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
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
Quantum Process Tomography of an Optically-Controlled Kerr Non-linearity
NASA Astrophysics Data System (ADS)
Kupchak, Connor; Rind, Samuel; Jordaan, Bertus; Figueroa, Eden
2015-11-01
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.
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.
Transitional behavior between self-Kerr and cross-Kerr effects by two photons
Koshino, Kazuki
2007-06-15
The transitional behavior of the two-photon Kerr effect between the self-Kerr and cross-Kerr cases is investigated. To this end, we have developed a semiclassical method for evaluating the two-photon Kerr effect that is applicable to any two-photon input state. It is revealed that the maximum Kerr effect is obtained when the second photon is input with a delay time that corresponds to the absorption time of the first photon by the optical material.
NASA Astrophysics Data System (ADS)
Menezes, J. W. M.; Fraga, W. B.; Lima, F. T.; Guimarães, G. F.; Ferreira, A. C.; Lyra, M. L.; Sombra, A. S. B.
2011-06-01
Recently, much attention has been given to the influence of the relaxation process of the non-linear response, because the usual assumption of instantaneous non-linear response fails for ultra-short pulses, and additional contributions coming from non-linear dispersion and delayed non-linearity have to be taken into account. This article presents a numerical analysis of the symmetric planar and asymmetric planar three-core non-linear directional fiber couplers operating with a soliton pulse, where effects of both delayed and instantaneous non-linear Kerr responses are analyzed for implementation of an all-optical half-adder. To implement this all-optical half-adder, eight configurations were analyzed for the non-linear directional fiber coupler, with two symmetric and six asymmetric configurations. The half-adder is the key building block for many digital processing functions, such as shift register, binary counter, and serial parallel data converters. The optical coupler is an important component for applications in optical-fiber telecommunication systems and all integrated optical circuit because of its very high switching speeds. In this numerical simulation, the symmetric/asymmetric planar presents a structure with three cores in a parallel equidistant arrangement, three logical inputs, and two output energy. To prove the effectiveness of the theoretical model for generation of the all-optical half-adder, the best phase to be applied to the control pulse was sought, and a study was done of the extinction ratio level as a function of the Δ > parameter, the normalized time duration, and the Sum and Carry outputs of the (symmetric planar/asymmetric planar) non-linear directional fiber coupler. In this article, the interest is in transmission characteristics, extinction ratio level, normalized time duration, and pulse evolution along the non-linear directional fiber coupler. To compare the performance of the all-optical half-adders, the figure of merit of the
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
Tewarie, P; Bright, M G; Hillebrand, A; Robson, S E; Gascoyne, L E; Morris, P G; Meier, J; Van Mieghem, P; Brookes, M J
2016-04-15
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.
Passive CPHASE Gate via Cross-Kerr Nonlinearities.
Brod, Daniel J; Combes, Joshua
2016-08-19
A fundamental and open question is whether cross-Kerr nonlinearities can be used to construct a controlled-phase (cphase) gate. Here we propose a gate constructed from a discrete set of atom-mediated cross-Kerr interaction sites with counterpropagating photons. We show that the average gate fidelity F between a cphase and our proposed gate increases as the number of interaction sites increases and the spectral width of the photon decreases; e.g., with 12 sites we find F>99%. PMID:27588840
Breakdown of the cross-Kerr scheme for photon counting.
Fan, Bixuan; Kockum, Anton F; Combes, Joshua; Johansson, Göran; Hoi, Io-chun; Wilson, C M; Delsing, Per; Milburn, G J; Stace, Thomas M
2013-02-01
We show, in the context of single-photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarizability model known as the cross-Kerr effect. We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single-photon applications. Our results are presented in the context of a transmon in a one-dimensional microwave waveguide, but the conclusions also apply to optical systems. PMID:23414018
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.
Semiclassical evaluation of the two-photon cross-Kerr effect
Koshino, Kazuki
2006-11-15
When two distinguishable photons are simultaneously input into a nonlinear system, the output photons undergo nonlinear optical effects of the cross-Kerr type. Theoretical quantification of this two-photon cross-Kerr effect requires, in principle, a fully quantum-mechanical analysis involving heavy computation. In this paper, we propose a method for evaluating the two-photon cross-Kerr effect using a semiclassical optical response theory. The semiclassical method enables precise evaluation of the cross-Kerr effect with greatly reduced computation. The validity of the method is confirmed using a model nonlinear system.
Linear vs non-linear QCD evolution in the neutrino-nucleon cross section
NASA Astrophysics Data System (ADS)
Albacete, Javier L.; Illana, José I.; Soto-Ontoso, Alba
2016-03-01
Evidence for an extraterrestrial flux of ultra-high-energy neutrinos, in the order of PeV, has opened a new era in Neutrino Astronomy. An essential ingredient for the determination of neutrino fluxes from the number of observed events is the precise knowledge of the neutrino-nucleon cross section. In this work, based on [1], we present a quantitative study of σνN in the neutrino energy range 104 < Eν < 1014 GeV within two transversal QCD approaches: NLO DGLAP evolution using different sets of PDFs and BK small-x evolution with running coupling and kinematical corrections. Further, we translate this theoretical uncertainty into upper bounds for the ultra-high-energy neutrino flux for different experiments.
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.
Cross-Kerr effect on an optomechanical system
NASA Astrophysics Data System (ADS)
Xiong, Wei; Jin, Da-Yu; Qiu, Yueyin; Lam, Chi-Hang; You, J. Q.
2016-02-01
We study the cross-Kerr (CK) effect on an optomechanical system driven by two-tone fields. We show that in the presence of the CK effect, a bistable behavior of the mean photon number in the cavity becomes more robust against the fluctuations of the frequency detuning between the cavity mode and the control field. The bistability can also be turned into a tristability within the experimentally accessible range of the system parameters. Also, we find that the symmetric profile of the optomechanically induced transparency is broken and the zero-absorption point is shifted in the presence of the CK effect. This shift can be used to measure the strength of the CK effect and the asymmetric absorption profiles can be employed to engineer a high quality factor of the cavity.
Quantum teleportation of a generic two-photon state with weak cross-Kerr nonlinearities
NASA Astrophysics Data System (ADS)
Wang, Meiyu; Yan, Fengli
2016-05-01
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.
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.
Enhanced cross-Kerr effect for probing tunnelling in coupled quantum dots
NASA Astrophysics Data System (ADS)
Peng, Yandong; Yang, Aihong; Chen, Bing; Zhang, Shaomei; Liu, Shande; Wang, Xueshui
2016-02-01
An efficient scheme for probing electron tunnelling is proposed based on the enhanced cross-Kerr nonlinearity in a double-dot system. Due to resonant tunnelling, the cross-Kerr nonlinearity arises in a transparency window. Its intensity is nearly two orders of magnitude greater than that of the self-Kerr effect under any given conditions, where residual absorption is suppressed due to the competition of nonlinear gain and absorption. The enhanced cross-Kerr effect is sensitive to the tunnelling, so the probe spectrum can detect subtle tunnelling changes. The simulation results show that the probe sensitivity of the nonlinear phase shift is about 0.28 rad/μeV.
Kundi, Varun; Thankachan, Pompozhi Protasis
2015-05-14
A detailed theoretical study of linear and non-linear optical susceptibilities (NLOS), one- and two-photon absorption (OPA and TPA) properties for a series of push-pull trans-stilbene (TSB) derivatives with introduction of different electron donor (D) and acceptor (A) groups on either side of the TSB ring system is presented. The objective of the work is to design new TSB derivatives with large TPA cross-section values and to explore their linear and non-linear optical susceptibilities, OPA and TPA properties. We have used linear and quadratic response theory methods and CAM-B3LYP functional in conjunction with the 6-31+G* basis set for all property calculations. We have explained the results of the first hyperpolarizability and TP transition probability using two-state model (2SM) calculations, the results of which are in excellent agreement with the response theory methods. The TP tensor elements have been analysed to explain the large TP activity of molecules. Orbitals involved in the transition processes have been studied both qualitatively (molecular orbital pictures) and quantitatively (Λ-values) in order to explain the nature of charge transfer in different TSB derivatives. The study reveals that the novel derivatives TSBD-10, TSBD-11, TSBD-12 and TSBD-13 have large non-linear optical susceptibilities and TPA cross-section values, the largest being found for TSBD-13 (5560 G.M.). PMID:25894609
Ramos, Daniel Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko
2014-11-03
We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.
Siuly; Yin, Xiaoxia; Hadjiloucas, Sillas; Zhang, Yanchun
2016-04-01
This work provides a performance comparison of four different machine learning classifiers: multinomial logistic regression with ridge estimators (MLR) classifier, k-nearest neighbours (KNN), support vector machine (SVM) and naïve Bayes (NB) as applied to terahertz (THz) transient time domain sequences associated with pixelated images of different powder samples. The six substances considered, although have similar optical properties, their complex insertion loss at the THz part of the spectrum is significantly different because of differences in both their frequency dependent THz extinction coefficient as well as differences in their refractive index and scattering properties. As scattering can be unquantifiable in many spectroscopic experiments, classification solely on differences in complex insertion loss can be inconclusive. The problem is addressed using two-dimensional (2-D) cross-correlations between background and sample interferograms, these ensure good noise suppression of the datasets and provide a range of statistical features that are subsequently used as inputs to the above classifiers. A cross-validation procedure is adopted to assess the performance of the classifiers. Firstly the measurements related to samples that had thicknesses of 2mm were classified, then samples at thicknesses of 4mm, and after that 3mm were classified and the success rate and consistency of each classifier was recorded. In addition, mixtures having thicknesses of 2 and 4mm as well as mixtures of 2, 3 and 4mm were presented simultaneously to all classifiers. This approach provided further cross-validation of the classification consistency of each algorithm. The results confirm the superiority in classification accuracy and robustness of the MLR (least accuracy 88.24%) and KNN (least accuracy 90.19%) algorithms which consistently outperformed the SVM (least accuracy 74.51%) and NB (least accuracy 56.86%) classifiers for the same number of feature vectors across all studies
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.
NASA Astrophysics Data System (ADS)
Pan, Jun; Zhou, Lan; Gu, Shi-Pu; Wang, Xing-Fu; Sheng, Yu-Bo; Wang, Qin
2016-04-01
Concatenated Greenberger-Horne-Zeilinger (C-GHZ) state, which encodes physical qubits in a logic qubit, has great application in the future quantum communication. We present an efficient entanglement concentration protocol (ECP) for recovering less-entangled C-GHZ state into the maximally entangled C-GHZ state with the help of cross-Kerr nonlinearities and photon detectors. With the help of the cross-Kerr nonlinearity, the obtained maximally entangled C-GHZ state can be remained for other applications. Moreover, the ECP can be used repeatedly, which can increase the success probability largely. Based on the advantages above, our ECP may be useful in the future long-distance quantum communication.
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.
Energy Science and Technology Software Center (ESTSC)
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.more » 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.« less
Complete Analysis of Four-Photon χ-Type Entangled State via Cross-Kerr Nonlinearity
NASA Astrophysics Data System (ADS)
Zeng, Zhi; Li, Xi-Han; Wang, Chun; Wang, Li-Li; Liu, Zhen-Zhen; Wei, Hua
2015-09-01
We propose an efficient method to construct an optical four-photon |χ> state analyzer via the cross-Kerr nonlinearity combined with linear optical elements. In this protocol, two four-qubit parity-check gates and two controlled phase gates are employed. We show that all the 16 orthogonal four-qubit |χ> states can be completely discriminated with our apparatus. The scheme is feasible and realizable with current technology. It may have useful potential applications in quantum information processing which based on |χ> state. Supported by the National Natural Science Foundation of China under Grant No. 11004258, and Fundamental Research Funds for the Central Universities Project under Grant No. CQDXWL-2012-014, the Natural Science Foundation Project of CQ CSTC 2011jjA90017
Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity
NASA Astrophysics Data System (ADS)
Li, Xi-Han; Ghose, Shohini
2016-02-01
We present two complete maximally hyperentangled state analysis protocols for photons entangled in the polarization and spatial-mode degrees of freedom. The first protocol is a hyperentangled Bell state analysis scheme for two photons, and the second is a hyperentangled Greenberger-Horne-Zeilinger (GHZ) state analysis scheme for three photons. In each scheme, a set of mutually orthogonal hyperentangled basis states are completely and deterministically discriminated with the aid of cross-Kerr nonlinearities and linear optics. We also generalize the schemes to unambiguously analyze the N -photon hyperentangled GHZ state. Compared with previous protocols, our schemes greatly simplify the discrimination process and reduce the requirements on nonlinearities by using the measured spatial-mode state to assist in the analysis of the polarization state. These advantages make our schemes useful for practical applications in long-distance high-capacity quantum communication.
Single-Photon-Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-Number States.
Holland, E T; Vlastakis, B; Heeres, R W; Reagor, M J; Vool, U; Leghtas, Z; Frunzio, L; Kirchmair, G; Devoret, M H; Mirrahimi, M; Schoelkopf, R J
2015-10-30
Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying an active feedback condition on an ancillary system or through reservoir engineering. Reservoir engineering maintains a desired quantum state through a combination of drives and designed entropy evacuation. We propose and implement a quantum-reservoir engineering protocol that stabilizes Fock states in a microwave cavity. This protocol is realized with a circuit quantum electrodynamics platform where a Josephson junction provides direct, nonlinear coupling between two superconducting waveguide cavities. The nonlinear coupling results in a single-photon-resolved cross-Kerr effect between the two cavities enabling a photon-number-dependent coupling to a lossy environment. The quantum state of the microwave cavity is discussed in terms of a net polarization and is analyzed by a measurement of its steady state Wigner function. PMID:26565448
Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities
NASA Astrophysics Data System (ADS)
Dong, Li; Wang, Jun-Xi; Li, Qing-Yang; Shen, Hong-Zhi; Dong, Hai-Kuan; Xiu, Xiao-Ming; Gao, Ya-Jun; Oh, Choo Hiap
2016-01-01
Relying on weak cross-Kerr nonlinearities, we propose a nearly deterministic generation scheme of the three-photon polarization-entangled perfect W state which can be applied to the perfect teleportation of an unknown single-photon state and has robust entanglement against the loss of one photon of them. Three photons entangle together by virtue of the bus function of the coherent state serving as the intermediate among them. In the scheme, three processes are executed successively and two kinds of modules are inserted into the circuit, where the homodyne measurement and the photon number measurement are aptly performed. By means of classical feedforward techniques, single-photon unitary transformation operations are performed on the corresponding photons based on the obtained measurement outcomes, by which the generation efficiency of the perfect W state aims to nearly unity. Moreover, some currently available optical elements are applied in the generation process, which offer facilities for the practical implementation.
Liu, Qian; Wang, Guan-Yu; Ai, Qing; Zhang, Mei; Deng, Fu-Guo
2016-01-01
Hyperentanglement, the entanglement in several degrees of freedom (DOFs) of a quantum system, has attracted much attention as it can be used to increase both the channel capacity of quantum communication and its security largely. Here, we present the first scheme to completely distinguish the hyperentangled Bell states of two-photon systems in three DOFs with the help of cross-Kerr nonlinearity without destruction, including two longitudinal momentum DOFs and the polarization DOF. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors which can be used to make a parity-check measurement and analyze Bell states of two-photon systems in different DOFs. Our complete scheme for two-photon six-qubit hyperentangled Bell-state analysis may be useful for the practical applications in quantum information, especially in long-distance high-capacity quantum communication. PMID:26912172
Liu, Qian; Wang, Guan-Yu; Ai, Qing; Zhang, Mei; Deng, Fu-Guo
2016-01-01
Hyperentanglement, the entanglement in several degrees of freedom (DOFs) of a quantum system, has attracted much attention as it can be used to increase both the channel capacity of quantum communication and its security largely. Here, we present the first scheme to completely distinguish the hyperentangled Bell states of two-photon systems in three DOFs with the help of cross-Kerr nonlinearity without destruction, including two longitudinal momentum DOFs and the polarization DOF. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors which can be used to make a parity-check measurement and analyze Bell states of two-photon systems in different DOFs. Our complete scheme for two-photon six-qubit hyperentangled Bell-state analysis may be useful for the practical applications in quantum information, especially in long-distance high-capacity quantum communication. PMID:26912172
NASA Astrophysics Data System (ADS)
Liu, Qian; Wang, Guan-Yu; Ai, Qing; Zhang, Mei; Deng, Fu-Guo
2016-02-01
Hyperentanglement, the entanglement in several degrees of freedom (DOFs) of a quantum system, has attracted much attention as it can be used to increase both the channel capacity of quantum communication and its security largely. Here, we present the first scheme to completely distinguish the hyperentangled Bell states of two-photon systems in three DOFs with the help of cross-Kerr nonlinearity without destruction, including two longitudinal momentum DOFs and the polarization DOF. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors which can be used to make a parity-check measurement and analyze Bell states of two-photon systems in different DOFs. Our complete scheme for two-photon six-qubit hyperentangled Bell-state analysis may be useful for the practical applications in quantum information, especially in long-distance high-capacity quantum communication.
Katashima, Takuya; Urayama, Kenji; Chung, Ung-il; Sakai, Takamasa
2015-05-01
The pure shear deformation of the Tetra-polyethylene glycol gels reveals the presence of an explicit cross-effect of strains in the strain energy density function even for the polymer networks with nearly regular structure including no appreciable amount of structural defect such as trapped entanglement. This result is in contrast to the expectation of the classical Gaussian network model (Neo Hookean model), i.e., the vanishing of the cross effect in regular networks with no trapped entanglement. The results show that (1) the cross effect of strains is not dependent on the network-strand length; (2) the cross effect is not affected by the presence of non-network strands; (3) the cross effect is proportional to the network polymer concentration including both elastically effective and ineffective strands; (4) no cross effect is expected exclusively in zero limit of network concentration in real polymer networks. These features indicate that the real polymer networks with regular network structures have an explicit cross-effect of strains, which originates from some interaction between network strands (other than entanglement effect) such as nematic interaction, topological interaction, and excluded volume interaction. PMID:25956121
Cross Kerr and Raman effects on the switching efficiency of soliton optical fiber gates
NASA Astrophysics Data System (ADS)
Chimfwembe, Patrick Chilufya
Scope and method of study. The purpose of this study was to examine the cross Kerr and Raman effects on the switching efficiency of soliton optical fiber gates. Analytical propagation models were derived via the reductive perturbation method, and the numerical propagation models via the symmetrized split-step Fourier method. Zero propagation attenuation is assumed. The second and higher order dispersion parameters, in the two orthogonal axes of the strongly birefringent fiber, are assumed to be equal. Findings and conclusions. The traditional propagation equation of two orthogonally polarized solitons, in a strongly birefringent singlemode fiber, is significantly modified by the introduction of cross steepening and cross frequency shifting effects. Co-propagation numerical solutions of the coupled nonlinear Schrödinger equation, using the symmetrized split-step Fourier method, were used to simulate an inverter soliton trapping gate (STG), inverter soliton dragging gate (SDG), and two newly discovered soliton optical fiber gates. The two newly discovered gates are the STG-NOLM gate (NOLM stands for nonlinear optical loop mirror), and the STG-PSI-NOLM gate (PSI stands for partial shuffle interaction). It was found that the inverter STG, with the control pulse on the fast axis, is much more immune to the delay effects introduced by the higher order nonlinear and dispersion effects. The STG is still capable of switching efficiently under these delaying effects. The inverter SDG, however, is less immune to these effects, especially when the control pulse is on the slow axis (at angle 30°). The clock time window needs only to be slightly reduced for the SDG, when the control pulse is on the fast axis (at angle 60°). Inference from these results indicates that a STG is better than a SDG, when operated under the higher order nonlinear and dispersion effects. The switching performance of the STG-PSI-NOLM gate (with segment length equal to walk-off length) is very
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)
Kang, Yi-Hao; Xia, Yan; Lu, Pei-Min
2014-02-01
The controlled phase gate is one of the most important logic gates in the quantum computation field. In this paper, we proposed a protocol for implementing the two-qubit controlled phase gates with the help of cross-Kerr nonlinearity, optical elements and the conventional photon detectors, which are feasible with existing experimental technology. The protocol also can be applied to implement the controlled phase gates of many different atomic and photonic degrees of freedom with successful probability of 100%, that is, our protocol is efficient and flexible.
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
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)
Wang, Mei-Yu; Yan, Feng-Li; Gao, Ting
2016-07-01
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.
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)
Liu, Huan-Juan; Xia, Yan; Song, Jie
2016-05-01
In this scheme, based on the weak cross-Kerr nonlinearity, an hyperconcentration protocol for the arbitrary partially hyperentangled N-particle Greenberger-Horne-Zeilinger (GHZ) state is presented. Considering the N photons initially in the nonmaximally hyperentangled GHZ state in which photons are entangled simultaneously in the polarization and the spatial-mode degrees of freedom, we can obtain the maximally hyperentangled N-particle GHZ state by the projection measurements on the additional photons. Numerical simulation demonstrates that by iterating the entanglement concentration process, we can improve the success probability of the scheme. Furthermore, we discuss the feasibility of the setups of the protocol, concluding that the present protocol is feasible with existing experimental technology. All these advantages make this scheme more efficient and more convenient in quantum communication.
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.
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.
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. PMID:12787180
NASA Astrophysics Data System (ADS)
Jino, Heo; Chang-Ho, Hong; Dong-Hoon, Lee; Hyung-Jin, Yang
2016-02-01
We propose an arbitrary controlled-unitary (CU) gate and a bidirectional transfer scheme of quantum information (BTQI) for unknown photons. The proposed CU gate utilizes quantum non-demolition photon-number-resolving measurement based on the weak cross-Kerr nonlinearities (XKNLs) and two quantum bus beams; the proposed CU gate consists of consecutive operations of a controlled-path gate and a gathering-path gate. It is almost deterministic and is feasible with current technology when a strong amplitude of the coherent state and weak XKNLs are employed. Compared with the existing optical multi-qubit or controlled gates, which utilize XKNLs and homodyne detectors, the proposed CU gate can increase experimental realization feasibility and enhance robustness against decoherence. According to the CU gate, we present a BTQI scheme in which the two unknown states of photons between two parties (Alice and Bob) are mutually swapped by transferring only a single photon. Consequently, by using the proposed CU gate, it is possible to experimentally implement the BTQI scheme with a certain probability of success.
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
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
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 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,
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.
NASA Astrophysics Data System (ADS)
Thomson, Mark J.; McKellar, Bruce H. J.
1991-04-01
A simple, non-linear generalization of the MSW equation is presented and its analytic solution is outlined. The orbits of the polarization vector are shown to be periodic, and to lie on a sphere. Their non-trivial flow patterns fall into two topological categories, the more complex of which can become chaotic if perturbed.
Non-linear dark energy clustering
Anselmi, Stefano; Ballesteros, Guillermo; Pietroni, Massimo E-mail: ballesteros@pd.infn.it
2011-11-01
We consider a dark energy fluid with arbitrary sound speed and equation of state and discuss the effect of its clustering on the cold dark matter distribution at the non-linear level. We write the continuity, Euler and Poisson equations for the system in the Newtonian approximation. Then, using the time renormalization group method to resum perturbative corrections at all orders, we compute the total clustering power spectrum and matter power spectrum. At the linear level, a sound speed of dark energy different from that of light modifies the power spectrum on observationally interesting scales, such as those relevant for baryonic acoustic oscillations. We show that the effect of varying the sound speed of dark energy on the non-linear corrections to the matter power spectrum is below the per cent level, and therefore these corrections can be well modelled by their counterpart in cosmological scenarios with smooth dark energy. We also show that the non-linear effects on the matter growth index can be as large as 10–15 per cent for small scales.
Phototube non-linearity correction technique
NASA Astrophysics Data System (ADS)
Riboldi, S.; Blasi, N.; Brambilla, S.; Camera, F.; Giaz, A.; Million, B.
2015-06-01
Scintillation light is often detected by photo-multiplier tube (PMT) technology. PMTs are however intrinsically non linear devices, especially when operated with high light yield scintillators and high input photon flux. Many physical effects (e.g. inter-dynode field variation, photocathode resistivity, etc.) can spoil the ideal PMT behavior in terms of gain, ending up in what are addressed as the under-linearity and over-linearity effects. Established techniques implemented in the PMT base (e.g. increasing bleeding current, active voltage divider, etc.) can mitigate these effects, but given the unavoidable spread in manufacturing and materials, it turns out that, with respect to linearity at the percent level, every PMT sample is a story of its own. The residual non linearity is usually accounted for with polynomial correction of the spectrum energy scale, starting from the position of a few known energy peaks of calibration sources, but uncertainly remains in between of calibration peaks. We propose to retrieve the calibration information from the entire energy spectrum and not only the position of full energy peaks (FEP), by means of an automatic procedure that also takes into account the quality (signal/noise ratio) of the information about the non-linearity extracted from the various regions of the spectrum.
Spin waves cause non-linear friction
NASA Astrophysics Data System (ADS)
Magiera, M. P.; Brendel, L.; Wolf, D. E.; Nowak, U.
2011-07-01
Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate.
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 Models for Longitudinal Data
Serroyen, Jan; Molenberghs, Geert; Verbeke, Geert; Davidian, Marie
2009-01-01
While marginal models, random-effects models, and conditional models are routinely considered to be the three main modeling families for continuous and discrete repeated measures with linear and generalized linear mean structures, respectively, it is less common to consider non-linear models, let alone frame them within the above taxonomy. In the latter situation, indeed, when considered at all, the focus is often exclusively on random-effects models. In this paper, we consider all three families, exemplify their great flexibility and relative ease of use, and apply them to a simple but illustrative set of data on tree circumference growth of orange trees. PMID:20160890
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 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
Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model
NASA Astrophysics Data System (ADS)
Singh, Sudha; Gilhare, Karuna
2016-08-01
We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.
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
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
NASA Astrophysics Data System (ADS)
Canabarro, Askery; Santos, B.; de Lima Bernardo, B.; Moura, André L.; Soares, W. C.; de Lima, E.; Gléria, Iram; Lyra, M. L.
2016-02-01
Taking into account relaxing Kerr nonlinearity and walk-off effects, the conditions and gain spectra of cross-phase modulation-induced modulational instability (XPM-MI) of two incoherently copropagating optical waves of different frequencies and same polarization are investigated. We devote particular attention to the mixed case in which one pulse propagates under the normal group-velocity dispersion (GVD) regime, while the second one is under an anomalous GVD regime. We unveil that in the limit of an instantaneuous nonlinear response, the typical frequency with maximum gain converges to a finite value in the mixed GDV regime, while it continuously grows with the group-velocity mismatch in the normal GVD regime. As a result, the maximum gain typically decreases with the group-velocity mismatch in the mixed regime, contrasting with the opposite trend in the normal GVD regime. Further, we show that besides the mode having maximum gain at a frequency decaying with 1 /τ1 /3 in the slow response limit, there is a second mode having maximum gain with a distinct scaling behavior Ωmax∝1 /τ in the absence of group-velocity mismatch. The associated maximum gains scale, respectively, as 1 /τ2 /3 and 1 /τ , thus signaling the corresponding quadratic and linear dispersion relation of these modes in the low-frequency limit. A detailed analysis of the influence of the nonlinear response time and group-velocity dispersion on the MI gain spectrum is also provided.
NASA Astrophysics Data System (ADS)
Heo, Jino; Hong, Chang-Ho; Lim, Jong-In; Yang, Hyung-Jin
2015-05-01
We propose an arbitrary controlled-unitary (CU) gate and a bidirectional quantum teleportation (BQTP) scheme. The proposed CU gate utilizes photonic qubits (photons) with cross-Kerr nonlinearities (XKNLs), X-homodyne detectors, and linear optical elements, and consists of the consecutive operation of a controlled-path (C-path) gate and a gathering-path (G-path) gate. It is almost deterministic and feasible with current technology when a strong coherent state and weak XKNLs are employed. Based on the CU gate, we present a BQTP scheme that simultaneously teleports two unknown photons between distant users by transmitting only one photon in a path-polarization intra-particle hybrid entangled state. Consequently, it is possible to experimentally implement BQTP with a certain success probability using the proposed CU gate. Project supported by the Ministry of Science, ICT&Future Planning, Korea, under the C-ITRC (Convergence Information Technology Research Center) Support program (NIPA-2013-H0301-13-3007) supervised by the National IT Industry Promotion Agency.
Non-linear interaction of elastic waves in rocks
NASA Astrophysics Data System (ADS)
Kuvshinov, B. N.; Smit, T. J. H.; Campman, X. H.
2013-09-01
We study theoretically the interaction of elastic waves caused by non-linearities of rock elastic moduli, and assess the possibility to use this phenomenon in hydrocarbon exploration and in the analysis of rock samples. In our calculations we use the five-constant model by Gol'dberg. It is shown that the interaction of plane waves in isotropic solids is completely described by five coupling coefficients, which have the same order of magnitude. By considering scattering of compressional waves generated by controlled sources at the Earth surface from a non-linear layer at the subsurface, we conclude that non-linear signals from deep formations are unlikely to be measured with the current level of technology. Our analysis of field tests where non-linear signals were measured, suggests that these signals are generated either in the shallow subsurface or in the vicinity of sources. Non-linear wave interaction might be observable in lab tests with focused ultrasonic beams. In this case, the non-linear response is generated in the secondary parametric array formed by linear beams scattered from inclusions. Although the strength of this response is controlled by non-linearity of the surrounding medium rather than by non-linearity of inclusions, its measurement can help to obtain better images of rock samples.
Simulation of non-linear coregionalization models by FFTMA
NASA Astrophysics Data System (ADS)
Liang, Min; Marcotte, Denis; Shamsipour, Pejman
2016-04-01
A fast and efficient method to simulate multivariate fields with non-linear models of coregionalization (N-LMC) is described. The method generalizes FFTMA to the multivariate simulation of the N-LMC with symmetric cross-covariances, hence the name GFFTMA. It allows us for example to use an exponential model as the direct covariance for the main variable, a Cauchy model for the secondary variable and a K-Bessel model for the cross-covariance. Each covariance and cross-covariance are Fast Fourier Transformed (FFT) to get the discrete spectral densities. Then the spectral matrix is eigen-decomposed at each frequency separately to provide the square root matrix and to enforce positive-definiteness in cases where small negative eigenvalues are found. Finally the simulated spectrum is obtained as multiplication of the root matrix and the white noise coefficients. The method is particularly fast for covariances having derivatives at the origin and/or for covariances with long range. Hence, two-variables' 2D fields of 100 million pixels with all-Gaussian or all-cubic covariances and cross-covariance are both simulated in less than 200 s. The CPU-time increases only as N log(N) (N, the number of points to simulate). Additional realizations are obtained at a low marginal cost as the eigen-decomposition step needs to be done only once for the first realization. The main limitation of the approach is its rather stringent memory requirement. Synthetic examples illustrate the simulations of N-LMC with two and three variables for different combinations of the seven available models. It shows that the theoretical models are all well reproduced. An illustrative case-study on overburden thickness simulation is provided where the secondary information consists of a latent Gaussian variable identifying the geological domain.
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.
NASA Astrophysics Data System (ADS)
Dymnikova, Irina; Galaktionov, Evgeny
2015-08-01
In non-linear electrodynamics coupled to gravity, regular spherically symmetric electrically charged solutions satisfy the weak energy condition and have an obligatory de Sitter center. By the Gürses-Gürsey algorithm they are transformed to spinning electrically charged solutions that are asymptotically Kerr-Newman for a distant observer. Rotation transforms the de Sitter center into a de Sitter vacuum surface which contains the equatorial disk r = 0 as a bridge. We present a general analysis of the horizons, ergoregions and de Sitter surfaces, as well as the conditions of the existence of regular solutions to the field equations. We find asymptotic solutions and show that de Sitter vacuum surfaces have properties of a perfect conductor and ideal diamagnetic, violation of the weak energy condition is prevented by the basic requirement of electrodynamics of continued media, and the Kerr ring singularity is replaced with the superconducting current.
NASA Astrophysics Data System (ADS)
Chimfwembe, Patrick C.; Krasinski, Jerzy S.
1999-06-01
The reductive perturbation method was applied to the propagation of two orthogonal polarized sub-100 fs soliton pulses, in a singlemode fiber, to give an analytical propagation model. The analytical propagation model was transformed into a numerical propagation model via the symmetrized split-step Fourier method. The numerical propagation model was then used to analyze the switching efficiency of an inverter soliton-trapping gate (STG) and an inverter soliton-dragging gate (SDG), with a clock time window of about four pulse widths. For the STG and the SDG, with the control on the slow axis, the switching maximum clock time windows are reduced by 32 percent and 62 percent respectively, due to the self and cross Raman effects. However, for the STG and SDG, operated with the control on the fast axis, it was found that the switching maximum clock time windows are increased by 30 percent and 28 percent respectively, due to the self and cross Raman effects.
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.
Analysis of non-linearity in differential wavefront sensing technique.
Duan, Hui-Zong; Liang, Yu-Rong; Yeh, Hsien-Chi
2016-03-01
An analytical model of a differential wavefront sensing (DWS) technique based on Gaussian Beam propagation has been derived. Compared with the result of the interference signals detected by quadrant photodiode, which is calculated by using the numerical method, the analytical model has been verified. Both the analytical model and numerical simulation show milli-radians level non-linearity effect of DWS detection. In addition, the beam clipping has strong influence on the non-linearity of DWS. The larger the beam clipping is, the smaller the non-linearity is. However, the beam walking effect hardly has influence on DWS. Thus, it can be ignored in laser interferometer. PMID:26974079
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.
Stochastic differential equations for non-linear hydrodynamics
NASA Astrophysics Data System (ADS)
Español, Pep
1998-02-01
We formulate the stochastic differential equations for non-linear hydrodynamic fluctuations. The equations incorporate the random forces through a random stres tensor and random heat flux as in the Landau and Lifshitz theory. However, the equations are non-linear and the random forces are non-Gaussian. We provide explicit expressions for these random quantities in terms of the well-defined increments of the Wienner process.
NASA Astrophysics Data System (ADS)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey; Zakharian, Aramis R.; Moloney, Jerome V.
2004-04-01
The vector Maxwell equations of non-linear optics coupled to a single Lorentz oscillator and with instantaneous Kerr non-linearity are investigated by using Lie symmetry group methods. Lagrangian and Hamiltonian formulations of the equations are obtained. The aim of the analysis is to explore the properties of Maxwell’s equations in non-linear optics, without resorting to the commonly used non-linear Schrödinger (NLS) equation approximation in which a high frequency carrier wave is modulated on long length and time scales due to non-linear sideband wave interactions. This is important in femto-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field E, in terms of the canonical variables, with possible multiple real roots for E. In order to circumvent this problem, non-canonical Poisson bracket formulations of the equations are obtained in which the electric field is one of the non-canonical variables. Noether’s theorem, and the Lie point symmetries admitted by the equations are used to obtain four conservation laws, including the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr non-linearity, are shown to reduce to a single ordinary differential equation for the variable y= E2, where E is the electric field intensity. The differential equation has solutions y= y( ξ), where ξ= z- st is the traveling wave variable and s is the velocity of the wave. These solutions exhibit new phenomena not obtainable by the NLS approximation. The characteristics of the solutions depends on the values of the wave velocity s and the energy integration constant ɛ. Both smooth periodic traveling waves and
Correcting the NICMOS count-rate dependent non-linearity
NASA Astrophysics Data System (ADS)
de Jong, Roelof S.
2006-03-01
We describe a routine to correct NICMOS imaging data for the NICMOS count-rate dependent non-linearity recently discovered by Bohlin et al. (2005) and quantified by deJong et al. (2006) and Bohlin et al. (2006). The routine has been implemented in the python scripting language and is callable from the shell command line and from iraf. The routine corrects NICMOS count-rate images assuming the non-linearity follows a powerlaw behavior. The wavelength dependence of the non-linearity is interpolated between the measured points of de Jong et al. (2006) and Bohlin et al. (2006) if necessary. The count rates in the output images are modified and hence the standard NICMOS calibration zero-points are no longer valid. New calibration zero-points have been derived from standard star images corrected with the routine. The routine was tested on the lamp-on/off data used in de Jong et al. (2006) to measure the non-linearity effect. We apply the correction to the NGC1850 stellar cluster field and the Hubble Ultra Deep Field (HUDF) to show the magnitude offsets expected due to the non-linearity on objects with a range in luminosity and surface brightness.
Theoretical studies for novel non-linear optical crystals
NASA Astrophysics Data System (ADS)
Wu, Kechen; Chen, Chuangtian
1996-09-01
To fulfil the "molecular engineering" of non-linear optical crystals, two theoretical models suitable respectively for the studies of the absorption edge and birefringence of a non-linear optical crystal have been set up. Molecular quantum chemical methods have been adopted in the systematic calculations of some typical crystals. DV-SCM-X α methods have been used to calculate the absorption edge on the UV side of BBO, LBO, KB5, KDP, Na 2SbF 5, Ba 2TiSi 2O 8, iodate and NaNO 2 crystals. Ab initio methods have been adopted to study the birefringence of NaNO 2, BBO, LiIO 3 and urea crystals. All the theoretical results agreed well with the experimental values. The relationship between structure and properties has been discussed. The results will be helpful to the search for novel non-linear optical crystals.
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.
Non-linear dynamic analysis of anisotropic cylindrical shells
Lakis, A.A.; Selmane, A.; Toledano, A.
1996-12-01
A theory to predict the influence of geometric non-linearities on the natural frequencies of an empty anisotropic cylindrical shell is presented in this paper. It is a hybrid of finite element and classical thin shell theories. Sanders-Koiter non-linear and strain-displacement relations are used. Displacement functions are evaluated using linearized equations of motion. Modal coefficients are then obtained for these displacement functions. Expressions for the mass, linear and non-linear stiffness matrices are derived through the finite element method. The uncoupled equations are solved with the help of elliptic functions. The period and frequency variations are first determined as a function of shell amplitudes and then compared with the results in the literature.
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.
Neural network modelling of non-linear hydrological relationships
NASA Astrophysics Data System (ADS)
Abrahart, R. J.; See, L. M.
2007-09-01
Two recent studies have suggested that neural network modelling offers no worthwhile improvements in comparison to the application of weighted linear transfer functions for capturing the non-linear nature of hydrological relationships. The potential of an artificial neural network to perform simple non-linear hydrological transformations under controlled conditions is examined in this paper. Eight neural network models were developed: four full or partial emulations of a recognised non-linear hydrological rainfall-runoff model; four solutions developed on an identical set of inputs and a calculated runoff coefficient output. The use of different input combinations enabled the competencies of solutions developed on a reduced number of parameters to be assessed. The selected hydrological model had a limited number of inputs and contained no temporal component. The modelling process was based on a set of random inputs that had a uniform distribution and spanned a modest range of possibilities. The initial cloning operations permitted a direct comparison to be performed with the equation-based relationship. It also provided more general information about the power of a neural network to replicate mathematical equations and model modest non-linear relationships. The second group of experiments explored a different relationship that is of hydrological interest; the target surface contained a stronger set of non-linear properties and was more challenging. Linear modelling comparisons were performed against traditional least squares multiple linear regression solutions developed on identical datasets. The reported results demonstrate that neural networks are capable of modelling non-linear hydrological processes and are therefore appropriate tools for hydrological modelling.
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.
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.
Non-linear optics of ultrastrongly coupled cavity polaritons
NASA Astrophysics Data System (ADS)
Crescimanno, Michael; Liu, Bin; McMaster, Michael; Singer, Kenneth
2016-05-01
Experiments at CWRU have developed organic cavity polaritons that display world-record vacuum Rabi splittings of more than an eV. This ultrastrongly coupled polaritonic matter is a new regime for exploring non-linear optical effects. We apply quantum optics theory to quantitatively determine various non-linear optical effects including types of low harmonic generation (SHG and THG) in single and double cavity polariton systems. Ultrastrongly coupled photon-matter systems such as these may be the foundation for technologies including low-power optical switching and computing.
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.
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.
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.
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.
Arithmetic coding as a non-linear dynamical system
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin; Vaidya, Prabhakar G.; Bhat, Kishor G.
2009-04-01
In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luröth Series (GLS). GLS achieves Shannon's entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.
Rare earth ion doped non linear laser crystals
NASA Astrophysics Data System (ADS)
Jaque, D.; Romero, J. J.; Ramirez, M. O.; Garcia, J. A. S.; de Las Heras, C.; Bausa, L. E.; Sole, J. G.
2003-01-01
We show how non linear crystals activated with Yb3+ or Nd3+ ions can be used to develop diode pumped solid state lasers emitting in the visible region of the electromagnetic spectrum. For this purpose we have selected relevant examples of systems investigated in our laboratory.
Non-linear protocell models: synchronization and chaos
NASA Astrophysics Data System (ADS)
Filisetti, A.; Serra, R.; Carletti, T.; Villani, M.; Poli, I.
2010-09-01
We consider generic protocells models allowing linear and non-linear kinetics for the main involved chemical reactions. We are interested in understanding if and how the protocell division and the metabolism do synchronise to give rise to sustainable evolution of the protocell.
Is 3D true non linear traveltime tomography reasonable ?
NASA Astrophysics Data System (ADS)
Herrero, A.; Virieux, J.
2003-04-01
The data sets requiring 3D analysis tools in the context of seismic exploration (both onshore and offshore experiments) or natural seismicity (micro seismicity surveys or post event measurements) are more and more numerous. Classical linearized tomographies and also earthquake localisation codes need an accurate 3D background velocity model. However, if the medium is complex and a priori information not available, a 1D analysis is not able to provide an adequate background velocity image. Moreover, the design of the acquisition layouts is often intrinsically 3D and renders difficult even 2D approaches, especially in natural seismicity cases. Thus, the solution relies on the use of a 3D true non linear approach, which allows to explore the model space and to identify an optimal velocity image. The problem becomes then practical and its feasibility depends on the available computing resources (memory and time). In this presentation, we show that facing a 3D traveltime tomography problem with an extensive non-linear approach combining fast travel time estimators based on level set methods and optimisation techniques such as multiscale strategy is feasible. Moreover, because management of inhomogeneous inversion parameters is more friendly in a non linear approach, we describe how to perform a jointly non-linear inversion for the seismic velocities and the sources locations.
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.
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.
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.
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.
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.
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. PMID:25794166
Non-linearity in Bayesian 1-D magnetotelluric inversion
NASA Astrophysics Data System (ADS)
Guo, Rongwen; Dosso, Stan E.; Liu, Jianxin; Dettmer, Jan; Tong, Xiaozhong
2011-05-01
This paper applies a Bayesian approach to examine non-linearity for the 1-D magnetotelluric (MT) inverse problem. In a Bayesian formulation the posterior probability density (PPD), which combines data and prior information, is interpreted in terms of parameter estimates and uncertainties, which requires optimizing and integrating the PPD. Much work on 1-D MT inversion has been based on (approximate) linearized solutions, but more recently fully non-linear (numerical) approaches have been applied. This paper directly compares results of linearized and non-linear uncertainty estimation for 1-D MT inversion; to do so, advanced methods for both approaches are applied. In the non-linear formulation used here, numerical optimization is carried out using an adaptive-hybrid algorithm. Numerical integration applies Metropolis-Hastings sampling, rotated to a principal-component parameter space for efficient sampling of correlated parameters, and employing non-unity sampling temperatures to ensure global sampling. Since appropriate model parametrizations are generally not known a priori, both under- and overparametrized approaches are considered. For underparametrization, the Bayesian information criterion is applied to determine the number of layers consistent with the resolving power of the data. For overparametrization, prior information is included which favours simple structure in a manner similar to regularized inversion. The data variance and/or trade-off parameter regulating data and prior information are treated in several ways, including applying fixed optimal estimates (an empirical Bayesian approach) or including them as hyperparameters in the sampling (hierarchical Bayesian). The latter approach has the benefit of accounting for the uncertainty in the hyperparameters in estimating model parameter uncertainties. Non-linear and linearized inversion results are compared for synthetic test cases and for the measured COPROD1 MT data by considering marginal probability
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
A non-linear model of economic production processes
NASA Astrophysics Data System (ADS)
Ponzi, A.; Yasutomi, A.; Kaneko, K.
2003-06-01
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
Non-linear Higgs portal to Dark Matter
NASA Astrophysics Data System (ADS)
Brivio, I.; Gavela, M. B.; Merlo, L.; Mimasu, K.; No, J. M.; del Rey, R.; Sanz, V.
2016-04-01
The Higgs portal to scalar Dark Matter is considered in the context of non-linearly realised electroweak symmetry breaking. We determine the dominant interactions of gauge bosons and the physical Higgs particle h to a scalar singlet Dark Matter candidate. Phenomenological consequences are also studied in detail, including the possibility of distinguishing this scenario from the standard Higgs portal in which the electroweak symmetry breaking is linearly realised. Two features of significant impact are: i) the connection between the electroweak scale v and the Higgs particle departs from the ( v + h) functional dependence, as the Higgs field is not necessarily an exact electroweak doublet; ii) the presence of specific couplings that arise at different order in the non-linear and in the linear expansions. These facts deeply affect the Dark Matter relic abundance, as well as the expected signals in direct and indirect searches and collider phenomenology, where Dark Matter production rates are enhanced with respect to the standard portal.
Non-linear microscopy and spectroscopy of skin tissues
NASA Astrophysics Data System (ADS)
Palero, Jonathan A.; Latouche, Gwendal; de Bruijn, Henri"tte S.; Gerritsen, Hans C.; Sterenborg, Henricus J. C. M.
2005-11-01
We combined a non-linear microscope with a sensitive prism-based spectrograph and employed it for the imaging of the auto fluorescence of skin tissues. The system has a sub-micron spatial resolution and a spectral resolution of better than 5 nm. The spectral images contain signals arising from two-photon excited fluorescence (TPEF) of endogenous fluorophores in the skin and from second harmonic generation (SHG) produced by the collagen fibers, which have non-centrosymmetric structure. Non-linear microscopy has the potential to image deep into optically thick specimens because it uses near-infrared (NIR) laser excitation. In addition, the phototoxicity of the technique is comparatively low. Here, the technique is used for the spectral imaging of unstained skin tissue sections. We were able to image weak cellular autofluorescence as well as strong collagen SHG. The images were analyzed by spectral unmixing and the results exhibit a clear spectral signature for the different skin layers.
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.
On the non-linear scale of cosmological perturbation theory
Blas, Diego; Garny, Mathias; Konstandin, Thomas E-mail: mathias.garny@desy.de
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
NASA Astrophysics Data System (ADS)
Teukolsky, Saul A.
2015-06-01
This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the ‘miraculous’ nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity.
Energy loss of ions in solids: Non-linear calculations for slow and swift ions
NASA Astrophysics Data System (ADS)
Arista, Néstor R.
2002-10-01
The historical approach to describe the energy loss of swift ions in solids is based on the Bohr, Bethe and Bloch theories. As is well known, the central parameter in these theories is the ratio η= Z1e2/ℏ v, whose value is generally used to delimit the ranges of applicability of the Bohr ( η>1) and Bethe ( η<1) theories. The transition between these regimes can be obtained by changing the ratio Z1/ v, although not by simply changing v. In fact, this scheme breaks down at low velocities, where quantum and non-linear effects arise. This domain is characterized by the strong oscillatory Z1 dependence of the stopping powers. This paper proposes a self-consistent non-linear approach to calculate the energy loss of heavy ions on a wide range of velocities. The model is based on the transport cross-section approach and on a previous extension of the Friedel sum rule for moving ions. The purpose of this study is to develop a non-linear stopping power evaluation method that could be applied at finite ion velocities, bridging the current gap between the low- and high-energy models.
Non-linear stochastic growth rates and redshift space distortions
NASA Astrophysics Data System (ADS)
Jennings, Elise; Jennings, David
2015-06-01
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 = nabla \\cdot 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 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 × 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) for k < 0.1 h Mpc-1. 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. 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.
Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas
Hnat, B.
2011-09-22
Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.
Approximate solutions for non-linear iterative fractional differential equations
NASA Astrophysics Data System (ADS)
Damag, Faten H.; Kiliçman, Adem; Ibrahim, Rabha W.
2016-06-01
This paper establishes approximate solution for non-linear iterative fractional differential equations: d/γv (s ) d sγ =ℵ (s ,v ,v (v )), where γ ∈ (0, 1], s ∈ I := [0, 1]. Our method is based on some convergence tools for analytic solution in a connected region. We show that the suggested solution is unique and convergent by some well known geometric functions.
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 Dynamics and Emergence in Laboratory Fusion Plasmas
NASA Astrophysics Data System (ADS)
Hnat, B.
2011-09-01
Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.
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 identities between unitary minimal Virasoro characters
NASA Astrophysics Data System (ADS)
Taormina, Anne
Non linear identities between unitary minimal Virasoro characters at low levels (m = 3, 4, 5) are presented as well as a sketch of some proofs. The first identity gives the Ising model characters (m = 3) as bilinears in tricritical Ising model characters (m = 4), while the second one gives the tricritical Ising model characters as bilinears in the Ising model characters and the six combinations of m = 5 Virasoro characters which do not appear in the spectrum of the three state Potts model.
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 power spectra in the synchronous gauge
NASA Astrophysics Data System (ADS)
Hwang, Jai-chan; Noh, Hyerim; Jeong, Donghui; Gong, Jinn-Ouk; Biern, Sang Gyu
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.
Liapunov functions for non-linear difference equation stability analysis.
NASA Technical Reports Server (NTRS)
Park, K. E.; Kinnen, E.
1972-01-01
Liapunov functions to determine the stability of non-linear autonomous difference equations can be developed through the use of auxiliary exact difference equations. For this purpose definitions are introduced for the gradient of an implicit function of a discrete variable, a principal sum, a definite sum and an exact difference equation, and a theorem for exactness of a difference form is proved. Examples illustrate the procedure.
Can the Non-linear Ballooning Model describe ELMs?
NASA Astrophysics Data System (ADS)
Henneberg, S. A.; Cowley, S. C.; Wilson, H. R.
2015-11-01
The explosive, filamentary plasma eruptions described by the non-linear ideal MHD ballooning model is tested quantitatively against experimental observations of ELMs in MAST. The equations describing this model were derived by Wilson and Cowley for tokamak-like geometry which includes two differential equations: the linear ballooning equation which describes the spatial distribution along the field lines and the non-linear ballooning mode envelope equation, which is a two-dimensional, non-linear differential equation which can involve fractional temporal-derivatives, but is often second-order in time and space. To employ the second differential equation for a specific geometry one has to evaluate the coefficients of the equation which is non-trivial as it involves field line averaging of slowly converging functions. We have solved this system for MAST, superimposing the solutions of both differential equations and mapping them onto a MAST plasma. Comparisons with the evolution of ELM filaments in MAST will be reported in order to test the model. The support of the EPSRC for the FCDT (Grant EP/K504178/1), of Euratom research and training programme 2014-2018 (No 633053) and of the RCUK Energy Programme [grant number EP/I501045] is gratefully acknowledged.
Non-linear Compton Scattering in Short Laser Pulses
NASA Astrophysics Data System (ADS)
Krajewska, Katarzyna; Kamiński, Jerzy
2012-06-01
The generation of short X-ray laser pulses attracts a great deal of attention. One of mechanisms to achieve this goal is the non-linear Compton scattering at very high laser powers. The majority of previous works on the non-linear Compton scattering have been devoted to the case when the incident laser field is treated as a monochromatic plane wave. There is, however, recent interest in analyzing the effect of a pulsed laser field on the non-linear Compton scattering [1-4]. We study the process for different durations of the incident laser pulse and compare it with the results for both a plane wave laser field and a laser pulse train. [4pt] [1] M. Boca and V. Florescu, Phys. Rev. A 80, 053403 (2009).[0pt] [2] M. Boca and V. Florescu, Eur. Phys. J. D 61, 446 (2011).[0pt] [3] D. Seipt and B. Kämpfer, Phys. Rev. A 83, 022101 (2011).[0pt] [4] F. Mackenroth and A. Di Piazza, Phys. Rev. A 83, 032106 (2011).
A Technique for Determining Non-Linear Circuit Parameters from Ring Down Data
ROMERO, LOUIS; DICKEY, FRED M.; DISON, HOLLY
2003-01-01
We present a technique for determining non-linear resistances, capacitances, and inductances from ring down data in a non-linear RLC circuit. Although the governing differential equations are non-linear, we are able to solve this problem using linear least squares without doing any sort of non-linear iteration.
Measurement of the Kerr nonlinear refractive index of Cs vapor
NASA Astrophysics Data System (ADS)
Araújo, Michelle O.; de S. Cavalcante, Hugo L. D.; Oriá, Marcos; Chevrollier, Martine; de Silans, Thierry Passerat; Castro, Romeu; Moretti, Danieverton
2013-12-01
Atomic vapors are systems well suited for nonlinear optics studies but very few direct measurements of their nonlinear refractive index have been reported. Here we use the z-scan technique to measure the Kerr coefficient, n2, for a Cs vapor. Our results are analyzed through a four-level model, and we show that coherence between excited levels as well as cross-population effects contribute to the Kerr nonlinearity.
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.
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. PMID:26503051
Support Vector Machines for Non-linear Geophysical Inversion
NASA Astrophysics Data System (ADS)
Kuzma, H. A.; Rector, J. W.
2004-12-01
Classical non-linear geophysical inversion can be simulated using computer learning via Support Vector Machines. Geophysical inverse problems are almost always ill-posed which means that many different models (i.e. descriptions of the earth) can be found to explain a given noisy or incomplete data set. Regularization and constraints encourage inversions to find physically realistic models. The set of preferred models needs to be defined a priori using as much geologic knowledge as is available. In inversion, it is assumed that data and a forward modeling process is known. The goal is to solve for a model. In the SVM paradigm, a series of models and associated data are known. The goal is to solve for a reverse modeling process. Starting with a series of initial models assembled using all available geologic information, synthetic data is created using the most realistic forward modeling program available. With the synthetic data as inputs and the known models as outputs, a Support Vector Machine is trained to approximate a local inverse to the forward modeling program. The advantages of this approach are that it is honest about the need to establish, a priori, the kinds of models that are reasonable in a particular field situation. There is no need to adjust the forward process to accommodate inversion, because SVMs can be easily modified to capture complicated, non-linear relationships. SVMs are transparent and require very little programming. If an SVM is trained using model/data pairs that are drawn from the same probability distribution that is implicit in the regularization of an inversion, then it will get very similar results to the inversion. Because SVMs can interpret as much data as desired so long as the conditions of an experiment do not change, they can be used to perform otherwise computationally expensive procedures. Support Vector Machines are trained to emulate non-linear seismic Amplitude Variation with Offset (AVO) inversions, gravity inversions
Response of a rotorcraft model with damping non-linearities
NASA Astrophysics Data System (ADS)
Tongue, B. H.
1985-11-01
The linearized equations of motion of a helicopter in contact with the ground have solutions which can be linearly stable or unstable, depending on the system parameters. The present study includes physical non-linearities in the helicopter model. This allows one to determine if a steady-state response exists and, if so, what the frequency and amplitude of the oscillations will be. In this way, one can determine how serious the linearly unstable operating regime is and whether destructive oscillations are possible when the system is in the linearly stable regime. The present analysis applies to helicopters having fully articulated rotors.
Non-linear wave interaction in a plasma column
NASA Technical Reports Server (NTRS)
Larsen, J.-M.; Crawford, F. W.
1979-01-01
Non-linear three-wave interaction is analysed for propagation along a cylindrical plasma column surrounded by an infinite dielectric, in the absence of a static magnetic field. An averaged-Lagrangian method is used, and the results are specialized to parametric interaction and mode conversion, assuming an undepleted pump wave. The theory for these two types of interactions is extended to include imperfect synchronism, and the effects of loss. Computations are presented indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma column parameters.
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.
Non-linear dynamics of compound sawteeth in tokamaks
NASA Astrophysics Data System (ADS)
Ahn, J.-H.; Garbet, X.; Lütjens, H.; Marx, A.; Nicolas, T.; Sabot, R.; Luciani, J.-F.; Guirlet, R.; Février, O.; Maget, P.
2016-05-01
Compound sawteeth is studied with the XTOR-2F code. Non-linear full 3D magnetohydrodynamic simulations show that the plasma hot core is radially displaced and rotates during the partial crash, but is not fully expelled out of the q = 1 surface. Partial crashes occur when the radius of the q = 1 surface exceeds a critical value, at fixed poloidal beta. This critical value depends on the plasma elongation. The partial crash time is larger than the collapse time of an ordinary sawtooth, likely due to a weaker diamagnetic stabilization. This suggests that partial crashes result from a competition between destabilizing effects such as the q = 1 radius and diamagnetic stabilization.
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 dielectric spectroscopy of microbiological suspensions
Treo, Ernesto F; Felice, Carmelo J
2009-01-01
Background Non-linear dielectric spectroscopy (NLDS) of microorganism was characterized by the generation of harmonics in the polarization current when a microorganism suspension was exposed to a sinusoidal electric field. The biological nonlinear response initially described was not well verified by other authors and the results were susceptible to ambiguous interpretation. In this paper NLDS was performed to yeast suspension in tripolar and tetrapolar configuration with a recently developed analyzer. Methods Tripolar analysis was carried out by applying sinusoidal voltages up to 1 V at the electrode interface. Tetrapolar analysis was carried on with sinusoidal field strengths from 0.1 V cm-1 to 70 V cm-1. Both analyses were performed within a frequency range from 1 Hz through 100 Hz. The harmonic amplitudes were Fourier-analyzed and expressed in dB. The third harmonic, as reported previously, was investigated. Statistical analysis (ANOVA) was used to test the effect of inhibitor an activator of the plasma membrane enzyme in the measured response. Results No significant non-linearities were observed in tetrapolar analysis, and no observable changes occurred when inhibitor and activator were added to the suspension. Statistical analysis confirmed these results. When a pure sinus voltage was applied to an electrode-yeast suspension interface, variations higher than 25 dB for the 3rd harmonic were observed. Variation higher than 20 dB in the 3rd harmonics has also been found when adding an inhibitor or activator of the membrane-bounded enzymes. These variations did not occur when the suspension was boiled. Discussion The lack of result in tetrapolar cells suggest that there is no, if any, harmonic generation in microbiological bulk suspension. The non-linear response observed was originated in the electrode-electrolyte interface. The frequency and voltage windows observed in previous tetrapolar analysis were repeated in the tripolar measurements, but maximum were not
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.
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
Halo model predictions of the cosmic magnification statistics: the full non-linear contribution
NASA Astrophysics Data System (ADS)
Takada, Masahiro; Hamana, Takashi
2003-12-01
The lensing magnification effect due to large-scale structure is statistically measurable by the correlation of size fluctuations in distant galaxy images as well as by cross-correlation between foreground galaxies and background sources such as the QSO-galaxy cross-correlation. We use the halo model formulation of Takada & Jain to compute these magnification-induced correlations without employing the weak lensing approximation, μ~ 1 + 2κ. Our predictions thus include the full contribution from non-linear magnification, δμ>~ 1, that is due to lensing haloes. We compare the model prediction with ray-tracing simulations and find excellent agreement over the range of angular scales we consider (0.5 <~θ<~ 30 arcmin). In addition, we derive the dependence of the correlation amplitude on the maximum magnification cut-off μmax, which it is necessary to introduce in order to avoid the contributions from strong lensing events. For a general correlation function parametrized as <μpf> (f is any cosmic field correlated with the magnification field), the amplitude remains finite for p < 1 and diverges for p>= 1 as μmax->∞, independent of the details of the lensing mass distribution and of the separation angle. This consequence is verified by the halo model as well as by the simulations. Thus, the magnification correlation with p<= 1 has a practical advantage in that it is insensitive to a selection effect of how strong lensing events with μ>> 1 are observationally excluded from the sample. The non-linear magnification contribution enhances the amplitude of the magnification correlation relative to the weak lensing approximation, and the non-linear correction is more significant on smaller angular scales and for sources at higher redshifts. The enhancement amounts to 10-25 per cent on arcmin scales for the QSO-galaxy cross-correlation, even after the inclusion of a realistic model of galaxy clustering within the host halo. Therefore, it is necessary to account for the
Manganite-based memristive heterojunction with tunable non-linear I-V characteristics
NASA Astrophysics Data System (ADS)
Lee, Hong-Sub; Park, Hyung-Ho; Rozenberg, M. J.
2015-04-01
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 Pr1-xCaxMnO3 (PCMO) and CaMnO3-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.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 Pr1-xCaxMnO3 (PCMO) and CaMnO3-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. Electronic supplementary information (ESI) available: Experimental method of spectromicroscopy; a scheme of the resistive switching mechanism, work function measurement of the CaMnO3-δ film; linear scale current-voltage characteristics; simulation method of the readout margin of a
Kerr Non-linerity in Slow Light Propagation for Quantum Teleportation
NASA Astrophysics Data System (ADS)
Tombesi, Paolo
2001-05-01
Quantum teleportation(C.H. Bennett et al)., Phys. Rev. Lett. 70, 1895 (1993). is the ``reconstruction" with 100% success, of an unknown state given to one station (Alice), performed at another remote station (Bob), on the basis of two bits of classical information sent by Alice to Bob. Perfect teleportation is possible only if the two parties share a maximally entangled state. The most delicate part needed for the effective realization of teleportation is the Bell-state measurement, i.e. the discrimination between the four, maximally entangled, Bell states which has to be performed by Alice and whose result is communicated to Bob through the classical channel. There have been numerous proposals for its realization in different systems and recently beautiful, pioneering experiments have provided convincing experimental proof-of-principle of the correctness of the teleportation concept. These experiments differ by the degrees of freedom used as qubits and for the different ways in which the Bell-state measurement is performed. The Innsbruck experiment (D.Bouwmeester et al)., Nature (London) 390, 575 (1997). is the conceptually simplest one, since each qubit is represented by the polarization state of a single photon pulse. In this experiment, however, only two out of the four Bell states can be discriminated and therefore the success rate cannot be larger than 50%. It is therefore desirable to have a scheme for a Bell-state measurement that can be used in the simplest case of the Innsbruck experiment. This would imply the possibility of realizing the first complete verification of the original quantum teleportation scheme(C.H. Bennett et al)., Phys. Rev. Lett. 70, 1895 (1993). and also of having a device useful for other quantum protocols, as quantum dense coding. A scheme for perfect Bell-state discrimination based on a non-linear optical effect, the cross-phase modulation taking place in Kerr media, will be discussed. We shall show that the needed crossed-Kerr non-linearity
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 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.
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.
Polycarbonate-Based Blends for Optical Non-linear Applications.
Stanculescu, F; Stanculescu, A
2016-12-01
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. PMID:26873262
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.
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.
Modified non-linear Burgers' equations and cosmic ray shocks
NASA Technical Reports Server (NTRS)
Zank, G. P.; Webb, G. M.; Mckenzie, J. F.
1988-01-01
A reductive perturbation scheme is used to derive a generalized non-linear Burgers' equation, which includes the effects of dispersion, in the long wavelength regime for the two-fluid hydrodynamical model used to describe cosmic ray acceleration by the first-order Fermi process in astrophysical shocks. The generalized Burger's equation is derived for both relativistic and non-relativistic cosmic ray shocks, and describes the time evolution of weak shocks in the theory of diffusive shock acceleration. The inclusion of dispersive effects modifies the phase velocity of the shock obtained from the lower order non-linear Burger's equation through the introduction of higher order terms from the long wavelength dispersion equation. The travelling wave solution of the generalized Burgers' equation for a single shock shows that larger cosmic ray pressures result in broader shock transitions. The results for relativistic shocks show a steepening of the shock as the shock speed approaches the relativistic cosmic ray sound speed. The dependence of the shock speed on the cosmic ray pressure is also discussed.
NASA Astrophysics Data System (ADS)
RoyChoudhury, Raja; RoyChoudhury, Arundhati
2011-02-01
This paper presents a semi analytical formulation of modal properties of a non linear optical fiber having Kerr non linearity with a three parameter approximation of fundamental modal field. The minimization of core parameter ( U) which involves Kerr nonlinearity through the non-stationary expression of propagation constant, is carried out by Nelder-Mead Simplex method of non linear unconstrained minimization, suitable for problems with non-smooth functions as the method does not require any derivative information. Use of three parameters in modal approximation and implementation of Simplex methods enables our semi analytical description to be an alternative way having less computational burden for calculation of modal parameters than full numerical methods.
Magnetized Kerr/CFT correspondence
NASA Astrophysics Data System (ADS)
Siahaan, Haryanto M.
2016-08-01
We extend the conjectured Kerr/CFT correspondence to the case of extremal Kerr black holes immersed by a magnetic field, namely the extremal Melvin–Kerr black holes. We compute the central charge which appears in the associated Virasoro algebra generated by a class of diffeomorphisms that satisfies a set of boundary conditions in the near horizon of an extremal Melvin–Kerr black hole. Our results support the Kerr/CFT conjecture, where the macroscopic Bekenstein–Hawking entropy for an extremal Melvin–Kerr black hole matches the result obtained from a dual 2D CFT microscopic computation using Cardy formula. Interestingly, the dual CFT description could be non-unitary, due to the possibility of negative central charge.
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
Anderson Localization, Non-linearity and Stable Genetic Diversity
NASA Astrophysics Data System (ADS)
Epstein, Charles L.
2006-07-01
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and mutation. Mutation operates as a generalized diffusion process on genotype space. In the large time asymptotics, the replication term tends to produce a single dominant quasi-species, unless the mutation rate is too high, in which case the asymptotic population becomes de-localized. We introduce a more macroscopic picture of genotypic evolution wherein a random fitness term in the linear model produces features analogous to Anderson localization. When coupled with density dependent non-linearities, which limit the population of any given genotype, we obtain a model whose large time asymptotics display stable genotypic diversity.
Engineering Non-Classical Light with Non-Linear Microwaveguides
NASA Astrophysics Data System (ADS)
Grimsmo, Arne; Clerk, Aashish; Blais, Alexandre
The quest for ever increasing fidelity and scalability in measurement of superconducting qubits to be used for fault-tolerant quantum computing has recently led to the development of near quantum-limited broadband phase preserving amplifiers in the microwave regime. These devices are, however, more than just amplifiers: They are sources of high-quality, broadband two-mode squeezed light. We show how bottom-up engineering of Josephson junction embedded waveguides can be used to design novel squeezing spectra. Furthermore, the entanglement in the two-mode squeezed output field can be imprinted onto quantum systems coupled to the device's output. These broadband microwave amplifiers constitute a realization of non-linear waveguide QED, a very interesting playground for non-equilibrium many-body physics.
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).
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.
Non-linear dielectric response of ferrofluids under magnetic field
NASA Astrophysics Data System (ADS)
Licinio, Pedro; Teixeira, Alvaro V.; Figueiredo, José Marcos A.
2005-03-01
The dielectric response of a water-based magnetic fluid is investigated at room temperature and in the frequency range of 100-10 7 rad/s. The response is linear in the electric fields used. Upon application of a constant magnetic field of 40 mT, which is well below the sample saturation, the response becomes non-linear. Magnetic field effects are isolated by performing a differential analysis of the inverse dielectric permittivity with and without applied field in both perpendicular and parallel configurations. The imaginary part of the differential inverse permittivity displays two peaks. The low-frequency peak is seen to correspond to the orientation relaxation of aggregates also detected in SAXS, photon correlation and atomic force microscopy measurements. The high-frequency peak corresponds to single magnetic particle reorientation.
Memristive non-linear system and hidden attractor
NASA Astrophysics Data System (ADS)
Saha, P.; Saha, D. C.; Ray, A.; Chowdhury, A. R.
2015-07-01
Effects of memristor on non-linear dynamical systems exhibiting chaos are analysed both form the view point of theory and experiment. It is observed that the memristive system has always fewer number of fixed points than the original one. Sometimes there is no fixed point in the memristive system. But its chaotic properties are retained. As such we have a situation known as hidden attractor because if it is a stable fixed point then the attractor does not evolve from its basin of attraction(obtained from its stable fixed point) or if there is no fixed point, the question of basin of attraction from fixed point does not arise at all [1, 2]. Our analysis gives a detailed accounts of properties related to its chaotic behavior. Important observations are also obtained with the help of electronic circuits to support the numerical simulations.
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
Ferrite core non-linearity in coils for magnetic neurostimulation
Lazzi, Gianluca
2014-01-01
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. PMID:26609390
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.
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.
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.
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.
Spontaneous Lorentz symmetry breaking in non-linear electrodynamics
Urrutia, Luis F.
2010-07-29
A recently proposed model of non-linear electrodynamics arising from a gauge invariant spontaneous Lorentz symmetry breaking is reviewed. The potential providing the symmetry breaking is argued to arise from the integration of gauge bosons and fermions in an underlying theory. The invariant subgroups remaining after the symmetry breaking are determined, as well as the dispersion relations and polarization modes of the propagating linear sector or the model. Strong bounds upon the predicted anisotropy of the speed of light are obtained by embedding the model in the electromagnetic sector of the Standard Model Extension and taking advantage of the restrictions in the parameters derived there. Finally, a reasonable estimation of the intergalactic magnetic field is obtained by assuming that the vacuum energy of the model is described by the standard cosmological constant.
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.
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.
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.
Reducing sample variance: halo biasing, non-linearity and stochasticity
NASA Astrophysics Data System (ADS)
Gil-Marín, Héctor; Wagner, Christian; Verde, Licia; Jimenez, Raul; Heavens, Alan F.
2010-09-01
Comparing clustering of differently biased tracers of the dark matter distribution offers the opportunity to reduce the sample or cosmic variance error in the measurement of certain cosmological parameters. We develop a formalism that includes bias non-linearities and stochasticity. Our formalism is general enough that it can be used to optimize survey design and tracers selection and optimally split (or combine) tracers to minimize the error on the cosmologically interesting quantities. Our approach generalizes the one presented by McDonald & Seljak of circumventing sample variance in the measurement of f ≡ d lnD/d lna. We analyse how the bias, the noise, the non-linearity and stochasticity affect the measurements of Df and explore in which signal-to-noise regime it is significantly advantageous to split a galaxy sample in two differently biased tracers. We use N-body simulations to find realistic values for the parameters describing the bias properties of dark matter haloes of different masses and their number density. We find that, even if dark matter haloes could be used as tracers and selected in an idealized way, for realistic haloes, the sample variance limit can be reduced only by up to a factor σ2tr/σ1tr ~= 0.6. This would still correspond to the gain from a three times larger survey volume if the two tracers were not to be split. Before any practical application one should bear in mind that these findings apply to dark matter haloes as tracers, while realistic surveys would select galaxies: the galaxy-host halo relation is likely to introduce extra stochasticity, which may reduce the gain further.
Limit cycle oscillation of missile control fin with structural non-linearity
NASA Astrophysics Data System (ADS)
Bae, J. S.; Lee, I.
2004-01-01
Non-linear aeroelastic characteristics of a deployable missile control fin with structural non-linearity are investigated. A deployable missile control fin is modelled as a two-dimensional typical section model. Doublet-point method is used for the calculation of supersonic unsteady aerodynamic forces, and aerodynamic forces are approximated by using the minimum-state approximation. For non-linear flutter analysis structural non-linearity is represented by an asymmetric bilinear spring and is linearized by using the describing function method. The linear and non-linear flutter analyses indicate that the flutter characteristics are significantly dependent on the frequency ratio. From the non-linear flutter analysis, various types of limit cycle oscillations are observed in a wide range of air speeds below or above the linear divergent flutter boundary. The non-linear flutter characteristics and the non-linear aeroelastic responses are investigated.
Uniqueness of extremal Kerr and Kerr-Newman black holes
Amsel, Aaron J.; Horowitz, Gary T.; Marolf, Donald; Roberts, Matthew M.
2010-01-15
We prove that the only four-dimensional, stationary, rotating, asymptotically flat (analytic) vacuum black hole with a single degenerate horizon is given by the extremal Kerr solution. We also prove a similar uniqueness theorem for the extremal Kerr-Newman solution. This closes a long-standing gap in the black hole uniqueness theorems.
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…
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.
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.
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
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
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
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
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.
Experimental study of a linear/non-linear flux rope
NASA Astrophysics Data System (ADS)
DeHaas, Timothy; Gekelman, Walter; Van Compernolle, Bart
2015-08-01
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, rplasma = 30 cm, no = 1012 cm-3, Te = 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 > πr2B0c/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.
STATISTICAL BASED NON-LINEAR MODEL UPDATING USING FEATURE EXTRACTION
Schultz, J.F.; Hemez, F.M.
2000-10-01
This research presents a new method to improve analytical model fidelity for non-linear systems. The approach investigates several mechanisms to assist the analyst in updating an analytical model based on experimental data and statistical analysis of parameter effects. The first is a new approach at data reduction called feature extraction. This is an expansion of the update metrics to include specific phenomena or character of the response that is critical to model application. This is an extension of the classical linear updating paradigm of utilizing the eigen-parameters or FRFs to include such devices as peak acceleration, time of arrival or standard deviation of model error. The next expansion of the updating process is the inclusion of statistical based parameter analysis to quantify the effects of uncertain or significant effect parameters in the construction of a meta-model. This provides indicators of the statistical variation associated with parameters as well as confidence intervals on the coefficients of the resulting meta-model, Also included in this method is the investigation of linear parameter effect screening using a partial factorial variable array for simulation. This is intended to aid the analyst in eliminating from the investigation the parameters that do not have a significant variation effect on the feature metric, Finally an investigation of the model to replicate the measured response variation is examined.
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.
Non-linear methods in remotely sensed multispectral data classification
NASA Astrophysics Data System (ADS)
Nikolov, Hs; Petkov, Di; Jeliazkova, N.; Ruseva, S.; Boyanov, K.
The aim of this research is to examine existing geoinformation processing systems and to develop a new system, able to cope with the stochastic nature of remote sensing data. In order to achieve this objective, it is necessary to structure the methodological knowledge in the area of data mining and reveal the most suitable methods for the prediction and decision support based on large amounts of multispectral data. Non-linear methods are a vast and quickly advancing field of research, but in the case of geoinformatics they are far away from applications targeted to end-users. The idea is to establish a framework by decomposing the task into functionality objectives and to allow the end-user to experiment with a set of classification methods and select the best methods for specific applications. In this framework we consider Bayesian analysis tools, nonlinear regression models, neural networks, fuzzy reasoning systems, kernel methods, evolutionary programming, genetic algorithms and decision trees. In particular we compare our results from Bayesian classification based on estimated probability densities of the data to the results obtained from other classification methods. We demonstrate that the theoretically optimal Bayesian classification also provides optimal classification in practice.
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.
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 processes modulated by low doses of radiation exposure
NASA Astrophysics Data System (ADS)
Mariotti, Luca; Ottolenghi, Andrea; Alloni, Daniele; Babini, Gabriele; Morini, Jacopo; Baiocco, Giorgio
The perturbation induced by radiation impinging on biological targets can stimulate the activation of several different pathways, spanning from the DNA damage processing to intra/extra -cellular signalling. In the mechanistic investigation of radiobiological damage this complex “system” response (e.g. omics, signalling networks, micro-environmental modifications, etc.) has to be taken into account, shifting from a focus on the DNA molecule solely to a systemic/collective view. An additional complication comes from the finding that the individual response of each of the involved processes is often not linear as a function of the dose. In this context, a systems biology approach to investigate the effects of low dose irradiations on intra/extra-cellular signalling will be presented, where low doses of radiation act as a mild perturbation of a robustly interconnected network. Results obtained through a multi-level investigation of both DNA damage repair processes (e.g. gamma-H2AX response) and of the activation kinetics for intra/extra cellular signalling pathways (e.g. NFkB activation) show that the overall cell response is dominated by non-linear processes - such as negative feedbacks - leading to possible non equilibrium steady states and to a poor signal-to-noise ratio. Together with experimental data of radiation perturbed pathways, different modelling approaches will be also discussed.
Non-linear saturation mechanism of electron temperature gradient modes
Tokluoglu, E. K.; Sokolov, V.; Sen, A. K.
2012-10-15
The electron temperature gradient (ETG) mode is a very plausible candidate to explain the large electron particle transport and thermal conduction. Production and identification of slab ETG modes and measurement electron transport have been already reported [X. Wei, V. Sokolov, and A. K. Sen, Phys. Plasmas 17, 042108 (2010); V. Sokolov and A. K. Sen, Phys. Rev. Lett. (2011)]. Now, we develop a theoretical model of non-linear saturation mechanism of ETG mode based on the three wave coupling of an unstable high frequency ETG mode with a damped ETG radial harmonic and a damped ion acoustic (IA) mode. Bicoherence analysis of Columbia linear machine (CLM) data show coupling between ETG modes ({approx}2.4 MHz) and a low frequency mode ({approx}50 kHz). The large damping drive of the ETG radial harmonic accompanied by the smaller but finite damping of the IA mode presents an energy sink for the unstable ETG mode, thus causing saturation. This model predicts a saturation level of {approx}10% and agrees with the observed levels of ETG modes in the CLM.
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.
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.
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.
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.
Non-Linear Optical Flow Cytometry Using a Scanned, Bessel Beam Light-Sheet
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-01-01
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. PMID:26021750
Non-Linear Signal Detection Improvement by Radiation Damping in Single-Pulse NMR Spectra
Schlagnitweit, Judith; Morgan, Steven W; Nausner, Martin; Müller, Norbert; Desvaux, Hervé
2012-01-01
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. PMID:22266720
Non-linear optical flow cytometry using a scanned, Bessel beam light-sheet.
Collier, Bradley B; Awasthi, Samir; Lieu, Deborah K; Chan, James W
2015-01-01
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. PMID:26021750
NASA Astrophysics Data System (ADS)
Adcock, T. A. A.; Taylor, P. H.
2016-01-01
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 scission/recombination kinetics of living polymerization
NASA Astrophysics Data System (ADS)
Nyrkova, I. A.; Semenov, A. N.
2007-10-01
Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M* (M* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M* ≪ M ≪ M*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t1, t2, t3 and t*; 2) there are transient regimes (t1 ≲ t ≲ t3) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t2. The chain growth is auto-accelerated for t1 ≲ t ≲ t2 : the cut-off chain length (= polymerization degree
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
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.
Phenomenon of life: between equilibrium and non-linearity.
Galimov, E M
2004-12-01
A model of ordering applicable to biological evolution is presented. It is shown that a steady state (more precisely approaching to a steady state) system of irreversible processes, under conditions of disproportionation of entropy, produces a lower-entropy product, that is, ordering. The ordering is defined as restricting of degrees of freedom: freedom of motion, interactions etc. The model differs from previous ones in that it relates the ordering to processes running not far from equilibrium, described in the linear field of non-equilibrium thermodynamics. It is shown that a system, which includes adenosine triphosphate (ATP) to adenosine diphosphate (ADP) conversion meets the demands of the physical model: it provides energy maintaining steady state conditions, and hydrolysis of ATP proceeding with consumption of water can be tightly conjugated with the most important reactions of synthesis of organic polymers (peptides, nucleotide chains etc.), which proceed with release of water. For these and other reasons ATP seems to be a key molecule of prebiotic evolution. It is argued that the elementary chemical reaction proceeding under control of an enzyme is not necessarily far from equilibrium. The experimental evidence supporting this idea, is presented. It is based on isotope data. Carbon isotope distribution in biochemical systems reveals regularity, which is inherent to steady state systems of chemical reactions, proceeding not far from equilibrium. In living organisms this feature appears at the statistical level, as many completely irreversible and non-linear processes occur in organisms. However not-far-from-equilibrium reactions are inherent to biochemical systems as a matter of principle. They are reconcilable with biochemical behavior. Extant organisms are highly evolved entities which, however, show in their basis the same features, as the simplest chemical systems must have had been involved in the origin of life. Some consequences following from the
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. PMID:26374047
Linear and non-linear wall friction of wet foams.
Le Merrer, Marie; Lespiat, Rémi; Höhler, Reinhard; Cohen-Addad, Sylvie
2015-01-14
We study the wall slip of aqueous foams with a high liquid content. We use a set-up where, driven by buoyancy, a foam creeps along an inclined smooth solid wall which is immersed in the foaming solution. This configuration allows the force driving the bubble motion and the bubble confinement in the vicinity of the wall to be tuned independently. First, we consider bubble monolayers with small Bond number Bo < 1 and measure the relation between the friction force F and the bubble velocity V. For bubbles which are so small that they are almost spherical, the friction law F ∝ V is Stokes-like. The analysis shows that the minimal thickness of the lubricating contact between the bubble and the wall is governed by DLVO long-range forces. Our results are the first evidence of this predicted linear friction regime for creeping bubbles. Due to buoyancy, large bubbles flatten against the wall. In this case, dissipation arises because of viscous flow in the dynamic meniscus between the contact film and the spherical part of the bubble. It leads to a non-linear Bretherton-like friction law F ∝ V(2/3), as expected for slipping bubbles with mobile liquid-gas interfaces. The Stokes-like friction dominates for capillary numbers Ca larger than the crossover value Ca* ∼ Bo(3/2). The overall friction force can be expressed as the sum of these two contributions. On this basis, we then study 3D foams close to the jamming transition with osmotic pressures Π small compared to the capillary pressure Pc. We measure the wall shear stress τ as a function of the capillary number, and we evidence two friction regimes that are consistent with those found for the monolayer. Similarly to this latter case, the total shear stress can be expressed as the sum of the Stokes-like friction term τ ∝ Ca and the Bretherton-like one τ ∝ Ca(2/3). However, for a 3D foam, the crossover at a capillary number Ca** between both regimes is governed by the ratio of the osmotic pressure to the
Entropy, non-linearity and hierarchy in ecosystems
NASA Astrophysics Data System (ADS)
Addiscott, T.
2009-04-01
Soil-plant systems are open systems thermodynamically because they exchange both energy and matter with their surroundings. Thus they are properly described by the second and third of the three stages of thermodynamics defined by Prigogine and Stengers (1984). The second stage describes a system in which the flow is linearly related to the force. Such a system tends towards a steady state in which entropy production is minimized, but it depends on the capacity of the system for self-organization. In a third stage system, flow is non-linearly related to force, and the system can move far from equilibrium. This system maximizes entropy production but in so doing facilitates self-organization. The second stage system was suggested earlier to provide a useful analogue of the behaviour of natural and agricultural ecosystems subjected to perturbations, but it needs the capacity for self-organization. Considering an ecosystem as a hierarchy suggests this capacity is provided by the soil population, which releases from dead plant matter nutrients such as nitrate, phosphate and captions needed for growth of new plants and the renewal of the whole ecosystem. This release of small molecules from macromolecules increases entropy, and the soil population maximizes entropy production by releasing nutrients and carbon dioxide as vigorously as conditions allow. In so doing it behaves as a third stage thermodynamic system. Other authors (Schneider and Kay, 1994, 1995) consider that it is in the plants in an ecosystem that maximize entropy, mainly through transpiration, but studies on transpiration efficiency suggest that this is questionable. Prigogine, I. & Stengers, I. 1984. Order out of chaos. Bantam Books, Toronto. Schneider, E.D. & Kay, J.J. 1994. Life as a manifestation of the Second Law of Thermodynamics. Mathematical & Computer Modelling, 19, 25-48. Schneider, E.D. & Kay, J.J. 1995. Order from disorder: The Thermodynamics of Complexity in Biology. In: What is Life: the Next
Kerr response of nematic liquids.
NASA Technical Reports Server (NTRS)
Johnston, A. R.
1973-01-01
Description of the results of recent observations of the Kerr effect in nematic liquid crystals in a temperature range just above their nematic-isotropic transition. These results indicate that the intermolecular ordering forces in a nematic substance can enhance the Kerr effect just above the nematic transition in their isotropic state. It is felt that existing theory provides a useful approximation for relating molecular size to response time.
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.
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
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.
Challenges in predicting non-linear creep and recovery in glassy polymers
NASA Astrophysics Data System (ADS)
Medvedev, Grigori; Caruthers, James
2014-03-01
The phenomenon of non-linear creep of amorphous polymeric glasses is difficult to predict using the traditional viscoelastic and viscoplastic constitutive frameworks, where two features present a particular challenge: (i) the tertiary stage of the creep and (ii) the recovery from large creep upon removal of the load. Representative examples of these two nonlinear responses will be shown for lightly cross-linked PMMA and an epoxy material, where the creep and recovery behavior has been studied as a function of temperature and aging time. The acceleration of creep during the tertiary stage is not caused by damage since the original dimensions of a cross-linked sample are fully recoverable by annealing above Tg. The assumption that the relaxation time is a function of strain runs into qualitative problems when predicting multi-step constant strain rate loading experiments. Recovery from creep as predicted by the constitutive models where the relaxation time depends on the deformation history is too abrupt compared to the experiment - this known as the ``accelerated aging'' problem. A recently developed Stochastic Constitutive Model that acknowledges dynamic heterogeneity in the glass state naturally predicts both the tertiary creep and the smooth recovery from creep.
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. PMID:27187988
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
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
Magnetised Kerr/CFT correspondence
NASA Astrophysics Data System (ADS)
Astorino, Marco
2015-12-01
The tools of Kerr/CFT correspondence are applied to the Kerr black hole embedded in an axial external magnetic field. Its extremal near horizon geometry remains a warped and twisted product of AdS2 ×S2. The central charge of the Virasoro algebra, generating the asymptotic symmetries of the near horizon geometry, is found. It is used to reproduce, via the Cardy formula, the Bekenstein-Hawking entropy of the magnetised Kerr black hole as the statistical microscopic entropy of a dual CFT. The presence of the background magnetic field makes available also a second dual CFT picture, based on the U (1) electromagnetic symmetry, instead of the only rotational one of the standard non-magnetised Kerr spacetime. A Meissner-like effect, where at extremality the external magnetic field is expelled out of the black hole, allows us to infer the value of the mass for these magnetised extremal black holes. The generalisation to the CFT dual for the magnetised extreme Kerr-Newman black hole is also presented.
Fast and Robust Newton strategies for non-linear geodynamics problems
NASA Astrophysics Data System (ADS)
Le Pourhiet, Laetitia; May, Dave
2014-05-01
Geodynamic problems are inherently non-linear, with sources of non-inearities arising from the (i) rheology, (ii) boundary conditions and (iii) the choice of time integration scheme. We have developed a robust non-linear scheme utilizing PETSc's non-linear solver framework; SNES. Through the SNES framework, we have access to a wide range of globalization techniques. In this work we extensively use line search implementation. We explored a wide range different strategies for solving a variety of non-linear problems specific to geodynamics. In this presentation, we report of the most robust line-searching techniques which we have found for the three classes of non-linearities previously identified. Among the class of rheological non-linearities, the shear banding instability using visco-plastic flow rules is the most difficult to solve. Distinctively from its sibling, the elasto-plastic rheology, the visco-plastic rheology causes instantaneous shear localisation. As a results, decreasing time-stepping is not a viable approach to better capture the initial phase of localisation. Furthermore, return map algorithms based on a consistent tangent cannot be used as the slope of the tangent is infinite. Obtaining a converged non-linear solution to this problem only relies on the robustness non-linear solver. After presenting a Newton methodology suitable for rheological non-linearities, we examine the performance of this formulation when frictional sliding boundary conditions are introduced. We assess the robustness of the non-linear solver when applied to critical taper type problems.
Characteristic Dynamics of a Non-Linear Flux Rope
NASA Astrophysics Data System (ADS)
Dehaas, Timothy; Gekelman, Walter; van Compernolle, Bart
2015-11-01
A magnetic flux rope is a tube-like, current carrying plasma embedded in an external magnetic field. 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 often recreated in laboratory environments. In a series of experiments, a single flux rope of varying cross-section and length was formed in the cylindrical, magnetized plasma of the Large Plasma Device (LaPD, L = 2200 cm, r = 30 cm, no = 1012 cm-3, Te = 4 eV, He). The flux rope was generated via a DC discharge between a cathode and anode with a fixed-free boundary condition. Upon the initiation of the kink instability (IKink > πr2Bzc/2L), the displacement of the flux rope saturates, commencing complex motion. The flux ropes exhibit two types of motion, common to all cases of varying Alfven speeds, injection currents, lengths, and cross-sections. The first motion is characterized by a circular path in the transverse plane, whose displacement depends on the input power and whose frequency varies with injection current. The second motion is characterized by random Lorentzian pulses in the magnetic signals. The polarity of these pulses align with the transverse magnetic field and manifest with greater frequency with increases in magnetic field and injection current. This work is supported by LANL-UC research grant and done at the Basic Plasma Science Facility, which is funded by DOE and NSF.
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.
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.
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.
The origin of off-resonance non-linear optical activity of a gold chiral nanomaterial
NASA Astrophysics Data System (ADS)
Abdulrahman, Nadia; Syme, Christopher D.; Jack, Calum; Karimullah, Affar; Barron, Laurence D.; Gadegaard, Nikolaj; Kadodwala, Malcolm
2013-11-01
We demonstrate that engineered artificial gold chiral nanostructures display significant levels of non-linear optical activity even without plasmonic enhancement. Our work suggests that although plasmonic excitation enhances the intensity of second harmonic emission it is not a prerequisite for significant non-linear (second harmonic) optical activity. It is also shown that the non-linear optical activities of both the chiral nanostructures and simple chiral molecules on surfaces have a common origin, namely pure electric dipole excitation. This is a surprising observation given the significant difference in length scales, three orders of magnitude, between the nanostructures and simple chiral molecules. Intuitively, given that the dimensions of the nanostructures are comparable to the wavelength of visible light, one would expect non-localised higher multipole excitation (e.g. electric quadrupole and magnetic dipole) to make the dominant contribution to non-linear optical activity. This study provides experimental evidence that the electric dipole origin of non-linear optical activity is a generic phenomenon which is not limited to sub-wavelength molecules and assemblies. Our work suggests that viewing non-plasmonic nanostructures as ``meta-molecules'' could be useful for rationally designing substrates for optimal non-linear optical activity.We demonstrate that engineered artificial gold chiral nanostructures display significant levels of non-linear optical activity even without plasmonic enhancement. Our work suggests that although plasmonic excitation enhances the intensity of second harmonic emission it is not a prerequisite for significant non-linear (second harmonic) optical activity. It is also shown that the non-linear optical activities of both the chiral nanostructures and simple chiral molecules on surfaces have a common origin, namely pure electric dipole excitation. This is a surprising observation given the significant difference in length scales
Non linear volume flow dependence on osmotic pressure difference in frog skin.
Celentano, F; Monticelli, G; Orsenigo, M N
1978-01-01
The volume flow dependence upon the osmotic pressure difference of both impermeant (sucrose) and permeable (NaCl) species has been investigated in leg skin bags of Rana esculenta. It is concluded: 1. The hydration-dehydration error in the flow measurement with leg skin bags is negligible. 2. The flow-force relationship is non-linear. 3. Unstirred layers and solute permeation have little, if any, influence on non linearity. 4. Structural modifications of the skin induced with hypertonic solutions have been observed and may contribute to non linearity, as well as the multiple-barrier effect. PMID:310878
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.
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.
Spontaneous Fluctuations and Non-linear Ignitions: Two Dynamic Faces of Cortical Recurrent Loops.
Moutard, Clément; Dehaene, Stanislas; Malach, Rafael
2015-10-01
Recent human neurophysiological recordings have uncovered two fundamental modes of cerebral cortex activity with distinct dynamics: an active mode characterized by a rapid and sustained activity ("ignition") and a spontaneous (resting-state) mode, manifesting ultra-slow fluctuations of low amplitude. We propose that both dynamics reflect two faces of the same recurrent loop mechanism: an integration device that accumulates ongoing stochastic activity and, either spontaneously or in a task-driven manner, crosses a dynamic threshold and ignites, leading to content-specific awareness. The hypothesis can explain a rich set of behavioral and neuronal phenomena, such as perceptual threshold, the high non-linearity of visual responses, the subliminal nature of spontaneous activity fluctuations, and the slow activity buildup anticipating spontaneous behavior (e.g., readiness potential). Further elaborations of this unified scheme, such as a cascade of integrators with different ignition thresholds or multi-stable states, can account for additional complexities in the repertoire of human cortical dynamics. PMID:26447581
Remote synchronization of amplitudes across an experimental ring of non-linear oscillators
NASA Astrophysics Data System (ADS)
Minati, Ludovico
2015-12-01
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.
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 .
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.
Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique
Shafie, Suhaidi; Kawahito, Shoji; Halin, Izhal Abdul; Hasan, Wan Zuha Wan
2009-01-01
The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region. PMID:22303133
Tortajada-Genaro, L A; Campíns-Falcó, P
2007-05-15
Multivariate standardisation is proposed for the successful chemiluminescence determination of chromium based on luminol-hydrogen peroxide reaction. In an extended concentration range, non-linear calibration model is needed. The studied instrumental situations were different detection cells, instruments, assemblies, time and their possible combinations. Chemiluminescence kinetic registers have been transferred using piecewise direct standardisation (PDS) method. The optimisation of transfer parameters has been carried out based on the prediction residual error criteria. Non-linear principal component regression (NL-PCR) and non-linear partial least square regression (NL-PLS) were chosen for modelling the relationship signal-concentration of transferred registers. Good accuracy and precision were obtained for water samples. The concentrations of chromium were statistically in agreement with reference method values and with recovery studies. Therefore, it is possible to transfer chemiluminescence curves without loosing ability of prediction, even the presence of a non-linear behaviour. PMID:19071716
Optimal feedback control of strongly non-linear systems excited by bounded noise
NASA Astrophysics Data System (ADS)
Zhu, W. Q.; Huang, Z. L.; Ko, J. M.; Ni, Y. Q.
2004-07-01
A strategy for non-linear stochastic optimal control of strongly non-linear systems subject to external and/or parametric excitations of bounded noise is proposed. A stochastic averaging procedure for strongly non-linear systems under external and/or parametric excitations of bounded noise is first developed. Then, the dynamical programming equation for non-linear stochastic optimal control of the system is derived from the averaged Itô equations by using the stochastic dynamical programming principle and solved to yield the optimal control law. The Fokker-Planck-Kolmogorov equation associated with the fully completed averaged Itô equations is solved to give the response of optimally controlled system. The application and effectiveness of the proposed control strategy are illustrated with the control of cable vibration in cable-stayed bridges and the feedback stabilization of the cable under parametric excitation of bounded noise.
Optical measurement of the weak non-linearity in the eardrum vibration response to auditory stimuli
NASA Astrophysics Data System (ADS)
Aerts, Johan
The mammalian hearing organ consists of the external ear (auricle and ear canal) followed by the middle ear (eardrum and ossicles) and the inner ear (cochlea). Its function is to convert the incoming sound waves and convert them into nerve pulses which are processed in the final stage by the brain. The main task of the external and middle ear is to concentrate the incoming sound waves on a smaller surface to reduce the loss that would normally occur in transmission from air to inner ear fluid. In the past it has been shown that this is a linear process, thus without serious distortions, for sound waves going up to pressures of 130 dB SPL (˜90 Pa). However, at large pressure changes up to several kPa, the middle ear movement clearly shows non-linear behaviour. Thus, it is possible that some small non-linear distortions are also present in the middle ear vibration at lower sound pressures. In this thesis a sensitive measurement set-up is presented to detect this weak non-linear behaviour. Essentially, this set-up consists of a loud-speaker which excites the middle ear, and the resulting vibration is measured with an heterodyne vibrometer. The use of specially designed acoustic excitation signals (odd random phase multisines) enables the separation of the linear and non-linear response. The application of this technique on the middle ear demonstrates that there are already non-linear distortions present in the vibration of the middle ear at a sound pressure of 93 dB SPL. This non-linear component also grows strongly with increasing sound pressure. Knowledge of this non-linear component can contribute to the improvement of modern hearing aids, which operate at higher sound pressures where the non-linearities could distort the signal considerably. It is also important to know the contribution of middle ear non-linearity to otoacoustic emissions. This are non-linearities caused by the active feedback amplifier in the inner ear, and can be detected in the external and
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.
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.
Discriminative analysis of non-linear brain connectivity in schizophrenia: an fMRI Study
Su, Longfei; Wang, Lubin; Shen, Hui; Feng, Guiyu; Hu, Dewen
2013-01-01
Background: Dysfunctional integration of distributed brain networks is believed to be the cause of schizophrenia, and resting-state functional connectivity analyses of schizophrenia have attracted considerable attention in recent years. Unfortunately, existing functional connectivity analyses of schizophrenia have been mostly limited to linear associations. Objective: The objective of the present study is to evaluate the discriminative power of non-linear functional connectivity and identify its changes in schizophrenia. Method: A novel measure utilizing the extended maximal information coefficient was introduced to construct non-linear functional connectivity. In conjunction with multivariate pattern analysis, the new functional connectivity successfully discriminated schizophrenic patients from healthy controls with relative higher accuracy rate than the linear measure. Result: We found that the strength of the identified non-linear functional connections involved in the classification increased in patients with schizophrenia, which was opposed to its linear counterpart. Further functional network analysis revealed that the changes of the non-linear and linear connectivity have similar but not completely the same spatial distribution in human brain. Conclusion: The classification results suggest that the non-linear functional connectivity provided useful discriminative power in diagnosis of schizophrenia, and the inverse but similar spatial distributed changes between the non-linear and linear measure may indicate the underlying compensatory mechanism and the complex neuronal synchronization underlying the symptom of schizophrenia. PMID:24155713
Second-order optical non-linearity of proton exchanged lithium tantalate waveguides
NASA Astrophysics Data System (ADS)
Korkishko, Y. N.; Fedorov, V. A.; Alkaev, A. N.; Laurell, F.
2001-10-01
A detailed correlation between the fabrication conditions, crystallographic phase state of HxLi1-xTaO3 waveguides and second-order optical non-linearity has been investigated by using reflected SHG measurements from the polished waveguide end face. The non-linearity, strongly reduced after the initial proton exchange, is found to be restored and even increased after annealing. However, this apparent increase in the non-linearity is accompanied by a strong degradation of the quality of the SHG reflected beam in the region of the initial as-exchanged waveguide due to beam scattering. The high temperature proton exchange technique has been shown to produce high-quality α-phase waveguides with essentially undegraded non-linear optical properties. There is no phase transition when the α-phase waveguides are fabricated by direct exchange. This phase presents the same crystalline structure as that of LiTaO3 and maintains the excellent non-linear properties of the bulk material. The results obtained are important for the design, fabrication and optimization of guided-wave non-linear optical devices in LiTaO3.
Geometrically non-linear vibration of spinning structures by finite element method
NASA Astrophysics Data System (ADS)
Leung, A. Y. T.; Fung, T. C.
1990-05-01
The geometrically non-linear steady state vibration of spinning structures is studied. Full flap-lag-torsional gyroscopic coupling effects are considered. The non-linearity arises mainly from the non-linear axial strain-displacement relation. The equations of motion are derived from Lagrangian equations. Spatial discretization is achieved by the finite element method and steady state nodal displacements are expanded into Fourier series. The harmonic balance method gives a set of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The non-linear algebraic equations are solved by a Newtonian algorithm iteratively. The importance of the conditions of completeness and balanceability in choosing the number of harmonic terms to be used is discussed. General frame structures with arbitrary orientation in a rotating frame can be investigated by the present method. Rotating blades and shafts are treated as special cases. Examples of a rotating ring with different orientations are given. The non-linear amplitude-frequency relation can be constructed parametrically.
Detecting non-linearities in neuro-electrical signals: A study of synchronous local field potentials
NASA Astrophysics Data System (ADS)
Müller-Gerking, Johannes; Martinerie, Jacques; Neuenschwander, Sergio; Pezard, Laurent; Renault, Bernard; Varela, Francisco J.
The question of the presence and detection of non-linear dynamics and possibly low-dimensional chaos in the brain is still an open question, with recent results indicating that initial claims for low dimensionality were faulted by incomplete statistical testing. To make some progress on this question, our approach was to use stringent data analysis of precisely controlled and behaviorally significant neuroelectric data. There are strong indications that functional brain activity is correlated with synchronous local field potentials. We examine here such synchronous episodes in data recorded from the visual system of behaving cats and pigeons. Our purpose was to examine under these ideal conditions whether the time series showed any evidence of non-linearity concommitantly with the arising of synchrony. To test for non-linearity we have used surrogate sets for non-linear forecasting, the false nearest strands method, and an examination of deterministic vs stochastic modeling. Our results indicate that the time series under examination do show evidence for traces of non-linear dynamics but weakly, since they are not robust under changes of parameters. We conclude that low-dimensional chaos is unlikely to be found in the brain, and that a robust detection and characterization of higher-dimensional non-linear dynamics is beyond the reach of current analytical tools.
Neural potentials and micro-signals of non-linear deep and shallow conical shells
NASA Astrophysics Data System (ADS)
Chai, W. K.; Smithmaitrie, P.; Tzou, H. S.
2004-07-01
Conventional sensors, such as proximeters and accelerometers, are add-on devices usually adding additional weights to structures and machines. Health monitoring of flexible structures by electroactive smart materials has been investigated over the years. Thin-film piezoelectric material, e.g. polyvinylidene fluoride (PVDF) polymeric material, is a lightweight and dynamic sensitive material appearing to be a perfect candidate in monitoring structure's dynamic state and health status of flexible shell structures with complex geometries. The complexity of shell structures has thwarted the progress in studying the distributed sensing of shell structures. Linear distributed sensing of various structures have been studied, e.g. beams, plates, cylindrical shells, conical shells, spherical shells, paraboloidal shells and toroidal shells. However, distributed microscopic neural signals of non-linear shell structures has not been carried out rigorously. This study is to evaluate microscopic signals, modal voltages and distributed micro-neural signal components of truncated non-linear conical shells laminated with distributed infinitesimal piezoelectric neurons. Signal generation of distributed neuron sensors laminated on conical shells is defined first. The dynamic neural signal of truncated non-linear conical shells consists of microscopic linear and non-linear membrane components and linear bending component based on the von Karman geometric non-linearity. Micro-signals, modal voltages and distributed neural signal components of two different truncated non-linear conical shells are investigated and their sensitivities discussed.
Domain walls of linear polarization in isotropic Kerr media
NASA Astrophysics Data System (ADS)
Louis, Y.; Sheppard, A. P.; Haelterman, M.
1997-09-01
We present a new type of domain-wall vector solitary waves in isotropic self-defocusing Kerr media. These domain walls consist of localized structures separating uniform field domains of orthogonal linear polarizations. They result from the interplay between diffraction, self-phase modulation and cross-phase modulation in cases where the nonlinear birefringence coefficient B = {χxyyx(3)}/{χxxxx(3)} is negative. Numerical simulations show that these new vector solitary waves are stable.
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
Non-linear dual-axis biodynamic response to vertical whole-body vibration
NASA Astrophysics Data System (ADS)
Nawayseh, N.; Griffin, M. J.
2003-11-01
Seated human subjects have been exposed to vertical whole-body vibration so as to investigate the non-linearity in their biodynamic responses and quantify the response in directions other than the direction of excitation. Twelve males were exposed to random vertical vibration in the frequency range 0.25-25 Hz at four vibration magnitudes (0.125, 0.25, 0.625, and 1.25 m s -2 r.m.s.). The subjects sat in four sitting postures having varying foot heights so as to produce differing thigh contact with the seat (feet hanging, feet supported with maximum thigh contact, feet supported with average thigh contact, and feet supported with minimum thigh contact). Forces were measured in the vertical, fore-and-aft, and lateral directions on the seat and in the vertical direction at the footrest. The characteristic non-linear response of the human body with reducing resonance frequency at increasing vibration magnitudes was seen in all postures, but to a lesser extent with minimum thigh contact. Appreciable forces in the fore-and-aft direction also showed non-linearity, while forces in the lateral direction were low and showed no consistent trend. Forces at the feet were non-linear with a multi-resonant behaviour and were affected by the position of the legs. The decreased non-linearity with the minimum thigh contact posture suggests the tissues of the buttocks affect the non-linearity of the body more than the tissues of the thighs. The forces in the fore-and-aft direction are consistent with the body moving in two directions when exposed to vertical vibration. The non-linear behaviour of the body, and the considerable forces in the fore-aft direction should be taken into account when optimizing vibration isolation devices.
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
Massive vector particles tunneling from Kerr and Kerr-Newman black holes
NASA Astrophysics Data System (ADS)
Li, Xiang-Qian; Chen, Ge-Rui
2015-12-01
In this paper, we investigate the Hawking radiation of massive spin-1 particles from 4-dimensional Kerr and Kerr-Newman black holes. By applying the Hamilton-Jacobi ansatz and the WKB approximation to the field equations of the massive bosons in Kerr and Kerr-Newman space-time, the quantum tunneling method is successfully implemented. As a result, we obtain the tunneling rate of the emitted vector particles and recover the standard Hawking temperature of both the two black holes.
A three-dimensional network model describing a non-linear composite material
NASA Astrophysics Data System (ADS)
Mårtensson, E.; Gäfvert, U.
2004-01-01
A three-dimensional network model for performing non-linear time-dependent simulations of the electrical characteristics related to a composite material is presented. The considered compounds are represented by a cubic lattice and consist of conducting particles distributed in an insulating matrix. Earlier studies of the non-linear characteristics of silicon carbide (SiC) grains and of the linear frequency-dependent electrical properties of composites are combined and extended. The calculations are compared to measurements on ethylene-propylene-diene monomer rubber filled with angular SiC grains. The field-dependent conductivity measured for the unconsolidated SiC powder is used as input to the simulations. The model can manage the conductivity difference of seven decades between the constituents and the strong exponential non-linearity of the conducting particles. The network calculations replicate the experimental characteristic at high filler concentrations, where direct 'face' contacts between the filler grains dominate the behaviour. At lower concentrations, it is shown that indirect 'edge' contacts involving the polymer control the current transport also in the non-linear high field range. The general effective conductivity describing an edge connection in the linear case is no longer appropriate. Non-linear mechanisms in the polymer and the conducting grains within a field enhanced limited region around the contact need to be represented by an equivalent circuit element with a case-dependent resulting expression.
On the Slow Transition across Instabilities in Non-Linear Dissipative Systems
NASA Astrophysics Data System (ADS)
Raman, A.; Bajaj, A. K.; Davies, P.
1996-05-01
Non-linear vibratory systems are often characterized by external or excitation parameters which vary with time (i.e., are "non-stationary"). A general methodology is presented to predict analytically the response of some weakly non-linear dissipative systems as an excitation parameter varies slowly across points of instability corresponding to co-dimensional-1 bifurcations. It is shown that the motion near the bifurcation/critical point can be approximated by motion along a center manifold, and can be represented by a 1-dimensional dynamical system with a slowly varying parameter. Techniques expounded by Haberman [1] for analyzing such 1-dimensional equations using matched asymptotic expansions and non-linear boundary layers are summarized. The results are then used to obtain responses of some classical non-linear vibratory systems in the presence of non-stationary excitation. The problem of transition across saddle-node bifurcations or jumps during passage through primary resonance in the forced Duffing's oscillator is studied. Then, the transition across the points of dynamic instability (pitchfork bifurcations) in the parametrically excited non-linear Mathieu equation is analyzed. Lastly, the transition across a Hopf bifurcation in the Parkinson-Smith model for galloping of bluff bodies is discussed. The methodology described here is found to be effective in approximating the behavior of the systems in the vicinity of bifurcation points. The solutions and their qualitative features predicted by the analysis are in good agreement with those obtained from direct numerical integration of the equations.
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
An iterative method to solve the heat transfer problem under the non-linear boundary conditions
NASA Astrophysics Data System (ADS)
Zhu, Zhenggang; Kaliske, Michael
2012-02-01
The aim of the paper is to determine the approximation of the tangential matrix for solving the non-linear heat transfer problem. Numerical model of the strongly non-linear heat transfer problem based on the theory of the finite element method is presented. The tangential matrix of the Newton method is formulated. A method to solve the heat transfer with the non-linear boundary conditions, based on the secant slope of a reference function, is developed. The contraction mapping principle is introduced to verify the convergence of this method. The application of the method is shown by two examples. Numerical results of these examples are comparable to the ones solved with the Newton method and the commercial software COMSOL for the heat transfer problem under the radiative boundary conditions.
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
DSP-based Mitigation of RF Front-end Non-linearity in Cognitive Wideband Receivers
NASA Astrophysics Data System (ADS)
Grimm, Michael; Sharma, Rajesh K.; Hein, Matthias A.; Thomä, Reiner S.
2012-09-01
Software defined radios are increasingly used in modern communication systems, especially in cognitive radio. Since this technology has been commercially available, more and more practical deployments are emerging and its challenges and realistic limitations are being revealed. One of the main problems is the RF performance of the front-end over a wide bandwidth. This paper presents an analysis and mitigation of RF impairments in wideband front-ends for software defined radios, focussing on non-linear distortions in the receiver. We discuss the effects of non-linear distortions upon spectrum sensing in cognitive radio and analyse the performance of a typical wideband software-defined receiver. Digital signal processing techniques are used to alleviate non-linear distortions in the baseband signal. A feed-forward mitigation algorithm with an adaptive filter is implemented and applied to real measurement data. The results obtained show that distortions can be suppressed significantly and thus increasing the reliability of spectrum sensing.
Stability analysis, non-linear pulsations and mass loss of models for 55 Cygni (HD 198478)
NASA Astrophysics Data System (ADS)
Yadav, Abhay Pratap; Glatzel, Wolfgang
2016-04-01
55 Cygni is a variable supergiant. Recent observational studies revealed that this star pulsates in pressure, gravity and strange modes. The pulsations seem to be associated with episodes of mass loss. In this paper we present a theoretical study of stellar models with parameters close to that of 55 Cygni. A linear non-adiabatic stability analysis with respect to radial perturbations is performed and the evolution of instabilities into the non-linear regime is followed by numerical simulation. Our study indicates that the mass of 55 Cygni lies below 28 M⊙. As the final consequence of the instabilities the non-linear simulations revealed finite amplitude pulsations with periods consistent with the observations. The non-linear results also indicate a connection between pulsations and mass loss and allow for an estimate of the mean mass-loss rate. It is consistent with the observed values.
Non-Linear Fuzzy Logic Control for Forced Large Motions of Spinning Shafts
NASA Astrophysics Data System (ADS)
LEI, SHULIANG; PALAZZOLO, ALAN; NA, UHNJOO; KASCAK, ALBERT
2000-08-01
A unique control approach is developed for prescribed large motion control using magnetic bearings in a proposed active stall control test rig. A finite element based, flexible shaft is modeled in a closed loop system with PD controllers that generate the control signals to support and to shake the rotor shaft. A linearized force model of the stall rig with 16 magnetic poles (4 opposing C-cores) yields stability and frequency responses. The non-linear model retains the non-linearities in Ampere's law, Faraday's law and the Maxwell stress tensor. A fuzzy logic control system is then designed to show the advantages over the conventional controllers with the fully non-linear model.
Roles of Different Forms of Scale Factor in Non-linear Electrodynamics for Accelerating Universe
NASA Astrophysics Data System (ADS)
Maity, Sayani; Debnath, Ujjal
2013-07-01
In this work, we have assumed the modified Lagrangian of non-linear electrodynamics for accelerated universe. The energy density and pressure for non-linear electromagnetic theory have been considered in terms of both electric and magnetic fields. The Einstein's filed equations have been considered in FRW universe for Hořava-Lifshitz gravity. Since we are considering the non-linear form of Lagrangian for accelerating universe, so four forms of scale factors like logamediate, intermediate, emergent and power law forms are chosen in our investigation. For every expansion, the natures of electric field and magnetic field have been shown through graphical representation. The electric and magnetic fields increase for logamediate, intermediate and emergent expansion and decrease in power law expansion.
Instantaneous stepped-frequency, non-linear radar part 2: experimental confirmation
NASA Astrophysics Data System (ADS)
Ranney, Kenneth; Mazzaro, Gregory; Gallagher, Kyle; Martone, Anthony; Sherbondy, Kelly; Narayanan, Ram
2016-05-01
Last year, we presented the theory behind "instantaneous stepped-frequency, non-linear radar". We demonstrated through simulation that certain devices (when interrogated by a multi-tone transmit signal) could be expected to produce a multi-tone output signal near harmonics of the transmitted tones. This hypothesized non-linear (multitone) response was then shown to be suitable for pulse compression via standard stepped-frequency processing techniques. At that time, however, we did not have measured data to support the theoretical and simulated results. We now present laboratory measurements confirming our initial hypotheses. We begin with a brief description of the experimental system, and then describe the data collection exercise. Finally, we present measured data demonstrating the accurate ranging of a non-linear target.
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.