Quantum Process Tomography of an Optically-Controlled Kerr Non-linearity
Kupchak, Connor; Rind, Samuel; Jordaan, Bertus; Figueroa, Eden
2015-01-01
Any optical quantum information processing machine would be comprised of fully-characterized constituent devices for both single state manipulations and tasks involving the interaction between multiple quantum optical states. Ideally for the latter, would be an apparatus capable of deterministic optical phase shifts that operate on input quantum states with the action mediated solely by auxiliary signal fields. Here we present the complete experimental characterization of a system designed for optically controlled phase shifts acting on single-photon level probe coherent states. Our setup is based on a warm vapor of rubidium atoms under the conditions of electromagnetically induced transparency with its dispersion properties modified through the use of an optically triggered N-type Kerr non-linearity. We fully characterize the performance of our device by sending in a set of input probe states and measuring the corresponding output via time-domain homodyne tomography and subsequently performing the technique of coherent state quantum process tomography. This method provides us with the precise knowledge of how our optical phase shift will modify any arbitrary input quantum state engineered in the mode of the reconstruction. PMID:26585904
Dynamics of atom-field probability amplitudes in a coupled cavity system with Kerr non-linearity
Priyesh, K. V.; Thayyullathil, Ramesh Babu
2014-01-28
We have investigated the dynamics of two cavities coupled together via photon hopping, filled with Kerr non-linear medium and each containing a two level atom in it. The evolution of various atom (field) state probabilities of the coupled cavity system in two excitation sub space are obtained numerically. Detailed analysis has been done by taking different initial conditions of the system, with various coupling strengths and by varying the susceptibility of the medium. The role of susceptibility factor, on the dynamics atom field probability has been examined. In a coupled cavity system with strong photon hopping it is found that the susceptibility factor modifies the behaviour of probability amplitudes.
Tewarie, P.; Bright, M.G.; Hillebrand, A.; Robson, S.E.; Gascoyne, L.E.; Morris, P.G.; Meier, J.; Van Mieghem, P.; Brookes, M.J.
2016-01-01
Understanding the electrophysiological basis of resting state networks (RSNs) in the human brain is a critical step towards elucidating how inter-areal connectivity supports healthy brain function. In recent years, the relationship between RSNs (typically measured using haemodynamic signals) and electrophysiology has been explored using functional Magnetic Resonance Imaging (fMRI) and magnetoencephalography (MEG). Significant progress has been made, with similar spatial structure observable in both modalities. However, there is a pressing need to understand this relationship beyond simple visual similarity of RSN patterns. Here, we introduce a mathematical model to predict fMRI-based RSNs using MEG. Our unique model, based upon a multivariate Taylor series, incorporates both phase and amplitude based MEG connectivity metrics, as well as linear and non-linear interactions within and between neural oscillations measured in multiple frequency bands. We show that including non-linear interactions, multiple frequency bands and cross-frequency terms significantly improves fMRI network prediction. This shows that fMRI connectivity is not only the result of direct electrophysiological connections, but is also driven by the overlap of connectivity profiles between separate regions. Our results indicate that a complete understanding of the electrophysiological basis of RSNs goes beyond simple frequency-specific analysis, and further exploration of non-linear and cross-frequency interactions will shed new light on distributed network connectivity, and its perturbation in pathology. PMID:26827811
NASA Astrophysics Data System (ADS)
Leyva, J. Francisco; Málaga, Carlos; Plaza, Ramón G.
2013-11-01
This paper studies a reaction-diffusion-chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.
NASA Astrophysics Data System (ADS)
Giaccu, Gian Felice; Caracoglia, Luca
2017-04-01
Pre-tensioned-cable bracing systems are widely employed in structural engineering to limit lateral deflections and stabilize structures. A suitable configuration of the pre-tensioned-cable bracing systems in a structure is an important issue since the internal force distribution, emerging from the interaction with the existing structure, significantly affects the structural dynamic behavior. The design, however, is often based on the intuition and the previous experience of the engineer. In recent years, the authors have been investigating the non-linear dynamic response of cable systems, installed on cable-stayed bridges, and in particular the so-called ;cable-cross-tie systems; forming a cable network. The bracing cables (cross-ties) can exhibit slackening or snapping. Therefore, a non-linear unilateral model, combined with the taut-cable theory, is required to simulate the incipient slackening conditions in the stays. Capitalizing from this work on non-linear cable dynamics, this paper proposes a new approach to analyze, in laterally- braced truss structures, the unilateral effects and dynamic response accounting for the loss in the pre-tensioning force imparted to the bracing cables. This effect leads to non-linear vibration of the structure. In this preliminary study, the free vibrations of the structure are investigated by using the ;Equivalent Linearization Method;. A performance coefficient, a real positive number between 0.5 and 1.0, is defined and employed to monitor the relative reduction in the apparent stiffness of the braces during structural vibration, ;mode by mode;. It is shown that the system can exhibit alternate unilateral behavior of the cross-braces. A reduction of the performance coefficient close to fifty percent is observed in the braces when the initial pre-tensioning force is small. On the other hand the performance coefficient tends to one in the case of a high level of pre-stress. It is concluded that the performance coefficient may
Extension of non-linear beam models with deformable cross sections
NASA Astrophysics Data System (ADS)
Sokolov, I.; Krylov, S.; Harari, I.
2015-12-01
Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.
NASA Astrophysics Data System (ADS)
Radu, A.; Duque, C. A.
2015-08-01
The conduction subband structure of a triangular cross-section GaAs/AlGaAs quantum well wire under intense laser field is theoretically investigated by taking into account a finite confining potential. The calculation of the subband energy levels is based on a two-dimensional finite element method within the effective mass approximation. It is shown that a transversally polarized laser field non-uniformly shifts the subband energy levels and could be used for tuning the intersubband transitions and altering the related optical susceptibilities. We found that the non-resonant laser field allows the magnification and the red- or blueshift of the third-order non-linear susceptibility peaks for particular polarizations of the pump light and proper laser parameter values. The effects of the laser dressing field on the intersubband third harmonic generation and quadratic electro-optical process are discussed.
NASA Astrophysics Data System (ADS)
Muñoz-Diosdado, A.
2005-01-01
We analyzed databases with gait time series of adults and persons with Parkinson, Huntington and amyotrophic lateral sclerosis (ALS) diseases. We obtained the staircase graphs of accumulated events that can be bounded by a straight line whose slope can be used to distinguish between gait time series from healthy and ill persons. The global Hurst exponent of these series do not show tendencies, we intend that this is because some gait time series have monofractal behavior and others have multifractal behavior so they cannot be characterized with a single Hurst exponent. We calculated the multifractal spectra, obtained the spectra width and found that the spectra of the healthy young persons are almost monofractal. The spectra of ill persons are wider than the spectra of healthy persons. In opposition to the interbeat time series where the pathology implies loss of multifractality, in the gait time series the multifractal behavior emerges with the pathology. Data were collected from healthy and ill subjects as they walked in a roughly circular path and they have sensors in both feet, so we have one time series for the left foot and other for the right foot. First, we analyzed these time series separately, and then we compared both results, with direct comparison and with a cross correlation analysis. We tried to find differences in both time series that can be used as indicators of equilibrium problems.
Quantum teleportation of a generic two-photon state with weak cross-Kerr nonlinearities
NASA Astrophysics Data System (ADS)
Wang, Meiyu; Yan, Fengli
2016-08-01
We present a scheme for teleporting a generic two-photon polarization state by using two EPR states as quantum channel based on weak cross-Kerr nonlinearities. As the core component of the present framework, the quantum nondemolition detector based on the weak cross-Kerr nonlinearity acts as an EPR entangler as well as the Bell-state analyzer. This makes the teleportation protocol be achieved near deterministically and be feasible in the current experimental technology.
Complete four-photon cluster-state analyzer based on cross-Kerr nonlinearity
NASA Astrophysics Data System (ADS)
Wang, Zhi-Hui; Zhu, Long; Su, Shi-Lei; Guo, Qi; Cheng, Liu-Yong; Zhu, Ai-Dong; Zhang, Shou
2013-09-01
We propose a method to construct an optical cluster-state analyzer based on cross-Kerr nonlinearity combined with linear optics elements. In the scheme, we employ two four-qubit parity gates and the controlled phase gate (CPG) from only the cross-Kerr nonlinearity and show that all the orthogonal four-qubit cluster states can be completely identified. The scheme is significant for the large-scale quantum communication and quantum information processing networks. In addition, the scheme is feasible and deterministic under current experimental conditions.
Implementing Toffoli gate via weak cross-Kerr nonlinearity and classical feedback
NASA Astrophysics Data System (ADS)
Sun, Qian; Ye, Liu
2015-04-01
We design an efficient optical circuit to realize a Toffoli gate via weak cross-Kerr nonlinearity and classical feedback. To obtain a high-fidelity gate, we probe different path detectors to minimize the influence from the environmental noise. Compared to previous proposals, our scheme does not need external auxiliary photons and is easy to implement in experiment.
Generation of four-photon polarization entangled states with cross-Kerr nonlinearity
NASA Astrophysics Data System (ADS)
Wang, Meiyu; Yan, Fengli
2015-05-01
We show how to prepare three different types of four-photon polarization entangled states among four modes. The scheme only use cross-Kerr medium, polarization beam splitters and X homodyne measurements on coherent light fields, which can be efficiently implemented in quantum optical laboratories. GHZ states and symmetric Dick states can be generated in deterministic way based on the scheme. With the possible availability of suitable strong Kerr nonlinearity, another type of entangled state called genuine four-photon entangled state can be realized as well.
Highly non-Gaussian states created via cross-Kerr nonlinearity
NASA Astrophysics Data System (ADS)
Tyc, Tomáš; Korolkova, Natalia
2008-02-01
We propose a feasible scheme for generation of strongly non-Gaussian states using the cross-Kerr nonlinearity. The resultant states are highly non-classical states of an electromagnetic field and exhibit negativity of their Wigner function, sub-Poissonian photon statistics and amplitude squeezing. Furthermore, the Wigner function has a distinctly pronounced 'banana' or 'crescent' shape specific for the Kerr-type interactions, which so far has not been demonstrated experimentally. We show that creating and detecting such states should be possible with the present technology using electromagnetically induced transparency in a four-level atomic system in N-configuration.
NASA Astrophysics Data System (ADS)
Marcotte, D.
2016-04-01
The turning bands method (TBM) is a commonly used method of simulation for large Gaussian fields, its O(N) complexity being unsurpassed (N denotes the number of points to simulate). TBM can be implemented either in the spatial or the spectral domains. In the multivariate anisotropic case, spatial versions of TBM are currently available only for the linear model of coregionalization (LMC). For anisotropic non-LMC with symmetrical covariances only the spectral version is currently available. The spectral domain approach can be slow in the case of non-differentiable covariances due to the numerous frequencies to sample. Here a derivation of the equations is provided for simulating the anisotropic non-LMC directly in the spatial domain and the method is illustrated with two synthetic examples. The approach allows the specification of many different direct and cross-covariance components, each with possibly different geometric anisotropies and different model types. The complexity of the new multivariate approach remains O(N). Hence, a case of two variables defining an anisotropic non-LMC is simulated over one billion points in less than one hour on a desktop computer. These results help enlarge the scope of application of the TBM. The method can be easily implemented in any existing TBM program.
Simplified optical quantum-information processing via weak cross-Kerr nonlinearities
Guo Qi; Bai Juan; Cheng Liuyong; Wang Hongfu; Zhang Shou; Shao Xiaoqiang
2011-05-15
We propose a simplified parity meter for photonic qubits with cross-Kerr nonlinearities, homodyne measurement, and some optical elements. Our scheme has lower error probability than the protocol proposed in Nemoto and Munro [Phys. Rev. Lett. 93, 250502 (2004)]. Based on the present parity meter, we achieve cluster-state preparation, a complete Bell-state analyzer, and quantum teleportation. All of these schemes are nearly deterministic in the regime with little noise and include less optical elements, which makes our schemes more meaningful for large-scale quantum computing.
Spatial Kerr solitons in optical fibres of finite size cross section: beyond the Townes soliton
NASA Astrophysics Data System (ADS)
Drouart, F.; Renversez, G.; Nicolet, A.; Geuzaine, C.
2008-12-01
We propose a new and efficient numerical method to find spatial solitons in optical fibres with a nonlinear Kerr effect including microstructured ones. A nonlinear non-paraxial scalar model of the electric field in the fibre is used (nonlinear Helmholtz equation) and an iterative algorithm is proposed to obtain the nonlinear solutions using the finite element method. The field is supposed to be harmonic in time and along the direction of invariance of the fibre but inhomogeneous in the cross section. In our approach, we solve a nonlinear eigenvalue problem in which the propagation constant is the eigenvalue. Several examples dealing with step-index fibres and microstructured optical fibres with a finite size cross section are described. In each geometry, a single self-coherent nonlinear solution is obtained. This solution, which also depends on the size of the structure, is different from the Townes soliton—but converges towards it at small wavelengths.
NASA Astrophysics Data System (ADS)
Xiu, Xiao-Ming; Li, Qing-Yang; Lin, Yan-Fang; Dong, Hai-Kuan; Dong, Li; Gao, Ya-Jun
2016-10-01
With the assistance of weak cross-Kerr nonlinearities, we present a preparation scheme of four-photon polarization-entangled decoherence-free states, which can be used to construct the minimal optical decoherence-free subspaces where a logical qubit is fully protected against collective decoherence. To complete the preparation task, one spatial entanglement process, two polarization entanglement processes, and one detecting process are applied. The fulfillments of the above processes are contributed by a cross-Kerr nonlinear interaction between the signal photons and a coherent state via Kerr media. Exploiting the available single-photon resource and simple linear optics elements, this scheme is feasible and desirable to be extended to the construction of multiphoton decoherence-free states against the collective decoherence.
Newman, Gregory A.; Commer, Michael
2006-11-17
Software that simulates and inverts electromagnetic field data for subsurface electrical properties (electrical conductivity) of geological media. The software treats data produced by a time harmonic source field excitation arising from the following antenna geometery: loops and grounded bipoles, as well as point electric and magnetic dioples. The inversion process is carried out using a non-linear conjugate gradient optimization scheme, which minimizes the misfit between field data and model data using a least squares criteria. The software is an upgrade from the code NLCGCS_MP ver 1.0. The upgrade includes the following components: Incorporation of new 1 D field sourcing routines to more accurately simulate the 3D electromagnetic field for arbitrary geologic& media, treatment for generalized finite length transmitting antenna geometry (antennas with vertical and horizontal component directions). In addition, the software has been upgraded to treat transverse anisotropy in electrical conductivity.
Wang, Meiyu; Yan, Fengli; Gao, Ting
2016-01-01
We propose a theoretical protocol for preparing four-photon polarization entangled decoherence-free states, which are immune to the collective noise. With the assistance of the cross-Kerr nonlinearities, a two-photon spatial entanglement gate, two controlled-NOT gates, a four-photon polarization entanglement gate are inserted into the circuit, where X homodyne measurements are aptly applied. Combined with some swap gates and simple linear optical elements, four-photon polarization entangled decoherence-free states which can be utilized to represent two logical qubits, |0〉L and |1〉L are achieved at the output ports of the circuit. This generation scheme may be implemented with current experimental techniques. PMID:27901116
Non-linear Young's double-slit experiment.
San Roman, Julio; Ruiz, Camilo; Perez, Jose Antonio; Delgado, Diego; Mendez, Cruz; Plaja, Luis; Roso, Luis
2006-04-03
The Young's double slit experiment is recreated using intense and short laser pulses. Our experiment evidences the role of the non-linear Kerr effect in the formation of interference patterns. In particular, our results evidence a mixed mechanism in which the zeroth diffraction order of each slit are mainly affected by self-focusing and self-phase modulation, while the higher orders propagate linearly. Despite of the complexity of the general problem of non-linear propagation, we demonstrate that this experiment retains its simplicity and allows for a geometrical interpretation in terms of simple optical paths. In consequence, our results may provide key ideas on experiments on the formation of interference patterns with intense laser fields in Kerr media.
Wang, Mei-Yu; Yan, Feng-Li; Gao, Ting
2016-01-01
We present two deterministic quantum entanglement distribution protocols for a four-photon Dicke polarization entangled state resorting to the frequency and spatial degrees of freedom, which are immune to an arbitrary collective-noise channel. Both of the protocols adopt the X homodyne measurement based on the cross-Kerr nonlinearity to complete the task of the single-photon detection with nearly unit probability in principle. After the four receivers share the photons, they add some local unitary operations to obtain a standard four-photon Dicke polarization entangled state. PMID:27412489
NASA Astrophysics Data System (ADS)
Dutta, Srimonti; Ghosh, Dipak; Samanta, Shukla
2016-04-01
This paper studies the human gait pattern of normal people and patients suffering from Parkinson's disease using the MFDXA (Multifractal Detrended Cross-correlation Analysis) methodology. The auto correlation and cross correlation of the time series of the total force under the left foot and right foot were studied. The study reveals that the degree of multifractality (W) and degree of correlation (γ) are generally more for normal patients than the diseased set. It is also observed that the values of W and γ are nearly same for left foot and right. It is also observed that the study of autocorrelation alone is not sufficient, cross correlations should also be studied to get a better concept of neurodegenerative diseases.
NASA Astrophysics Data System (ADS)
Jia, Yueqian; Bai, Yuanli
2016-08-01
A fully modularized framework was established to combine isotropic, kinematic, and cross hardening behaviors under non-monotonic loading conditions. Three sets of state variables were defined and applied to consider the effects of, a) loading history, b) twinning and de-twinning and c) different pre-strain. Experiments under two types of non-proportional loading conditions were conducted along different orientations, 1) uniaxial compression-tension reversal loading with different amounts of compressive strains, and 2) two-step uniaxial tension, known as cross-loading conditions, with different pre-strains. No apparent cross-hardening effect was observed for this material. The calibrated new hardening model, with an anisotropic CPB06ex2 yield criterion and an eMMC anisotropic fracture model, has been implemented into Abaqus/ Explicit as a user material subroutine (VUMAT). Good correlation was observed between experimental and simulation results.
Organic-inorganic hybrid glass: non-linear optical properties
NASA Astrophysics Data System (ADS)
Domínguez Cruz, R.; Mendez-Perez, A.; Romero Galván, G.; Mendoza-Panduro, M.; Trejo-Duran, M.; Alvarado-Mendez, E.; Estudillo-Ayala, J. M.; Rojas-Laguna, R.; Martínez-Richa, A.; Castano, V. M.
2008-04-01
In this paper we report the preliminary results about the optical characterization of a new kind of organic-inorganic hybrid glass named 4-((5-dichloromethylsily1)-penty)oxy-cyanobenzene (DCN) synthesized by sol-gel process. We obtain the sign and magnitude of the sample by the Z-scan technique using a low power He-Ne laser at 632 nm in CW operation. The experimental data show that the DNC glass has a negative Kerr optical non-linearity and is estimated a nonlinear coefficient as Δn˜10-6.
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong
2016-07-18
Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.
NASA Astrophysics Data System (ADS)
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong
2016-07-01
Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.
NASA Astrophysics Data System (ADS)
de Jong, Roelof
2005-07-01
This program incorporates a number of tests to analyse the count rate dependent non-linearity seen in NICMOS spectro-photometric observations. In visit 1 we will observe a few fields with stars of a range in luminosity in NGC1850 with NICMOS in NIC1 in F090M, F110W and F160W and NIC2 F110W, F160W, and F180W. We will repeat the observations with flatfield lamp on, creating artificially high count-rates, allowing tests of NICMOS linearity as function of count rate. To access the effect of charge trapping and persistence, we first take darks {so there is not too much charge already trapped}, than take exposures with the lamp off, exposures with the lamp on, and repeat at the end with lamp off. Finally, we continue with taking darks during occultation. In visit 2 we will observe spectro-photometric standard P041C using the G096 and G141 grisms in NIC3, and repeat the lamp off/on/off test to artificially create a high background. In visits 3&4 we repeat photometry measurements of faint standard stars SNAP-2 and WD1657+343, on which the NICMOS non-linearity was originally discovered using grism observations. These measurements are repeated, because previous photometry was obtained with too short exposure times, hence substantially affected by charge trapping non-linearity. Measurements will be made with NIC1: Visit 5 forms the persistence test of the program. The bright star GL-390 {used in a previous persistence test} will iluminate the 3 NICMOS detectors in turn for a fixed time, saturating the center many times, after which a series of darks will be taken to measure the persistence {i.e. trapped electrons and the decay time of the traps}. To determine the wavelength dependence of the trap chance, exposures of the bright star in different filters will be taken, as well as one in the G096 grism with NIC3. Most exposures will be 128s long, but two exposures in the 3rd orbit will be 3x longer, to seperate the effects of count rate versus total counts of the trap
NASA Astrophysics Data System (ADS)
Abdel-Wahab, N. H.; Thabet, Lamia E.
2016-01-01
In this paper, some properties through the moving four-level N-type atom interacting with a two-mode radiation field are presented. We study this system in the presence of the nonlinearity. The exact solution of this model is given by using the Schrödinger equation when the atom and the field are initially in an excited state and a squeezed state, respectively. We employed the results to perform a careful investigation of the temporal evolution of the cross-correlation function, the momentum increment, the difference mean photon numbers and the normal squeezing. The influence of the Kerr and the cross-Kerr medium parameters on these aspects is examined. It is found that the atom-field properties are affected by the changing of these parameters.
Ghost Dark Energy with Non-Linear Interaction Term
NASA Astrophysics Data System (ADS)
Ebrahimi, E.
2016-06-01
Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w D = p/ ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω D ). We find that in one case, w D cross the phantom line ( w D < -1). However in two other classes w D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w D , q. We study squared sound speed {vs2}, and find that for one case of non-linear interaction term {vs2} can achieves positive values at late time of evolution.
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong
2016-01-01
Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding. PMID:27424767
Non-linearity in clinical practice.
Petros, Peter
2003-05-01
The whole spectrum of medicine consists of complex non-linear systems that are balanced and interact with each other. How non-linearity confers stability on a system and explains variation and uncertainty in clinical medicine is discussed. A major theme is that a small alteration in initial conditions may have a major effect on the end result. In the context of non-linearity, it is argued that 'evidence-based medicine' (EBM) as it exists today can only ever be relevant to a small fraction of the domain of medicine, that the 'art of medicine' consists of an intuitive 'tuning in' to these complex systems and as such is not so much an art as an expression of non-linear science. The main cause of iatrogenic disease is interpreted as a failure to understand the complexity of the systems being treated. Case study examples are given and analysed in non-linear terms. It is concluded that good medicine concerns individualized treatment of an individual patient whose body functions are governed by non-linear processes. EBM as it exists today paints with a broad and limited brush, but it does promise a fresh new direction. In this context, we need to expand the spectrum of scientific medicine to include non-linearity, and to look upon the 'art of medicine' as a historical (but unstated) legacy in this domain.
Gain optimization with non-linear controls
NASA Technical Reports Server (NTRS)
Slater, G. L.; Kandadai, R. D.
1984-01-01
An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.
Non-linear Post Processing Image Enhancement
NASA Technical Reports Server (NTRS)
Hunt, Shawn; Lopez, Alex; Torres, Angel
1997-01-01
A non-linear filter for image post processing based on the feedforward Neural Network topology is presented. This study was undertaken to investigate the usefulness of "smart" filters in image post processing. The filter has shown to be useful in recovering high frequencies, such as those lost during the JPEG compression-decompression process. The filtered images have a higher signal to noise ratio, and a higher perceived image quality. Simulation studies comparing the proposed filter with the optimum mean square non-linear filter, showing examples of the high frequency recovery, and the statistical properties of the filter are given,
Stability of non-linear integrable accelerator
Batalov, I.; Valishev, A.; /Fermilab
2011-09-01
The stability of non-linear Integrable Optics Test Accelerator (IOTA) model developed in [1] was tested. The area of the stable region in transverse coordinates and the maximum attainable tune spread were found as a function of non-linear lens strength. Particle loss as a function of turn number was analyzed to determine whether a dynamic aperture limitation present in the system. The system was also tested with sextupoles included in the machine for chromaticity compensation. A method of evaluation of the beam size in the linear part of the accelerator was proposed.
Non-linear dynamic analysis of beams with variable stiffness
NASA Astrophysics Data System (ADS)
Katsikadelis, J. T.; Tsiatas, G. C.
2004-03-01
In this paper the analog equation method (AEM), a BEM-based method, is employed to the non-linear dynamic analysis of a Bernoulli-Euler beam with variable stiffness undergoing large deflections, under general boundary conditions which maybe non-linear. As the cross-sectional properties of the beam vary along its axis, the coefficients of the differential equations governing the dynamic equilibrium of the beam are variable. The formulation is in terms of the displacements. The governing equations are derived in both deformed and undeformed configuration and the deviations of the two approaches are studied. Using the concept of the analog equation, the two coupled non-linear hyperbolic differential equations with variable coefficients are replaced by two uncoupled linear ones pertaining to the axial and transverse deformation of a substitute beam with unit axial and bending stiffness, respectively, under fictitious time-dependent load distributions. A significant advantage of this method is that the time history of the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. Beams with constant and varying stiffness are analyzed under various boundary conditions and loadings to illustrate the merits of the method as well as its applicability, efficiency and accuracy.
Non-linear cord-rubber composites
NASA Technical Reports Server (NTRS)
Clark, S. K.; Dodge, R. N.
1989-01-01
A method is presented for calculating the stress-strain relations in a multi-layer composite made up of materials whose individual stress-strain characteristics are non-linear and possibly different. The method is applied to the case of asymmetric tubes in tension, and comparisons with experimentally measured data are given.
Possibilities Of Optically Non Linear Thin Films
NASA Astrophysics Data System (ADS)
De Micheli, Marc; Zyss, Joseph; Azema, Alain
1983-11-01
Efficient integrated frequency doubling devices transparent in the visible and near I.R. are demanded by a number of applications. The optimization of both wave interaction configurations and material intrinsic nonlinear susceptibility are successively discussed within this scope. Basic features such as power confinement, interaction length dependence, phase matching techniques, underlying the second harmonic generation conversion rate in bulk and waveguided structures are compared. Undoped Ga As film epitaxied over n+ doped Ga As substrate and TIPE Lithium Lobate waveguides exemplify the possibilities of non linear thin films. The higher non linear susceptibility of certain organic molecular single crys-tals should help raise the efficiency of doubling devices. We report the definition and bulk performances of two non linear organic crystals, namely POM (3-methyl-4 nitropyridine-1-oxyde) and MAP (methyl-(2,4-dinitropheny1)-aminopropanoate) with a figure of merit up to one order of magnitude above that of Li Nb 03. The combination of organic materials and waveguided configuration should lead to a new generation of non linear devices.
Pharmaceutical applications of non-linear imaging.
Strachan, Clare J; Windbergs, Maike; Offerhaus, Herman L
2011-09-30
Non-linear optics encompasses a range of optical phenomena, including two- and three-photon fluorescence, second harmonic generation (SHG), sum frequency generation (SFG), difference frequency generation (DFG), third harmonic generation (THG), coherent anti-Stokes Raman scattering (CARS), and stimulated Raman scattering (SRS). The combined advantages of using these phenomena for imaging complex pharmaceutical systems include chemical and structural specificities, high optical spatial and temporal resolutions, no requirement for labels, and the ability to image in an aqueous environment. These features make such imaging well suited for a wide range of pharmaceutical and biopharmaceutical investigations, including material and dosage form characterisation, dosage form digestion and drug release, and drug and nanoparticle distribution in tissues and within live cells. In this review, non-linear optical phenomena used in imaging will be introduced, together with their advantages and disadvantages in the pharmaceutical context. Research on pharmaceutical and biopharmaceutical applications is discussed, and potential future applications of the technology are considered.
NASA Astrophysics Data System (ADS)
Heo, Jino; Hong, Chang-Ho; Yang, Hyung-Jin; Hong, Jong-Phil; Choi, Seong-Gon
2017-04-01
We demonstrate the advantages of an optical parity gate using weak cross-Kerr nonlinearities (XKNLs), quantum bus (qubus) beams, and photon number resolving (PNR) measurement through our analysis, utilizing a master equation under the decoherence effect (occurred the dephasing and photon loss). To generate Bell states, parity gates based on quantum non-demolition measurement using XKNL are extensively employed in quantum information processing. When designing a parity gate via XKNL, the parity gate can be diversely constructed according to the measurement strategies. In practice, the interactions of XKNLs in optical fiber are inevitable under the decoherence effect. Thus, by our analysis of the decoherence effect, we show that the designed parity gate employing homodyne measurement would not be expected to provide reliable quantum operation. Furthermore, compared with a parity gate using a displacement operator and PNR measurement, we conclude there is experimental benefit from implementation of a parity gate via qubus beams and PNR measurement under the decoherence effect.
NASA Astrophysics Data System (ADS)
Heo, Jino; Kang, Min-Sung; Hong, Chang-Ho; Yang, Hyeon; Choi, Seong-Gon
2016-12-01
We present a scheme for implementing discrete quantum Fourier transform (DQFT) with robustness against the decoherence effect using weak cross-Kerr nonlinearities (XKNLs). The multi-photon DQFT scheme can be achieved by operating the controlled path and merging path gates that are formed with weak XKNLs and linear optical devices. To enhance feasibility under the decoherence effect, in practice, we utilize a displacement operator and photon-number-resolving measurement in the optical gate using XKNLs. Consequently, when there is a strong amplitude of the coherent state, we demonstrate that it is possible to experimentally implement the DQFT scheme, utilizing current technology, with a certain probability of success under the decoherence effect.
Investigation of non-linear imaging in high-resolution transmission electron microscopy.
Chang, Yunjie; Wang, Yumei; Cui, Yanxiang; Ge, Binghui
2016-12-01
Transmission cross-coefficient theory and pseudo-weak-phase object approximation theory were combined to investigate the non-linear imaging in high-resolution transmission electron microscopy (HRTEM). The analytical expressions of linear and non-linear imaging components in diffractogram were obtained and changes of linear and non-linear components over sample thickness were analyzed. Moreover, the linear and non-linear components are found to be an odd and even-function of the defocus and Cs, respectively. Based on this, a method for separating the linear and non-linear contrasts in Cs-corrected (non-zero Cs conditions included) HRTEM images was proposed, and its effectiveness was confirmed by image simulations with AlN as an example.
Non-linear dynamics in parkinsonism.
Darbin, Olivier; Adams, Elizabeth; Martino, Anthony; Naritoku, Leslie; Dees, Daniel; Naritoku, Dean
2013-12-25
Over the last 30 years, the functions (and dysfunctions) of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the "rate hypothesis" and the "oscillatory hypothesis." In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively. More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e., parkinsonism, dyskinesia, healthy control) and are responsive to treatments (i.e., l-DOPA, deep brain stimulation). A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series) is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG), muscular activities (EMG), or kinetic of motor symptoms (tremor, gait) of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity, and hypokinesia.
Non-Linear Dynamics of Saturn's Rings
NASA Astrophysics Data System (ADS)
Esposito, L. W.
2015-10-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Results of driven N-body systems by Stuart Robbins: Even unforced rings show large variations; Forcing triggers aggregation; Some limit cycles and phase lags seen, but not always as predicted by predator-prey model. Summary of Halo Results: A predatorprey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw'. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon
Non-Linear Dynamics of Saturn's Rings
NASA Astrophysics Data System (ADS)
Esposito, Larry W.
2015-04-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible Results of driven N-body systems by Stuart Robbins: Even unforced rings show large variations; Forcing triggers aggregation; Some limit cycles and phase lags seen, but not always as predicted by predator-prey model. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw'. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon
Non-linear memristor switching model
NASA Astrophysics Data System (ADS)
Chernov, A. A.; Islamov, D. R.; Pik'nik, A. A.
2016-10-01
We introduce a thermodynamical model of filament growing when a current pulse via memristor flows. The model is the boundary value problem, which includes nonstationary heat conduction equation with non-linear Joule heat source, Poisson equation, and Shockley- Read-Hall equations taking into account strong electron-phonon interactions in trap ionization and charge transport processes. The charge current, which defines the heating in the model, depends on the rate of the oxygen vacancy generation. The latter depends on the local temperature. The solution of the introduced problem allows one to describe the kinetics of the switch process and the final filament morphology.
Thinking about Non-Linear Smoothers.
1986-05-01
interesting possibilities for future study . These seem at the moment to fall into 3 categories: 1) Do we need the step that works on ends of abutting swooshes...Unear’smoothers to00 31. Recent work at Stanford 100 32. Coments an ocaly-lnear ttu.ng 101 .’ .. 33. Qevelnd’s i.ow 102 34. smelting 103 APPENDIX C: A...limited degree, with "Benchmarks’. We are, in most subareas, early in our study of non-linear smoothers. As as consequence, we often have to emphasize
Non-linearities in Holocene floodplain sediment storage
NASA Astrophysics Data System (ADS)
Notebaert, Bastiaan; Nils, Broothaerts; Jean-François, Berger; Gert, Verstraeten
2013-04-01
Floodplain sediment storage is an important part of the sediment cascade model, buffering sediment delivery between hillslopes and oceans, which is hitherto not fully quantified in contrast to other global sediment budget components. Quantification and dating of floodplain sediment storage is data and financially demanding, limiting contemporary estimates for larger spatial units to simple linear extrapolations from a number of smaller catchments. In this paper we will present non-linearities in both space and time for floodplain sediment budgets in three different catchments. Holocene floodplain sediments of the Dijle catchment in the Belgian loess region, show a clear distinction between morphological stages: early Holocene peat accumulation, followed by mineral floodplain aggradation from the start of the agricultural period on. Contrary to previous assumptions, detailed dating of this morphological change at different shows an important non-linearity in geomorphologic changes of the floodplain, both between and within cross sections. A second example comes from the Pre-Alpine French Valdaine region, where non-linearities and complex system behavior exists between (temporal) patterns of soil erosion and floodplain sediment deposition. In this region Holocene floodplain deposition is characterized by different cut-and-fill phases. The quantification of these different phases shows a complicated image of increasing and decreasing floodplain sediment storage, which hampers the image of increasing sediment accumulation over time. Although fill stages may correspond with large quantities of deposited sediment and traditionally calculated sedimentation rates for such stages are high, they do not necessary correspond with a long-term net increase in floodplain deposition. A third example is based on the floodplain sediment storage in the Amblève catchment, located in the Belgian Ardennes uplands. Detailed floodplain sediment quantification for this catchments shows
Non-linear dynamic compensation system
NASA Technical Reports Server (NTRS)
Lin, Yu-Hwan (Inventor); Lurie, Boris J. (Inventor)
1992-01-01
A non-linear dynamic compensation subsystem is added in the feedback loop of a high precision optical mirror positioning control system to smoothly alter the control system response bandwidth from a relatively wide response bandwidth optimized for speed of control system response to a bandwidth sufficiently narrow to reduce position errors resulting from the quantization noise inherent in the inductosyn used to measure mirror position. The non-linear dynamic compensation system includes a limiter for limiting the error signal within preselected limits, a compensator for modifying the limiter output to achieve the reduced bandwidth response, and an adder for combining the modified error signal with the difference between the limited and unlimited error signals. The adder output is applied to control system motor so that the system response is optimized for accuracy when the error signal is within the preselected limits, optimized for speed of response when the error signal is substantially beyond the preselected limits and smoothly varied therebetween as the error signal approaches the preselected limits.
A survey on non-linear oscillations
NASA Astrophysics Data System (ADS)
Atherton, D. P.; Dorrah, H. T.
1980-06-01
This survey paper presents a comprehensive review of work in the field of non-linear oscillations. A brief discussion of second-order systems is followed by a presentation of exact criteria, approximate analytical methods and computational techniques for limit cycles in single variable systems. Multivariable systems are then covered from an analogous viewpoint which allows the reader to clearly identify both how single variable methods have been extended and the possibilities for further research. Particular emphasis is placed on describing function methods since it is believed that, where exact solutions are not possible, the approach may not only give approximate solutions but provides good insight for further computational or simulation studies. The coverage is essentially restricted to continuous lumped parameter systems and includes both free and forced oscillations. Several applications of the theories in various fields of engineering and science are discussed and indicate the broad interest in non-linear oscillatory phenomena. Finally, a detailed bibliography on the subject is provided.
Controllability of non-linear biochemical systems.
Ervadi-Radhakrishnan, Anandhi; Voit, Eberhard O
2005-07-01
Mathematical methods of biochemical pathway analysis are rapidly maturing to a point where it is possible to provide objective rationale for the natural design of metabolic systems and where it is becoming feasible to manipulate these systems based on model predictions, for instance, with the goal of optimizing the yield of a desired microbial product. So far, theory-based metabolic optimization techniques have mostly been applied to steady-state conditions or the minimization of transition time, using either linear stoichiometric models or fully kinetic models within biochemical systems theory (BST). This article addresses the related problem of controllability, where the task is to steer a non-linear biochemical system, within a given time period, from an initial state to some target state, which may or may not be a steady state. For this purpose, BST models in S-system form are transformed into affine non-linear control systems, which are subjected to an exact feedback linearization that permits controllability through independent variables. The method is exemplified with a small glycolytic-glycogenolytic pathway that had been analyzed previously by several other authors in different contexts.
NASA Astrophysics Data System (ADS)
Wiltshire, David L.; Visser, Matt; Scott, Susan M.
2009-01-01
List of illustrations; Contributors; Foreword; Part I. General Relativity: Classical Studies of the Kerr Geometry: 1. The Kerr spacetime: a brief introduction Matt Visser; 2. The Kerr and Kerr-Schild metrics Roy P. Kerr; 3. Roy Kerr and twistor theory Roger Penrose; 4. Global and local problems solved by the Kerr metric Brandon Carter; 5. Four decades of black hole uniqueness theorems David C. Robinson; 6. Ray-traced visualisations Benjamin R. Lewis, Susan M. Scott; Part II. Astrophysics: The Ongoing Observational Revolution: 7. The ergosphere and dyadosphere of the Kerr black hole Remo Ruffini; 8. Supermassive Black Holes Fulvio Melia; 9. The X-ray spectra of accreting Kerr black holes Andrew C. Fabian, Giovanni Miniutti; 10. Cosmological flashes from rotating black holes Maurice H.P.M. van Putten; Part III. Quantum Gravity: Rotating Black Holes at the Theoretical Frontiers: 11. Horizon constraints and black hole entropy Steve Carlip; 12. Higher dimensional generalizations of the Kerr black hole Gary T. Horowitz; Part IV. Appendices: 13. Gravitational field of a spinning mass … Roy P. Kerr; 14. Gravitational collapse and rotation Roy P. Kerr; Index.
Non-Linear Dynamics of Saturn's Rings
NASA Astrophysics Data System (ADS)
Esposito, L. W.
2015-12-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from
Non-linear Flood Risk Assessment
NASA Astrophysics Data System (ADS)
Mazzarella, A.
The genesis of floodings is very complex depending on hydrologic, meteorological and evapo-transpirative factors that are linked among themselves in a non linear way with numerous feedback processes. The Cantor dust and the rank-ordering statistics supply a proper framework for identifying a kind of a non linear order in the time succession of the floodings and so provide a basis for their prediction. When a catalogue is analysed, it is necessary to test its completeness with respect to the size of the recorded events and results obtained from analysis of catalogues that do not take into account such a test are suspect and possibly wrong, or, at least, unreliable. Floodings have no instrumentally determined magnitude scale, like that conventionally used for earthquakes, and this is why they are generally described in qualitative terms. For this reason, a semi-quantitative index, called ASI (Alluvial Strength Index) has been here developed that combines attributes of alluvial triggering mechanisms and effects on the territorial and hydraulic system.The historical succession of alluvial events occurred at high valley of Po river (Northern Italy), mean valley of Calore river (Southern Italy) and at Sarno, near Naples, have been accurately reconstructed on the basis of old documents and classified according to their ASI. The catalogues have been verified to be complete only for events classified at least as moderate and this probably because many of the lowest energetic events, especially in the past, escaped the detection. The identification of scale-invariances in the time clustering of alluvial events, both on short and long time scales, even if indicative of the complexity of their genesis, might be very helpful for the assessment and reduction of the hazard of future disasters. For example, on the basis of the results of the rank-ordering statistics, the most probable occurrence of an alluvial event at Sarno, classified at least as strong, is predicted to occur
Non-linear sequencing and cognizant failure
NASA Astrophysics Data System (ADS)
Gat, Erann
1999-01-01
Spacecraft are traditionally commanded using linear sequences of time-based commands. Linear sequences work fairly well, but they are difficult and expensive to generate, and are usually not capable of responding to contingencies. Any anomalous behavior while executing a linear sequence generally results in the spacecraft entering a safe mode. Critical sequences like orbit insertions which must be able to respond to faults without going into safe mode are particularly difficult to design and verify. The effort needed to generate command sequences can be reduced by extending the vocabulary of sequences to include more sophisticated control constructs. The simplest extensions are conditionals and loops. Adding these constructs would make a sequencing language look more or less like a traditional programming language or scripting language, and would come with all the difficulties associated with such a language. In particular, verifying the correctness of a sequence would be tantamount to verifying the correctness of a program, which is undecidable in general. We describe an extended vocabulary for non-linear sequencing based on the architectural notion of cognizant failure. A cognizant failure architecture is divided into components whose contract is to either achieve (or maintain) a certain condition, or report that they have failed to do so. Cognizant failure is an easier condition to verify than correctness, but it can provide high confidence in the safety of the spacecraft. Because cognizant failure inherently implies some kind of representation of the intent of an action, the system can respond to contingencies in more robust and general ways. We will describe an implemented non-linear sequencing system that is being flown on the NASA New Millennium Deep Space 1 Mission as part of the Remote Agent Experiment.
Non-Linear Electrohydrodynamics in Microfluidic Devices
Zeng, Jun
2011-01-01
Since the inception of microfluidics, the electric force has been exploited as one of the leading mechanisms for driving and controlling the movement of the operating fluid and the charged suspensions. Electric force has an intrinsic advantage in miniaturized devices. Because the electrodes are placed over a small distance, from sub-millimeter to a few microns, a very high electric field is easy to obtain. The electric force can be highly localized as its strength rapidly decays away from the peak. This makes the electric force an ideal candidate for precise spatial control. The geometry and placement of the electrodes can be used to design electric fields of varying distributions, which can be readily realized by Micro-Electro-Mechanical Systems (MEMS) fabrication methods. In this paper, we examine several electrically driven liquid handling operations. The emphasis is given to non-linear electrohydrodynamic effects. We discuss the theoretical treatment and related numerical methods. Modeling and simulations are used to unveil the associated electrohydrodynamic phenomena. The modeling based investigation is interwoven with examples of microfluidic devices to illustrate the applications. PMID:21673912
In situ characterisation of non linear capacitors
NASA Astrophysics Data System (ADS)
Laudebat, L.; Bley, V.; Lebey, T.; Schneider, H.; Tounsi, P.
2001-05-01
Multilayers ceramic capacitors (MLCC) presenting non linear behaviours of their C(V) characteristics may have interesting applications in power electronics. Most of them have already been described. Nevertheless, the choice of a particular type instead of another one is all the more so difficult since, on one hand the physical mechanisms able to explain this behaviour is far from being understood. On the other hand, C(V) characteristics are in general obtained for low voltage values different from the ones they are going to be involved in. In this paper, direct in situ characterisations of different BaTiO3 based capacitors commercially available are achieved. The role of the capacitors' type (X7R,Z5U), of the temperature and of the voltage waveform (and more particularly its polarity) is demonstrated. Temperature values up to 200 oC are measured during normal operations in a RCD dissipative snubber without any alterations of the C(V) characteristics. All these results are discussed as regards the main physical properties of the constitutive materials in order to reach an optimisation of their use through an appropriate dimensioning.
Non-Linear Dielectrics and Ferrites in ICEPIC
2012-04-10
Technical Paper 3. DATES COVERED (From - To) 2010-2011 4. TITLE AND SUBTITLE Non-linear Dielectrics and Ferrites in ICEPIC 5a. CONTRACT...Electromagnetics Government Purpose Rights 14. ABSTRACT Models for non-linear dielectrics and magnetic ferrites are developed and coded into the particle...be longer than an FDTD time step. The ferrite model accounts for the non-linearity of the Landau-Lifshitz-Gibert equation, and the magnetization
Discriminant power analyses of non-linear dimension expansion methods
NASA Astrophysics Data System (ADS)
Woo, Seongyoun; Lee, Chulhee
2016-05-01
Most non-linear classification methods can be viewed as non-linear dimension expansion methods followed by a linear classifier. For example, the support vector machine (SVM) expands the dimensions of the original data using various kernels and classifies the data in the expanded data space using a linear SVM. In case of extreme learning machines or neural networks, the dimensions are expanded by hidden neurons and the final layer represents the linear classification. In this paper, we analyze the discriminant powers of various non-linear classifiers. Some analyses of the discriminating powers of non-linear dimension expansion methods are presented along with a suggestion of how to improve separability in non-linear classifiers.
Employment of CB models for non-linear dynamic analysis
NASA Technical Reports Server (NTRS)
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Finite element simulation of non-linear acoustic generation in a horn loudspeaker
NASA Astrophysics Data System (ADS)
Tsuchiya, T.; Kagawa, Y.; Doi, M.; Tsuji, T.
2003-10-01
The loudspeaker is an electro-acoustic device for sound reproduction which requires the distortion as small as possible. The distortion may arise from the magnetic non-linearity of the york, the uneven magnetic field distribution, the mechanical non-linearity at the diaphragm suspension and the acoustic non-linearity due to the high sound pressure and velocity in the duct-radiation system. A horn is sometimes provided in front of the vibrating diaphragm radiator, which plays an important role to increase the efficiency by matching the acoustic impedance between the radiator and the ambient medium. The horn is in many cases folded twice or three times to shorten the length, which further degrades the reproduction quality. The sound intensity and velocity are apt to attain very high in the small cross-sectional area in the throat and in the folded regions, which may cause the distortion due to the non-linear effect of the medium. The present paper is to investigate the frequency characteristics of the loudspeaker numerically evaluating the generation of the harmonics and sub-harmonics. An axisymmetric folded horn is considered for which the wave equation with the non-linear term retained is solved by the finite element method. The solution is made in time domain in which the sound pressure calculated at the opening end of the horn is Fourier-transformed to the frequency domain to evaluate the distortion, while the wave marching in the horn is visualized.
Complete quantum teleportation with a kerr nonlinearity
Vitali; Fortunato; Tombesi
2000-07-10
We present a scheme for the quantum teleportation of the polarization state of a photon employing a cross-Kerr medium. The experimental feasibility of the scheme is discussed and we show that, using the recently demonstrated ultraslow light propagation in cold atomic media, our proposal can be realized with presently available technology.
Computer modeling of batteries from non-linear circuit elements
NASA Technical Reports Server (NTRS)
Waaben, S.; Federico, J.; Moskowitz, I.
1983-01-01
A simple non-linear circuit model for battery behavior is given. It is based on time-dependent features of the well-known PIN change storage diode, whose behavior is described by equations similar to those associated with electrochemical cells. The circuit simulation computer program ADVICE was used to predict non-linear response from a topological description of the battery analog built from advice components. By a reasonable choice of one set of parameters, the circuit accurately simulates a wide spectrum of measured non-linear battery responses to within a few millivolts.
Dilatonic non-linear sigma models and Ricci flow extensions
NASA Astrophysics Data System (ADS)
Carfora, M.; Marzuoli, A.
2016-09-01
We review our recent work describing, in terms of the Wasserstein geometry over the space of probability measures, the embedding of the Ricci flow in the renormalization group flow for dilatonic non-linear sigma models.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
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.
Visual discrimination and adaptation using non-linear unsupervised learning
NASA Astrophysics Data System (ADS)
Jiménez, Sandra; Laparra, Valero; Malo, Jesus
2013-03-01
Understanding human vision not only involves empirical descriptions of how it works, but also organization principles that explain why it does so. Identifying the guiding principles of visual phenomena requires learning algorithms to optimize specific goals. Moreover, these algorithms have to be flexible enough to account for the non-linear and adaptive behavior of the system. For instance, linear redundancy reduction transforms certainly explain a wide range of visual phenomena. However, the generality of this organization principle is still in question:10 it is not only that and additional constraints such as energy cost may be relevant as well, but also, statistical independence may not be the better solution to make optimal inferences in squared error terms. Moreover, linear methods cannot account for the non-uniform discrimination in different regions of the image and color space: linear learning methods necessarily disregard the non-linear nature of the system. Therefore, in order to account for the non-linear behavior, principled approaches commonly apply the trick of using (already non-linear) parametric expressions taken from empirical models. Therefore these approaches are not actually explaining the non-linear behavior, but just fitting it to image statistics. In summary, a proper explanation of the behavior of the system requires flexible unsupervised learning algorithms that (1) are tunable to different, perceptually meaningful, goals; and (2) make no assumption on the non-linearity. Over the last years we have worked on these kind of learning algorithms based on non-linear ICA,18 Gaussianization, 19 and principal curves. In this work we stress the fact that these methods can be tuned to optimize different design strategies, namely statistical independence, error minimization under quantization, and error minimization under truncation. Then, we show (1) how to apply these techniques to explain a number of visual phenomena, and (2) suggest the
Non-linear modal analysis of structural components subjected to unilateral constraints
NASA Astrophysics Data System (ADS)
Attar, M.; Karrech, A.; Regenauer-Lieb, K.
2017-02-01
In this paper, we present a detailed numerical study of the non-linear dynamics in structural components under unilateral contact constraints. Here, the unilateral term characterises the constitutive law of the restoring force in the constraints as they only sustain elastic reactions in one direction, either compressive or tensile. Thus, the non-differentiability of the contact law at the discontinuity point is the only source of non-linearity. In our approach, the discrete lattice method (DLM) is used to treat the continuous system as a piecewise linear model. Thus, the trajectory of each node in the discrete model would be a sequence of smooth solutions with the switching times between them. The application of the one-step integration scheme allows us to detect the occurrence of contact (i.e. the instants that the lattice nodes cross the discontinuity boundary) and consequently update the active constraints. We also consider embedding the bisection algorithm into the time integration procedure to localise the instants at which the nodes cross the boundary and minimise the accumulative error. Subsequently, the resulting unconditionally stable integration scheme is utilised as the modelling tool in combination with the shooting technique to perform a novel non-smooth modal analysis. In analogy with the smooth non-linear systems, the evolution of non-smooth periodic motions is presented in the frequency-stiffness plots. We apply our method to obtain non-linear normal modes (NNMs) for a number of representative problems, including a bar-obstacle system, a beam-substrate system and a granular chain with tensionless interactions. These numerical examples demonstrate the efficiency of the solution procedure to trace the family of energy-independent non-linear modes across the range of contact stiffnesses. Moreover, the stability analysis of the modes on the plot backbone reveal that they may become unstable due to the interaction with the higher modes or bifurcation of
NASA Astrophysics Data System (ADS)
Gonçalves Correia, Dayse; Viana Ávila, Kilvia Maria; Cavalcante, Daniel do Nascimento e. Sá; Ferreira Pinto, Paulo Victor; Tadeu de Carvalho Belchior Magalhães, Francisco; Pinheiro de Moura, Lucas; da Conceição Ferreira, Alisson; Mendonça Menezes, Jose Wally; de Freitas Guimarães, Glendo
2016-03-01
In this work, we investigated the optical switching process for three shapes of femtosecond pulses (soliton, Gaussian and super-Gaussian) propagating inside a symmetrical dual-core non-linear directional coupler by simulating their propagation via the coupled non-linear Schrödinger equations. In all simulations, we considered the dispersive effects of second and third order, besides the self-phase modulation and self-steepening non-linear effects. We studied three scenarios for each of the three pulse shapes under investigation. In the first scenario, we added only cross-phase modulation (XPM); in the second approach, we added only Raman scattering; in the third one, we combined both. The study was performed for distinct polarization modes and for different values of the Raman factor, with power range varying from 1 to 300 W. We noted that the XPM non-linear effect results in a decrease in the critical power threshold, whereas the Raman scattering causes an increase. For the first scenario (only XPM effect), the critical power threshold reduced from 113.72 to 104.69 W for the soliton pulse, from 111.49 to 100.77 W for the Gaussian and from 92.79 to 80.47 W for the Super-Gaussian pulse shape. For the second scenario (only Raman scattering), the critical power increased for a Raman factor varying from 1 to 10 fs, and the three pulse shapes reached thresholds above 150 W from a 5 fs factor, reaching more than 200 W for the super-Gaussian pulse as the Raman factor increased. For the third scenario (with both effects combined), we highlight that for a fixed XPM factor of 2, the critical power remained unchanged with the variation of the Raman factor. Hence, we observed that the Super-Gaussian pulse reached lower values for critical power when compared to the other pulse shapes.
Non-linear material characterisation using the noncollinear method
NASA Astrophysics Data System (ADS)
Croxford, Anthony J.; Wilcox, Paul D.; Drinkwater, Bruce W.
2010-04-01
Conventional ultrasonic NDT techniques are limited in their ability to detect small defects by the diffraction limit, that is there is much reduced sensitivity to defects smaller than the wavelength of the interrogating ultrasonic wave. While not a major issue for most inspection, this problem becomes particularly significant for the detection of fatigue damage prior to crack formation. In this regime conventional NDT has proven to be inadequate. For this reason significant effort has been expended on the development of non-linear techniques. These techniques rely on deviations of the material from linear stress strain behaviour which create harmonics in the resulting frequency response. Evidence suggests that changes to a materials condition, such as fatigue damage, change this non-linear response. This paper presents a non-linear inspection method using a non-collinear interaction. This technique has several advantages over other harmonic approaches in that there is spatial separation, modal separation and frequency separation of the non-linear signal. This allows the origin of the non-linear signal and underlying noise levels to be well defined. The capability of the technique is demonstrated using plastically strained material and samples subjected to low cycle fatigue.
Isolating Non-Linear Signatures of Two Colliding Black Holes
NASA Astrophysics Data System (ADS)
Garrido, Rita
2012-03-01
The early and late stages of the binary-black-hole collision can be approximated by perturbations to a background, solutions to linearization of the Einstein's equations. However, once the two black holes are within several radii of each other, and ultimately collide, the solution is intrinsically non-linear. The main objective is to intuitively understand the non-linear portion of the solution to the Einstein equation by performing simulations of such mergers. I will identify the non-linear regime through a process of elimination. The early stages of the coalescence are well known by post-Newtonian theory. The end state is approximated very well by perturbation theory, the waveforms decay as a damped sinusoidal with a frequency and decay time uniquely determined by the mass and spin of the final black hole in theory. I will isolate the non-linear portion of the waveform by fitting the early stages to the post-Newtonian solution and the late stages to the perturbative solution. What remains is the non-linear region. Once isolated, we will search through the physics parameter space of the binary black holes for bulk features. These features can then be used to fine-tune the search algorithms hunting for these collisions with LIGO.
A general non-linear multilevel structural equation mixture model
Kelava, Augustin; Brandt, Holger
2014-01-01
In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include non-linear interaction and quadratic effects (e.g., Klein and Moosbrugger, 2000), and multilevel modeling (Rabe-Hesketh et al., 2004). We present a general non-linear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric non-linear structural equation models (Kelava and Nagengast, 2012; Kelava et al., 2014) with multilevel structural equation mixture models (Muthén and Asparouhov, 2009) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework. PMID:25101022
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.
Non-Linear Vibration Characteristics of Clamped Laminated Shallow Shells
NASA Astrophysics Data System (ADS)
ABE, A.; KOBAYASHI, Y.; YAMADA, G.
2000-07-01
This paper examines non-linear free vibration characteristics of first and second vibration modes of laminated shallow shells with rigidly clamped edges. Non-linear equations of motion for the shells based on the first order shear deformation and classical shell theories are derived by means of Hamilton's principle. We apply Galerkin's procedure to the equations of motion in which eigenvectors for first and second modes of linear vibration obtained by the Ritz method are employed as trial functions. Then simultaneous non-linear ordinary differential equations are derived in terms of amplitudes of the first and second vibration modes. Backbone curves for the first and second vibration modes are solved numerically by the Gauss-Legendre integration method and the shooting method respectively. The effects of lamination sequences and transverse shear deformation on the behavior are discussed. It is also shown that the motion of the first vibration mode affects the response for the second vibration mode.
Pattern formation due to non-linear vortex diffusion
NASA Astrophysics Data System (ADS)
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
Non-linear effects in bunch compressor of TARLA
NASA Astrophysics Data System (ADS)
Yildiz, Hüseyin; Aksoy, Avni; Arikan, Pervin
2016-03-01
Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects on bunch compressor of TARLA.
Realization of non-linear coherent states by photonic lattices
Dehdashti, Shahram Li, Rujiang; Chen, Hongsheng; Liu, Jiarui Yu, Faxin
2015-06-15
In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Non-linear analysis of moderately thick sector plates
NASA Astrophysics Data System (ADS)
Nath, Y.; Sharda, H. B.; Sharma, Ashish
2005-10-01
Non-linear static analysis of moderately thick sector plates under uniformly distributed loading is presented. Using the first-order shear deformation theory and Von Karman type non-linearity, the governing equations of equilibrium are developed and expressed in terms of displacement components. The Chebyshev polynomial is used for spatial discretization of the differential equations. An iterative incremental approach based on Newton-Raphson method is used for the solution. Convergence study is carried out. Effects of annularity, thickness ratio, sector angle and boundary conditions are investigated. Results are compared with those available from the literature.
Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators
NASA Technical Reports Server (NTRS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-01-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
Photocrosslinkable copolymers for non-linear optical applications
Kawatsuki, N.; Pakbaz, K.; Schmidt, H.W.
1993-12-31
New photocrosslinkable copolymers have been synthesized and applied as non-linear optical materials. The copolymers are based on methyl methacrylate, a photo-excitable benzophenone monomer, a non-linear optical active 4`-[(2-hydroxyethyl)ethylamino]-4-nitro-azobenzene (disperse red 1) side chain monomer and a crosslinkable 2-butenyl monomer. These copolymers can be crosslinked by UV light at 366 nm in the poled state and show a stable alignment of NLO chromophore by monitoring the adsorption spectra. The crosslinked and poled film did not change its alignment after storing 4 weeks at room temperature.
Proceedings of the Non-Linear Aero Prediction Requirements Workshop
NASA Technical Reports Server (NTRS)
Logan, Michael J. (Editor)
1994-01-01
The purpose of the Non-Linear Aero Prediction Requirements Workshop, held at NASA Langley Research Center on 8-9 Dec. 1993, was to identify and articulate requirements for non-linear aero prediction capabilities during conceptual/preliminary design. The attendees included engineers from industry, government, and academia in a variety of aerospace disciplines, such as advanced design, aerodynamic performance analysis, aero methods development, flight controls, and experimental and theoretical aerodynamics. Presentations by industry and government organizations were followed by panel discussions. This report contains copies of the presentations and the results of the panel discussions.
BEAM-BASED NON-LINEAR OPTICS CORRECTIONS IN COLLIDERS.
PILAT, R.; LUO, Y.; MALITSKY, N.; PTITSYN, V.
2005-05-16
A method has been developed to measure and correct operationally the non-linear effects of the final focusing magnets in colliders, that gives access to the effects of multi-pole errors by applying closed orbit bumps, and analyzing the resulting tune and orbit shifts. This technique has been tested and used during 4 years of RHIC (the Relativistic Heavy Ion Collider at BNL) operations. I will discuss here the theoretical basis of the method, the experimental set-up, the correction results, the present understanding of the machine model, the potential and limitations of the method itself as compared with other non-linear correction techniques.
Non-linear aeroelastic prediction for aircraft applications
NASA Astrophysics Data System (ADS)
de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.
2007-05-01
Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. To evaluate the methodologies on real aircraft problems. To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research
Non-linear Langmuir waves in a warm quantum plasma
Dubinov, Alexander E. Kitaev, Ilya N.
2014-10-15
A non-linear differential equation describing the Langmuir waves in a warm quantum electron-ion plasma has been derived. Its numerical solutions of the equation show that ordinary electronic oscillations, similar to the classical oscillations, occur along with small-scale quantum Langmuir oscillations induced by the Bohm quantum force.
Tunneling control using classical non-linear oscillator
Kar, Susmita; Bhattacharyya, S. P.
2014-04-24
A quantum particle is placed in symmetric double well potential which is coupled to a classical non-linear oscillator via a coupling function. With different spatial symmetry of the coupling and under various controlling fashions, the tunneling of the quantum particle can be enhanced or suppressed, or totally destroyed.
Characterising dynamic non-linearity in floating wind turbines
NASA Astrophysics Data System (ADS)
Lupton, R. C.
2014-12-01
Fully coupled aero-hydro-control-elastic codes are being developed to cope with the new modelling challenges presented by floating wind turbines, but there is also a place for more efficient methods of analysis. One option is linearisation and analysis in the frequency domain. For this to be an effective method, the non-linearities in the system must be well understood. The present study focusses on understanding the dynamic response of the rotor to the overall platform motion, as would arise from wave loading, by using a simple model of a floating wind turbine with a rigid tower and flexible rotor (represented by hinged rigid blades). First, an equation of motion of the blade is derived and an approximate solution for the blade response is found using the perturbation method. Secondly, the full non-linear solution is found by time- domain simulation. The response is found to be linear at lower platform pitching frequencies, becoming non-linear at higher frequencies, with the approximate solution giving good results for weakly non-linear behaviour. Higher rotor speeds have a stabilising effect on the response. In the context of typical floating turbine parameters, it is concluded that the blade flapwise response is likely to be linear.
Non-linear dynamic analysis of geared systems, part 2
NASA Technical Reports Server (NTRS)
Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet
1990-01-01
A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.
Evolution equation for non-linear cosmological perturbations
Brustein, Ram; Riotto, Antonio E-mail: Antonio.Riotto@cern.ch
2011-11-01
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations, with some possibly important differences. We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance.
Using Non-Linear Statistical Methods with Laboratory Kinetic Data
NASA Technical Reports Server (NTRS)
Anicich, Vincent
1997-01-01
This paper will demonstrate the usefulness of standard non-linear statistical analysis on ICR and SIFT kinetic data. The specific systems used in the demonstration are the isotopic and change transfer reactions in the system of H2O+/D2O, H30+/D2O, and other permutations.
Manganite-based memristive heterojunction with tunable non-linear I-V characteristics.
Lee, Hong-Sub; Park, Hyung-Ho; Rozenberg, M J
2015-04-21
A resistive random access memory (ReRAM) based on the memristive effect allows high-density integration through a cross-point array (CPA) structure. However, a significant common drawback of the CPA configuration is the crosstalk between cells. Here, we introduce a solution based on a novel heterojunction stack solely made of members of the perovskite manganite family Pr(1-x)Ca(x)MnO3 (PCMO) and CaMnO(3-δ) (CMO) which show electroforming-free bipolar resistive switching. The heterojunction consists of rectifying interfaces and shows a symmetrical and tunable non-linear current-voltage curve. The spectromicroscopic measurements support the scenario of specialized roles, with the memristive effect taking place at the active Al-PCMO interface via a redox mechanism, while non-linearity was achieved by adopting a rectifying double interface PCMO-CMO-PCMO.
Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data
NASA Technical Reports Server (NTRS)
Kukreja, Sunil L.
2008-01-01
Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.
New non-linear photovoltaic effect in uniform bipolar semiconductor
Volovichev, I.
2014-11-21
A linear theory of the new non-linear photovoltaic effect in the closed circuit consisting of a non-uniformly illuminated uniform bipolar semiconductor with neutral impurities is developed. The non-uniform photo-excitation of impurities results in the position-dependant current carrier mobility that breaks the semiconductor homogeneity and induces the photo-electromotive force (emf). As both the electron (or hole) mobility gradient and the current carrier generation rate depend on the light intensity, the photo-emf and the short-circuit current prove to be non-linear functions of the incident light intensity at an arbitrarily low illumination. The influence of the sample size on the photovoltaic effect magnitude is studied. Physical relations and distinctions between the considered effect and the Dember and bulk photovoltaic effects are also discussed.
SSNN toolbox for non-linear system identification
NASA Astrophysics Data System (ADS)
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
Non-linear Poisson-Boltzmann theory for swollen clays
NASA Astrophysics Data System (ADS)
Leote de Carvalho, R. J. F.; Trizac, E.; Hansen, J.-P.
1998-08-01
The non-linear Poisson-Boltzmann (PB) equation for a circular, uniformly char ged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving the latter iteratively. This method proves efficient and robust, and can be readily generalized to other problems based on cell models, treated within non-linear Poisson-like theory. The solution to the PB equation is computed over a wide range of physical conditions, and the resulting osmotic equation of state is shown to be in semi-quantitative agreement with recent experimental data for Laponite clay suspensions, in the concentrated gel phase.
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.
Non-Linear Control Allocation Using Piecewise Linear Functions
2003-08-01
A novel method is presented for the solution of the non- linear control allocation problem. Historically, control allocation has been performed by... linear control allocation problem to be cast as a piecewise linear program. The piecewise linear program is ultimately cast as a mixed-integer linear...piecewise linear control allocation method is shown to be markedly improved when compared to the performance of a more traditional control allocation approach that assumes linearity.
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.
NON-LINEAR MODELING OF THE RHIC INTERACTION REGIONS.
TOMAS,R.FISCHER,W.JAIN,A.LUO,Y.PILAT,F.
2004-07-05
For RHIC's collision lattices the dominant sources of transverse non-linearities are located in the interaction regions. The field quality is available for most of the magnets in the interaction regions from the magnetic measurements, or from extrapolations of these measurements. We discuss the implementation of these measurements in the MADX models of the Blue and the Yellow rings and their impact on beam stability.
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.
Non-linear power spectra in the synchronous gauge
Hwang, Jai-chan; Noh, Hyerim; Jeong, Donghui; Gong, Jinn-Ouk; Biern, Sang Gyu E-mail: hr@kasi.re.kr E-mail: jinn-ouk.gong@apctp.org
2015-05-01
We study the non-linear corrections to the matter and velocity power spectra in the synchronous gauge (SG). For the leading correction to the non-linear power spectra, we consider the perturbations up to third order in a zero-pressure fluid in a flat cosmological background. Although the equations in the SG happen to coincide with those in the comoving gauge (CG) to linear order, they differ from second order. In particular, the second order hydrodynamic equations in the SG are apparently in the Lagrangian form, whereas those in the CG are in the Eulerian form. The non-linear power spectra naively presented in the original SG show rather pathological behavior quite different from the result of the Newtonian theory even on sub-horizon scales. We show that the pathology in the nonlinear power spectra is due to the absence of the convective terms in, thus the Lagrangian nature of, the SG. We show that there are many different ways of introducing the corrective convective terms in the SG equations. However, the convective terms (Eulerian modification) can be introduced only through gauge transformations to other gauges which should be the same as the CG to the second order. In our previous works we have shown that the density and velocity perturbation equations in the CG exactly coincide with the Newtonian equations to the second order, and the pure general relativistic correction terms starting to appear from the third order are substantially suppressed compared with the relativistic/Newtonian terms in the power spectra. As a result, we conclude that the SG per se is an inappropriate coordinate choice in handling the non-linear matter and velocity power spectra of the large-scale structure where observations meet with theories.
Non-linear characteristics of Rayleigh-Taylor instable perturbations
NASA Astrophysics Data System (ADS)
Fan, Zhengfeng; Luo, Jisheng
2008-04-01
The direct numerical simulation method is adopted to study the non-linear characteristics of Rayleigh-Taylor instable perturbations at the ablation front of a 200 μm planar CH ablation target. In the simulation, the classical electrical thermal conductivity is included, and NND difference scheme is used. The linear growth rates obtained from the simulation agree with the Takabe formula. The amplitude distribution of the density perturbation at the ablation front is obtained for the linear growth case. The non-linear characteristics of Rayleigh-Taylor instable perturbations are analyzed and the numerical results show that the amplitude distributions of the compulsive harmonics are very different from that of the fundamental perturbation. The characteristics of the amplitude distributions of the harmonics and their fast growth explain why spikes occur at the ablation front. The numerical results also show that non-linear effects have relations with the phase differences of double mode initial perturbations, and different phase differences lead to varied spikes.
Non-linear Oscillations of Compact Stars and Gravitational Waves
NASA Astrophysics Data System (ADS)
Passamonti, Andrea
2006-07-01
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions. As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative order this configuration does not exhibit any gravitational radiation, we have found a new interesting gravitational signal at non-linear order, in which the radial normal modes are precisely mirrored. In addition, a resonance effect is present when the frequencies of the radial pulsations are close to the first axial w-mode. Finally, we have roughly estimated the damping times of the radial pulsations due to the non-linear gravitational emission. The coupling near the resonance results to be a very effective mechanism for extracting energy from the radial oscillations.
Plasmon-enhanced Kerr nonlinearity via subwavelength-confined anisotropic Purcell factors.
Ren, Juanjuan; Chen, Hongyi; Gu, Ying; Zhao, Dongxing; Zhou, Haitao; Zhang, Junxiang; Gong, Qihuang
2016-10-21
We theoretically investigate the enhancement of Kerr nonlinearity through anisotropic Purcell factors provided by plasmon nanostructures. In a three-level atomic system with crossing damping, larger anisotropism of Purcell factors leads to more enhanced Kerr nonlinearity in electromagnetically induced transparency windows. While for fixed anisotropic Purcell factors, Kerr nonlinearity with orthogonal dipole moments increases with the decrease of its crossing damping, and Kerr nonlinearity with nonorthogonal dipole moments is very sensitive to both the value of crossing damping and the orientation of the dipole moments. We design the non-resonant gold nanorods array, which only provides subwavelength-confined anisotropic Purcell factors, and demonstrate that the Kerr nonlinearity of cesium atoms close to the nanorods array can be modulated at the nanoscale. These findings should have potential application in ultracompact quantum logic devices.
Plasmon-enhanced Kerr nonlinearity via subwavelength-confined anisotropic Purcell factors
NASA Astrophysics Data System (ADS)
Ren, Juanjuan; Chen, Hongyi; Gu, Ying; Zhao, Dongxing; Zhou, Haitao; Zhang, Junxiang; Gong, Qihuang
2016-10-01
We theoretically investigate the enhancement of Kerr nonlinearity through anisotropic Purcell factors provided by plasmon nanostructures. In a three-level atomic system with crossing damping, larger anisotropism of Purcell factors leads to more enhanced Kerr nonlinearity in electromagnetically induced transparency windows. While for fixed anisotropic Purcell factors, Kerr nonlinearity with orthogonal dipole moments increases with the decrease of its crossing damping, and Kerr nonlinearity with nonorthogonal dipole moments is very sensitive to both the value of crossing damping and the orientation of the dipole moments. We design the non-resonant gold nanorods array, which only provides subwavelength-confined anisotropic Purcell factors, and demonstrate that the Kerr nonlinearity of cesium atoms close to the nanorods array can be modulated at the nanoscale. These findings should have potential application in ultracompact quantum logic devices.
Non-linear fluorescence in dye solutions induced by a low power laser
NASA Astrophysics Data System (ADS)
Catalano, I. M.; Cingolani, A.
1980-01-01
Measurements of the fluorescence intensity IF, excited by two-photon pumping, have been carried out in different dye solutions by utilizing a low power cw laser ( IL ≈ 12 mW) and a particular experimental technique. A considerable departure from the quadratic law IF ∝ I2L with the varying of 2 hω - ΔEi quantity has been detected. This behaviour has bee n accounted for by considering the dependence of the non-linear and linear cross sections relative to the S 0 → S 1 and S 0 → S 2 transitions on the laser frequency.
NASA Astrophysics Data System (ADS)
Namboodiri, Vinu V.; Guleria, Apurav; Singh, Ajay K.
2017-04-01
Considering the impending applications of room temperature ionic liquids (RTILs) in various areas involving high optical and radiation fields, it is pertinent to probe the structure-property correlation of these solvents exposed to such conditions. Herein, femtosecond Z-scan technique (at high pulse repetition rate, 80 MHz) was employed to investigate the non-linear optical response of imidazolium RTILs in 3 scenarios: (1) -OH functionalization, (2) C2 methylation, and (3) influence of high radiation fields. Large negative non-linear refractive values ( n 2) were observed in all the RTIL samples and have been attributed predominantly due to the thermal effects. In order to isolate and determine the contribution of electronic Kerr effect, the Z-scan experiments were also carried out at low pulse repetition rate (i.e. 500 Hz) by means of a mechanical chopper. The closed aperture transmittance profile showed the valley-peak pattern, which signifies positive non-linearity. Nonetheless, the variation in the n2 values of the RTILs follows the same trend in low pulse repetition rate as was observed in case of high pulse repetition rate. The trend in the n 2 values clearly showed the decrease in the non-linearity in the first two cases and has been attributed to the weakening of the ion-pair formation, which adversely affects the charge transfer between the ionic moieties via C2 position. However, an increase in the n 2 values was observed in case of ILs irradiated to high radiation doses. This enhancement in the non-linearity has been assigned to the formation of double bond order radiolytic products. These results clearly indicate a strong correlation between the non-linearity and the strength of cation-anion interaction amongst them. Therefore, such information about these solvents may significantly contribute to the fundamental understanding of their structure-property relationships.
Global non-linear effect of temperature on economic production
NASA Astrophysics Data System (ADS)
Burke, Marshall; Hsiang, Solomon M.; Miguel, Edward
2015-11-01
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
Non-linear structure in modified action theories of gravity
NASA Astrophysics Data System (ADS)
Lima, Marcos V.
We study the effects and carry out a suite of cosmological simulations of modified action f(R) models where cosmic acceleration arises from an alteration of gravity instead of dark energy. These models introduce an extra scalar degree of freedom which enhances the force of gravity below the Compton scale of the scalar. The simulations exhibit the so-called chameleon mechanism, necessary for satisfying local constraints on gravity, where this scale depends on environment, in particular the depth of the local gravitational potential. We find that the chameleon mechanism can substantially suppress the enhancement of power spectrum in the non-linear regime if the background field value is comparable to or smaller than the depth of the gravitational potentials of typical structures. Nonetheless power spectrum enhancements at intermediate scales remain at a measurable level even when the expansion history is indistinguishable from a cosmological constant, cold dark matter model. We also investigate the effects of the modified dynamics on halo properties such as their abundance and clustering. We find that the f(R) effects on the halo mass- function and bias depend mostly on the linear power spectrum modifications, but that the chameleon mechanism suppresses the modifications at high-mass halos with deep potential wells. The f(R) modifications also affect the threshold density for collapse, or similarly the overdensity for virialization and therefore can change halo definitions from those of ACDM. As a result, simple scaling relations that take the linear matter power spectrum into a non-linear spectrum fail to capture the modifications of f(R) due to the change in collapsed structures, the chameleon mechanism, and the time evolution of the modifications. A quantification of these effects, including modifications on halo profiles, is necessary to accurately describe halo properties and potentially construct a halo model of the non-linear power spectrum.
Global non-linear effect of temperature on economic production.
Burke, Marshall; Hsiang, Solomon M; Miguel, Edward
2015-11-12
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
Simulation of magnetisation switching by non-linear resonance
NASA Astrophysics Data System (ADS)
Thirion, C.; Wernsdorfer, W.
2004-05-01
The sub-nanosecond dynamics have recently been probed via non-linear resonance on single magnetic nanoparticles using the micro-SQUID technique. In the presence of a magnetic field considerably smaller than the switching field, the magnetisation of a nanoparticle can be reversed by the application of a small RF field. The experimental determination of the most effective frequency is a direct probe of the small oscillations of the magnetisation in the metastable energy well. We present here a simulation of this experiment using the Landau-Lifschitz-Gilbert equation.
Non-Linear Dynamics of Saturn’s Rings
NASA Astrophysics Data System (ADS)
Esposito, Larry W.
2015-11-01
Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects
Disorder and Quantum Chromodynamics -- Non-Linear σ Models
NASA Astrophysics Data System (ADS)
Guhr, Thomas; Wilke, Thomas
2001-10-01
The statistical properties of Quantum Chromodynamics (QCD) show universal features which can be modeled by random matrices. This has been established in detailed analyses of data from lattice gauge calculations. Moreover, systematic deviations were found which link QCD to disordered systems in condensed matter physics. To furnish these empirical findings with analytical arguments, we apply and extend the methods developed in disordered systems to construct a non-linear σ model for the spectral correlations in QCD. Our goal is to derive connections to other low-energy effective theories, such as the Nambu-Jona-Lasinio model, and to chiral perturbation theory.
Disorder and Quantum Chromodynamics - Non-Linear σ Models
NASA Astrophysics Data System (ADS)
Guhr, Thomas; Wilke, Thomas
The statistical properties of Quantum Chromodynamics (QCD) show universal features which can be modeled by random matrices. This has been established in detailed analyses of data from lattice gauge calculations. Moreover, systematic deviations were found which link QCD to disordered systems in condensed matter physics. To furnish these empirical findings with analytical arguments, we apply and extend the methods developed in disordered systems to construct a non-linear σ model for the spectral correlations in QCD. Our goal is to derive connections to other low-energy effective theories, such as the Nambu-Jona-Lasinio model, and to chiral perturbation theory.
Non-linear isocurvature perturbations and non-Gaussianities
Langlois, David; Vernizzi, Filippo; Wands, David E-mail: filippo.vernizzi@cea.fr
2008-12-15
We study non-linear primordial adiabatic and isocurvature perturbations and their non-Gaussianity. After giving a general formulation in the context of an extended {delta}N formalism, we analyse in detail two illustrative examples. The first is a mixed curvaton-inflaton scenario in which fluctuations of both the inflaton and a curvaton (a light isocurvature field during inflation) contribute to the primordial density perturbation. The second example is that of double inflation involving two decoupled massive scalar fields during inflation. In the mixed curvaton-inflaton scenario we find that the bispectrum of primordial isocurvature perturbations may be large and comparable to the bispectrum of adiabatic curvature perturbations.
A non-linear UAV altitude PSO-PD control
NASA Astrophysics Data System (ADS)
Orlando, Calogero
2015-12-01
In this work, a nonlinear model based approach is presented for the altitude stabilization of a hexarotor unmanned aerial vehicle (UAV). The mathematical model and control of the hexacopter airframe is presented. To stabilize the system along the vertical direction, a Proportional Derivative (PD) control is taken into account. A particle swarm optimization (PSO) approach is used in this paper to select the optimal parameters of the control algorithm taking into account different objective functions. Simulation sets are performed to carry out the results for the non-linear system to show how the PSO tuned PD controller leads to zero the error of the position along Z earth direction.
8-PSK Signaling over non-linear satellite channels
NASA Technical Reports Server (NTRS)
Horan, Sheila B.; Caballero, Ruben B. Eng.
1996-01-01
Space agencies are under pressure to utilize better bandwidth-efficient communication methods due to the actual allocated frequency bands becoming more congested. Also budget reductions is another problem that the space agencies must deal with. This budget constraint results in simpler spacecraft carrying less communication capabilities and also the reduction in staff to capture data in the earth stations. It is then imperative that the most bandwidth efficient communication methods be utilized. This thesis presents a study of 8-ary Phase Shift Keying (8PSK) modulation with respect to bandwidth, power efficiency, spurious emissions and interference susceptibility over a non-linear satellite channel.
Non-linear optical titanyl arsenates: Crystal growth and properties
NASA Astrophysics Data System (ADS)
Nordborg, Jenni Eva Louise
Crystals are appreciated not only for their appearance, but also for their unique physical properties which are utilized by the photonic industry in appliances that we come across every day. An important part of enabling the technical use of optical devices is the manufacture of crystals. This dissertation deals with a specific group of materials called the potassium titanyl phosphate (KIP) family, known for their non-linear optical and ferroelectric properties. The isomorphs vary in their linear optical and dielectric properties, which can be tuned to optimize device performance by forming solid solutions of the different materials. Titanyl arsenates have a wide range of near-infrared transmission which makes them useful for tunable infrared lasers. The isomorphs examined in the present work were primarily RbTiOASO4 (RTA) and CsTiOAsO4 (CTA) together with the mixtures RbxCs 1-xTiOAsO4 (RCTA). Large-scale crystals were grown by top seeding solution growth utilizing a three-zone furnace with excellent temperature control. Sufficiently slow cooling and constant upward lifting produced crystals with large volumes useable for technical applications. Optical quality RTA crystals up to 10 x 12 x 20 mm were grown. The greater difficulty in obtaining good crystals of CTA led to the use of mixed RCTA materials. The mixing of rubidium and cesium in RCTA is more favorable to crystal growth than the single components in pure RTA and CTA. Mixed crystals are rubidium-enriched and contain only 20-30% of the cesium concentration in the flux. The cesium atoms show a preference for the larger cation site. The network structure is very little affected by the cation substitution; consequently, the non-linear optical properties of the Rb-rich isomorphic mixtures of RTA and CTA can be expected to remain intact. Crystallographic methods utilizing conventional X-ray tubes, synchrotron radiation and neutron diffraction have been employed to investigate the properties of the atomic
Non-linear identification of a squeeze-film damper
NASA Technical Reports Server (NTRS)
Stanway, Roger; Mottershead, John; Firoozian, Riaz
1987-01-01
Described is an experimental study to identify the damping laws associated with a squeeze-film vibration damper. This is achieved by using a non-linear filtering algorithm to process displacement responses of the damper ring to synchronous excitation and thus to estimate the parameters in an nth-power velocity model. The experimental facility is described in detail and a representative selection of results is included. The identified models are validated through the prediction of damper-ring orbits and comparison with observed responses.
PHOTON RINGS AROUND KERR AND KERR-LIKE BLACK HOLES
Johannsen, Tim
2013-11-10
Very long baseline interferometric observations have resolved structure on scales of only a few Schwarzschild radii around the supermassive black holes at the centers of our Galaxy and M87. In the near future, such observations are expected to image the shadows of these black holes together with a bright and narrow ring surrounding their shadows. For a Kerr black hole, the shape of this photon ring is nearly circular unless the black hole spins very rapidly. Whether or not, however, astrophysical black holes are truly described by the Kerr metric as encapsulated in the no-hair theorem still remains an untested assumption. For black holes that differ from Kerr black holes, photon rings have been shown numerically to be asymmetric for small to intermediate spins. In this paper, I calculate semi-analytic expressions of the shapes of photon rings around black holes described by a new Kerr-like metric which is valid for all spins. I show that photon rings in this spacetime are affected by two types of deviations from the Kerr metric which can cause the ring shape to be highly asymmetric. I argue that the ring asymmetry is a direct measure of a potential violation of the no-hair theorem and that both types of deviations can be detected independently if the mass and distance of the black hole are known. In addition, I obtain approximate expressions of the diameters, displacements, and asymmetries of photon rings around Kerr and Kerr-like black holes.
The Linear-Non-Linear Frontier for the Goldstone Higgs
Gavela, M. B.; Kanshin, K.; Machado, P. A.N.; Saa, S.
2016-10-25
The minimal $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $\\sigma$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.
Filtering Non-Linear Transfer Functions on Surfaces.
Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice
2013-07-18
Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to surface textures, as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. Our framework is also compatible with the case of transfer functions used to warp surface geometry.
Non-linear plasma wake growth of electron holes
NASA Astrophysics Data System (ADS)
Hutchinson, I. H.; Haakonsen, C. B.; Zhou, C.
2015-03-01
An object's wake in a plasma with small Debye length that drifts across the magnetic field is subject to electrostatic electron instabilities. Such situations include, for example, the moon in the solar wind and probes in magnetized laboratory plasmas. The instability drive mechanism can equivalently be considered drift down the potential-energy gradient or drift up the density-gradient. The gradients arise because the plasma wake has a region of depressed density and electrostatic potential into which ions are attracted along the field. The non-linear consequences of the instability are analysed in this paper. At physical ratios of electron to ion mass, neither linear nor quasilinear treatment can explain the observation of large-amplitude perturbations that disrupt the ion streams well before they become ion-ion unstable. We show here, however, that electron holes, once formed, continue to grow, driven by the drift mechanism, and if they remain in the wake may reach a maximum non-linearly stable size, beyond which their uncontrolled growth disrupts the ions. The hole growth calculations provide a quantitative prediction of hole profile and size evolution. Hole growth appears to explain the observations of recent particle-in-cell simulations.
The linear-non-linear frontier for the Goldstone Higgs
NASA Astrophysics Data System (ADS)
Gavela, M. B.; Kanshin, K.; Machado, P. A. N.; Saa, S.
2016-12-01
The minimal SO(5) / SO(4) σ -model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.
Charged relativistic fluids and non-linear electrodynamics
NASA Astrophysics Data System (ADS)
Dereli, T.; Tucker, R. W.
2010-01-01
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these modified theories are tenable. However with the advent of high-intensity lasers and powerful laboratory magnetic fields this situation may be changing. We argue that an approach involving the self-consistent relativistic motion of a smooth fluid-like distribution of matter (composed of a large number of charged or neutral particles) in an electromagnetic field offers a viable theoretical framework in which to explore the experimental consequences of non-linear electrodynamics. We construct such a model based on the theory of Born and Infeld and suggest that a simple laboratory experiment involving the propagation of light in a static magnetic field could be used to place bounds on the fundamental coupling in that theory. Such a framework has many applications including a new description of the motion of particles in modern accelerators and plasmas as well as phenomena in astrophysical contexts such as in the environment of magnetars, quasars and gamma-ray bursts.
Effects on non-linearities on aircraft poststall motion
Rohacs, J.; Thomasson, P.; Mosehilde, E.
1994-12-31
The poststall maneuverability controlled by thrust vectoring has become one of the important aspects of new fighter development projects. In simplified case, the motion of aircraft can be described by 6DOF nonlinear system. The lecture deals with the longitudinal motion of poststall maneuverable aircraft. The investigation made about the effects of non-linearities in aerodynamic coefficients having considerable non-linearities and hysteresisis an the poststall motions. There were used some different models of aerodynamic coefficients. The results of investigation have shown that the poststall domain of vectored aircraft can be divided into five different pHs in field of thrust - pitch vector angle, and the chaotic motions of aircraft can be found at the different frequencies of thrust deflection. There were defined an unstable right domain with an unstable oscillation and a field of overpulling at poststall motion. The certain frequency chaotic attractors were got at frequencies of Oxitation between the 0.15 and 0.65 rad/sec. The pitching moment derivatives had the big influence on the chaotic motions, while the lift coefficient derivatives bad the reasonable effects, only.
Left-Right Non-Linear Dynamical Higgs
NASA Astrophysics Data System (ADS)
Shu, Jing; Yepes, Juan
2016-12-01
All the possible CP-conserving non-linear operators up to the p4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically, from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)L × SU(2)R × U(1)B-L. Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV-2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators. J. Y. also acknowledges KITPC financial support during the completion of this work
Non-linear plasma wake growth of electron holes
Hutchinson, I. H.; Haakonsen, C. B.; Zhou, C.
2015-03-15
An object's wake in a plasma with small Debye length that drifts across the magnetic field is subject to electrostatic electron instabilities. Such situations include, for example, the moon in the solar wind and probes in magnetized laboratory plasmas. The instability drive mechanism can equivalently be considered drift down the potential-energy gradient or drift up the density-gradient. The gradients arise because the plasma wake has a region of depressed density and electrostatic potential into which ions are attracted along the field. The non-linear consequences of the instability are analysed in this paper. At physical ratios of electron to ion mass, neither linear nor quasilinear treatment can explain the observation of large-amplitude perturbations that disrupt the ion streams well before they become ion-ion unstable. We show here, however, that electron holes, once formed, continue to grow, driven by the drift mechanism, and if they remain in the wake may reach a maximum non-linearly stable size, beyond which their uncontrolled growth disrupts the ions. The hole growth calculations provide a quantitative prediction of hole profile and size evolution. Hole growth appears to explain the observations of recent particle-in-cell simulations.
Polycarbonate-Based Blends for Optical Non-linear Applications
NASA Astrophysics Data System (ADS)
Stanculescu, F.; Stanculescu, A.
2016-02-01
This paper presents some investigations on the optical and morphological properties of the polymer (matrix):monomer (inclusion) composite materials obtained from blends of bisphenol A polycarbonate and amidic monomers. For the preparation of the composite films, we have selected monomers characterised by a maleamic acid structure and synthesised them starting from maleic anhydride and aniline derivatives with -COOH, -NO2, -N(C2H5)2 functional groups attached to the benzene ring. The composite films have been deposited by spin coating using a mixture of two solutions, one containing the matrix and the other the inclusion, both components of the composite system being dissolved in the same solvent. The optical transmission and photoluminescence properties of the composite films have been investigated in correlation with the morphology of the films. The scanning electron microscopy and atomic force microscopy have revealed a non-uniform morphology characterised by the development of two distinct phases. We have also investigated the generation of some optical non-linear (ONL) phenomena in these composite systems. The composite films containing as inclusions monomers characterised by the presence of one -COOH or two -NO2 substituent groups to the aromatic nucleus have shown the most intense second-harmonic generation (SHG). The second-order optical non-linear coefficients have been evaluated for these films, and the effect of the laser power on the ONL behaviour of these materials has also been emphasised.
Non-linear leak currents affect mammalian neuron physiology
Huang, Shiwei; Hong, Sungho; De Schutter, Erik
2015-01-01
In their seminal works on squid giant axons, Hodgkin, and Huxley approximated the membrane leak current as Ohmic, i.e., linear, since in their preparation, sub-threshold current rectification due to the influence of ionic concentration is negligible. Most studies on mammalian neurons have made the same, largely untested, assumption. Here we show that the membrane time constant and input resistance of mammalian neurons (when other major voltage-sensitive and ligand-gated ionic currents are discounted) varies non-linearly with membrane voltage, following the prediction of a Goldman-Hodgkin-Katz-based passive membrane model. The model predicts that under such conditions, the time constant/input resistance-voltage relationship will linearize if the concentration differences across the cell membrane are reduced. These properties were observed in patch-clamp recordings of cerebellar Purkinje neurons (in the presence of pharmacological blockers of other background ionic currents) and were more prominent in the sub-threshold region of the membrane potential. Model simulations showed that the non-linear leak affects voltage-clamp recordings and reduces temporal summation of excitatory synaptic input. Together, our results demonstrate the importance of trans-membrane ionic concentration in defining the functional properties of the passive membrane in mammalian neurons as well as other excitable cells. PMID:26594148
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
Renormalization and non-linear symmetries in quantum field theory
NASA Astrophysics Data System (ADS)
Velenich, Andrea
Most of the phenomena we experience, from the microscopic world to the universe at its largest scales, are out of equilibrium and their comprehensive formalization is one of the open problems in theoretical physics. Fluids of interacting particles cooled down or compressed quickly enough to become amorphous solids are an example of rich out-of-equilibrium systems with very slow relaxation dynamics. Even though the equilibrium phases are ordered, these systems remain trapped in glassy metastable states, with disordered microscopic structures. As a realistic model of this phenomenology, in the first part of this work I focused on a field theory of particles obeying a Brownian dynamics. The field-theoretic action displays a time-reversal symmetry leading to Fluctuation-Dissipation relations. For non-interacting particles I solved the field theory exactly, providing the explicit form of all the correlation functions, with their space and time dependence. As a non-perturbative result, the distribution of the density field has been proven to be Poissonian and not Gaussian. For interacting particles the field theory presents two major challenges: its apparent non-renormalizability and a non-linear implementation of the time-reversal symmetry. Non-linear field redefinitions can be used to make the symmetry linear and might even lead to the solution of the interacting equations of motion. However they also alter the renormalizability properties of a field theory. These challenges inspired the second part of the work, where a more abstract approach was taken. Using algebraic methods I investigated the effect of non-linear field redefinitions both on symmetry and on renormalization by focusing on simple scalar field theories as toy models. In the formal setting of the Hopf algebra of Feynman diagrams, symmetries take the form of Hopf ideals and enforce relations among scattering amplitudes; such relations can drastically reduce the number of independent couplings in a field
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.
Transformation matrices between non-linear and linear differential equations
NASA Technical Reports Server (NTRS)
Sartain, R. L.
1983-01-01
In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.
Non-linear optical crystal vibration sensing device
Kalibjian, R.
1994-08-09
A non-linear optical crystal vibration sensing device including a photorefractive crystal and a laser is disclosed. The laser produces a coherent light beam which is split by a beam splitter into a first laser beam and a second laser beam. After passing through the crystal the first laser beam is counter-propagated back upon itself by a retro-mirror, creating a third laser beam. The laser beams are modulated, due to the mixing effect within the crystal by vibration of the crystal. In the third laser beam, modulation is stable and such modulation is converted by a photodetector into a usable electrical output, intensity modulated in accordance with vibration applied to the crystal. 3 figs.
Non-linear optical crystal vibration sensing device
Kalibjian, Ralph
1994-01-11
A non-linear optical crystal vibration sensing device (10) including a photorefractive crystal (26) and a laser (12). The laser (12 ) produces a coherent light beam (14) which is split by a beam splitter (18) into a first laser beam (20) and a second laser beam (22). After passing through the crystal (26) the first laser beam (20) is counter-propagated back upon itself by a retro-mirror (32), creating a third laser beam (30). The laser beams (20, 22, 30) are modulated, due to the mixing effect within the crystal (26) by vibration of the crystal (30). In the third laser beam (30), modulation is stable and such modulation is converted by a photodetector (34) into a usable electrical output, intensity modulated in accordance with vibration applied to the crystal (26).
Predictability of extremes in non-linear hierarchically organized systems
NASA Astrophysics Data System (ADS)
Kossobokov, V. G.; Soloviev, A.
2011-12-01
Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare
Method and system for non-linear motion estimation
NASA Technical Reports Server (NTRS)
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
The mathematics of non-linear metrics for nested networks
NASA Astrophysics Data System (ADS)
Wu, Rui-Jie; Shi, Gui-Yuan; Zhang, Yi-Cheng; Mariani, Manuel Sebastian
2016-10-01
Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness-complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness-complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness-complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.
Black hole hair removal: non-linear analysis
NASA Astrophysics Data System (ADS)
Jatkar, Dileep P.; Sen, Ashoke; Srivastava, Yogesh K.
2010-02-01
BMPV black holes in flat transverse space and in Taub-NUT space have identical near horizon geometries but different microscopic degeneracies. It has been proposed that this difference can be accounted for by different contribution to the degeneracies of these black holes from hair modes, — degrees of freedom living outside the horizon. In this paper we explicitly construct the hair modes of these two black holes as finite bosonic and fermionic deformations of the black hole solution satisfying the full non-linear equations of motion of supergravity and preserving the supersymmetry of the original solutions. Special care is taken to ensure that these solutions do not have any curvature singularity at the future horizon when viewed as the full ten dimensional geometry. We show that after removing the contribution due to the hair degrees of freedom from the microscopic partition function, the partition functions of the two black holes agree.
Detector noise statistics in the non-linear regime
NASA Technical Reports Server (NTRS)
Shopbell, P. L.; Bland-Hawthorn, J.
1992-01-01
The statistical behavior of an idealized linear detector in the presence of threshold and saturation levels is examined. It is assumed that the noise is governed by the statistical fluctuations in the number of photons emitted by the source during an exposure. Since physical detectors cannot have infinite dynamic range, our model illustrates that all devices have non-linear regimes, particularly at high count rates. The primary effect is a decrease in the statistical variance about the mean signal due to a portion of the expected noise distribution being removed via clipping. Higher order statistical moments are also examined, in particular, skewness and kurtosis. In principle, the expected distortion in the detector noise characteristics can be calibrated using flatfield observations with count rates matched to the observations. For this purpose, some basic statistical methods that utilize Fourier analysis techniques are described.
Model of intermodulation distortion in non-linear multicarrier systems
NASA Astrophysics Data System (ADS)
Frigo, Nicholas J.
1994-02-01
A heuristic model is proposed which allows calculation of the individual spectral components of the intermodulation distortion present in a non-linear system with a multicarrier input. Noting that any given intermodulation product (IMP) can only be created by a subset of the input carriers, we partition them into 'signal' carriers (which create the IMP) and 'noise' carriers, modeled as a Gaussian process. The relationship between an input signal and the statistical average of its output (averaged over the Gaussian noise) is considered to be an effective transfer function. By summing all possible combinations of signal carriers which create power at the IMP frequencies, the distortion power can be calculated exactly as a function of frequency. An analysis of clipping in lightwave CATV links for AM-VSB signals is used to introduce the model, and is compared to a series of experiments.
Computational models of signalling networks for non-linear control.
Fuente, Luis A; Lones, Michael A; Turner, Alexander P; Stepney, Susan; Caves, Leo S; Tyrrell, Andy M
2013-05-01
Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.
Non-linear radial spinwave modes in thin magnetic disks
Helsen, M. De Clercq, J.; Vansteenkiste, A.; Van Waeyenberge, B.; Weigand, M.
2015-01-19
We present an experimental investigation of radial spin-wave modes in magnetic nano-disks with a vortex ground state. The spin-wave amplitude was measured using a frequency-resolved magneto-optical spectrum analyzer, allowing for high-resolution resonance curves to be recorded. It was found that with increasing excitation amplitude up to about 10 mT, the lowest-order mode behaves strongly non-linearly as the mode frequency redshifts and the resonance peak strongly deforms. This behavior was quantitatively reproduced by micromagnetic simulations. Micromagnetic simulations showed that at higher excitation amplitudes, the spinwaves are transformed into a soliton by self-focusing, and collapse onto the vortex core, dispersing the energy in short-wavelength spinwaves. Additionally, this process can lead to switching of the vortex polarization through the injection of a Bloch point.
Attractor reconstruction for non-linear systems: a methodological note
Nichols, J.M.; Nichols, J.D.
2001-01-01
Attractor reconstruction is an important step in the process of making predictions for non-linear time-series and in the computation of certain invariant quantities used to characterize the dynamics of such series. The utility of computed predictions and invariant quantities is dependent on the accuracy of attractor reconstruction, which in turn is determined by the methods used in the reconstruction process. This paper suggests methods by which the delay and embedding dimension may be selected for a typical delay coordinate reconstruction. A comparison is drawn between the use of the autocorrelation function and mutual information in quantifying the delay. In addition, a false nearest neighbor (FNN) approach is used in minimizing the number of delay vectors needed. Results highlight the need for an accurate reconstruction in the computation of the Lyapunov spectrum and in prediction algorithms.
DYNAMIC NON LINEAR IMPACT ANALYSIS OF FUEL CASK CONTAINMENT VESSELS
Leduc, D
2008-06-10
Large fuel casks present challenges when evaluating their performance in the accident sequence specified in 10CFR 71. Testing is often limited because of cost, difficulty in preparing test units and the limited availability of facilities which can carry out such tests. In the past, many casks were evaluated without testing using simplified analytical methods. This paper details the use of dynamic non-linear analysis of large fuel casks using advanced computational techniques. Results from the dynamic analysis of two casks, the T-3 Spent Fuel Cask and the Hanford Un-irradiated Fuel Package are examined in detail. These analyses are used to fully evaluate containment vessel stresses and strains resulting from complex loads experienced by cask components during impacts. Importantly, these advanced analytical analyses are capable of examining stresses in key regions of the cask including the cask closure. This paper compares these advanced analytical results with the results of simplified cask analyses like those detailed in NUREG 3966.
Non-linear hydrodynamical simulations of delta Scuti star pulsations
NASA Astrophysics Data System (ADS)
Templeton, M. R.; Guzik, J. A.; McNamara, B. J.
1998-12-01
We present the initial results of non-linear hydrodynamic simulations of the pulsation modes of delta Scuti stars. These models use the Ostlie and Cox (1993) Lagrangian hydrodynamic code, adapted to use the most recent OPAL (1996) opacities, the Stellingwerf (1974) periodic relaxation method of obtaining stable limit cycle pulsations, and time-dependent convection. Initial tests of first- and second-overtone pulsation models are consistent with the models of Bono, et al (1997) showing asymmetric lightcurves for first overtone rather than fundamental pulsations. Future modeling work will test several stellar models with varying masses, ages, metal and helium abundances and envelope abundance gradients. Ultimately, we hope to determine the role that abundances and, more specifically, helium abundance gradients in delta Scuti envelopes play in light curve shape. This work will be applied to a test sample of known radially-pulsating delta Scuti field stars and the newly-discovered delta Scuti/SX Phoenicis variables in the Galactic Bulge.
Neural networks: What non-linearity to choose
NASA Technical Reports Server (NTRS)
Kreinovich, Vladik YA.; Quintana, Chris
1991-01-01
Neural networks are now one of the most successful learning formalisms. Neurons transform inputs (x(sub 1),...,x(sub n)) into an output f(w(sub 1)x(sub 1) + ... + w(sub n)x(sub n)), where f is a non-linear function and w, are adjustable weights. What f to choose? Usually the logistic function is chosen, but sometimes the use of different functions improves the practical efficiency of the network. The problem of choosing f as a mathematical optimization problem is formulated and solved under different optimality criteria. As a result, a list of functions f that are optimal under these criteria are determined. This list includes both the functions that were empirically proved to be the best for some problems, and some new functions that may be worth trying.
Ferrite core non-linearity in coils for magnetic neurostimulation.
RamRakhyani, Anil Kumar; Lazzi, Gianluca
2014-10-01
The need to correctly predict the voltage across terminals of mm-sized coils, with ferrite core, to be employed for magnetic stimulation of the peripheral neural system is the motivation for this work. In such applications, which rely on a capacitive discharge on the coil to realise a transient voltage curve of duration and strength suitable for neural stimulation, the correct modelling of the non-linearity of the ferrite core is critical. A demonstration of how a finite-difference model of the considered coils, which include a model of the current-controlled inductance in the coil, can be used to correctly predict the time-domain voltage waveforms across the terminals of a test coil is presented. Five coils of different dimensions, loaded with ferrite cores, have been fabricated and tested: the measured magnitude and width of the induced pulse are within 10% of simulated values.
NOLB : Non-linear rigid block normal mode analysis method.
Hoffmann, Alexandre; Grudinin, Sergei
2017-04-05
We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy and topology analyses, and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes. A graphical user interfaces created for the SAMSON software platform will be made available at https: //www.samson-connect.net.
Non-linearities in Theory-of-Mind Development.
Blijd-Hoogewys, Els M A; van Geert, Paul L C
2016-01-01
Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72-78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths.
Non-linear dynamics of a spur gear pair
NASA Astrophysics Data System (ADS)
Kahraman, A.; Singh, R.
1990-10-01
Non-linear frequency response characteristics of a spur gear pair with backlash are examined in this paper for both external and internal excitations. The internal excitation is of importance from the high frequency noise and vibration control viewpoint and it represents the overall kinematic or static transmission error. Such problems may be significantly different from the rattle problems associated with external, low frequency torque excitation. Two solution methods, namely the digital simulation technique and the method of harmonic balance, have been used to develop the steady state solutions for the internal sinusoidal excitation. Difficulties associated with the determination of the multiple solutions at a given frequency in the digital simulation technique have been resolved, as one must search the entire initial conditions map. Such solutions and the transition frequencies for various impact situations are easily found by the method of harmonic balance. Further, the principle of superposition can be employed to analyze the periodic transmission error excitation and/or combined excitation problems provided that the excitation frequencies are sufficiently apart from each other. Our analytical predictions match satisfactorily with the limited experimental data available in the literature. Using the digital simulation, we have also observed that the chaotic and subharmonic resonances may exist in a gear pair depending upon the mean or design load, mean to alternating force ratio, damping and backlash. Specifically, the mean load determines the conditions for no impacts, single-sided impacts and double-sided impacts. Our results are different from the frequency response characteristics of the conventional, single-degree-of-freedom, clearance type non-linear system. Our formulation should form the basis of further analytical and experimental work in the geared rotor dynamics area.
Non-linear diffusion and pattern formation in vortex matter
NASA Astrophysics Data System (ADS)
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Griessen, R.; Einfeld, J.; Woerdenweber, R.
2000-03-01
Penetration of magnetic flux in YBa_2Cu_3O7 superconducting thin films and crystals in externally applied magnetic fields is visualized with a magneto-optical technique. A variety of flux patterns due to non-linear vortex behavior is observed: 1. Roughening of the flux front^1 with scaling exponents identical to those observed in burning paper^2. Two regimes are found where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. 2. Roughening of the flux profile similar to the Oslo model for rice-piles. 3. Fractal penetration of flux^3 with Hausdorff dimension depending on the critical current anisotropy. 4. Penetration as 'flux-rivers'. 5. The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori^4. By comparison with numerical simulations, it is shown that most of the observed behavior can be explained in terms of non-linear diffusion of vortices. ^1R. Surdeanu, R.J. Wijngaarden, E. Visser, J.M. Huijbregtse, J.H. Rector, B. Dam and R. Griessen, Phys.Rev. Lett. 83 (1999) 2054 ^2J. Maunuksela, M. Myllys, O.-P. Kähkönen, J. Timonen, N. Provatas, M.J. Alava, T. Ala-Nissila, Phys. Rev. Lett. 79, 1515 (1997) ^3R. Surdeanu, R.J. Wijngaarden, B. Dam, J. Rector, R. Griessen, C. Rossel, Z.F. Ren and J.H. Wang, Phys Rev B 58 (1998) 12467 ^4C. Reichhardt, C.J. Olson and F. Nori, Phys. Rev. B 58, 6534 (1998)
Non-linearities in Theory-of-Mind Development
Blijd-Hoogewys, Els M. A.; van Geert, Paul L. C.
2017-01-01
Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72–78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths. PMID:28101065
State-variable analysis of non-linear circuits with a desk computer
NASA Technical Reports Server (NTRS)
Cohen, E.
1981-01-01
State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.
Discriminating Non-Linearity from Linearity: Its Cognitive Foundations in Five-Year-Olds
ERIC Educational Resources Information Center
Ebersbach, Mirjam; Van Dooren, Wim; Goudriaan, Margje N.; Verschaffel, Lieven
2010-01-01
People often have difficulties in understanding situations that involve non-linear processes. Also, the topic of non-linear functions is introduced relatively late in the curriculum. Previous research has nevertheless shown that already children aged 6 years and older are able to discriminate non-linear from linear processes. Within the present…
Fitness Effects of Network Non-Linearity Induced by Gene Expression Noise
NASA Astrophysics Data System (ADS)
Ray, Christian; Cooper, Tim; Balazsi, Gabor
2012-02-01
In the non-equilibrium dynamics of growing microbial cells, metabolic enzymes can create non-linearities in metabolite concentration because of non-linear degradation (utilization): an enzyme can saturate in the process of metabolite utilization. Increasing metabolite production past the saturation point then results in an ultrasensitive metabolite response. If the production rate of a metabolite depends on a second enzyme or other protein-mediated process, uncorrelated gene expression noise can thus cause transient metabolite concentration bursts. Such bursts are physiologically unnecessary and may represent a source of selection against the ultrasensitive switch, especially if the fluctuating metabolic intermediate is toxic. Selection may therefore favor correlated gene expression fluctuations for enzymes in the same pathway, such as by same-operon membership in bacteria. Using a modified experimental lac operon system, we are undertaking a combined theoretical-experimental approach to demonstrate that (i) the lac operon has an implicit ultrasensitive switch that we predict is avoided by gene expression correlations induced by same-operon membership; (ii) bacterial growth rates are sensitive to crossing the ultrasensitive threshold. Our results suggest that correlations in intrinsic gene expression noise are exploited by evolution to ameliorate the detrimental effects of nonlinearities in metabolite concentrations.
Nonequatorial charged particle confinement around Kerr black holes
Preti, Giovanni
2010-01-15
We analyze the nonequatorial charged particle dynamics around a rotating black hole in the presence of an external magnetic field, the latter being given by Wald's exact analytical solution to the Maxwell's equations in the Kerr background. At variance with the corresponding Schwarzschild case, the behavior of the particle becomes here markedly charge-sign dependent, and the more so the more the Kerr parameter increases. The interplay between the rotating black hole and the magnetic field is shown to provide a mechanism both for selective charge ejection in axially collimated jetlike trajectories, and for selective charge confinement into nonequatorial bound orbits around the hole; the possibility of such a confinement allows the fate of an accreting particle to not necessarily be doomed: infall into the hole can be prevented, and the neutrality of the Kerr source could therefore be preserved, while the charge is safely parked into bound cross-equatorial orbits all around it.
Rapid Non-Linear Uncertainty Propagation via Analytical Techniques
NASA Astrophysics Data System (ADS)
Fujimoto, K.; Scheeres, D. J.
2012-09-01
Space situational awareness (SSA) is known to be a data starved problem compared to traditional estimation problems in that observation gaps per object may span over days if not weeks. Therefore, consistent characterization of the uncertainty associated with these objects including non-linear effects is crucial in maintaining an accurate catalog of objects in Earth orbit. Simultaneously, the motion of satellites in Earth orbit is well-modeled in that it is particularly amenable to having their solution and their uncertainty described through analytic or semi-analytic techniques. Even when stronger non-gravitational perturbations such as solar radiation pressure and atmospheric drag are encountered, these perturbations generally have deterministic components that are substantially larger than their time-varying stochastic components. Analytic techniques are powerful because time propagation is only a matter of changing the time parameter, allowing for rapid computational turnaround. These two ideas are combined in this paper: a method of analytically propagating non-linear orbit uncertainties is discussed. In particular, the uncertainty is expressed as an analytic probability density function (pdf) for all time. For a deterministic system model, such pdfs may be obtained if the initial pdf and the system states for all time are also given analytically. Even when closed-form solutions are not available, approximate solutions exist in the form of Edgeworth series for pdfs and Taylor series for the states. The coefficients of the latter expansion are referred to as state transition tensors (STTs), which are a generalization of state transition matrices to arbitrary order. Analytically expressed pdfs can be incorporated in many practical tasks in SSA. One can compute the mean and covariance of the uncertainty, for example, with the moments of the initial pdf as inputs. This process does not involve any sampling and its accuracy can be determined a priori. Analytical
THE RESPONSE OF DRUG EXPENDITURE TO NON-LINEAR CONTRACT DESIGN: EVIDENCE FROM MEDICARE PART D.
Einav, Liran; Finkelstein, Amy; Schrimpf, Paul
2015-05-01
We study the demand response to non-linear price schedules using data on insurance contracts and prescription drug purchases in Medicare Part D. We exploit the kink in individuals' budget set created by the famous "donut hole," where insurance becomes discontinuously much less generous on the margin, to provide descriptive evidence of the drug purchase response to a price increase. We then specify and estimate a simple dynamic model of drug use that allows us to quantify the spending response along the entire non-linear budget set. We use the model for counterfactual analysis of the increase in spending from "filling" the donut hole, as will be required by 2020 under the Affordable Care Act. In our baseline model, which considers spending decisions within a single year, we estimate that "filling" the donut hole will increase annual drug spending by about $150, or about 8 percent. About one-quarter of this spending increase reflects "anticipatory" behavior, coming from beneficiaries whose spending prior to the policy change would leave them short of reaching the donut hole. We also present descriptive evidence of cross-year substitution of spending by individuals who reach the kink, which motivates a simple extension to our baseline model that allows - in a highly stylized way - for individuals to engage in such cross year substitution. Our estimates from this extension suggest that a large share of the $150 drug spending increase could be attributed to cross-year substitution, and the net increase could be as little as $45 per year.
THE RESPONSE OF DRUG EXPENDITURE TO NON-LINEAR CONTRACT DESIGN: EVIDENCE FROM MEDICARE PART D*
Einav, Liran; Finkelstein, Amy; Schrimpf, Paul
2016-01-01
We study the demand response to non-linear price schedules using data on insurance contracts and prescription drug purchases in Medicare Part D. We exploit the kink in individuals’ budget set created by the famous “donut hole,” where insurance becomes discontinuously much less generous on the margin, to provide descriptive evidence of the drug purchase response to a price increase. We then specify and estimate a simple dynamic model of drug use that allows us to quantify the spending response along the entire non-linear budget set. We use the model for counterfactual analysis of the increase in spending from “filling” the donut hole, as will be required by 2020 under the Affordable Care Act. In our baseline model, which considers spending decisions within a single year, we estimate that “filling” the donut hole will increase annual drug spending by about $150, or about 8 percent. About one-quarter of this spending increase reflects “anticipatory” behavior, coming from beneficiaries whose spending prior to the policy change would leave them short of reaching the donut hole. We also present descriptive evidence of cross-year substitution of spending by individuals who reach the kink, which motivates a simple extension to our baseline model that allows – in a highly stylized way – for individuals to engage in such cross year substitution. Our estimates from this extension suggest that a large share of the $150 drug spending increase could be attributed to cross-year substitution, and the net increase could be as little as $45 per year. PMID:26769984
Filtering Non-Linear Transfer Functions on Surfaces.
Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice
2014-07-01
Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few
Non-linear evolution of the cosmic neutrino background
Villaescusa-Navarro, Francisco; Viel, Matteo; Peña-Garay, Carlos E-mail: spb@ias.edu E-mail: viel@oats.inaf.it
2013-03-01
We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size, high resolution N-body simulations which incorporate cold dark matter (CDM) and neutrinos as independent particle species. Our set of simulations explore the properties of neutrinos in a reference ΛCDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass 10{sup 11}−10{sup 15} h{sup −1}M{sub s}un, over a redshift range z = 0−2. We compute the halo mass function and show that it is reasonably well fitted by the Sheth-Tormen formula, once the neutrino contribution to the total matter is removed. More importantly, we focus on the CDM and neutrino properties of the density and peculiar velocity fields in the cosmological volume, inside and in the outskirts of virialized haloes. The dynamical state of the neutrino particles depends strongly on their momentum: whereas neutrinos in the low velocity tail behave similarly to CDM particles, neutrinos in the high velocity tail are not affected by the clustering of the underlying CDM component. We find that the neutrino (linear) unperturbed momentum distribution is modified and mass and redshift dependent deviations from the expected Fermi-Dirac distribution are in place both in the cosmological volume and inside haloes. The neutrino density profiles around virialized haloes have been carefully investigated and a simple fitting formula is provided. The neutrino profile, unlike the cold dark matter one, is found to be cored with core size and central density that depend on the neutrino mass, redshift and mass of the halo, for halos of masses larger than ∼ 10{sup 13.5}h{sup −1}M{sub s}un. For lower masses the neutrino profile is best fitted by a simple power-law relation in the range probed by the simulations. The results we obtain are numerically converged in terms of neutrino profiles at the 10% level for scales above ∼ 200 h{sup −1}kpc at z = 0, and are stable with
Optimum Damping in a Non-Linear Base Isolation System
NASA Astrophysics Data System (ADS)
Jangid, R. S.
1996-02-01
Optimum isolation damping for minimum acceleration of a base-isolated structure subjected to earthquake ground excitation is investigated. The stochastic model of the El-Centro1940 earthquake, which preserves the non-stationary evolution of amplitude and frequency content of ground motion, is used as an earthquake excitation. The base isolated structure consists of a linear flexible shear type multi-storey building supported on a base isolation system. The resilient-friction base isolator (R-FBI) is considered as an isolation system. The non-stationary stochastic response of the system is obtained by the time dependent equivalent linearization technique as the force-deformation of the R-FBI system is non-linear. The optimum damping of the R-FBI system is obtained under important parametric variations; i.e., the coefficient of friction of the R-FBI system, the period and damping of the superstructure; the effective period of base isolation. The criterion selected for optimality is the minimization of the top floor root mean square (r.m.s.) acceleration. It is shown that the above parameters have significant effects on optimum isolation damping.
CMB hemispherical asymmetry from non-linear isocurvature perturbations
Assadullahi, Hooshyar; Wands, David; Firouzjahi, Hassan; Namjoo, Mohammad Hossein E-mail: firouz@mail.ipm.ir E-mail: david.wands@port.ac.uk
2015-04-01
We investigate whether non-adiabatic perturbations from inflation could produce an asymmetric distribution of temperature anisotropies on large angular scales in the cosmic microwave background (CMB). We use a generalised non-linear δ N formalism to calculate the non-Gaussianity of the primordial density and isocurvature perturbations due to the presence of non-adiabatic, but approximately scale-invariant field fluctuations during multi-field inflation. This local-type non-Gaussianity leads to a correlation between very long wavelength inhomogeneities, larger than our observable horizon, and smaller scale fluctuations in the radiation and matter density. Matter isocurvature perturbations contribute primarily to low CMB multipoles and hence can lead to a hemispherical asymmetry on large angular scales, with negligible asymmetry on smaller scales. In curvaton models, where the matter isocurvature perturbation is partly correlated with the primordial density perturbation, we are unable to obtain a significant asymmetry on large angular scales while respecting current observational constraints on the observed quadrupole. However in the axion model, where the matter isocurvature and primordial density perturbations are uncorrelated, we find it may be possible to obtain a significant asymmetry due to isocurvature modes on large angular scales. Such an isocurvature origin for the hemispherical asymmetry would naturally give rise to a distinctive asymmetry in the CMB polarisation on large scales.
Searching for Non-linearities in Natural Language
NASA Astrophysics Data System (ADS)
Ribarov, Kiril; Smrz, Otakar
2003-08-01
Inspired by wide range of applicability of what is commonly referred to as chaos theories, we explore the nature of energy series of a signal of human speech in the light of nonlinear dynamics. Using the TISEAN software package, analyses on various recordings of the language energy series were carried out (single speaker — different speeches; single speech - different speakers; dialogues; talkshows). Also correlated to other tenths of experiments conveyed on different linguistic inputs as written and morphologically analyzed texts, the presented experiment outputs (up to our knowledge, similar experiments have not been performed yet) reveal the complex and tricky nature of the language and are in favor of certain linguistic hypotheses. However, without further research, they do not encourage us to make explicit claims about the language signal such as dimension estimations (although probably possible) or attractor reconstruction. Our main considerations include: (a) a look into the stochastic nature of the language aiming towards reduction of the currently very large number of parameters present in language models based on Hidden Markov Models on language n-grams; (b) visualization of the behavior of the language and revelation of what could possibly be behind the `noisy' stream of sounds/letters/word-classes observed in our experiments; and last but not least (c) presentation of a new type of signal to the community exploring natural non-linear phenomena.
Tailored Excitation using Non-Linear B0-Shims
Duan, Qi; van Gelderen, Peter; Duyn, Jeff
2011-01-01
In high field MRI, RF flip angle inhomogeneity due to wavelength effects can lead to spatial variations in contrast and sensitivity. Improved flip angle homogeneity can be achieved through multi-dimensional excitation, but long RF pulse durations limit practical application. A recent approach to reduce RF pulse duration is based on parallel excitation through multiple RF channels. Here, an alternative approach to shorten multi-dimensional excitation is proposed that makes use of non-linear spatial variations in the stationary (B0) magnetic field during a B0-sensitive excitation pulse. As initial demonstration, the method was applied to 2D gradient echo (GE) MRI of human brain at 7T. Using B0 shims with up to second order spatial dependence, it is demonstrated that root-mean-squared flip angle variation can be reduced from 20% to 11% with RF pulse lengths that are practical for general GE imaging applications without requiring parallel excitation. The method is expected to improve contrast and sensitivity in GE MRI of human brain at high field. PMID:22222623
Amplitude relations in non-linear sigma model
NASA Astrophysics Data System (ADS)
Chen, Gang; Du, Yi-Jian
2014-01-01
In this paper, we investigate tree-level scattering amplitude relations in U( N) non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [23,24], both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell U(1) identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy U(1)-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total 2 m-point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation.
Non-linear optical measurements using a scanned, Bessel beam
NASA Astrophysics Data System (ADS)
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-03-01
Oftentimes cells are removed from the body for disease diagnosis or cellular research. This typically requires fluorescent labeling followed by sorting with a flow cytometer; however, possible disruption of cellular function or even cell death due to the presence of the label can occur. This may be acceptable for ex vivo applications, but as cells are more frequently moving from the lab to the body, label-free methods of cell sorting are needed to eliminate these issues. This is especially true of the growing field of stem cell research where specialized cells are needed for treatments. Because differentiation processes are not completely efficient, cells must be sorted to eliminate any unwanted cells (i.e. un-differentiated or differentiated into an unwanted cell type). In order to perform label-free measurements, non-linear optics (NLO) have been increasingly utilized for single cell analysis because of their ability to not disrupt cellular function. An optical system was developed for the measurement of NLO in a microfluidic channel similar to a flow cytometer. In order to improve the excitation efficiency of NLO, a scanned Bessel beam was utilized to create a light-sheet across the channel. The system was tested by monitoring twophoton fluorescence from polystyrene microbeads of different sizes. Fluorescence intensity obtained from light-sheet measurements were significantly greater than measurements made using a static Gaussian beam. In addition, the increase in intensity from larger sized beads was more evident for the light-sheet system.
Channel Capacity of Non-Linear Transmission Systems
NASA Astrophysics Data System (ADS)
Ellis, Andrew D.; Zhao, Jian
Since their introduction in the late 1970s, the capacity of optical communication links has grown exponentially, fuelled by a series of key innovations including movement between the three telecommunication windows of 850 nm, 1,310 nm and 1,550 nm, distributed feedback laser, erbium-doped fibre amplifiers (EDFAs), dispersion-shifted and dispersion-managed fibre links, external modulation, wavelength division multiplexing, optical switching, forward error correction (FEC), Raman amplification, and most recently, coherent detection, electronic signal processing and optical orthogonal frequency division multiplexing (OFDM). Throughout this evolution, one constant factor has been the use of single-mode optical fibre, whose fundamental principles dated back to the 1800s, when Irish scientist, John Tyndall demonstrated in a lecture to the Royal Society in London that light could be guided through a curved stream of water [1]. Following many developments, including the proposal for waveguides by J.J. Thompson [2], the presentation of detailed calculations for dielectric waveguides by Snitzer [3], the proposal [4] and fabrication [5] of ultra low loss fibres, single-mode fibres were first adopted for non-experimental use in Dorset, UK in 1975, and are still in use today, despite the evolving designs to control chromatic dispersion and non-linearity.
Primordial Black Holes in non-linear perturbation theory
NASA Astrophysics Data System (ADS)
Hidalgo, Juan Carlos
2009-10-01
This thesis begins with a study of the origin of cosmological fluctuations with special attention to those cases in which the non-Gaussian correlation functions are large. The analysis shows that perturbations from an almost massless auxiliary field generically produce large values of the non-linear parameter f_NL. The effects of including non-Gaussian correlation functions in the statistics of cosmological structure are explored by constructing a non-Gaussian probability distribution function (PDF). Such PDF is derived for the comoving curvature perturbation from first principles in the context of quantum field theory, with n-point correlation functions as the only input. The non-Gaussian PDF is then used to explore two important problems in the physics of primordial black holes (PBHs): First, to compute non-Gaussian corrections to the number of PBHs generated from the primordial curvature fluctuations. The second application concerns new cosmological observables. The formation of PBHs is known to depend on two main physical characteristics: the strength of the gravitational field produced by the initial curvature inhomogeneity and the pressure gradient at the edge of the curvature configuration. We account for the probability of finding these configurations by using two parameters: The amplitude of the inhomogeneity and its second radial derivative, evaluated at the centre of the configuration. The implications of the derived probability for the fraction of mass in the universe in the form of PBHs are discussed.
A non linear analytical model of switched reluctance machines
NASA Astrophysics Data System (ADS)
Sofiane, Y.; Tounzi, A.; Piriou, F.
2002-06-01
Nowadays, the switched reluctance machine are widely used. To determine their performances and to elaborate control strategy, we generally use the linear analytical model. Unhappily, this last is not very accurate. To yield accurate modelling results, we use then numerical models based on either 2D or 3D Finite Element Method. However, this approach is very expensive in terms of computation time and remains suitable to study the behaviour of eventually a whole device. However, it is not, a priori, adapted to elaborate control strategy for electrical machines. This paper deals with a non linear analytical model in terms of variable inductances. The theoretical development of the proposed model is introduced. Then, the model is applied to study the behaviour of a whole controlled switched reluctance machine. The parameters of the structure are identified from a 2D numerical model. They can also be determined from an experimental bench. Then, the results given by the proposed model are compared to those issue from the 2D-FEM approach and from the classical linear analytical model.
Non-linear modulation of short wavelength compressional Alfven eigenmodes
Fredrickson, E. D.; Gorelenkov, N. N.; Podesta, M.; Gerhardt, S. P.; Bell, R. E.; Diallo, A.; LeBlanc, B.; Bortolon, A.; Crocker, N. A.; Levinton, F. M.; Yuh, H.
2013-04-15
Most Alfvenic activity in the frequency range between toroidal Alfven eigenmodes and roughly one half of the ion cyclotron frequency on National Spherical Torus eXperiment [Ono et al., Nucl. Fusion 40, 557 (2000)], that is, approximately 0.3 MHz up to Almost-Equal-To 1.2 MHz, are modes propagating counter to the neutral beam ions. These have been modeled as Compressional and Global Alfven Eigenmodes (CAE and GAE) and are excited through a Doppler-shifted cyclotron resonance with the beam ions. There is also a class of co-propagating modes at higher frequency than the counter-propagating CAE and GAE. These modes have been identified as CAE, and are seen mostly in the company of a low frequency, n = 1 kink-like mode. In this paper, we present measurements of the spectrum of these high frequency CAE (hfCAE) and their mode structure. We compare those measurements to a simple model of CAE and present a predator-prey type model of the curious non-linear coupling of the hfCAE and the low frequency kink-like mode.
Experimental study of a linear/non-linear flux rope
DeHaas, Timothy; Gekelman, Walter; Van Compernolle, Bart
2015-08-15
Flux ropes are magnetic structures of helical field lines, accompanied by spiraling currents. Commonly observed on the solar surface extending into the solar atmosphere, flux ropes are naturally occurring and have been observed by satellites in the near earth and in laboratory environments. In this experiment, a single flux rope (r = 2.5 cm, L = 1100 cm) was formed in the cylindrical, magnetized plasma of the Large Plasma Device (LaPD, L = 2200 cm, r{sub plasma} = 30 cm, n{sub o} = 10{sup 12 }cm{sup −3}, T{sub e} = 4 eV, He). The flux rope was generated by a DC discharge between an electron emitting cathode and anode. This fixes the rope at its source while allowing it to freely move about the anode. At large currents (I > πr{sup 2}B{sub 0}c/2 L), the flux rope becomes helical in structure and oscillates about a central axis. Under varying Alfven speeds and injection current, the transition of the flux rope from stable to kink-unstable was examined. As it becomes non-linear, oscillations in the magnetic signals shift from sinusoidal to Sawtooth-like, associated with elliptical motion of the flux rope; or the signal becomes intermittent as its current density increases.
Passive dynamic controllers for non-linear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1991-01-01
A methodology for model-independent controller design for controlling large angular motion of multi-body dynamic systems is outlined.The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system, and at the same time suppress the vibrations due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameters, even if the controlled system is non-linear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach applied to a flexible six-degree-of-freedom manipulator.
Organic non-linear optics and opto-electronics
NASA Astrophysics Data System (ADS)
Maldonado, J. L.; Ramos-Ortíz, G.; Rodríguez, M.; Meneses-Nava, M. A.; Barbosa-García, O.; Santillán, R.; Farfán, N.
2010-12-01
π-conjugated organic molecules and polymers are of great importance in physics, chemistry, material science and engineering. It is expected that, in the near future, organic materials will find widespread use in many technological applications. In the case of organic opto-electronic systems, the list of devices includes light emitting diodes (OLEDs), photovoltaic cells (OPVs), field-effect transistors (OFET), photorefractive materials for light manipulation, among others. These materials are also used for photonic applications: all-optical switching, modulators, optical correlators, plastic waveguides, all polymeric integrated circuits, solid-state lasers, and for biophotonic applications as in the case of the development of organic labels for multiphoton microscopy and photodynamic therapy. The advances in the developing of organic compounds with better mechanical, electrical, and optical (linear and non-linear) characteristics are of a great importance for this field. Here, we present the research on this area carried out at the Centro de Investigaciones en Óp-tica (CIO), in collaboration with Chemistry Departments of different institutions. This work focuses on the optical characterization of materials through several techniques such as TOF, FWM, TBC, THG Maker Fringes, HRS, Z-scan, and TPEF. Additionally, some applications, such as dynamic holography by using photorefractive polymers, and OPVs cells will be discussed.
Multigrid approaches to non-linear diffusion problems on unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.
Non-linear optical flow cytometry using a scanned, Bessel beam light-sheet.
Collier, Bradley B; Awasthi, Samir; Lieu, Deborah K; Chan, James W
2015-05-29
Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers.
Non-linear signal detection improvement by radiation damping in single-pulse NMR spectra.
Schlagnitweit, Judith; Morgan, Steven W; Nausner, Martin; Müller, Norbert; Desvaux, Hervé
2012-02-01
When NMR lines overlap and at least one of them is affected by radiation damping, the resonance line shapes of all lines are no longer Lorentzian. We report the appearance of narrow signal distortions, which resemble hole-burnt spectra. This new experimental phenomenon facilitates the detection of tiny signals hidden below the main resonance. Theoretical analysis based on modified Maxwell-Bloch equations shows that the presence of strong transverse magnetization creates a feedback through the coil, which influences the magnetization of all spins with overlapping resonance lines. In the time domain this leads to cross-precession terms between magnetization densities, which ultimately cause non-linear behavior. Numerical simulations corroborate this interpretation.
A limit analysis approach to derive a thermodynamic damage potential for non-linear geomaterials
NASA Astrophysics Data System (ADS)
Karrech, A.; Poulet, T.; Regenauer-Lieb, K.
2012-10-01
This paper introduces a mathematical model which describes the continuum damage of non-linear geo-materials. The model accounts for full thermo-mechanical coupling as well as irreversible failure and its effect on shear heating. It involves multi-mechanisms creep to describe the material rheology depending on time, temperature, pressure and water content. This coupled thermo-mechanical model combined with the upper bound theory is used to formulate a potential capable of predicting the damage evolution. The model is implemented and applied to a cross-sectional geological layer subjected to extension. It reveals that damage accelerates the creation of faults and accentuates the localization of shear zones, thereby competing with the increase in material rigidity due to rate dependency, especially at high temperature.
NASA Astrophysics Data System (ADS)
Young-Gonzales, Amanda R.; Samanta, Subarna; Richert, Ranko
2015-09-01
For glycerol and three monohydroxy alcohols, we have measured the non-linear dielectric effects resulting from the application and removal of a high dc bias electric field. The field effects are detected by virtue of a small amplitude harmonic field, from which time resolved changes in the dielectric loss are derived. The changes in permittivity are dominated by modifications of the time constants (rather than amplitudes) which display two contributions: a heating-like decrease of relaxation times that originates from the time dependent field when the bias is switched on and off and a slowing down of the dynamics resulting from the field induced reduction of configurational entropy. As observed for the electro-optical Kerr effect, the rise of the entropy change is slower than its decay, a feature that we rationalize on the basis of the quadratic dependence of the entropy change on polarization. For glycerol, the observed steady state level of the field induced shift of the glass transition temperature (+84 mK) matches the expectation based on the entropy change and its impact on dynamics via the Adam-Gibbs relation (+88 mK). For the alcohols, these non-linear effects rise and decay on the time scales of the prominent dielectric Debye process, underscoring the relation of these features to polarization anisotropy, opposed to mechanical or enthalpy relaxation which are orders of magnitude faster in these systems. A model is discussed which captures the observed magnitudes as well as time dependences in a near quantitative fashion. It is demonstrated that the high bias field modifies the response of polarization to the ac field, including a temporary change in the low field susceptibility.
Young-Gonzales, Amanda R; Samanta, Subarna; Richert, Ranko
2015-09-14
For glycerol and three monohydroxy alcohols, we have measured the non-linear dielectric effects resulting from the application and removal of a high dc bias electric field. The field effects are detected by virtue of a small amplitude harmonic field, from which time resolved changes in the dielectric loss are derived. The changes in permittivity are dominated by modifications of the time constants (rather than amplitudes) which display two contributions: a heating-like decrease of relaxation times that originates from the time dependent field when the bias is switched on and off and a slowing down of the dynamics resulting from the field induced reduction of configurational entropy. As observed for the electro-optical Kerr effect, the rise of the entropy change is slower than its decay, a feature that we rationalize on the basis of the quadratic dependence of the entropy change on polarization. For glycerol, the observed steady state level of the field induced shift of the glass transition temperature (+84 mK) matches the expectation based on the entropy change and its impact on dynamics via the Adam-Gibbs relation (+88 mK). For the alcohols, these non-linear effects rise and decay on the time scales of the prominent dielectric Debye process, underscoring the relation of these features to polarization anisotropy, opposed to mechanical or enthalpy relaxation which are orders of magnitude faster in these systems. A model is discussed which captures the observed magnitudes as well as time dependences in a near quantitative fashion. It is demonstrated that the high bias field modifies the response of polarization to the ac field, including a temporary change in the low field susceptibility.
Adcock, T. A. A.; Taylor, P. H.
2016-01-15
The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.
Non-Linear Pattern Formation in Bone Growth and Architecture
Salmon, Phil
2014-01-01
The three-dimensional morphology of bone arises through adaptation to its required engineering performance. Genetically and adaptively bone travels along a complex spatiotemporal trajectory to acquire optimal architecture. On a cellular, micro-anatomical scale, what mechanisms coordinate the activity of osteoblasts and osteoclasts to produce complex and efficient bone architectures? One mechanism is examined here – chaotic non-linear pattern formation (NPF) – which underlies in a unifying way natural structures as disparate as trabecular bone, swarms of birds flying, island formation, fluid turbulence, and others. At the heart of NPF is the fact that simple rules operating between interacting elements, and Turing-like interaction between global and local signals, lead to complex and structured patterns. The study of “group intelligence” exhibited by swarming birds or shoaling fish has led to an embodiment of NPF called “particle swarm optimization” (PSO). This theoretical model could be applicable to the behavior of osteoblasts, osteoclasts, and osteocytes, seeing them operating “socially” in response simultaneously to both global and local signals (endocrine, cytokine, mechanical), resulting in their clustered activity at formation and resorption sites. This represents problem-solving by social intelligence, and could potentially add further realism to in silico computer simulation of bone modeling. What insights has NPF provided to bone biology? One example concerns the genetic disorder juvenile Pagets disease or idiopathic hyperphosphatasia, where the anomalous parallel trabecular architecture characteristic of this pathology is consistent with an NPF paradigm by analogy with known experimental NPF systems. Here, coupling or “feedback” between osteoblasts and osteoclasts is the critical element. This NPF paradigm implies a profound link between bone regulation and its architecture: in bone the architecture is the regulation. The former is the
Non-linear pattern formation in bone growth and architecture.
Salmon, Phil
2014-01-01
The three-dimensional morphology of bone arises through adaptation to its required engineering performance. Genetically and adaptively bone travels along a complex spatiotemporal trajectory to acquire optimal architecture. On a cellular, micro-anatomical scale, what mechanisms coordinate the activity of osteoblasts and osteoclasts to produce complex and efficient bone architectures? One mechanism is examined here - chaotic non-linear pattern formation (NPF) - which underlies in a unifying way natural structures as disparate as trabecular bone, swarms of birds flying, island formation, fluid turbulence, and others. At the heart of NPF is the fact that simple rules operating between interacting elements, and Turing-like interaction between global and local signals, lead to complex and structured patterns. The study of "group intelligence" exhibited by swarming birds or shoaling fish has led to an embodiment of NPF called "particle swarm optimization" (PSO). This theoretical model could be applicable to the behavior of osteoblasts, osteoclasts, and osteocytes, seeing them operating "socially" in response simultaneously to both global and local signals (endocrine, cytokine, mechanical), resulting in their clustered activity at formation and resorption sites. This represents problem-solving by social intelligence, and could potentially add further realism to in silico computer simulation of bone modeling. What insights has NPF provided to bone biology? One example concerns the genetic disorder juvenile Pagets disease or idiopathic hyperphosphatasia, where the anomalous parallel trabecular architecture characteristic of this pathology is consistent with an NPF paradigm by analogy with known experimental NPF systems. Here, coupling or "feedback" between osteoblasts and osteoclasts is the critical element. This NPF paradigm implies a profound link between bone regulation and its architecture: in bone the architecture is the regulation. The former is the emergent
Linear and non-linear bias: predictions versus measurements
NASA Astrophysics Data System (ADS)
Hoffmann, K.; Bel, J.; Gaztañaga, E.
2017-02-01
We study the linear and non-linear bias parameters which determine the mapping between the distributions of galaxies and the full matter density fields, comparing different measurements and predictions. Associating galaxies with dark matter haloes in the Marenostrum Institut de Ciències de l'Espai (MICE) Grand Challenge N-body simulation, we directly measure the bias parameters by comparing the smoothed density fluctuations of haloes and matter in the same region at different positions as a function of smoothing scale. Alternatively, we measure the bias parameters by matching the probability distributions of halo and matter density fluctuations, which can be applied to observations. These direct bias measurements are compared to corresponding measurements from two-point and different third-order correlations, as well as predictions from the peak-background model, which we presented in previous papers using the same data. We find an overall variation of the linear bias measurements and predictions of ∼5 per cent with respect to results from two-point correlations for different halo samples with masses between ∼1012and1015 h-1 M⊙ at the redshifts z = 0.0 and 0.5. Variations between the second- and third-order bias parameters from the different methods show larger variations, but with consistent trends in mass and redshift. The various bias measurements reveal a tight relation between the linear and the quadratic bias parameters, which is consistent with results from the literature based on simulations with different cosmologies. Such a universal relation might improve constraints on cosmological models, derived from second-order clustering statistics at small scales or higher order clustering statistics.
The non-linear initiation of diapirs and plume heads
NASA Astrophysics Data System (ADS)
Bercovici, David; Kelly, Amanda
1997-04-01
A simple theory is devised to describe the non-linear feedback mechanisms involved in the initial growth of a single diapir or plume head from a low viscosity channel overlain by a much more viscous layer. Such feedbacks arise primarily from the relation between the growth of a proto-diapir (i.e. an undulation on the upper boundary of the low viscosity channel) and the draining of the low viscosity channel. In the period of time between its initial exponential growth (characterized by linear stability analysis) and its separation from the low viscosity channel as a fully formed diapir, the proto-diapir can undergo a significant cessation in its development due to deflation of the low viscosity channel; i.e. the proto-diapir's growth can essentially stall for a long period of time before it separates and begins its ascent through the overlying medium. The theory is used to determine a criterion for separation of the diapir from the low viscosity channel that is in terms of the geometrical and mechanical properties of the channel, instead of the ad hoc volume flux widely used in many models of mantle plumes and plume heads (e.g. Whitehead and Luther, 1975; Richards et al., 1989; Olson, 1990; Sleep, 1990; Bercovici and Mahoney, 1994). From this separation criterion, self-consistent scaling laws can be formulated to relate the size of the fully developed diapir and its trailing conduit to the properties of the initial channel, instead of to the ad hoc volume flux. Basic laboratory experiments involving highly viscous fluids are presented and demonstrate that the so-called 'stalling' period between initial growth and separation does indeed occur. These results suggest that nascent mantle plume heads may stall for extended periods at the base of the mantle and thereby contribute to variations in thickness of the D″ layer.
NASA Astrophysics Data System (ADS)
Dautcourt, G.
2009-06-01
Roy P. Kerr has discovered his celebrated metric 45 years ago, yet the problem to find a generalization of the Schwarzschild metric for a rotating mass was faced much earlier. Lense and Thirring, Bach, Andress, Akeley, Lewis, van Stockum and others have tried to solve it or to find an approximative solution at least. In particular Achilles Papapetrou, from 1952 to 1961 in Berlin, was interested in an exact solution. He directed the author in the late autumn of 1959 to work on the problem. Why did these pre-Kerr attempts fail? Comments based on personal reminiscences and old notes.
2007-08-01
Advanced non- linear control algorithms applied to design highly maneuverable Autonomous Underwater Vehicles (AUVs) Vladimir Djapic, Jay A. Farrell...hierarchical such that an ”inner loop” non- linear controller (outputs the appropriate thrust values) is the same for all mission scenarios while a...library of ”outer-loop” non- linear controllers are available to implement specific maneuvering scenarios. On top of the outer-loop is the mission planner
NASA Astrophysics Data System (ADS)
Uieda, Leonardo; Barbosa, Valéria C. F.
2016-10-01
Estimating the relief of the Moho from gravity data is a computationally intensive non-linear inverse problem. What is more, the modeling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized non-linear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyper-parameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30-35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basins, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.
Comparison of Linear and Non-Linear Regression Models to Estimate Leaf Area Index of Dryland Shrubs.
NASA Astrophysics Data System (ADS)
Dashti, H.; Glenn, N. F.; Ilangakoon, N. T.; Mitchell, J.; Dhakal, S.; Spaete, L.
2015-12-01
Leaf area index (LAI) is a key parameter in global ecosystem studies. LAI is considered a forcing variable in land surface processing models since ecosystem dynamics are highly correlated to LAI. In response to environmental limitations, plants in semiarid ecosystems have smaller leaf area, making accurate estimation of LAI by remote sensing a challenging issue. Optical remote sensing (400-2500 nm) techniques to estimate LAI are based either on radiative transfer models (RTMs) or statistical approaches. Considering the complex radiation field of dry ecosystems, simple 1-D RTMs lead to poor results, and on the other hand, inversion of more complex 3-D RTMs is a demanding task which requires the specification of many variables. A good alternative to physical approaches is using methods based on statistics. Similar to many natural phenomena, there is a non-linear relationship between LAI and top of canopy electromagnetic waves reflected to optical sensors. Non-linear regression models can better capture this relationship. However, considering the problem of a few numbers of observations in comparison to the feature space (n
non-linear regression techniques were investigated to estimate LAI. Our study area is located in southwestern Idaho, Great Basin. Sagebrush (Artemisia tridentata spp) serves a critical role in maintaining the structure of this ecosystem. Using a leaf area meter (Accupar LP-80), LAI values were measured in the field. Linear Partial Least Square regression and non-linear, tree based Random Forest regression have been implemented to estimate the LAI of sagebrush from hyperspectral data (AVIRIS-ng) collected in late summer 2014. Cross validation of results indicate that PLS can provide comparable results to Random Forest.
Shandilya, Sharad; Kurz, Michael C.; Ward, Kevin R.; Najarian, Kayvan
2016-01-01
Objective The timing of defibrillation is mostly at arbitrary intervals during cardio-pulmonary resuscitation (CPR), rather than during intervals when the out-of-hospital cardiac arrest (OOH-CA) patient is physiologically primed for successful countershock. Interruptions to CPR may negatively impact defibrillation success. Multiple defibrillations can be associated with decreased post-resuscitation myocardial function. We hypothesize that a more complete picture of the cardiovascular system can be gained through non-linear dynamics and integration of multiple physiologic measures from biomedical signals. Materials and Methods Retrospective analysis of 153 anonymized OOH-CA patients who received at least one defibrillation for ventricular fibrillation (VF) was undertaken. A machine learning model, termed Multiple Domain Integrative (MDI) model, was developed to predict defibrillation success. We explore the rationale for non-linear dynamics and statistically validate heuristics involved in feature extraction for model development. Performance of MDI is then compared to the amplitude spectrum area (AMSA) technique. Results 358 defibrillations were evaluated (218 unsuccessful and 140 successful). Non-linear properties (Lyapunov exponent > 0) of the ECG signals indicate a chaotic nature and validate the use of novel non-linear dynamic methods for feature extraction. Classification using MDI yielded ROC-AUC of 83.2% and accuracy of 78.8%, for the model built with ECG data only. Utilizing 10-fold cross-validation, at 80% specificity level, MDI (74% sensitivity) outperformed AMSA (53.6% sensitivity). At 90% specificity level, MDI had 68.4% sensitivity while AMSA had 43.3% sensitivity. Integrating available end-tidal carbon dioxide features into MDI, for the available 48 defibrillations, boosted ROC-AUC to 93.8% and accuracy to 83.3% at 80% sensitivity. Conclusion At clinically relevant sensitivity thresholds, the MDI provides improved performance as compared to AMSA
Biomagnetic activity and non linear analysis in obstetrics and gynecology in a Greek population.
Anninos, P; Anastasiadis, P; Adamopoulos, A; Kotini, A
2016-01-01
This article reports the application of non-linear analysis to biomagnetic signals recorded from fetal growth restriction, fetal brain activity, ovarian lesions, breast lesions, umbilical arteries, uterine myomas, and uterine arteries in a Greek population. The results were correlated with clinical findings. The biomagnetic measurements and the application of non-linear analysis are promising procedures in Obstetrics and Gynecology.
Non-Linear Dose-Response Relationships in Biology, Toxicology and Medicine
2007-11-02
The purpose of the conference was to attract researchers from diverse backgrounds who are working in the common area of non-linear dose - response relationships...This unique interdisciplinary conference represents an important step in furthering the understanding of the occurrence, origin, mechanisms, significance and practical applications of non-linear dose - response relationships.
NASA Astrophysics Data System (ADS)
Bogatyrev, I. B.; Grojo, D.; Delaporte, P.; Leyder, S.; Sentis, M.; Marine, W.; Itina, T. E.
2011-11-01
We present a theoretical model, which describes local energy deposition inside IR-transparent silicon and gallium arsenide with focused 1.3-μm wavelength femtosecond laser pulses. Our work relies on the ionization rate equation and two temperature model (TTM), as we simulate the non-linear propagation of focused femtosecond light pulses by using a 3D finite difference time domain method. We find a strong absorption dependence on the initial free electron density (doping concentration) that evidences the role of avalanche ionization. Despite an influence of Kerr-type self-focusing at intensity required for non-linear absorption, we show the laser energy deposition remains confined when the focus position is moved down to 1-mm below the surface. Our simulation results are in agreement with the degree of control observed in a simple model experiment.
Rigatos, Gerasimos G
2016-06-01
It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.
Single-photon non-linear optics with a quantum dot in a waveguide.
Javadi, A; Söllner, I; Arcari, M; Hansen, S Lindskov; Midolo, L; Mahmoodian, S; Kiršanskė, G; Pregnolato, T; Lee, E H; Song, J D; Stobbe, S; Lodahl, P
2015-10-23
Strong non-linear interactions between photons enable logic operations for both classical and quantum-information technology. Unfortunately, non-linear interactions are usually feeble and therefore all-optical logic gates tend to be inefficient. A quantum emitter deterministically coupled to a propagating mode fundamentally changes the situation, since each photon inevitably interacts with the emitter, and highly correlated many-photon states may be created. Here we show that a single quantum dot in a photonic-crystal waveguide can be used as a giant non-linearity sensitive at the single-photon level. The non-linear response is revealed from the intensity and quantum statistics of the scattered photons, and contains contributions from an entangled photon-photon bound state. The quantum non-linearity will find immediate applications for deterministic Bell-state measurements and single-photon transistors and paves the way to scalable waveguide-based photonic quantum-computing architectures.
Single-photon non-linear optics with a quantum dot in a waveguide
Javadi, A.; Söllner, I.; Arcari, M.; Hansen, S. Lindskov; Midolo, L.; Mahmoodian, S.; Kiršanskė, G; Pregnolato, T.; Lee, E. H.; Song, J. D.; Stobbe, S.; Lodahl, P.
2015-01-01
Strong non-linear interactions between photons enable logic operations for both classical and quantum-information technology. Unfortunately, non-linear interactions are usually feeble and therefore all-optical logic gates tend to be inefficient. A quantum emitter deterministically coupled to a propagating mode fundamentally changes the situation, since each photon inevitably interacts with the emitter, and highly correlated many-photon states may be created. Here we show that a single quantum dot in a photonic-crystal waveguide can be used as a giant non-linearity sensitive at the single-photon level. The non-linear response is revealed from the intensity and quantum statistics of the scattered photons, and contains contributions from an entangled photon–photon bound state. The quantum non-linearity will find immediate applications for deterministic Bell-state measurements and single-photon transistors and paves the way to scalable waveguide-based photonic quantum-computing architectures. PMID:26492951
Travelling and standing envelope solitons in discrete non-linear cyclic structures
NASA Astrophysics Data System (ADS)
Grolet, Aurelien; Hoffmann, Norbert; Thouverez, Fabrice; Schwingshackl, Christoph
2016-12-01
Envelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery.
Non-linear wave propagation in acoustically lined circular ducts
NASA Technical Reports Server (NTRS)
Nayfeh, A. H.; Tsai, M.-S.
1974-01-01
An analysis is presented of the nonlinear effects of the gas motion as well as of the acoustic lining material on the transmission and attenuation of sound in a circular duct with a uniform cross-section and no mean flow. The acoustic material is characterized by an empirical, nonlinear impedance in which the instantaneous resistance is a nonlinear function of both the frequency and the acoustic velocity. The results show that there exist frequency bandwidths around the resonant frequencies in which the nonlinearity decreases the attenuation rate, and outside which the nonlinearity increases the attenuation rate, in qualitative agreement with experimental observations. Moreover, the effect of the gas nonlinearity increases with increasing sound frequency, whereas the effect of the material nonlinearity decreases with increasing sound frequency.
Topographical studies on GNF crystals of non linear optical origin
NASA Astrophysics Data System (ADS)
Khandpekar, M. M.; Pati, S. P.
2013-02-01
α-glycine has been combined with equal amount of nitric acid and hydrofluoric acid to form GNF crystals. Transparent and elongated crystals of appreciable sizes (2.5 cm length) useful for dislocation studies have been obtained from solution by slow evaporation in 3-4 weeks time. Crystals were found to be delicate and care is needed while handling them. The external geometry of the crystals was found to vary with composition. Glacial acetic acid (GAA) is found to be universal etching agent. GAA produces well defined elongated etch pits on the habit faces and curved triangular pits on cleavage faces in 15 seconds time. Evidence of impurity inclusions and pits on these inclusions have been detected. The orientation of pits on partial cleavage faces are clearly seen to differ. Occasional presence of long domain lines crossing the field of view has been observed. The curvature of pits edges indicates an optically active material with lower symmetry.
Spectral Hole Burning via Kerr Nonlinearity
NASA Astrophysics Data System (ADS)
Khan, Anwar Ali; Abdul Jabar, M. S.; Jalaluddin, M.; Bacha, Bakht Amin; Iftikhar, Ahmad
2015-10-01
Spectral hole burning is investigated in an optical medium in the presence of Doppler broadening and Kerr nonlinearity. The Kerr nonlinearity generates coherent hole burning in the absorption spectrum. The higher order Kerr nonlinearity enhances the typical lamb dip of the hole. Normal dispersion in the hole burning region while Steep anomalous dispersion between the two hole burning regions also enhances with higher order Kerr effect. A large phase shift creates large delay or advancement in the pulse propagation while no distortion is observed in the pulse. These results provide significant steps to improve optical memory, telecom devices, preservation of information and image quality. Supported by Higher Education Commission (HEC) of Pakistan
A New Multi-tanh-Based Non-linear Function Synthesiser
NASA Astrophysics Data System (ADS)
Taher Abuelma'atti, Muhammad; Radhi Al-Abbas, Saad
2016-11-01
A new complementary metal-oxide-semiconductor transadmittance-mode with input voltage and output current, analogue non-linear odd-function synthesiser is presented. The proposed circuit is based on the assumption that a non-linear odd- function can be approximated by the summation of hyperbolic tangent (tanh) functions with different arguments. Each term of the tanh function expansion is realised by exploiting to advantage the inherent non-linearity of a current-controlled current-conveyor (CCCCII) (or an operational transconductance amplifier (OTA)) with a different bias current. The output currents of these CCCCIIs (OTAs) are weighted using the gains of current amplifiers. These weighted currents are algebraically added to form the required non-linear function. The proposed circuit is suitable for integration, can be easily extended to include higher order terms of the tanh-odd-function expansion and can be programmed to realise arbitrary hard non-linear odd-functions that cannot be easily realised using already existing techniques, based on the Taylor-series expansion, for synthesising non-linear functions. PSPICE simulation results, obtained from CCCCII-based realisations of selected hard non-linearities, demonstrating the functionality of the proposed circuit are included.
Freiwald, W A; Valdes, P; Bosch, J; Biscay, R; Jimenez, J C; Rodriguez, L M; Rodriguez, V; Kreiter, A K; Singer, W
1999-12-15
Information processing in the visual cortex depends on complex and context sensitive patterns of interactions between neuronal groups in many different cortical areas. Methods used to date for disentangling this functional connectivity presuppose either linearity or instantaneous interactions, assumptions that are not necessarily valid. In this paper a general framework that encompasses both linear and non-linear modelling of neurophysiological time series data by means of Local Linear Non-linear Autoregressive models (LLNAR) is described. Within this framework a new test for non-linearity of time series and for non-linearity of directedness of neural interactions based on LLNAR is presented. These tests assess the relative goodness of fit of linear versus non-linear models via the bootstrap technique. Additionally, a generalised definition of Granger causality is presented based on LLNAR that is valid for both linear and non-linear systems. Finally, the use of LLNAR for measuring non-linearity and directional influences is illustrated using artificial data, reference data as well as local field potentials (LFPs) from macaque area TE. LFP data is well described by the linear variant of LLNAR. Models of this sort, including lagged values of the preceding 25 to 60 ms, revealed the existence of both uni- and bi-directional influences between recording sites.
Non-linear modelling and optimal control of a hydraulically actuated seismic isolator test rig
NASA Astrophysics Data System (ADS)
Pagano, Stefano; Russo, Riccardo; Strano, Salvatore; Terzo, Mario
2013-02-01
This paper investigates the modelling, parameter identification and control of an unidirectional hydraulically actuated seismic isolator test rig. The plant is characterized by non-linearities such as the valve dead zone and frictions. A non-linear model is derived and then employed for parameter identification. The results concerning the model validation are illustrated and they fully confirm the effectiveness of the proposed model. The testing procedure of the isolation systems is based on the definition of a target displacement time history of the sliding table and, consequently, the precision of the table positioning is of primary importance. In order to minimize the test rig tracking error, a suitable control system has to be adopted. The system non-linearities highly limit the performances of the classical linear control and a non-linear one is therefore adopted. The test rig mathematical model is employed for a non-linear control design that minimizes the error between the target table position and the current one. The controller synthesis is made by taking no specimen into account. The proposed approach consists of a non-linear optimal control based on the state-dependent Riccati equation (SDRE). Numerical simulations have been performed in order to evaluate the soundness of the designed control with and without the specimen under test. The results confirm that the performances of the proposed non-linear controller are not invalidated because of the presence of the specimen.
Effect of directional distribution on non-linear energy transfer in wind wave spectrum
NASA Astrophysics Data System (ADS)
Lavrenov, I.; Krogstad, H.
2003-04-01
Different directional distribution is investigated from the point of view a non-linear energy transfer in wind wave spectrum. In order to produce a numerical simulation of the non-linear interaction in wind wave spectrum a method of numerical integration of the highest accuracy is used. It is shown that the value of non-linear energy transfer is very sensitive to details of frequency-angular approximation of wave spectrum. The non-linear energy transfer is non-zero in wide frequency - angular range, depending on spectrum angular distribution. The calculation results reveal the presence of non-linear energy transfer to spectral components, which propagation is opposite to wind direction for a wide spectrum angular distribution. It should be noted that neither the discrete interaction approximation (DIA) used in the WAM model (Komen et al., 1994), no diffusive approximation of the non-linear transfer (Pushkarev and Zakharov, 1999) are able not to produce this effect. Numerical results show that the bi-model angular distribution, obtained by Hwang et al. (2000) in field experiments, can be generated by the non-linear energy transfer, sending energy in side direction. Present study has been supported by the INTAS-99-666, INTAS-01-25, INTAS-01-234, INTAS-01-2156, RFBR- 01- 05-64846 Grants.
NASA Astrophysics Data System (ADS)
Royston, T. J.; Singh, R.
1996-07-01
While significant non-linear behavior has been observed in many vibration mounting applications, most design studies are typically based on the concept of linear system theory in terms of force or motion transmissibility. In this paper, an improved analytical strategy is presented for the design optimization of complex, active of passive, non-linear mounting systems. This strategy is built upon the computational Galerkin method of weighted residuals, and incorporates order reduction and numerical continuation in an iterative optimization scheme. The overall dynamic characteristics of the mounting system are considered and vibratory power transmission is minimized via adjustment of mount parameters by using both passive and active means. The method is first applied through a computational example case to the optimization of basic passive and active, non-linear isolation configurations. It is found that either active control or intentionally introduced non-linearity can improve the mount's performance; but a combination of both produces the greatest benefit. Next, a novel experimental, active, non-linear isolation system is studied. The effect of non-linearity on vibratory power transmission and active control are assessed via experimental measurements and the enhanced Galerkin method. Results show how harmonic excitation can result in multiharmonic vibratory power transmission. The proposed optimization strategy offers designers some flexibility in utilizing both passive and active means in combination with linear and non-linear components for improved vibration mounts.
Remote synchronization of amplitudes across an experimental ring of non-linear oscillators
Minati, Ludovico E-mail: ludovico.minati@unitn.it
2015-12-15
In this paper, the emergence of remote synchronization in a ring of 32 unidirectionally coupled non-linear oscillators is reported. Each oscillator consists of 3 negative voltage gain stages connected in a loop to which two integrators are superimposed and receives input from its preceding neighbour via a “mixing” stage whose gains form the main system control parameters. Collective behaviour of the network is investigated numerically and experimentally, based on a custom-designed circuit board featuring 32 field-programmable analog arrays. A diverse set of synchronization patterns is observed depending on the control parameters. While phase synchronization ensues globally, albeit imperfectly, for certain control parameter values, amplitudes delineate subsets of non-adjacent but preferentially synchronized nodes; this cannot be trivially explained by synchronization paths along sequences of structurally connected nodes and is therefore interpreted as representing a form of remote synchronization. Complex topology of functional synchronization thus emerges from underlying elementary structural connectivity. In addition to the Kuramoto order parameter and cross-correlation coefficient, other synchronization measures are considered, and preliminary findings suggest that generalized synchronization may identify functional relationships across nodes otherwise not visible. Further work elucidating the mechanism underlying this observation of remote synchronization is necessary, to support which experimental data and board design materials have been made freely downloadable.
Non-Linear Optical Response Simulations for Strongly Corellated Hybrid Carbon Nanotube Systems
NASA Astrophysics Data System (ADS)
Meliksetyan, Areg; Bondarev, Igor; Gelin, Maxim
2013-03-01
Hybrid carbon nanotube systems, nanotubes containing extrinsic atomic type species (dopants) such as semiconductor quantum dots, extrinsic atoms, or ions, are promising candidates for the development of the new generation of tunable nanooptoelectronic devices - both application oriented, e.g., photovoltaic devices of improved light-harvesting efficiency, and devices for use in fundamental research. Here, we simulate non-linear optical response signals for a pair of spatially separated two-level dipole emitters (to model the dopants above) in the regime where they are coupled strongly to a low-energy surface plasmon resonance of a metallic carbon nanotube. Such a coupling makes them entangled, and we show that the cross-peaks in 2D photon-echo spectra are indicative of the bipartite entanglement being present in the system. We simulate various experimental conditions and formulate practical recommendations for the reliable experimental observation of this unique quantum phenomenon of relevance to the solid-state quantum information science. ARO-W911NF-11-1-0189 (AM), DOE-DE-SC0007117 (IB), DFG-MAP (MG)
Valero, C.; Javierre, E.; García-Aznar, J. M.; Gómez-Benito, M. J.
2015-01-01
SUMMARY Wound healing is a process driven by biochemical and mechanical variables in which new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Due to the regularity of this morphology, we approximate the evolution of the wound through its cross-section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem while maintaining allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the non-linear problem we use the Finite Element Method and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. PMID:24443355
Friese, Daniel H; Ruud, Kenneth
2016-02-07
We present the theory of three-photon circular dichroism (3PCD), a novel non-linear chiroptical property not yet described in the literature. We derive the observable absorption cross section including the orientational average of the necessary seventh-rank tensors and provide origin-independent expressions for 3PCD using either a velocity-gauge treatment of the electric dipole operator or a length-gauge formulation using London atomic orbitals. We present the first numerical results for hydrogen peroxide, 3-methylcyclopentanone (MCP) and 4-helicene, including also a study of the origin dependence and basis set convergence of 3PCD. We find that for the 3PCD-brightest low-lying Rydberg state of hydrogen peroxide, the dichroism is extremely basis set dependent, with basis set convergence not being reached before a sextuple-zeta basis is used, whereas for the MCP and 4-helicene molecules, the basis set dependence is more moderate and at the triple-zeta level the 3PCD contributions are more or less converged irrespective of whether the considered states are Rydberg states or not. The character of the 3PCD-brightest states in MCP is characterized by a fairly large charge-transfer character from the carbonyl group to the ring system. In general, the quadrupole contributions to 3PCD are found to be very small.
Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers
NASA Astrophysics Data System (ADS)
Schell, Andreas W.; Tran, Toan Trong; Takashima, Hideaki; Takeuchi, Shigeki; Aharonovich, Igor
2016-12-01
Two-photon absorption is an important non-linear process employed for high resolution bio-imaging and non-linear optics. In this work, we realize two-photon excitation of a quantum emitter embedded in a two-dimensional (2D) material. We examine defects in hexagonal boron nitride (hBN) and show that the emitters exhibit similar spectral and quantum properties under one-photon and two-photon excitation. Furthermore, our findings are important to deploy two-dimensional hexagonal boron nitride for quantum non-linear photonic applications.
Neural Network Associative Memory Using Non-Linear Holographic Storage Media
1989-12-01
T’,?T Cýy’ ( AFIT/GEO/ENG/89D-3 AD-A214 340 L NEURAL NETWORK ASSOCIATIVE MEMORY USING NON-LINEAR HOLOGRAPHIC STORAGE MEDIA I THESIS I Presented to...order approximations of the required gain were provided. - - -In= unazn A FIT/GEO/ENG/89D-3 NEURAL NETWORK ASSOCIATIVE MEMORY USING NON-LINEAR...approxi- mations of the required gain were provided. vi NEURAL NETWORK ASSOCIATIVE MEMORY USING NON-LINEAR HOLOGRAPHIC STORAGE MEDIA I. Introduction The
Uncertainty due to non-linearity in radiation thermometers calibrated by multiple fixed points
Yamaguchi, Y.; Yamada, Y.
2013-09-11
A new method to estimate the uncertainty due to non-linearity is described on the n= 3 scheme basis. The expression of uncertainty is mathematically derived applying the random walk method. The expression is simple and requires only the temperatures of the fixed points and a relative uncertainty value for each flux-doubling derived from the non-linearity measurement. We also present an example of the method, in which the uncertainty of temperature measurement by a radiation thermometer is calculated on the basis of non-linearity measurement.
Linear and non-linear fluorescence imaging of neuronal activity
NASA Astrophysics Data System (ADS)
Fisher, Jonathan A. N.
-photon absorption (TPA) cross sections, Sigma2 of various fluorophores are described as well. Utilizing single-beam two-photon microscopy, action potentials were recorded optically from individual (˜1 mum) nerve terminals of the intact mouse neurohypophysis, in a single sweep. Single-trial recordings of action potentials exhibited signal-to-noise ratios ˜5 and fractional fluorescence changes of up to ˜10%. These results represent the first single-trial optical recording of action potentials from individual nerve terminals in an intact mammalian preparation using 180° detection, and may serve as an alternative to invasive electrode arrays for studying neuronal systems in vivo .
Enhanced studies on a composite time integration scheme in linear and non-linear dynamics
NASA Astrophysics Data System (ADS)
Klarmann, S.; Wagner, W.
2015-03-01
In Bathe and Baig (Comput Struct 83:2513-2524, 2005), Bathe (Comput Struct 85:437-445, 2007), Bathe and Noh (Comput Struct 98-99:1-6, 2012) Bathe et al. have proposed a composite implicit time integration scheme for non-linear dynamic problems. This paper is aimed at the further investigation of the scheme's behaviour for use in case of linear and non-linear problems. Therefore, the examination of the amplification matrix of the scheme will be extended in order to get in addition the properties for linear calculations. Besides, it will be demonstrated that the integration scheme also has an impact on some of these properties when used for non-linear calculations. In conclusion, a recommendation for the only selectable parameter of the scheme will be given for application in case of geometrically non-linear calculations.
Non-linear analysis of EEG signals at various sleep stages.
Acharya U, Rajendra; Faust, Oliver; Kannathal, N; Chua, TjiLeng; Laxminarayan, Swamy
2005-10-01
Application of non-linear dynamics methods to the physiological sciences demonstrated that non-linear models are useful for understanding complex physiological phenomena such as abrupt transitions and chaotic behavior. Sleep stages and sustained fluctuations of autonomic functions such as temperature, blood pressure, electroencephalogram (EEG), etc., can be described as a chaotic process. The EEG signals are highly subjective and the information about the various states may appear at random in the time scale. Therefore, EEG signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. The sleep data analysis is carried out using non-linear parameters: correlation dimension, fractal dimension, largest Lyapunov entropy, approximate entropy, Hurst exponent, phase space plot and recurrence plots. These non-linear parameters quantify the cortical function at different sleep stages and the results are tabulated.
Non-Linear Noise Contributions in Highly Dispersive Optical Transmission Systems
NASA Astrophysics Data System (ADS)
Matera, Francesco
2016-01-01
This article reports an analytical investigation, confirmed by numerical simulations, about the non-linear noise contribution in single-channel systems adopting generic modulation-detection formats in long links with both managed and unmanaged dispersion compensation and its impact in system performance. This noise contribution is expressed in terms of a pulse non-linear interaction length and permits a simple calculation of the Q-factor. Results point out the dependence of this non-linear noise on the number of amplifiers spans, N, according to the adopted chromatic dispersion compensation scheme, the modulation-detection format, and the signal baud rate. It is also shown how the effects of polarization multiplexing can be taken into account and how this single-channel non-linear noise contribution can be used in a wavelength-division multiplexing (WDM) environment.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
ERIC Educational Resources Information Center
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Finite-time H∞ filtering for non-linear stochastic systems
NASA Astrophysics Data System (ADS)
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Absolute measurement of ultrasonic non-linearity parameter at contact interface
NASA Astrophysics Data System (ADS)
Yuan, Maodan; Lee, Taekgyu; Kang, To; Zhang, Jianhai; Song, Sung-Jin; Kim, Hak-Joon
2015-10-01
Non-linear interaction of waves with contact interfaces has been widely applied in non-destructive evaluation fields such as bonding quality evaluation, and the detection of closed microcracks and composite delamination. This paper proposes an absolute measurement of the ultrasonic non-linearity parameter using a piezoelectric detection method for two aluminum alloy blocks of different lengths. The results of a two-dimensional finite element method model verified by models for hard and soft contact interfaces, depending on the interface property, were compared with the measured non-linearity parameter. The measured values show good agreement with the modelled results, indicating good potential for measuring the non-linearity parameter at interfaces experimentally and numerically.
Construction of the wave operator for non-linear dispersive equations
NASA Astrophysics Data System (ADS)
Tsuruta, Kai Erik
In this thesis, we will study non-linear dispersive equations. The primary focus will be on the construction of the positive-time wave operator for such equations. The positive-time wave operator problem arises in the study of the asymptotics of a partial differential equation. It is a map from a space of initial data X into itself, and is loosely defined as follows: Suppose that for a solution ψlin to the dispersive equation with no non-linearity and initial data ψ +, there exists a unique solution ψ to the non-linear equation with initial data ψ0 such that ψ behaves as ψ lin as t → infinity. Then the wave operator is the map W+ that takes ψ + to ψ0. By its definition, W+ is injective. An important additional question is whether or not the map is also surjective. If so, then every non-linear solution emanating from X behaves, in some sense, linearly as it evolves (this is known as asymptotic completeness). Thus, there is some justification for treating these solutions as their much simpler linear counterparts. The main results presented in this thesis revolve around the construction of the wave operator(s) at critical non-linearities. We will study the "semi-relativistic" Schrodinger equation as well as the Klein-Gordon-Schrodinger system on R2 . In both cases, we will impose fairly general quadratic non-linearities for which conservation laws cannot be relied upon. These non-linearities fall below the scaling required to employ such tools as the Strichartz estimates. We instead adapt the "first iteration method" of Jang, Li, and Zhang to our setting which depends crucially on the critical decay of the non-linear interaction of the linear evolution. To see the critical decay in our problem, careful analysis is needed to treat the regime where one has spatial and/or time resonance.
Optimal control of a satellite-robot system using direct collocation with non-linear programming
NASA Astrophysics Data System (ADS)
Coverstone-Carroll, V. L.; Wilkey, N. M.
1995-08-01
The non-holonomic behavior of a satellite-robot system is used to develop the system's equations of motion. The resulting non-linear differential equations are transformed into a non-linear programming problem using direct collocation. The link rates of the robot are minimized along optimal reorientations. Optimal solutions to several maneuvers are obtained and the results are interpreted to gain an understanding of the satellite-robot dynamics.
How does non-linear dynamics affect the baryon acoustic oscillation?
Sugiyama, Naonori S.; Spergel, David N. E-mail: dns@astro.princeton.edu
2014-02-01
We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-k solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-k solutions, some of the recently proposed improved perturbation theories do not guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-k regions. We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at z = 0.35 as ∼ 7.7Mpc/h and describes the small non-linear shift in the peak position due to the galaxy random motions.
Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes
2016-04-20
AFRL-RV-PS- AFRL-RV-PS- TR-2015-0182 TR-2015-0182 CHARACTERIZATION OF NON-LINEARIZED SPACECRAFT RELATIVE MOTION USING NONLINEAR NORMAL MODES Eric...Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62601F...public release; distribution is unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT Characterize the nonlinear dynamics for large amplitude relative motion
The 'Schwarzschild-Kerr' Equilibrium Configurations
Manko, V. S.; Ruiz, E.
2010-12-07
We discuss the possibility of equilibrium between a Schwarzschild black hole possessing zero intrinsic angular momentum and a hyperextreme Kerr source. The balance occurs due to frame-dragging exerted by the latter source on the black-hole constituent, thus giving rise to a non-zero horizon's angular velocity parallel to the angular momentum of the Kerr object.
Fault-tolerant control for a class of non-linear systems with dead-zone
NASA Astrophysics Data System (ADS)
Chen, Mou; Jiang, Bin; Guo, William W.
2016-05-01
In this paper, a fault-tolerant control scheme is proposed for a class of single-input and single-output non-linear systems with the unknown time-varying system fault and the dead-zone. The non-linear state observer is designed for the non-linear system using differential mean value theorem, and the non-linear fault estimator that estimates the unknown time-varying system fault is developed. On the basis of the designed fault estimator, the observer-based fault-tolerant tracking control is then developed using the backstepping technique for non-linear systems with the dead-zone. The stability of the whole closed-loop system is rigorously proved via Lyapunov analysis and the satisfactory tracking control performance is guaranteed in the presence of the unknown time-varying system fault and the dead-zone. Numerical simulation results are presented to illustrate the effectiveness of the proposed backstepping fault-tolerant control scheme for non-linear systems.
Trumpet slices in Kerr spacetimes.
Dennison, Kenneth A; Baumgarte, Thomas W; Montero, Pedro J
2014-12-31
We introduce a new time-independent family of analytical coordinate systems for the Kerr spacetime representing rotating black holes. We also propose a (2+1)+1 formalism for the characterization of trumpet geometries. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes, even for charged black holes in the presence of a cosmological constant. We present results for metric functions in this slicing and analyze the geometry of the rotating trumpet surface.
Structural Dynamic Analyses And Test Predictions For Spacecraft Structures With Non-Linearities
NASA Astrophysics Data System (ADS)
Vergniaud, Jean-Baptiste; Soula, Laurent; Newerla, Alfred
2012-07-01
The overall objective of the mechanical development and verification process is to ensure that the spacecraft structure is able to sustain the mechanical environments encountered during launch. In general the spacecraft structures are a-priori assumed to behave linear, i.e. the responses to a static load or dynamic excitation, respectively, will increase or decrease proportionally to the amplitude of the load or excitation induced. However, past experiences have shown that various non-linearities might exist in spacecraft structures and the consequences of their dynamic effects can significantly affect the development and verification process. Current processes are mainly adapted to linear spacecraft structure behaviour. No clear rules exist for dealing with major structure non-linearities. They are handled outside the process by individual analysis and margin policy, and analyses after tests to justify the CLA coverage. Non-linearities can primarily affect the current spacecraft development and verification process on two aspects. Prediction of flights loads by launcher/satellite coupled loads analyses (CLA): only linear satellite models are delivered for performing CLA and no well-established rules exist how to properly linearize a model when non- linearities are present. The potential impact of the linearization on the results of the CLA has not yet been properly analyzed. There are thus difficulties to assess that CLA results will cover actual flight levels. Management of satellite verification tests: the CLA results generated with a linear satellite FEM are assumed flight representative. If the internal non- linearities are present in the tested satellite then there might be difficulties to determine which input level must be passed to cover satellite internal loads. The non-linear behaviour can also disturb the shaker control, putting the satellite at risk by potentially imposing too high levels. This paper presents the results of a test campaign performed in
Advances in quantitative Kerr microscopy
NASA Astrophysics Data System (ADS)
Soldatov, I. V.; Schäfer, R.
2017-01-01
An advanced wide-field Kerr microscopy approach to the vector imaging of magnetic domains is demonstrated. Utilizing the light from eight monochrome light emitting diodes, guided to the microscope by glass fibers, and being properly switched in synchronization with the camera exposure, domain images with orthogonal in-plane sensitivity are obtained simultaneously at real time. After calibrating the Kerr contrast under the same orthogonal sensitivity conditions, the magnetization vector field of complete magnetization cycles along the hysteresis loop can be calculated and plotted as a coded color or vector image. In the pulsed mode also parasitic, magnetic field-dependent Faraday rotations in the microscope optics are eliminated, thus increasing the accuracy of the measured magnetization angles to better than 5∘. The method is applied to the investigation of the magnetization process in a patterned Permalloy film element. Furthermore it is shown that the effective magnetic anisotropy axes in a GaMnAs semiconducting film can be quantitatively measured by vectorial analysis of the domain structure.
2007-10-01
Design and initial in-water testing of advanced non- linear control algorithms onto an Unmanned Underwater Vehicle (UUV) Vladimir Djapic Unmanned...attitude or translating in a direction different from that of the surface. Non- linear controller that compensates for non-linear forces (such as drag...loop” non- linear controller (outputs the appropriate thrust values) is the same for all mission scenarios while an appropriate ”outer-loop” non
Characterization and correction of non-linearity effect on oxygen spectra of TANSO-FTS onboard GOSAT
NASA Astrophysics Data System (ADS)
Suto, H.; Frankenberg, C.; Crisp, D.; kuze, A.
2011-12-01
The Thermal and Near Infrared Sensor for carbon Observations Fourier Transform Spectrometer (TANSO-FTS) onboard the Greenhouse gases Observing SATellite (GOSAT) collects high spectral resolution spectra of reflected sunlight in the molecular oxygen (O2) A-band near 760 nm, the carbon dioxide (CO2) bands near 1600 and 2060 nm, and the methane (CH4) band near 1660 nm. The O2 measurements are used to estimate the surface pressure and the dry air column, which are used to define the column-averaged CO2 and CH4 dry air mole fractions, XCO2 and XCH4. O2 measurements are ideal for this application because the O2 dry air mole fraction is almost constant and well known. However, systematic errors in the O2 measurements can introduce biases in the XCO2 and XCH4 retrievals from TANSO-FTS. For example, 1% overestimate of the O2 column retrievals introduced a 10 hPa high bias in surface pressure and a 4 hPa low bias in XCO2 in early retrievals. This near-global bias has been traced to uncertainties in the O2 A-band absorption cross sections. Other spatially-varying O2 errors have been traced to uncertainties in the calibration of the TANSO-FTS A-band channel. For example, non-linearity in the A-band channel response introduces errors in the depths of both O2 lines and solar Fraunhofer lines. There are three possible sources of non-linearity: detector, analogue circuit (amplifier and electric filters), and analogue to digital converter (ADC). Observations acquired with the flight instrument and laboratory experiments with TANSO-FTS engineering model (EM) is being used to discriminate and correct these errors. The EM tests have largely vindicated the silicon photo-diode detector, but show that the non-linearity of the analogue circuit and ADC is almost identical to that seen in data acquired by the on-orbit flight model. We have developed and applied a correction to the measured interferograms from the flight instrument and confirmed it validity by showing that the Fraunhofer
Development of experimental verification techniques for non-linear deformation and fracture.
Moody, Neville Reid; Bahr, David F.
2003-12-01
This project covers three distinct features of thin film fracture and deformation in which the current experimental technique of nanoindentation demonstrates limitations. The first feature is film fracture, which can be generated either by nanoindentation or bulge testing thin films. Examples of both tests will be shown, in particular oxide films on metallic or semiconductor substrates. Nanoindentations were made into oxide films on aluminum and titanium substrates for two cases; one where the metal was a bulk (effectively single crystal) material and the other where the metal was a 1 pm thick film grown on a silica or silicon substrate. In both cases indentation was used to produce discontinuous loading curves, which indicate film fracture after plastic deformation of the metal. The oxides on bulk metals fractures occurred at reproducible loads, and the tensile stress in the films at fracture were approximately 10 and 15 GPa for the aluminum and titanium oxides respectively. Similarly, bulge tests of piezoelectric oxide films have been carried out and demonstrate film fracture at stresses of only 100's of MPa, suggesting the importance of defects and film thickness in evaluating film strength. The second feature of concern is film adhesion. Several qualitative and quantitative tests exist today that measure the adhesion properties of thin films. A relatively new technique that uses stressed overlayers to measure adhesion has been proposed and extensively studied. Delamination of thin films manifests itself in the form of either telephone cord or straight buckles. The buckles are used to calculate the interfacial fracture toughness of the film-substrate system. Nanoindentation can be utilized if more energy is needed to initiate buckling of the film system. Finally, deformation in metallic systems can lead to non-linear deformation due to 'bursts' of dislocation activity during nanoindentation. An experimental study to examine the structure of dislocations around
NASA Astrophysics Data System (ADS)
Vismara, S. O.; Ricci, S.; Bellini, M.; Trittoni, L.
2016-06-01
The objective of the present paper is to describe a procedure to identify and model the non-linear behaviour of structural elements. The procedure herein applied can be divided into two main steps: the system identification and the finite element model updating. The application of the restoring force surface method as a strategy to characterize and identify localized non-linearities has been investigated. This method, which works in the time domain, has been chosen because it has `built-in' characterization capabilities, it allows a direct non-parametric identification of non-linear single-degree-of-freedom systems and it can easily deal with sine-sweep excitations. Two different application examples are reported. At first, a numerical test case has been carried out to investigate the modelling techniques in the case of non-linear behaviour based on the presence of a free-play in the model. The second example concerns the flap of the Intermediate eXperimental Vehicle that successfully completed its 100-min mission on 11 February 2015. The flap was developed under the responsibility of Thales Alenia Space Italia, the prime contractor, which provided the experimental data needed to accomplish the investigation. The procedure here presented has been applied to the results of modal testing performed on the article. Once the non-linear parameters were identified, they were used to update the finite element model in order to prove its capability of predicting the flap behaviour for different load levels.
The effect of non-linear human visual system components on linear model observers
NASA Astrophysics Data System (ADS)
Zhang, Yani; Pham, Binh T.; Eckstein, Miguel P.
2004-05-01
Linear model observers have been used successfully to predict human performance in clinically relevant visual tasks for a variety of backgrounds. On the other hand, there has been another family of models used to predict human visual detection of signals superimposed on one of two identical backgrounds (masks). These masking models usually include a number of non-linear components in the channels that reflect properties of the firing of cells in the primary visual cortex (V1). The relationship between these two traditions of models has not been extensively investigated in the context of detection in noise. In this paper, we evaluated the effect of including some of these non-linear components into a linear channelized Hotelling observer (CHO), and the associated practical implications for medical image quality evaluation. In particular, we evaluate whether the rank order evaluation of two compression algorithms (JPEG vs. JPEG 2000) is changed by inclusion of the non-linear components. The results show: a) First that the simpler linear CHO model observer outperforms CHO model with the nonlinear components investigated. b) The rank order of model observer performance for the compression algorithms did not vary when the non-linear components were included. For the present task, the results suggest that the addition of the physiologically based channel non-linearities to a channelized Hotelling might add complexity to the model observers without great impact on medical image quality evaluation.
Coherence properties of Kerr frequency combs.
Erkintalo, Miro; Coen, Stéphane
2014-01-15
We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over sequences of output fields separated by a fixed number of resonator roundtrips allows the coherence of Kerr combs to be quantified in terms of the complex degree of first-order coherence. We identify different regimes of comb coherence, linked to the solutions of the LLE. Our approach provides a practical and unambiguous way of assessing the stability of Kerr combs that is directly connected to an accessible experimental quantity.
On incremental non-linearity in granular media: phenomenological and multi-scale views
NASA Astrophysics Data System (ADS)
Darve, Félix; Nicot, François
2005-12-01
On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto-viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro-mechanical models based on multi-scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro-mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non-linear character of their behaviour. It is shown that both phenomenological and micro-mechanical models exhibit an incremental non-linearity. In addition, the multi-scale approach reveals that the macroscopic incremental non-linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright
Real-Time Monitoring of Non-linear Suicidal Dynamics: Methodology and a Demonstrative Case Report
Fartacek, Clemens; Schiepek, Günter; Kunrath, Sabine; Fartacek, Reinhold; Plöderl, Martin
2016-01-01
In recent years, a number of different authors have stressed the usefulness of non-linear dynamic systems approach in suicide research and suicide prevention. This approach applies specific methods of time series analysis and, consequently, it requires a continuous and fine-meshed assessment of the processes under consideration. The technical means for this kind of process assessment and process analysis are now available. This paper outlines how suicidal dynamics can be monitored in high-risk patients by an Internet-based application for continuous self-assessment with integrated tools of non-linear time series analysis: the Synergetic Navigation System. This procedure is illustrated by data from a patient who attempted suicide at the end of a 90-day monitoring period. Additionally, future research topics and clinical applications of a non-linear dynamic systems approach in suicidology are discussed. PMID:26913016
A Signal Transmission Technique for Stability Analysis of Multivariable Non-Linear Control Systems
NASA Technical Reports Server (NTRS)
Jackson, Mark; Zimpfer, Doug; Adams, Neil; Lindsey, K. L. (Technical Monitor)
2000-01-01
Among the difficulties associated with multivariable, non-linear control systems is the problem of assessing closed-loop stability. Of particular interest is the class of non-linear systems controlled with on/off actuators, such as spacecraft thrusters or electrical relays. With such systems, standard describing function techniques are typically too conservative, and time-domain simulation analysis is prohibitively extensive, This paper presents an open-loop analysis technique for this class of non-linear systems. The technique is centered around an innovative use of multivariable signal transmission theory to quantify the plant response to worst case control commands. The technique has been applied to assess stability of thruster controlled flexible space structures. Examples are provided for Space Shuttle attitude control with attached flexible payloads.
Non-linear effects of soda taxes on consumption and weight outcomes.
Fletcher, Jason M; Frisvold, David E; Tefft, Nathan
2015-05-01
The potential health impacts of imposing large taxes on soda to improve population health have been of interest for over a decade. As estimates of the effects of existing soda taxes with low rates suggest little health improvements, recent proposals suggest that large taxes may be effective in reducing weight because of non-linear consumption responses or threshold effects. This paper tests this hypothesis in two ways. First, we estimate non-linear effects of taxes using the range of current rates. Second, we leverage the sudden, relatively large soda tax increase in two states during the early 1990s combined with new synthetic control methods useful for comparative case studies. Our findings suggest virtually no evidence of non-linear or threshold effects.
Russell, Steven J.; Carlsten, Bruce E.
2012-06-26
We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.
Non-Linear Dynamics Tools for the Motion Analysis and Condition Monitoring of Robot Joints
NASA Astrophysics Data System (ADS)
Trendafilova, I.; van Brussel, H.
2001-11-01
Time series from non-damaged and three types of damaged robot joints are considered and analysed from the viewpoint of non-linear dynamics. The embedding spaces for the four types of signals are recovered. The application of surrogate data tests is used to prove the presence of non-linearities in the joints. The results suggest a rise in unstable behaviour due to the introduction of backlash in robot joints. The chaotic behaviour gets stronger with the increase of the backlash extent. This is confirmed by the increase of the embedding dimension as well as by the increase of the Lyapunov exponents and the correlation dimension with the backlash increase. A straightforward method for condition monitoring using non-linear dynamics characteristics, based on a classification procedure, is suggested.
Characterization of non-linear Potassium crystals in the Terahertz frequency domain
NASA Astrophysics Data System (ADS)
Mounaix, P.; Sarger, L.; Caumes, J. P.; Freysz, E.
2004-12-01
Systematic measurements of the dielectric properties of KDP, KNbO3, KTP and KTA non-linear crystals in the Terahertz (THz) spectral range are presented. The index of refraction and the absorption coefficients are measured between 0.1 and 1.5 THz for different crystallographic orientations. The data are deduced from an experimental set-up based on standard Terahertz time domain spectroscopy system at room temperature. These data, key parameters for the optimization of non-linear THz generation by optical rectification as well as electro-optic detection, are analysed in term of non-linear capabilities. We finally review different methods making possible to generate THz wave in these crystals and compare their characteristics.
The non-linear power spectrum of the Lyman alpha forest
Arinyo-i-Prats, Andreu; Miralda-Escudé, Jordi; Viel, Matteo; Cen, Renyue E-mail: miralda@icc.ub.edu E-mail: cen@astro.princeton.edu
2015-12-01
The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate the comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula.
Analysis of linear and non-linear genotype × environment interaction.
Yang, Rong-Cai
2014-01-01
The usual analysis of genotype × environment interaction (G × E) is based on the linear regression of genotypic performance on environmental changes (e.g., classic stability analysis). This linear model may often lead to lumping together of the non-linear responses to the whole range of environmental changes from suboptimal and super optimal conditions, thereby lowering the power of detecting G × E variation. On the other hand, the G × E is present when the magnitude of the genetic effect differs across the range of environmental conditions regardless of whether the response to environmental changes is linear or non-linear. The objectives of this study are: (i) explore the use of four commonly used non-linear functions (logistic, parabola, normal and Cauchy functions) for modeling non-linear genotypic responses to environmental changes and (ii) to investigate the difference in the magnitude of estimated genetic effects under different environmental conditions. The use of non-linear functions was illustrated through the analysis of one data set taken from barley cultivar trials in Alberta, Canada (Data A) and the examination of change in effect sizes is through the analysis another data set taken from the North America Barley Genome Mapping Project (Data B). The analysis of Data A showed that the Cauchy function captured an average of >40% of total G × E variation whereas the logistic function captured less G × E variation than the linear function. The analysis of Data B showed that genotypic responses were largely linear and that strong QTL × environment interaction existed as the positions, sizes and directions of QTL detected differed in poor vs. good environments. We conclude that (i) the non-linear functions should be considered when analyzing multi-environmental trials with a wide range of environmental variation and (ii) QTL × environment interaction can arise from the difference in effect sizes across environments.
Analysis of linear and non-linear genotype × environment interaction
Yang, Rong-Cai
2014-01-01
The usual analysis of genotype × environment interaction (G × E) is based on the linear regression of genotypic performance on environmental changes (e.g., classic stability analysis). This linear model may often lead to lumping together of the non-linear responses to the whole range of environmental changes from suboptimal and super optimal conditions, thereby lowering the power of detecting G × E variation. On the other hand, the G × E is present when the magnitude of the genetic effect differs across the range of environmental conditions regardless of whether the response to environmental changes is linear or non-linear. The objectives of this study are: (i) explore the use of four commonly used non-linear functions (logistic, parabola, normal and Cauchy functions) for modeling non-linear genotypic responses to environmental changes and (ii) to investigate the difference in the magnitude of estimated genetic effects under different environmental conditions. The use of non-linear functions was illustrated through the analysis of one data set taken from barley cultivar trials in Alberta, Canada (Data A) and the examination of change in effect sizes is through the analysis another data set taken from the North America Barley Genome Mapping Project (Data B). The analysis of Data A showed that the Cauchy function captured an average of >40% of total G × E variation whereas the logistic function captured less G × E variation than the linear function. The analysis of Data B showed that genotypic responses were largely linear and that strong QTL × environment interaction existed as the positions, sizes and directions of QTL detected differed in poor vs. good environments. We conclude that (i) the non-linear functions should be considered when analyzing multi-environmental trials with a wide range of environmental variation and (ii) QTL × environment interaction can arise from the difference in effect sizes across environments. PMID:25101112
Non-linear dynamics of a geared rotor-bearing system with multiple clearances
NASA Astrophysics Data System (ADS)
Kahraman, A.; Singh, R.
1991-02-01
Non-linear frequency response characteristics of a geared rotor-bearing system are examined in this paper. A three-degree-of-freedom dynamic model is developed which includes non-linearities associated with radial clearances in the radial rolling element bearings and backlash between a spur gear pair; linear time-invariant gear meshing stiffness is assumed. The corresponding linear system problem is also solved, and predicted natural frequencies and modes match with finite element method results. The bearing non-linear stiffness function is approximated for the sake of convenience by a simple model which is identical to that used for the gear mesh. This approximate bearing model has been verified by comparing steady state frequency spectra. Applicability of both analytical and numerical solution techniques to the multi-degree-of-freedom non-linear problem is investigated. Satisfactory agreement has been found between our theory and available experimental data. Several key issues such as non-linear modal interactions and differences between internal static transmission error excitation and external torque excitation are discussed. Additionally, parametric studies are performed to understand the effect of system parameters such as bearing stiffness to gear mesh stiffness ratio, alternating to mean force ratio and radial bearing preload to mean force ratio on the non-linear dynamic behavior. A criterion used to classify the steady state solutions is presented, and the conditions for chaotic, quasi-periodic and subharmonic steady state solutions are determined. Two typical routes to chaos observed in this geared system are also identified.
The non-linear power spectrum of the Lyman alpha forest
NASA Astrophysics Data System (ADS)
Arinyo-i-Prats, Andreu; Miralda-Escudé, Jordi; Viel, Matteo; Cen, Renyue
2015-12-01
The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z~ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate the comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula.
Non-linear spectroscopic processes in water and their significance in the atmosphere
NASA Astrophysics Data System (ADS)
Goss, Lisa Mae
1998-12-01
This thesis examines the interaction of water and light in the atmosphere. The two non-linear spectroscopic processes studied are the vibrational spectroscopy of water clusters, where one photon is absorbed by a cluster of water molecules, and the sequential two photon dissociation of water, where one molecular of water absorbs two different photons. To evaluate the contribution of water clusters to absorption of solar and terrestrial radiation, the abundance and adsorption cross sections of the clusters are needed. The equilibrium constants for the formation of water clusters, which allow calculation of the abundances, were calculated using inputs from ab initio calculations in the literature. Calculations for the dimer and trimer with different inputs which include the anharmonicity of the vibrations show some agreement. Experiments in supersonic expansions probed wavelength regions where the vibrational spectroscopy of water clusters had not previously been studied. This led to the observation of two new features, the bending vibration and an unresolved group of intermolecular vibrations. Experimental information, together with literature results, was used to provide the cross sections needed for radiative transfer modeling of these clusters. The model results show that the effect of absorption due to water clusters is small due to the overlap of spectroscopic features with other absorbers and the small abundances. The sequential two photon process was examined to determine whether it provides a pathway for substantial OH formation driven by light of wavelengths longer than 310 nm. This process involved a near-UV transition from the ground electronic, ground vibrational state to a highly vibrationally excited state in the ground electronic state. Most of these vibrationally excited molecules are collisionally quenched back to the ground vibrational state. A few may absorb a second photon to reach the first excited electronic state. This state is repulsive and
Non-linear performance of a three-bearing rotor incorporating a squeeze-film damper
NASA Technical Reports Server (NTRS)
Holmes, R.; Dede, M.
1987-01-01
This paper is concerned with the non-linear vibration performance of a rigid rotor supported on three bearings, one being surrounded by a squeeze-film damper. This damper relies on the pressure built up in the squeeze film to help counter-act external forces arising from unbalance and other effects. As a result a vibration orbit of a certain magnetude results. Such vibration orbits illustrate features found in other non-linear systems, in particular sub-harmonic resonances and jump phenomena. Comparisons between theoretical prediction and experimental observations of these phenomena are made.
[Non-linear rectification of sensor based on immune genetic algorithm].
Lu, Lirong; Zhou, Jinyang; Niu, Xiaodong
2014-08-01
A non-linear rectification based on immune genetic algorithm (IGA) is proposed in this paper, for the shortcoming of the non-linearity rectification. This algorithm introducing the biologic immune mechanism into the genetic algorithm can restrain the disadvantages that the poor precision, slow convergence speed and early maturity of the genetic algorithm. Computer simulations indicated that the algorithm not only keeps population diversity, but also increases the convergent speed, precision and the stability greatly. The results have shown the correctness and effectiveness of the method.
Free Convective Nonaligned Non-Newtonian Flow with Non-linear Thermal Radiation
NASA Astrophysics Data System (ADS)
Rana, S.; Mehmood, R.; Narayana, PV S.; Akbar, N. S.
2016-12-01
The present study explores the free convective oblique Casson fluid over a stretching surface with non-linear thermal radiation effects. The governing physical problem is modelled and transformed into a set of coupled non-linear ordinary differential equations by suitable similarity transformation, which are solved numerically with the help of shooting method keeping the convergence control of 10-5 in computations. Influence of pertinent physical parameters on normal, tangential velocity profiles and temperature are expressed through graphs. Physical quantities of interest such as skin friction coefficients and local heat flux are investigated numerically.
Optimal design of linear and non-linear dynamic vibration absorbers
NASA Astrophysics Data System (ADS)
Jordanov, I. N.; Cheshankov, B. I.
1988-05-01
An efficient numerical method is applied to obtain optimal parameters for both linear and non-linear damped dynamic vibration absorbers. The minimization of the vibration response has been carried out for damped as well as undamped force excited primary systems with linear and non-linear spring characteristics. Comparison is made with the optimum absorber parameters that are determined by using Den Hartog's classical results in the linear case. Six optimization criteria by which the response is minimized over narrow and broad frequency bands are examined. Pareto optimal solutions of the multi-objective decision making problem are obtained.
NASA Astrophysics Data System (ADS)
Zausner, Tobi
Chaos theory may provide models for creativity and for the personality of the artist. A collection of speculative hypotheses examines the connection between art and such fundamentals of non-linear dynamics as iteration, dissipative processes, open systems, entropy, sensitivity to stimuli, autocatalysis, subsystems, bifurcations, randomness, unpredictability, irreversibility, increasing levels of organization, far-from-equilibrium conditions, strange attractors, period doubling, intermittency and self-similar fractal organization. Non-linear dynamics may also explain why certain individuals suffer mental disorders while others remain intact during a lifetime of sustained creative output.
Solution algorithms for non-linear singularly perturbed optimal control problems
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1983-01-01
The applicability and usefulness of several classical and other methods for solving the two-point boundary-value problem which arises in non-linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non-linear problem are obtained by each method and compared.
Airframe structural damage detection: a non-linear structural surface intensity based technique.
Semperlotti, Fabio; Conlon, Stephen C; Barnard, Andrew R
2011-04-01
The non-linear structural surface intensity (NSSI) based damage detection technique is extended to airframe applications. The selected test structure is an upper cabin airframe section from a UH-60 Blackhawk helicopter (Sikorsky Aircraft, Stratford, CT). Structural damage is simulated through an impact resonator device, designed to simulate the induced vibration effects typical of non-linear behaving damage. An experimental study is conducted to prove the applicability of NSSI on complex mechanical systems as well as to evaluate the minimum sensor and actuator requirements. The NSSI technique is shown to have high damage detection sensitivity, covering an extended substructure with a single sensing location.
Non-perturbative aspects of particle acceleration in non-linear electrodynamics
Burton, David A.; Flood, Stephen P.; Wen, Haibao
2015-04-15
We undertake an investigation of particle acceleration in the context of non-linear electrodynamics. We deduce the maximum energy that an electron can gain in a non-linear density wave in a magnetised plasma, and we show that an electron can “surf” a sufficiently intense Born-Infeld electromagnetic plane wave and be strongly accelerated by the wave. The first result is valid for a large class of physically reasonable modifications of the linear Maxwell equations, whilst the second result exploits the special mathematical structure of Born-Infeld theory.
Influence of shear in the non-linear analysis of RC members
Diotallevi, Pier Paolo; Landi, Luca; Cardinetti, Filippo
2008-07-08
The purpose of this study is to develop an analytical model characterized by a beam-column finite element which is able to reproduce the non-linear flexural-shear behavior of RC structures. The paper shows a brief description of the finite element formulation, the theory used for modeling the constitutive relationship and the scheme of the algorithm, transformed in a computer program, which was developed for implementing the theoretical model. Finally it illustrates a comparison with available experimental results for the calibration and validation of the model and a study on the influence of the non-linear shear response.
On the non-linear attachment characteristics of blood to bacterial cellulose/kaolin biomaterials.
Véliz, Diosángeles Soto; Alam, Catharina; Toivola, Diana M; Toivakka, Martti; Alam, Parvez
2014-04-01
In this communication, we report a non-linear variation in the strength of blood attachment to bacterial cellulose/kaolin biomaterials as the fractions of bacterial cellulose to kaolin are increased. The changes observed for attachment strength are elucidated following both experimental and numerical investigations on both the biomaterial and the blood-biomaterial interface. Our research reveals that the non-linear strength of attachment of blood is related to topographical characteristics on the surface of the biomaterial, the maleability of the biomaterial and the intermolecular strength of attraction between clotted blood proteins (fibrinogen) with the cellulose/kaolin components of the biomaterial.
Guillermin, Régine; Lasaygues, Philippe; Rabau, Guy; Lefebvre, Jean-Pierre
2013-08-01
This study deals with the reconstruction, from ultrasonic measured data, of the sound speed profile of a penetrable two-dimensional target of arbitrary cross-section embedded in an infinite medium. Green's theorem is used to obtain a domain integral representation of the acoustical scattered field, and a discrete formulation of the inverse problem is obtained using a moment method. An iterative non-linear algorithm minimizing the discrepancy between the measured and computed scattered fields is used to reconstruct the sound speed profile in the region of interest. The minimization process is performed using a conjugated-gradient method. An experimental study with significant acoustical impedance contrast targets immersed in water was performed. Images of the sound speed profile obtained by inversion of experimental data are presented.
Superradiant instability of the Kerr brane
NASA Astrophysics Data System (ADS)
Ishibashi, Akihiro; Pani, Paolo; Gualtieri, Leonardo; Cardoso, Vitor
2015-09-01
We consider linear gravitational perturbations of the Kerr brane, an exact solution of vacuum Einstein's equations in dimensions higher than four and a low-energy solution of string theory. Decomposing the perturbations in tensor harmonics of the trans-verse Ricci-flat space, we show that tensor- and vector-type metric perturbations of the Kerr brane satisfy respectively a massive Klein-Gordon equation and a Proca equation on the four-dimensional Kerr space, where the mass term is proportional to the eigenvalue of the harmonics. Massive bosonic fields trigger a well-known superradiant instability on a Kerr black hole. We thus establish that Kerr branes in dimensions D ≥ 6 are gravi-tationally unstable due to superradiance. These solutions are also unstable against the Gregory-Laflamme instability and we discuss the conditions for either instability to occur and their rather different nature. When the transverse dimensions are compactified and much smaller than the Kerr horizon, only the superradiant instability is present, with a time scale much longer than the dynamical time scale. Our formalism can be also used to discuss other types of higher-dimensional black objects, taking advantage of recent progress in studying linear perturbations of four-dimensional black holes.
Introduction to the Treatment of Non-Linear Effects Using a Gravitational Pendulum
ERIC Educational Resources Information Center
Weltner, Klaus; Esperidiao, Antonio Sergio C.; Miranda, Paulo
2004-01-01
We show that the treatment of pendulum movement, other than the linear approximation,may be an instructive experimentally based introduction to the physics of non-linear effects. Firstly the natural frequency of a gravitational pendulum is measured as function of its amplitude. Secondly forced oscillations of a gravitational pendulum are…
Non-Gaussian inference from non-linear and non-Poisson biased distributed data
NASA Astrophysics Data System (ADS)
Ata, Metin; Kitaura, Francisco-Shu; Müller, Volker
2014-05-01
We study the statistical inference of the cosmological dark matter density field from non-Gaussian, non-linear and non-Poisson biased distributed tracers. We have implemented a Bayesian posterior sampling computer-code solving this problem and tested it with mock data based on N-body simulations.
Phase Structure of the Non-Linear σ-MODEL with Oscillator Representation Method
NASA Astrophysics Data System (ADS)
Mishchenko, Yuriy; Ji, Chueng-R.
2004-03-01
Non-Linear σ-model plays an important role in many areas of theoretical physics. Been initially uintended as a simple model for chiral symmetry breaking, this model exhibits such nontrivial effects as spontaneous symmetry breaking, asymptotic freedom and sometimes is considered as an effective field theory for QCD. Besides, non-linear σ-model can be related to the strong-coupling limit of O(N) ϕ4-theory, continuous limit of N-dim. system of quantum spins, fermion gas and many others and takes important place in undertanding of how symmetries are realized in quantum field theories. Because of this variety of connections, theoretical study of the critical properties of σ-model is interesting and important. Oscillator representation method is a theoretical tool for studying the phase structure of simple QFT models. It is formulated in the framework of the canonical quantization and is based on the view of the unitary non-equivalent representations as possible phases of a QFT model. Successfull application of the ORM to ϕ4 and ϕ6 theories in 1+1 and 2+1 dimensions motivates its study in more complicated models such as non-linear σ-model. In our talk we introduce ORM, establish its connections with variational approach in QFT. We then present results of ORM in non-linear σ-model and try to interprete them from the variational point of view. Finally, we point out possible directions for further research in this area.
Non-Linear EMG Parameters for Differential and Early Diagnostics of Parkinson's Disease.
Meigal, Alexander Y; Rissanen, Saara M; Tarvainen, Mika P; Airaksinen, Olavi; Kankaanpää, Markku; Karjalainen, Pasi A
2013-01-01
The pre-clinical diagnostics is essential for management of Parkinson's disease (PD). Although PD has been studied intensively in the last decades, the pre-clinical indicators of that motor disorder have yet to be established. Several approaches were proposed but the definitive method is still lacking. Here we report on the non-linear characteristics of surface electromyogram (sEMG) and tremor acceleration as a possible diagnostic tool, and, in prospective, as a predictor for PD. Following this approach we calculated such non-linear parameters of sEMG and accelerometer signal as correlation dimension, entropy, and determinism. We found that the non-linear parameters allowed discriminating some 85% of healthy controls from PD patients. Thus, this approach offers considerable potential for developing sEMG-based method for pre-clinical diagnostics of PD. However, non-linear parameters proved to be more reliable for the shaking form of PD, while diagnostics of the rigid form of PD using EMG remains an open question.
The Poincaré-Bendixson Theorem and the non-linear Cauchy-Riemann equations
NASA Astrophysics Data System (ADS)
van den Berg, J. B.; Munaò, S.; Vandervorst, R. C. A. M.
2016-11-01
Fiedler and Mallet-Paret (1989) prove a version of the classical Poincaré-Bendixson Theorem for scalar parabolic equations. We prove that a similar result holds for bounded solutions of the non-linear Cauchy-Riemann equations. The latter is an application of an abstract theorem for flows with a(n) (unbounded) discrete Lyapunov function.
Re-Mediating Classroom Activity with a Non-Linear, Multi-Display Presentation Tool
ERIC Educational Resources Information Center
Bligh, Brett; Coyle, Do
2013-01-01
This paper uses an Activity Theory framework to evaluate the use of a novel, multi-screen, non-linear presentation tool. The Thunder tool allows presenters to manipulate and annotate multiple digital slides and to concurrently display a selection of juxtaposed resources across a wall-sized projection area. Conventional, single screen presentation…
Gravitational-wave tail effects to quartic non-linear order
NASA Astrophysics Data System (ADS)
Marchand, Tanguy; Blanchet, Luc; Faye, Guillaume
2016-12-01
Gravitational-wave tails are due to the backscattering of linear waves onto the space-time curvature generated by the total mass of the matter source. The dominant tails correspond to quadratic non-linear interactions and arise at the one-and-a-half post-Newtonian (1.5 PN) order in the gravitational waveform. The ‘tails-of-tails’, which are cubic non-linear effects appearing at the 3 PN order in the waveform, are also known. We derive here higher non-linear tail effects, namely those associated with quartic non-linear interactions or ‘tails-of-tails-of-tails’, which are shown to arise at the 4.5 PN order. As an application, we obtain at that order the complete coefficient in the total gravitational-wave energy flux of compact binary systems moving on circular orbits. Our result perfectly agrees with black-hole perturbation calculations in the limit of extreme mass ratio of the two compact objects.
Non-linear controls influence functions in an aircraft dynamics simulator
NASA Astrophysics Data System (ADS)
Guerreiro, Nelson M.; Hubbard, James E., Jr.; Motter, Mark A.
2006-03-01
In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft's control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland's continuing study of active wing load control.
Non-Linear Stability of an Electrified Plane Interface in Porous Media
NASA Astrophysics Data System (ADS)
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Towards a non-linear theory for induced seismicity in shales
NASA Astrophysics Data System (ADS)
Salusti, Ettore; Droghei, Riccardo
2014-05-01
We here analyze the pore transmission of fluid pressure pand solute density ρ in porous rocks, within the framework of the Biot theory of poroelasticity extended to include physico-chemical interactions. In more details we here analyze the effect of a strong external stress on the non-linear evolution of p and ρ in a porous rock. We here focus on the consequent deformation of the rock pores, relative to a non-linear Hooke equation among strain, linear/quadratic pressure and osmosis in 1-D. We in particular analyze cases with a large pressure, but minor than the 'rupture point'. All this gives relations similar to those discussed by Shapiro et al. (2013), which assume a pressure dependent permeability. Thus we analyze the external stress necessary to originate quick non-linear transients of combined fluid pressure and solute density in a porous matrix, which perturb in a mild (i.e. a linear diffusive phenomenon) or a more dramatic non-linear way (Burgers solitons) the rock structure. All this gives a novel, more realistic insight about the rock evolution, fracturing and micro-earthquakes under a large external stress.
The Non-Linear Nature of Information and its Implications for Advanced Technology Forces
1998-05-18
anticipated tremendous benefits from the growth of information based technology. It is now axiomatic that the ability to achieve information dominance against...the commercial world are mix. To achieve the information dominance anticipated through advances in technology, military decision makers must understand and accommodate the non-linear nature of the information systems they employ.
Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin E-mail: izumi@phys.ntu.edu.tw
2012-12-01
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.
Comments on "arithmetic coding as a non-linear dynamical system"
NASA Astrophysics Data System (ADS)
Pande, Amit; Zambreno, Joseph; Mohapatra, Prasant
2012-12-01
Nagaraj et al. [1,2] present a skewed-non-linear generalized Luroth Series (s-nGLS) framework. S-nGLS uses non-linear maps for GLS to introduce a security parameter a which is used to build a keyspace for image or data encryption. The map introduces non-linearity to the system to add an "encryption key parameter". The skew is added to achieve optimal compression efficiency. s-nGLS used as such for joint encryption and compression is a weak candidate, as explained in this communication. First, we show how the framework is vulnerable to known plaintext based attacks and that a key of size 256 bits can be broken within 1000 trials. Next, we demonstrate that the proposed non-linearity exponentially increases the hardware complexity of design. We also discover that s-nGlS cannot be implemented as such for large bitstreams. Finally, we demonstrate how correlation of key parameter with compression performance leads to further key vulnerabilities.
NASA Astrophysics Data System (ADS)
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
1999-08-01
The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence.
Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer
NASA Technical Reports Server (NTRS)
Pai, P. F.; Lee, S.-Y.
2003-01-01
This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \\ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.
A Quantitative and Combinatorial Approach to Non-Linear Meanings of Multiplication
ERIC Educational Resources Information Center
Tillema, Erik; Gatza, Andrew
2016-01-01
We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative…
An Assessment of Linear Versus Non-linear Multigrid Methods for Unstructured Mesh Solvers
2001-05-01
problems is investigated. The first case consists of a transient radiation-diffusion problem for which an exact linearization is available, while the...to the Jacobian of a second-order accurate discretization. When an exact linearization is employed, the linear and non-linear multigrid methods
CONSEQUENCES OF NON-LINEAR DENSITY EFFECTS ON BUOYANCY AND PLUME BEHAVIOR
Aquatic plumes, as turbulent streams, grow by entraining ambient water. Buoyant plumes rise and dense ones sink, but, non-linear kinetic effects can reverse the buoyant force in mid-phenomenon. The class of nascent-density plumes begin as buoyant, upwardly accelerating plumes tha...
Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system
NASA Astrophysics Data System (ADS)
Kahraman, A.; Singh, R.
1991-04-01
Frequency response characteristics of a non-linear geared rotor-bearing system with time-varying mesh stiffness k h( overlinet) are examined in this paper. First, the single-degree-of-freedom spur gear pair model with backlash is extended to include sinusoidal or periodic mesh stiffness k h( overlinet) . Second, a three-degree-of-freedom model with k h( overlinet) and clearance non-lineariries associated with gear backlash and rolling element bearings, as excited by the static transmission error overlinee( overlinet) under a mean torque load, is developed. The governing equations are solved using digital simulation technique and only the primary resonances are studied. Resonances of the corresponding linear time-varying system associated with parametric and external excitations are identified using the method of multiple scales and digital simulation. Interactions between the mesh stiffness variation and clearance non-linearities have been investigated; a strong interaction between time-varying mesh stiffness k h( overlinet) and gear backlash is found, whereas the coupling between k h( overlinet) and bearing non-linearities is weak. Finally, our time-varying non-linear formulations yield reasonably good predictions when compared with the benchmark experimental results available in the literature.
Fitting and forecasting coupled dark energy in the non-linear regime
Casas, Santiago; Amendola, Luca; Pettorino, Valeria; Vollmer, Adrian; Baldi, Marco E-mail: l.amendola@thphys.uni-heidelberg.de E-mail: v.pettorino@thphys.uni-heidelberg.de
2016-01-01
We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β{sup 2}, with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications.
Testing procedures for non-stationarity and non-linearity in physiological signals.
Popivanov, D; Mineva, A
1999-03-15
Most of the physiological signals (EEG, ECG, blood flow, human gait, etc.) characterize by complex dynamics including both non-stationarities and non-linearities. These time series resemble red noise with long-range correlation and 1/(f beta) power spectrum. A question arises as to how to distinguish the characteristics of the process underlying the signal dynamics from the properties of the observed time series. The classical methods to determine possible non-linear (chaotic) dynamics (e.g. correlation dimension) often fail in such signals because of relatively short data records containing stochastic components and non-stationarities. We report an application of several approaches, aimed at (1) determining of the non-stationarities in the signals and (2) testing whether non-linear dynamics exists. Assessment of the intrinsic correlation properties of the dynamic process and distinguishing the same from external trends was performed using singular spectra and detrended fluctuation analysis. The existence of non-linear dynamics was tested by correlation dimension (modified algorithm of re-embedding) and by correlation integrals of real and surrogate data. The correlation integrals of real signal and surrogate data sets were statistically compared using Kolmogorov-Smirnov (K-S) test. The procedures were tested on EEG and laser-Doppler (LD) blood flow. Our suggestion is that no one approach taken alone is the best for our aims. Instead, a battery of methods should be used.
NASA Astrophysics Data System (ADS)
Bertolesi, Elisa; Milani, Gabriele; Poggi, Carlo
2016-12-01
Two FE modeling techniques are presented and critically discussed for the non-linear analysis of tuff masonry panels reinforced with FRCM and subjected to standard diagonal compression tests. The specimens, tested at the University of Naples (Italy), are unreinforced and FRCM retrofitted walls. The extensive characterization of the constituent materials allowed adopting here very sophisticated numerical modeling techniques. In particular, here the results obtained by means of a micro-modeling strategy and homogenization approach are compared. The first modeling technique is a tridimensional heterogeneous micro-modeling where constituent materials (bricks, joints, reinforcing mortar and reinforcing grid) are modeled separately. The second approach is based on a two-step homogenization procedure, previously developed by the authors, where the elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. The non-linear structural analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM). All the simulations here presented are performed using the commercial software Abaqus. Pros and cons of the two approaches are herein discussed with reference to their reliability in reproducing global force-displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies.
Design curves for non-linear analysis of simply-supported, uniformly-loaded rectangular plates
NASA Technical Reports Server (NTRS)
Moore, D.
1979-01-01
Design curves for the non-linear analysis of simply-supported rectangular plates subjected to uniform normal pressure loads have been developed. These curves yield the center deflection, center stress and corner stress in non-dimensionalized form plotted against a dimensionless parameter describing the load intensity. The results presented are based on extensive non-linear finite element analysis employing the ARGUS structural analysis program. Plates with length to width ratios of 1, 1.5, 2, 3 and 4 are included. The load range considered extends to 1000 times the load at which the behavior of the plate becomes significantly non-linear. Over the load range considered, the analysis shows that the ratio of center deflection to plate thickness for a square plate is less than 16 to 1, whereas linear theory would predict a center deflection 400 times the plate thickness. Likewise, the stress is markedly lower than would be predicted by linear theory. The present results are shown to be in excellent agreement with the classical linear theory up to a central deflection to plate thickness ratio of about one-half. In the non-linear regime the present results for deflection and stress are in very good agreement with the analytical and experimental work of other investigators.
Twofold hidden conformal symmetries of the Kerr-Newman black hole
Chen, C.-M.; Huang, Y.-M.; Sun, J.-R.; Wu, M.-F.; Zou, S.-J.
2010-09-15
In this paper, we suggest that there are two different individual two-dimensional conformal field theories (CFTs) holographically dual to the Kerr-Newman black hole, coming from the corresponding two possible limits - the Kerr/CFT and Reissner-Nordstroem/CFT correspondences, namely, there exist the Kerr-Newman/CFTs dualities. A probe scalar field at low frequencies turns out can exhibit two different two-dimensional conformal symmetries (named by J and Q pictures, respectively) in its equation of motion when the associated parameters are suitably specified. These twofold dualities are supported by the matchings of entropies, absorption cross sections, and real-time correlators computed from both the gravity and the CFT sides. Our results lead to a fascinating 'microscopic hair conjecture' - for each macroscopic hair parameter, in addition to the mass of a black hole in the Einstein-Maxwell theory, there should exist an associated holographic CFT{sub 2} description.
Metal-organic frameworks as competitive materials for non-linear optics.
Mingabudinova, L R; Vinogradov, V V; Milichko, V A; Hey-Hawkins, E; Vinogradov, A V
2016-09-26
The last five years have witnessed a huge breakthrough in the creation and the study of the properties of a new class of compounds - metamaterials. The next stage of this technological revolution will be the development of active, controllable, and non-linear metamaterials, surpassing natural media as platforms for optical data processing and quantum information applications. However, scientists are constantly faced with the need to find new methods that can ensure the formation of quantum and non-linear metamaterials with higher resolution. One such method of producing metamaterials in the future, which will provide scalability and availability, is chemical synthesis. Meanwhile, the chemical synthesis of organized 3D structures with a period of a few nanometers and a size of up to a few millimeters is not an easy task and is yet to be resolved. The most promising avenue seems to be the use of highly porous structures based on metal-organic frameworks that have demonstrated their unique properties in the field of non-linear optics (NLO) over the past three years. Thus, the aim of this review is to examine current progress and the possibilities of using metal-organic frameworks in the field of non-linear optics as chemically obtained metamaterials of the future. The review begins by presenting the theoretical principles of physical phenomena represented by mathematical descriptions for clarity. Major attention is paid to the second harmonic generation (SHG) effect. In this section we compare inorganic single crystals, which are most commonly used to study the effect in question, to organic materials, which also possess the required properties. Based on these data, we present a rationale for the possibility of studying the non-linear optical properties of metal-organic structures as well as describing the use of synthetic approaches and the difficulties associated with them. The second part of the review explicitly acquaints the reader with a new class of materials
Non-linear Elasticity and Monitoring of Stress in the Focus of an Earthquake
NASA Astrophysics Data System (ADS)
Bakulin, V.; Bakulin, A.
2001-05-01
Non-linear elasticity proved to give comprehensive framework for relating seismic velocities in rocks to stress. This powerful theory allows attacking the problem of estimating stress state at the focus of earthquakes. Such idea has been proposed long time ago [Kostrov and Nikitin, 1968] however its implementation requires a-priori knowledge of non-linear rock properties. Three non-linear constants needed to describe variation of any velocity with stress are typically estimated from core measurements [Bakulin et al., 2000]. More reliable estimates can be obtained from multi-mode inversions of borehole acoustic data [Sinha, 1996]. Nevertheless database of non-linear formation constants is still very limited. More measurements are required to estimate non-linear rock properties on larger scale and with independent stress constraints. Such measurements can be done in mines [Bakulin and Bakulin, 1999] or in hydrocarbon reservoirs where time-dependent pressure measurements are available. Without knowledge of non-linear rock properties seismic waves can still bring information about directions of tectonic stresses. In particular, shear wave polarizations can deliver directions of principal stresses in the focus of an earthquake, provided the overburden effects were removed. If rock non-linear properties are independently derived then estimation of stress magnitudes becomes feasible. Such techniques were applied in mining environment [Bakulin and Bakulin, 1999]. They may become routine for monitoring stress state in the focus of earthquakes and therefore can be used for forecasting the seismic activity. Bakulin, A. V., Troyan, V. N., and Bakulin, V. N., 2000, Acoustoelasticity of rocks, St. Petersburg (in Russian). Bakulin, V. and Bakulin, A., 1999, Acoustopolarizational method of measuring stress in rock mass and determination of Murnaghan constants: 69th Annual Internat. Mtg., Soc. Expl. Geophys., 1971-1974. Kostrov, B.V., and Nikitin, L.V., 1968, Influence of initial
Bosgra, Sieto; Vlaming, Maria L H; Vaes, Wouter H J
2016-01-01
Microdosing studies allow clinical investigation of pharmacokinetics earlier in drug development, before all high-dose safety concerns have been sorted out. Furthermore, microdosing allows inclusion of target groups that are inadmissible in high-dose phase I trials. A potential concern when considering a microdosing study is that a particular drug candidate may display non-linear pharmacokinetics. Saturation of, for example, membrane transport or metabolism at exposure levels between the microdose and therapeutic dose may limit the predictivity of high-dose pharmacokinetics from microdose observations. Guidance on the likelihood of appreciable non-linear pharmacokinetics based on preclinical information can be helpful in staging the clinical phase and the place of microdosing in it. We present a decision tree that evaluates concerns about non-linearities raised in the preclinical phase and their potential impact on the proportionality between microdose and intended therapeutic dose as predicted from preclinical information. The expected maximum concentrations at relevant sites are estimated by non-compartmental methods. These are compared with dissolution, Michaelis constants for active or enzymatic processes, and binding protein concentrations to assess the potential saturation of the processes below therapeutic doses. The decision tree was applied to ten published cases comparing microdose and therapeutic dose pharmacokinetics, for which concerns about non-linear pharmacokinetics were raised a priori. The decision tree was able to discriminate cases showing substantial non-linearities from cases displaying dose-proportional pharmacokinetics. The recommendations described in this paper may be useful in deciding whether a microdosing study is a sensible option to gain early insight in clinical pharmacokinetics of drug candidates.
Cremophor EL causes (pseudo-) non-linear pharmacokinetics of paclitaxel in patients.
van Tellingen, O; Huizing, M T; Panday, V R; Schellens, J H; Nooijen, W J; Beijnen, J H
1999-09-01
The non-linear plasma pharmacokinetics of paclitaxel in patients has been well established, however, the exact underlying mechanism remains to be elucidated. We have previously shown that the non-linear plasma pharmacokinetics of paclitaxel in mice results from Cremophor EL. To investigate whether Cremophor EL also plays a role in the non-linear pharmacokinetics of paclitaxel in patients, we have established its pharmacokinetics in patients receiving paclitaxel by 3-, 24- or 96-h intravenous infusion. The pharmacokinetics of Cremophor EL itself was non-linear as the clearance (Cl) in the 3-h schedules was significantly lower than when using the longer 24- or 96-h infusions (Cl175-3 h = 42.8+/-24.9 ml h(-1) m(-2); CI175-24 h = 79.7+/-24.3; P = 0.035 and Cl135-3 h = 44.1+/-21.8 ml h(-1) m(-1); Cl140-96 h = 211.8+/-32.0; P < 0.001). Consequently, the maximum plasma levels were much higher (0.62%) in the 3-h infusions than when using longer infusion durations. By using an in vitro equilibrium assay and determination in plasma ultrafiltrate we have established that the fraction of unbound paclitaxel in plasma is inversely related with the Cremophor EL level. Despite its relatively low molecular weight, no Cremophor EL was found in the ultrafiltrate fraction. Our results strongly suggest that entrapment of paclitaxel in plasma by Cremophor EL, probably by inclusion in micelles, is the cause of the apparent nonlinear plasma pharmacokinetics of paclitaxel. This mechanism of a (pseudo-)non-linearity contrasts previous postulations about saturable distribution and elimination kinetics and means that we must re-evaluate previous assumptions on pharmacokinetics-pharmacodynamics relationships.
Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.
Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J
2016-10-03
Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods.
The algebra of physical observables in non-linearly realized gauge theories
NASA Astrophysics Data System (ADS)
Quadri, Andrea
2010-11-01
We classify the physical observables in spontaneously broken non-linearly realized gauge theories in the recently proposed loopwise expansion governed by the Weak Power-Counting (WPC) and the Local Functional Equation. The latter controls the non-trivial quantum deformation of the classical non-linearly realized gauge symmetry, to all orders in the loop expansion. The Batalin-Vilkovisky (BV) formalism is used. We show that the dependence of the vertex functional on the Goldstone fields is obtained via a canonical transformation w.r.t. the BV bracket associated with the BRST symmetry of the model. We also compare the WPC with strict power-counting renormalizability in linearly realized gauge theories. In the case of the electroweak group we find that the tree-level Weinberg relation still holds if power-counting renormalizability is weakened to the WPC condition.
Sulthana, Ayesha; Latha, K C; Imran, Mohammad; Rathan, Ramya; Sridhar, R; Balasubramanian, S
2014-01-01
Fuzzy principal component regression (FPCR) is proposed to model the non-linear process of sewage treatment plant (STP) data matrix. The dimension reduction of voluminous data was done by principal component analysis (PCA). The PCA score values were partitioned by fuzzy-c-means (FCM) clustering, and a Takagi-Sugeno-Kang (TSK) fuzzy model was built based on the FCM functions. The FPCR approach was used to predict the reduction in chemical oxygen demand (COD) and biological oxygen demand (BOD) of treated wastewater of Vidyaranyapuram STP with respect to the relations modeled between fuzzy partitioned PCA scores and target output. The designed FPCR model showed the ability to capture the behavior of non-linear processes of STP. The predicted values of reduction in COD and BOD were analyzed by performing the linear regression analysis. The predicted values for COD and BOD reduction showed positive correlation with the observed data.
GPU linear and non-linear Poisson–Boltzmann solver module for DelPhi
Colmenares, José; Ortiz, Jesús; Rocchia, Walter
2014-01-01
Summary: In this work, we present a CUDA-based GPU implementation of a Poisson–Boltzmann equation solver, in both the linear and non-linear versions, using double precision. A finite difference scheme is adopted and made suitable for the GPU architecture. The resulting code was interfaced with the electrostatics software for biomolecules DelPhi, which is widely used in the computational biology community. The algorithm has been implemented using CUDA and tested over a few representative cases of biological interest. Details of the implementation and performance test results are illustrated. A speedup of ∼10 times was achieved both in the linear and non-linear cases. Availability and implementation: The module is open-source and available at http://www.electrostaticszone.eu/index.php/downloads. Contact: walter.rocchia@iit.it Supplementary information: Supplementary data are available at Bioinformatics online PMID:24292939
Global search of non-linear systems periodic solutions: A rotordynamics application
NASA Astrophysics Data System (ADS)
Sarrouy, E.; Thouverez, F.
2010-08-01
Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions—where T is known—of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited.
Characterization of memory load in an arithmetic task using non-linear analysis of EEG signals.
Zarjam, Pega; Epps, Julien; Lovell, Nigel H; Chen, Fang
2012-01-01
In this paper, we investigate non-linear analysis of electroencephalogram (EEG) signals to examine changes in working memory load during the performance of a cognitive task with varying difficulty levels. EEG signals were recorded during an arithmetic task while the induced load was varying in seven levels from very easy to extremely difficult. The EEG signals were analyzed using three different non-linear/dynamic measures; namely: correlation dimension, Hurst exponent and approximate entropy. Experimental results show that the values of the measures extracted from the delta frequency band of signals acquired from the frontal and occipital lobes of the brain vary in accordance with the task difficulty level induced. The values of the correlation dimension increased as the task difficulty increased, showing a rise in complexity of the EEG signals, while the values of the Hurst exponent and approximate entropy decreased as task difficulty increased, indicating more regularity and predictability in the signals.
Model Order and Identifiability of Non-Linear Biological Systems in Stable Oscillation.
Wigren, Torbjörn
2015-01-01
The paper presents a theoretical result that clarifies when it is at all possible to determine the nonlinear dynamic equations of a biological system in stable oscillation, from measured data. As it turns out the minimal order needed for this is dependent on the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a simulated fourth order Hodgkin-Huxley spiking neuron model, which is identified using a non-linear second order differential equation model. The simulated result illustrates that the underlying higher order model of the spiking neuron cannot be uniquely determined given only the periodic measured data. The result of the paper is of general validity when the dynamics of biological systems in stable oscillation is identified, and illustrates the need to carefully address non-linear identifiability aspects when validating models based on periodic data.
NASA Astrophysics Data System (ADS)
Vasant, P.; Ganesan, T.; Elamvazuthi, I.
2012-11-01
A fairly reasonable result was obtained for non-linear engineering problems using the optimization techniques such as neural network, genetic algorithms, and fuzzy logic independently in the past. Increasingly, hybrid techniques are being used to solve the non-linear problems to obtain better output. This paper discusses the use of neuro-genetic hybrid technique to optimize the geological structure mapping which is known as seismic survey. It involves the minimization of objective function subject to the requirement of geophysical and operational constraints. In this work, the optimization was initially performed using genetic programming, and followed by hybrid neuro-genetic programming approaches. Comparative studies and analysis were then carried out on the optimized results. The results indicate that the hybrid neuro-genetic hybrid technique produced better results compared to the stand-alone genetic programming method.
Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates
NASA Astrophysics Data System (ADS)
Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier
2017-01-01
A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.
Vuori, Kaarina; Strandén, Ismo; Sevón-Aimonen, Marja-Liisa; Mäntysaari, Esa A
2006-01-01
A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.
Linear to non linear analysis for positron acceleration in plasma hollow channel wakefields
NASA Astrophysics Data System (ADS)
Amorim, Ligia Diana; An, Weiming; Mori, Warren B.; Vieira, Jorge
2016-10-01
Plasma wakefield accelerators are promising candidates for future generation compact accelerators. The standard regime of operation, non-linear or blowout regime, is reached when a particle bunch space charge or laser pulse ponderomotive force radially expels plasma electrons forming a bucket of ions that defocus positron bunches, thus preventing their acceleration. To avoid defocusing, hollow plasma channels have been considered. The corresponding wakefields have been examined in the linear and non-linear excitation regimes for electrons. It is therefore important to extend the theory for positron acceleration, particularly in the nonlinear regime where the wakefields strongly differ. In this work we explore the wakefield structure, examine the differences between the electron and positron beam cases, and explore positron acceleration in nonlinear regimes. We support our findings with multi-dimensional particle-in-cell simulations performed with OSIRIS and quasi-3D and QuickPIC.
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.
Learning from observation, feedback, and intervention in linear and non-linear task environments.
Henriksson, Maria P; Enkvist, Tommy
2016-12-12
This multiple-cue judgment study investigates whether we can manipulate the judgment strategy and increase accuracy in linear and non-linear cue-criterion environments just by changing the training mode. Three experiments show that accuracy in simple linear additive task environments are improved with feedback training and intervention training, while accuracy in complex multiplicative tasks are improved with observational training. The observed interaction effect suggests that the training mode invites different strategies that are adjusted as a function of experience to the demands from the underlying cue-criterion structure. Thus, feedback and the intervention training modes invite cue abstraction, an effortful but successful strategy in combination with simple linear task structures, and observational training invites exemplar memory processes, a simple but successful strategy in combination with complex non-linear task structures. The study discusses adaptive cognition and the implication of the different training modes across a life span and for clinical populations.
A new line-of-sight approach to the non-linear Cosmic Microwave Background
NASA Astrophysics Data System (ADS)
Fidler, Christian; Koyama, Kazuya; Pettinari, Guido W.
2015-04-01
We develop the transport operator formalism, a new line-of-sight integration framework to calculate the anisotropies of the Cosmic Microwave Background (CMB) at the linear and non-linear level. This formalism utilises a transformation operator that removes all inhomogeneous propagation effects acting on the photon distribution function, thus achieving a split between perturbative collisional effects at recombination and non-perturbative line-of-sight effects at later times. The former can be computed in the framework of standard cosmological perturbation theory with a second-order Boltzmann code such as SONG, while the latter can be treated within a separate perturbative scheme allowing the use of non-linear Newtonian potentials. We thus provide a consistent framework to compute all physical effects contained in the Boltzmann equation and to combine the standard remapping approach with Boltzmann codes at any order in perturbation theory, without assuming that all sources are localised at recombination.
Local instabilities and the transition to chaos of non-linear waves
NASA Astrophysics Data System (ADS)
1993-03-01
The object of this research contract was to study the singularities of non-linear structures through numerical simulations. The waiting times involved in the use of a Cray II prompted the lab to replace it with an HP 720 work station, which they found to be irreplaceable for the fine analysis of convection, despite the huge amount of calculations involved. The team simulated a fairly large number of two-dimensional phenomenological models, with satisfactory results. Examples described in this report include convection, dislocations in rolled structures, dislocation nucleation using the Landau-Ginzburg equation, the Pesch-Kramer equation (large-scale flows), non-linear wave defects, the optical model, and others.
Theoretically informed entangled polymer simulations: linear and non-linear rheology of melts.
Ramirez-Hernandez, Abelardo; Miller, Marcus; De Pablo, Juan J.
2013-01-02
In recent years, there has been a resurgence in developing models and theories for the non-equilibrium behavior of polymeric liquids. The so-called “tube” models, gradually refined over decades of research, can now provide a description of the linear and non-linear rheology of entangled polymers that is qualitatively consistent with experiments. Such approaches, however, have been limited to homopolymers. Here we present a general formalism that relies on the concept of slip links to describe the dynamics of high polymers. In this work, it is shown to be capable of describing quantitatively the linear response of pure homopolymers and blends, the non-linear rheology of highly entangled systems, and the dynamics of diblock copolymers.
Iterated non-linear model predictive control based on tubes and contractive constraints.
Murillo, M; Sánchez, G; Giovanini, L
2016-05-01
This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle.
The quadratically damped oscillator: A case study of a non-linear equation of motion
NASA Astrophysics Data System (ADS)
Smith, B. R.
2012-09-01
The equation of motion for a quadratically damped oscillator, where the damping is proportional to the square of the velocity, is a non-linear second-order differential equation. Non-linear equations of motion such as this are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions. Like all second-order ordinary differential equations, it has a corresponding first-order partial differential equation, whose independent solutions constitute the constants of the motion. These constants readily provide an approximate solution correct to first order in the damping constant. They also reveal that the quadratically damped oscillator is never critically damped or overdamped, and that to first order in the damping constant the oscillation frequency is identical to the natural frequency. The technique described has close ties to standard tools such as integral curves in phase space and phase portraits.
Simulation of non-linear rf losses derived from characteristic Nb topography
Reece, Charles E.; Xu, Chen; Kelley, Michael
2013-09-01
A simplified model has been developed to simulate non-linear RF losses on Nb surfaces exclusively due to topographical enhancement of surface magnetic fields. If local sharp edges are small enough, at locations where local surface fields exceed Hc, small volumes of material may become normal conducting without thermal leading to quench. These small volumes of normal material yield increases in the effective surface resistance of the Nb. Using topographic data from typical BCP?d and EP?d fine grain niobium surfaces, we have simulated field-dependent losses and found that when extrapolated to resulting cavity performance, these losses correspond well to characteristic BCP/EP high field Q0 performance differences for fine grain Nb. We describe the structure of the model, its limitations, and the effects of this type of non-linear loss contribution on SRF cavities.
Model predictive control of non-linear systems over networks with data quantization and packet loss.
Yu, Jimin; Nan, Liangsheng; Tang, Xiaoming; Wang, Ping
2015-11-01
This paper studies the approach of model predictive control (MPC) for the non-linear systems under networked environment where both data quantization and packet loss may occur. The non-linear controlled plant in the networked control system (NCS) is represented by a Tagaki-Sugeno (T-S) model. The sensed data and control signal are quantized in both links and described as sector bound uncertainties by applying sector bound approach. Then, the quantized data are transmitted in the communication networks and may suffer from the effect of packet losses, which are modeled as Bernoulli process. A fuzzy predictive controller which guarantees the stability of the closed-loop system is obtained by solving a set of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
Sabatini, R.; Bailly, C.; Marsden, O.; Gainville, O.
2016-12-01
The long-range atmospheric propagation of explosion-like waves of frequency in the infrasound range is investigated using non-linear ray theory. Simulations are performed for sources of increasing amplitude on rays up to the lower thermosphere and for distances of hundreds of kilometres. A study of the attenuation of the waveforms observed at ground level induced by both the classical mechanisms and the vibrational relaxation of the molecules comprising the atmospheric gas is carried out. The relative importance of classical absorption and vibrational relaxation along the typical atmospheric propagation trajectories is assessed. Non-linear effects are highlighted as well and particular emphasis is placed on their strong interaction with absorption phenomena. A detailed description of the propagation model and of the numerical algorithm used in this work is first reported. Results are then discussed and the importance of the different mechanisms is clarified.
Fully non-linear cosmological perturbations of multicomponent fluid and field systems
NASA Astrophysics Data System (ADS)
Hwang, Jai-chan; Noh, Hyerim; Park, Chan-Gyung
2016-09-01
We present fully non-linear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. We include the anisotropic stress. Even in the absence of anisotropic stress of individual component, the multiple component nature introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully non-linear equations and the third-order perturbation equations of the non-relativistic pressure fluids in the CDM-comoving gauge.
On robustness of constrained non-linear H ∞ predictive controllers with disturbances
NASA Astrophysics Data System (ADS)
He, De-Feng; Ji, Hai-Bo; Zheng, Tao
2010-02-01
This article considers the robustness problem of H ∞ model predictive controllers for constrained non-linear discrete-time systems subject to disturbances, which are dependent on the system state and input. The notions of input-to-state stability and finite L 2-gain of non-linear systems are introduced and exploited to investigate the robustness properties of this predictive controller under the state and input constraints and the disturbance. Moreover, this robustness of the controller is extended to the case of suboptimality of the solution. With its feasibility at initial time, the feasibility of the online optimisation problem is guaranteed for all times in the presence of disturbances and constraints. Finally, an example is employed to illustrate the proposed results.
Non-Linear Analysis of Mode II Fracture in the end Notched Flexure Beam
NASA Astrophysics Data System (ADS)
Rizov, V.
2016-03-01
Analysis is carried-out of fracture in the End Notched Flex- ure (ENF) beam configuration, taking into account the material nonlin- earity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical be- haviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF con- figuration.
McDonald, Alison C; Sanei, Kia; Keir, Peter J
2013-06-01
Muscle force estimates are important for full understanding of the musculoskeletal system and EMG is a modeling method used to estimate muscle force. The purpose of this investigation was to examine the effect of high pass filtering and non-linear normalization on the EMG-force relationship of sub-maximal finger exertions. Sub-maximal isometric ramp exertions were performed under three conditions (i) extension with restraint at the mid-proximal phalanx, (ii) flexion at the proximal phalanx and (iii) flexion at the distal phalanx. Thirty high pass filter designs were compared to a standardized processing procedure and an exponential fit equation was used for non-linear normalization. High pass filtering significantly reduced the %RMS error and increased the peak cross correlation between EMG and force in the distal flexion condition and in the other two conditions there was a trend towards improving force predictions with high pass filtering. The degree of linearity differed between the three contraction conditions and high pass filtering improved the linearity in all conditions. Non-linear normalization had greater impact on the EMG-force relationship than high pass filtering. The difference in optimal processing parameters suggests that high pass filtering and linearity are dependent on contraction mode as well as the muscle analyzed.
FDATMOS16 non-linear partitioning and organic volatility distributions in urban aerosols
Madronich, Sasha; Kleinman, Larry; Conley, Andrew; Lee-Taylor, Julie; Hodzic, A.; Aumont, Bernard
2015-12-17
Gas-to-particle partitioning of organic aerosols (OA) is represented in most models by Raoult’s law, and depends on the existing mass of particles into which organic gases can dissolve. This raises the possibility of non-linear response of particle-phase OA to the emissions of precursor volatile organic compounds (VOCs) that contribute to this partitioning mass. Implications for air quality management are evident: A strong non-linear dependence would suggest that reductions in VOC emission would have a more-than-proportionate benefit in lowering ambient OA concentrations. Chamber measurements on simple VOC mixtures generally confirm the non-linear scaling between OA and VOCs, usually stated as a mass-dependence of the measured OA yields. However, for realistic ambient conditions including urban settings, no single component dominates the composition of the organic particles, and deviations from linearity are presumed to be small. Here we re-examine the linearity question using volatility spectra from several sources: (1) chamber studies of selected aerosols, (2) volatility inferred for aerosols sampled in two megacities, Mexico City and Paris, and (3) an explicit chemistry model (GECKO-A). These few available volatility distributions suggest that urban OA may be only slightly super-linear, with most values of the sensitivity exponent in the range 1.1-1.3, also substantially lower than seen in chambers for some specific aerosols. Furthermore, the rather low values suggest that OA concentrations in megacities are not an inevitable convergence of non-linear effects, but can be addressed (much like in smaller urban areas) by proportionate reductions in emissions.
Improving Non-Linear Approaches to Anomaly Detection, Class Separation, and Visualization
2014-12-26
CLASS SEPARATION, AND VISUALIZATION DISSERTATION Presented to the Faculty Graduate School of Engineering and Management Air Force Institute of...Date 4 Dec 2014 Date 4 Dec 2014 Date Accepted: Adedeji B. Badiru , Ph.D. Dean, Graduate School of Engineering and Management Date AFIT-ENS-DS-14-D-15...existing non-linear techniques are investigated for the purposes of providing better, timely class separation and improved anomaly detection on various
Beyond the borders--Biomedical applications of non-linear Raman microscopy.
Winterhalder, Martin Josef; Zumbusch, Andreas
2015-07-15
Raman spectroscopy offers great promise for label free imaging in biomedical applications. Its use, however, is hampered by the long integration times required and the presence of autofluorescence in many samples which outshines the Raman signals. In order to overcome these limitations, a variety of different non-linear Raman imaging techniques have been developed over the last decade. This review describes biomedical applications of these novel but already mature imaging techniques.
Non-linear partitioning and organic volatility distributions of urban aerosols.
Madronich, S; Conley, A J; Lee-Taylor, J; Kleinman, L I; Hodzic, A; Aumont, B
2016-07-18
Gas-to-particle partitioning of organic aerosols (OA) is represented in most models by Raoult's law, and depends on the existing mass of particles into which organic gases can dissolve. This raises the possibility of non-linear response of particle-phase OA mass to the emissions of precursor volatile organic compounds (VOCs) that contribute to this partitioning mass. Implications for air quality management are evident: a strong non-linear dependence would suggest that reductions in VOC emission would have a more-than-proportionate benefit in lowering ambient OA concentrations. Chamber measurements on simple VOC mixtures generally confirm the non-linear scaling between OA and VOCs, usually stated as a mass-dependence of the measured OA yields. However, for realistic ambient conditions including urban settings, no single component dominates the composition of the organic particles, and deviations from linearity are presumed to be small. Here we re-examine the linearity question using volatility spectra from several sources: (1) chamber studies of selected aerosols, (2) volatility inferred for aerosols sampled in two megacities, Mexico City and Paris, and (3) an explicit chemistry model (GECKO-A). These few available volatility distributions suggest that urban OA may be only slightly super-linear, with most values of the normalized sensitivity exponent in the range 1.1-1.3, also substantially lower than seen in chambers for some specific aerosols. The rather low exponents suggest that OA concentrations in megacities are not an inevitable convergence of non-linear effects, but can be addressed (much like in smaller urban areas) by proportionate reductions in emissions.
Design and implementation of non-linear image processing functions for CMOS image sensor
NASA Astrophysics Data System (ADS)
Musa, Purnawarman; Sudiro, Sunny A.; Wibowo, Eri P.; Harmanto, Suryadi; Paindavoine, Michel
2012-11-01
Today, solid state image sensors are used in many applications like in mobile phones, video surveillance systems, embedded medical imaging and industrial vision systems. These image sensors require the integration in the focal plane (or near the focal plane) of complex image processing algorithms. Such devices must meet the constraints related to the quality of acquired images, speed and performance of embedded processing, as well as low power consumption. To achieve these objectives, low-level analog processing allows extracting the useful information in the scene directly. For example, edge detection step followed by a local maxima extraction will facilitate the high-level processing like objects pattern recognition in a visual scene. Our goal was to design an intelligent image sensor prototype achieving high-speed image acquisition and non-linear image processing (like local minima and maxima calculations). For this purpose, we present in this article the design and test of a 64×64 pixels image sensor built in a standard CMOS Technology 0.35 μm including non-linear image processing. The architecture of our sensor, named nLiRIC (non-Linear Rapid Image Capture), is based on the implementation of an analog Minima/Maxima Unit. This MMU calculates the minimum and maximum values (non-linear functions), in real time, in a 2×2 pixels neighbourhood. Each MMU needs 52 transistors and the pitch of one pixel is 40×40 mu m. The total area of the 64×64 pixels is 12.5mm2. Our tests have shown the validity of the main functions of our new image sensor like fast image acquisition (10K frames per second), minima/maxima calculations in less then one ms.
Gupta, Rahul Kumar; Shi, Qiongfeng; Dhakar, Lokesh; Wang, Tao; Heng, Chun Huat; Lee, Chengkuo
2017-01-25
Over the years, several approaches have been devised to widen the operating bandwidth, but most of them can only be triggered at high accelerations. In this work, we investigate a broadband energy harvester based on combination of non-linear stiffening effect and multimodal energy harvesting to obtain high bandwidth over wide range of accelerations (0.1 g-2.0 g). In order to achieve broadband behavior, a polymer based spring exhibiting multimodal energy harvesting is used. Besides, non-linear stiffening effect is introduced by using mechanical stoppers. At low accelerations (<0.5 g), the nearby mode frequencies of polymer spring contribute to broadening characteristics, while proof mass engages with mechanical stoppers to introduce broadening by non-linear stiffening at higher accelerations. The electromagnetic mechanism is employed in this design to enhance its output at low accelerations when triboelectric output is negligible. Our device displays bandwidth of 40 Hz even at low acceleration of 0.1 g and it is increased up to 68 Hz at 2 g. When non-linear stiffening is used along with multimodal energy-harvesting, the obtained bandwidth increases from 23 Hz to 68 Hz with percentage increment of 295% at 1.8 g. Further, we have demonstrated the triboelectric output measured as acceleration sensing signals in terms of voltage and current sensitivity of 4.7 Vg(-1) and 19.7 nAg(-1), respectively.
Non-Linear Susceptibility of Spin-Glasses on Frustrated Triangular Cactus Tree
NASA Astrophysics Data System (ADS)
Yasumura, Kaoru; Ono, Ikuo
1984-01-01
In order to explore the frustration effects on a non-linear susceptibility χ2 of spin-glasses, ferro-antiferromagnetic mixtures, diluted antiferromagnets and Mattis model are comperatively investigated in line with a random ordered phase. The jump of χ2 in the vicinity of the transition temperature is common in these models, and the magnitude of the jump is proved to depend strongly on the concentration of antiferromagnetic bond, but weakly on that of frustration.
Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions
NASA Astrophysics Data System (ADS)
Feng, Lili; Yu, Fajun; Li, Li
2017-01-01
Starting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.
A Family of Ellipse Methods for Solving Non-Linear Equations
ERIC Educational Resources Information Center
Gupta, K. C.; Kanwar, V.; Kumar, Sanjeev
2009-01-01
This note presents a method for the numerical approximation of simple zeros of a non-linear equation in one variable. In order to do so, the method uses an ellipse rather than a tangent approach. The main advantage of our method is that it does not fail even if the derivative of the function is either zero or very small in the vicinity of the…
FDATMOS16 non-linear partitioning and organic volatility distributions in urban aerosols
Madronich, Sasha; Kleinman, Larry; Conley, Andrew; ...
2015-12-17
Gas-to-particle partitioning of organic aerosols (OA) is represented in most models by Raoult’s law, and depends on the existing mass of particles into which organic gases can dissolve. This raises the possibility of non-linear response of particle-phase OA to the emissions of precursor volatile organic compounds (VOCs) that contribute to this partitioning mass. Implications for air quality management are evident: A strong non-linear dependence would suggest that reductions in VOC emission would have a more-than-proportionate benefit in lowering ambient OA concentrations. Chamber measurements on simple VOC mixtures generally confirm the non-linear scaling between OA and VOCs, usually stated as amore » mass-dependence of the measured OA yields. However, for realistic ambient conditions including urban settings, no single component dominates the composition of the organic particles, and deviations from linearity are presumed to be small. Here we re-examine the linearity question using volatility spectra from several sources: (1) chamber studies of selected aerosols, (2) volatility inferred for aerosols sampled in two megacities, Mexico City and Paris, and (3) an explicit chemistry model (GECKO-A). These few available volatility distributions suggest that urban OA may be only slightly super-linear, with most values of the sensitivity exponent in the range 1.1-1.3, also substantially lower than seen in chambers for some specific aerosols. Furthermore, the rather low values suggest that OA concentrations in megacities are not an inevitable convergence of non-linear effects, but can be addressed (much like in smaller urban areas) by proportionate reductions in emissions.« less
Non-linear regimes in mean-field full-sphere dynamo
NASA Astrophysics Data System (ADS)
Pipin, V. V.
2017-04-01
The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3 M⊙ rotating with period of 10 d. For intermediate value of parameter of the turbulent magnetic Prandl number, PmT = 3, we found the oscillating dynamo regimes with period about 40 yr. The higher PmT results to longer dynamo periods. If the large-scale flows is fixed, we find that the dynamo transits from axisymmetric to non-axisymmetric regimes for the overcritical parameter of the α-effect. The change of dynamo regime occurs because of the non-axisymmetric non-linear α-effect. The situation persists in the fully non-linear dynamo models with regards for the magnetic feedback on the angular momentum balance and the heat transport in the star. It is found that the large-scale magnetic field quenches the latitudinal shear in the bulk of the star. However, the strong radial shear operates in the subsurface layer of the star. In the non-linear case, the profile of the angular velocity inside the star become close to the spherical surfaces. This supports the equator-ward migration of the axisymmetric magnetic field dynamo waves. It was found that the magnetic configuration of the star dominates by the regular non-axisymmetric mode m = 1. As a result of the differential rotation, it forms the Yin Yang magnetic polarity pattern with the strong (>500 G) poloidal magnetic field in polar regions.
NASA Astrophysics Data System (ADS)
Gupta, Rahul Kumar; Shi, Qiongfeng; Dhakar, Lokesh; Wang, Tao; Heng, Chun Huat; Lee, Chengkuo
2017-01-01
Over the years, several approaches have been devised to widen the operating bandwidth, but most of them can only be triggered at high accelerations. In this work, we investigate a broadband energy harvester based on combination of non-linear stiffening effect and multimodal energy harvesting to obtain high bandwidth over wide range of accelerations (0.1 g–2.0 g). In order to achieve broadband behavior, a polymer based spring exhibiting multimodal energy harvesting is used. Besides, non-linear stiffening effect is introduced by using mechanical stoppers. At low accelerations (<0.5 g), the nearby mode frequencies of polymer spring contribute to broadening characteristics, while proof mass engages with mechanical stoppers to introduce broadening by non-linear stiffening at higher accelerations. The electromagnetic mechanism is employed in this design to enhance its output at low accelerations when triboelectric output is negligible. Our device displays bandwidth of 40 Hz even at low acceleration of 0.1 g and it is increased up to 68 Hz at 2 g. When non-linear stiffening is used along with multimodal energy-harvesting, the obtained bandwidth increases from 23 Hz to 68 Hz with percentage increment of 295% at 1.8 g. Further, we have demonstrated the triboelectric output measured as acceleration sensing signals in terms of voltage and current sensitivity of 4.7 Vg‑1 and 19.7 nAg‑1, respectively.
Non-linear controls influence functions in an aircraft dynamics simulator
NASA Technical Reports Server (NTRS)
Guerreiro, Nelson M.; Hubbard, James E., Jr.; Motter, Mark A.
2006-01-01
In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft s control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland s continuing study of active wing load control.
On the linear and non-linear electronic spectroscopy of chlorophylls: a computational study.
Graczyk, Alicja; Żurek, Justyna M; Paterson, Martin J
2014-01-01
A theoretical analysis of linear and non-linear (two-photon absorption) electronic spectroscopy of all known porphyrinic pigments has been performed using linear and quadratic density functional response theory, with the long-range corrected CAM-B3LYP functional. We found that higher Soret transitions often contain non-Gouterman contributions and that each chlorophyll has the possibility for resonance enhanced TPA in the Soret region, although there is also significant TPA in the Q region.
A single-degree-of-freedom model for non-linear soil amplification
Erdik, Mustafa Ozder
1979-01-01
For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.
NASA Technical Reports Server (NTRS)
Jobson, Daniel J.; Rahman, Zia-Ur; Woodell, Glenn A.; Hines, Glenn D.
2004-01-01
Noise is the primary visibility limit in the process of non-linear image enhancement, and is no longer a statistically stable additive noise in the post-enhancement image. Therefore novel approaches are needed to both assess and reduce spatially variable noise at this stage in overall image processing. Here we will examine the use of edge pattern analysis both for automatic assessment of spatially variable noise and as a foundation for new noise reduction methods.
On removability of singularities on manifolds for solutions of non-linear elliptic equations
Skrypnik, I I
2003-10-31
A precise condition is found for the removability of a singularity on a smooth manifold for solutions of non-linear second-order elliptic equations of divergence form. The condition is stated in the form of a dependence of the pointwise behaviour of the solution on the distance to the singular manifold. The condition obtained is weaker than Serrin's well-known sufficient condition for the removability of a singularity on a manifold.
Gupta, Rahul Kumar; Shi, Qiongfeng; Dhakar, Lokesh; Wang, Tao; Heng, Chun Huat; Lee, Chengkuo
2017-01-01
Over the years, several approaches have been devised to widen the operating bandwidth, but most of them can only be triggered at high accelerations. In this work, we investigate a broadband energy harvester based on combination of non-linear stiffening effect and multimodal energy harvesting to obtain high bandwidth over wide range of accelerations (0.1 g–2.0 g). In order to achieve broadband behavior, a polymer based spring exhibiting multimodal energy harvesting is used. Besides, non-linear stiffening effect is introduced by using mechanical stoppers. At low accelerations (<0.5 g), the nearby mode frequencies of polymer spring contribute to broadening characteristics, while proof mass engages with mechanical stoppers to introduce broadening by non-linear stiffening at higher accelerations. The electromagnetic mechanism is employed in this design to enhance its output at low accelerations when triboelectric output is negligible. Our device displays bandwidth of 40 Hz even at low acceleration of 0.1 g and it is increased up to 68 Hz at 2 g. When non-linear stiffening is used along with multimodal energy-harvesting, the obtained bandwidth increases from 23 Hz to 68 Hz with percentage increment of 295% at 1.8 g. Further, we have demonstrated the triboelectric output measured as acceleration sensing signals in terms of voltage and current sensitivity of 4.7 Vg−1 and 19.7 nAg−1, respectively. PMID:28120924
Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN
NASA Technical Reports Server (NTRS)
Sheerer, T. J.
1986-01-01
The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.
PkANN: Non-Linear Matter Power Spectrum Interpolation through Artificial Neural Networks
NASA Astrophysics Data System (ADS)
Agarwal, Shankar
We investigate the interpolation of power spectra of matter fluctuations using artificial neural networks (ANNs). We present a new approach to confront small-scale non-linearities in the matter power spectrum. This ever-present and pernicious uncertainty is often the Achilles' heel in cosmological studies and must be reduced if we are to see the advent of precision cosmology in the late-time Universe. We detail how an accurate interpolation of the matter power spectrum is achievable with only a sparsely sampled grid of cosmological parameters. We show that an optimally trained ANN, when presented with a set of cosmological parameters (Omh2 , Obh2, ns, w0, sigma8, sum mnu and z), can provide a worst-case error ≤ 1 per cent (for redshift z ≤ 2) fit to the non-linear matter power spectrum deduced through large-scale N-body simulations, for modes up to k ≤ 0.9 hMpc-1 . Our power spectrum interpolator, which we label 'PkANN', is designed to simulate a range of cosmological models including massive neutrinos and dark energy equation of state w 0 ≠ -1. PkANN is accurate in the quasi-non-linear regime (0.1 hMpc-1 ≤ k ≤ 0.9 hMpc -1) over the entire parameter space and marks a significant improvement over some of the current power spectrum calculators. The response of the power spectrum to variations in the cosmological parameters is explored using PkANN. Using a compilation of existing peculiar velocity surveys, we investigate the cosmic Mach number statistic and show that PkANN not only successfully accounts for the non-linear motions on small scales, but also, unlike N-body simulations which are computationally expensive and/or infeasible, it can be an extremely quick and reliable tool in interpreting cosmological observations and testing theories of structure-formation.
Correlation spectroscopy based on non-linear response of silver colloids (including SEHRS)
NASA Astrophysics Data System (ADS)
Brehm, G.; Sauer, G.; Fritz, N.; Schneider, S.; Zaitsev, S.
2005-02-01
The non-linear response (second harmonic generation, SHG, hyper-Rayleigh scattering, HRS, surface-enhanced hyper-Raman scattering, SEHRS, and continuum generation) of two different types of silver colloids is compared by stationary and correlation spectroscopy. Employing a poly-disperse colloid prepared after the protocol of Lee and Meisel we found that the efficiency of all types of non-linear response is greatly enhanced if the colloid is 'activated' by addition of chloride ions. This activation is also necessary to observe SEHRS with both the Lee-Meisel and the mono-disperse colloid prepared by hydrazine reduction. The correlation curves of both types of colloid show one step (τ1/2∼10 ms) which can be associated with lateral diffusion of the individual particles. Its τ1/2-value is larger for the poly-disperse colloid, which contains larger particles. In addition, we find a second step, its relative amplitude being dependent on experimental parameters, whose τ1/2-value is, however, essentially the same for all samples investigated (τ‧1/2∼50 μs). We assign this correlation time to processes that lead to a restructuring of the surface and the formation and destruction of so-called 'hot spots'. Under optimum condition, the efficiency for all non-linear processes connected with one such 'hot spot' is extremely high. 'Hot particles' contain at least one hot spot and can therefore dominate the non-linear signal without the need of aggregation (field enhancement in the gap between particles).
Potential for Terahertz/Optical, Two Color Non-linear Sensing of Liquid Biochemical Agents
2011-05-18
solutions1,2 in the infrared frequency band. To explore the lowest frequency macromo- lecular modes of biomolecules, which occur at terahertz fre- quencies, in...resonant with elec- tronic excitations and macromolecular vibrations . A configuration that optimizes SDFG in the face of strong terahertz absorption by...REPORT Potential for terahertz /optical, two color non-linear sensing of liquid biochemical agents 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: A high
Agent based reasoning for the non-linear stochastic models of long-range memory
NASA Astrophysics Data System (ADS)
Kononovicius, A.; Gontis, V.
2012-02-01
We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. The agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.
HIGH SPEED KERR CELL FRAMING CAMERA
Goss, W.C.; Gilley, L.F.
1964-01-01
The present invention relates to a high speed camera utilizing a Kerr cell shutter and a novel optical delay system having no moving parts. The camera can selectively photograph at least 6 frames within 9 x 10/sup -8/ seconds during any such time interval of an occurring event. The invention utilizes particularly an optical system which views and transmits 6 images of an event to a multi-channeled optical delay relay system. The delay relay system has optical paths of successively increased length in whole multiples of the first channel optical path length, into which optical paths the 6 images are transmitted. The successively delayed images are accepted from the exit of the delay relay system by an optical image focusing means, which in turn directs the images into a Kerr cell shutter disposed to intercept the image paths. A camera is disposed to simultaneously view and record the 6 images during a single exposure of the Kerr cell shutter. (AEC)
NASA Astrophysics Data System (ADS)
El-Menoufi, Basem Kamal
2016-05-01
In the context of effective field theory, we consider quantum gravity with minimally coupled massless particles. Fixing the background geometry to be of the Kerr-Schild type, we fully determine the one-loop effective action of the theory whose finite non-local part is induced by the long-distance portion of quantum loops. This is accomplished using the non-local expansion of the heat kernel in addition to a non-linear completion technique through which the effective action is expanded in gravitational curvatures. Via Euclidean methods, we identify a logarithmic correction to the Bekenstein-Hawking entropy of Schwarzschild black hole. Using dimensional transmutation the result is shown to exhibit an interesting interplay between the UV and IR properties of quantum gravity.
A non-linear homogeneous model for bone-like materials under compressive load.
Mengoni, M; Voide, R; de Bien, C; Freichels, H; Jérôme, C; Léonard, A; Toye, D; Müller, R; van Lenthe, G H; Ponthot, J P
2012-02-01
Finite element (FE) models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. In order to simulate non-linear behavior, which currently is only feasible at the expense of extremely high computational costs, coarser models can be used if the local morphology has been linked to the apparent mechanical behavior. The aim of this paper is to implement and validate such a constitutive law. This law is able to capture the non-linear structural behavior of bone-like materials through the use of fabric tensors. It also allows for irreversible strains using an elastoplastic material model incorporating hardening. These features are expressed in a constitutive law based on the anisotropic continuum damage theory coupled with isotropic elastoplasticity in a finite strain framework. This material model was implemented into metafor (LTAS-MNNL, University of Liège, Belgium), a non-linear FE software. The implementation was validated against experimental data of cylindrical samples subjected to compression. Three materials with bone-like microstructure were tested: aluminum foams of variable density (ERG, Oakland, CA, USA), polylactic acid foam (CERM, University of Liège, Liège, Belgium), and cancellous bone tissue of a deer antler (Faculty of Veterinary Medicine, University of Liège, Liège, Belgium).
a Frequency Domain Based NUMERIC-ANALYTICAL Method for Non-Linear Dynamical Systems
NASA Astrophysics Data System (ADS)
Narayanan, S.; Sekar, P.
1998-04-01
In this paper a multiharmonic balancing technique is used to develop certain algorithms to determine periodic orbits of non-liner dynamical systems with external, parametric and self excitations. Essentially, in this method the non-linear differential equations are transformed into a set of non-linear algebraic equations in terms of the Fourier coefficients of the periodic solutions which are solved by using the Newton-Raphson technique. The method is developed such that both fast Fourier transform and discrete Fourier transform algorithms can be used. It is capable of treating all types of non-linearities and higher dimensional systems. The stability of periodic orbits is investigated by obtaining the monodromy matrix. A path following algorithm based on the predictor-corrector method is also presented to enable the bifurcation analysis. The prediction is done with a cubic extrapolation technique with an arc length incrementation while the correction is done with the use of the least square minimisation technique. The under determined system of equations is solved by singular value decomposition. The suitability of the method is demonstrated by obtaining the bifurcational behaviour of rolling contact vibrations modelled by Hertz contact law.
Non-linear effects on solute transfer between flowing water and a sediment bed.
Higashino, Makoto; Stefan, Heinz G
2011-11-15
A previously developed model of periodic pore water flow in space and time, and associated solute transport in a stream bed of fine sand is extended to coarse sand and fine gravel. The pore water flow immediately below the sediment/water interface becomes intermittently a non-Darcy flow. The periodic pressure and velocity fluctuations considered are induced by near-bed coherent turbulent motions in the stream flow; they penetrate from the sediment/water interface into the sediment pore system and are described by a wave number (χ) and a period (T) that are given as functions of the shear velocity (U(∗)) between the flowing water and the sediment bed. The stream bed has a flat surface without bed forms. The flow field in the sediment pore system is described by the continuity equation and a resistance law that includes both viscous (Darcy) and non-linear (inertial) effects. Simulation results show that non-linear (inertial) effects near the sediment/water interface increase flow resistance and reduce mean flow velocities. Compared to pure Darcy flow, non-linear (inertial) effects reduce solute exchange rates between overlying water and the sediment bed but only by a moderate amount (less than 50%). Turbulent coherent flow structures in the stream flow enhance solute transfer in the pore system of a stream bed compared to pure molecular diffusion, but by much less than standing surface waves or bed forms.
A Comparison of PDE-based Non-Linear Anisotropic Diffusion Techniques for Image Denoising
Weeratunga, S K; Kamath, C
2003-01-06
PDE-based, non-linear diffusion techniques are an effective way to denoise images. In a previous study, we investigated the effects of different parameters in the implementation of isotropic, non-linear diffusion. Using synthetic and real images, we showed that for images corrupted with additive Gaussian noise, such methods are quite effective, leading to lower mean-squared-error values in comparison with spatial filters and wavelet-based approaches. In this paper, we extend this work to include anisotropic diffusion, where the diffusivity is a tensor valued function which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. We consider several anisotropic diffusivity functions as well as approaches for discretizing the diffusion operator that minimize the mesh orientation effects. We investigate how these tensor-valued diffusivity functions compare in image quality, ease of use, and computational costs relative to simple spatial filters, the more complex bilateral filters, wavelet-based methods, and isotropic non-linear diffusion based techniques.
Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors
NASA Astrophysics Data System (ADS)
Kraczek, Brent; Kanp, Jaroslaw
Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.
Non-linear optical deformation potentials in uniaxially strained ZnO microwires
NASA Astrophysics Data System (ADS)
Sturm, C.; Wille, M.; Lenzner, J.; Khujanov, S.; Grundmann, M.
2017-02-01
The emission properties of bent ZnO microwires with diameters ranging from 1.5 μm to 7.3 μm are systematically investigated by cathodoluminescence spectroscopy at T ≈ 10 K . We induced uniaxial strains along the c-axis of up to ± 2.9 % . At these high strain values, we observe a non-linear shift of the emission energy with respect to the induced strain, and the magnitude of the energy shift depends on the sign of the strain. The linear and non-linear deformation potentials were determined to be D 1 = - 2.50 ± 0.05 eV and D 2 = - 15.0 ± 0.5 eV , respectively. The non-linearity of the energy shift is also reflected in the observed spectral broadening of the emission peak as a function of the locally induced strain, which decreases with increasing strain on the compressive side and increases on the tensile side.
Comparison of PDE-based non-linear anistropic diffusion techniques for image denoising
NASA Astrophysics Data System (ADS)
Weeratunga, Sisira K.; Kamath, Chandrika
2003-05-01
PDE-based, non-linear diffusion techniques are an effective way to denoise images.In a previous study, we investigated the effects of different parameters in the implementation of isotropic, non-linear diffusion. Using synthetic and real images, we showed that for images corrupted with additive Gaussian noise, such methods are quite effective, leading to lower mean-squared-error values in comparison with spatial filters and wavelet-based approaches. In this paper, we extend this work to include anisotropic diffusion, where the diffusivity is a tensor valued function which can be adapted to local edge orientation. This allows smoothing along the edges, but not perpendicular to it. We consider several anisotropic diffusivity functions as well as approaches for discretizing the diffusion operator that minimize the mesh orientation effects. We investigate how these tensor-valued diffusivity functions compare in image quality, ease of use, and computational costs relative to simple spatial filters, the more complex bilateral filters, wavelet-based methods, and isotropic non-linear diffusion based techniques.
A review on non-linear aeroelasticity of high aspect-ratio wings
NASA Astrophysics Data System (ADS)
Afonso, Frederico; Vale, José; Oliveira, Éder; Lau, Fernando; Suleman, Afzal
2017-02-01
Current economic constraints and environmental regulations call for design of more efficient aircraft configurations. An observed trend in aircraft design to reduce the lift induced drag and improve fuel consumption and emissions is to increase the wing aspect-ratio. However, a slender wing is more flexible and subject to higher deflections under the same operating conditions. This effect may lead to changes in dynamic behaviour and in aeroelastic response, potentially resulting in instabilities. Therefore, it is important to take into account geometric non-linearities in the design of high aspect-ratio wings, as well as having accurate computational codes that couple the aerodynamic and structural models in the presence of non-linearities. Here, a review on the state-of-the-art on non-linear aeroelasticity of high aspect-ratio wings is presented. The methodologies employed to analyse high aspect-ratio wings are presented and their applications discussed. Important observations from the state-of-the-art studies are drawn and the current challenges in the field are identified.
NASA Astrophysics Data System (ADS)
Singh, Gajbir; Venkateswara Rao, G.; Iyengar, N. G. R.
1995-03-01
The influence of finite amplitudes on the free flexural vibration response of moderately thick laminated plates is investigated. For this purpose, a simple higher order theory involving only four unknowns and satisfying the stress free conditions at the top and bottom surface of the composite plate is proposed. The proposed theory eliminates the use of shear correction factors which are otherwise required in Mindlin's plate theory. A rectangular four-node[formula]continuous finite element is developed based on this theory. The non-linear finite element equations are reduced to two non-linear ordinary differential equations governing the response of positive and negative deflection cycles. Direct numerical integration method is then employed to obtain the periods or non-linear frequencies. The finite element developed and the direct numerical integration method employed are validated for the case of isotropic rectangular plates. It is found that unsymmetrically laminated rectangular plates with hinged-hinged edge conditions oscillate with different amplitudes in the positive and negative deflection cycles. Furthermore, such plates would oscillate with a frequency less than the fundamental frequency for finite small amplitudes of oscillation. It is shown that this behaviour is strongly influenced by the boundary conditions. Results are presented for many configurations of composite plates.
Noury, Nima; Hipp, Joerg F; Siegel, Markus
2016-10-15
Transcranial electric stimulation (tES) is a promising tool to non-invasively manipulate neuronal activity in the human brain. Several studies have shown behavioral effects of tES, but stimulation artifacts complicate the simultaneous investigation of neural activity with EEG or MEG. Here, we first show for EEG and MEG, that contrary to previous assumptions, artifacts do not simply reflect stimulation currents, but that heartbeat and respiration non-linearly modulate stimulation artifacts. These modulations occur irrespective of the stimulation frequency, i.e. during both transcranial alternating and direct current stimulations (tACS and tDCS). Second, we show that, although at first sight previously employed artifact rejection methods may seem to remove artifacts, data are still contaminated by non-linear stimulation artifacts. Because of their complex nature and dependence on the subjects' physiological state, these artifacts are prone to be mistaken as neural entrainment. In sum, our results uncover non-linear tES artifacts, show that current techniques fail to fully remove them, and pave the way for new artifact rejection methods.
The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions
NASA Astrophysics Data System (ADS)
Linander, Hampus; Nilsson, Bengt E. W.
2016-07-01
In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F = 0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.
Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation
NASA Astrophysics Data System (ADS)
Kolesov, Andrei Yu; Rozov, Nikolai Kh
2002-02-01
For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied.
Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation
Kolesov, Andrei Yu; Rozov, Nikolai Kh
2002-02-28
For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied.
Spherical collapse, formation hysteresis and the deeply non-linear cosmological power spectrum
NASA Astrophysics Data System (ADS)
Mead, A. J.
2017-01-01
I examine differences in non-linear structure formation between cosmological models that share a z = 0 linear power spectrum in both shape and amplitude, but that differ via their growth history. N-body simulations of these models display an approximately identical large-scale-structure skeleton, but reveal deeply non-linear differences in the demographics and properties of haloes. I investigate to what extent the spherical-collapse model can help in understanding these differences, in both real and redshift space. I discuss how this is difficult to do if one attempts to identify haloes directly, because in that case one is subject to the vagaries of halo-finding algorithms. However, I demonstrate that the halo model of structure formation provides an accurate non-linear response in the power spectrum, but only if results from spherical collapse that include formation hysteresis are properly incorporated. I comment on how this fact can be used to provide per cent level accurate matter power-spectrum predictions for dark energy models for k ≤ 5 h Mpc-1 by using the halo model as a correction to accurate ΛCDM simulations. In the Appendix, I provide some fitting functions for the linear-collapse threshold (δc) and virialized overdensity (Δv) that are valid for a wide range of dark energy models. I also make my spherical-collapse code available at https://github.com/alexander-mead/collapse.
NASA Astrophysics Data System (ADS)
Zhang, Ruikun; Hou, Zhongsheng; Ji, Honghai; Yin, Chenkun
2016-04-01
In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov-Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L2[0, T] convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.
Mayorga, René V; Arriaga, Mariano
2007-10-01
In this article, a novel technique for non-linear global optimization is presented. The main goal is to find the optimal global solution of non-linear problems avoiding sub-optimal local solutions or inflection points. The proposed technique is based on a two steps concept: properly keep decreasing the value of the objective function, and calculating the corresponding independent variables by approximating its inverse function. The decreasing process can continue even after reaching local minima and, in general, the algorithm stops when converging to solutions near the global minimum. The implementation of the proposed technique by conventional numerical methods may require a considerable computational effort on the approximation of the inverse function. Thus, here a novel Artificial Neural Network (ANN) approach is implemented to reduce the computational requirements of the proposed optimization technique. This approach is successfully tested on some highly non-linear functions possessing several local minima. The results obtained demonstrate that the proposed approach compares favorably over some current conventional numerical (Matlab functions) methods, and other non-conventional (Evolutionary Algorithms, Simulated Annealing) optimization methods.
An evaluation of bias in propensity score-adjusted non-linear regression models.
Wan, Fei; Mitra, Nandita
2016-04-19
Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.
Non-linear dynamic analysis of a flexible rotor supported on porous oil journal bearings
NASA Astrophysics Data System (ADS)
Laha, S. K.; Kakoty, S. K.
2011-03-01
In the present paper, the non-linear dynamic analysis of a flexible rotor with a rigid disk under unbalance excitation mounted on porous oil journal bearings at the two ends is carried out. The system equation of motion is obtained by finite element formulation of Timoshenko beam and the disk. The non-linear oil-film forces are calculated from the solution of the modified Reynolds equation simultaneously with Darcy's equation. The system equation of motion is then solved by the Wilson- θ method. Bifurcation diagrams, Poincaré maps, time response, journal trajectories, FFT-spectrum, etc. are obtained to study the non-linear dynamics of the rotor-bearing system. The effect of various non-dimensional rotor-bearing parameters on the bifurcation characteristics of the system is studied. It is shown that the system undergoes Hopf bifurcation as the speed increases. Further, slenderness ratio, material properties of the rotor, ratio of disk mass to shaft mass and permeability of the porous bush are shown to have profound effect on the bifurcation characteristics of the rotor-bearing system.
NASA Astrophysics Data System (ADS)
Ouyang, Wei; Mao, Weijian; Li, Wuqun; Zhang, Pan
2017-02-01
An approach for approximate direct quadratic non-linear inversion in two-parameter (density and bulk modulus) heterogeneous acoustic media is being presented and discussed in this paper. The approach consists of two parts: the first is a linear generalized Radon transform (GRT) migration procedure based on the weighted true-amplitude summation of pre-stack seismic scattered data that is adapted to a virtually arbitrary observing system, and the second is a non-iterative quadratic inversion operation, produced from the explicit expression of amplitude radiation pattern that is acting on the migrated data. This ensures the asymptotic inversion can continue to simultaneously locate the discontinuities and reconstruct the size of the discontinuities in the perturbation parameters describing the acoustic media. We identify that the amplitude radiation pattern is the binary quadratic combination of the parameters in the process of formulating non-linear inverse scattering problems based on second-order Born approximation. The coefficients of the quadratic terms are computed by appropriately handling the double scattering effects. These added quadratic terms provide a better amplitude correction for the parameters inversion. Through numerical tests, we show that for strong perturbations, the errors of the linear inversion are significant and unacceptable. In contrast, the quadratic non-linear inversion can give fairly accurate inversion results and keep almost the same computational complexity as conventional GRT liner inversion.
Relativistic weak lensing from a fully non-linear cosmological density field
Thomas, D.B.; Bruni, M.; Wands, D. E-mail: marco.bruni@port.ac.uk
2015-09-01
In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- and B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a well-defined manner. Specifying General Relativity, we write down a complete set of equations for a GR+ΛCDM universe for computing all of the possible lensing terms from Newtonian N-body simulations. We illustrate this with the vector potential and show that, in a GR+ΛCDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a ΛCDM cosmology.
Localization of non-linearly modeled autonomous mobile robots using out-of-sequence measurements.
Besada-Portas, Eva; Lopez-Orozco, Jose A; Lanillos, Pablo; de la Cruz, Jesus M
2012-01-01
This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS) measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors) and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost.
Localization of Non-Linearly Modeled Autonomous Mobile Robots Using Out-of-Sequence Measurements
Besada-Portas, Eva; Lopez-Orozco, Jose A.; Lanillos, Pablo; de la Cruz, Jesus M.
2012-01-01
This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS) measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors) and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost. PMID:22736962
Non-linear analysis and calculation of the performance of a shelving protection system by FEM
NASA Astrophysics Data System (ADS)
García Nieto, P. J.; del Coz Díaz, J. J.; Vilán Vilán, J. A.; Suárez Sierra, J. L.
2012-12-01
The aim of this paper consists on the study, analysis and calculation of the efficiency of a shelving protection system by means of the finite element method (FEM). These shelving protection systems are intended to prevent the eventual damage due to the impacts of transport elements in motion, such as: forklifts, dumpers, hand pallet trucks, and so on. The impact loads may threaten the structural integrity of the shelving system. The present structural problem is highly non-linear, due to the simultaneous presence of the following nonlinearities: material non-linearity (plasticity in this case), geometrical non-linearity (large displacements) and contact-type boundary conditions (between the rigid body and the protection system). A total of forty eight different FEM models are built varying the thickness of the steel plate (4, 5 and 6 mm), the impact height (0.1, 0.2, 0.3 and 0.4 meters) and the impact direction (head-on collision and side impact). Once the models are solved, the stress distribution, the overall displacements and the absorbed impact energy were calculated. In order to determine the best shelving protection's candidate, some constraints must be taken into account: the maximum allowable stress (235 MPa), the maximum displacement (0.05 m) and the absorbed impact energy (400 J according to the European Standard Rule PREN-15512). Finally, the most important results are shown and conclusions of this study are exposed.
Reservoir computing and extreme learning machines for non-linear time-series data analysis.
Butcher, J B; Verstraeten, D; Schrauwen, B; Day, C R; Haycock, P W
2013-02-01
Random projection architectures such as Echo state networks (ESNs) and Extreme Learning Machines (ELMs) use a network containing a randomly connected hidden layer and train only the output weights, overcoming the problems associated with the complex and computationally demanding training algorithms traditionally used to train neural networks, particularly recurrent neural networks. In this study an ESN is shown to contain an antagonistic trade-off between the amount of non-linear mapping and short-term memory it can exhibit when applied to time-series data which are highly non-linear. To overcome this trade-off a new architecture, Reservoir with Random Static Projections (R(2)SP) is investigated, that is shown to offer a significant improvement in performance. A similar approach using an ELM whose input is presented through a time delay (TD-ELM) is shown to further enhance performance where it significantly outperformed the ESN and R(2)SP as well other architectures when applied to a novel task which allows the short-term memory and non-linearity to be varied. The hard-limiting memory of the TD-ELM appears to be best suited for the data investigated in this study, although ESN-based approaches may offer improved performance when processing data which require a longer fading memory.
Effects of Kerr strong gravity on quasar x-ray microlensing
Chen, Bin; Dai, Xinyu; Baron, E.; Kantowski, R.
2013-06-01
Recent quasar microlensing observations have constrained the sizes of X-ray emission regions to be within about 10 gravitational radii of the central supermassive black hole. Therefore, the X-ray emission from lensed quasars is first strongly lensed by the black hole before it is lensed by the foreground galaxy and star fields. We present a scheme that combines the initial strong lensing of a Kerr black hole with standard linearized microlensing by intervening stars. We find that X-ray microlensed light curves incorporating Kerr strong gravity can differ significantly from standard curves. The amplitude of the fluctuations in the light curves can increase or decrease by ∼0.65-0.75 mag by including Kerr strong gravity. Larger inclination angles give larger amplitude fluctuations in the microlensing light curves. Consequently, current X-ray microlensing observations can under or overestimate the sizes of the X-ray emission regions. We estimate this bias using a simple metric based on the amplitude of magnitude fluctuations. The half-light radius of the X-ray emission region can be underestimated by up to ∼50% or overestimated by up to ∼20% depending on the spin of the black hole, the emission profile, and the inclination angle of the observer. Underestimates were found in most situations we investigated. The only exception was for a disk with large spin and a radially flat emission profile, observed nearly face-on. We thus conclude that more accurate microlensing size constraints should be obtainable by including Kerr lensing. We also find that the caustic crossing time can differ by months when Kerr strong gravity is included. A simultaneous monitoring of gravitational lensed quasars in both X-ray and optical bands with densely sampled X-ray light curves should reveal this feature. We conclude that it should be possible to constrain important parameters such as inclination angles and black hole spins from combined Kerr and microlensing effects.
NASA Astrophysics Data System (ADS)
Puķīte, Jānis; Wagner, Thomas
2016-05-01
We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on
de la Cruz, Rolando; Fuentes, Claudio; Meza, Cristian; Núñez-Antón, Vicente
2016-07-08
Consider longitudinal observations across different subjects such that the underlying distribution is determined by a non-linear mixed-effects model. In this context, we look at the misclassification error rate for allocating future subjects using cross-validation, bootstrap algorithms (parametric bootstrap, leave-one-out, .632 and [Formula: see text]), and bootstrap cross-validation (which combines the first two approaches), and conduct a numerical study to compare the performance of the different methods. The simulation and comparisons in this study are motivated by real observations from a pregnancy study in which one of the main objectives is to predict normal versus abnormal pregnancy outcomes based on information gathered at early stages. Since in this type of studies it is not uncommon to have insufficient data to simultaneously solve the classification problem and estimate the misclassification error rate, we put special attention to situations when only a small sample size is available. We discuss how the misclassification error rate estimates may be affected by the sample size in terms of variability and bias, and examine conditions under which the misclassification error rate estimates perform reasonably well.
Ma, Rongfei
2015-01-01
In this paper, ammonia quantitative analysis based on miniaturized Al ionization gas sensor and non-linear bistable dynamic model was proposed. Al plate anodic gas-ionization sensor was used to obtain the current-voltage (I-V) data. Measurement data was processed by non-linear bistable dynamics model. Results showed that the proposed method quantitatively determined ammonia concentrations. PMID:25975362
NASA Astrophysics Data System (ADS)
Wang, Gang; Wang, Chaoli; Du, Qinghui; Cai, Xuan
2016-10-01
In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.
Kerr black holes with scalar hair.
Herdeiro, Carlos A R; Radu, Eugen
2014-06-06
We present a family of solutions of Einstein's gravity minimally coupled to a complex, massive scalar field, describing asymptotically flat, spinning black holes with scalar hair and a regular horizon. These hairy black holes (HBHs) are supported by rotation and have no static limit. Besides mass M and angular momentum J, they carry a conserved, continuous Noether charge Q measuring the scalar hair. HBHs branch off from the Kerr metric at the threshold of the superradiant instability and reduce to spinning boson stars in the limit of vanishing horizon area. They overlap with Kerr black holes for a set of (M, J) values. A single Killing vector field preserves the solutions, tangent to the null geodesic generators of the event horizon. HBHs can exhibit sharp physical differences when compared to the Kerr solution, such as J/M^{2}>1, a quadrupole moment larger than J^{2}/M, and a larger orbital angular velocity at the innermost stable circular orbit. Families of HBHs connected to the Kerr geometry should exist in scalar (and other) models with more general self-interactions.
Caring about Teachers. Response to Donna Kerr.
ERIC Educational Resources Information Center
Sykes, Gary
1983-01-01
In discussing Donna Kerr's recommendations for improving teaching through better preservice training (Teachers College Record, Spring 1983), Sykes points out the need to enhance the quality of a teacher's work life in the schools as a requisite for reform. Specific changes at the school level are suggested. (PP)
Universal scaling laws of Kerr frequency combs.
Coen, Stéphane; Erkintalo, Miro
2013-06-01
Using the known solutions of the Lugiato-Lefever equation, we derive universal trends of Kerr frequency combs. In particular, normalized properties of temporal cavity soliton solutions lead us to a simple analytic estimate of the maximum attainable bandwidth for given pump resonator parameters. The result is validated via comparison with past experiments encompassing a diverse range of resonator configurations and parameters.
SLIM DISKS AROUND KERR BLACK HOLES REVISITED
Sadowski, Aleksander
2009-08-01
We investigate stationary slim accretion disks around Kerr black holes. We construct a new numerical method based on the relaxation technique. We systematically cover the whole parameter space relevant to stellar mass X-ray binaries. We also notice some non-monotonic features in the disk structure, overlooked in previous studies.
Robert S. Kerr Environmental Research Center
The Kerr Center, situated on 16 acres three miles south of Ada, Oklahoma, houses the Ground Water and Ecosystems Restoration Division (GWERD) of the National Risk Management Research Laboratory (NRMRL). The division develops strategies and technologies to protect and restore grou...
Physical Properties of the Double Kerr Solution
NASA Astrophysics Data System (ADS)
Herdeiro, Carlos A. R.; Rebelo, Carmen
We consider two special cases, dubbed counter-rotating and co-rotating of the double-Kerr solution, in four spacetime dimensions. We discuss how various physical properties of the black holes vary as the distance between them varies, namely: the horizon angular velocity and extremality condition, the horizon and ergo-surface geometry.
Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series
NASA Technical Reports Server (NTRS)
Gnoffo, Peter A.
2015-01-01
Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.
Non-linear analyses of heart rate variability during heavy exercise and recovery in cyclists.
Casties, J-F; Mottet, D; Le Gallais, D
2006-10-01
We investigated the time course of RR interval variability during exercise and subsequent 50 minutes of recovery in seven well-trained male cyclists who performed an exercise with 3 successive 8 min stages at 40 %, 70 % and 90 % of their maximal oxygen uptake. The goal of the study was to check whether the decrease in the amplitude of heart rate variability during heavy exercise was accompanied by changes in the chaotic structure of the fluctuations. Heart rate variability was analysed in the temporal and frequency domain using traditional tools and using non-linear methods (Largest Lyapunov Exponent, Detrended Fluctuation Analysis, Minimum Embedding Dimension). When compared to rest, variability at the heaviest exercise intensity was significantly lower (RR: 0.94 +/- 0.22 vs. 0.34 +/- 0.01 ms; SDRR: 0.11 +/- 0.04 vs. 0.01 +/- 0.00 ms) due to a decrease in both LF (2101 +/- 1450 vs. 0.14 +/- 0.09 ms (2) . Hz (-1)) and HF spectral energy (1148 +/- 1126 vs. 7.88 +/- 9.24 ms (2) . Hz (-1)). Non-linear analyses showed that heart rate variability remained chaotic whatever the exercise intensity (the largest Lyapunov exponent was positive at 90 % of the maximal oxygen uptake), with a fractal organisation that tended towards white noise (DFA value close to 0.5) during heavy exercise. During recovery, temporal and spectral variables came back to their rest values within about 30 minutes following an exponential pattern. Non-linear analyses revealed that heartbeat dynamics were disorganised at the beginning of recovery, and involved more regulating systems than at rest, even after 50 minutes of recovery. We concluded that, during heavy exercise, heart rate variability was mainly influenced by other factors than autonomous nervous system, and suggest that mechanical or neurological couplings between the cardiac, locomotor and respiratory systems could play an important part in the observed changes.
Extracting a common pulse like signal from Time Serie using a non linear Kalman Filter
NASA Astrophysics Data System (ADS)
Gazeaux, J.; Batista, D.; Ammann, C.; Naveau, P.; Jégat, C.; Gao, C.
2009-04-01
To understand the nature and cause of natural climate variability, it is important to attribute past climate variations to particular forcing factors. In this work, our main focus is to introduce an automatic assimilation procedure to estimate the magnitude of strong but short-lived perturbations, such as large explosive volcanic eruptions, using climate/proxies time series. The extraction and decomposition procedure is run on real multivariate time series of sulfate from ice cores drilled at different sites in Greenland. The sulfate ejected by volcanoes is transported through the stratosphere towards the poles and deposited via sedimentation near the pole. Sulfate in Greenland is then a marker of huge volcanic eruptions which occur all over the world. Such pulse-like processes are highly non linear, as much in time as for their intensity. If they are not detected, such pulse-like signals of extreme and rare events can perturb an objective calculation of the trend. This work is then as much an estimation procedure for such signals, as a first step to estimate a posteriori trend in the time series. Our extraction algorithm handles multivariate time series with a common but unknown forcing. This statistical procedure is based on a multivariate multi-state space model and a non linear Kalman Filter. The non linearity is solved using the calculation of a twice conditional expectation and variance. It can provide an accurate estimate of the timing and duration of individual pulse-like events from a set of different series covering the same temporal space. It not only allows for a more objective estimation of its associated peak amplitude and the subsequent time evolution of the signal, but at the same time it provides a measure of confidence through the posterior probability for each pulse-like event. The flexibility, robustness and limitations of our approach are discussed by applying our method to simulated time series and to the Monte-Carlo method to test the
Towards a non-linear theory for fluid pressure and osmosis in shales
NASA Astrophysics Data System (ADS)
Droghei, Riccardo; Salusti, Ettore
2015-04-01
In exploiting deep hydrocarbon reservoirs, often injections of fluid and/or solute are used. To control and avoid troubles as fluid and gas unexpected diffusions, a reservoir characterization can be obtained also from observations of space and time evolution of micro-earthquake clouds resulting from such injections. This is important since several among the processes caused by fluid injections can modify the deep matrix. Information about the evolution of such micro-seismicity clouds therefore plays a realistic role in the reservoir analyses. To reach a better insight about such processes, and obtain a better system control, we here analyze the initial stress necessary to originate strong non linear transients of combined fluid pressure and solute density (osmosis) in a porous matrix. All this can indeed perturb in a mild (i.e. a linear diffusion) or dramatic non linear way the rock structure, till inducing rock deformations, micro-earthquakes or fractures. I more detail we here assume first a linear Hooke law relating strain, stress, solute density and fluid pressure, and analyze their effect in the porous rock dynamics. Then we analyze its generalization, i.e. the further non linear effect of a stronger external pressure, also in presence of a trend of pressure or solute in the whole region. We moreover characterize the zones where a sudden arrival of such a front can cause micro-earthquakes or fractures. All this allows to reach a novel, more realistic insight about the control of rock evolution in presence of strong pressure fronts. We thus obtain a more efficient reservoir control to avoid large geological perturbations. It is of interest that our results are very similar to those found by Shapiro et al.(2013) with a different approach.
Analysis of non linear partially standing waves from 3D velocity measurements
NASA Astrophysics Data System (ADS)
Drevard, D.; Rey, V.; Svendsen, Ib; Fraunie, P.
2003-04-01
Surface gravity waves in the ocean exhibit an energy spectrum distributed in both frequency and direction of propagation. Wave data collection is of great importance in coastal zones for engineering and scientific studies. In particular, partially standing waves measurements near coastal structures and steep or barred beaches may be a requirement, for instance for morphodynamic studies. The aim of the present study is the analysis of partially standing surface waves icluding non-linear effects. According to 1st order Stokes theory, synchronous measurements of horizontal and vertical velocity components allow calculation of rate of standing waves (Drevard et al, 2003). In the present study, it is demonstrated that for deep water conditions, partially standing 2nd order Stokes waves induced velocity field is still represented by the 1st order solution for the velocity potential contrary to the surface elevation which exhibits harmonic components. For intermediate water depth, harmonic components appear not only in the surface elevation but also in the velocity fields, but their weight remains much smaller, because of the vertical decreasing wave induced motion. For irregular waves, the influence of the spectrum width on the non-linear effects in the analysis is discussed. Keywords: Wave measurements ; reflection ; non-linear effects Acknowledgements: This work was initiated during the stay of Prof. Ib Svendsen, as invited Professor, at LSEET in autumn 2002. This study is carried out in the framework of the Scientific French National Programmes PNEC ART7 and PATOM. Their financial supports are acknowledged References: Drevard, D., Meuret, A., Rey, V. Piazzola, J. And Dolle, A.. (2002). "Partially reflected waves measurements using Acoustic Doppler Velocimeter (ADV)", Submitted to ISOPE 03, Honolulu, Hawaii, May 2003.
Scarneciu, Camelia C.; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D.; Varciu, Mihai S.; Andreescu, Oana; Scarneciu, Ioan
2017-01-01
Objectives: This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. Methods: The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). Results: From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. Conclusions: The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is
Dependence of the non-linear mass power spectrum on the equationof state of dark energy
NASA Astrophysics Data System (ADS)
McDonald, Patrick; Trac, Hy; Contaldi, Carlo
2006-02-01
We present N-body simulation calculations of the dependence of the power spectrum of non-linear cosmological mass density fluctuations on the equation of state of the dark energy, w=p/ρ. At fixed linear theory power, increasing w leads to an increase in non-linear power, with the effect increasing with k. By k= 10hMpc-1, a model with w=-0.75 has ~12 per cent more power than a standard cosmological constant model (w=-1), while a model with w=-0.5 has ~33 per cent extra power (at z= 0). The size of the effect increases with increasing dark energy fraction, and to a lesser extent increasing power spectrum normalization, but is insensitive to the power spectrum shape (the numbers above are for Ωm= 0.281 and σ8= 0.897). A code quantifying the non-linear effect of varying w, as a function of k, z and other cosmological parameters, which should be accurate to a few per cent for k<~ 10hMpc-1 for models that fit the current observations, is available at http://www.cita.utoronto.ca/~pmcdonal/code.html. This paper also serves as an example of a detailed exploration of the numerical convergence properties of ratios of power spectra for different models, which can be useful because some kinds of numerical error cancel in a ratio. When precision calculations based on numerical simulations are needed for many different models, efficiency may be gained by breaking the problem into a calculation of the absolute prediction at a central point, and calculations of the relative change in the prediction with model parameters.
Kerr black holes with Proca hair
NASA Astrophysics Data System (ADS)
Herdeiro, Carlos; Radu, Eugen; Rúnarsson, Helgi
2016-08-01
Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we show this model admits asymptotically flat, stationary, axi-symmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in [1, 2], that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the nonlinear level. We confirm this expectation and explicitly construct examples of such Kerr BHs with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families with three continuous parameters (ADM mass, ADM angular momentum and Noether charge). They branch off from the Kerr solutions that can support stationary Proca clouds and reduce to Proca stars [3] when the horizon size vanishes. We present the domain of existence of one family of KBHsPH, as well as its phase space in terms of ADM quantities. Some physical properties of the solutions are discussed; in particular, and in contrast with Kerr BHs with scalar hair, some spacetime regions can be counter-rotating with respect to the horizon. We further establish a no-Proca-hair theorem for static, spherically symmetric BHs but allowing the complex Proca field to have a harmonic time dependence, which shows BHs with Proca hair in this model require rotation and have no static limit. KBHsPH are also disconnected from Kerr-Newman BHs with a real, massless vector field.
Linear and non-linear interdependence of EEG and HRV frequency bands in human sleep.
Chaparro-Vargas, Ramiro; Dissanayaka, P Chamila; Patti, Chanakya Reddy; Schilling, Claudia; Schredl, Michael; Cvetkovic, Dean
2014-01-01
The characterisation of functional interdependencies of the autonomic nervous system (ANS) stands an evergrowing interest to unveil electroencephalographic (EEG) and Heart Rate Variability (HRV) interactions. This paper presents a biosignal processing approach as a supportive computational resource in the estimation of sleep dynamics. The application of linear, non-linear methods and statistical tests upon 10 overnight polysomnographic (PSG) recordings, allowed the computation of wavelet coherence and phase locking values, in order to identify discerning features amongst the clinical healthy subjects. Our findings showed that neuronal oscillations θ, α and σ interact with cardiac power bands at mid-to-high rank of coherence and phase locking, particularly during NREM sleep stages.
Experimental characterization and modeling of non-linear coupling of the LHCD power on Tore Supra
Preynas, M.; Goniche, M.; Hillairet, J.; Litaudon, X.; Ekedahl, A.
2014-02-12
To achieve steady state operation on future tokamaks, in particular on ITER, the unique capability of a LHCD system to efficiently drive off-axis non-inductive current is needed. In this context, it is of prime importance to study and master the coupling of LH wave to the core plasma at high power density (tens of MW/m{sup 2}). In some specific conditions, deleterious effects on the LHCD coupling are sometimes observed on Tore Supra. At high power the waves may modify the edge parameters that change the wave coupling properties in a non-linear manner. In this way, dedicated LHCD experiments have been performed using the LHCD system of Tore Supra, composed of two different conceptual designs of launcher: the Fully Active Multijunction (FAM) and the new Passive Active Multijunction (PAM) antennas. A nonlinear interaction between the electron density and the electric field has been characterized in a thin plasma layer in front of the two LHCD antennas. The resulting dependence of the power reflection coefficient with the LHCD power, leading occasionally to trips in the output power, is not predicted by the standard linear theory of the LH wave coupling. Therefore, it is important to investigate and understand the possible origin of such non-linear effects in order to avoid their possible deleterious consequences. The PICCOLO-2D code, which self-consistently treats the wave propagation in the antenna vicinity and its interaction with the local edge plasma density, is used to simulate Tore Supra discharges. The simulation reproduces very well the occurrence of a non-linear behavior in the coupling observed in the LHCD experiments. The important differences and trends between the FAM and the PAM antennas, especially a larger increase in RC for the FAM, are also reproduced by the PICCOLO-2D simulation. The working hypothesis of the contribution of the ponderomotive effect in the non-linear observations of LHCD coupling is therefore validated through this comprehensive
Tidal propagation and its non-linear characteristics in the Head Bay of Bengal
NASA Astrophysics Data System (ADS)
Rose, Linta; Bhaskaran, Prasad K.
2017-03-01
The Head Bay of Bengal is highly vulnerable to flooding events caused due to monsoons, cyclones and sea-level rise, owing to its funnel-like shape, high tidal range, presence of numerous river drainage systems, low-lying topography, and shallow bathymetry. Tides dominate the hydrodynamic behaviour and coastal processes in this region and its propagation is quite distinct. The present study uses ADCIRC hydrodynamic model customized for the Head Bay of Bengal, discretized using unstructured finite elements and validated against limited available observations in this data sparse region. The water-level elevations derived from ADCIRC simulation was used to understand the pattern of non-linear tidal propagation with respect to complex coastal geomorphology prevalent in this region. The study finds a marginal amplification of diurnal tide, nearly double amplification of semi-diurnal components, and existence of a degenerate amphidromic point near Meghna delta consistent with previous studies. The spatial and temporal variability of tidal spectral components were examined by applying the techniques of wavelet, harmonic, and time-series analysis at various locations. Maximum amplification of tides occurs at the head of the bay, along a zone enclosing the mouth of tidal inlets; and for regions northward, the tides decay with progressively increasing phase lags. The study signifies dominance of a forced fortnightly tide and tidal asymmetry leading to flood-dominance in the rivers Hooghly, Meghna, and Tetulia. The non-linear properties of tides have been elucidated, and their origin and spatio-temporal variability in these riverine systems were further investigated. Shallow depth and sharp depth gradients were discerned to be the important conditions for the origin of non-linear components. It has been deduced that non-linear tides are generated in regions where propagating tides are accumulated, and amplified in regions where they are funneled. A study of tidal energetics
Scaling effects in a non-linear electromagnetic energy harvester for wearable sensors
NASA Astrophysics Data System (ADS)
Geisler, M.; Boisseau, S.; Perez, M.; Ait-Ali, I.; Perraud, S.
2016-11-01
In the field of inertial energy harvesters targeting human mechanical energy, the ergonomics of the solutions impose to find the best compromise between dimensions reduction and electrical performance. In this paper, we study the properties of a non-linear electromagnetic generator at different scales, by performing simulations based on an experimentally validated model and real human acceleration recordings. The results display that the output power of the structure is roughly proportional to its scaling factor raised to the power of five, which indicates that this system is more relevant at lengths over a few centimetres.
NASA Astrophysics Data System (ADS)
Rudin, Sergey; Rupper, Greg
2012-02-01
The non-linear electron plasma response to electromagnetic signal applied to a gated graphene conduction channel can be used to make a graphene based Dyakonov-Shur terahertz detector. The hydrodynamic model predicts a resonance response to electromagnetic radiation at the plasma oscillation frequency. With less damping and higher mobility, the graphene conduction channels may provide higher quality plasma response than possible with semiconductor channels. Our analysis of plasma oscillations in a graphene channel is based on the hydrodynamic equations which we derive from the Boltzmann equation accounting for both electrons and holes, and including the effects of viscosity and finite mobility.
NASA Astrophysics Data System (ADS)
Rozite, L.; Joffe, R.; Varna, J.; Nyström, B.
2012-02-01
The behaviour of highly non-linear cellulosic fibers and their composite is characterized. Micro-mechanisms occurring in these materials are identified. Mechanical properties of regenerated cellulose fibers and composites are obtained using simple tensile test. Material visco-plastic and visco-elastic properties are analyzed using creep tests. Two bio-based resins are used in this study - Tribest and EpoBioX. The glass and flax fiber composites are used as reference materials to compare with Cordenka fiber laminates.
Dynamics of heavy impurities in non-linear MHD simulations of sawtoothing tokamak plasmas
NASA Astrophysics Data System (ADS)
Ahn, Jae-H.; Garbet, X.; Lütjens, H.; Guirlet, R.
2016-12-01
The effect of sawteeth on impurity dynamics is studied with the XTOR-2F code. Non-linear full 3D MHD simulations including appropriate fluid equations for impurities in the high collisional regime show that the presence of regular sawtooth crashes affects the impurity behaviour. A spatial non-uniformity of 5 % in post-crash impurity density profiles persists due to 2D structures of impurity density which appear during sawtooth crashes. They are shown to be mainly driven by the \\mathbf{E}× \\mathbf{B} velocity, and are responsible for the sudden impurity transport in the core plasmas.
Describing Adequacy of cure with maximum hardness ratios and non-linear regression.
Bouschlicher, Murray; Berning, Kristen; Qian, Fang
2008-01-01
Knoop Hardness (KH) ratios (HR) > or = 80% are commonly used as criteria for the adequate cure of a composite. These per-specimen HRs can be misleading, as both numerator and denominator may increase concurrently, prior to reaching an asymptotic, top-surface maximum hardness value (H(MAX)). Extended cure times were used to establish H(MAX) and descriptive statistics, and non-linear regression analysis were used to describe the relationship between exposure duration and HR and predict the time required for HR-H(MAX) = 80%. Composite samples 2.00 x 5.00 mm diameter (n = 5/grp) were cured for 10 seconds, 20 seconds, 40 seconds, 60 seconds, 90 seconds, 120 seconds, 180 seconds and 240 seconds in a 2-composite x 2-light curing unit design. A microhybrid (Point 4, P4) or microfill resin (Heliomolar, HM) composite was cured with a QTH or LED light curing unit and then stored in the dark for 24 hours prior to KH testing. Non-linear regression was calculated with: H = (H(MAX)-c)(1-e(-kt)) +c, H(MAX) = maximum hardness (a theoretical asymptotic value), c = constant (t = 0), k = rate constant and t = exposure duration describes the relationship between radiant exposure (irradiance x time) and HRs. Exposure durations for HR-H(MAX) = 80% were calculated. Two-sample t-tests for pairwise comparisons evaluated relative performance of the light curing units for similar surface x composite x exposure (10-90s). A good measure of goodness-of-fit of the non-linear regression, r2, ranged from 0.68-0.95. (mean = 0.82). Microhybrid (P4) exposure to achieve HR-H(MAX = 80% was 21 seconds for QTH and 34 seconds for the LED light curing unit. Corresponding values for microfill (HM) were 71 and 74 seconds, respectively. P4 HR-H(MAX) of LED vs QTH was statistically similar for 10 to 40 seconds, while HM HR-H(MAX) of LED was significantly lower than QTH for 10 to 40 seconds. It was concluded that redefined hardness ratios based on maximum hardness used in conjunction with non-linear regression
A process fault estimation strategy for non-linear dynamic systems
NASA Astrophysics Data System (ADS)
Pazera, Marcin; Korbicz, Józef
2017-01-01
The paper deals with the problem of simultaneous state and process fault estimation for non-linear dynamic systems. Instead of estimating the fault directly, its product with state and the state itself are estimated. To derive the fault from the product, a simple algebraic approach is proposed. The estimation strategy is based on the quadratic boundedness approach. The final part of the paper presents an illustrative example concerning a laboratory multi-tank system. The real data experiments clearly exhibit the performance of the proposed approach.
Non-linear dielectric effect in the isotropic phase above the isotropic-cholesteric phase transition
NASA Astrophysics Data System (ADS)
Mukherjee, Prabir K.; Chakraborty, Sumanta; Rzoska, Sylwester J.
2011-11-01
Using the Landau-de Gennes theory, the temperature, pressure and frequency dependence of the non-linear effect in the isotropic phase above the isotropic-cholesteric phase transition is calculated. The influence of pressure on the isotropic-cholesteric phase transition is discussed by varying the coupling between the orientational order parameter and the macroscopic polarization of polar cholesterics. Comparing the results of the calculations with existing data, we finally conclude that the model provides a description of the isotropic-cholesteric transition that takes all experimentally known features of the unusual negative and positive pretransitional effect in the isotropic phase of the system into account in a qualitatively correct way.
Hamiltonian Lattice Studies of Pionic Collective Excitations in the Non-linear Sigma Model
NASA Astrophysics Data System (ADS)
Chin, Siu A.
2001-04-01
The latticization of the non-linear sigma model reduces a chiral meson field theory to an O(4) spin system with quantum fluctuations. By solving the resulting lattice Hamiltonian by Monte Carlo methods, the dynamics and thermodynamics of pions can be determined non-perturbatively. In particular, the mas gap of pionic collective excitations with quantum number of vector mesons can be determined as the chiral phase transition is approached. Results based on a newly discovered 4th order method of solving for the ground state of a quantum many-body Hamitonian will be presented.
A non-linear mathematical model for a three species ecosystem: Hippos in Lake Edward.
Bologna, Mauro; Chandía, Kristopher J; Flores, J C
2016-01-21
In this work we study a non-linear mathematical model based on three different interacting species. We apply our model to Lake Edward ecosystem consisting in hippos, tilapia fishes and human inhabitants. In this case, we estimate the values of the key parameters using actual data and show the reliability of the proposed model as a predictive tool. We also show, via numerical calculations and parameter values that the ecosystem associated to the lake is very far from reaching a stable equilibrium. Through our analysis we provide the conditions for a possible coexistence among the three species.
Non-linear control of the ''clam'' wave energy device. Final report
Not Available
1983-09-01
A promising wave energy device being currently investigated is the ''clam'' device. The clam extracts energy by pumping air through a specially designed (Wells) turbine. Although operation of the Wells turbine does not require a rectified air flow, some additional control will be necessary to optimize the phase of the clam motion for good efficiencies. An examination of the equation of motion in the time domain suggests the possibility of non-linear phase control by mechanical, power take-off, or pneumatic latching. Latching can be shown to increase the efficiency of the device in the longer wavelengths of the wave spectrum, i.e. those of high incident wave power.
Simulating the effect of non-linear mode coupling in cosmological parameter estimation
NASA Astrophysics Data System (ADS)
Kiessling, A.; Taylor, A. N.; Heavens, A. F.
2011-09-01
Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment and to optimize the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimization it is usually assumed that the power-spectrum covariance matrix is diagonal in Fourier space. However, in the low-redshift Universe, non-linear mode coupling will tend to correlate small-scale power, moving information from lower to higher order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naïve Gaussian Fisher matrix forecasts with a maximum likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2D and tomographic shear analysis of a Euclid-like survey. In both cases, we find that the 68 per cent confidence area of the Ωm-σ8 plane increases by a factor of 5. However, the marginal errors increase by just 20-40 per cent. We propose a new method to model the effects of non-linear shear-power mode coupling in the Fisher matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68 per cent confidence regions of the full maximum likelihood analysis in the Ωm-σ8 plane to high accuracy for both 2D and tomographic weak lensing surveys. Finally, we perform a multiparameter analysis of Ωm, σ8, h, ns, w0 and wa to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The 6D volume of the 1σ error contours for the non-linear Fisher analysis is a factor of 3 larger than for the Gaussian case, and the shape of the 68 per cent confidence
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
NASA Astrophysics Data System (ADS)
Tokluoglu, Erinc K.
Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged
Higgs physics beyond the SM: The non-linear EFT approach
NASA Astrophysics Data System (ADS)
Brivio, I.
2016-07-01
Depending on whether electroweak physics beyond the Standard Model is based on a linear or on a non-linear implementation of the electroweak symmetry breaking, a linear or a chiral Effective Lagrangian is more appropriate. In this talk, the main low-energy signals that allow to recognize whether the observed Higgs scalar is a dynamical (composite) particle or rather an elementary one are presented, in a model-independent way. The patterns of effective couplings produced upon the assumption of specific composite Higgs models are also discussed.=1
Application of non-linear dynamics to the characterization of cardiac electrical instability
NASA Technical Reports Server (NTRS)
Kaplan, D. T.; Cohen, R. J.
1987-01-01
Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.
Investigating Mesoscopic Non-linear Series Circuit with the Coherent Thermo State Representation
NASA Astrophysics Data System (ADS)
Wang, Xiu-Xia
2017-03-01
For the first time we considered the quantum effects of mesoscopic non-linear series circuit with the coherent thermo state representation | τ rangle . After introducing the representation |τ rangle , we derived the expression of the density matrix ρ and find that | ρ rangle T presents Gauss type with the representation | τ rangle . In addition, we derived the Wigner function and calculated the quantum fluctuation in the thermo vacuum state |0( β)>. It is shown that the circuit has the zero current fluctuation because the diode has the reverse saturation current, and the temperature affects the Wigner function of the circuit in thermo vacuum state deeply.
A computerized implementation of a non-linear equation to predict barrier shielding requirements.
Chamberlain, A C; Strydom, W J
1997-04-01
A non-linear equation to predict barrier shielding thickness from the work function of x- and gamma-ray generators is presented. This equation is incorporated into a model that takes into account primary, scatter, and leakage radiation components to determine the amount of shielding necessary. The case of multiple wall materials is also considered. The equation accurately models the radiation attenuation curves given in NCRP 49 for concrete and lead, thus eliminating the necessity to use graphical or tabular methods to calculate shielding thickness, which can be inaccurate.
On psychoanalysis and non-linear dynamics: the paradigm of bifurcation.
Priel, B; Schreiber, G
1994-09-01
Some of Freud's main theoretical conceptualizations drew on metaphors from 19th century physics. However, though the physics of Freud's era was based on deterministic Newtonian mechanics and equilibrium thermodynamics, his descriptions of the dynamics of instincts, therapeutic change, and even transference, were far beyond this model. Freud's dynamic description of psychic development evokes contemporary theories of irreversible, far-from-equilibrium thermodynamics and non-linear dynamics. The present paper focuses on bifurcation theory, which offers a paradigm for the investigation of unpredictable but deterministic phenomena; this paradigm sheds a retroactive light on the classical psychoanalytical conceptualizations of complemental series, repetition compulsion, transference and cure.
Annular pupil filter under shot-noise condition for linear and non linear microscopy.
Ronzitti, Emiliano; Vicidomini, Giuseppe; Caorsi, Valentina; Diaspro, Alberto
2009-04-13
The imaging performances of multiphoton excitation and confocal laser scanning microscopy are herby considered: in typical experimental imaging conditions, a small finite amount of photon reaches the detector giving shot-noise fluctuations which affects the signal acquired. A significant detriment in the high frequencies transmission capability is obtained. In order to partially recover the high frequencies information lost, the insertion of a pupil plane filter in the microscope illumination light pathway on the objective lens is proposed. We demonstrate high-frequency and resolution enhancement in the case of linear and non linear fluorescence microscope approach under shot-noise condition.
Intelligent control of non-linear dynamical system based on the adaptive neurocontroller
NASA Astrophysics Data System (ADS)
Engel, E.; Kovalev, I. V.; Kobezhicov, V.
2015-10-01
This paper presents an adaptive neuro-controller for intelligent control of non-linear dynamical system. The formed as the fuzzy selective neural net the adaptive neuro-controller on the base of system's state, creates the effective control signal under random perturbations. The validity and advantages of the proposed adaptive neuro-controller are demonstrated by numerical simulations. The simulation results show that the proposed controller scheme achieves real-time control speed and the competitive performance, as compared to PID, fuzzy logic controllers.
NASA Astrophysics Data System (ADS)
Ruiz Pérez, Guiomar; Medici, Chiara; Latron, Jérôme; Llorens, Pilar; Gallart, Francesc; Francés, Félix
2013-04-01
It is well known that Mediterranean catchments are characterized by a complex hydrological behavior and strong non-linearities (Ye et al., 1998, Piñol et al., 1999). Therefore, modeling hydrology of a small Mediterranean catchment still represents a great challenge for modelers. To this end, the practical superiority of distributed or semi-distributed approaches over lumped ones remains an open question (see e.g. Loague and Freeze, 1985; Michaud and Sorooshian, 1994; Refsgaard and Knudsen, 1996; Loumagne et al., 1999; Zhang et al., 2003). In fact, a variety of earlier studies have inter-compared distributed versus lumped model simulations reaching opposite conclusions. With the present work, we tried to answer the following research question: Are observed non-linearities due to spatial heterogeneity or to non-linear mechanisms that should be taken into account in a model conceptual scheme? To address these issues the hydrological modeling of the Can Vila catchment (Vallcebre, Eastern Pyrenees, Spain) was carried out. Three hydrological models were considered: two lumped models called LU3 and LU4 (Medici et al., 2008), and a fully distributed model called TETIS (Francés et al., 2007). The TETIS model has the same conceptual schema as the LU3 model at cell-scale and the LU4 model's structure is based on the LU3 model, but it splits the aquifer storage in two tanks: shallow aquifer and deep aquifer. Percolation to the deep aquifer occurs only when soil water content exceeds a threshold value. So, the difference between the LU3 model and the TETIS model is the incorporation of the spatial heterogeneity and the difference between the LU3 model and the LU4 model is an additional strong non-linearity with the threshold which actives the deep percolation. The graphical comparison with the observations and the goodness of fit indexes employed showed that: (1) the LU3 model could not reproduce reasonably well the wet and dry period with the same set of parameters while (2
NASA Astrophysics Data System (ADS)
Li, Wangnan; Cai, Hongneng; Li, Chao
2014-11-01
This paper deals with the characterization of the strength of the constituents of carbon fiber reinforced plastic laminate (CFRP), and a prediction of the static compressive strength of open-hole structure of polymer composites. The approach combined with non-linear analysis in macro-level and a linear elastic micromechanical failure analysis in microlevel (non-linear MMF) is proposed to improve the prediction accuracy. A face-centered cubic micromechanics model is constructed to analyze the stresses in fiber and matrix in microlevel. Non-interactive failure criteria are proposed to characterize the strength of fiber and matrix. The non-linear shear behavior of the laminate is studied experimentally, and a novel approach of cubic spline interpolation is used to capture significant non-linear shear behavior of laminate. The user-defined material subroutine UMAT for the non-linear share behavior is developed and combined in the mechanics analysis in the macro-level using the Abaqus Python codes. The failure mechanism and static strength of open-hole compressive (OHC) structure of polymer composites is studied based on non-linear MMF. The UTS50/E51 CFRP is used to demonstrate the application of theory of non-linear MMF.
Loizou, Philipos C.; Ma, Jianfen
2011-01-01
The conventional articulation index (AI) measure cannot be applied in situations where non-linear operations are involved and additive noise is present. This is because the definitions of the target and masker signals become vague following non-linear processing, as both the target and masker signals are affected. The aim of the present work is to modify the basic form of the AI measure to account for non-linear processing. This was done using a new definition of the output or effective SNR obtained following non-linear processing. The proposed output SNR definition for a specific band was designed to handle cases where the non-linear processing affects predominantly the target signal rather than the masker signal. The proposed measure also takes into consideration the fact that the input SNR in a specific band cannot be improved following any form of non-linear processing. Overall, the proposed measure quantifies the proportion of input band SNR preserved or transmitted in each band after non-linear processing. High correlation (r = 0.9) was obtained with the proposed measure when evaluated with intelligibility scores obtained by normal-hearing listeners in 72 noisy conditions involving noise-suppressed speech corrupted in four different real-world maskers. PMID:21877811
NASA Astrophysics Data System (ADS)
Ondra, V.; Sever, I. A.; Schwingshackl, C. W.
2017-01-01
This paper presents a method for detection and characterisation of structural non-linearities from a single frequency response function using the Hilbert transform in the frequency domain and artificial neural networks. A frequency response function is described based on its Hilbert transform using several common and newly introduced scalar parameters, termed non-linearity indexes, to create training data of the artificial neural network. This network is subsequently used to detect the existence of non-linearity and classify its type. The theoretical background of the method is given and its usage is demonstrated on different numerical test cases created by single degree of freedom non-linear systems and a lumped parameter multi degree of freedom system with a geometric non-linearity. The method is also applied to several experimentally measured frequency response functions obtained from a cantilever beam with a clearance non-linearity and an under-platform damper experimental rig with a complex friction contact interface. It is shown that the method is a fast and noise-robust means of detecting and characterising non-linear behaviour from a single frequency response function.
On a zero-gravity limit of the Kerr-Newman spacetimes and their electromagnetic fields
NASA Astrophysics Data System (ADS)
Tahvildar-Zadeh, A. Shadi
2015-04-01
We discuss the limit of vanishing G (Newton's constant of universal gravitation) of the maximal analytically extended Kerr-Newman electrovacuum spacetimes represented in Boyer-Lindquist coordinates. We investigate the topologically nontrivial spacetime M 0 emerging in this limit and show that it consists of two copies of flat Minkowski spacetime cross-linked at a timelike solid cylinder (spacelike 2-disk × timelike ℝ). As G → 0, the electromagnetic fields of the Kerr-Newman spacetimes converge to nontrivial solutions of Maxwell's equations on this background spacetime M 0 . We show how to obtain these fields by solving Maxwell's equations with singular sources supported only on a circle in a spacelike slice of M 0 . These sources do not suffer from any of the pathologies that plague the alternate sources found in previous attempts to interpret the Kerr-Newman fields on the topologically simple Minkowski spacetime. We characterize the singular behavior of these sources and prove that the Kerr-Newman electrostatic potential and magnetic scalar potential are the unique solutions of the Maxwell equations among all functions that have the same blow-up behavior at the ring singularity.
Webb-Robertson, Bobbie-Jo M.; Bunn, Amoret L.; Bailey, Vanessa L.
2011-01-01
Phospholipid fatty acids (PLFA) have been widely used to characterize environmental microbial communities, generating community profiles that can distinguish phylogenetic or functional groups within the community. The poor specificity of organism groups with fatty acid biomarkers in the classic PLFA-microorganism associations is a confounding factor in many of the statistical classification/clustering approaches traditionally used to interpret PLFA profiles. In this paper we demonstrate that non-linear statistical learning methods, such as a support vector machine (SVM), can more accurately find patterns related to uranyl nitrate exposure in a freshwater periphyton community than linear methods, such as partial least squares discriminant analysis. In addition, probabilistic models of exposure can be derived from the identified lipid biomarkers to demonstrate the potential model-based approach that could be used in remediation. The SVM probability model separates dose groups at accuracies of ~87.0%, ~71.4%, ~87.5%, and 100% for the four groups; Control (non-amended system), low-dose (amended at 10 µg U L-1), medium dose (amended at 100 µg U L-1), and high dose (500 µg U L-1). The SVM model achieved an overall cross-validated classification accuracy of ~87% in contrast to ~59% for the best linear classifier.
NASA Astrophysics Data System (ADS)
Soares Dos Santos, Marco P.; Ferreira, Jorge A. F.; Simões, José A. O.; Pascoal, Ricardo; Torrão, João; Xue, Xiaozheng; Furlani, Edward P.
2016-01-01
Magnetic levitation has been used to implement low-cost and maintenance-free electromagnetic energy harvesting. The ability of levitation-based harvesting systems to operate autonomously for long periods of time makes them well-suited for self-powering a broad range of technologies. In this paper, a combined theoretical and experimental study is presented of a harvester configuration that utilizes the motion of a levitated hard-magnetic element to generate electrical power. A semi-analytical, non-linear model is introduced that enables accurate and efficient analysis of energy transduction. The model predicts the transient and steady-state response of the harvester a function of its motion (amplitude and frequency) and load impedance. Very good agreement is obtained between simulation and experiment with energy errors lower than 14.15% (mean absolute percentage error of 6.02%) and cross-correlations higher than 86%. The model provides unique insight into fundamental mechanisms of energy transduction and enables the geometric optimization of harvesters prior to fabrication and the rational design of intelligent energy harvesters.
Soares dos Santos, Marco P.; Ferreira, Jorge A. F.; Simões, José A. O.; Pascoal, Ricardo; Torrão, João; Xue, Xiaozheng; Furlani, Edward P.
2016-01-01
Magnetic levitation has been used to implement low-cost and maintenance-free electromagnetic energy harvesting. The ability of levitation-based harvesting systems to operate autonomously for long periods of time makes them well-suited for self-powering a broad range of technologies. In this paper, a combined theoretical and experimental study is presented of a harvester configuration that utilizes the motion of a levitated hard-magnetic element to generate electrical power. A semi-analytical, non-linear model is introduced that enables accurate and efficient analysis of energy transduction. The model predicts the transient and steady-state response of the harvester a function of its motion (amplitude and frequency) and load impedance. Very good agreement is obtained between simulation and experiment with energy errors lower than 14.15% (mean absolute percentage error of 6.02%) and cross-correlations higher than 86%. The model provides unique insight into fundamental mechanisms of energy transduction and enables the geometric optimization of harvesters prior to fabrication and the rational design of intelligent energy harvesters. PMID:26725842
Performance analysis of an all-optical OFDM system in presence of non-linear phase noise.
Hmood, Jassim K; Harun, Sulaiman W; Emami, Siamak D; Khodaei, Amin; Noordin, Kamarul A; Ahmad, Harith; Shalaby, Hossam M H
2015-02-23
The potential for higher spectral efficiency has increased the interest in all-optical orthogonal frequency division multiplexing (OFDM) systems. However, the sensitivity of all-optical OFDM to fiber non-linearity, which causes nonlinear phase noise, is still a major concern. In this paper, an analytical model for estimating the phase noise due to self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in an all-optical OFDM system is presented. The phase noise versus power, distance, and number of subcarriers is evaluated by implementing the mathematical model using Matlab. In order to verify the results, an all-optical OFDM system, that uses coupler-based inverse fast Fourier transform/fast Fourier transform without any nonlinear compensation, is demonstrated by numerical simulation. The system employs 29 subcarriers; each subcarrier is modulated by a 4-QAM or 16-QAM format with a symbol rate of 25 Gsymbol/s. The results indicate that the phase variance due to FWM is dominant over those induced by either SPM or XPM. It is also shown that the minimum phase noise occurs at -3 dBm and -1 dBm for 4-QAM and 16-QAM, respectively. Finally, the error vector magnitude (EVM) versus subcarrier power and symbol rate is quantified using both simulation and the analytical model. It turns out that both EVM results are in good agreement with each other.
Triphenylamine-Based Fluorescent Styryl Dyes: DFT, TD-DFT and Non-Linear Optical Property Study.
Katariya, Santosh; Rhyman, Lydia; Alswaidan, Ibrahim A; Ramasami, Ponnadurai; Sekar, Nagaiyan
2017-01-31
The electronic structures and spectroscopic properties of triphenylamine-based monostyryl and bis(styryl) dyes were studied using quantum chemical methods. The ground-state geometries of these dyes were optimized using the density functional theory (DFT) method. The lowest singlet excited state was optimized using time-dependent density functional theory (TD-DFT). The absorption was also calculated using the ground-state geometries. All the calculations were carried out in the gas phase and in solvent. The results indicate that the absorption maxima calculated using the TD-DFT are in good agreement with those obtained experimentally. These dyes possess a large second-order non-linear property and this is mainly due to the strong donor-π-acceptor conjugation which is attributed to the excited state intramolecular charge transfer (ICT). There is a relationship between the hardness and first hyperpolarizability and second hyperpolarizability of mono- and bis(styryl) dyes. The efficiency of the intersystem crossing process can be improved by reducing the energy gap between the singlet and triplet excited states.
Soares Dos Santos, Marco P; Ferreira, Jorge A F; Simões, José A O; Pascoal, Ricardo; Torrão, João; Xue, Xiaozheng; Furlani, Edward P
2016-01-04
Magnetic levitation has been used to implement low-cost and maintenance-free electromagnetic energy harvesting. The ability of levitation-based harvesting systems to operate autonomously for long periods of time makes them well-suited for self-powering a broad range of technologies. In this paper, a combined theoretical and experimental study is presented of a harvester configuration that utilizes the motion of a levitated hard-magnetic element to generate electrical power. A semi-analytical, non-linear model is introduced that enables accurate and efficient analysis of energy transduction. The model predicts the transient and steady-state response of the harvester a function of its motion (amplitude and frequency) and load impedance. Very good agreement is obtained between simulation and experiment with energy errors lower than 14.15% (mean absolute percentage error of 6.02%) and cross-correlations higher than 86%. The model provides unique insight into fundamental mechanisms of energy transduction and enables the geometric optimization of harvesters prior to fabrication and the rational design of intelligent energy harvesters.
Wu, Tsan-Pei; Wang, Xiao-Qun; Guo, Guang-Yu; Anders, Frithjof; Chung, Chung-Hou
2016-05-05
The quantum criticality of the two-lead two-channel pseudogap Anderson impurity model is studied. Based on the non-crossing approximation (NCA) and numerical renormalization group (NRG) approaches, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, ρc(ω) proportional |ω − μF|(r) (0 < r < 1) near the Fermi energy μF. At a fixed lead-impurity hybridization, a quantum phase transition from the two-channel Kondo (2CK) to the local moment (LM) phase is observed with increasing r from r = 0 to r = rc < 1. Surprisingly, in the 2CK phase, different power-law scalings from the well-known [Formula: see text] or [Formula: see text] form is found. Moreover, novel power-law scalings in conductances at the 2CK-LM quantum critical point are identified. Clear distinctions are found on the critical exponents between linear and non-linear conductance at criticality. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed.
NASA Astrophysics Data System (ADS)
Gómez-Ullate, D.; Lombardo, S.; Mañas, M.; Mazzocco, M.; Nijhoff, F.; Sommacal, M.
2009-12-01
may be found at www.iop.org/Journals/jphysa. Contributions to the special issue should if possible be submitted electronically by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting 'JPhysA Special Issue: Current Trends in Integrability and Non Linear Phenomena' Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, IOP Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. Please quote 'JPhysA Special Issue—Current Trends in Integrability and Non Linear Phenomena'. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. This special issue will be published in the paper and online version of the journal.
NASA Astrophysics Data System (ADS)
Gómez-Ullate, D.; Lombardo, S.; Mañas, M.; Mazzocco, M.; Nijhoff, F.; Sommacal, M.
2009-11-01
may be found at www.iop.org/Journals/jphysa. Contributions to the special issue should if possible be submitted electronically by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting 'JPhysA Special Issue: Current Trends in Integrability and Non Linear Phenomena' Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, IOP Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. Please quote 'JPhysA Special Issue—Current Trends in Integrability and Non Linear Phenomena'. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. This special issue will be published in the paper and online version of the journal.
Non-linear states of a positive or negative refraction index material in a cavity with feedback
NASA Astrophysics Data System (ADS)
Mártin, D. A.; Hoyuelos, M.
2010-06-01
We study a system composed by a cavity with plane mirrors containing a positive or negative refraction index material with third order effective electric and magnetic non-linearities. The aim of the work is to present a general picture of possible non-linear states in terms of the relevant parameters of the system. The parameters are the ones that appear in a reduced description that has the form of the Lugiato-Lefever equation. This equation is obtained from two coupled non-linear Schrödinger equations for the electric and magnetic field amplitudes.
NASA Astrophysics Data System (ADS)
Kumar, Santosh; Kumari, Anamika; Raghuwanshi, Sanjeev K.
2015-05-01
In this paper, dispersion equation of optical waveguide using metamaterial as buffer layer with non-linear cladding and substrate is pointed. The sensitivity of TE in metamaterial optical waveguide sensor is computed mathematically. The impacts of buffer layer with non-linear cladding and substrate on metamaterial optical waveguide sensor are also tried out. The effects of various parameters on sensitivity of sensor are obtained through MATLAB. It is expected that metamaterial as buffer layer with non-linear cladding and substrate profile has a huge application in leaky fibre sensor, gas sensor and chemical sensor for oil and under grounds mining industries.
Exciton dynamics and non-linearities in two-dimensional hybrid organic perovskites
NASA Astrophysics Data System (ADS)
Abdel-Baki, K.; Boitier, F.; Diab, H.; Lanty, G.; Jemli, K.; Lédée, F.; Garrot, D.; Deleporte, E.; Lauret, J. S.
2016-02-01
Due to their high potentiality for photovoltaic applications or coherent light sources, a renewed interest in hybrid organic perovskites has emerged for few years. When they are arranged in two dimensions, these materials can be considered as hybrid quantum wells. One consequence of the unique structure of 2D hybrid organic perovskites is a huge exciton binding energy that can be tailored through chemical engineering. We present experimental investigations of the exciton non-linearities by means of femtosecond pump-probe spectroscopy. The exciton dynamics is fitted with a bi-exponential decay with a free exciton life-time of ˜100 ps. Moreover, an ultrafast intraband relaxation (<150 fs) is also reported. Finally, the transient modification of the excitonic line is analyzed through the moment analysis and described in terms of reduction of the oscillator strength and linewidth broadening. We show that excitonic non-linearities in 2D hybrid organic perovskites share some behaviours of inorganic semiconductors despite their high exciton binding energy.
Addressing the unemployment-mortality conundrum: non-linearity is the answer.
Bonamore, Giorgio; Carmignani, Fabrizio; Colombo, Emilio
2015-02-01
The effect of unemployment on mortality is the object of a lively literature. However, this literature is characterized by sharply conflicting results. We revisit this issue and suggest that the relationship might be non-linear. We use data for 265 territorial units (regions) within 23 European countries over the period 2000-2012 to estimate a multivariate regression of mortality. The estimating equation allows for a quadratic relationship between unemployment and mortality. We control for various other determinants of mortality at regional and national level and we include region-specific and time-specific fixed effects. The model is also extended to account for the dynamic adjustment of mortality and possible lagged effects of unemployment. We find that the relationship between mortality and unemployment is U shaped. In the benchmark regression, when the unemployment rate is low, at 3%, an increase by one percentage point decreases average mortality by 0.7%. As unemployment increases, the effect decays: when the unemployment rate is 8% (sample average) a further increase by one percentage point decreases average mortality by 0.4%. The effect changes sign, turning from negative to positive, when unemployment is around 17%. When the unemployment rate is 25%, a further increase by one percentage point raises average mortality by 0.4%. Results hold for different causes of death and across different specifications of the estimating equation. We argue that the non-linearity arises because the level of unemployment affects the psychological and behavioural response of individuals to worsening economic conditions.
Non-linear boundary-layer receptivity due to distributed surface roughness
NASA Technical Reports Server (NTRS)
Amer, Tahani Reffet
1995-01-01
The process by which a laminar boundary layer internalizes the external disturbances in the form of instability waves is known as boundary-layer receptivity. The objective of the present research was to determine the effect of acoustic excitation on boundary-layer receptivity for a flat plate with distributed variable-amplitude surface roughness through measurements with a hot-wire probe. Tollmien-Schlichting mode shapes due to surface roughness receptivity have also been determined, analyzed, and shown to be in agreement with theory and other experimental work. It has been shown that there is a linear relationship between the surface roughness and receptivity for certain roughness configurations with constant roughness wavelength. In addition, strong non-linear receptivity effects exist for certain surface roughness configurations over a band where the surface roughness and T-S wavelength are matched. The results from the present experiment follow the trends predicted by theory and other experimental work for linear receptivity. In addition, the results show the existence of non-linear receptivity effects for certain combinations of surface roughness elements.
Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics
NASA Astrophysics Data System (ADS)
Nazem, M.; Carter, J. P.; Airey, D. W.
2010-06-01
In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.
Inverse modelling of NOx emissions over eastern China: uncertainties due to chemical non-linearity
NASA Astrophysics Data System (ADS)
Gu, Dasa; Wang, Yuhang; Yin, Ran; Zhang, Yuzhong; Smeltzer, Charles
2016-10-01
Satellite observations of nitrogen dioxide (NO2) have often been used to derive nitrogen oxides (NOx = NO + NO2) emissions. A widely used inversion method was developed by Martin et al. (2003). Refinements of this method were subsequently developed. In the context of this inversion method, we show that the local derivative (of a first-order Taylor expansion) is more appropriate than the "bulk ratio" (ratio of emission to column) used in the original formulation for polluted regions. Using the bulk ratio can lead to biases in regions of high NOx emissions such as eastern China due to chemical non-linearity. Inverse modelling using the local derivative method is applied to both GOME-2 and OMI satellite measurements to estimate anthropogenic NOx emissions over eastern China. Compared with the traditional method using bulk ratio, the local derivative method produces more consistent NOx emission estimates between the inversion results using GOME-2 and OMI measurements. The results also show significant changes in the spatial distribution of NOx emissions, especially over high emission regions of eastern China. We further discuss a potential pitfall of using the difference of two satellite measurements to derive NOx emissions. Our analysis suggests that chemical non-linearity needs to be accounted for and that a careful bias analysis is required in order to use the satellite differential method in inverse modelling of NOx emissions.
Mahfouz, Ahmed; van de Giessen, Martijn; van der Maaten, Laurens; Huisman, Sjoerd; Reinders, Marcel; Hawrylycz, Michael J; Lelieveldt, Boudewijn P F
2015-02-01
The Allen Brain Atlases enable the study of spatially resolved, genome-wide gene expression patterns across the mammalian brain. Several explorative studies have applied linear dimensionality reduction methods such as Principal Component Analysis (PCA) and classical Multi-Dimensional Scaling (cMDS) to gain insight into the spatial organization of these expression patterns. In this paper, we describe a non-linear embedding technique called Barnes-Hut Stochastic Neighbor Embedding (BH-SNE) that emphasizes the local similarity structure of high-dimensional data points. By applying BH-SNE to the gene expression data from the Allen Brain Atlases, we demonstrate the consistency of the 2D, non-linear embedding of the sagittal and coronal mouse brain atlases, and across 6 human brains. In addition, we quantitatively show that BH-SNE maps are superior in their separation of neuroanatomical regions in comparison to PCA and cMDS. Finally, we assess the effect of higher-order principal components on the global structure of the BH-SNE similarity maps. Based on our observations, we conclude that BH-SNE maps with or without prior dimensionality reduction (based on PCA) provide comprehensive and intuitive insights in both the local and global spatial transcriptome structure of the human and mouse Allen Brain Atlases.
Multiclass first-order simulation model to explain non-linear traffic phenomena
NASA Astrophysics Data System (ADS)
Ngoduy, D.; Liu, R.
2007-11-01
With the first-order traffic model of Lighthill, Whitham and Richard (LWR), many simple traffic problems can be represented analytically such as a shock formation. However, the LWR model has some deficiencies. For example, among the other things, it fails to replicate interesting non-linear phenomena such as hysteresis and capacity drop as well as the dispersion of traffic platoon when there exists a distribution of desired speeds in heterogeneous traffic. To this end, in this paper, we propose a novel multiclass first-order simulation model based on an approximation of Riemann solver. In the developed model, each vehicle class is only characterized by their desired speeds in a free-flow traffic state where overtaking is allowed. However, when traffic is congested, all vehicle classes must travel at the same congested speed and overtaking is not possible. Numerical results show that the proposed model is not only more accurate and reliable than the existing models but also able to explain non-linear traffic phenomena on freeways.
NASA Astrophysics Data System (ADS)
Deglint, Jason; Kazemzadeh, Farnoud; Wong, Alexander; Clausi, David A.
2015-09-01
One method to acquire multispectral images is to sequentially capture a series of images where each image contains information from a different bandwidth of light. Another method is to use a series of beamsplitters and dichroic filters to guide different bandwidths of light onto different cameras. However, these methods are very time consuming and expensive and perform poorly in dynamic scenes or when observing transient phenomena. An alternative strategy to capturing multispectral data is to infer this data using sparse spectral reflectance measurements captured using an imaging device with overlapping bandpass filters, such as a consumer digital camera using a Bayer filter pattern. Currently the only method of inferring dense reflectance spectra is the Wiener adaptive filter, which makes Gaussian assumptions about the data. However, these assumptions may not always hold true for all data. We propose a new technique to infer dense reflectance spectra from sparse spectral measurements through the use of a non-linear regression model. The non-linear regression model used in this technique is the random forest model, which is an ensemble of decision trees and trained via the spectral characterization of the optical imaging system and spectral data pair generation. This model is then evaluated by spectrally characterizing different patches on the Macbeth color chart, as well as by reconstructing inferred multispectral images. Results show that the proposed technique can produce inferred dense reflectance spectra that correlate well with the true dense reflectance spectra, which illustrates the merits of the technique.
Characterization of atherosclerotic arterial tissue using multimodal non-linear optical microscopy
NASA Astrophysics Data System (ADS)
Cicchi, Riccardo; Matthäus, Christian; Meyer, Tobias; Lattermann, Annika; Dietzek, Benjamin; Brehm, Bernhard R.; Popp, Jürgen; Pavone, Francesco S.
2013-06-01
Atherosclerosis is among the most widespread cardiovascular diseases and one of the leading cause of death in the Western World. Characterization of arterial tissue in atherosclerotic condition is extremely interesting from the diagnostic point of view. Routinely used diagnostic methods, such as histopathological examination, are limited to morphological analysis of the examined tissues, whereas an exhaustive characterization requires a morpho-functional approach. Non-linear microscopy techniques have the potential to bridge this gap by providing morpho-functional information in a label-free way. Here we employed multiple non-linear microscopy techniques, including CARS, TPF, and SHG to provide intrinsic optical contrast from various tissue components in both arterial wall and atherosclerotic plaques. CARS and TPF microscopy were used to respectively image lipid depositions within plaques and elastin in the arterial wall. Cholesterol deposition in the lumen and collagen in the arterial wall were selectively imaged by SHG microscopy and distinguished by forward-backward SHG ratio. Image pattern analysis allowed characterizing collagen organization in different tissue regions. The presented method has the potential to find a stable place in clinical setting as well as to be applied in vivo in the near future.
A new adaptive multiple modelling approach for non-linear and non-stationary systems
NASA Astrophysics Data System (ADS)
Chen, Hao; Gong, Yu; Hong, Xia
2016-07-01
This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.
Monitoring Technical Conditions of Engineering Structures Using the Non-Linear Approach
NASA Astrophysics Data System (ADS)
Volkova, V. E.
2015-11-01
Conventional methods of monitoring technical condition are based on detection of damage in the structures of buildings or facilities during the entire period of their operation. In spite of considerable interest displayed to this issue and a significant number of publications, there is no unity of opinions. These methods differ from each other in the sets of values fixed for investigations, the techniques of their recording, transfer and further processing. Today's rules and regulations for structural designs expand the scope of application of the structures operating in the elastic-plastic stage. These damage-free structures originally display the nonlinear properties and can be adequately described only by the non-linear models. This paper presents a method for determining the type and level of non-linearity from the structural oscillations data for monitoring the change in the health of structures. It is shown that a plot of acceleration against the magnitude of the displacement represents the restoring force of a structure. If the structure is damaged during a new striking motion, the phase trajectories in plane “acceleration-displacement” will deviate from its healthy signature.
A Fully Associative, Non-Linear Kinematic, Unified Viscoplastic Model for Titanium Based Matrices
NASA Technical Reports Server (NTRS)
Arnold, S. M.; Saleeb, A. F.; Castelli, M. G.
1994-01-01
Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential based multiaxial unified viscoplastic model is obtained. This model possesses one tensorial internal state variable that is associated with dislocation substructure, with an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of non-linear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This non-linear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated) and greatly influences the multiaxial response under non-proportional loading paths. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. Specification of an experimental program for the complete determination of the material functions and parameters for characterizing a metallic matrix, e.g., TIMETAL 21S, is given. The experiments utilized are tensile, creep, and step creep tests. Finally, a comparison of this model and a commonly used Bodner-Partom model is made on the basis of predictive accuracy and numerical efficiency.
Non-linear Resistivity of a Two-Dimensional Electron Gas in a Magnetic Field
NASA Astrophysics Data System (ADS)
Vavilov, Maxim G.; Aleiner, Igor L.; Glazman, Leonid I.
2007-03-01
We develop a theory of nonlinear response to an electric field of a two-dimensional electron gas (2DEG) placed in a classically strong magnetic field. The latter leads to a non-linear current-voltage characteristic at a relatively weak electric field. The origin of the non-linearity is two-fold: the formation of a non-equilibrium electron distribution function, and the geometrical resonance in the inter-Landau-levels transitions rates. We find the dependence of the current-voltage characteristics on the electron relaxation rates in the 2DEG. Our results can be applied for analysis of measurements at low [1] and high [2,3] current densities. [1] J. Zhang, S. Vitkalov, A. A. Bykov, A. K. Kalagin and A. K. Bakarov, cond-mat/0607741. [2] C. L. Yang, J. Zhang, R. R. Du, J. A. Simmons and J. L. Reno, Phys. Rev. Lett. 89, 076801 (2002). [3] W. Zhang, H. -S. Chiang, M. A. Zudov, L. N. Pfeiffer and K. W. West, cond-mat/0608727.
Haematite natural crystals: non-linear initial susceptibility at low temperature
NASA Astrophysics Data System (ADS)
Guerrero-Suarez, S.; Martín-Hernández, F.
2016-06-01
Several works have reported that haematite has non-linear initial susceptibility at room temperature, like pyrrhotite or titanomagnetite, but there is no explanation for the observed behaviours yet. This study sets out to determine which physical property (grain size, foreign cations content and domain walls displacements) controls the initial susceptibility. The performed measurements include microprobe analysis to determine magnetic phases different to haematite; initial susceptibility (300 K); hysteresis loops, SIRM and backfield curves at 77 and 300 K to calculate magnetic parameters and minor loops at 77 K, to analyse initial susceptibility and magnetization behaviours below Morin transition. The magnetic moment study at low temperature is completed with measurements of zero field cooled-field cooled and AC susceptibility in a range from 5 to 300 K. The minor loops show that the non-linearity of initial susceptibility is closely related to Barkhausen jumps. Because of initial magnetic susceptibility is controlled by domain structure it is difficult to establish a mathematical model to separate magnetic subfabrics in haematite-bearing rocks.
NASA Astrophysics Data System (ADS)
Volk, Wolfram; Suh, Joungsik
2013-12-01
The prediction of formability is one of the most important tasks in sheet metal process simulation. The common criterion in industrial applications is the Forming Limit Curve (FLC). The big advantage of FLCs is the easy interpretation of simulation or measurement data in combination with an ISO standard for the experimental determination. However, the conventional FLCs are limited to almost linear and unbroken strain paths, i.e. deformation histories with non-linear strain increments often lead to big differences in comparison to the prediction of the FLC. In this paper a phenomenological approach, the so-called Generalized Forming Limit Concept (GFLC), is introduced to predict the localized necking on arbitrary deformation history with unlimited number of non-linear strain increments. The GFLC consists of the conventional FLC and an acceptable number of experiments with bi-linear deformation history. With the idea of the new defined "Principle of Equivalent Pre-Forming" every deformation state built up of two linear strain increments can be transformed to a pure linear strain path with the same used formability of the material. In advance this procedure can be repeated as often as necessary. Therefore, it allows a robust and cost effective analysis of beginning instability in Finite Element Analysis (FEA) for arbitrary deformation histories. In addition, the GFLC is fully downwards compatible to the established FLC for pure linear strain paths.
Non-linear dense core formation in the dark cloud L1517
NASA Astrophysics Data System (ADS)
Heigl, S.; Burkert, A.; Hacar, A.
2016-12-01
We present a solution for the observed core fragmentation of filaments in the Taurus L1517 dark cloud which previously could not be explained. Core fragmentation is a vital step for the formation of stars. Observations suggest a connection to the filamentary structure of the cloud gas, but it remains unclear which process is responsible. We show that the gravitational instability process of an infinite, isothermal cylinder can account for the exhibited fragmentation under the assumption that the perturbation grows on the dominant wavelength. We use numerical simulations with the code RAMSES, estimate observed column densities and line-of-sight velocities, and compare them to the observations. A critical factor for the observed fragmentation is that cores grow by redistributing mass within the filament and thus the density between the cores decreases over the fragmentation process. This often leads to wrong dominant wavelength estimates, as it is strongly dependent on the initial central density. We argue that non-linear effects also play an important role in the evolution of the fragmentation. Once the density perturbation grows above the critical line mass, non-linearity leads to an enhancement of the central core density in comparison to the analytical prediction. Choosing the correct initial conditions with perturbation strengths of around 20 per cent leads to inclination-corrected line-of-sight velocities and central core densities within the observational measurement error in a realistic evolution time.
Non-linear modelling and control of semi-active suspensions with variable damping
NASA Astrophysics Data System (ADS)
Chen, Huang; Long, Chen; Yuan, Chao-Chun; Jiang, Hao-Bin
2013-10-01
Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f-v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief-desire-intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.
Cerebral autoregulation of preterm neonates--a non-linear control system?
Zernikow, B; Michel, E; Kohlmann, G; Steck, J; Schmitt, R M; Jorch, G
1994-05-01
The low frequency cerebral blood flow velocity (CBFV) oscillations in neonates are commonly attributed to an under-dampened immature linear type cerebral autoregulation, and the 'instability' is regarded as causative for peri-intraventricular haemorrhage/periventricular leukomalacia. In contrast, oscillations susceptible to frequency entrainment are a fundamental part of the stable function of non-linear control systems. To classify the autoregulation an observational study was done on the relationship between CBFV oscillations, heart rate variability, and artificial ventilation. In 10 preterm neonates (gestational age 26 to 35 weeks) we serially Doppler traced arterial CBFV continuously for 12 minutes between days 1 and 49 of life. The individual time series of CBFV and heart rate were subjected to spectral analysis. Forty six of 47 tracings showed significant low frequency CBFV oscillations. Low frequency heart rate oscillations were not a prerequisite thereof. All patients with < 30% of total power in the low frequency band of CBFV oscillations were on the ventilator. Three of them demonstrated a shift of spectral power from low frequency to a frequency equal or harmonic to the ventilator rate indicating entrainment. The findings of CBFV oscillations combined with entrainment classify the autoregulation as a non-linear system. It is suggested that entrainment by periodic high amplitude stimuli might challenge the regulatory capacity to its limits thus increasing the risk for cerebral damage.
Non-linear finite-amplitude transfer of basal perturbations to a glacier surface
NASA Astrophysics Data System (ADS)
Raymond, M.; Gudmundsson, G. H.; Funk, M.
2003-04-01
Disturbances of surface topography and velocity fields on ice streams can be caused by spatial variations in basal properties. Understanding the relationship between basal and surface perturbations allows estimates of the role of basal control on the dynamics of ice streams to be made. This relationship is well understood for linear medium and small-amplitude basal perturbations where analytical methods can be applied. Studies of the non-linear problems have so far been limited to special cases where semi-analytical methods can be used. Here the transfer of basal variability to a glacier surface is investigated using a numerical model for non-linear ice rheology. Two dimensional steady-state transfer functions for both sinusoidal bedrock undulations and variations in till resistance are determined using Glen's flow law and the full momentum equation system. Amplitude ratios and phase shifts are calculated for wavelengths up to thousand times the mean ice thickness and compared with predictions based on small-amplitude perturbation theory.
High Intensity Focused Ultrasound for Cancer Therapy--harnessing its non-linearity
Haar, Gail ter
2008-06-24
In medicine in general, and for cancer treatments in particular, there is a drive to find effective non-invasive therapies. High Intensity Focused Ultrasound (HIFU) represents one such technique. In principle, it is simple--a high energy ultrasound beam is brought to a tight focus within a target which may lie several centimetres below the skin surface (for example, in a tumour of the liver), and is used to destroy a selected tissue volume. The main mechanism for cell killing in a HIFU beam is heat. Ultrasound energy absorption is frequency dependent, the higher frequencies being absorbed most strongly. Significant thermal advantage may therefore be gained from non-linear propagation, which generates higher harmonics, in tissue. Acoustic cavitation and thermal exsolution of gas (boiling) also contribute to tissue damage. This activity leads to the local mechanical disruption of cells. In addition, the non-linear oscillation of these bubbles leads to enhanced energy deposition. The acoustic emissions from such bubbles are characteristic of their behaviour and may be correlated to some extent with the appearance of the disruption produced. The more widespread clinical acceptance of HIFU is awaiting faster, and more efficient, energy delivery and treatment monitoring. A better understanding of the nonlinear aspects of HIFU propagation in tissue is thus important if this technique is to benefit more patients.
The non-linearity of risk and the promotion of environmentally sustainable transport.
Elvik, Rune
2009-07-01
Several studies show that the risks of injury to pedestrians and cyclists are highly non-linear. This means that the more pedestrians or cyclists there are, the lower is the risk faced by each pedestrian or cyclist. On the other hand, the more motor vehicles there are, the higher becomes the risk faced by each pedestrian or cyclist. The relationships found in previous studies suggest that if very large transfers of trips from motor vehicles to walking or cycling take place, the total number of accidents may be reduced. The "safety in numbers" effect for pedestrians and cyclists would then combine favourably with the effect of a lower number of motor vehicles to produce a lower total number of accidents. This paper explores if such an effect is possible, relying on the findings of studies that show the non-linearity of injury risks for pedestrians and cyclists. It is found that for very large transfers of trips from motor vehicles to walking or cycling, a reduction of the total number of accidents is indeed possible. This shows that the high injury rate for pedestrians and cyclists in the current transport system does not necessarily imply that encouraging walking or cycling rather than driving will lead to more accidents.
A review on prognostic techniques for non-stationary and non-linear rotating systems
NASA Astrophysics Data System (ADS)
Kan, Man Shan; Tan, Andy C. C.; Mathew, Joseph
2015-10-01
The field of prognostics has attracted significant interest from the research community in recent times. Prognostics enables the prediction of failures in machines resulting in benefits to plant operators such as shorter downtimes, higher operation reliability, reduced operations and maintenance cost, and more effective maintenance and logistics planning. Prognostic systems have been successfully deployed for the monitoring of relatively simple rotating machines. However, machines and associated systems today are increasingly complex. As such, there is an urgent need to develop prognostic techniques for such complex systems operating in the real world. This review paper focuses on prognostic techniques that can be applied to rotating machinery operating under non-linear and non-stationary conditions. The general concept of these techniques, the pros and cons of applying these methods, as well as their applications in the research field are discussed. Finally, the opportunities and challenges in implementing prognostic systems and developing effective techniques for monitoring machines operating under non-stationary and non-linear conditions are also discussed.
NASA Astrophysics Data System (ADS)
Drzewiecki, Wojciech
2016-12-01
In this work nine non-linear regression models were compared for sub-pixel impervious surface area mapping from Landsat images. The comparison was done in three study areas both for accuracy of imperviousness coverage evaluation in individual points in time and accuracy of imperviousness change assessment. The performance of individual machine learning algorithms (Cubist, Random Forest, stochastic gradient boosting of regression trees, k-nearest neighbors regression, random k-nearest neighbors regression, Multivariate Adaptive Regression Splines, averaged neural networks, and support vector machines with polynomial and radial kernels) was also compared with the performance of heterogeneous model ensembles constructed from the best models trained using particular techniques. The results proved that in case of sub-pixel evaluation the most accurate prediction of change may not necessarily be based on the most accurate individual assessments. When single methods are considered, based on obtained results Cubist algorithm may be advised for Landsat based mapping of imperviousness for single dates. However, Random Forest may be endorsed when the most reliable evaluation of imperviousness change is the primary goal. It gave lower accuracies for individual assessments, but better prediction of change due to more correlated errors of individual predictions. Heterogeneous model ensembles performed for individual time points assessments at least as well as the best individual models. In case of imperviousness change assessment the ensembles always outperformed single model approaches. It means that it is possible to improve the accuracy of sub-pixel imperviousness change assessment using ensembles of heterogeneous non-linear regression models.
NASA Astrophysics Data System (ADS)
Tetzlaff, D.; Soulsby, C.; Birkel, C.; Capell, R.; Speed, M.
2009-12-01
The non-linearities of catchment hydrological behaviour are strongly influenced by the connectivity of hillslopes and channel networks, particularly where overland flow is an important runoff mechanism. Such surface connectivity also controls the flux of microbiological pollutants (coliform bacteria) from areas of live stock grazing which can have serious health implications for potable water supplies. We report a nested catchment study where hydrological and tracer monitoring over a two year period has been coupled with regular sampling for faecal indicator organisms (FIOs). The study has been based in catchments with mixed landuse where FIOs are derived from livestock (sheep and cows) in agricultural land and wild animals (red deer) on moorlands. At all scales (3-1800km2), high levels of FIO were transient and episodic and strongly correlated with periods of high hydrological connectivity. We show how this non-linearity in connectivity can be captured within a dynamic hydrological model. The model was used, along with climate change predictions, to assess possible scenarios of change in connectivity and microbiological contamination in catchments with different land use.
Non-linear methods for inferring lidar metrics using SPOT-5 textural data
NASA Astrophysics Data System (ADS)
Shamsoddini, A.; Trinder, J. C.; Turner, R.
2013-10-01
Although many studies have demonstrated the utility of airborne lidar for forest inventory, the acquisition and processing of the data can be cost prohibitive for small areas. In such cases, it may be possible to emulate lidar metrics using more affordable optical data. This study explored processing methods for predicting lidar metrics using SPOT-5 textural data. Multiple-linear regression (MLR) was compared with non-linear machine learning techniques including multi-layer perceptron (MLP) artificial neural networks (ANN), rational basis function (RBF) ANN and regression tree (RT). For this purpose, 11 grey level co-occurrence matrix (GLCM) indices were calculated for bands, band ratios and principal components (PCs) of SPOT-5 multispectral image. SPOT-5 metrics were correlated with 25 lidar metrics collected over a Pinus radiata plantation. After dimensionality reduction, random forest feature selection was applied to select the most relevant SPOT-5 textural attributes for inferring each lidar metric. The results showed that the non-linear methods including MLP and RBF methods are more promising for modelling lidar metrics using SPOT-5 data than MLR and RT.
Non-linear dynamics and instability of a rotating shaft-disk system
NASA Astrophysics Data System (ADS)
Chang, C. O.; Cheng, J. W.
1993-01-01
The instability and non-linear dynamics of a slender rotating shaft with a rigid disk at the mid-span are analyzed. The shaft is simply supported at both ends and is made of a viscoelastic material. The stability criteria are determined from the linear equations of motion based on the small strain assumption. The bifurcation of the double zero eigenvalue point on the stability boundaries in the parametric space is analyzed by using center manifold theory on the non-linear equations of motion, for which a large transverse displacement of the shaft is assumed. Analytical expressions for the radius of synchronous whirling and the radius and precession rate of non-synchronous whirling near the double zero eigenvalue point are obtained explicitly. The behaviors of the parametric points away from the stability boundaries are analyzed numerically. The general effects on the precession rate for these points are somewhat different from those for the parametric points in the vicinity of the double zero eigenvalue.
Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank
Bardoscia, Marco; Caccioli, Fabio; Perotti, Juan Ignacio; Vivaldo, Gianna; Caldarelli, Guido
2016-01-01
We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013. PMID:27701457
Development of a non-ideal plasma target for non-linear beam plasma interaction experiments
NASA Astrophysics Data System (ADS)
Katagiri, K.; Nishinomiya, S.; Niinou, T.; Kaneko, J.; Hasegawa, J.; Ogawa, M.; Oguri, Y.
2007-07-01
A shock-driven plasma target was developed to examine non-linear interactions between low-energy heavy ions and cold-dense plasmas. MD calculations predicted that beam-plasma coupling constant γ˜0.1 must be achieved to observe the non-linearity, which corresponds to the plasma coupling constant Γ≈0.2 for projectiles of vproj≈10 keV/u and q≈2. One-dimensional numerical estimations using SESAME equation of state showed that a shock wave propagating in 5-Torr H2 gas with 47 km/s must be produced to satisfy Γ≈0.2. Utilizing an electromagnetic shock tube with a peak current of 50 kA and a current rise time of 800 ns, we achieved a shock speed of 45 km/s. The electron density distribution of the shock-produced plasma along the beam axis was measured by a Mach-Zehnder interferometer. From this measurement we confirmed that the electron density was over 1017 cm-3 and the homogeneity was acceptable during several hundred nanoseconds. The electron temperature was also determined by optical spectroscopic measurements. The Coulomb coupling constant was evaluated using these experimental data to investigate feasibility of the beam-plasma interaction experiments.
Study of non-linear deformation of vocal folds in simulations of human phonation
NASA Astrophysics Data System (ADS)
Saurabh, Shakti; Bodony, Daniel
2014-11-01
Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).
Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank.
Bardoscia, Marco; Caccioli, Fabio; Perotti, Juan Ignacio; Vivaldo, Gianna; Caldarelli, Guido
2016-01-01
We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013.
Podesta, M; Crocker, N A; Fredrickson, E D; Gorelenkov, N N; Heidbrink, W W; Kubota, S; LeBlanc, B P
2011-04-26
The National Spherical Torus Experiment (NSTX, [M. Ono et al., Nucl. Fusion 40, 557 (2000)]) routinely operates with neutral beam injection as the primary system for heating and current drive. The resulting fast ion population is super-Alfv enic, with velocities 1 < vfast=vAlfven < 5. This provides a strong drive for toroidicity-induced Alfv en eigenmodes (TAEs). As the discharge evolves, the fast ion population builds up and TAEs exhibit increasing bursts in amplitude and down-chirps in frequency, which eventually lead to a so-called TAE avalanche. Avalanches cause large (≤ 30%) fast ion losses over ~ 1 ms, as inferred from the neutron rate. The increased fast ion losses correlate with a stronger activity in the TAE band. In addition, it is shown that a n = 1 mode with frequency well below the TAE gap appears in the Fourier spectrum of magnetic fluctuations as a result of non-linear mode coupling between TAEs during avalanche events. The non-linear coupling between modes, which leads to enhanced fast ion transport during avalanches, is investigated.
Non-linear analysis and the design of Pumpkin Balloons: stress, stability and viscoelasticity
NASA Astrophysics Data System (ADS)
Rand, J. L.; Wakefield, D. S.
Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures Founded upon their inTENS finite element analysis suite these activities have broadened to encompass lighter than air structures such as aerostats hybrid air-vehicles and stratospheric balloons Winzen Engineering couple many years of practical balloon design and fabrication experience with both academic and practical knowledge of the characterisation of the non-linear viscoelastic response of the polymeric films typically used for high-altitude scientific balloons Both companies have provided consulting services to the NASA Ultra Long Duration Balloon ULDB Program Early implementations of pumpkin balloons have shown problems of geometric instability characterised by improper deployment and these difficulties have been reproduced numerically using inTENS The solution lies in both the shapes of the membrane lobes and also the need to generate a biaxial stress field in order to mobilise in-plane shear stiffness Balloons undergo significant temperature and pressure variations in flight The different thermal characteristics between tendons and film can lead to significant meridional stress Fabrication tolerances can lead to significant local hoop stress concentrations particularly adjacent to the base and apex end fittings The non-linear viscoelastic response of the envelope film acts positively to help dissipate stress concentrations However creep over time may produce lobe geometry variations that may
Non-Linear Dynamic Response of a Spur Gear Pair: Modelling and Experimental Comparisons
NASA Astrophysics Data System (ADS)
PARKER, R. G.; VIJAYAKAR, S. M.; IMAJO, T.
2000-10-01
The dynamic response of a spur gear pair is investigated using a finite element/contact mechanics model that offers significant advantages for dynamic gear analyses. The gear pair is analyzed across a wide range of operating speeds and torques. Comparisons are made to other researchers' published experiments that reveal complex non-linear phenomena. The non-linearity source is contact loss of the meshing teeth, which, in contrast to the prevailing understanding, occurs even for large torques despite the use of high-precision gears. A primary feature of the modelling is that dynamic mesh forces are calculated using a detailed contact analysis at each time step as the gears roll through the mesh; there is no need to externally specify the excitation in the form of time-varying mesh stiffness, static transmission error input, or the like. A semi-analytical model near the tooth surface is matched to a finite element solution away from the tooth surface, and the computational efficiency that results permits dynamic analysis. Two-single-degree-of-freedom models are also studied. While one gives encouragingly good results, the other, which appears to have better mesh stiffness modelling, gives poor comparisons with experiments. The results indicate the sensitivity of such models to the Fourier spectrum of the changing mesh stiffness.
Spectral coupling issues in a two-degree-of-freedom system with clearance non-linearities
NASA Astrophysics Data System (ADS)
Padmanabhan, C.; Singh, R.
1992-06-01
In an earlier study [14], the frequency response characteristics of a multi-degree-of-freedom system with clearance non-linearities were presented. The current study is an extension of this prior work and deals specifically with the issue of dynamic interactions between resonances. The harmonic balance method, digital solutions and analog computer simulation are used to investigate a two-degree-of-freedom system under a mean load, when subjected to sinusoidal excitations. The existence of harmonic, periodic and chaotic solutions is demonstrated using digital simulation. The method of harmonic balance is employed to construct approximate solutions at the excitation frequency which are then used to classify weak, moderate and strong non-linear spectral interactions. The effects of parameters such as damping ratio, mean load, alternating load and frequency spacing between the resonances have been quantified. The applicability of the methodology is demonstrated through the following practical examples: (i) neutral gear rattle in an automotive transmission system; and (ii) steady state characteristics of a spur gear pair with backlash. In the second case, measured dynamic transmission error data at the gear mesh frequency are used to investigate spectral interactions. Limitations associated with solution methods and interaction classification schemes are also discussed.
Exciton dynamics and non-linearities in two-dimensional hybrid organic perovskites
Abdel-Baki, K.; Boitier, F.; Diab, H.; Lanty, G.; Jemli, K.; Lédée, F.; Deleporte, E.; Lauret, J. S.; Garrot, D.
2016-02-14
Due to their high potentiality for photovoltaic applications or coherent light sources, a renewed interest in hybrid organic perovskites has emerged for few years. When they are arranged in two dimensions, these materials can be considered as hybrid quantum wells. One consequence of the unique structure of 2D hybrid organic perovskites is a huge exciton binding energy that can be tailored through chemical engineering. We present experimental investigations of the exciton non-linearities by means of femtosecond pump-probe spectroscopy. The exciton dynamics is fitted with a bi-exponential decay with a free exciton life-time of ∼100 ps. Moreover, an ultrafast intraband relaxation (<150 fs) is also reported. Finally, the transient modification of the excitonic line is analyzed through the moment analysis and described in terms of reduction of the oscillator strength and linewidth broadening. We show that excitonic non-linearities in 2D hybrid organic perovskites share some behaviours of inorganic semiconductors despite their high exciton binding energy.
Darville, Nicolas; Saarinen, Jukka; Isomäki, Antti; Khriachtchev, Leonid; Cleeren, Dirk; Sterkens, Patrick; van Heerden, Marjolein; Annaert, Pieter; Peltonen, Leena; Santos, Hélder A; Strachan, Clare J; Van den Mooter, Guy
2015-10-01
Drug nano-/microcrystals are being used for sustained parenteral drug release, but safety and efficacy concerns persist as the knowledge of the in vivo fate of long-living particulates is limited. There is a need for techniques enabling the visualization of drug nano-/microcrystals in biological matrices. The aim of this work was to explore the potential of coherent anti-Stokes Raman scattering (CARS) microscopy, supported by other non-linear optical methods, as an emerging tool for the investigation of cellular and tissue interactions of unlabeled and non-fluorescent nano-/microcrystals. Raman and CARS spectra of the prodrug paliperidone palmitate (PP), paliperidone (PAL) and several suspension stabilizers were recorded. PP nano-/microcrystals were incubated with RAW 264.7 macrophages in vitro and their cellular disposition was investigated using a fully-integrated multimodal non-linear optical imaging platform. Suitable anti-Stokes shifts (CH stretching) were identified for selective CARS imaging. CARS microscopy was successfully applied for the selective three-dimensional, non-perturbative and real-time imaging of unlabeled PP nano-/microcrystals having dimensions larger than the optical lateral resolution of approximately 400nm, in relation to the cellular framework in cell cultures and ex vivo in histological sections. In conclusion, CARS microscopy enables the non-invasive and label-free imaging of (sub)micron-sized (pro-)drug crystals in complex biological matrices and could provide vital information on poorly understood nano-/microcrystal-cell interactions in future.
Non-linear dynamics of viscoelastic liquid trilayers subjected to an electric field
NASA Astrophysics Data System (ADS)
Karapetsas, George; Bontozoglou, Vasilis
2014-11-01
The scope of this work is to investigate the non-linear dynamics of the electro-hydrodynamic instability of a trilayer of immiscible liquids. We consider the case of a polymer film which is separated from the top electrode by two viscous fluids. We develop a computational model and carry out 2D numerical simulations fully accounting for the flow and electric field in all phases. For the numerical solution of the governing equations we employ the mixed finite element method combined with a quasi-elliptic mesh generation scheme which is capable of following the large deformations of the liquid-liquid interface. We model the viscoelastic behavior using the Phan-Thien and Tanner (PTT) constitutive equation taking fully into account the non-linear elastic effects as well as a varying shear and extensional viscosity. We perform a thorough parametric study and investigate the influence of the electric properties of fluids, applied voltage and various rheological parameters. The authors acknowledge the support by the General Secretariat of Research and Technology of Greece under the action ``Supporting Postdoctoral Researchers'' (Grant Number PE8/906), co-funded by the European Social Fund and National Resources.
Controlling the non-linear intracavity dynamics of large He-Ne laser gyroscopes
NASA Astrophysics Data System (ADS)
Cuccato, D.; Beghi, A.; Belfi, J.; Beverini, N.; Ortolan, A.; Di Virgilio, A.
2014-02-01
A model based on Lamb's theory of gas lasers is applied to a He-Ne ring laser (RL) gyroscope to estimate and remove the laser dynamics contribution from the rotation measurements. The intensities of the counter-propagating laser beams exiting one cavity mirror are continuously observed together with a monitor of the laser population inversion. These observables, once properly calibrated with a dedicated procedure, allow us to estimate cold cavity and active medium parameters driving the main part of the non-linearities of the system. The quantitative estimation of intrinsic non-reciprocal effects due to cavity and active medium non-linear coupling plays a key role in testing fundamental symmetries of space-time with RLs. The parameter identification and noise subtraction procedure has been verified by means of a Monte Carlo study of the system, and experimentally tested on the G-PISA RL oriented with the normal to the ring plane almost parallel to the Earth's rotation axis. In this configuration the Earth's rotation rate provides the maximum Sagnac effect while the contribution of the orientation error is reduced to a minimum. After the subtraction of laser dynamics by a Kalman filter, the relative systematic errors of G-PISA reduce from 50 to 5 parts in 103 and can be attributed to the residual uncertainties on geometrical scale factor and orientation of the ring.
Dosage-dependent non-linear effect of L-dopa on human motor cortex plasticity.
Monte-Silva, Katia; Liebetanz, David; Grundey, Jessica; Paulus, Walter; Nitsche, Michael A
2010-09-15
The neuromodulator dopamine affects learning and memory formation and their likely physiological correlates, long-term depression and potentiation, in animals and humans. It is known from animal experiments that dopamine exerts a dosage-dependent, inverted U-shaped effect on these functions. However, this has not been explored in humans so far. In order to reveal a non-linear dose-dependent effect of dopamine on cortical plasticity in humans, we explored the impact of 25, 100 and 200 mg of L-dopa on transcranial direct current (tDCS)-induced plasticity in twelve healthy human subjects. The primary motor cortex served as a model system, and plasticity was monitored by motor evoked potential amplitudes elicited by transcranial magnetic stimulation. As compared to placebo medication, low and high dosages of L-dopa abolished facilitatory as well as inhibitory plasticity, whereas the medium dosage prolonged inhibitory plasticity, and turned facilitatory plasticity into inhibition. Thus the results show clear non-linear, dosage-dependent effects of dopamine on both facilitatory and inhibitory plasticity, and support the assumption of the importance of a specific dosage of dopamine optimally suited to improve plasticity. This might be important for the therapeutic application of dopaminergic agents, especially for rehabilitative purposes, and explain some opposing results in former studies.
NASA Astrophysics Data System (ADS)
Konstantinou, Konstantinos I.
2002-03-01
Observations and theoretical considerations have cast doubt on the suggestion that volcanic tremor source processes may be modelled by a linear oscillator that is set into resonance by a sustained disturbance. Volcanic tremor signals that accompanied the 1996 Vatnajökull subglacial eruption, central Iceland, have been analysed using methods from the discipline of non-linear dynamics in order to investigate the possibility that they originated from a non-linear source. The volcano-seismic phenomena associated with the eruption were recorded by a permanent network equipped with broad-band seismometers (HOTSPOT) using a sampling rate of 20 samples s-1 . The eruption was preceded by increased seismic activity for a period of 2 days, which also included a large earthquake with a moment magnitude of 5.6. The tremor during the first 2 days of the eruption has a high signal-to-noise ratio at the nearest station to the eruption site and starts as a continuous signal, later evolving to low-amplitude background tremor interrupted by high-amplitude, cigar-shaped bursts having an average duration of 250 s. The phase space, which describes the evolution of the behaviour of a non-linear system, was reconstructed from the original tremor seismograms using the delay embedding theorem suggested by Takens. The delay time used for the reconstruction was selected after examining the autocorrelation function, which showed a first zero crossing at a timelag of 4 samples and the average mutual information that showed no minimum, indicating that the tremor process may have been undersampled. Based also on phase space portraits for different delay times, a delay time of one sample interval (0.05 s) was used. The sufficient embedding dimension for phase space reconstruction was selected by applying the false nearest-neighbours method, which revealed complete unfolding of the tremor attractor at dimensions 7-8, implying upper bounds of its fractal dimension in the range 3.5-4.0. The phase
Hager, Robert; Yoon, E.S.; Ku, S.; D'Azevedo, E.F.; Worley, P.H.; Chang, C.S.
2016-06-15
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.
Hager, Robert; Yoon, E. S.; Ku, S.; D'Azevedo, E. F.; Worley, P. H.; Chang, C. S.
2016-04-04
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.
Hager, Robert; Yoon, E. S.; Ku, S.; ...
2016-04-04
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computingmore » systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.« less
Bifurcation and Resonance of a Mathematical Model for Non-Linear Motion of a Flooded Ship in Waves
NASA Astrophysics Data System (ADS)
Murashige, S.; Aihara, K.; Komuro, M.
1999-02-01
A flooded ship can exhibit undesirable non-linear roll motion even in waves of moderate amplitude. In order to understand the mechanism of this non-linear phenomenon, the non-linearly coupled dynamics of a ship and flood water are considered using a mathematical model for the simplified motion of a flooded ship in regular beam waves. This paper describes bifurcation and resonance of this coupled system. A bifurcation diagram shows that large-amplitude subharmonic motion exists in a wide range of parameters, and that the Hopf bifurcation is observed due to the dynamic effects of flood water. Resonance frequencies can be determined by linearization of this model. Comparison between the resonant points and the bifurcation curves suggests that non-linear resonance of this model can bring about large-amplitude subharmonic motion, even if it is in the non-resonate state of the linearized system.
NASA Astrophysics Data System (ADS)
Hager, Robert; Yoon, E. S.; Ku, S.; D'Azevedo, E. F.; Worley, P. H.; Chang, C. S.
2016-06-01
Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker-Planck-Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker-Planck-Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.
An on-site modal testing method for the detection of structural non-linearities Part II: Application
NASA Astrophysics Data System (ADS)
Lee, Gun-Myung; Trethewey, Martin W.
1992-03-01
The work presented in this paper discusses the practical implementation of an experimental testing/analysis method to detect non-linear structural behaviour in an effective on-site fashion. The testing/evaluation method is based on the linear analysis of non-linear systems with increasing amplitude random excitation signals and is presented in Part I of this work. In the second part of this work, the method is applied to two distinctly different types of structures; (1) a simple beam structure and; (2) an industrial robot. The analysis shows that the beam structure behaves in a linear fashion throughout the operating range. The robot structure exhibited non-linear characteristics over the frequency range of interest. The analysis of the robot data provided a means to classify the types of non-linearities present in the structure. These actual testing applications indicate the feasibility and capability of the proposed method.
Interior solution for the Kerr metric
NASA Astrophysics Data System (ADS)
Hernandez-Pastora, J. L.; Herrera, L.
2017-01-01
A recently presented general procedure to find static and axially symmetric, interior solutions to the Einstein equations is extended to the stationary case, and applied to find an interior solution for the Kerr metric. The solution, which is generated by an anisotropic fluid, verifies the energy conditions for a wide range of values of the parameters, and matches smoothly to the Kerr solution, thereby representing a globally regular model describing a nonspherical and rotating source of gravitational field. In the spherically symmetric limit, our model converges to the well-known incompressible perfect fluid solution. The key stone of our approach is based on an ansatz allowing to define the interior metric in terms of the exterior metric functions evaluated at the boundary source. The physical variables of the energy-momentum tensor are calculated explicitly, as well as the geometry of the source in terms of the relativistic multipole moments.
Analysis of structural seismic behaviour: from non stationary to non linear effects
NASA Astrophysics Data System (ADS)
Carlo Ponzo, Felice; Ditommaso, Rocco; Monaco, Lisa
2014-05-01
The change in fundamental frequency of a building is considered the simplest way to detect the onset of damage. Several authors in the past proposed that the difference in periods that can be observed among ambient noise, earthquake weak-motion measurements can be attributed to transient non-linearity due to reversible modification of the building characteristic (e.g. the degree of coupling between frame and infill in reinforced concrete buildings). The necessity of effective and efficient seismic protection of vast and aging structures and infrastructure has increased markedly the interest in the development of structural monitoring techniques. Damage to any structure alters its dynamic properties and for that dynamic monitoring techniques enable the identification of damage by comparing pre and post seismic excitation characteristic. The principle parameters usually monitored are: fundamental period, damping factors and modal shapes. Several damage identification and localization techniques are based on variations in these parameters (see, e.g Ponzo et al. 2010 and reference therein). Non Destructive Evaluation (NDE) methods can be rank on four different levels with the higher levels requiring increased quality and quantity of available information. The most common methods are therefore related to Level 1, due to their simplified and economic implementation. These methods are based mainly upon the variation of vibration frequencies and/or variations in Equivalent Viscous Damping associated with these vibration modes. It is important to underline however that although the presence of damage will lead to alterations in vibration modes the opposite does not necessarily hold true. Two types of frequency variation can be distinguished; long time period variations (due to variations in temperature, foundation soil moisture content etc.) and short period variations (for example due to a seismic event). For short period variations, changes in frequency can be attributed
A kinetic formulation of piezoresistance in N-type silicon: Application to non-linear effects
NASA Astrophysics Data System (ADS)
Charbonnieras, A. R.; Tellier, C. R.
1999-07-01
This paper is devoted to the theoretical study of the influence of the temperature and of the doping on the piezoresistance of N-type silicon. In the first step the fractional change in the resistivity caused by stresses is calculated in the framework of a multivalley model using a kinetic transport formulation based on the Boltzmann transport equation. In the second step shifts in the minima of the conduction band and the resulting shift of the Fermi level are expressed in terms of deformation potentials and of stresses. General expressions for the fundamental linear, π_{11} and π_{12}, and non-linear, π_{111}, π_{112}, π_{122} and π_{123}, piezoresistance coefficients are then derived. Plots of the non-linear piezoresistance coefficients against the reduced shift of the Fermi level or against temperature allow us to characterize the influence of doping and temperature. Finally some attempts are made to estimate the non-linearity for heavily doped semiconductor gauges. Cette publication est consacrée à l'étude théorique de l'influence de la température et du dopage sur la piezorésistivité du silicium type N. Dans une première étape nous adoptons le modèle de vallées et nous utilisons une formulation cinétique du transport électronique faisant appel à l'équation de transport de Boltzmann pour calculer la variation de la résistivité du semiconducteur sous contrainte. Dans la deuxième étape nous exprimons les déplacements des minima de la bande de conduction et du niveau de Fermi en termes de potentiels de déformation et de contraintes. Nous proposons ensuite des expressions générales pour les coefficients piezorésistifs fondamentaux linéaires, π_{11} et π_{12}, et non-linéaires, π_{111}, π_{112}, π_{122} et π_{123}. Des représentations graphiques des variations des coefficients non-linéaires permettent de caractériser l'influence du dopage et de la température. Enfin nous fournissons une première pré-estimation des effets
A non-Linear transport model for determining shale rock characteristics
NASA Astrophysics Data System (ADS)
Ali, Iftikhar; Malik, Nadeem
2016-04-01
Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007
2012-01-01
Background This paper lies in the context of modeling the evolution of gene expression away from stationary states, for example in systems subject to external perturbations or during the development of an organism. We base our analysis on experimental data and proceed in a top-down approach, where we start from data on a system's transcriptome, and deduce rules and models from it without a priori knowledge. We focus here on a publicly available DNA microarray time series, representing the transcriptome of Drosophila across evolution from the embryonic to the adult stage. Results In the first step, genes were clustered on the basis of similarity of their expression profiles, measured by a translation-invariant and scale-invariant distance that proved appropriate for detecting transitions between development stages. Average profiles representing each cluster were computed and their time evolution was analyzed using coupled differential equations. A linear and several non-linear model structures involving a transcription and a degradation term were tested. The parameters were identified in three steps: determination of the strongest connections between genes, optimization of the parameters defining these connections, and elimination of the unnecessary parameters using various reduction schemes. Different solutions were compared on the basis of their abilities to reproduce the data, to keep realistic gene expression levels when extrapolated in time, to show the biologically expected robustness with respect to parameter variations, and to contain as few parameters as possible. Conclusions We showed that the linear model did very well in reproducing the data with few parameters, but was not sufficiently robust and yielded unrealistic values upon extrapolation in time. In contrast, the non-linear models all reached the latter two objectives, but some were unable to reproduce the data. A family of non-linear models, constructed from the exponential of linear combinations
Surface and Atmospheric Parameter Retrieval From AVIRIS Data: The Importance of Non-Linear Effects
NASA Technical Reports Server (NTRS)
Green Robert O.; Moreno, Jose F.
1996-01-01
AVIRIS data represent a new and important approach for the retrieval of atmospheric and surface parameters from optical remote sensing data. Not only as a test for future space systems, but also as an operational airborne remote sensing system, the development of algorithms to retrieve information from AVIRIS data is an important step to these new approaches and capabilities. Many things have been learned since AVIRIS became operational, and the successive technical improvements in the hardware and the more sophisticated calibration techniques employed have increased the quality of the data to the point of almost meeting optimum user requirements. However, the potential capabilities of imaging spectrometry over the standard multispectral techniques have still not been fully demonstrated. Reasons for this are the technical difficulties in handling the data, the critical aspect of calibration for advanced retrieval methods, and the lack of proper models with which to invert the measured AVIRIS radiances in all the spectral channels. To achieve the potential of imaging spectrometry, these issues must be addressed. In this paper, an algorithm to retrieve information about both atmospheric and surface parameters from AVIRIS data, by using model inversion techniques, is described. Emphasis is put on the derivation of the model itself as well as proper inversion techniques, robust to noise in the data and an inadequate ability of the model to describe natural variability in the data. The problem of non-linear effects is addressed, as it has been demonstrated to be a major source of error in the numerical values retrieved by more simple, linear-based approaches. Non-linear effects are especially critical for the retrieval of surface parameters where both scattering and absorption effects are coupled, as well as in the cases of significant multiple-scattering contributions. However, sophisticated modeling approaches can handle such non-linear effects, which are especially
Hemanth, M; Deoli, Shilpi; Raghuveer, H P; Rani, M S; Hegde, Chatura; Vedavathi, B
2015-01-01
Background: Simulation of periodontal ligament (PDL) using non-linear finite element method (FEM) analysis gives better insight into understanding of the biology of tooth movement. The stresses in the PDL were evaluated for intrusion and lingual root torque using non-linear properties. Materials and Methods: A three-dimensional (3D) FEM model of the maxillary incisors was generated using Solidworks modeling software. Stresses in the PDL were evaluated for intrusive and lingual root torque movements by 3D FEM using ANSYS software. These stresses were compared with linear and non-linear analyses. Results: For intrusive and lingual root torque movements, distribution of stress over the PDL was within the range of optimal stress value as proposed by Lee, but was exceeding the force system given by Proffit as optimum forces for orthodontic tooth movement with linear properties. When same force load was applied in non-linear analysis, stresses were more compared to linear analysis and were beyond the optimal stress range as proposed by Lee for both intrusive and lingual root torque. To get the same stress as linear analysis, iterations were done using non-linear properties and the force level was reduced. Conclusion: This shows that the force level required for non-linear analysis is lesser than that of linear analysis. PMID:26435629
NASA Astrophysics Data System (ADS)
Krak, Michael D.; Dreyer, Jason T.; Singh, Rajendra
2016-03-01
A vehicle clutch damper is intentionally designed to contain multiple discontinuous non-linearities, such as multi-staged springs, clearances, pre-loads, and multi-staged friction elements. The main purpose of this practical torsional device is to transmit a wide range of torque while isolating torsional vibration between an engine and transmission. Improved understanding of the dynamic behavior of the device could be facilitated by laboratory measurement, and thus a refined vibratory experiment is proposed. The experiment is conceptually described as a single degree of freedom non-linear torsional system that is excited by an external step torque. The single torsional inertia (consisting of a shaft and torsion arm) is coupled to ground through parallel production clutch dampers, which are characterized by quasi-static measurements provided by the manufacturer. Other experimental objectives address physical dimensions, system actuation, flexural modes, instrumentation, and signal processing issues. Typical measurements show that the step response of the device is characterized by three distinct non-linear regimes (double-sided impact, single-sided impact, and no-impact). Each regime is directly related to the non-linear features of the device and can be described by peak angular acceleration values. Predictions of a simplified single degree of freedom non-linear model verify that the experiment performs well and as designed. Accordingly, the benchmark measurements could be utilized to validate non-linear models and simulation codes, as well as characterize dynamic parameters of the device including its dissipative properties.
Kumar, P; Kumar, Dinesh; Rai, K N
2016-08-01
In this article, a non-linear dual-phase-lag (DPL) bio-heat transfer model based on temperature dependent metabolic heat generation rate is derived to analyze the heat transfer phenomena in living tissues during thermal ablation treatment. The numerical solution of the present non-linear problem has been done by finite element Runge-Kutta (4,5) method which combines the essence of Runge-Kutta (4,5) method together with finite difference scheme. Our study demonstrates that at the thermal ablation position temperature predicted by non-linear and linear DPL models show significant differences. A comparison has been made among non-linear DPL, thermal wave and Pennes model and it has been found that non-linear DPL and thermal wave bio-heat model show almost same nature whereas non-linear Pennes model shows significantly different temperature profile at the initial stage of thermal ablation treatment. The effect of Fourier number and Vernotte number (relaxation Fourier number) on temperature profile in presence and absence of externally applied heat source has been studied in detail and it has been observed that the presence of externally applied heat source term highly affects the efficiency of thermal treatment method.
Chronology protection in the Kerr metric
NASA Astrophysics Data System (ADS)
Bini, Donato; de Felice, Fernando
2015-11-01
We show that causality violation in a Kerr naked singularity spacetime is constrained by the existence of (radial) potential barriers. We extend to the class of vortical non-equatorial null geodesics confined to θ = constant hyperboloids ( boreal orbits) previous results concerning timelike ones (Calvani et al. in Gen Rel Gravit 9:155, 1978), showing that within this class of orbits, the causality principle is rigorously satisfied.
Giant Kerr nonlinearities in circuit quantum electrodynamics.
Rebić, Stojan; Twamley, Jason; Milburn, Gerard J
2009-10-09
The very small size of optical nonlinearities places strict restrictions on the types of novel physics one can explore. This work describes how a single artificial multilevel Cooper pair box molecule, interacting with a superconducting microwave coplanar resonator, when suitably driven, can generate extremely large optical nonlinearities at microwave frequencies, with no associated absorption. We describe how the giant self-Kerr effect can be detected by measuring the second-order correlation function and quadrature squeezing spectrum.
Kerr-Schild–Kundt metrics are universal
NASA Astrophysics Data System (ADS)
Gürses, Metin; Çağrı Şişman, Tahsin; Tekin, Bayram
2017-04-01
We define (non-Einsteinian) universal metrics as the metrics that solve the source-free covariant field equations of generic gravity theories. Here, extending the rather scarce family of universal metrics known in the literature, we show that the Kerr-Schild–Kundt class of metrics are universal. Besides being interesting on their own, these metrics can provide consistent backgrounds for quantum field theory at extremely high energies.
Casimir energy in Kerr space-time
NASA Astrophysics Data System (ADS)
Sorge, F.
2014-10-01
We investigate the vacuum energy of a scalar massless field confined in a Casimir cavity moving in a circular equatorial orbit in the exact Kerr space-time geometry. We find that both the orbital motion of the cavity and the underlying space-time geometry conspire in lowering the absolute value of the (renormalized) Casimir energy ⟨ɛvac⟩ren , as measured by a comoving observer, with respect to whom the cavity is at rest. This, in turn, causes a weakening in the attractive force between the Casimir plates. In particular, we show that the vacuum energy density ⟨ɛvac⟩ren→0 when the orbital path of the Casimir cavity comes close to the corotating or counter-rotating circular null orbits (possibly geodesic) allowed by the Kerr geometry. Such an effect could be of some astrophysical interest on relevant orbits, such as the Kerr innermost stable circular orbits, being potentially related to particle confinement (as in some interquark models). The present work generalizes previous results obtained by several authors in the weak field approximation.
Non-linear shrinkage estimation of large-scale structure covariance
NASA Astrophysics Data System (ADS)
Joachimi, Benjamin
2017-03-01
In many astrophysical settings, covariance matrices of large data sets have to be determined empirically from a finite number of mock realizations. The resulting noise degrades inference and precludes it completely if there are fewer realizations than data points. This work applies a recently proposed non-linear shrinkage estimator of covariance to a realistic example from large-scale structure cosmology. After optimizing its performance for the usage in likelihood expressions, the shrinkage estimator yields subdominant bias and variance comparable to that of the standard estimator with a factor of ∼50 less realizations. This is achieved without any prior information on the properties of the data or the structure of the covariance matrix, at a negligible computational cost.
Dyson, Doris H
2003-01-01
A possible reason for superficial learning in an introductory anesthesia course was considered to be a lack of visual reinforcement at the time of examination preparation. Students had limited access to live animal laboratories and clinical cases during the course, reducing their ability to depend on experiential learning. In an attempt to improve student learning, simple presentation software was used to develop a supplemental CD. The design involved multiple PowerPoint presentations that incorporated text, pictures, videos, and self-assessments. Non-linear exploration of the topics covered was made possible by extensive use of hyperlinks within and between presentations, moving the student to definitions, background material, videos, advanced details, and previously covered information. Comments received from students on a prototype were positive overall, and improvements were made related to their feedback. Other supplemental materials and lecture presentations can easily incorporate the techniques described here.
Wave Driven Non-linear Flow Oscillator for the 22-Year Solar Cycle
NASA Technical Reports Server (NTRS)
Mayr, Hans G.; Wolff, Charles L.; Hartle, Richard E.; Einaudi, Franco (Technical Monitor)
2000-01-01
In the Earth's atmosphere, a zonal flow oscillation is observed with periods between 20 and 32 months, the Quasi Biennial Oscillation. This oscillation does not require external time dependent forcing but is maintained by non-linear wave momentum deposition. It is proposed that such a mechanism also drives long-period oscillations in planetary and stellar interiors. We apply this mechanism to generate a flow oscillation for the 22-year solar cycle. The oscillation would occur just below the convective envelope where waves can propagate. Using scale analysis, we present results from a simplified model that incorporates Hines' gravity wave parameterization. Wave amplitudes less than 10 m/s can produce reversing zonal flows of 25 m/s that should be sufficient to generate a corresponding oscillation in the poloidal magnetic field. Low buoyancy frequency and the associated increase in turbulence help to produce the desired oscillation period of the flow.
Ultrafast Rotation of Light Fields Applied to Highly Non-Linear Optics
NASA Astrophysics Data System (ADS)
Quéré, Fabien
2014-05-01
Femtosecond laser beams can exhibit spatio-temporal couplings (STC), i.e. a temporal dependence of their spatial properties, or vice versa. Although these couplings have long been considered as detrimental for high-intensity and ultrafast experiments, moderate and controlled STC provide a powerful means of controlling high-intensity laser-matter interactions. This talk will first explain the basics of a particular STC, where the propagation direction of laser light rotates in time on the femtosecond time scale. Laser pulses with such ultrafast wavefront rotation can be used to generate attosecond pulses of light through non-linear optical processes. We show that these pulses, periodically generated in each laser cycle, can then be emitted in spatially separated beamlets. This effects provides a new type of light sources called attosecond lighthouses, and can be exploited for ultrafast measurements with femtosecond resolution, in a scheme called photonic streaking.
Scanning Electron Microscope Calibration Using a Multi-Image Non-Linear Minimization Process
NASA Astrophysics Data System (ADS)
Cui, Le; Marchand, Éric
2015-04-01
A scanning electron microscope (SEM) calibrating approach based on non-linear minimization procedure is presented in this article. A part of this article has been published in IEEE International Conference on Robotics and Automation (ICRA), 2014. . Both the intrinsic parameters and the extrinsic parameters estimations are achieved simultaneously by minimizing the registration error. The proposed approach considers multi-images of a multi-scale calibration pattern view from different positions and orientations. Since the projection geometry of the scanning electron microscope is different from that of a classical optical sensor, the perspective projection model and the parallel projection model are considered and compared with distortion models. Experiments are realized by varying the position and the orientation of a multi-scale chessboard calibration pattern from 300× to 10,000×. The experimental results show the efficiency and the accuracy of this approach.
Study of non-linear photoemission effects in III-V semiconductors
Tang, H.; Alley, R.K.; Aoyagi, H.
1993-10-01
Our experience at SLAC with photoemission-based polarized electron sources has shown that charge limit is an important phenomenon that may significantly limit the performance of a photocathode for applications requiring high intensity electron beams. In the process of developing high performance photocathodes for the ongoing and future SLC high energy physics programs, we have studied the various aspects of the charge limit phenomenon. We find that the charge limit effect arises as a result of non-linear response of a photocathode to high intensity light illumination. The size of the charge limit not only depends on the quantum efficiency of the cathode but also depends critically on the extraction electric field. In addition, we report the observation of charge oversaturation when the intensity of the incident light becomes too large.
Numerical Demultiplexing of Color Image Sensor Measurements via Non-linear Random Forest Modeling
Deglint, Jason; Kazemzadeh, Farnoud; Cho, Daniel; Clausi, David A.; Wong, Alexander
2016-01-01
The simultaneous capture of imaging data at multiple wavelengths across the electromagnetic spectrum is highly challenging, requiring complex and costly multispectral image devices. In this study, we investigate the feasibility of simultaneous multispectral imaging using conventional image sensors with color filter arrays via a novel comprehensive framework for numerical demultiplexing of the color image sensor measurements. A numerical forward model characterizing the formation of sensor measurements from light spectra hitting the sensor is constructed based on a comprehensive spectral characterization of the sensor. A numerical demultiplexer is then learned via non-linear random forest modeling based on the forward model. Given the learned numerical demultiplexer, one can then demultiplex simultaneously-acquired measurements made by the color image sensor into reflectance intensities at discrete selectable wavelengths, resulting in a higher resolution reflectance spectrum. Experimental results demonstrate the feasibility of such a method for the purpose of simultaneous multispectral imaging. PMID:27346434
Non-Linear Dynamics Approach to Assessing Woody-Encroachment in Grasslands
NASA Astrophysics Data System (ADS)
Brunsell, N. A.; Nippert, J. B.; Van Vleck, E.
2015-12-01
Woody species are encroaching on grasslands globally. Here, we investigate the spatial and temporal dynamics of this encroachment in relation to climate and fire regimes in the central U.S. A low-dimensional model is used to assess stability of species composition. Sixe years of eddy covariance data at a paired grassland and woody encroachment site at the Konza Prairie LTER site are used to verify carbon and water dynamics. Historical aerial photography and remote sensing data are used to quantify the spatial diffusion of woody tree fraction into grasslands. Non-linear dynamics approaches are used to quantify the stability of vegetation and the presence of tipping points in relation to woody fraction, fire frequency and precipitation and temperature variability. Understanding the roles of multiple confounding forcing factors operating at disparate timescales is essential for predicting future woody encroachment and the water and climate implications of land cover transitions.
Synthesis of monodispersed palladium nanoparticles using tannic acid and its optical non-linearity
NASA Astrophysics Data System (ADS)
Meena Kumari, M.; Aromal, S. Aswathy; Philip, Daizy
2013-02-01
Palladium nanoparticles with average size 11.3 nm have been synthesized via a one-step reduction and capping method. This colloidal route using tannic acid does not require any other surfactant or capping agent to direct the growth of palladium nanoparticles. The effect of temperature on the conversion of Pd2+ ion to Pd0 is investigated. The growth process of nanoparticles is monitored using UV-visible spectra. The morphology and phase transformation have been confirmed by transmission electron microscopy and X-ray diffraction. An attempt to reveal the capping mechanism of tannic acid is done through FTIR analysis. The optical non-linearity of the samples was studied using open aperture Z-scan technique. The significance of this protocol for the generation of environmentally benign palladium nanoparticles lies mainly in its simplicity and cost effectiveness.
Non-linear characteristics and long-range correlations in Asian stock markets
NASA Astrophysics Data System (ADS)
Jiang, J.; Ma, K.; Cai, X.
2007-05-01
We test several non-linear characteristics of Asian stock markets, which indicates the failure of efficient market hypothesis and shows the essence of fractal of the financial markets. In addition, by using the method of detrended fluctuation analysis (DFA) to investigate the long range correlation of the volatility in the stock markets, we find that the crossover phenomena exist in the results of DFA. Further, in the region of small volatility, the scaling behavior is more complicated; in the region of large volatility, the scaling exponent is close to 0.5, which suggests the market is more efficient. All these results may indicate the possibility of characteristic multifractal scaling behaviors of the financial markets.
Following the course of pre-implantation embryo patterning by non-linear microscopy.
Kyvelidou, Christiana; Tserevelakis, George J; Filippidis, George; Ranella, Anthi; Kleovoulou, Anastasia; Fotakis, Costas; Athanassakis, Irene
2011-12-01
Embryo patterning is subject to intense investigation. So far only large, microscopically obvious structures like polar body, cleavage furrow, pro-nucleus shape can be evaluated in the intact embryo. Using non-linear microscopic techniques, the present work describes new methodologies to evaluate pre-implantation mouse embryo patterning. Third Harmonic Generation (THG) imaging, by detecting mitochondrial/lipid body structures, could provide valuable and complementary information as to the energetic status of pre-implantation embryos, time evolution of different developmental stages, embryo polarization prior to mitotic division and blastomere equivalence. Quantification of THG imaging detected highest signalling in the 2-cell stage embryos, while evaluating a 12-18% difference between blastomeres at the 8-cell stage embryos. Such a methodology provides novel, non-intrusive imaging assays to follow up intracellular structural patterning associated with the energetic status of a developing embryo, which could be successfully used for embryo selection during the in vitro fertilization process.
A non-linear camera calibration with modified teaching-learning-based optimization algorithm
NASA Astrophysics Data System (ADS)
Zhang, Buyang; Yang, Hua; Yang, Shuo
2015-12-01
In this paper, we put forward a novel approach based on hierarchical teaching-and-learning-based optimization (HTLBO) algorithm for nonlinear camera calibration. This algorithm simulates the teaching-learning ability of teachers and learners of a classroom. Different from traditional calibration approach, the proposed technique can find the nearoptimal solution without the need of accurate initial parameters estimation (with only very loose parameter bounds). With the introduction of cascade of teaching, the convergence speed is rapid and the global search ability is improved. Results from our study demonstrate the excellent performance of the proposed technique in terms of convergence, accuracy, and robustness. The HTLBO can also be used to solve many other complex non-linear calibration optimization problems for its good portability.
Non-linear interactions of plasma waves in the context of solar particle acceleration
NASA Astrophysics Data System (ADS)
Gallegos-Cruz, A.; Perez-Peraza, J.
2001-08-01
Stochastic particle acceleration in plasmas by means of MHD turbulence in-volves a wide range of alternatives according to, the specific wave mode, the frequency regime of the turbulence, the kind of particles to be accelerated, the assumed plasma model and so on. At present most of the alternatives have been studied with relatively deepness, though some features are not yet com-pletely understood. One of them is the delimitation of the real importance of non-lineal effects of turbulence waves in the process of particle acceleration. In this work we analyse such effects taking into account the temporal evolution of the turbulence. For illustration we exemplify our analysis with the fast MHD mode. Our results show that in some specific stages of the turbulence evolu-tion, non-linear interactions have important effects in the process of particle acceleration.
Tracing Analytic Ray Curves for Light and Sound Propagation in Non-Linear Media.
Mo, Qi; Yeh, Hengchin; Manocha, Dinesh
2016-11-01
The physical world consists of spatially varying media, such as the atmosphere and the ocean, in which light and sound propagates along non-linear trajectories. This presents a challenge to existing ray-tracing based methods, which are widely adopted to simulate propagation due to their efficiency and flexibility, but assume linear rays. We present a novel algorithm that traces analytic ray curves computed from local media gradients, and utilizes the closed-form solutions of both the intersections of the ray curves with planar surfaces, and the travel distance. By constructing an adaptive unstructured mesh, our algorithm is able to model general media profiles that vary in three dimensions with complex boundaries consisting of terrains and other scene objects such as buildings. Our analytic ray curve tracer with the adaptive mesh improves the efficiency considerably over prior methods. We highlight the algorithm's application on simulation of visual and sound propagation in outdoor scenes.
The massive O(N) non-linear sigma model at high orders
NASA Astrophysics Data System (ADS)
Bijnens, Johan; Carloni, Lisa
2011-02-01
We extend our earlier work on the massive O(N) non-linear sigma model to other observables. We derive expressions at leading order in the large N expansion at all orders in the loop expansion for the decay constant, vacuum expectation value, meson-meson scattering and the scalar and vector form factors. This is done using cactus diagram resummation using a generalized gap equation and other recursion relations. For general N we derive the expressions for the n-th-loop-order leading logarithms (M/Flog (/M))n, up to five loops for the decay constant and vacuum expectation value (VEV) and up to four loops for meson-meson scattering, the scalar and vector form factors. We also quote our earlier result for the mass. The large N results do not give a good approximation for the case N=3. We use our results to study the convergence of the perturbative series and compare with elastic unitarity.
Design and fabrication of ytterbium-doped photonic crystal fiber with low non-linearity
NASA Astrophysics Data System (ADS)
Wu, Jiale; Zhang, Wei; Zhou, Guiyao; Xia, Changming; Liu, Jiantao; Zheng, Yan; Tian, Hongchun; Hou, Zhiyun
2015-05-01
We report on an ytterbium-doped photonic crystal fiber fabricated by laser sintering technology combined with a solution doping method. This novel fabrication process has never been reported to the best of our knowledge. Together with low non-linearity, this PCF combines the advantages of high pump absorption efficiency and bend-insensitive, which makes this fiber predestinated for the high power fiber laser applications. The fiber laser experiment was conducted with a simple Fabry-Perot cavity to verify the performance of the PCF. A high slope efficiency of ~70.6% was obtained from a 1.5 m-long fiber. During the experiment, no roll over was observed up to the highest power level, which was only limited by the available pump power. The experimental results reveal the enormous output power scaling potential of the PCF.
Vibration and chaos control of non-linear torsional vibrating systems
NASA Astrophysics Data System (ADS)
El-Bassiouny, A. F.
2006-07-01
Vibration of a mechanical system is often an undesirable phenomenon, as it may cause damage, disturbance, discomfort and, sometimes, destruction of systems and structures. To reduce vibration, many methods can be used. The most famous method is using dynamic absorbers or dampers. In the present work, a non-linear elastomeric damper or absorber is used to control the torsional vibrations of the crankshaft in internal combustion engines, when subjected to both external and parametric excitation torques. The multiple time scale perturbation method is applied to determine the equations governing the modulation of both amplitudes and phases of the crankshaft and the absorber. These equations are used to determine the steady-state amplitudes and system stability. Numerical integration of the basic equations is applied to investigate the effects of the different parameters on system behavior. A comparison is made with the available published work. Some recommendations are given at the end of the work.
Relativistic cosmic ray spectra in the full non-linear theory of shock acceleration
NASA Technical Reports Server (NTRS)
Eichler, D.; Ellison, D. C.
1985-01-01
The non-linear theory of shock acceleration was generalized to include wave dynamics. In the limit of rapid wave damping, it is found that a finite ave velocity tempers the acceleration of high Mach number shocks and limits the maximum compression ratio even when energy loss is important. For a given spectrum, the efficiency of relativistic particle production is essentially independent of v sub Ph. For the three families shown, the percentage of kinetic energy flux going into relativistic particles is (1) 72%, 2) 44%, and (3) 26% (this includes the energy loss at the upper energy cuttoff). Even small v sub ph, typical of the HISM, produce quasi-universal spectra that depend only weakly on the acoustic Mach number. These spectra should be close enough to e(-2) to satisfy cosmic ray source requirements.
Can the ZoMBieS method be used to characterise scintillator non-linearity?
Bignell, L J
2014-05-01
Measurements of the detection efficiency as a function of deposited electron energy in a liquid scintillation cocktail between 4 keV and 49 keV are obtained using the ZoMBieS method. Comparison is made between the measured data and the Poisson-Birks detection efficiency model. Measurements of the Birks non-linearity parameter, kB, and the linearised scintillation response of each photomultiplier, ω(i), were made using these data. However, the value of kB that best linearises the scintillator response is found to vary depending upon which photomultiplier is used in its determination, and the measured kB and ω(i) vary depending on the external source geometry. The cause of this behaviour is unknown. The triple-coincident detection efficiency appears to be unaffected by any systematic errors.
Non-linear Parameter Estimates from Non-stationary MEG Data
Martínez-Vargas, Juan D.; López, Jose D.; Baker, Adam; Castellanos-Dominguez, German; Woolrich, Mark W.; Barnes, Gareth
2016-01-01
We demonstrate a method to estimate key electrophysiological parameters from resting state data. In this paper, we focus on the estimation of head-position parameters. The recovery of these parameters is especially challenging as they are non-linearly related to the measured field. In order to do this we use an empirical Bayesian scheme to estimate the cortical current distribution due to a range of laterally shifted head-models. We compare different methods of approaching this problem from the division of M/EEG data into stationary sections and performing separate source inversions, to explaining all of the M/EEG data with a single inversion. We demonstrate this through estimation of head position in both simulated and empirical resting state MEG data collected using a head-cast. PMID:27597815
Scalar field-perfect fluid correspondence and non-linear perturbation equations
Mainini, Roberto
2008-07-15
The properties of dynamical dark energy (DE) and, in particular, the possibility that it can form or contribute to stable inhomogeneities have been widely debated in recent literature, and also in association with a possible coupling between DE and dark matter (DM). In order to clarify this issue, in this paper we present a general framework for the study of the non-linear phases of structure formation, showing the equivalence of two possible descriptions of DE: a scalar field {phi} self-interacting through a potential V ({phi}) and a perfect fluid with an assigned negative equation of state w(a). This enables us to show that, in the presence of coupling, the mass of DE quanta may increase where large DM condensations are present, with the result that also DE may be involved in the clustering process.
A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation
Banks, J W; Hittinger, J A
2009-11-24
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.