale of days after synthesis to ensure its arrival on the primitive Earth.
Hydrogen peroxide catalytic decomposition
NASA Technical Reports Server (NTRS)
Parrish, Clyde F. (Inventor)
2010-01-01
Nitric oxide in a gaseous stream is converted to nitrogen dioxide using oxidizing species generated through the use of concentrated hydrogen peroxide fed as a monopropellant into a catalyzed thruster assembly. The hydrogen peroxide is preferably stored at stable concentration levels, i.e., approximately 50%-70% by volume, and may be increased in concentration in a continuous process preceding decomposition in the thruster assembly. The exhaust of the thruster assembly, rich in hydroxyl and/or hydroperoxy radicals, may be fed into a stream containing oxidizable components, such as nitric oxide, to facilitate their oxidation.
Mode decomposition evolution equations
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-01-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
Hierarchical decomposition of metabolic networks using k-modules.
Reimers, Arne C
2015-12-01
The optimal solutions obtained by flux balance analysis (FBA) are typically not unique. Flux modules have recently been shown to be a very useful tool to simplify and decompose the space of FBA-optimal solutions. Since yield-maximization is sometimes not the primary objective encountered in vivo, we are also interested in understanding the space of sub-optimal solutions. Unfortunately, the flux modules are too restrictive and not suited for this task. We present a generalization, called k-module, which compensates the limited applicability of flux modules to the space of sub-optimal solutions. Intuitively, a k-module is a sub-network with low connectivity to the rest of the network. Recursive application of k-modules yields a hierarchical decomposition of the metabolic network, which is also known as branch decomposition in matroid theory. In particular, decompositions computed by existing methods, like the null-space-based approach, introduced by Poolman et al. [(2007) J. Theor. Biol. 249: , 691-705] can be interpreted as branch decompositions. With k-modules we can now compare alternative decompositions of metabolic networks to the classical sub-systems of glycolysis, tricarboxylic acid (TCA) cycle, etc. They can be used to speed up algorithmic problems [theoretically shown for elementary flux modes (EFM) enumeration] and have the potential to present computational solutions in a more intuitive way independently from the classical sub-systems.
NASA Astrophysics Data System (ADS)
Geniet, F.; Leon, J.
2003-05-01
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
NASA Astrophysics Data System (ADS)
Piersanti, Mirko; Materassi, Massimo; Spogli, Luca; Cicone, Antonio; Alberti, Tommaso
2016-04-01
Highly irregular fluctuations of the power of trans-ionospheric GNSS signals, namely radio power scintillation, are, at least to a large extent, the effect of ionospheric plasma turbulence, a by-product of the non-linear and non-stationary evolution of the plasma fields defining the Earth's upper atmosphere. One could expect the ionospheric turbulence characteristics of inter-scale coupling, local randomness and high time variability to be inherited by the scintillation on radio signals crossing the medium. On this basis, the remote sensing of local features of the turbulent plasma could be expected as feasible by studying radio scintillation. The dependence of the statistical properties of the medium fluctuations on the space- and time-scale is the distinctive character of intermittent turbulent media. In this paper, a multi-scale statistical analysis of some samples of GPS radio scintillation is presented: the idea is that assessing how the statistics of signal fluctuations vary with time scale under different Helio-Geophysical conditions will be of help in understanding the corresponding multi-scale statistics of the turbulent medium causing that scintillation. In particular, two techniques are tested as multi-scale decomposition schemes of the signals: the discrete wavelet analysis and the Empirical Mode Decomposition. The discussion of the results of the one analysis versus the other will be presented, trying to highlight benefits and limits of each scheme, also under suitably different helio-geophysical conditions.
O'Keefe, Dennis R.; Norman, John H.
1983-01-01
Liquid hydrogen iodide is decomposed to form hydrogen and iodine in the presence of water using a soluble catalyst. Decomposition is carried out at a temperature between about 350.degree. K. and about 525.degree. K. and at a corresponding pressure between about 25 and about 300 atmospheres in the presence of an aqueous solution which acts as a carrier for the homogeneous catalyst. Various halides of the platinum group metals, particularly Pd, Rh and Pt, are used, particularly the chlorides and iodides which exhibit good solubility. After separation of the H.sub.2, the stream from the decomposer is countercurrently extracted with nearly dry HI to remove I.sub.2. The wet phase contains most of the catalyst and is recycled directly to the decomposition step. The catalyst in the remaining almost dry HI-I.sub.2 phase is then extracted into a wet phase which is also recycled. The catalyst-free HI-I.sub.2 phase is finally distilled to separate the HI and I.sub.2. The HI is recycled to the reactor; the I.sub.2 is returned to a reactor operating in accordance with the Bunsen equation to create more HI.
Numeric Modified Adomian Decomposition Method for Power System Simulations
Dimitrovski, Aleksandar D; Simunovic, Srdjan; Pannala, Sreekanth
2016-01-01
This paper investigates the applicability of numeric Wazwaz El Sayed modified Adomian Decomposition Method (WES-ADM) for time domain simulation of power systems. WESADM is a numerical method based on a modified Adomian decomposition (ADM) technique. WES-ADM is a numerical approximation method for the solution of nonlinear ordinary differential equations. The non-linear terms in the differential equations are approximated using Adomian polynomials. In this paper WES-ADM is applied to time domain simulations of multimachine power systems. WECC 3-generator, 9-bus system and IEEE 10-generator, 39-bus system have been used to test the applicability of the approach. Several fault scenarios have been tested. It has been found that the proposed approach is faster than the trapezoidal method with comparable accuracy.
Spatiotemporal mode structure of nonlinearly coupled drift wave modes
Brandt, Christian; Grulke, Olaf; Klinger, Thomas; Negrete, Jose Jr.; Bousselin, Guillaume; Brochard, Frederic; Bonhomme, Gerard; Oldenbuerger, Stella
2011-11-15
This paper presents full cross-section measurements of drift waves in the linear magnetized plasma of the Mirabelle device. Drift wave modes are studied in regimes of weakly developed turbulence. The drift wave modes develop azimuthal space-time structures of plasma density, plasma potential, and visible light fluctuations. A fast camera diagnostic is used to record visible light fluctuations of the plasma column in an azimuthal cross section with a temporal resolution of 10 {mu}s corresponding approximately to 10% of the typical drift wave period. Mode coupling and drift wave dispersion are studied by spatiotemporal Fourier decomposition of the camera frames. The observed coupling between modes is compared to calculations of nonlinearly coupled oscillators described by the Kuramoto model.
A machine learning approach to nonlinear modal analysis
NASA Astrophysics Data System (ADS)
Worden, K.; Green, P. L.
2017-02-01
Although linear modal analysis has proved itself to be the method of choice for the analysis of linear dynamic structures, its extension to nonlinear structures has proved to be a problem. A number of competing viewpoints on nonlinear modal analysis have emerged, each of which preserves a subset of the properties of the original linear theory. From the geometrical point of view, one can argue that the invariant manifold approach of Shaw and Pierre is the most natural generalisation. However, the Shaw-Pierre approach is rather demanding technically, depending as it does on the analytical construction of a mapping between spaces, which maps physical coordinates into invariant manifolds spanned by independent subsets of variables. The objective of the current paper is to demonstrate a data-based approach motivated by Shaw-Pierre method which exploits the idea of statistical independence to optimise a parametric form of the mapping. The approach can also be regarded as a generalisation of the Principal Orthogonal Decomposition (POD). A machine learning approach to inversion of the modal transformation is presented, based on the use of Gaussian processes, and this is equivalent to a nonlinear form of modal superposition. However, it is shown that issues can arise if the forward transformation is a polynomial and can thus have a multi-valued inverse. The overall approach is demonstrated using a number of case studies based on both simulated and experimental data.
Scare Tactics: Evaluating Problem Decompositions Using Failure Scenarios
NASA Technical Reports Server (NTRS)
Helm, B. Robert; Fickas, Stephen
1992-01-01
Our interest is in the design of multi-agent problem-solving systems, which we refer to as composite systems. We have proposed an approach to composite system design by decomposition of problem statements. An automated assistant called Critter provides a library of reusable design transformations which allow a human analyst to search the space of decompositions for a problem. In this paper we describe a method for evaluating and critiquing problem decompositions generated by this search process. The method uses knowledge stored in the form of failure decompositions attached to design transformations. We suggest the benefits of our critiquing method by showing how it could re-derive steps of a published development example. We then identify several open issues for the method.
A Novel Nonlinear Precoding Detection Algorithm for VBLAST in MIMO-MC-CDMA Downlink System
NASA Astrophysics Data System (ADS)
Fu, Hongliang; Tao, Yong
Considering the error propagation effect and high complexity of the Vertical Bell Labs Layered Space Time (V-BLAST), a novel nonlinear ZF-THP algorithm for VBLAST in MIMO-MC-CDMA downlink system is proposed in this paper. QR decomposition is used for precoding matrix, the nonlinear Tomlinson-Harashima Precoding (THP) is used between the sub-carrier channels of MC-CDMA to eliminate interference from other signals at the transmitter, and can obtain frequency diversity gain and eliminate effectively the error propagation effect. At the receiver, zero forcing criterion is used, and the complexity of the receiver can be reduced. Simulation results show that the proposed algorithm is better than the traditional zero forcing algorithm and the linear precoding algorithm in the system BER.
NASA Astrophysics Data System (ADS)
Kyoung, Ho Han; H. J., Shin
2010-12-01
We investigate the Painlevé integrability of nonautonomous nonlinear Schrödinger (NLS) equations with both space- and time-dependent dispersion, nonlinearity, and external potentials. The Painlevé analysis is carried out without using the Kruskal's simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painlevé analyses and/or become unknown new equations.
Chen Xiangsong; Sun Weimin; Wang Fan; Goldman, T.
2011-04-01
We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular-momentum eigenstates. We split, from the total angular-momentum operator, a proper part which can be separately conserved for a stationary state. This part commutes with the total Hamiltonian and thus specifies the quantum angular momentum. We first show how this can be done in a gauge-dependent way, by seeking a specific gauge in which part of the total angular-momentum operator vanishes identically. We then construct a gauge-invariant operator with the desired property. Our analysis clarifies what is the most pertinent choice among the various proposals for decomposing the nucleon spin. A similar analysis is performed for extracting a proper part from the total Hamiltonian to construct energy eigenstates.
Algebraic Nonlinear Collective Motion
NASA Astrophysics Data System (ADS)
Troupe, J.; Rosensteel, G.
1998-11-01
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).
Direct Sum Decomposition of Groups
ERIC Educational Resources Information Center
Thaheem, A. B.
2005-01-01
Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…
Domain decomposition methods in computational fluid dynamics
NASA Technical Reports Server (NTRS)
Gropp, William D.; Keyes, David E.
1991-01-01
The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.
Observations on the Proper Orthogonal Decomposition
NASA Technical Reports Server (NTRS)
Berkooz, Gal
1992-01-01
The Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L(2) optimal sense. It is used in diverse disciplines from image processing to turbulence. Recently the P.O.D. is receiving much attention as a tool for studying dynamics of systems in infinite dimensional space. This paper reviews the mathematical fundamentals of this theory. Also included are results on the span of the eigenfunction basis, a geometric corollary due to Chebyshev's inequality and a relation between the P.O.D. symmetry and ergodicity.
KOALA: A program for the processing and decomposition of transient spectra
NASA Astrophysics Data System (ADS)
Grubb, Michael P.; Orr-Ewing, Andrew J.; Ashfold, Michael N. R.
2014-06-01
Extracting meaningful kinetic traces from time-resolved absorption spectra is a non-trivial task, particularly for solution phase spectra where solvent interactions can substantially broaden and shift the transition frequencies. Typically, each spectrum is composed of signal from a number of molecular species (e.g., excited states, intermediate complexes, product species) with overlapping spectral features. Additionally, the profiles of these spectral features may evolve in time (i.e., signal nonlinearity), further complicating the decomposition process. Here, we present a new program for decomposing mixed transient spectra into their individual component spectra and extracting the corresponding kinetic traces: KOALA (Kinetics Observed After Light Absorption). The software combines spectral target analysis with brute-force linear least squares fitting, which is computationally efficient because of the small nonlinear parameter space of most spectral features. Within, we demonstrate the application of KOALA to two sets of experimental transient absorption spectra with multiple mixed spectral components. Although designed for decomposing solution-phase transient absorption data, KOALA may in principle be applied to any time-evolving spectra with multiple components.
Mass decomposition of SLACS lens galaxies in Weyl conformal gravity
NASA Astrophysics Data System (ADS)
Potapov, Alexander A.; Izmailov, Ramil N.; Nandi, Kamal K.
2016-06-01
We study here, using the Mannheim-Kazanas solution of Weyl conformal theory, the mass decomposition in the representative subsample of 57 early-type elliptical lens galaxies of the Sloan Lens Advanced Camera for Surveys (SLACS) on board the Hubble Space Telescope. We begin by showing that the solution need not be an exclusive solution of conformal gravity but can also be viewed as a solution of a class of f (R ) gravity theories coupled to nonlinear electrodynamics thereby rendering the ensuing results more universal. Since lensing involves light bending, we shall first show that the solution adds to Schwarzschild light bending caused by the luminous mass (M*) a positive contribution +γ R contrary to the previous results in the literature, thereby resolving a long-standing problem. The cause of the error is critically examined. Next, applying the expressions for light bending together with an input equating Einstein and Weyl angles, we develop a novel algorithm for separating the luminous component from the total lens mass (luminous+dark ) within the Einstein radius. Our results indicate that the luminous mass estimates differ from the observed total lens masses by a linear proportionality factor across the subsample, which qualitatively agrees with the common conclusion from a number of different simulations in the literature. In quantitative detail, we observe that the ratios of luminous over total lens mass (f*) within the Einstein radius of individual galaxies take on values near unity, many of which remarkably fall inside or just marginally outside the specified error bars obtained from a simulation based on the Bruzual-Charlot stellar population synthesis model together with the Salpeter initial mass function favored on the ground of metallicity [Grillo et al., Astron. Astrophys. 501, 461 (2009)]. We shall also calculate the average dark matter density ⟨ρ⟩ av of individual galaxies within their respective Einstein spheres. To our knowledge, the present
NASA Technical Reports Server (NTRS)
Bennett, William H.; Kwatny, Harry G.; Lavigna, Chris; Blankenship, Gilmer
1994-01-01
The following topics are discussed: (1) modeling of articulated spacecraft as multi-flex-body systems; (2) nonlinear attitude control by adaptive partial feedback linearizing (PFL) control; (3) attitude dynamics and control for SSF/MRMS; and (4) performance analysis results for attitude control of SSF/MRMS.
NASA Astrophysics Data System (ADS)
Bennett, William H.; Kwatny, Harry G.; Lavigna, Chris; Blankenship, Gilmer
1994-06-01
The following topics are discussed: (1) modeling of articulated spacecraft as multi-flex-body systems; (2) nonlinear attitude control by adaptive partial feedback linearizing (PFL) control; (3) attitude dynamics and control for SSF/MRMS; and (4) performance analysis results for attitude control of SSF/MRMS.
Decomposition in northern Minnesota peatlands
Farrish, K.W.
1985-01-01
Decomposition in peatlands was investigated in northern Minnesota. Four sites, an ombrotrophic raised bog, an ombrotrophic perched bog and two groundwater minerotrophic fens, were studied. Decomposition rates of peat and paper were estimated using mass-loss techniques. Environmental and substrate factors that were most likely to be responsible for limiting decomposition were monitored. Laboratory incubation experiments complemented the field work. Mass-loss over one year in one of the bogs, ranged from 11 percent in the upper 10 cm of hummocks to 1 percent at 60 to 100 cm depth in hollows. Regression analysis of the data for that bog predicted no mass-loss below 87 cm. Decomposition estimates on an area basis were 2720 and 6460 km/ha yr for the two bogs; 17,000 and 5900 kg/ha yr for the two fens. Environmental factors found to limit decomposition in these peatlands were reducing/anaerobic conditions below the water table and cool peat temperatures. Substrate factors found to limit decomposition were low pH, high content of resistant organics such as lignin, and shortages of available N and K. Greater groundwater influence was found to favor decomposition through raising the pH and perhaps by introducing limited amounts of dissolved oxygen.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan
2016-01-01
In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite
Structural optimization by multilevel decomposition
NASA Technical Reports Server (NTRS)
Sobieszczanski-Sobieski, J.; James, B.; Dovi, A.
1983-01-01
A method is described for decomposing an optimization problem into a set of subproblems and a coordination problem which preserves coupling between the subproblems. The method is introduced as a special case of multilevel, multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given for an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers, using different computers to work concurrently on the same large problem.
Perfluoropolyalkylether decomposition on catalytic aluminas
NASA Technical Reports Server (NTRS)
Morales, Wilfredo
1994-01-01
The decomposition of Fomblin Z25, a commercial perfluoropolyalkylether liquid lubricant, was studied using the Penn State Micro-oxidation Test, and a thermal gravimetric/differential scanning calorimetry unit. The micro-oxidation test was conducted using 440C stainless steel and pure iron metal catalyst specimens, whereas the thermal gravimetric/differential scanning calorimetry tests were conducted using catalytic alumina pellets. Analysis of the thermal data, high pressure liquid chromatography data, and x-ray photoelectron spectroscopy data support evidence that there are two different decomposition mechanisms for Fomblin Z25, and that reductive sites on the catalytic surfaces are responsible for the decomposition of Fomblin Z25.
AUTONOMOUS GAUSSIAN DECOMPOSITION
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Dickey, John
2015-04-15
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
Autonomous Gaussian Decomposition
NASA Astrophysics Data System (ADS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-04-01
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
A Fantastic Decomposition: Unsettling the Fury of Having to Wait
ERIC Educational Resources Information Center
Holmes, Rachel
2012-01-01
This article draws on data from a single element of a larger project, which focused on the issue of "how children develop a reputation as "naughty" in the early years classroom." The author draws attention to the (in)corporeal (re)formation of the line in school, undertaking a decomposition of the topological spaces of research/art/education. She…
2014-10-01
IMFs ), and each of the IMFs has better behaved instan- taneous frequency analysis. This paper presents an alternative approach for EMD. The main idea is...Therefore, an IMF can be produced by simply subtracting the average from the signal without iteration. Our numerical examples illustrate that the...stationary signals. It aims at decomposing a signal, via an iterative sifting procedure into several intrinsic mode functions ( IMFs ), and each of the
Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan
2016-01-01
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740
A multilevel preconditioner for domain decomposition boundary systems
Bramble, J.H.; Pasciak, J.E.; Xu, Jinchao.
1991-12-11
In this note, we consider multilevel preconditioning of the reduced boundary systems which arise in non-overlapping domain decomposition methods. It will be shown that the resulting preconditioned systems have condition numbers which be bounded in the case of multilevel spaces on the whole domain and grow at most proportional to the number of levels in the case of multilevel boundary spaces without multilevel extensions into the interior.
Chatterjee, Kausik; Roadcap, John R.; Singh, Surendra
2014-11-01
The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.
Nonlinear optical studies of curcumin metal derivatives with cw laser
NASA Astrophysics Data System (ADS)
Henari, F. Z.; Cassidy, S.
2015-03-01
We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10-7 cm2/W and negative nonlinear absorption of the order of 10-6 cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition model with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated.
Nonlinear optical studies of curcumin metal derivatives with cw laser
Henari, F. Z. Cassidy, S.
2015-03-30
We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10{sup −7} cm{sup 2}/W and negative nonlinear absorption of the order of 10{sup −6} cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition model with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated.
Catalyst for sodium chlorate decomposition
NASA Technical Reports Server (NTRS)
Wydeven, T.
1972-01-01
Production of oxygen by rapid decomposition of cobalt oxide and sodium chlorate mixture is discussed. Cobalt oxide serves as catalyst to accelerate reaction. Temperature conditions and chemical processes involved are described.
NASA Technical Reports Server (NTRS)
Chang, Tom
2005-01-01
We have achieved all the goals stated in our grant proposal. Specifically, these include: 1. The understanding of the complexity induced nonlinear spatiotemporal coherent structures and the coexisting propagating modes. 2. The understanding of the intermittent turbulence and energization process of the observed Bursty Bulk Flows (BBF's) in the Earth s magnetotail. 3. The development of "anisotropic three-dimensional complexity" in the plasma sheet due to localized merging and interactions of the magnetic coherent structures. 4. The study of fluctuation-induced nonlinear instabilities and their role in the reconfiguration of magnetic topologies in the magnetotail based on the concepts of the dynamic renormalization group. 5. The acceleration of ions due to the intermittent turbulence of propagating and nonpropagating fluctuations. In the following, we include lists of our published papers, invited talks, and professional activities. A detailed description of our accomplished research results is given..
Chebabhi, Ali; Fellah, Mohammed Karim; Kessal, Abdelhalim; Benkhoris, Mohamed F
2016-07-01
In this paper is proposed a new balancing three-level three dimensional space vector modulation (B3L-3DSVM) strategy which uses a redundant voltage vectors to realize precise control and high-performance for a three phase three-level four-leg neutral point clamped (NPC) inverter based Shunt Active Power Filter (SAPF) for eliminate the source currents harmonics, reduce the magnitude of neutral wire current (eliminate the zero-sequence current produced by single-phase nonlinear loads), and to compensate the reactive power in the three-phase four-wire electrical networks. This strategy is proposed in order to gate switching pulses generation, dc bus voltage capacitors balancing (conserve equal voltage of the two dc bus capacitors), and to switching frequency reduced and fixed of inverter switches in same times. A Nonlinear Back Stepping Controllers (NBSC) are used for regulated the dc bus voltage capacitors and the SAPF injected currents to robustness, stabilizing the system and to improve the response and to eliminate the overshoot and undershoot of traditional PI (Proportional-Integral). Conventional three-level three dimensional space vector modulation (C3L-3DSVM) and B3L-3DSVM are calculated and compared in terms of error between the two dc bus voltage capacitors, SAPF output voltages and THDv, THDi of source currents, magnitude of source neutral wire current, and the reactive power compensation under unbalanced single phase nonlinear loads. The success, robustness, and the effectiveness of the proposed control strategies are demonstrated through simulation using Sim Power Systems and S-Function of MATLAB/SIMULINK.
Control of elastic robotic systems by nonlinear inversion and modal damping
NASA Technical Reports Server (NTRS)
Singh, S. N.; Schy, A. A.
1986-01-01
Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.
An Efficient Solver of Elasto-plastic Problems in Mechanics Based on TFETI Domain Decomposition
NASA Astrophysics Data System (ADS)
Čermák, M.; Kozubek, T.; Markopoulos, A.
2011-09-01
This paper illustrates how to implement efficiently solvers for elasto-plastic problems. We consider the time step problems formulated by nonlinear variational equations in terms of displacements. To treat nonlinearity and nonsmoothnes we use semismooth Newton method. In each Newton iteration we have to solve linear system of algebraic equations and for its numerical solution we use TFETI domain decomposition method. In our benchmark we demonstrate our approach on von Mises plasticity with isotropic hardening using the return mapping concept.
Wigner rotations and Iwasawa decompositions in polarization optics.
Han, D; Kim, Y S; Noz, M E
1999-07-01
Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions. This is possible because the combined effects of rotation, phase-shift, and attenuation filters lead to transformation matrices of the six-parameter Lorentz group applicable to Jones vectors and Stokes parameters for polarized light waves. The symmetry transformations in special relativity lead to a set of experiments which can be performed in optics laboratories.
High-temperature catalyst for catalytic combustion and decomposition
NASA Technical Reports Server (NTRS)
Mays, Jeffrey A. (Inventor); Lohner, Kevin A. (Inventor); Sevener, Kathleen M. (Inventor); Jensen, Jeff J. (Inventor)
2005-01-01
A robust, high temperature mixed metal oxide catalyst for propellant composition, including high concentration hydrogen peroxide, and catalytic combustion, including methane air mixtures. The uses include target, space, and on-orbit propulsion systems and low-emission terrestrial power and gas generation. The catalyst system requires no special preheat apparatus or special sequencing to meet start-up requirements, enabling a fast overall response time. Start-up transients of less than 1 second have been demonstrated with catalyst bed and propellant temperatures as low as 50 degrees Fahrenheit. The catalyst system has consistently demonstrated high decomposition effeciency, extremely low decomposition roughness, and long operating life on multiple test particles.
Prakash, J; Srinivasan, K
2009-07-01
In this paper, the authors have represented the nonlinear system as a family of local linear state space models, local PID controllers have been designed on the basis of linear models, and the weighted sum of the output from the local PID controllers (Nonlinear PID controller) has been used to control the nonlinear process. Further, Nonlinear Model Predictive Controller using the family of local linear state space models (F-NMPC) has been developed. The effectiveness of the proposed control schemes has been demonstrated on a CSTR process, which exhibits dynamic nonlinearity.
NASA Astrophysics Data System (ADS)
Fosas de Pando, Miguel; Schmid, Peter J.; Sipp, Denis
2016-11-01
Nonlinear model reduction for large-scale flows is an essential component in many fluid applications such as flow control, optimization, parameter space exploration and statistical analysis. In this article, we generalize the POD-DEIM method, introduced by Chaturantabut & Sorensen [1], to address nonlocal nonlinearities in the equations without loss of performance or efficiency. The nonlinear terms are represented by nested DEIM-approximations using multiple expansion bases based on the Proper Orthogonal Decomposition. These extensions are imperative, for example, for applications of the POD-DEIM method to large-scale compressible flows. The efficient implementation of the presented model-reduction technique follows our earlier work [2] on linearized and adjoint analyses and takes advantage of the modular structure of our compressible flow solver. The efficacy of the nonlinear model-reduction technique is demonstrated to the flow around an airfoil and its acoustic footprint. We could obtain an accurate and robust low-dimensional model that captures the main features of the full flow.
Revisiting the layout decomposition problem for double patterning lithography
NASA Astrophysics Data System (ADS)
Kahng, Andrew B.; Park, Chul-Hong; Xu, Xu; Yao, Hailong
2008-10-01
In double patterning lithography (DPL) layout decomposition for 45nm and below process nodes, two features must be assigned opposite colors (corresponding to different exposures) if their spacing is less than the minimum coloring spacing.5, 11, 14 However, there exist pattern configurations for which pattern features separated by less than the minimum coloring spacing cannot be assigned different colors. In such cases, DPL requires that a layout feature be split into two parts. We address this problem using a layout decomposition algorithm that incorporates integer linear programming (ILP), phase conflict detection (PCD), and node-deletion bipartization (NDB) methods. We evaluate our approach on both real-world and artificially generated testcases in 45nm technology. Experimental results show that our proposed layout decomposition method effectively decomposes given layouts to satisfy the key goals of minimized line-ends and maximized overlap margin. There are no design rule violations in the final decomposed layout. While we have previously reported other facets of our research on DPL pattern decomposition,6 the present paper differs from that work in the following key respects: (1) instead of detecting conflict cycles and splitting nodes in conflict cycles to achieve graph bipartization,6 we split all nodes of the conflict graph at all feasible dividing points and then formulate a problem of bipartization by ILP, PCD8 and NDB9 methods; and (2) instead of reporting unresolvable conflict cycles, we report the number of deleted conflict edges to more accurately capture the needed design changes in the experimental results.
Properties of Nonlinear Dynamo Waves
NASA Technical Reports Server (NTRS)
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
NASA Technical Reports Server (NTRS)
Keyes, David E.; Smooke, Mitchell D.
1987-01-01
A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.
An optimization approach for fitting canonical tensor decompositions.
Dunlavy, Daniel M.; Acar, Evrim; Kolda, Tamara Gibson
2009-02-01
Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methods have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.
Analytic solutions for time-dependent Schrödinger equations with linear of nonlinear Hamiltonians
NASA Astrophysics Data System (ADS)
Adomian, G.; Efinger, H. J.
1994-10-01
The decomposition method is applied to the time-dependent Schrödinger equation for linear or nonlinear Hamiltonian operators, without linearization, perturbation, or numerical methods, to obtain a rapidly converging analytic solution
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Feature Importance in Nonlinear Embeddings (FINE): Applications in Digital Pathology.
Ginsburg, Shoshana B; Lee, George; Ali, Sahirzeeshan; Madabhushi, Anant
2016-01-01
Quantitative histomorphometry (QH) refers to the process of computationally modeling disease appearance on digital pathology images by extracting hundreds of image features and using them to predict disease presence or outcome. Since constructing a robust and interpretable classifier is challenging in a high dimensional feature space, dimensionality reduction (DR) is often implemented prior to classifier construction. However, when DR is performed it can be challenging to quantify the contribution of each of the original features to the final classification result. We have previously presented a method for scoring features based on their importance for classification on an embedding derived via principal components analysis (PCA). However, nonlinear DR involves the eigen-decomposition of a kernel matrix rather than the data itself, compounding the issue of classifier interpretability. In this paper we present feature importance in nonlinear embeddings (FINE), an extension of our PCA-based feature scoring method to kernel PCA (KPCA), as well as several NLDR algorithms that can be cast as variants of KPCA. FINE is applied to four digital pathology datasets to identify key QH features for predicting the risk of breast and prostate cancer recurrence. Measures of nuclear and glandular architecture and clusteredness were found to play an important role in predicting the likelihood of recurrence of both breast and prostate cancers. Compared to the t-test, Fisher score, and Gini index, FINE was able to identify a stable set of features that provide good classification accuracy on four publicly available datasets from the NIPS 2003 Feature Selection Challenge.
Nonlinear growth of periodic patterns.
Villain-Guillot, Simon; Josserand, Christophe
2002-09-01
We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the nonlinearity cannot be neglected anymore, and before the coalescence dominates. The dynamics is captured through the standard technique of a solubility condition performed over a particular family of quasistatic solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple ordinary differential equation. The density profile of the stationary regime found at the end of the nonlinear growth is also well characterized. Numerical simulations correspond satisfactorily to the analytical results through three different methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold.
Non-overlapping domain decomposition method for a variational inequality with gradient constraints
NASA Astrophysics Data System (ADS)
Lapin, A.; Laitinen, E.; Lapin, S.
2016-11-01
Non-overlapping domain decomposition method is applied to a variational inequality with nonlinear diffusion-convection operator and gradient constraints. The method is based on the initial approximation of the problem and its subsequent splitting into subproblems. For the resulting constrained saddle point problem block relaxation-Uzawa iterative solution method is applied.
Tensor decomposition of EEG signals: a brief review.
Cong, Fengyu; Lin, Qiu-Hua; Kuang, Li-Dan; Gong, Xiao-Feng; Astikainen, Piia; Ristaniemi, Tapani
2015-06-15
Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current progress of tensor decomposition of EEG signals with three aspects. The first is about the existing modes and tensors of EEG signals. Second, two fundamental tensor decomposition models, canonical polyadic decomposition (CPD, it is also called parallel factor analysis-PARAFAC) and Tucker decomposition, are introduced and compared. Moreover, the applications of the two models for EEG signals are addressed. Particularly, the determination of the number of components for each mode is discussed. Finally, the N-way partial least square and higher-order partial least square are described for a potential trend to process and analyze brain signals of two modalities simultaneously.
Thermal decomposition products of butyraldehyde
NASA Astrophysics Data System (ADS)
Hatten, Courtney D.; Kaskey, Kevin R.; Warner, Brian J.; Wright, Emily M.; McCunn, Laura R.
2013-12-01
The thermal decomposition of gas-phase butyraldehyde, CH3CH2CH2CHO, was studied in the 1300-1600 K range with a hyperthermal nozzle. Products were identified via matrix-isolation Fourier transform infrared spectroscopy and photoionization mass spectrometry in separate experiments. There are at least six major initial reactions contributing to the decomposition of butyraldehyde: a radical decomposition channel leading to propyl radical + CO + H; molecular elimination to form H2 + ethylketene; a keto-enol tautomerism followed by elimination of H2O producing 1-butyne; an intramolecular hydrogen shift and elimination producing vinyl alcohol and ethylene, a β-C-C bond scission yielding ethyl and vinoxy radicals; and a γ-C-C bond scission yielding methyl and CH2CH2CHO radicals. The first three reactions are analogous to those observed in the thermal decomposition of acetaldehyde, but the latter three reactions are made possible by the longer alkyl chain structure of butyraldehyde. The products identified following thermal decomposition of butyraldehyde are CO, HCO, CH3CH2CH2, CH3CH2CH=C=O, H2O, CH3CH2C≡CH, CH2CH2, CH2=CHOH, CH2CHO, CH3, HC≡CH, CH2CCH, CH3C≡CH, CH3CH=CH2, H2C=C=O, CH3CH2CH3, CH2=CHCHO, C4H2, C4H4, and C4H8. The first ten products listed are direct products of the six reactions listed above. The remaining products can be attributed to further decomposition reactions or bimolecular reactions in the nozzle.
NASA Technical Reports Server (NTRS)
Hein, C.; Meystel, A.
1994-01-01
There are many multi-stage optimization problems that are not easily solved through any known direct method when the stages are coupled. For instance, we have investigated the problem of planning a vehicle's control sequence to negotiate obstacles and reach a goal in minimum time. The vehicle has a known mass, and the controlling forces have finite limits. We have developed a technique that finds admissible control trajectories which tend to minimize the vehicle's transit time through the obstacle field. The immediate applications is that of a space robot which must rapidly traverse around 2-or-3 dimensional structures via application of a rotating thruster or non-rotating on-off for such vehicles is located at the Marshall Space Flight Center in Huntsville Alabama. However, it appears that the development method is applicable to a general set of optimization problems in which the cost function and the multi-dimensional multi-state system can be any nonlinear functions, which are continuous in the operating regions. Other applications included the planning of optimal navigation pathways through a transversability graph; the planning of control input for under-water maneuvering vehicles which have complex control state-space relationships; the planning of control sequences for milling and manufacturing robots; the planning of control and trajectories for automated delivery vehicles; and the optimization and athletic training in slalom sports.
A nonlinear generalization of spectral Granger causality.
He, Fei; Wei, Hua-Liang; Billings, Stephen A; Sarrigiannis, Ptolemaios G
2014-06-01
Spectral measures of linear Granger causality have been widely applied to study the causal connectivity between time series data in neuroscience, biology, and economics. Traditional Granger causality measures are based on linear autoregressive with exogenous (ARX) inputs models of time series data, which cannot truly reveal nonlinear effects in the data especially in the frequency domain. In this study, it is shown that the classical Geweke's spectral causality measure can be explicitly linked with the output spectra of corresponding restricted and unrestricted time-domain models. The latter representation is then generalized to nonlinear bivariate signals and for the first time nonlinear causality analysis in the frequency domain. This is achieved by using the nonlinear ARX (NARX) modeling of signals, and decomposition of the recently defined output frequency response function which is related to the NARX model.
Refining signal decomposition for GRETINA detectors
NASA Astrophysics Data System (ADS)
Prasher, V. S.; Campbell, C. M.; Cromaz, M.; Crawford, H. L.; Wiens, A.; Lee, I. Y.; Macchiavelli, A. O.; Lister; Merchan, E.; Chowdhury, P.; Radford, D. C.
2013-04-01
The reconstruction of the original direction and energy of gamma rays through locating their interaction points in solid state detectors is a crucial evolving technology for nuclear physics, space science and homeland security. New arrays AGATA and GRETINA have been built for nuclear science based on highly segmented germanium crystals. The signal decomposition process fits the observed waveform from each crystal segment with a linear combination of pre-calculated basis signals. This process occurs on an event-by-event basis in real time to extract the position and energy of γ-ray interactions. The methodology for generating a basis of pulse shapes, varying according to the position of the charge generating interactions, is in place. Improvements in signal decomposition can be realized by better modeling the crystals. Specifically, a better understanding of the true impurity distributions, internal electric fields, and charge mobilities will lead to more reliable bases, more precise definition of the interaction points, and hence more reliable tracking. In this presentation we will cover the current state-of-the-art for basis generation and then discuss the sensitivity of the predicted pulse shapes when varying some key parameters.
NASA Astrophysics Data System (ADS)
Sierra, Carlos A.; Malghani, Saadatullah; Loescher, Henry W.
2017-02-01
Determining environmental controls on soil organic matter decomposition is of importance for developing models that predict the effects of environmental change on global soil carbon stocks. There is uncertainty about the environmental controls on decomposition rates at temperature and moisture extremes, particularly at high water content levels and high temperatures. It is uncertain whether observed declines in decomposition rates at high temperatures are due to declines in the heat capacity of extracellular enzymes as predicted by thermodynamic theory, or due to simultaneous declines in soil moisture. It is also uncertain whether oxygen limits decomposition rates at high water contents. Here we present the results of a full factorial experiment using organic soils from a boreal forest incubated at high temperatures (25 and 35 °C), a wide range of water-filled pore space (WFPS; 15, 30, 60, 90 %), and contrasting oxygen concentrations (1 and 20 %). We found support for the hypothesis that decomposition rates are high at high temperatures, provided that enough moisture and oxygen are available for decomposition. Furthermore, we found that decomposition rates are mostly limited by oxygen concentrations at high moisture levels; even at 90 % WFPS, decomposition proceeded at high rates in the presence of oxygen. Our results suggest an important degree of interaction among temperature, moisture, and oxygen in determining decomposition rates at the soil core scale.
Park, D H; Pagán, V R; Murphy, T E; Luo, J; Jen, A K-Y; Herman, W N
2015-04-06
We report in-plane slotted patch antenna-coupled electro-optic phase modulators with a carrier-to-sideband ratio (CSR) of 22 dB under an RF power density of 120 W/m(2) and a figure of merit of 2.0 W(-1/2) at the millimeter wave frequencies of 36-37 GHz based on guest-host type of second-order nonlinear polymer SEO125. CSR was improved more than 20 dB by using a SiO(2) protection layer. We demonstrate detection of 3 GHz modulation of the RF carrier. We also derive closed-form expressions for the modulated phase of optical wave and carrier-to-sideband ratio. Design, simulation, fabrication, and experimental results are discussed.
NASA Astrophysics Data System (ADS)
Jang, Juhi; Kim, Eun Heui
2016-01-01
We consider a configuration where a planar shock reflects and diffracts as it hits a semi-infinite rigid screen. The diffracted reflected shock meets the diffracted expansion wave, created by the incident shock that does not hit the screen, and changes continuously from a shock into an expansion. The governing equation changes its type and becomes degenerate as the wave changes continuously from a shock to an expansion. Furthermore the governing equation has multiple free boundaries (transonic shocks) and an additional degenerate sonic boundary (the expansion wave). We develop an analysis to understand the solution structure near which the shock strength approaches zero and the shock turns continuously into an expansion wavefront, and show the existence of the global solution to this configuration for the nonlinear wave system. Moreover we provide an asymptotic analysis to estimate the position of the change of the wave, and present intriguing numerical results.
Nagurney, A.; Kim, D.S.
1989-01-01
The authors have applied parallel and serial variational inequality (VI) diagonal decomposition algorithms to large-scale multicommodity market equilibrium problems. These decomposition algorithms resolve the VI problems into single commodity problems, which are then solved as quadratic programming problems. The algorithms are implemented on an IBM 3090-600E, and randomly generated linear and nonlinear problems with as many as 100 markets and 12 commodities are solved. The computational results demonstrate that the parallel diagonal decomposition scheme is amenable to parallelization. This is the first time that multicommodity equilibrium problems of this scale and level of generality have been solved. Furthermore, this is the first study to compare the efficiencies of parallel and serial VI decomposition algorithms. Although the authors have selected as a prototype an equilibrium problem in economics, virtually any equilibrium problem can be formulated and studied as a variational inequality problem. Hence, their results are not limited to applications in economics and operations research.
1974-02-14
Wester- velt. [60] Streaming. In 1831, Michael Faraday [61] noted that currents of air were set up in the neighborhood of vibrating plates-the first... ducei in the case of a paramettc amy (from Berktay an Leahy 141). C’ "". k•, SEC 10.1 NONLINEAR ACOUSTICS 345 The principal results of their analysis
NASA Astrophysics Data System (ADS)
Kevorkian, J.
This report discusses research in the area of slowly varying nonlinear oscillatory systems. Some of the topics discussed are as follows: adiabatic invariants and transient resonance in very slowly varying Hamiltonian systems; sustained resonance in very slowly varying Hamiltonian systems; free-electron lasers with very slow wiggler taper; and bursting oscillators.
Nonlinear electromagnetic interactions in energetic materials
Wood, Mitchell Anthony; Dalvit, Diego Alejandro; Moore, David Steven
2016-01-12
We study the scattering of electromagnetic waves in anisotropic energetic materials. Nonlinear light-matter interactions in molecular crystals result in frequency-conversion and polarization changes. Applied electromagnetic fields of moderate intensity can induce these nonlinear effects without triggering chemical decomposition, offering a mechanism for the nonionizing identification of explosives. We use molecular-dynamics simulations to compute such two-dimensional THz spectra for planar slabs made of pentaerythritol tetranitrate and ammonium nitrate. Finally, we discuss third-harmonic generation and polarization-conversion processes in such materials. These observed far-field spectral features of the reflected or transmitted light may serve as an alternative tool for standoff explosive detection.
Reactive Goal Decomposition Hierarchies for On-Board Autonomy
NASA Astrophysics Data System (ADS)
Hartmann, L.
2002-01-01
As our experience grows, space missions and systems are expected to address ever more complex and demanding requirements with fewer resources (e.g., mass, power, budget). One approach to accommodating these higher expectations is to increase the level of autonomy to improve the capabilities and robustness of on- board systems and to simplify operations. The goal decomposition hierarchies described here provide a simple but powerful form of goal-directed behavior that is relatively easy to implement for space systems. A goal corresponds to a state or condition that an operator of the space system would like to bring about. In the system described here goals are decomposed into simpler subgoals until the subgoals are simple enough to execute directly. For each goal there is an activation condition and a set of decompositions. The decompositions correspond to different ways of achieving the higher level goal. Each decomposition contains a gating condition and a set of subgoals to be "executed" sequentially or in parallel. The gating conditions are evaluated in order and for the first one that is true, the corresponding decomposition is executed in order to achieve the higher level goal. The activation condition specifies global conditions (i.e., for all decompositions of the goal) that need to hold in order for the goal to be achieved. In real-time, parameters and state information are passed between goals and subgoals in the decomposition; a termination indication (success, failure, degree) is passed up when a decomposition finishes executing. The lowest level decompositions include servo control loops and finite state machines for generating control signals and sequencing i/o. Semaphores and shared memory are used to synchronize and coordinate decompositions that execute in parallel. The goal decomposition hierarchy is reactive in that the generated behavior is sensitive to the real-time state of the system and the environment. That is, the system is able to react
Nonlinear projection trick in kernel methods: an alternative to the kernel trick.
Kwak, Nojun
2013-12-01
In kernel methods such as kernel principal component analysis (PCA) and support vector machines, the so called kernel trick is used to avoid direct calculations in a high (virtually infinite) dimensional kernel space. In this brief, based on the fact that the effective dimensionality of a kernel space is less than the number of training samples, we propose an alternative to the kernel trick that explicitly maps the input data into a reduced dimensional kernel space. This is easily obtained by the eigenvalue decomposition of the kernel matrix. The proposed method is named as the nonlinear projection trick in contrast to the kernel trick. With this technique, the applicability of the kernel methods is widened to arbitrary algorithms that do not use the dot product. The equivalence between the kernel trick and the nonlinear projection trick is shown for several conventional kernel methods. In addition, we extend PCA-L1, which uses L1-norm instead of L2-norm (or dot product), into a kernel version and show the effectiveness of the proposed approach.
LUPOD: Collocation in POD via LU decomposition
NASA Astrophysics Data System (ADS)
Rapún, M.-L.; Terragni, F.; Vega, J. M.
2017-04-01
A collocation method is developed for the (truncated) POD of a set of snapshots. In other words, POD computations are performed using only a set of collocation points, whose number is comparable to the number of retained modes, in a similar fashion as in collocation spectral methods. Intending to rely on simple ideas which, moreover, are consistent with the essence of POD, collocation points are computed via the LU decomposition with pivoting of the snapshot matrix. The new method is illustrated in simple applications in which POD is used as a data-processing method. The performance of the method is tested in the computationally efficient construction of reduced order models based on POD plus Galerkin projection for the complex Ginzburg-Landau equation in one and two space dimensions.
Neurocomputing strategies in decomposition based structural design
NASA Technical Reports Server (NTRS)
Szewczyk, Z.; Hajela, P.
1993-01-01
The present paper explores the applicability of neurocomputing strategies in decomposition based structural optimization problems. It is shown that the modeling capability of a backpropagation neural network can be used to detect weak couplings in a system, and to effectively decompose it into smaller, more tractable, subsystems. When such partitioning of a design space is possible, parallel optimization can be performed in each subsystem, with a penalty term added to its objective function to account for constraint violations in all other subsystems. Dependencies among subsystems are represented in terms of global design variables, and a neural network is used to map the relations between these variables and all subsystem constraints. A vector quantization technique, referred to as a z-Network, can effectively be used for this purpose. The approach is illustrated with applications to minimum weight sizing of truss structures with multiple design constraints.
The ecology of carrion decomposition
Technology Transfer Automated Retrieval System (TEKTRAN)
Carrion, or the remains of dead animals, is something that most people would like to avoid. It is visually unpleasant, emits foul odors, and may be the source of numerous pathogens. Decomposition of carrion, however, provides a unique opportunity for scientists to investigate how nutrients cycle t...
Microbial interactions during carrion decomposition
Technology Transfer Automated Retrieval System (TEKTRAN)
This addresses the microbial ecology of carrion decomposition in the age of metagenomics. It describes what is known about the microbial communities on carrion, including a brief synopsis about the communities on other organic matter sources. It provides a description of studies using state-of-the...
Cadaver decomposition in terrestrial ecosystems
NASA Astrophysics Data System (ADS)
Carter, David O.; Yellowlees, David; Tibbett, Mark
2007-01-01
A dead mammal (i.e. cadaver) is a high quality resource (narrow carbon:nitrogen ratio, high water content) that releases an intense, localised pulse of carbon and nutrients into the soil upon decomposition. Despite the fact that as much as 5,000 kg of cadaver can be introduced to a square kilometre of terrestrial ecosystem each year, cadaver decomposition remains a neglected microsere. Here we review the processes associated with the introduction of cadaver-derived carbon and nutrients into soil from forensic and ecological settings to show that cadaver decomposition can have a greater, albeit localised, effect on belowground ecology than plant and faecal resources. Cadaveric materials are rapidly introduced to belowground floral and faunal communities, which results in the formation of a highly concentrated island of fertility, or cadaver decomposition island (CDI). CDIs are associated with increased soil microbial biomass, microbial activity (C mineralisation) and nematode abundance. Each CDI is an ephemeral natural disturbance that, in addition to releasing energy and nutrients to the wider ecosystem, acts as a hub by receiving these materials in the form of dead insects, exuvia and puparia, faecal matter (from scavengers, grazers and predators) and feathers (from avian scavengers and predators). As such, CDIs contribute to landscape heterogeneity. Furthermore, CDIs are a specialised habitat for a number of flies, beetles and pioneer vegetation, which enhances biodiversity in terrestrial ecosystems.
An analysis of scatter decomposition
NASA Technical Reports Server (NTRS)
Nicol, David M.; Saltz, Joel H.
1990-01-01
A formal analysis of a powerful mapping technique known as scatter decomposition is presented. Scatter decomposition divides an irregular computational domain into a large number of equal sized pieces, and distributes them modularly among processors. A probabilistic model of workload in one dimension is used to formally explain why, and when scatter decomposition works. The first result is that if correlation in workload is a convex function of distance, then scattering a more finely decomposed domain yields a lower average processor workload variance. The second result shows that if the workload process is stationary Gaussian and the correlation function decreases linearly in distance until becoming zero and then remains zero, scattering a more finely decomposed domain yields a lower expected maximum processor workload. Finally it is shown that if the correlation function decreases linearly across the entire domain, then among all mappings that assign an equal number of domain pieces to each processor, scatter decomposition minimizes the average processor workload variance. The dependence of these results on the assumption of decreasing correlation is illustrated with situations where a coarser granularity actually achieves better load balance.
NASA Astrophysics Data System (ADS)
Xie, Dexuan
2014-10-01
The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent, but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms. To effectively deal with such a challenge, in this paper, new solution decomposition and minimization schemes are proposed, together with a new PBE analysis on solution existence and uniqueness. Moreover, a PBE finite element program package is developed in Python based on the FEniCS program library and GAMer, a molecular surface and volumetric mesh generation program package. Numerical tests on proteins and a nonlinear Born ball model with an analytical solution validate the new solution decomposition and minimization schemes, and demonstrate the effectiveness and efficiency of the new PBE finite element program package.
Nonlinear dynamics experiments
Fischer, W.
2011-01-01
The goal of nonlinear dynamics experiments is to improve the understanding of single particle effects that increase the particle amplitude and lead to loss. Particle motion in storage rings is nearly conservative and for transverse dynamics the Hamiltonian in action angle variables (I{sub x},I{sub y},{phi}{sub x},{phi}{sub y}) near an isolated resonance k{nu}{sub x} + l{nu}{sub y} {approx} p is H = I{sub x}{nu}{sub x0} + I{sub y}{nu}{sub y0} + g(I{sub x}, I{sub y}) + h(I{sub x}, I{sub y})cos(k{phi}{sub x} + l{phi}{sub y} - p{theta}), (1) where k, l, p are integers, {theta} = 2{pi}s/L is the azimuth, and s and L are the path length and circumference respectively. The amplitude dependent tunes are given by {nu}{sub x,y}(I{sub x},I{sub y}) = {nu}{sub x0,y0} + {partial_derivative}g(I{sub x},I{sub y})/{partial_derivative}I{sub x,y} (2) and h(I{sub x},I{sub y}) is the resonance driving term (RDT). If the motion is governed by multiple resonances, h(I{sub x},I{sub y}) has to be replace by a series of terms. The particle motion is completely determined by the terms g and h, which can be calculated from higher order multipoles (Sec. ??), or obtained from simulations. Deviations from pure Hamiltonian motion occur due to synchrotron radiation damping (Sec. ??) in lepton or very high energy hadron rings, parameter variations, and diffusion processes such as residual gas and intrabeam scattering. The time scale of the non-Hamiltonian process determines the applicability of the Hamiltonian analysis. Transverse nonlinearities are introduced through sextupoles or higher order multipoles and magnetic field errors in dipoles and quadrupoles. Sextupoles can already drive all resonances. The beam-beam interaction and space charge also introduce nonlinear fields. Intentionally introduced nonlinearities are used to extract beam on a resonance or through capture in stable islands. Localization and minimization of nonlinearities in a ring is a general strategy to decrease emittance growth
Nonlinearity effects on the directed momentum current.
Zhao, Wen-Lei; Fu, Li-Bin; Liu, Jie
2014-08-01
We investigate the quantum transport dynamics governed by the nonlinear Schrödinger equation with a periodically-δ-kicking potential and discover the emergence of a directed current in momentum space. With the increase of nonlinearity, we find strikingly that the momentum current decreases, reverses, and finally vanishes, indicating that the quantum transport can be effectively manipulated through adjusting the nonlinearity. The underlying dynamic mechanism is uncovered and some important implications are addressed.
Nonlinear Real-Time Optical Signal Processing.
1981-06-30
bandwidth and space-bandwidth products. Real-time homonorphic and loga- rithmic filtering by halftone nonlinear processing has been achieved. A...Page ABSTRACT 1 1. RESEARCH OBJECTIVES AND PROGRESS 3 I-- 1.1 Introduction and Project overview 3 1.2 Halftone Processing 9 1.3 Direct Nonlinear...time homomorphic and logarithmic filtering by halftone nonlinear processing has been achieved. A detailed analysis of degradation due to the finite gamma
NASA Astrophysics Data System (ADS)
Kawata, Y.; Niki, N.; Ohmatsu, H.; Aokage, K.; Kusumoto, M.; Tsuchida, T.; Eguchi, K.; Kaneko, M.
2015-03-01
Advantages of CT scanners with high resolution have allowed the improved detection of lung cancers. In the recent release of positive results from the National Lung Screening Trial (NLST) in the US showing that CT screening does in fact have a positive impact on the reduction of lung cancer related mortality. While this study does show the efficacy of CT based screening, physicians often face the problems of deciding appropriate management strategies for maximizing patient survival and for preserving lung function. Several key manifold-learning approaches efficiently reveal intrinsic low-dimensional structures latent in high-dimensional data spaces. This study was performed to investigate whether the dimensionality reduction can identify embedded structures from the CT histogram feature of non-small-cell lung cancer (NSCLC) space to improve the performance in predicting the likelihood of RFS for patients with NSCLC.
Interior Tomography With Continuous Singular Value Decomposition
Jin, Xin; Katsevich, Alexander; Yu, Hengyong; Wang, Ge; Li, Liang; Chen, Zhiqiang
2013-01-01
The long-standing interior problem has important mathematical and practical implications. The recently developed interior tomography methods have produced encouraging results. A particular scenario for theoretically exact interior reconstruction from truncated projections is that there is a known subregion in the region of interest (ROI). In this paper, we improve a novel continuous singular value decomposition (SVD) method for interior reconstruction assuming a known subregion. First, two sets of orthogonal eigen-functions are calculated for the Hilbert and image spaces respectively. Then, after the interior Hilbert data are calculated from projection data through the ROI, they are projected onto the eigen-functions in the Hilbert space, and an interior image is recovered by a linear combination of the eigen-functions with the resulting coefficients. Finally, the interior image is compensated for the ambiguity due to the null space utilizing the prior subregion knowledge. Experiments with simulated and real data demonstrate the advantages of our approach relative to the projection onto convex set type interior reconstructions. PMID:22907966
Maharaj, S. K.; Bharuthram, R.; Singh, S. V.; Lakhina, G. S.
2012-07-15
Using the Sagdeev pseudopotential technique, the existence of large amplitude ion-acoustic solitons is investigated for a plasma composed of ions, and hot and cool electrons. Not only are all species treated as adiabatic fluids but the model for which inertial effects of the hot electrons is neglected whilst retaining inertia and pressure for the ions and cool electrons has also been considered. The focus of this investigation has been on identifying the admissible Mach number ranges for large amplitude nonlinear ion-acoustic soliton structures. The lower Mach number limit yields a minimum velocity for the existence of ion-acoustic solitons. The upper Mach number limit for positive potential solitons is found to coincide with the limiting value of the potential (positive) beyond which the ion number density ceases to be real valued, and ion-acoustic solitons can no longer exist. Small amplitude solitons having negative potentials are found to be supported when the temperature of the cool electrons is negligible.
Nonlinear waves: Dynamics and evolution
NASA Astrophysics Data System (ADS)
Gaponov-Grekhov, A. V.; Rabinovich, M. I.
Papers on nonlinear waves are presented, covering topics such as the history of studies on nonlinear dynamics since Poincare, attractors, pattern formation and the dynamics of two-dimensional structures in nonequilibirum dissipative media, the onset of spatial chaos in one-dimensional systems, and self-organization phenomena in laser thermochemistry. Additional topics include criteria for the existence of moving structures in two-component reaction-diffusion systems, space-time structures in optoelectronic devices, stimulated scattering and surface structures, and distributed wave collapse in the nonlinear Schroedinger equation. Consideration is also given to dimensions and entropies in multidimensional systems, measurement methods for correlation dimensions, quantum localization and dynamic chaos, self-organization in bacterial cells and populations, nonlinear phenomena in condensed matter, and the origin and evolutionary dynamics of Uranian rings.
Improved nonlinear prediction method
NASA Astrophysics Data System (ADS)
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
Investigating hydrogel dosimeter decomposition by chemical methods
NASA Astrophysics Data System (ADS)
Jordan, Kevin
2015-01-01
The chemical oxidative decomposition of leucocrystal violet micelle hydrogel dosimeters was investigated using the reaction of ferrous ions with hydrogen peroxide or sodium bicarbonate with hydrogen peroxide. The second reaction is more effective at dye decomposition in gelatin hydrogels. Additional chemical analysis is required to determine the decomposition products.
A domain decomposition scheme for Eulerian shock physics codes
Bell, R.L.; Hertel, E.S. Jr.
1994-08-01
A new algorithm which allows for complex domain decomposition in Eulerian codes was developed at Sandia National Laboratories. This new feature allows a user to customize the zoning for each portion of a calculation and to refine volumes of the computational space of particular interest This option is available in one, two, and three dimensions. The new technique will be described in detail and several examples of the effectiveness of this technique will also be discussed.
Parallel CE/SE Computations via Domain Decomposition
NASA Technical Reports Server (NTRS)
Himansu, Ananda; Jorgenson, Philip C. E.; Wang, Xiao-Yen; Chang, Sin-Chung
2000-01-01
This paper describes the parallelization strategy and achieved parallel efficiency of an explicit time-marching algorithm for solving conservation laws. The Space-Time Conservation Element and Solution Element (CE/SE) algorithm for solving the 2D and 3D Euler equations is parallelized with the aid of domain decomposition. The parallel efficiency of the resultant algorithm on a Silicon Graphics Origin 2000 parallel computer is checked.
Thermal decomposition and non-isothermal decomposition kinetics of carbamazepine
NASA Astrophysics Data System (ADS)
Qi, Zhen-li; Zhang, Duan-feng; Chen, Fei-xiong; Miao, Jun-yan; Ren, Bao-zeng
2014-12-01
The thermal stability and kinetics of isothermal decomposition of carbamazepine were studied under isothermal conditions by thermogravimetry (TGA) and differential scanning calorimetry (DSC) at three heating rates. Particularly, transformation of crystal forms occurs at 153.75°C. The activation energy of this thermal decomposition process was calculated from the analysis of TG curves by Flynn-Wall-Ozawa, Doyle, distributed activation energy model, Šatava-Šesták and Kissinger methods. There were two different stages of thermal decomposition process. For the first stage, E and log A [s-1] were determined to be 42.51 kJ mol-1 and 3.45, respectively. In the second stage, E and log A [s-1] were 47.75 kJ mol-1 and 3.80. The mechanism of thermal decomposition was Avrami-Erofeev (the reaction order, n = 1/3), with integral form G(α) = [-ln(1 - α)]1/3 (α = ˜0.1-0.8) in the first stage and Avrami-Erofeev (the reaction order, n = 1) with integral form G(α) = -ln(1 - α) (α = ˜0.9-0.99) in the second stage. Moreover, Δ H ≠, Δ S ≠, Δ G ≠ values were 37.84 kJ mol-1, -192.41 J mol-1 K-1, 146.32 kJ mol-1 and 42.68 kJ mol-1, -186.41 J mol-1 K-1, 156.26 kJ mol-1 for the first and second stage, respectively.
Bahadur Zada, Mian; Sarwar, Muhammad; Radenović, Stojan
2017-01-01
In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], u, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], are real-valued measurable functions both in s and r on [Formula: see text].
NASA Astrophysics Data System (ADS)
Pratt, Michael A.; Chu, Henry
2016-05-01
Performance of healthcare providers such as hospitals varies from one locale to another. Our goal is to study whether there is a geographical pattern of performance using metrics reported from over 3,000 hospitals distributed across the U.S. Empirical mode decomposition (EMD) is an effective analysis tool for nonlinear and non-stationary signals. It decomposes a data sequence into a series of intrinsic mode functions (IMFs) along with a residue sequence that represents the trend. Each IMF has zero local mean and has exactly one zero crossing between any two consecutive local extrema. An IMF can be used to assess the instantaneous frequency. Reconstruction of a signal using the residue and those IMFs of the lower frequency can reveal the underlying pattern of the signal without undue influence of the higher frequency fluctuations of the data. We used a space-filling curve to turn a set of performance metrics distributed irregularly across the two-dimensional planar surface into a one-dimensional sequence. The EMD decomposed a set of hospital emergency department median waiting times into 9 IMFs along with a residue. We used the residue and the lower frequency IMFs to reconstruct a sequence with fewer fluctuations. The sequence was transformed back to a two-dimensional map to reveal the geographical variations.
Anisotropic decomposition of energetic materials
Pravica, Michael; Quine, Zachary; Romano, Edward; Bajar, Sean; Yulga, Brian; Yang Wenge; Hooks, Daniel
2007-12-12
Using a white x-ray synchrotron beam, we have dynamically studied radiation-induced decomposition in single crystalline PETN and TATB. By monitoring the integrated intensity of selected diffraction spots via a CCD x-ray camera as a function of time, we have found that the decomposition rate varies dramatically depending upon the orientation of the crystalline axes relative to polarized x-ray beam and for differing diffracting conditions (spots) within the same crystalline orientation. We suggest that this effect is due to Compton scattering of the polarized x-rays with electron clouds that is dependent upon their relative orientation. This novel effect may yield valuable insight regarding anisotropic detonation sensitivity in energetic materials such as PETN.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Nonlinear instability and chaos in plasma wave-wave interactions, I., Introduction
Kueny, C.S.; Morrison, P.J.
1994-11-01
Conventional linear stability analyses may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper [submitted to Physics of Plasmas], this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various (integrable) systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper.
Aflatoxin decomposition in various soils
Angle, J.S.
1986-08-01
The persistence of aflatoxin in the soil environment could potentially result in a number of adverse environmental consequences. To determine the persistence of aflatoxin in soil, /sup 14/C-labeled aflatoxin B1, was added to silt loam, sandy loam, and silty clay loam soils and the subsequent release of /sup 14/CO/sub 2/ was determined. After 120 days of incubation, 8.1% of the original aflatoxin added to the silt loam soil was released as CO/sub 2/. Aflatoxin decomposition in the sandy loam soil proceeded more quickly than the other two soils for the first 20 days of incubation. After this time, the decomposition rate declined and by the end of the study, 4.9% of the aflatoxin was released as CO/sub 2/. Aflatoxin decomposition proceeded most slowly in the silty clay loam soil. Only 1.4% of aflatoxin added to the soil was released as CO/sub 2/ after 120 days incubation. To determine whether aflatoxin was bound to the silty clay loam soil, aflatoxin B1 was added to this soil and incubated for 20 days. The soil was periodically extracted and the aflatoxin species present were determined using thin layer chromatographic (TLC) procedures. After one day of incubation, the degradation products, aflatoxins B2 and G2, were observed. It was also found that much of the aflatoxin extracted from the soil was not mobile with the TLC solvent system used. This indicated that a conjugate may have formed and thus may be responsible for the lack of aflatoxin decomposition.
NASA Astrophysics Data System (ADS)
Silambarasan, A.; Krishna Kumar, M.; Thirunavukkarasu, A.; Mohan Kumar, R.; Umarani, P. R.
2015-01-01
An organic nonlinear optical bulk single crystal, Ammonium 3-carboxy-4-hydroxy benzenesulfonate monohydrate (ACHBS) was successfully grown by solution growth technique. Single crystal X-ray diffraction study confirms that, the grown crystal belongs to P21/c space group. Powder X-ray diffraction and high resolution X-ray diffraction analyses revealed the crystallinity of the grown crystal. Infrared spectral analysis showed the vibrational behavior of chemical bonds and its functional groups. The thermal stability and decomposition stages of the grown crystal were studied by TG-DTA analysis. UV-Visible transmittance studies showed the transparency region and cut-off wavelength of the grown crystal. The third-order nonlinear optical susceptibility of the grown crystal was estimated by Z-scan technique using Hesbnd Ne laser source. The mechanical property of the grown crystal was studied by using Vicker's microhardness test.
Phlogopite Decomposition, Water, and Venus
NASA Technical Reports Server (NTRS)
Johnson, N. M.; Fegley, B., Jr.
2005-01-01
Venus is a hot and dry planet with a surface temperature of 660 to 740 K and 30 parts per million by volume (ppmv) water vapor in its lower atmosphere. In contrast Earth has an average surface temperature of 288 K and 1-4% water vapor in its troposphere. The hot and dry conditions on Venus led many to speculate that hydrous minerals on the surface of Venus would not be there today even though they might have formed in a potentially wetter past. Thermodynamic calculations predict that many hydrous minerals are unstable under current Venusian conditions. Thermodynamics predicts whether a particular mineral is stable or not, but we need experimental data on the decomposition rate of hydrous minerals to determine if they survive on Venus today. Previously, we determined the decomposition rate of the amphibole tremolite, and found that it could exist for billions of years at current surface conditions. Here, we present our initial results on the decomposition of phlogopite mica, another common hydrous mineral on Earth.
Methanethiol decomposition on Ni(100)
Castro, M.E.; Ahkter, S.; Golchet, A.; White, J.M. ); Sahin, T. )
1991-01-01
Static secondary ion mass spectroscopy (SSIMS), temperature programmed desorption (TPD), and Auger electron spectroscopy (AES) were used under ultrahigh vacuum conditions to study the decomposition of CH{sub 3}SH on Ni(100). Only methane, hydrogen, and the parent molecule are observed in TPD. Complete decomposition to C(a), S(a) and desorbing H{sub 2} is the preferred reaction pathway for low exposures, while desorption of methane is observed at higher coverages. Preadsorbed hydrogen promoted methane desorption. Upon adsorption, and for low coverages, SSIMS evidence indicates S-H bond cleavage into CH{sub 3}S and surface hydrogen. S-H bond cleavage is inhibited for high coverages. The TP-SSIMS data are consistent with an activated C-S bond cleavage in CH{sub 3}S, with an activation energy of 8.81 kcal/mol and preexponential factor of 10{sup 6.5}s{sup {minus}1}. The low preexponential factor is taken as indicating a complex decomposition pathway. A mechanism consistent with the observed data is discussed.
Mostafanezhad, Isar; Boric-Lubecke, Olga; Lubecke, Victor; Mandic, Danilo P
2009-01-01
Empirical Mode Decomposition has been shown effective in the analysis of non-stationary and non-linear signals. As an application in wireless life signs monitoring in this paper we use this method in conditioning the signals obtained from the Doppler device. Random physical movements, fidgeting, of the human subject during a measurement can fall on the same frequency of the heart or respiration rate and interfere with the measurement. It will be shown how Empirical Mode Decomposition can break the radar signal down into its components and help separate and remove the fidgeting interference.
NASA Astrophysics Data System (ADS)
Lai, Xian-Jing; Cai, Xiao-Ou
2010-09-01
In this paper, the decomposition method is implemented for solving the bidirectional Sawada- Kotera (bSK) equation with two kinds of initial conditions. As a result, the Adomian polynomials have been calculated and the approximate and exact solutions of the bSK equation are obtained by means of Maple, such as solitary wave solutions, doubly-periodic solutions, two-soliton solutions. Moreover, we compare the approximate solution with the exact solution in a table and analyze the absolute error and the relative error. The results reported in this article provide further evidence of the usefulness of the Adomian decomposition method for obtaining solutions of nonlinear problems
Algebraic Davis Decomposition and Asymmetric Doob Inequalities
NASA Astrophysics Data System (ADS)
Hong, Guixiang; Junge, Marius; Parcet, Javier
2016-09-01
In this paper we investigate asymmetric forms of Doob maximal inequality. The asymmetry is imposed by noncommutativity. Let {({M}, τ)} be a noncommutative probability space equipped with a filtration of von Neumann subalgebras {({M}_n)_{n ≥ 1}}, whose union {bigcup_{n≥1}{M}_n} is weak-* dense in {{M}}. Let {{E}_n} denote the corresponding family of conditional expectations. As an illustration for an asymmetric result, we prove that for {1 < p < 2} and {x in L_p({M},τ)} one can find {a, b in L_p({M},τ)} and contractions {u_n, v_n in {M}} such that {E}_n(x) = a u_n + v_n b quad and quad max big{ |a|_p,|b|_p big} ≤ c_p |x|_p. Moreover, it turns out that {a u_n} and {v_n b} converge in the row/column Hardy spaces {{H}_p^r({M})} and {{H}_p^c({M})} respectively. In particular, this solves a problem posed by the Defant and Junge in 2004. In the case p = 1, our results establish a noncommutative form of the Davis celebrated theorem on the relation betwe en martingale maximal and square functions in L 1, whose noncommutative form has remained open for quite some time. Given {1 ≤ p ≤ 2}, we also provide new weak type maximal estimates, which imply in turn left/right almost uniform convergence of {{E}_n(x)} in row/column Hardy spaces. This improves the bilateral convergence known so far. Our approach is based on new forms of Davis martingale decomposition which are of independent interest, and an algebraic atomic description for the involved Hardy spaces. The latter results are new even for commutative von Neumann algebras.
Limited-memory adaptive snapshot selection for proper orthogonal decomposition
Oxberry, Geoffrey M.; Kostova-Vassilevska, Tanya; Arrighi, Bill; Chand, Kyle
2015-04-02
Reduced order models are useful for accelerating simulations in many-query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floating-point operation costs in high-performance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive time-stepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decomposition-based reduced order models, and memory usage is minimized by computing the singular value decomposition using a single-pass incremental algorithm. Results for a viscous Burgers’ test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full order model is recovered to within discretization error. The resulting method can be used on supercomputers to generate proper orthogonal decomposition-based reduced order models, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space.
Postmortem imaging: MDCT features of postmortem change and decomposition.
Levy, Angela D; Harcke, Howard Theodore; Mallak, Craig T
2010-03-01
Multidetector computed tomography (MDCT) has emerged as an effective imaging technique to augment forensic autopsy. Postmortem change and decomposition are always present at autopsy and on postmortem MDCT because they begin to occur immediately upon death. Consequently, postmortem change and decomposition on postmortem MDCT should be recognized and not mistaken for a pathologic process or injury. Livor mortis increases the attenuation of vasculature and dependent tissues on MDCT. It may also produce a hematocrit effect with fluid levels in the large caliber blood vessels and cardiac chambers from dependent layering erythrocytes. Rigor mortis and algor mortis have no specific MDCT features. In contrast, decomposition through autolysis, putrefaction, and insect and animal predation produce dramatic alterations in the appearance of the body on MDCT. Autolysis alters the attenuation of organs. The most dramatic autolytic changes on MDCT are seen in the brain where cerebral sulci and ventricles are effaced and gray-white matter differentiation is lost almost immediately after death. Putrefaction produces a pattern of gas that begins with intravascular gas and proceeds to gaseous distension of all anatomic spaces, organs, and soft tissues. Knowledge of the spectrum of postmortem change and decomposition is an important component of postmortem MDCT interpretation.
Two-body scattering without angular-momentum decomposition
Rodriguez-Gallardo, M.; Deltuva, A.; Cravo, E.; Fonseca, A. C.; Crespo, R.
2008-09-15
Two-body scattering is studied by solving the Lippmann-Schwinger equation in momentum space without angular-momentum decomposition for a local spin-dependent short-range interaction plus Coulomb. The screening and renormalization approach is employed to treat the Coulomb interaction. Benchmark calculations are performed by comparing our procedure with partial-wave calculations in configuration space for p-{sup 10}Be,p-{sup 16}O, and {sup 12}C-{sup 10}Be elastic scattering, using a simple optical potential model.
EEMD Independent Extraction for Mixing Features of Rotating Machinery Reconstructed in Phase Space
Ma, Zaichao; Wen, Guangrui; Jiang, Cheng
2015-01-01
Empirical Mode Decomposition (EMD), due to its adaptive decomposition property for the non-linear and non-stationary signals, has been widely used in vibration analyses for rotating machinery. However, EMD suffers from mode mixing, which is difficult to extract features independently. Although the improved EMD, well known as the ensemble EMD (EEMD), has been proposed, mode mixing is alleviated only to a certain degree. Moreover, EEMD needs to determine the amplitude of added noise. In this paper, we propose Phase Space Ensemble Empirical Mode Decomposition (PSEEMD) integrating Phase Space Reconstruction (PSR) and Manifold Learning (ML) for modifying EEMD. We also provide the principle and detailed procedure of PSEEMD, and the analyses on a simulation signal and an actual vibration signal derived from a rubbing rotor are performed. The results show that PSEEMD is more efficient and convenient than EEMD in extracting the mixing features from the investigated signal and in optimizing the amplitude of the necessary added noise. Additionally PSEEMD can extract the weak features interfered with a certain amount of noise. PMID:25871723
The helical decomposition and the instability assumption
NASA Technical Reports Server (NTRS)
Waleffe, Fabian A.
1993-01-01
Direct numerical simulations show that the triadic transfer function T(k,p,q) peaks sharply when q (or p) is much smaller than k. The triadic transfer function T(k,p,q) gives the rate of energy input into wave number k from all interactions with modes of wave number p and q, where k, p, q form a triangle. This observation was thought to suggest that energy is cascaded downscale through non-local interactions with local transfer and that there was a strong connection between large and small scales. Both suggestions were in contradiction with the classical Kolmogorov picture of the energy cascade. The helical decomposition was found useful in distinguishing between kinematically independent interactions. That analysis has gone beyond the question of non-local interaction with local transfer. In particular, an assumption about the statistical direction of triadic energy transfer in any kinematically independent interaction was introduced (the instability assumption). That assumption is not necessary for the conclusions about non-local interactions with local transfer recalled above. In the case of turbulence under rapid rotation, the instability assumption leads to the prediction that energy is transferred in spectral space from the poles of the rotation axis toward the equator. The instability assumption is thought to be of general validity for any type of triad interactions (e.g. internal waves). The helical decomposition and the instability assumption offer detailed information about the homogeneous statistical dynamics of the Navier-Stokes equations. The objective was to explore the validity of the instability assumption and to study the contributions of the various types of helical interactions to the energy cascade and the subgrid-scale eddy-viscosity. This was done in the context of spectral closures of the Direct Interaction or Quasi-Normal type.
Iterative filtering decomposition based on local spectral evolution kernel
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-01-01
The synthesizing information, achieving understanding, and deriving insight from increasingly massive, time-varying, noisy and possibly conflicting data sets are some of most challenging tasks in the present information age. Traditional technologies, such as Fourier transform and wavelet multi-resolution analysis, are inadequate to handle all of the above-mentioned tasks. The empirical model decomposition (EMD) has emerged as a new powerful tool for resolving many challenging problems in data processing and analysis. Recently, an iterative filtering decomposition (IFD) has been introduced to address the stability and efficiency problems of the EMD. Another data analysis technique is the local spectral evolution kernel (LSEK), which provides a near prefect low pass filter with desirable time-frequency localizations. The present work utilizes the LSEK to further stabilize the IFD, and offers an efficient, flexible and robust scheme for information extraction, complexity reduction, and signal and image understanding. The performance of the present LSEK based IFD is intensively validated over a wide range of data processing tasks, including mode decomposition, analysis of time-varying data, information extraction from nonlinear dynamic systems, etc. The utility, robustness and usefulness of the proposed LESK based IFD are demonstrated via a large number of applications, such as the analysis of stock market data, the decomposition of ocean wave magnitudes, the understanding of physiologic signals and information recovery from noisy images. The performance of the proposed method is compared with that of existing methods in the literature. Our results indicate that the LSEK based IFD improves both the efficiency and the stability of conventional EMD algorithms. PMID:22350559
Kac-Moody algebra and nonlinear sigma model
NASA Astrophysics Data System (ADS)
Ogura, Waichi; Hosoya, Akio
1985-12-01
We investigate the nonlinear sigma model over an arbitrary homogeneous space. Then it is shown that the sigma model realizes the Kac-Moody algebra as current algebra only if the homogeneous space is restricted to the group manifold.
Application of the Nonlinear Vector Product to Lorentz Transformations.
ERIC Educational Resources Information Center
Farach, Horacio A.; And Others
1979-01-01
Shows that the nonlinear vector product developed by the author in a previous paper to treat successive space rotations can be employed to treat the space time rotations of special relativity in which the angle of rotation is imaginary. (HM)
Methodology for nonlinear quantification of a flexible beam with a local, strong nonlinearity
NASA Astrophysics Data System (ADS)
Herrera, Christopher A.; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2017-02-01
This study presents a methodology for nonlinear quantification, i.e., the identification of the linear and nonlinear regimes and estimation of the degree of nonlinearity, for a cantilever beam with a local, strongly nonlinear stiffness element. The interesting feature of this system is that it behaves linearly in the limits of extreme values of the nonlinear stiffness. An Euler-Bernoulli cantilever beam with two nonlinear configurations is used to develop and demonstrate the methodology. One configuration considers a cubic spring attached at a distance from the beam root to achieve a smooth nonlinear effect. The other configuration considers a vibro-impact element that generates non-smooth effects. Both systems have the property that, in the limit of small and large values of a configuration parameter, the system is almost linear and can be modeled as such with negligible error. For the beam with a cubic spring attachment, the forcing amplitude is the varied parameter, while for the vibro-impact beam, this parameter is the clearance between the very stiff stops and the beam at static equilibrium. Proper orthogonal decomposition is employed to obtain an optimal orthogonal basis used to describe the nonlinear system dynamics for varying parameter values. The frequencies of the modes that compose the basis are then estimated using the Rayleigh quotient. The variations of these frequencies are studied to identify parameter values for which the system behaves approximately linearly and those for which the dynamical response is highly nonlinear. Moreover, a criterion based on the Betti-Maxwell reciprocity theorem is used to verify the existence of nonlinear behavior for the set of parameter values suggested by the described methodology. The developed methodology is general and applicable to discrete or continuous systems with smooth or nonsmooth nonlinearities.
Edge detection by nonlinear dynamics
Wong, Yiu-fai
1994-07-01
We demonstrate how the formulation of a nonlinear scale-space filter can be used for edge detection and junction analysis. By casting edge-preserving filtering in terms of maximizing information content subject to an average cost function, the computed cost at each pixel location becomes a local measure of edgeness. This computation depends on a single scale parameter and the given image data. Unlike previous approaches which require careful tuning of the filter kernels for various types of edges, our scheme is general enough to be able to handle different edges, such as lines, step-edges, corners and junctions. Anisotropy in the data is handled automatically by the nonlinear dynamics.
Domain Decomposition Methods for Problems in H(curl)
NASA Astrophysics Data System (ADS)
Calvo, Juan Gabriel
Two domain decomposition methods for solving vector field problems posed in H(curl) and discretized with Nedelec finite elements are considered. These finite elements are conforming in H(curl). A two-level overlapping Schwarz algorithm in two dimensions is analyzed, where the subdomains are only assumed to be uniform in the sense of Peter Jones. The coarse space is based on energy minimization and its dimension equals the number of interior subdomain edges. Local direct solvers are based on the overlapping subdomains. The bound for the condition number depends only on a few geometric parameters of the decomposition. This bound is independent of jumps in the coefficients across the interface between the subdomains for most of the different cases considered. A bound is also obtained for the condition number of a balancing domain decomposition by constraints (BDDC) algorithm in two dimensions, with Jones subdomains. For the primal variable space, a continuity constraint for the tangential average over each interior subdomain edge is imposed. For the averaging operator, a new technique named deluxe scaling is used. The optimal bound is independent of jumps in the coefficients across the interface between the subdomains. Furthermore, a new coarse function for problems in three dimensions is introduced, with only one degree of freedom per subdomain edge. In all the cases, it is established that the algorithms are scalable. Numerical results that verify the results are provided, including some with subdomains with fractal edges and others obtained by a mesh partitioner.
Non-linear system identification in flow-induced vibration
Spanos, P.D.; Zeldin, B.A.; Lu, R.
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
An Algorithm for image removals and decompositions without inverse matrices
NASA Astrophysics Data System (ADS)
Yi, Dokkyun
2009-03-01
Partial Differential Equation (PDE) based methods in image processing have been actively studied in the past few years. One of the effective methods is the method based on a total variation introduced by Rudin, Oshera and Fatemi (ROF) [L.I. Rudin, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D 60 (1992) 259-268]. This method is a well known edge preserving model and an useful tool for image removals and decompositions. Unfortunately, this method has a nonlinear term in the equation which may yield an inaccurate numerical solution. To overcome the nonlinearity, a fixed point iteration method has been widely used. The nonlinear system based on the total variation is induced from the ROF model and the fixed point iteration method to solve the ROF model is introduced by Dobson and Vogel [D.C. Dobson, C.R. Vogel, Convergence of an iterative method for total variation denoising, SIAM J. Numer. Anal. 34 (5) (1997) 1779-1791]. However, some methods had to compute inverse matrices which led to roundoff error. To address this problem, we developed an efficient method for solving the ROF model. We make a sequence like Richardson's method by using a fixed point iteration to evade the nonlinear equation. This approach does not require the computation of inverse matrices. The main idea is to make a direction vector for reducing the error at each iteration step. In other words, we make the next iteration to reduce the error from the computed error and the direction vector. We describe that our method works well in theory. In numerical experiments, we show the results of the proposed method and compare them with the results by D. Dobson and C. Vogel and then we confirm the superiority of our method.
Decomposition Rate and Pattern in Hanging Pigs.
Lynch-Aird, Jeanne; Moffatt, Colin; Simmons, Tal
2015-09-01
Accurate prediction of the postmortem interval requires an understanding of the decomposition process and the factors acting upon it. A controlled experiment, over 60 days at an outdoor site in the northwest of England, used 20 freshly killed pigs (Sus scrofa) as human analogues to study decomposition rate and pattern. Ten pigs were hung off the ground and ten placed on the surface. Observed differences in the decomposition pattern required a new decomposition scoring scale to be produced for the hanging pigs to enable comparisons with the surface pigs. The difference in the rate of decomposition between hanging and surface pigs was statistically significant (p=0.001). Hanging pigs reached advanced decomposition stages sooner, but lagged behind during the early stages. This delay is believed to result from lower variety and quantity of insects, due to restricted beetle access to the aerial carcass, and/or writhing maggots falling from the carcass.
New Nonlinear Multigrid Analysis
NASA Technical Reports Server (NTRS)
Xie, Dexuan
1996-01-01
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
Conductimetric determination of decomposition of silicate melts
NASA Technical Reports Server (NTRS)
Kroeger, C.; Lieck, K.
1986-01-01
A description of a procedure is given to detect decomposition of silicate systems in the liquid state by conductivity measurements. Onset of decomposition can be determined from the temperature curves of resistances measured on two pairs of electrodes, one above the other. Degree of decomposition can be estimated from temperature and concentration dependency of conductivity of phase boundaries. This procedure was tested with systems PbO-B2O3 and PbO-B2O3-SiO2.
Measurement System for Energetic Materials Decomposition
2015-01-05
Measurement System for Energetic Materials Decomposition This DURIP grant was used to purchase: 1. Q600 SDT Simultaneous DSC-TGA 2... Decomposition Report Title This DURIP grant was used to purchase: 1. Q600 SDT Simultaneous DSC-TGA 2. Pfeiffer Vacuum Benchtop Thermostar Mass...Spectrometer 3. Vision Research Phantom V12.1-8G-M high speed camera These instruments have been used to evaluate and study decomposition and
Anatase-brookite mixed phase nano TiO2 catalyzed homolytic decomposition of ammonium nitrate.
Vargeese, Anuj A; Muralidharan, Krishnamurthi
2011-09-15
Compared to the conventional ammonium perchlorate based solid rocket propellants, burning of ammonium nitrate (AN) based propellants produce environmentally innocuous combustion gases. Application of AN as propellant oxidizer is restricted due to low reactivity and low energetics besides its near room temperature polymorphic phase transition. In the present study, anatase-brookite mixed phase TiO(2) nanoparticles (~ 10 nm) are synthesized and used as catalyst to enhance the reactivity of the environmental friendly propellant oxidizer ammonium nitrate. The activation energy required for the decomposition reactions, computed by differential and non-linear integral isoconversional methods are used to establish the catalytic activity. Presumably, the removal of NH(3) and H(2)O, known inhibitors of ammonium nitrate decomposition reaction, due to the surface reactions on active surface of TiO(2) changes the decomposition pathway and thereby the reactivity.
NASA Astrophysics Data System (ADS)
Yang, Lei; Falenty, Andrzej; Chaouachi, Marwen; Haberthür, David; Kuhs, Werner F.
2016-09-01
In-situ synchrotron X-ray computed microtomography with sub-micrometer voxel size was used to study the decomposition of gas hydrates in a sedimentary matrix. Xenon-hydrate was used instead of methane hydrate to enhance the absorption contrast. The microstructural features of the decomposition process were elucidated indicating that the decomposition starts at the hydrate-gas interface; it does not proceed at the contacts with quartz grains. Melt water accumulates at retreating hydrate surface. The decomposition is not homogeneous and the decomposition rates depend on the distance of the hydrate surface to the gas phase indicating a diffusion-limitation of the gas transport through the water phase. Gas is found to be metastably enriched in the water phase with a concentration decreasing away from the hydrate-water interface. The initial decomposition process facilitates redistribution of fluid phases in the pore space and local reformation of gas hydrates. The observations allow also rationalizing earlier conjectures from experiments with low spatial resolutions and suggest that the hydrate-sediment assemblies remain intact until the hydrate spacers between sediment grains finally collapse; possible effects on mechanical stability and permeability are discussed. The resulting time resolved characteristics of gas hydrate decomposition and the influence of melt water on the reaction rate are of importance for a suggested gas recovery from marine sediments by depressurization.
Robust nonlinear variable selective control for networked systems
NASA Astrophysics Data System (ADS)
Rahmani, Behrooz
2016-10-01
This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.
Domain decomposition for a mixed finite element method in three dimensions
Cai, Z.; Parashkevov, R.R.; Russell, T.F.; Wilson, J.D.; Ye, X.
2003-01-01
We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.
Previti, Alberto; Furfaro, Roberto; Picca, Paolo; Ganapol, Barry D; Mostacci, Domiziano
2011-08-01
This paper deals with finding accurate solutions for photon transport problems in highly heterogeneous media fastly, efficiently and with modest memory resources. We propose an extended version of the analytical discrete ordinates method, coupled with domain decomposition-derived algorithms and non-linear convergence acceleration techniques. Numerical performances are evaluated using a challenging case study available in the literature. A study of accuracy versus computational time and memory requirements is reported for transport calculations that are relevant for remote sensing applications.
Decomposition of heterogeneous organic matter and its long-term stabilization in soils
Sierra, C.A.; Harmon, M.E.; Perakis, S.S.
2011-01-01
Soil organic matter is a complex mixture of material with heterogeneous biological, physical, and chemical properties. Decomposition models represent this heterogeneity either as a set of discrete pools with different residence times or as a continuum of qualities. It is unclear though, whether these two different approaches yield comparable predictions of organic matter dynamics. Here, we compare predictions from these two different approaches and propose an intermediate approach to study organic matter decomposition based on concepts from continuous models implemented numerically. We found that the disagreement between discrete and continuous approaches can be considerable depending on the degree of nonlinearity of the model and simulation time. The two approaches can diverge substantially for predicting long-term processes in soils. Based on our alternative approach, which is a modification of the continuous quality theory, we explored the temporal patterns that emerge by treating substrate heterogeneity explicitly. The analysis suggests that the pattern of carbon mineralization over time is highly dependent on the degree and form of nonlinearity in the model, mostly expressed as differences in microbial growth and efficiency for different substrates. Moreover, short-term stabilization and destabilization mechanisms operating simultaneously result in long-term accumulation of carbon characterized by low decomposition rates, independent of the characteristics of the incoming litter. We show that representation of heterogeneity in the decomposition process can lead to substantial improvements in our understanding of carbon mineralization and its long-term stability in soils. ?? 2011 by the Ecological Society of America.
Decomposition of heterogeneous organic matterand its long-term stabilization in soils
Sierra, Carlos A.; Harmon, Mark E.; Perakis, Steven S.
2011-01-01
Soil organic matter is a complex mixture of material with heterogeneous biological, physical, and chemical properties. Decomposition models represent this heterogeneity either as a set of discrete pools with different residence times or as a continuum of qualities. It is unclear though, whether these two different approaches yield comparable predictions of organic matter dynamics. Here, we compare predictions from these two different approaches and propose an intermediate approach to study organic matter decomposition based on concepts from continuous models implemented numerically. We found that the disagreement between discrete and continuous approaches can be considerable depending on the degree of nonlinearity of the model and simulation time. The two approaches can diverge substantially for predicting long-term processes in soils. Based on our alternative approach, which is a modification of the continuous quality theory, we explored the temporal patterns that emerge by treating substrate heterogeneity explicitly. The analysis suggests that the pattern of carbon mineralization over time is highly dependent on the degree and form of nonlinearity in the model, mostly expressed as differences in microbial growth and efficiency for different substrates. Moreover, short-term stabilization and destabilization mechanisms operating simultaneously result in long-term accumulation of carbon characterized by low decomposition rates, independent of the characteristics of the incoming litter. We show that representation of heterogeneity in the decomposition process can lead to substantial improvements in our understanding of carbon mineralization and its long-term stability in soils.
Fano resonances in the nonlinear optical response of coupled plasmonic nanostructures.
Butet, Jérémy; Martin, Olivier J F
2014-12-01
The coupling between metallic nanostructures is a common and easy way to control the optical properties of plasmonic systems. Even though the coupling between plasmonic oscillators has been widely studied in the linear regime, its influence on the nonlinear optical response of metallic nanostructures has been sparsely considered. Using a surface integral equation method, we investigate the second order nonlinear optical response of plasmonic metamolecules supporting Fano resonances revealing that the typical lineshape of Fano resonances is also clearly observable in the nonlinear regime. The physical mechanisms leading to nonlinear Fano resonances are revealed by the coupled oscillator model and the symmetry subgroup decomposition. It is found that the origin of the nonlinear scattered wave, i. e. the active plasmonic oscillator, can be selectively chosen. Furthermore, interferences between nonlinear emissions are clearly observed in specific configurations. The results presented in this article pave the way for the design of efficient nonlinear plasmonic metamolecules with controlled nonlinear radiation.
Compressed sensing MRI exploiting complementary dual decomposition.
Park, Suhyung; Park, Jaeseok
2014-04-01
Compressed sensing (CS) MRI exploits the sparsity of an image in a transform domain to reconstruct the image from incoherently under-sampled k-space data. However, it has been shown that CS suffers particularly from loss of low-contrast image features with increasing reduction factors. To retain image details in such degraded experimental conditions, in this work we introduce a novel CS reconstruction method exploiting feature-based complementary dual decomposition with joint estimation of local scale mixture (LSM) model and images. Images are decomposed into dual block sparse components: total variation for piecewise smooth parts and wavelets for residuals. The LSM model parameters of residuals in the wavelet domain are estimated and then employed as a regional constraint in spatially adaptive reconstruction of high frequency subbands to restore image details missing in piecewise smooth parts. Alternating minimization of the dual image components subject to data consistency is performed to extract image details from residuals and add them back to their complementary counterparts while the LSM model parameters and images are jointly estimated in a sequential fashion. Simulations and experiments demonstrate the superior performance of the proposed method in preserving low-contrast image features even at high reduction factors.
Quasiparticle Representation of Coherent Nonlinear Optical Signals of Multiexcitons
NASA Astrophysics Data System (ADS)
Fingerhut, Benjamin; Bennet, Kochise; Roslyak, Oleksiy; Mukamel, Shaul
2013-03-01
Elementary excitations of many-Fermion systems can be described within the quasiparticle approach which is widely used in the calculation of transport and optical properties of metals, semiconductors, molecular aggregates and strongly correlated quantum materials. The excitations are then viewed as independent harmonic oscillators where the many-body interactions between the oscillators are mapped into anharmonicities. We present a Green's function approach based on coboson algebra for calculating nonlinear optical signals and apply it onwards the study of two and three exciton states. The method only requires the diagonalization of the single exciton manifold and avoids equations of motion of multi-exciton manifolds. Using coboson algebra many body effects are recast in terms of tetradic exciton-exciton interactions: Coulomb scattering and Pauli exchange. The physical space of Fermions is recovered by singular-value decomposition of the over-complete coboson basis set. The approach is used to calculate third and fifth order quantum coherence optical signals that directly probe correlations in two- and three exciton states and their projections on the two and single exciton manifold.
Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick.
Kwak, Nojun
2016-05-20
Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.
Nonlinear model reduction of unconfined groundwater flow using POD and DEIM
NASA Astrophysics Data System (ADS)
Stanko, Zachary P.; Boyce, Scott E.; Yeh, William W.-G.
2016-11-01
Nonlinear groundwater flow models have the propensity to be overly complex leading to burdensome computational demands. Reduced modeling techniques are used to develop an approximation of the original model that has smaller dimensionality and faster run times. The reduced model proposed is a combination of proper orthogonal decomposition (POD) and the discrete empirical interpolation method (DEIM). Solutions of the full model (snapshots) are collected to represent the physical dynamics of the system and Galerkin projection allows the formulation of a reduced model that lies in a subspace of the full model. Interpolation points are added through DEIM to eliminate the reduced model's dependence on the dimension of the full model. POD is shown to effectively reduce the dimension of the full model and DEIM is shown to speed up the solution by further reducing the dimension of the nonlinear calculations. To show the concept can work for unconfined groundwater flow model, with added nonlinear forcings, one-dimensional and two-dimensional test cases are constructed in MODFLOW-OWHM. POD and DEIM are added to MODFLOW as a modular package. Comparing the POD and the POD-DEIM reduced models, the experimental results indicate similar reduction in dimension size with additional computation speed up for the added interpolation. The hyper-reduction method presented is effective for models that have fine discretization in space and/or time as well as nonlinearities with respect to the state variable. The dual reduction approach ensures that, once constructed, the reduced model can be solved in an equation system that depends only on reduced dimensions.
Metallo-organic decomposition films
NASA Technical Reports Server (NTRS)
Gallagher, B. D.
1985-01-01
A summary of metallo-organic deposition (MOD) films for solar cells was presented. The MOD materials are metal ions compounded with organic radicals. The technology is evolving quickly for solar cell metallization. Silver compounds, especially silver neodecanoate, were developed which can be applied by thick-film screening, ink-jet printing, spin-on, spray, or dip methods. Some of the advantages of MOD are: high uniform metal content, lower firing temperatures, decomposition without leaving a carbon deposit or toxic materials, and a film that is stable under ambient conditions. Molecular design criteria were explained along with compounds formulated to date, and the accompanying reactions for these compounds. Phase stability and the other experimental and analytic results of MOD films were presented.
Sampling Stoichiometry: The Decomposition of Hydrogen Peroxide.
ERIC Educational Resources Information Center
Clift, Philip A.
1992-01-01
Describes a demonstration of the decomposition of hydrogen peroxide to provide an interesting, quantitative illustration of the stoichiometric relationship between the decomposition of hydrogen peroxide and the formation of oxygen gas. This 10-minute demonstration uses ordinary hydrogen peroxide and yeast that can be purchased in a supermarket.…
9 CFR 354.131 - Decomposition.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 9 Animals and Animal Products 2 2011-01-01 2011-01-01 false Decomposition. 354.131 Section 354.131 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... Carcasses and Parts § 354.131 Decomposition. Carcasses of rabbits deleteriously affected by...
9 CFR 354.131 - Decomposition.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 9 Animals and Animal Products 2 2014-01-01 2014-01-01 false Decomposition. 354.131 Section 354.131 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... Carcasses and Parts § 354.131 Decomposition. Carcasses of rabbits deleteriously affected by...
Code of Federal Regulations, 2014 CFR
2014-01-01
... 9 Animals and Animal Products 2 2014-01-01 2014-01-01 false Decomposition. 381.93 Section 381.93 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... § 381.93 Decomposition. Carcasses of poultry deleteriously affected by post mortem changes shall...
Code of Federal Regulations, 2012 CFR
2012-01-01
... 9 Animals and Animal Products 2 2012-01-01 2012-01-01 false Decomposition. 381.93 Section 381.93 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... § 381.93 Decomposition. Carcasses of poultry deleteriously affected by post mortem changes shall...
9 CFR 354.131 - Decomposition.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Decomposition. 354.131 Section 354.131 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... Carcasses and Parts § 354.131 Decomposition. Carcasses of rabbits deleteriously affected by...
Chinese Orthographic Decomposition and Logographic Structure
ERIC Educational Resources Information Center
Cheng, Chao-Ming; Lin, Shan-Yuan
2013-01-01
"Chinese orthographic decomposition" refers to a sense of uncertainty about the writing of a well-learned Chinese character following a prolonged inspection of the character. This study investigated the decomposition phenomenon in a test situation in which Chinese characters were repeatedly presented in a word context and assessed…
Code of Federal Regulations, 2011 CFR
2011-01-01
... 9 Animals and Animal Products 2 2011-01-01 2011-01-01 false Decomposition. 381.93 Section 381.93 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... § 381.93 Decomposition. Carcasses of poultry deleteriously affected by post mortem changes shall...
9 CFR 354.131 - Decomposition.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 9 Animals and Animal Products 2 2013-01-01 2013-01-01 false Decomposition. 354.131 Section 354.131 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... Carcasses and Parts § 354.131 Decomposition. Carcasses of rabbits deleteriously affected by...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Decomposition. 381.93 Section 381.93 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... § 381.93 Decomposition. Carcasses of poultry deleteriously affected by post mortem changes shall...
9 CFR 354.131 - Decomposition.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 9 Animals and Animal Products 2 2012-01-01 2012-01-01 false Decomposition. 354.131 Section 354.131 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... Carcasses and Parts § 354.131 Decomposition. Carcasses of rabbits deleteriously affected by...
English and Turkish Pupils' Understanding of Decomposition
ERIC Educational Resources Information Center
Cetin, Gulcan
2007-01-01
This study aimed to describe seventh grade English and Turkish students' levels of understanding of decomposition. Data were analyzed descriptively from the students' written responses to four diagnostic questions about decomposition. Results revealed that the English students had considerably higher sound understanding and lower no understanding…
Code of Federal Regulations, 2013 CFR
2013-01-01
... 9 Animals and Animal Products 2 2013-01-01 2013-01-01 false Decomposition. 381.93 Section 381.93 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... § 381.93 Decomposition. Carcasses of poultry deleteriously affected by post mortem changes shall...
Helmholtz Hodge decomposition of scalar optical fields.
Bahl, Monika; Senthilkumaran, P
2012-11-01
It is shown that the vector field decomposition method, namely, the Helmholtz Hodge decomposition, can also be applied to analyze scalar optical fields that are ubiquitously present in interference and diffraction optics. A phase gradient field that depicts the propagation and Poynting vector directions can hence be separated into solenoidal and irrotational components.
Metallo-Organic Decomposition (MOD) film development
NASA Technical Reports Server (NTRS)
Parker, J.
1986-01-01
The processing techniques and problems encountered in formulating metallo-organic decomposition (MOD) films used in contracting structures for thin solar cells are described. The use of thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) techniques performed at Jet Propulsion Laboratory (JPL) in understanding the decomposition reactions lead to improvements in process procedures. The characteristics of the available MOD films were described in detail.
A global HMX decomposition model
Hobbs, M.L.
1996-12-01
HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) decomposes by competing reaction pathways to form various condensed and gas-phase intermediate and final products. Gas formation is related to the development of nonuniform porosity and high specific surface areas prior to ignition in cookoff events. Such thermal damage enhances shock sensitivity and favors self-supported accelerated burning. The extent of HMX decomposition in highly confined cookoff experiments remains a major unsolved experimental and modeling problem. The present work is directed at determination of global HMX kinetics useful for predicting the elapsed time to thermal runaway (ignition) and the extent of decomposition at ignition. Kinetic rate constants for a six step engineering based global mechanism were obtained using gas formation rates measured by Behrens at Sandia National Laboratories with his Simultaneous Modulated Beam Mass Spectrometer (STMBMS) experimental apparatus. The six step global mechanism includes competition between light gas (H[sub 2]Awe, HCN, CO, H[sub 2]CO, NO, N[sub 2]Awe) and heavy gas (C[sub 2]H[sub 6]N[sub 2]Awe and C[sub 4]H[sub 10]N0[sub 2]) formation with zero order sublimation of HMX and the mononitroso analog of HMX (mn-HMX), C[sub 4]H[sub 8]N[sub 8]Awe[sub 7]. The global mechanism was applied to the highly confined, One Dimensional Time to eXplosion (ODTX) experiment and hot cell experiments by suppressing the sublimation of HMX and mn-HMX. An additional gas-phase reaction was also included to account for the gas-phase reaction of N[sub 2]Awe with H[sub 2]CO. Predictions compare adequately to the STMBMS data, ODTX data, and hot cell data. Deficiencies in the model and future directions are discussed.
Filtering by nonlinear systems.
Campos Cantón, E; González Salas, J S; Urías, J
2008-12-01
Synchronization of nonlinear systems forced by external signals is formalized as the response of a nonlinear filter. Sufficient conditions for a nonlinear system to behave as a filter are given. Some examples of generalized chaos synchronization are shown to actually be special cases of nonlinear filtering.
Nonlinear rotordynamics analysis
NASA Technical Reports Server (NTRS)
Day, W. B.; Zalik, R. A.
1986-01-01
Three analytic consequences of the nonlinear Jeffcott equations are examined. The primary application of these analyses is directed toward understanding the excessive vibrations recorded in the Liquid Oxygen (LOX) pump of the Space Shuttle Main Engine (SSME) during hot firing ground testing. The first task is to provide bounds on the coefficients of the equations which delimit the two cases of numerical solution as a circle or an annulus. The second task examines the mathematical generalization to multiple forcing functions, which includes the special problems of mass imbalance, side force, rubbing, and combination of these forces. Finally, stability and boundedness of the steady-state solutions is discussed and related to the corresponding linear problem.
Dynamic Mobility via Cellular Decompositions of Coordination Spaces
2012-01-01
instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send...used to describe the possible scenarios. When two actuators are considered together, a total of 33 cells exist , 5× 5 due to the Cartesian nature of the...half-bound, canter, and gallop gaits that actively recruit motion by the animal’s spine. It is posited that the increased performance of a cheetah
Multilinear operators for higher-order decompositions.
Kolda, Tamara Gibson
2006-04-01
We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to concisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outer-products of the columns of N matrices and allows a divorce from a matricized representation and a very concise expression of the PARAFAC decomposition. We explore the properties of the Tucker and Kruskal operators independently of the related decompositions. Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.
Unitary Operators on the Document Space.
ERIC Educational Resources Information Center
Hoenkamp, Eduard
2003-01-01
Discusses latent semantic indexing (LSI) that would allow search engines to reduce the dimension of the document space by mapping it into a space spanned by conceptual indices. Topics include vector space models; singular value decomposition (SVD); unitary operators; the Haar transform; and new algorithms. (Author/LRW)
Two Mathematical Models of Nonlinear Vibrations
NASA Technical Reports Server (NTRS)
Brugarolas, Paul; Bayard, David; Spanos, John; Breckenridge, William
2007-01-01
Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.
Nonlinearities in vegetation functioning
NASA Astrophysics Data System (ADS)
Ceballos-Núñez, Verónika; Müller, Markus; Metzler, Holger; Sierra, Carlos
2016-04-01
Given the current drastic changes in climate and atmospheric CO2 concentrations, and the role of vegetation in the global carbon cycle, there is increasing attention to the carbon allocation component in biosphere terrestrial models. Improving the representation of C allocation in models could be the key to having better predictions of the fate of C once it enters the vegetation and is partitioned to C pools of different residence times. C allocation has often been modeled using systems of ordinary differential equations, and it has been hypothesized that most models can be generalized with a specific form of a linear dynamical system. However, several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems with model structure. Although efforts have been made to compare different models, the outcome of these qualitative assessments has been a conceptual categorization of them. In this contribution, we introduce a new effort to identify the main properties of groups of models by studying their mathematical structure. For this purpose, we performed a literature research of the relevant models of carbon allocation in vegetation and developed a database with their representation in symbolic mathematics. We used the Python package SymPy for symbolic mathematics as a common language and manipulated the models to calculate their Jacobian matrix at fixed points and their eigenvalues, among other mathematical analyses. Our preliminary results show a tendency of inverse proportionality between model complexity and size of time/space scale; complex interactions between the variables controlling carbon allocation in vegetation tend to operate at shorter time/space scales, and vice-versa. Most importantly, we found that although the linear structure is common, other structures with non-linearities have been also proposed. We, therefore, propose a new General Model that can accommodate these
Gearbox fault diagnosis using empirical mode decomposition and Hilbert spectrum
NASA Astrophysics Data System (ADS)
Liu, B.; Riemenschneider, S.; Xu, Y.
2006-04-01
The empirical mode decomposition (EMD) and Hilbert spectrum are a new method for adaptive analysis of non-linear and non-stationary signals. This paper applies this method to vibration signal analysis for localised gearbox fault diagnosis. We first study the properties of the recently developed B-spline EMD as a filter bank, which is helpful in understanding the mechanisms behind EMD. Then we investigate the effectiveness of the original and the B-spline EMD as well as their corresponding Hilbert spectrum in the fault diagnosis. Vibration signals collected from an automobile gearbox with an incipient tooth crack are used in the investigation. The results show that the EMD algorithms and the Hilbert spectrum perform excellently. They are found to be more effective than the often used continuous wavelet transform in detection of the vibration signatures.
Dossa, Gbadamassi G O; Paudel, Ekananda; Cao, Kunfang; Schaefer, Douglas; Harrison, Rhett D
2016-10-04
Organic matter decomposition represents a vital ecosystem process by which nutrients are made available for plant uptake and is a major flux in the global carbon cycle. Previous studies have investigated decomposition of different plant parts, but few considered bark decomposition or its role in decomposition of wood. However, bark can comprise a large fraction of tree biomass. We used a common litter-bed approach to investigate factors affecting bark decomposition and its role in wood decomposition for five tree species in a secondary seasonal tropical rain forest in SW China. For bark, we implemented a litter bag experiment over 12 mo, using different mesh sizes to investigate effects of litter meso- and macro-fauna. For wood, we compared the decomposition of branches with and without bark over 24 mo. Bark in coarse mesh bags decomposed 1.11-1.76 times faster than bark in fine mesh bags. For wood decomposition, responses to bark removal were species dependent. Three species with slow wood decomposition rates showed significant negative effects of bark-removal, but there was no significant effect in the other two species. Future research should also separately examine bark and wood decomposition, and consider bark-removal experiments to better understand roles of bark in wood decomposition.
Dossa, Gbadamassi G. O.; Paudel, Ekananda; Cao, Kunfang; Schaefer, Douglas; Harrison, Rhett D.
2016-01-01
Organic matter decomposition represents a vital ecosystem process by which nutrients are made available for plant uptake and is a major flux in the global carbon cycle. Previous studies have investigated decomposition of different plant parts, but few considered bark decomposition or its role in decomposition of wood. However, bark can comprise a large fraction of tree biomass. We used a common litter-bed approach to investigate factors affecting bark decomposition and its role in wood decomposition for five tree species in a secondary seasonal tropical rain forest in SW China. For bark, we implemented a litter bag experiment over 12 mo, using different mesh sizes to investigate effects of litter meso- and macro-fauna. For wood, we compared the decomposition of branches with and without bark over 24 mo. Bark in coarse mesh bags decomposed 1.11–1.76 times faster than bark in fine mesh bags. For wood decomposition, responses to bark removal were species dependent. Three species with slow wood decomposition rates showed significant negative effects of bark-removal, but there was no significant effect in the other two species. Future research should also separately examine bark and wood decomposition, and consider bark-removal experiments to better understand roles of bark in wood decomposition. PMID:27698461
Management intensity alters decomposition via biological pathways
Wickings, Kyle; Grandy, A. Stuart; Reed, Sasha; Cleveland, Cory
2011-01-01
Current conceptual models predict that changes in plant litter chemistry during decomposition are primarily regulated by both initial litter chemistry and the stage-or extent-of mass loss. Far less is known about how variations in decomposer community structure (e.g., resulting from different ecosystem management types) could influence litter chemistry during decomposition. Given the recent agricultural intensification occurring globally and the importance of litter chemistry in regulating soil organic matter storage, our objectives were to determine the potential effects of agricultural management on plant litter chemistry and decomposition rates, and to investigate possible links between ecosystem management, litter chemistry and decomposition, and decomposer community composition and activity. We measured decomposition rates, changes in litter chemistry, extracellular enzyme activity, microarthropod communities, and bacterial versus fungal relative abundance in replicated conventional-till, no-till, and old field agricultural sites for both corn and grass litter. After one growing season, litter decomposition under conventional-till was 20% greater than in old field communities. However, decomposition rates in no-till were not significantly different from those in old field or conventional-till sites. After decomposition, grass residue in both conventional- and no-till systems was enriched in total polysaccharides relative to initial litter, while grass litter decomposed in old fields was enriched in nitrogen-bearing compounds and lipids. These differences corresponded with differences in decomposer communities, which also exhibited strong responses to both litter and management type. Overall, our results indicate that agricultural intensification can increase litter decomposition rates, alter decomposer communities, and influence litter chemistry in ways that could have important and long-term effects on soil organic matter dynamics. We suggest that future
NASA Astrophysics Data System (ADS)
Galuzio, P. P.; Benkadda, S.; Lopes, S. R.
2017-01-01
In this paper we characterized intermittent transitions from temporal chaos to turbulence in the forced and damped nonlinear Schrödinger equation. We demonstrate using finite time Lyapunov exponents that during the transition a fraction of unstable periodic orbits embedded in a low dimensional chaotic attractor loses transversal stability, in a way that nearby trajectories are expelled away from its vicinity (a mechanism referred to as intermittency induced by Unstable Dimension Variability). During the transition, an appropriate decomposition of the Fourier phase space into transversal and longitudinal modes is performed. The analysis of modes dynamics sheds new light in the understanding of intermittency in spatially extended dynamical systems. Subsequently a perturbation is applied to the system in order to control the intermittent extreme events and reduce their occurrence.
A closer look at arrested spinodal decomposition in protein solutions.
Gibaud, Thomas; Schurtenberger, Peter
2009-08-12
Concentrated aqueous solutions of the protein lysozyme undergo a liquid-solid transition upon a temperature quench into the unstable spinodal region below a characteristic arrest temperature of T(f) = 15 °C. We use video microscopy and ultra-small angle light scattering in order to investigate the arrested structures as a function of initial concentration, quench temperature and rate of the temperature quench. We find that the solid-like samples show all the features of a bicontinuous network that is formed through an arrested spinodal decomposition process. We determine the correlation length ξ and demonstrate that ξ exhibits a temperature dependence that closely follows the critical scaling expected for density fluctuations during the early stages of spinodal decomposition. These findings are in agreement with an arrest scenario based on a state diagram where the arrest or gel line extends far into the unstable region below the spinodal line. Arrest then occurs when during the early stage of spinodal decomposition the volume fraction φ(2) of the dense phase intersects the dynamical arrest threshold φ(2,Glass), upon which phase separation gets pinned into a space-spanning gel network with a characteristic length ξ.
Oxidative decomposition of formaldehyde catalyzed by a bituminous coal
Haim Cohen; Uri Green
2009-05-15
It has been observed that molecular hydrogen is formed during long-term storage of bituminous coals via oxidative decomposition of formaldehyde by coal surface peroxides. This study has investigated the effects of coal quantity, temperature, and water content on the molecular hydrogen formation with a typical American coal (Pittsburgh No. 6). The results indicate that the coal's surface serves as a catalyst in the formation processes of molecular hydrogen. Furthermore, the results also indicate that low temperature emission of molecular hydrogen may possibly be the cause of unexplained explosions in confined spaces containing bituminous coals, for example, underground mines or ship holds. 20 refs., 4 figs., 6 tabs.
Gordon Decomposition of Dirac Spinors in Gravitational Background
NASA Astrophysics Data System (ADS)
Parashar, D.
The scheme outlined earlier is continued here to investigate the structure of Dirac spinors in the background of a gravitational field within the context of cosmological Robertson-Walker metric where the treatment is based on general considerations of spatially curved (non-flat) hypersurfaces embracing open as well as closed versions of the Universe. A Gordon decomposition of the generalized Dirac current is then carried out in terms of the polarization and the magnetization densities. We also take a look at the Klein-Gordon equation in the curved space formalism.
Double-density complex wavelet cartoon-texture decomposition
NASA Astrophysics Data System (ADS)
Hewer, Gary A.; Kuo, Wei; Hanson, Grant
2007-09-01
Both the Kingsbury dual-tree and the subsequent Selesnick double-density dual-tree complex wavelet transform approximate an analytic function. The classification of the phase dependency across scales is largely unexplored except by Romberg et al.. Here we characterize the sub-band dependency of the orientation of phase gradients by applying the Helmholtz principle to bivariate histograms to locate meaningful modes. A further characterization using the Earth Mover's Distance with the fundamental Rudin-Osher-Meyer Banach space decomposition into cartoon and texture elements is presented. Possible applications include image compression and invariant descriptor selection for image matching.
Evaluating Pavement Cracks with Bidimensional Empirical Mode Decomposition
NASA Astrophysics Data System (ADS)
Ayenu-Prah, Albert; Attoh-Okine, Nii
2008-12-01
Crack evaluation is essential for effective classification of pavement cracks. Digital images of pavement cracks have been analyzed using techniques such as fuzzy set theory and neural networks. Bidimensional empirical mode decomposition (BEMD), a new image analysis method recently developed, can potentially be used for pavement crack evaluation. BEMD is an extension of the empirical mode decomposition (EMD), which can decompose nonlinear and nonstationary signals into basis functions called intrinsic mode functions (IMFs). IMFs are monocomponent functions that have well-defined instantaneous frequencies. EMD is a sifting process that is nonparametric and data driven; it does not depend on an a priori basis set. It is able to remove noise from signals without complicated convolution processes. BEMD decomposes an image into two-dimensional IMFs. The present paper explores pavement crack detection using BEMD together with the Sobel edge detector. A number of images are filtered with BEMD to remove noise, and the residual image analyzed with the Sobel edge detector for crack detection. The results are compared with results from the Canny edge detector, which uses a Gaussian filter for image smoothing before performing edge detection. The objective is to qualitatively explore how well BEMD is able to smooth an image for more effective edge detection with the Sobel method.
NASA Astrophysics Data System (ADS)
Lekgoathi, M. D. S.; Kock, L. D.
2016-12-01
Thermal decomposition and vibrational spectroscopic properties of pyridinium hexafluorophosphate (C5H5NHPF6) have been studied. The structure of the compound is better interpreted as having a cubic space group, based on Raman and infrared vibrational spectroscopy experiments and group theoretical correlation data between site symmetry species and the spectroscopic space group. The 13C NMR data shows three significant signals corresponding to the three chemical environments expected on the pyridinium ring i.e. γ, β and α carbons, suggesting that the position of the anion must be symmetrical with respect to the pyridinium ring's C2v symmetry. The process of thermal decomposition of the compound using TGA methods was found to follow a contracting volume model. The activation energy associated with the thermal decomposition reaction of the compound is 108.5 kJ mol-1, while the pre exponential factor is 1.51 × 109 sec-1.
NASA Astrophysics Data System (ADS)
Kunert, James Michael
Networks of many nonlinearly-coupled dynamical components are ubiquitous in the physical sciences, but often difficult to characterize. However, their dynamics are often low-dimensional, being dominated by a few functional, coherent patterns. We wish to understand: (1) How do nonlinear networks generate functional responses? (2) What role does the network's structure play in generating such responses? (3) To what extent are the network dynamics robust to network damage? Towards these ends we model the C. elegans neuronal network, the connectivity of which is known. Chapter 2 constructs a full-Connectome dynamical model which can generate proxies for known behaviors (specifically demonstrating a proxy for forward motion). Chapter 3 explores the input space via interpretable bifurcation diagrams. The highly multistable dynamics give rise to long transient timescales (orders of magnitude longer than intrinsic nodal timescales). Chapter 4 models network injuries, which significantly distort dynamics. We develop a metric to quantify the injury level and help predict an injury's functional outcome. Chapter 5 uses Dynamic Mode Decomposition to relate connectivity to low-dimensional dynamical structure. In the process, we demonstrate consistency with proprioception-driven locomotion which is facilitated by network structure.
Nonlinear Analysis of Spatiotemporal Heart Data
NASA Astrophysics Data System (ADS)
Simonotto, Jennifer; Spano, Mark; Ditto, William; Kavanagh, Katherine; Harrison, Robert G.
2002-03-01
Studying the nonlinear dynamics of ventricular fibrillation (VF) and ventricular tachycardia (VT) is necessary for the development of better models of and treatments for VF/VT. Through the use of voltage sensitive dyes and new high speed video cameras, we can now obtain optical mapping data that exhibit signal to noise ratios high enough to tackle (in 2D) the acquisition and analysis of spatiotemporal dynamics of VF/VT. It is now possible to effectively apply conventional statistical analyses (spatial correlation, coherence, signal decomposition), as well as techniques based upon wavefront motion (phase maps, propagation velocity vectors, waveform dynamics) of the electrical waves under study. Yet it is unclear if these measures alone will suffice to describe the complexity of the system. Thus we combine statistical and optical analysis with nonlinear analysis (entropy measures, symbolic dynamics, unstable periodic orbits (UPO) statistics) in order to extract the most information of the spatiotemporal behavior of VF/VT.
Domain decomposition algorithms and computational fluid dynamics
NASA Technical Reports Server (NTRS)
Chan, Tony F.
1988-01-01
Some of the new domain decomposition algorithms are applied to two model problems in computational fluid dynamics: the two-dimensional convection-diffusion problem and the incompressible driven cavity flow problem. First, a brief introduction to the various approaches of domain decomposition is given, and a survey of domain decomposition preconditioners for the operator on the interface separating the subdomains is then presented. For the convection-diffusion problem, the effect of the convection term and its discretization on the performance of some of the preconditioners is discussed. For the driven cavity problem, the effectiveness of a class of boundary probe preconditioners is examined.
On a Decomposition Model for Optical Flow
NASA Astrophysics Data System (ADS)
Abhau, Jochen; Belhachmi, Zakaria; Scherzer, Otmar
In this paper we present a variational method for determining cartoon and texture components of the optical flow of a noisy image sequence. The method is realized by reformulating the optical flow problem first as a variational denoising problem for multi-channel data and then by applying decomposition methods. Thanks to the general formulation, several norms can be used for the decomposition. We study a decomposition for the optical flow into bounded variation and oscillating component in greater detail. Numerical examples demonstrate the capabilities of the proposed approach.
Hamiltonian decomposition for bulk and surface states.
Sasaki, Ken-Ichi; Shimomura, Yuji; Takane, Yositake; Wakabayashi, Katsunori
2009-04-10
We demonstrate that a tight-binding Hamiltonian with nearest- and next-nearest-neighbor hopping integrals can be decomposed into bulk and boundary parts for honeycomb lattice systems. The Hamiltonian decomposition reveals that next-nearest-neighbor hopping causes sizable changes in the energy spectrum of surface states even if the correction to the energy spectrum of bulk states is negligible. By applying the Hamiltonian decomposition to edge states in graphene systems, we show that the next-nearest-neighbor hopping stabilizes the edge states. The application of Hamiltonian decomposition to a general lattice system is discussed.
NASA Astrophysics Data System (ADS)
Maier-Paape, Stanislaus; Wanner, Thomas
This paper is the first in a series of two papers addressing the phenomenon of spinodal decomposition for the Cahn-Hilliard equation
NASA Astrophysics Data System (ADS)
Shechter, M.; Chefetz, B.
2009-04-01
Plant cuticle materials, especially the highly aliphatic biopolymers cutin and cutan, have been reported as highly efficient natural sorbents. The objective of this study was to examine the effects of decomposition on their sorption behavior with naphthol and phenanthrene. The level of cutin and cutan was reduced by 15 and 27% respectively during the first 3 mo of incubation. From that point, the level of the cutan did not change, while the level of the cutin continued to decrease up to 32% after 20 mo. 13C NMR analysis suggested transformation of cutan mainly within its alkyl-C structure which are assigned as crystalline moieties. Cutin, however, did not exhibit significant structure changes with time. The level of humic-like substances increased due to cutin decomposition but was not influenced in the cutan system after 20 mo of incubation. This indicates that the cutin biopolymer has been decomposed and transformed into humic-like substances, whereas the cutan was less subject to transformation. Decomposition affected sorption properties in similar trends for both cutin and cutan. The Freundlich capacity coefficients (KFOC) of naphthol were much lower than phenanthrene and were less influenced by the decomposition, whereas with phenanthrene KFOC values increased significantly with time. Naphthol exhibited non-linear isotherms; and nonlinearity was decreased with incubation time. In contrast, phenanthrene isotherms were more linear and showed only moderate change with time. The decrease in the linearity of naphthol isotherms might relate to the transformation of the sorption sites due to structural changes in the biopolymers. However, with phenanthrene, these changes did not affect sorption linearity but increased sorption affinities mainly for cutan. This is probably due to decomposition of the rigid alkyl-C moieties in the cutan biopolymer. Our data suggest that both biopolymers were relatively stable in the soil for 20 mo. Cutan is less degradable than cutin
Hatch, David R.; Del-Castillo-Negrete, Diego B; Terry, P.W.
2012-01-01
Higher order singular value decomposition (HOSVD) is explored as a tool for analyzing and compressing gyrokinetic data. An efficient numerical implementation of an HOSVD algorithm is described. HOSVD is used to analyze the full six-dimensional (three spatial, two velocity space, and time dimensions) gyrocenter distribution function from gyrokinetic simulations of ion temperature gradient, electron temperature gradient, and trapped electron mode driven turbulence. The HOSVD eigenvalues for the velocity space coordinates decay very rapidly, indicating that only a few structures in velocity space can capture the most important dynamics. In almost all of the cases studied, HOSVD extracts parallel velocity space structures which are very similar to orthogonal polynomials. HOSVD is also used to compress gyrokinetic datasets, an application in which it is shown to significantly outperform the more commonly used singular value decomposition. It is shown that the effectiveness of the HOSVD compression improves as the dimensionality of the dataset increases. (C) 2012 Elsevier Inc. All rights reserved.
NASA Astrophysics Data System (ADS)
Beechler, B. E.; Vukicevic, T.; Weiss, J. B.
2008-12-01
In this study, the relationship between data assimilation solutions and nonlinear model properties together with observational constraint is analyzed using a numerical technique based on the inverse problem theory formulated by Mosegaard and Tarantola. By this theory, the inverse problem and solution are defined via convolution and conjunction of probability density functions (pdfs) that represent stochastic information obtained from the model, observations and prior knowledge in a joint multidimensional space. This theory provides an explicit analysis of the nonlinear model function, together with information about uncertainties in the model, observations, and prior knowledge through construction of the joint probability density, from which marginal posterior solution functions can then be evaluated. The numerical analysis technique derived from the theory computes the component probability density functions in discretized form via a combination of function mapping on a discrete grid in the model and observation phase space, and sampling from known parametric distributions. This numerical diagnostic analysis technique was first demonstrated in Vukicevic and Posselt (2008) on examples of two well known simplified models of Atmospheric physics: Damped oscillations and Lorenz' 3-component model of dry cellular convection. In the current study the diagnostic analysis of the controls of posterior pdf in data assimilation is performed using a beta plane quasi- geostrophic numerical model. The control parameter space in the model consists of coefficients of two- dimensional Fourier decomposition of stream function fields within regions of unstable dynamical modes. The impact of assumed modeling errors and spatial and temporal distribution of observations on the posterior multi dimensional pdf is studied to evaluate conditions which render this pdf uni-modal. The validity of the Gaussian approximation is then evaluated.
NASA Astrophysics Data System (ADS)
Aspiras, Theus H.; Asari, Vijayan K.; Sakla, Wesam
2015-03-01
The human brain has the capability to process high quantities of data quickly for detection and recognition tasks. These tasks are made simpler by the understanding of data, which intentionally removes redundancies found in higher dimensional data and maps the data onto a lower dimensional space. The brain then encodes manifolds created in these spaces, which reveal a specific state of the system. We propose to use a recurrent neural network, the nonlinear line attractor (NLA) network, for the encoding of these manifolds as specific states, which will draw untrained data towards one of the specific states that the NLA network has encoded. We propose a Gaussian-weighted modular architecture for reducing the computational complexity of the conventional NLA network. The proposed architecture uses a neighborhood approach for establishing the interconnectivity of neurons to obtain the manifolds. The modified NLA network has been implemented and tested on the Electro-Optic Synthetic Vehicle Model Database created by the Air Force Research Laboratory (AFRL), which contains a vast array of high resolution imagery with several different lighting conditions and camera views. It is observed that the NLA network has the capability for representing high dimensional data for the recognition of the objects of interest through its new learning strategy. A nonlinear dimensionality reduction scheme based on singular value decomposition has found to be very effective in providing a low dimensional representation of the dataset. Application of the reduced dimensional space on the modified NLA algorithm would provide fast and more accurate recognition performance for real time applications.
Martis, Roshan Joy; Acharya, U Rajendra; Tan, Jen Hong; Petznick, Andrea; Tong, Louis; Chua, Chua Kuang; Ng, Eddie Yin Kwee
2013-10-01
Intrinsic time-scale decomposition (ITD) is a new nonlinear method of time-frequency representation which can decipher the minute changes in the nonlinear EEG signals. In this work, we have automatically classified normal, interictal and ictal EEG signals using the features derived from the ITD representation. The energy, fractal dimension and sample entropy features computed on ITD representation coupled with decision tree classifier has yielded an average classification accuracy of 95.67%, sensitivity and specificity of 99% and 99.5%, respectively using 10-fold cross validation scheme. With application of the nonlinear ITD representation, along with conceptual advancement and improvement of the accuracy, the developed system is clinically ready for mass screening in resource constrained and emerging economy scenarios.
Bufetov, A I
2014-02-28
The aim of this paper is to prove ergodic decomposition theorems for probability measures which are quasi-invariant under Borel actions of inductively compact groups as well as for σ-finite invariant measures. For infinite measures the ergodic decomposition is not unique, but the measure class of the decomposing measure on the space of projective measures is uniquely defined by the initial invariant measure. Bibliography: 21 titles.
Noise decomposition of intracellular biochemical signaling networks using nonequivalent reporters
Rhee, Alex; Cheong, Raymond; Levchenko, Andre
2014-01-01
Experimental measurements of biochemical noise have primarily focused on sources of noise at the gene expression level due to limitations of existing noise decomposition techniques. Here, we introduce a mathematical framework that extends classical extrinsic–intrinsic noise analysis and enables mapping of noise within upstream signaling networks free of such restrictions. The framework applies to systems for which the responses of interest are linearly correlated on average, although the framework can be easily generalized to the nonlinear case. Interestingly, despite the high degree of complexity and nonlinearity of most mammalian signaling networks, three distinct tumor necrosis factor (TNF) signaling network branches displayed linearly correlated responses, in both wild-type and perturbed versions of the network, across multiple orders of magnitude of ligand concentration. Using the noise mapping analysis, we find that the c-Jun N-terminal kinase (JNK) pathway generates higher noise than the NF-κB pathway, whereas the activation of c-Jun adds a greater amount of noise than the activation of ATF-2. In addition, we find that the A20 protein can suppress noise in the activation of ATF-2 by separately inhibiting the TNF receptor complex and JNK pathway through a negative feedback mechanism. These results, easily scalable to larger and more complex networks, pave the way toward assessing how noise propagates through cellular signaling pathways and create a foundation on which we can further investigate the relationship between signaling system architecture and biological noise. PMID:25404303
Unimolecular decomposition of methyltrichlorosilane: RRKM calculations
Osterheld, T.H.; Allendorf, M.D.; Melius, C.F.
1993-06-01
Based on reaction thermochemistry and estimates of Arrhenius A-factors, it is expected that Si-C bond cleavage, C-H bond cleavage, and HCl elimination will be the primary channels for the unimolecular decomposition of methyltrichlorosilane. Using RRKM theory, we calculated rate constants for these three reactions. The calculations support the conclusion that these three reactions are the major decomposition pathways. Rate constants for each reaction were calculated in the high-pressure limit (800--1500 K) and in the falloff regime (1300--1500 K) for bath gases of both helium and hydrogen. These calculations thus provide branching fractions as well as decomposition rates. We also calculated bimolecular rate constants for the overall decomposition in the low-pressure limit. Interesting and surprising kinetic behavior of this system and the individual reactions is discussed. The reactivity of this chlorinated organosilane is compared to that of other organosilanes.
A Decomposition Theorem for Finite Automata.
ERIC Educational Resources Information Center
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Thermal Decomposition of Poly(methylphenylsilane)
NASA Astrophysics Data System (ADS)
Pan, Lujun; Zhang, Mei; Nakayama, Yoshikazu
2000-03-01
The thermal decomposition of poly(methylphenylsilane) was performed at constant heating rates and isothermal conditions. The evolved gases were studied by ionization-threshold mass spectroscopy. Pyrolysis under isothermal conditions reveals that the decomposition of poly(methylphenylsilane) is a type of depolymerization that has a first-order reaction. Kinetic analysis of the evolution spectra of CH3-Si-C6H5 radicals, phenyl and methyl substituents reveals the mechanism and activation energies of the decomposition reactions in main chains and substituents. It is found that the decomposition of main chains is a dominant reaction and results in the weight loss of approximately 90%. The effusion of phenyl and methyl substituents occurs in the two processes of rearrangement of main chains and the formation of stable Si-C containing residuals.
Adaptive Fourier decomposition based ECG denoising.
Wang, Ze; Wan, Feng; Wong, Chi Man; Zhang, Liming
2016-10-01
A novel ECG denoising method is proposed based on the adaptive Fourier decomposition (AFD). The AFD decomposes a signal according to its energy distribution, thereby making this algorithm suitable for separating pure ECG signal and noise with overlapping frequency ranges but different energy distributions. A stop criterion for the iterative decomposition process in the AFD is calculated on the basis of the estimated signal-to-noise ratio (SNR) of the noisy signal. The proposed AFD-based method is validated by the synthetic ECG signal using an ECG model and also real ECG signals from the MIT-BIH Arrhythmia Database both with additive Gaussian white noise. Simulation results of the proposed method show better performance on the denoising and the QRS detection in comparing with major ECG denoising schemes based on the wavelet transform, the Stockwell transform, the empirical mode decomposition, and the ensemble empirical mode decomposition.
Alternative Modal Basis Selection Procedures for Nonlinear Random Response Simulation
NASA Technical Reports Server (NTRS)
Przekop, Adam; Guo, Xinyun; Rizzi, Stephen A.
2010-01-01
Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of the three reduced-order analyses are compared with the results of the computationally taxing simulation in the physical degrees of freedom. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.
Minimax Techniques For Optimizing Non-Linear Image Algebra Transforms
NASA Astrophysics Data System (ADS)
Davidson, Jennifer L.
1989-08-01
It has been well established that the Air Force Armament Technical Laboratory (AFATL) image algebra is capable of expressing all linear transformations [7]. The embedding of the linear algebra in the image algebra makes this possible. In this paper we show a relation of the image algebra to another algebraic system called the minimax algebra. This system is used extensively in economics and operations research, but until now has not been investigated for applications to image processing. The relationship is exploited to develop new optimization methods for a class of non-linear image processing transforms. In particular, a general decomposition technique for templates in this non-linear domain is presented. Template decomposition techniques are an important tool in mapping algorithms efficiently to both sequential and massively parallel architectures.
Time Series Decomposition into Oscillation Components and Phase Estimation.
Matsuda, Takeru; Komaki, Fumiyasu
2017-02-01
Many time series are naturally considered as a superposition of several oscillation components. For example, electroencephalogram (EEG) time series include oscillation components such as alpha, beta, and gamma. We propose a method for decomposing time series into such oscillation components using state-space models. Based on the concept of random frequency modulation, gaussian linear state-space models for oscillation components are developed. In this model, the frequency of an oscillator fluctuates by noise. Time series decomposition is accomplished by this model like the Bayesian seasonal adjustment method. Since the model parameters are estimated from data by the empirical Bayes' method, the amplitudes and the frequencies of oscillation components are determined in a data-driven manner. Also, the appropriate number of oscillation components is determined with the Akaike information criterion (AIC). In this way, the proposed method provides a natural decomposition of the given time series into oscillation components. In neuroscience, the phase of neural time series plays an important role in neural information processing. The proposed method can be used to estimate the phase of each oscillation component and has several advantages over a conventional method based on the Hilbert transform. Thus, the proposed method enables an investigation of the phase dynamics of time series. Numerical results show that the proposed method succeeds in extracting intermittent oscillations like ripples and detecting the phase reset phenomena. We apply the proposed method to real data from various fields such as astronomy, ecology, tidology, and neuroscience.
Simplified approaches to some nonoverlapping domain decomposition methods
Xu, Jinchao
1996-12-31
An attempt will be made in this talk to present various domain decomposition methods in a way that is intuitively clear and technically coherent and concise. The basic framework used for analysis is the {open_quotes}parallel subspace correction{close_quotes} or {open_quotes}additive Schwarz{close_quotes} method, and other simple technical tools include {open_quotes}local-global{close_quotes} and {open_quotes}global-local{close_quotes} techniques, the formal one is for constructing subspace preconditioner based on a preconditioner on the whole space whereas the later one for constructing preconditioner on the whole space based on a subspace preconditioner. The domain decomposition methods discussed in this talk fall into two major categories: one, based on local Dirichlet problems, is related to the {open_quotes}substructuring method{close_quotes} and the other, based on local Neumann problems, is related to the {open_quotes}Neumann-Neumann method{close_quotes} and {open_quotes}balancing method{close_quotes}. All these methods will be presented in a systematic and coherent manner and the analysis for both two and three dimensional cases are carried out simultaneously. In particular, some intimate relationship between these algorithms are observed and some new variants of the algorithms are obtained.
Nonlinear reduced-order modeling with monotonicity property
NASA Astrophysics Data System (ADS)
Chaturantabut, Saifon
2016-10-01
This work proposes a general form of nonlinear model reduction approach that preserves the monotonicity property of the original full-order model, which can be used to guarantee the existence and uniqueness of the solution. The derivation of the proposed methodology is based on using basis from proper orthogonal decomposition method and modifying an interpolatory projection approach, called discrete empirical interpolation method, by enforcing a symmetric structure of the approximation. The efficiency and accuracy of the proposed method are illustrated through the numerical tests on a nonlinear model describing reaction diffusion problems.
High temperature decomposition of hydrogen peroxide
NASA Technical Reports Server (NTRS)
Parrish, Clyde F. (Inventor)
2005-01-01
Nitric oxide (NO) is oxidized into nitrogen dioxide (NO2) by the high temperature decomposition of a hydrogen peroxide solution to produce the oxidative free radicals, hydroxyl and hydroperoxyl. The hydrogen peroxide solution is impinged upon a heated surface in a stream of nitric oxide where it decomposes to produce the oxidative free radicals. Because the decomposition of the hydrogen peroxide solution occurs within the stream of the nitric oxide, rapid gas-phase oxidation of nitric oxide into nitrogen dioxide occurs.
High Temperature Decomposition of Hydrogen Peroxide
NASA Technical Reports Server (NTRS)
Parrish, Clyde F. (Inventor)
2004-01-01
Nitric oxide (NO) is oxidized into nitrogen dioxide (NO2) by the high temperature decomposition of a hydrogen peroxide solution to produce the oxidative free radicals, hydroxyl and hydropemxyl. The hydrogen peroxide solution is impinged upon a heated surface in a stream of nitric oxide where it decomposes to produce the oxidative free radicals. Because the decomposition of the hydrogen peroxide solution occurs within the stream of the nitric oxide, rapid gas-phase oxidation of nitric oxide into nitrogen dioxide occurs.
Decomposition of Balanced Matrices. Part 5: Goggles
1991-10-01
A D-A 247 462 Management Science Research Report #MSRR-573 1~ ~~112 Eil 11 I Decomposition of Balanced Matrices . Part V: Goggles Michele Conforti 12...9001705. I Dipartimento di Matematica Pura ed Applicata, UniversitA di Padova, Via Belzoni 7, 35131 Padova, Italy.f 2 Carnegie Mellon University...NUMBER 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED DECOMPOSITION OF BALANCED MATRICES . Technical Report, Oct 1991 PART V: GOGGLES 6
Moisture drives surface decomposition in thawing tundra
NASA Astrophysics Data System (ADS)
Hicks Pries, Caitlin E.; Schuur, E. A. G.; Vogel, Jason G.; Natali, Susan M.
2013-07-01
Permafrost thaw can affect decomposition rates by changing environmental conditions and litter quality. As permafrost thaws, soils warm and thermokarst (ground subsidence) features form, causing some areas to become wetter while other areas become drier. We used a common substrate to measure how permafrost thaw affects decomposition rates in the surface soil in a natural permafrost thaw gradient and a warming experiment in Healy, Alaska. Permafrost thaw also changes plant community composition. We decomposed 12 plant litters in a common garden to test how changing plant litter inputs would affect decomposition. We combined species' tissue-specific decomposition rates with species and tissue-level estimates of aboveground net primary productivity to calculate community-weighted decomposition constants at both the thaw gradient and warming experiment. Moisture, specifically growing season precipitation and water table depth, was the most significant driver of decomposition. At the gradient, an increase in growing season precipitation from 200 to 300 mm increased mass loss of the common substrate by 100%. At the warming experiment, a decrease in the depth to the water table from 30 to 15 cm increased mass loss by 100%. At the gradient, community-weighted decomposition was 21% faster in extensive than in minimal thaw, but was similar when moss production was included. Overall, the effect of climate change and permafrost thaw on surface soil decomposition are driven more by precipitation and soil environment than by changes to plant communities. Increasing soil moisture is thereby another mechanism by which permafrost thaw can become a positive feedback to climate change.
Hardware Implementation of Singular Value Decomposition
NASA Astrophysics Data System (ADS)
Majumder, Swanirbhar; Shaw, Anil Kumar; Sarkar, Subir Kumar
2016-06-01
Singular value decomposition (SVD) is a useful decomposition technique which has important role in various engineering fields such as image compression, watermarking, signal processing, and numerous others. SVD does not involve convolution operation, which make it more suitable for hardware implementation, unlike the most popular transforms. This paper reviews the various methods of hardware implementation for SVD computation. This paper also studies the time complexity and hardware complexity in various methods of SVD computation.
Domain Decomposition for the SPN Solver MINOS
NASA Astrophysics Data System (ADS)
Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques
2012-12-01
In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nédélec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3® code.
Tiling Models for Spatial Decomposition in AMTRAN
Compton, J C; Clouse, C J
2005-05-27
Effective spatial domain decomposition for discrete ordinate (S{sub n}) neutron transport calculations has been critical for exploiting massively parallel architectures typified by the ASCI White computer at Lawrence Livermore National Laboratory. A combination of geometrical and computational constraints has posed a unique challenge as problems have been scaled up to several thousand processors. Carefully scripted decomposition and corresponding execution algorithms have been developed to handle a range of geometrical and hardware configurations.
Domain decomposition for the SPN solver MINOS
Jamelot, Erell; Baudron, Anne-Marie; Lautard, Jean-Jacques
2012-07-01
In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nedelec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3 (R) code. (authors)
Nonlinear Hysteretic Torsional Waves
NASA Astrophysics Data System (ADS)
Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.
2015-07-01
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Nonlinear Hysteretic Torsional Waves.
Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V
2015-07-31
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Unimolecular thermal decomposition of dimethoxybenzenes
Robichaud, David J. Mukarakate, Calvin; Nimlos, Mark R.; Scheer, Adam M.; Ormond, Thomas K.; Buckingham, Grant T.; Ellison, G. Barney
2014-06-21
The unimolecular thermal decomposition mechanisms of o-, m-, and p-dimethoxybenzene (CH{sub 3}O-C{sub 6}H{sub 4}-OCH{sub 3}) have been studied using a high temperature, microtubular (μtubular) SiC reactor with a residence time of 100 μs. Product detection was carried out using single photon ionization (SPI, 10.487 eV) and resonance enhanced multiphoton ionization (REMPI) time-of-flight mass spectrometry and matrix infrared absorption spectroscopy from 400 K to 1600 K. The initial pyrolytic step for each isomer is methoxy bond homolysis to eliminate methyl radical. Subsequent thermolysis is unique for each isomer. In the case of o-CH{sub 3}O-C{sub 6}H{sub 4}-OCH{sub 3}, intramolecular H-transfer dominates leading to the formation of o-hydroxybenzaldehyde (o-HO-C{sub 6}H{sub 4}-CHO) and phenol (C{sub 6}H{sub 5}OH). Para-CH{sub 3}O-C{sub 6}H{sub 4}-OCH{sub 3} immediately breaks the second methoxy bond to form p-benzoquinone, which decomposes further to cyclopentadienone (C{sub 5}H{sub 4}=O). Finally, the m-CH{sub 3}O-C{sub 6}H{sub 4}-OCH{sub 3} isomer will predominantly follow a ring-reduction/CO-elimination mechanism to form C{sub 5}H{sub 4}=O. Electronic structure calculations and transition state theory are used to confirm mechanisms and comment on kinetics. Implications for lignin pyrolysis are discussed.
Liu, Li; Lai, Choi-Hong; Zhou, Shao-Dan; Xie, Fen; Rui, Lu
2011-04-01
In order to predict variations of drug concentration during a given period of time, numerical solutions of pharmacokinetic models need to be obtained efficiently. Analytical solutions of linear pharmacokinetic models are usually obtained using the Laplace transform and inverse Laplace tables. The derivations of solutions to complex nonlinear models are tedious, and such solution process may be difficult to implement as a robust software code. For nonlinear models, the fourth-order Runge-Kutta (RK4) is the most classical numerical method in obtaining approximate numerical solutions, which is impossible to be implemented in distributed computing environments without much modification. The reason is that numerical solutions obtained by using RK4 can only be computed in sequential time steps. In this paper, time-domain decomposition methods are adapted for nonlinear pharmacokinetic models. The numerical Inverse Laplace method for PharmacoKinetic models (ILPK) is implemented to solve pharmacokinetic models with iterative inverse Laplace transform in each time interval. The distributed ILPK algorithm, which is based on a two-level time-domain decomposition concept, is proposed to improve its efficiency. Solutions on the coarser temporal mesh at the top level are obtained one by one, and then those on the finer temporal mesh at the bottom level are calculated concurrently by using those initial solutions that have been obtained at the top level decomposition. Accuracy and efficiency of the proposed algorithm and its distributed equivalent are investigated by using several test models. Results indicate that the ILPK algorithm and its distributed equivalent are good candidates for both linear and nonlinear pharmacokinetic models.
NASA Technical Reports Server (NTRS)
Schroeder, M. A.
1980-01-01
A summary of a literature review on thermal decomposition of HMX and RDX is presented. The decomposition apparently fits first order kinetics. Recommended values for Arrhenius parameters for HMX and RDX decomposition in the gaseous and liquid phases and for decomposition of RDX in solution in TNT are given. The apparent importance of autocatalysis is pointed out, as are some possible complications that may be encountered in interpreting extending or extrapolating kinetic data for these compounds from measurements carried out below their melting points to the higher temperatures and pressure characteristic of combustion.
Linear Algebraic Method for Non-Linear Map Analysis
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Decomposition is always temperature dependent, except when its not
NASA Astrophysics Data System (ADS)
Davidson, E. A.
2011-12-01
Understanding of the temperature dependence of decomposition of soil organic matter has been complicated by the two following facts: (1) all enzymatic activity, including biologically mediated breakdown of organic matter in soils, is temperature dependent; and (2) much of the organic matter in soils is effectively isolated from enzymatic activity, either in space or time, through a wide variety of environmental constraints, including physical and chemical protection, spatial heterogeneity, lack of oxygen, or sub-zero temperatures. Because of the second fact, the first has been questioned in papers that report lack of observed temperature sensitivity of decomposition of soil organic matter. In my 2006 review paper with Ivan Janssens, we attempted to clarify these facts and their interactions and why temperature dependence is sometimes observed and sometimes not. However, it appears that our discussion of how Arrhenius kinetics affects enzymatic activity has become the paper's main recognized legacy, and it has been cited in support of the "carbon-quality-temperature" hypothesis. Here I will update and clarify aspects of that review as follows: (1) a Dual Arrhenius Michaelis-Menten (DAMM) model that merges these kinetic models with substrate diffusion processes can parsimoniously and mechanistically explain fast responses of carbon metabolism in soils as temperature and water content vary over time scales of minutes to months; and (2) variations in activation energies of enzymatic reactions have little or no effect on C metabolism when substrate is not available to enzymes, and this second point applies to both short and long-term turnover of soil organic matter. Because of this latter point, mean residence times and decomposition constants often do not correlate well with the chemical structure ("carbon quality") of soil organic matter, as is predicted by Arrhenius kinetics alone. While it is true that biological decomposition reactions, when they occur, are always
NASA Astrophysics Data System (ADS)
Vargeese, Anuj A.; Mija, S. J.; Muralidharan, Krishnamurthi
2014-07-01
Ammonium nitrate (AN) is crystallized along with copper oxide, titanium dioxide, and lithium fluoride. Thermal kinetic constants for the decomposition reaction of the samples were calculated by model-free (Friedman's differential and Vyzovkins nonlinear integral) and model-fitting (Coats-Redfern) methods. To determine the decomposition mechanisms, 12 solid-state mechanisms were tested using the Coats-Redfern method. The results of the Coats-Redfern method show that the decomposition mechanism for all samples is the contracting cylinder mechanism. The phase behavior of the obtained samples was evaluated by differential scanning calorimetry (DSC), and structural properties were determined by X-ray powder diffraction (XRPD). The results indicate that copper oxide modifies the phase transition behavior and can catalyze AN decomposition, whereas LiF inhibits AN decomposition, and TiO2 shows no influence on the rate of decomposition. Possible explanations for these results are discussed. Supplementary materials are available for this article. Go to the publisher's online edition of the Journal of Energetic Materials to view the free supplemental file.
Condition assessment of nonlinear processes
Hively, Lee M.; Gailey, Paul C.; Protopopescu, Vladimir A.
2002-01-01
There is presented a reliable technique for measuring condition change in nonlinear data such as brain waves. The nonlinear data is filtered and discretized into windowed data sets. The system dynamics within each data set is represented by a sequence of connected phase-space points, and for each data set a distribution function is derived. New metrics are introduced that evaluate the distance between distribution functions. The metrics are properly renormalized to provide robust and sensitive relative measures of condition change. As an example, these measures can be used on EEG data, to provide timely discrimination between normal, preseizure, seizure, and post-seizure states in epileptic patients. Apparatus utilizing hardware or software to perform the method and provide an indicative output is also disclosed.
Single-pool exponential decomposition models: potential pitfalls in their use in ecological studies.
Adair, E Carol; Hobbie, Sarah E; Hobbie, Russell K
2010-04-01
The importance of litter decomposition to carbon and nutrient cycling has motivated substantial research. Commonly, researchers fit a single-pool negative exponential model to data to estimate a decomposition rate (k). We review recent decomposition research, use data simulations, and analyze real data to show that this practice has several potential pitfalls. Specifically, two common decisions regarding model form (how to model initial mass) and data transformation (log-transformed vs. untransformed data) can lead to erroneous estimates of k. Allowing initial mass to differ from its true, measured value resulted in substantial over- or underestimation of k. Log-transforming data to estimate k using linear regression led to inaccurate estimates unless errors were lognormally distributed, while nonlinear regression of untransformed data accurately estimated k regardless of error structure. Therefore, we recommend fixing initial mass at the measured value and estimating k with nonlinear regression (untransformed data) unless errors are demonstrably lognormal. If data are log-transformed for linear regression, zero values should be treated as missing data; replacing zero values with an arbitrarily small value yielded poor k estimates. These recommendations will lead to more accurate k estimates and allow cross-study comparison of k values, increasing understanding of this important ecosystem process.
Boundary Terms and the 3 + 1 Decomposition of the Holst Action
NASA Astrophysics Data System (ADS)
Corichi, A.; Reyes, J. D.
2012-05-01
Starting from the Holst action with surface terms and the fall-off conditions that make the variational principle and the covariant phase space formulation well-defined for asymptotically flat spacetimes, we rewrite the surface terms in the 3+1 decomposition of the action. We explore their relation with the surface terms in the Hamiltonian formulation in terms of Ashtekar variables. Just as for the Einstein-Hilbert action, if variations respecting asymptotic flatness are allowed, the energy and momentum in the Hamiltonian framework are not directly recovered from the 3+1 decomposition and gauge fixing of these terms.
Linear and Nonlinear Electrostatic Waves in Unmagnetized Dusty Plasmas
Mamun, A. A.; Shukla, P. K.
2010-12-14
A rigorous and systematic theoretical study has been made of linear and nonlinear electrostatic waves propagating in unmagnetized dusty plasmas. The basic features of linear and nonlinear electrostatic waves (particularly, dust-ion-acoustic and dust-acoustic waves) for different space and laboratory dusty plasma conditions are described. The experimental observations of such linear and nonlinear features of dust-ion-acoustic and dust-acoustic waves are briefly discussed.
Efficient numerical methods for nonlinear Schrodinger equations
NASA Astrophysics Data System (ADS)
Liang, Xiao
The nonlinear Schrodinger equations are widely used to model a number of important physical phenomena, including solitary wave propagations in optical fibers, deep water turbulence, laser beam transmissions, and the Bose-Einstein condensation, just to mention a few. In the field of optics and photonics, the systems of nonlinear Schrodinger equations can be used to model multi-component solitons and the interaction of self-focusing laser beams. In three spatial dimensions, the nonlinear Schrodinger equation is known as the Gross-Pitaevskii equation, which models the soliton in a low-cost graded-index fiber. Recently, research on nonlinear space fractional Schrodinger equations, which capture the self-similarity in the fractional environment, has become prevalent. Our study includes the systems of multi-dimensional nonlinear space fractional Schrodinger equations. To solve the systems of multi-dimensional nonlinear Schrodinger equations efficiently, several novel numerical methods are presented. The central difference and quartic spline approximation based exponential time differencing Crank-Nicolson method is introduced for solving systems of one- and two-dimensional nonlinear Schrodinger equations. A local extrapolation is employed to achieve fourth-order accuracy in time. The numerical examples include the transmission of a self-focusing laser beam. The local discontinuous Galerkin methods combined with the fourth-order exponential time differencing Runge-Kutta time discretization are studied for solving the systems of nonlinear Schrodinger equations with hyperbolic terms, which are critical in modeling optical solitons in the birefringent fibers. The local discontinuous Galerkin method is able to achieve any order of accuracy in space, thanks to the usage of piecewise polynomial spaces. The exponential time differencing methods are employed to deal with the coupled nonlinearities for the reason that there is no need to solve nonlinear systems at every time step
Advanced control of nonlinear beams with Pancharatnam-Berry metasurfaces
NASA Astrophysics Data System (ADS)
Tymchenko, M.; Gomez-Diaz, J. S.; Lee, J.; Nookala, N.; Belkin, M. A.; Alù, A.
2016-12-01
The application of the Pancharatnam-Berry (PB) phase approach to the design of nonlinear metasurfaces has recently enabled subdiffractive phase control over the generated nonlinear fields, embedding phased array features in ultrathin structures. Here, we rigorously model, analyze, and design highly efficient nonlinear metasurfaces with advanced functionalities, including the generation of pencil beams steered in arbitrary directions in space, as well as vortex beams with polarization-dependent angular momentum, and we extend the PB approach to various nonlinear processes. To this purpose, we develop an accurate and efficient theoretical framework—inspired by the linear phase array theory—based on the effective nonlinear susceptibility method, thus avoiding the use of time-consuming numerical simulations. Our findings allow exploiting the flat nonlinear optics paradigm, enabling exciting applications based on subwavelength field control over flat and large-scale structures with giant nonlinear responses.
Localized Turing patterns in nonlinear optical cavities
NASA Astrophysics Data System (ADS)
Kozyreff, G.
2012-05-01
The subcritical Turing instability is studied in two classes of models for laser-driven nonlinear optical cavities. In the first class of models, the nonlinearity is purely absorptive, with arbitrary intensity-dependent losses. In the second class, the refractive index is real and is an arbitrary function of the intracavity intensity. Through a weakly nonlinear analysis, a Ginzburg-Landau equation with quintic nonlinearity is derived. Thus, the Maxwell curve, which marks the existence of localized patterns in parameter space, is determined. In the particular case of the Lugiato-Lefever model, the analysis is continued to seventh order, yielding a refined formula for the Maxwell curve and the theoretical curve is compared with recent numerical simulation by Gomila et al. [D. Gomila, A. Scroggie, W. Firth, Bifurcation structure of dissipative solitons, Physica D 227 (2007) 70-77.
Ultrathin nonlinear metasurface for optical image encoding.
Walter, Felicitas; Li, Guixin; Meier, Cedrik; Zhang, Shuang; Zentgraf, Thomas
2017-04-14
Security of optical information is of great importance in modern society. Many cryptography techniques based on classical and quantum optics have been widely explored in the linear optical regime. Nonlinear optical encryption, in which encoding and decoding involve nonlinear frequency conversions, represents a new strategy for securing optical information. Here, we demonstrate that an ultrathin nonlinear photonic metasurface, consisting of meta-atoms with three-fold rotational symmetry, can be used to hide optical images under illumination with a fundamental wave. However, the hidden image can be read out from second harmonic generation (SHG) waves. This is achieved by controlling the destructive and constructive interferences of SHG waves from two neighboring meta-atoms. In addition, we apply this concept to obtain grey-scale SHG imaging. Nonlinear metasurfaces based on space variant optical interference open new avenues for multi-level image encryption, anti-counterfeiting and background free image reconstruction.
Polarization Shaping for Control of Nonlinear Propagation
NASA Astrophysics Data System (ADS)
Bouchard, Frédéric; Larocque, Hugo; Yao, Alison M.; Travis, Christopher; De Leon, Israel; Rubano, Andrea; Karimi, Ebrahim; Oppo, Gian-Luca; Boyd, Robert W.
2016-12-01
We study the nonlinear optical propagation of two different classes of light beams with space-varying polarization—radially symmetric vector beams and Poincaré beams with lemon and star topologies—in a rubidium vapor cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that, by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.
Decomposition of forest products buried in landfills
Wang, Xiaoming; Padgett, Jennifer M.; Powell, John S.; Barlaz, Morton A.
2013-11-15
Highlights: • This study tracked chemical changes of wood and paper in landfills. • A decomposition index was developed to quantify carbohydrate biodegradation. • Newsprint biodegradation as measured here is greater than previous reports. • The field results correlate well with previous laboratory measurements. - Abstract: The objective of this study was to investigate the decomposition of selected wood and paper products in landfills. The decomposition of these products under anaerobic landfill conditions results in the generation of biogenic carbon dioxide and methane, while the un-decomposed portion represents a biogenic carbon sink. Information on the decomposition of these municipal waste components is used to estimate national methane emissions inventories, for attribution of carbon storage credits, and to assess the life-cycle greenhouse gas impacts of wood and paper products. Hardwood (HW), softwood (SW), plywood (PW), oriented strand board (OSB), particleboard (PB), medium-density fiberboard (MDF), newsprint (NP), corrugated container (CC) and copy paper (CP) were buried in landfills operated with leachate recirculation, and were excavated after approximately 1.5 and 2.5 yr. Samples were analyzed for cellulose (C), hemicellulose (H), lignin (L), volatile solids (VS), and organic carbon (OC). A holocellulose decomposition index (HOD) and carbon storage factor (CSF) were calculated to evaluate the extent of solids decomposition and carbon storage. Samples of OSB made from HW exhibited cellulose plus hemicellulose (C + H) loss of up to 38%, while loss for the other wood types was 0–10% in most samples. The C + H loss was up to 81%, 95% and 96% for NP, CP and CC, respectively. The CSFs for wood and paper samples ranged from 0.34 to 0.47 and 0.02 to 0.27 g OC g{sup −1} dry material, respectively. These results, in general, correlated well with an earlier laboratory-scale study, though NP and CC decomposition measured in this study were higher than
Kinetics of Thermal Decomposition of Ammonium Perchlorate by TG/DSC-MS-FTIR
NASA Astrophysics Data System (ADS)
Zhu, Yan-Li; Huang, Hao; Ren, Hui; Jiao, Qing-Jie
2014-01-01
The method of thermogravimetry/differential scanning calorimetry-mass spectrometry-Fourier transform infrared (TG/DSC-MS-FTIR) simultaneous analysis has been used to study thermal decomposition of ammonium perchlorate (AP). The processing of nonisothermal data at various heating rates was performed using NETZSCH Thermokinetics. The MS-FTIR spectra showed that N2O and NO2 were the main gaseous products of the thermal decomposition of AP, and there was a competition between the formation reaction of N2O and that of NO2 during the process with an iso-concentration point of N2O and NO2. The dependence of the activation energy calculated by Friedman's iso-conversional method on the degree of conversion indicated that the AP decomposition process can be divided into three stages, which are autocatalytic, low-temperature diffusion and high-temperature, stable-phase reaction. The corresponding kinetic parameters were determined by multivariate nonlinear regression and the mechanism of the AP decomposition process was proposed.
Nonlinear response of superconductors to alternating fields and currents
McDonald, Jason
1997-10-08
This report discusses the following topics on superconductivity: nonlinearities in hard superconductors such as surface impedance of a type II superconductimg half space and harmonic generation and intermodulation due to alternating transport currents; and nonlinearities in superconducting weak links such as harmonic generation by a long Josephson Junction in a superconducting slab.
Bright solitons in nonlinear media with a self-defocusing double-well nonlinearity
NASA Astrophysics Data System (ADS)
Xie, Qiongtao; Wang, Linmao; Wang, Yizhen; Shen, Zhenjiang; Fu, Jun
2014-12-01
We show that stable bright solitons can appear in a medium with spatially inhomogeneous self-defocusing (SDF) nonlinearity of a double-well structure. For a specific choice of the nonlinearity parameters, we obtain exact analytical solutions for the fundamental bright solitons. By making use of the linear stability analysis, the stability region in the parameter space for the exact fundamental bright soliton is obtained numerically. We also show the bifurcation from an antisymmetric to an asymmetric bright soliton for the SDF double-well nonlinearity.
A general framework of noise suppression in material decomposition for dual-energy CT
Petrongolo, Michael; Dong, Xue; Zhu, Lei
2015-08-15
Purpose: As a general problem of dual-energy CT (DECT), noise amplification in material decomposition severely reduces the signal-to-noise ratio on the decomposed images compared to that on the original CT images. In this work, the authors propose a general framework of noise suppression in material decomposition for DECT. The method is based on an iterative algorithm recently developed in their group for image-domain decomposition of DECT, with an extension to include nonlinear decomposition models. The generalized framework of iterative DECT decomposition enables beam-hardening correction with simultaneous noise suppression, which improves the clinical benefits of DECT. Methods: The authors propose to suppress noise on the decomposed images of DECT using convex optimization, which is formulated in the form of least-squares estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, the authors include the inverse of the estimated variance–covariance matrix of the decomposed images as the penalty weight in the least-squares term. Analytical formulas are derived to compute the variance–covariance matrix for decomposed images with general-form numerical or analytical decomposition. As a demonstration, the authors implement the proposed algorithm on phantom data using an empirical polynomial function of decomposition measured on a calibration scan. The polynomial coefficients are determined from the projection data acquired on a wedge phantom, and the signal decomposition is performed in the projection domain. Results: On the Catphan{sup ®}600 phantom, the proposed noise suppression method reduces the average noise standard deviation of basis material images by one to two orders of magnitude, with a superior performance on spatial resolution as shown in comparisons of line-pair images and modulation transfer function measurements. On the synthesized monoenergetic CT images, the noise standard deviation is
NASA Astrophysics Data System (ADS)
Tang, Yadan; Roberts, Charles A.; Perkins, Ryan T.; Wachs, Israel E.
2016-08-01
This study revisits the classic volcano curve for HCOOH decomposition by metal catalysts by taking a modern catalysis approach. The metal catalysts (Au, Ag, Cu, Pt, Pd, Ni, Rh, Co and Fe) were prepared by H2 reduction of the corresponding metal oxides. The number of surface active sites (Ns) was determined by formic acid chemisorption. In situ IR indicated that both monodentate and bidentate/bridged surface HCOO* were present on the metals. Heats of adsorption (ΔHads) for surface HCOO* values on metals were taken from recently reported DFT calculations. Kinetics for surface HCOO* decomposition (krds) were determined with TPD spectroscopy. Steady-state specific activity (TOF = activity/Ns) for HCOOH decomposition over the metals was calculated from steady-state activity (μmol/g-s) and Ns (μmol/g). Steady-state TOFs for HCOOH decomposition weakly correlated with surface HCOO* decomposition kinetics (krds) and ΔHads of surface HCOO* intermediates. The plot of TOF vs. ΔHads for HCOOH decomposition on metal catalysts does not reproduce the classic volcano curve, but shows that TOF depends on both ΔHads and decomposition kinetics (krds) of surface HCOO* intermediates. This is the first time that the classic catalysis study of HCOOH decomposition on metallic powder catalysts has been repeated since its original publication.
Parametric Identification of Nonlinear Dynamical Systems
NASA Technical Reports Server (NTRS)
Feeny, Brian
2002-01-01
In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.