Energy Technology Data Exchange (ETDEWEB)
Alvarez-Estrada, R.F.
1979-08-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly.
Non-Linear Logging Parameters Inversion
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The non-linear logging parameters inversion is based on the field theory, information optimization and predication theory. It uses seismic charaoters,geological model and logging data as a restriction to inverse 2D, 3D logging parameters data volume. Using this method,
Non linear inversion of gravity gradients and the GGI gradiometer
Talwani, Manik
2011-12-01
All gradiometers currently operating for exploration in the field are based on Lockheed Martin's GGI gradiometer. The working of this gradiometer is described and a method for robust non linear inversion of gravity gradients is presented. The inversion method involves obtaining the gradient response of a trial body consisting of vertical rectangular prisms. The inversion adjusts the depth to the tops or bases of the prisms. In the trial model all the prisms are not required to have the same area of cross section or the same density (which can also be allowed to vary with depth). The depth to the tops and bottoms of each prism can also be different. This response is compared with the observed values of gradient and through an iterative procedure, the difference is minimized in a least square sense to arrive at a best fitting model by varying the position of the tops or bottoms of the prisms. Each gradient can be individually inverted or one or more gradients can be jointly inverted. The method is extended to invert gravity values individually or jointly with gradient values. The use of Differential Curvature, a quantity which is directly obtained by current gradiometers in use and which is an invariant under a rotation in the horizontal plane, is emphasized. Synthetic examples as well as a field example of inversion are given.
Non-linear magnetorheological behaviour of an inverse ferrofluid
de Gans, B.J.; Hoekstra, Hans; Mellema, J.
1999-01-01
The non-linear magnetorheological behaviour is studied of a model system consisting of monodisperse silica particles suspended in a ferrofluid. The stress/strain curve as well as the flow curve was measured as a function of volume fraction silica particles and field strength, using a home-made
Alkhalifah, Tariq Ali
2012-09-25
Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.
THE APPLICATION OF GENETIC ALGORITHM IN NON-LINEAR INVERSION OF ROCK MECHANICS PARAMETERS
Institute of Scientific and Technical Information of China (English)
赵晓东
1998-01-01
The non-linear inversion of rock mechanics parameters based on genetic algorithm ispresented. The principle and step of genetic algorithm is also given. A brief discussion of thismethod and an application example is presented at the end of this paper. From the satisfied re-sult, quick, convenient and practical new approach is developed to solve this kind of problems.
A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics
DEFF Research Database (Denmark)
Engell-Nørregård, Morten; Erleben, Kenny
2009-01-01
Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...
Non-Linear Rheological Properties and Neutron Scattering Investigation on Dilute Ring-Linear Blends
DEFF Research Database (Denmark)
Pyckhout-Hintzen, W.; Bras, A.R.; Wischnewski, A.;
Linear and non-linear Rheology on dilute blends of polystyrene ring polymers in linear matrix is combined with Small Angle Neutron Scattering (SANS) investigations. In this way 2 different entanglement interactions become clear. After stretching the samples to different hencky strains up to 2 in ...
Uieda, Leonardo; Barbosa, Valéria C. F.
2016-10-01
Estimating the relief of the Moho from gravity data is a computationally intensive non-linear inverse problem. What is more, the modeling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized non-linear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyper-parameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30-35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basins, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.
Particle sizing by dynamic light scattering: non-linear cumulant analysis.
Mailer, Alastair G; Clegg, Paul S; Pusey, Peter N
2015-04-15
We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few cumulants (or moments) of the distribution of particle diffusion constants. Frisken (2001 Appl. Opt. 40 4087) has pointed out that, despite greater computational complexity, a non-linear, iterative, analysis of the data has advantages over the linear least-squares analysis used originally. In order to explore further the potential and limitations of cumulant methods we analyse, by both linear and non-linear methods, computer-generated data with realistic 'noise', where the parameters of the distribution can be set explicitly. We find that, with modern computers, non-linear analysis is straightforward and robust. The mean and variance of the distribution of diffusion constants can be obtained quite accurately for distributions of width (standard deviation/mean) up to about 0.6, but there appears to be little prospect of obtaining meaningful higher moments.
Inversion assuming weak scattering
DEFF Research Database (Denmark)
Xenaki, Angeliki; Gerstoft, Peter; Mosegaard, Klaus
2013-01-01
The study of weak scattering from inhomogeneous media or interface roughness has long been of interest in sonar applications. In an acoustic backscattering model of a stationary field of volume inhomogeneities, a stochastic description of the field is more useful than a deterministic description...... due to the complex nature of the field. A method based on linear inversion is employed to infer information about the statistical properties of the scattering field from the obtained cross-spectral matrix. A synthetic example based on an active high-frequency sonar demonstrates that the proposed...
Elizondo, D.; Cappelaere, B.; Faure, Ch.
2002-04-01
Emerging tools for automatic differentiation (AD) of computer programs should be of great benefit for the implementation of many derivative-based numerical methods such as those used for inverse modeling. The Odyssée software, one such tool for Fortran 77 codes, has been tested on a sample model that solves a 2D non-linear diffusion-type equation. Odyssée offers both the forward and the reverse differentiation modes, that produce the tangent and the cotangent models, respectively. The two modes have been implemented on the sample application. A comparison is made with a manually-produced differentiated code for this model (MD), obtained by solving the adjoint equations associated with the model's discrete state equations. Following a presentation of the methods and tools and of their relative advantages and drawbacks, the performances of the codes produced by the manual and automatic methods are compared, in terms of accuracy and of computing efficiency (CPU and memory needs). The perturbation method (finite-difference approximation of derivatives) is also used as a reference. Based on the test of Taylor, the accuracy of the two AD modes proves to be excellent and as high as machine precision permits, a good indication of Odyssée's capability to produce error-free codes. In comparison, the manually-produced derivatives (MD) sometimes appear to be slightly biased, which is likely due to the fact that a theoretical model (state equations) and a practical model (computer program) do not exactly coincide, while the accuracy of the perturbation method is very uncertain. The MD code largely outperforms all other methods in computing efficiency, a subject of current research for the improvement of AD tools. Yet these tools can already be of considerable help for the computer implementation of many numerical methods, avoiding the tedious task of hand-coding the differentiation of complex algorithms.
Simulation of non-linear ultrasound fields
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Fox, Paul D.; Wilhjelm, Jens E.
2002-01-01
An approach for simulating non-linear ultrasound imaging using Field II has been implemented using the operator splitting approach, where diffraction, attenuation, and non-linear propagation can be handled individually. The method uses the Earnshaw/Poisson solution to Burgcrs' equation for the non......-linear ultrasound imaging in 3D using filters or pulse inversion for any kind of transducer, focusing, apodization, pulse emission and scattering phantom. This is done by first simulating the non-linear emitted field and assuming that the scattered field is weak and linear. The received signal is then the spatial...
Non-Linear Compton Scattering in a Strong Rotating Electric Field
Raicher, Erez; Zigler, Arie
2016-01-01
The non-linear Compton scattering rate in a rotating electric field is explicitly calculated for the first time. For this purpose, a novel solution to the Klein-Gordon equation in the presence of a rotating electric field is applied. An analytical expression for the emission rate is obtained, as well as a simplified approximation adequate for emplementation in kinetic codes. The spectrum is numerically calculated for nowadays optical and X-ray laser parameters. The results are compared to the standard Volkov-Ritus rate for a particle in a plane wave, which is commonly assumed to be valid for a rotating electric field under certain conditions. Subsequent deviations between the two models, both in the radiated power and the spectral shape, are demonstrated. First, the typical number of photons participating in the scattering process is much smaller compared to the Volkov-Ritus rate, resulting in up to an order of magnitude lower emitted power. Furthermore, our model predicts a discrete harmonics spectrum for el...
Linearized versus non-linear inverse methods for seismic localization of underground sources
DEFF Research Database (Denmark)
Oh, Geok Lian; Jacobsen, Finn
2013-01-01
The problem of localization of underground sources from seismic measurements detected by several geophones located on the ground surface is addressed. Two main approaches to the solution of the problem are considered: a beamforming approach that is derived from the linearized inversion problem...... Difference elastic wave-field numerical method. In this paper, the accuracy and performance of the linear beamformer and nonlinear inverse methods to localize a underground seismic source are checked and compared using computer generated synthetic experimental data. © 2013 Acoustical Society of America....
Corbard, T; Berthomieu, G; Provost, J P
1999-01-01
Inversions of rotational splittings have shown that there exists at the base of the solar convection zone a region called the tachocline in which high radial gradients of the rotation rate occur. The usual linear regularization methods tend to smooth out any high gradients in the solution, and may not be appropriate for the study of this zone. In this paper we use, in the helioseismic context of rotation inversions, regularization methods that have been developed for edge-preserving regularization in computed imaging. It is shown from Monte-Carlo simulations that this approach can lead directly to results similar to those reached by linear inversions which however required some assumptions on the shape of the transition in order to be deconvolved. The application of this method to LOWL data leads to a very thin tachocline. From the discussions on the parameters entering the inversion and the Monte-Carlo simulations, our conclusion is that the tachocline width is very likely below 0.05R_sun which lowers our pr...
Towards adjoint-based inversion of time-dependent mantle convection with non-linear viscosity
Li, Dunzhu; Gurnis, Michael; Stadler, Georg
2017-01-01
We develop and study an adjoint-based inversion method for the simultaneous recovery of initial temperature conditions and viscosity parameters in time-dependent mantle convection from the current mantle temperature and historic plate motion. Based on a realistic rheological model with temperature- and strain rate-dependent viscosity, we formulate the inversion as a PDE-constrained optimization problem. The objective functional includes the misfit of surface velocity (plate motion) history, the misfit of the current mantle temperature, and a regularization for the uncertain initial condition. The gradient of this functional with respect to the initial temperature and the uncertain viscosity parameters is computed by solving the adjoint of the mantle convection equations. This gradient is used in a preconditioned quasi-Newton minimization algorithm. We study the prospects and limitations of the inversion, as well as the computational performance of the method using two synthetic problems, a sinking cylinder and a realistic subduction model. The subduction model is characterized by the migration of a ridge toward a trench whereby both plate motions and subduction evolve. The results demonstrate: (1) for known viscosity parameters, the initial temperature can be well recovered, as in previous initial condition-only inversions where the effective viscosity was given; (2) for known initial temperature, viscosity parameters can be recovered accurately, despite the existence of trade-offs due to ill-conditioning; (3) for the joint inversion of initial condition and viscosity parameters, initial condition and effective viscosity can be reasonably recovered, but the high dimension of the parameter space and the resulting ill-posedness may limit recovery of viscosity parameters.
Geodynamic inversion to constrain the non-linear rheology of the lithosphere
Baumann, T. S.; Kaus, Boris J. P.
2015-08-01
One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology
Directory of Open Access Journals (Sweden)
Murray L. Ireland
2015-06-01
Full Text Available Multirotor is the umbrella term for the family of unmanned aircraft, which include the quadrotor, hexarotor and other vertical take-off and landing (VTOL aircraft that employ multiple main rotors for lift and control. Development and testing of novel multirotor designs has been aided by the proliferation of 3D printing and inexpensive flight controllers and components. Different multirotor configurations exhibit specific strengths, while presenting unique challenges with regards to design and control. This article highlights the primary differences between three multirotor platforms: a quadrotor; a fully-actuated hexarotor; and an octorotor. Each platform is modelled and then controlled using non-linear dynamic inversion. The differences in dynamics, control and performance are then discussed.
Directory of Open Access Journals (Sweden)
G. Forget
2015-10-01
Full Text Available This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of data constraints and control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The baseline ECCO v4 solution is a dynamically consistent ocean state estimate without unidentified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found to be physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model–data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.
Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil
2017-01-01
3D non-linear inversion of total field magnetic anomalies caused by vertical-sided prismatic bodies has been achieved by differential evolution (DE), which is one of the population-based evolutionary algorithms. We have demonstrated the efficiency of the algorithm on both synthetic and field magnetic anomalies by estimating horizontal distances from the origin in both north and east directions, depths to the top and bottom of the bodies, inclination and declination angles of the magnetization, and intensity of magnetization of the causative bodies. In the synthetic anomaly case, we have considered both noise-free and noisy data sets due to two vertical-sided prismatic bodies in a non-magnetic medium. For the field case, airborne magnetic anomalies originated from intrusive granitoids at the eastern part of the Biga Peninsula (NW Turkey) which is composed of various kinds of sedimentary, metamorphic and igneous rocks, have been inverted and interpreted. Since the granitoids are the outcropped rocks in the field, the estimations for the top depths of two prisms representing the magnetic bodies were excluded during inversion studies. Estimated bottom depths are in good agreement with the ones obtained by a different approach based on 3D modelling of pseudogravity anomalies. Accuracy of the estimated parameters from both cases has been also investigated via probability density functions. Based on the tests in the present study, it can be concluded that DE is a useful tool for the parameter estimation of source bodies using magnetic anomalies.
Directory of Open Access Journals (Sweden)
G. Forget
2015-05-01
Full Text Available This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and highly integrated with the MITgcm. They are both subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of model-data constraints and adjustable control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The reference ECCO v4 solution is a dynamically consistent ocean state estimate (ECCO-Production, release 1 without un-identified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model-data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.
Non-Linear Compton Scattering of Ultrashort and Ultraintense Laser Pulses
Seipt, D
2010-01-01
The scattering of temporally shaped intense laser pulses off electrons is discussed by means of manifestly covariant quantum electrodynamics. We employ a framework based on Volkov states with a time dependent laser envelope in light-cone coordinates within the Furry picture. An expression for the cross section is constructed, which is independent of the considered pulse shape and pulse length. A broad distribution of scatted photons with a rich pattern of subpeaks like that obtained in Thomson scattering is found. These broad peaks may overlap at sufficiently high laser intensity, rendering inappropriate the notion of individual harmonics. The limit of monochromatic plane waves as well as the classical limit of Thomson scattering are discussed. As a main result, a scaling law is presented connecting the Thomson limit with the general result for arbitrary kinematics. In the overlapping regions of the spectral density, the classical and quantum calculations give different results, even in the Thomson limit. Thu...
Scattering-angle based filtering of the waveform inversion gradients
Alkhalifah, Tariq Ali
2014-11-22
Full waveform inversion (FWI) requires a hierarchical approach to maneuver the complex non-linearity associated with the problem of velocity update. In anisotropic media, the non-linearity becomes far more complex with the potential trade-off between the multiparameter description of the model. A gradient filter helps us in accessing the parts of the gradient that are suitable to combat the potential non-linearity and parameter trade-off. The filter is based on representing the gradient in the time-lag normalized domain, in which the low scattering angle of the gradient update is initially muted out in the FWI implementation, in what we may refer to as a scattering angle continuation process. The result is a low wavelength update dominated by the transmission part of the update gradient. In this case, even 10 Hz data can produce vertically near-zero wavenumber updates suitable for a background correction of the model. Relaxing the filtering at a later stage in the FWI implementation allows for smaller scattering angles to contribute higher-resolution information to the model. The benefits of the extended domain based filtering of the gradient is not only it\\'s ability in providing low wavenumber gradients guided by the scattering angle, but also in its potential to provide gradients free of unphysical energy that may correspond to unrealistic scattering angles.
Influence of Guided Waves in Tibia on Non-linear Scattering of Contrast Agents.
Wang, Diya; Zhong, Hui; Zhai, Yu; Hu, Hong; Jin, Bowen; Wan, Mingxi
2016-02-01
The aim of this study was to elucidate the linear and non-linear responses of ultrasound contrast agent (UCA) to frequency-dispersive guided waves from the tibia cortex, particularly two individual modes, S0 (1.23 MHz) and A1 (2.06 MHz). The UCA responses to guided waves were illustrated through the Marmottant model derived from measured guided waves, and then verified by continuous infusion experiments in a vessel-tibia flow phantom. These UCA responses were further evaluated by the enhanced ratio of peak values and the resolutions of UCA backscattered echoes. Because of the individual modes S0 and A1 in the tibia, the peak values of the UCA backscattered echoes were enhanced by 83.57 ± 7.35% (p < 0.05) and 80.77 ± 6.60% (p < 0.01) in the UCA subharmonic frequency and subharmonic imaging, respectively. However, corresponding resolutions were 0.78 ± 0.07 (p < 0.05) and 0.72 ± 0.12 (p < 0.01) times those without guided wave disturbances, respectively. Even though the resolution was partly degenerated, the subharmonic detection sensitivity of UCA was improved by the guided waves. Thus, UCA responses to the double-frequency guided waves should be further explored to benefit the detection of capillary perfusion in tissue layers near the bone cortex, particularly for perfusion imaging in the free flaps and skeletal muscles.
Inverse scattering: applications to nuclear physics
Mackintosh, Raymond S
2012-01-01
In what follows we first set the context for inverse scattering in nuclear physics with a brief account of inverse problems in general. We then turn to inverse scattering which involves the S-matrix, which connects the interaction potential between two scattering particles with the measured scattering cross section. The term `inverse' is a reference to the fact that instead of determining the scattering S-matrix from the interaction potential between the scattering particles, we do the inverse. That is to say, we calculate the interaction potential from the S-matrix. This review explains how this can now be done reliably, but the emphasis will be upon reasons why one should wish to do this, with an account of some of the ways this can lead to understanding concerning nuclear interactions.
Liu, Zhengwen; Liu, Shaopu; Wang, Lei; Peng, Juanjuan; He, Youqiu
2009-09-01
In pH 6.6 Britton-Robinson buffer medium, the CdS quantum dots capped by thioglycolic acid could react with aminoglycoside (AGs) antibiotics such as neomycin sulfate (NEO) and streptomycin sulfate (STP) to form the large aggregates by virtue of electrostatic attraction and the hydrophobic force, which resulted in a great enhancement of resonance Rayleigh scattering (RRS) and resonance non-linear scattering such as second-order scattering (SOS) and frequency doubling scattering (FDS). The maximum scattering peak was located at 310 nm for RRS, 568 nm for SOS and 390 nm for FDS, respectively. The enhancements of scattering intensity (Δ I) were directly proportional to the concentration of AGs in a certain ranges. A new method for the determination of trace NEO and STP using CdS quantum dots probe was developed. The detection limits (3 σ) were 1.7 ng mL -1 (NEO) and 4.4 ng mL -1 (STP) by RRS method, were 5.2 ng mL -1 (NEO) and 20.9 ng mL -1 (STP) by SOS method and were 4.4 ng mL -1 (NEO) and 25.7 ng mL -1 (STP) by FDS method, respectively. The sensitivity of RRS method was the highest. The optimum conditions and influence factors were investigated. In addition, the reaction mechanism was discussed.
Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem
Jung, C; Torres, J M
2005-01-01
The concept of measurement in classical scattering is interpreted as an overlap of a particle packet with some area in phase space that describes the detector. Considering that usually we record the passage of particles at some point in space, a common detector is described e.g. for one-dimensional systems as a narrow strip in phase space. We generalize this concept allowing this strip to be transformed by some, possibly non-linear, canonical transformation, introducing thus a canonically transformed detector. We show such detectors to be useful in the context of the inverse scattering problem in situations where recently discovered scattering echoes could not be seen without their help. More relevant applications in quantum systems are suggested.
Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem
Jung, C.; Seligman, T. H.; Torres, J. M.
The concept of measurement in classical scattering is interpreted as an overlap of a particle packet with some area in phase space that describes the detector. Considering that usually we record the passage of particles at some point in space, a common detector is described e.g. for one-dimensional systems as a narrow strip in phase space. We generalize this concept allowing this strip to be transformed by some, possibly non-linear, canonical transformation, introducing thus a canonically transformed detector. We show such detectors to be useful in the context of the inverse scattering problem in situations where recently discovered scattering echoes could not be seen without their help. More relevant applications in quantum systems are suggested.
Multidimensional Absorptive-Dispersive Inverse Scattering and Parameter Leakage at the Linear Step
Innanen, K. A.; Weglein, A. B.; Lira, J. E.
2008-12-01
Research is active into the use of inverse scattering to create direct non-linear methods for task-separated imaging, inversion, and Q compensation of primary reflections (Weglein et al., 2008). We will discuss some recent developments within the third of these efforts. First, we will describe an extension of the absorptive inverse scattering equations in multiple dimensions to the case of an absorptive reference medium. This requires a generalized definition of the perturbation as compared to the non-absorptive reference medium case. Second, because of its potential impact on a recently described prototype direct non-linear Q compensation algorithm (Innanen and Weglein, 2005; Innanen and Lira, 2008), we will discuss the issue of leakage of absorptive parameters. Leakage is an inverse phenomenon in which actual variations in one medium parameter lead to variations of the linear estimate of other parameters, especially at large angles and large contrasts. This is a linear issue exclusively; the full non-linear inverse scattering series addresses leakage, and corrects for it. Our prototype non-linear Q compensation algorithm involves the isolated use of some, but not all, of the non-linear terms of the inverse scattering series. The question we wish to address is: does this subset of the full inverse series also manage and correct for leakage, or will it over- or under-compensate at large angles and large contrasts? If the latter, further analysis and collection of inverse series components will likely be indicated. A. B. Weglein, A. C. Ramirez, K. A. Innanen, F. Liu, J. E. Lira and S. Jiang, 'The underlying unity of distinct processing algorithms for (1) the removal of free-surface and internal multiples, (2) Q compensation (without Q) (3) depth imaging, (4) nonlinear AVO, that derive from the inverse scattering series', 2008: Proc. Soc. Expl. Geop. K. A. Innanen and A. B. Weglein, 'Towards non-linear construction of a Q compensation operator directly from measured
J. Puķīte; T. Wagner
2016-01-01
We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer–Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, ...
Bayesian Inversion of Seabed Scattering Data
2014-09-30
uncertainties as well as parameter values, thereby quantifying the information content of the data to resolve the model parameters. Bayesian inversion...method based on deviance information criterion to determine the dominant scattering mechanism is in development. This work has been compiled in two... Bayesian Inversion of Seabed Scattering Data (Special Research Award in Ocean Acoustics) Gavin A.M.W. Steininger School of Earth & Ocean
Inverse acoustic problem of N homogeneous scatterers
DEFF Research Database (Denmark)
Berntsen, Svend
2002-01-01
The three-dimensional inverse acoustic medium problem of N homogeneous objects with known geometry and location is considered. It is proven that one scattering experiment is sufficient for the unique determination of the complex wavenumbers of the objects. The mapping from the scattered fields...
Inverse scattering problem in turbulent magnetic fluctuations
Treumann, R A; Narita, Y
2016-01-01
We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent response function, and reduce it to the solution of a special form of the famous Gel$'$fand-Levitan-Marchenko equation of quantum mechanical scattering theory.
Inverse acoustic problem of N homogeneous scatterers
DEFF Research Database (Denmark)
Berntsen, Svend
2002-01-01
The three-dimensional inverse acoustic medium problem of N homogeneous objects with known geometry and location is considered. It is proven that one scattering experiment is sufficient for the unique determination of the complex wavenumbers of the objects. The mapping from the scattered fields...
Voorhies, Coerte V.
1993-01-01
The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.
Puķīte, Jānis; Wagner, Thomas
2016-05-01
We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on
Inversion of Scattered Waves for Material Properties in Fractured Rock
Energy Technology Data Exchange (ETDEWEB)
Gritto, Roland; Korneev, Valeri A.; Johnson, Lane R.
1999-07-01
The authors apply a recently developed low-frequency, non-linear inversion method which includes near and far field terms to a crosshole data set to determine the bulk and shear modulus, as well as the density for a fractured zone in a granitic rock mass. The method uses the scattered elastic wavefield which is extracted from the recorded data before the inversion is performed. The inversion result is appraised by investigating the resolution and standard deviation of the model estimates. The sensitivity of the three parameters to different features of the medium is revealed. While the bulk modulus appears to be sensitive to voids and welded contacts, the density is mostly affected by fractured zones. The shear modulus is least constrained due to the absence of S wave anisotropy information. It is shown that the three medium parameters are generally sensitive to other medium features than those determined by velocity inversions. Thus this method is viewed as a complimentary approach to travel time tomography which provides more insight into the material properties of inhomogeneous media.
Inverse Scattering Approach to Improving Pattern Recognition
Energy Technology Data Exchange (ETDEWEB)
Chapline, G; Fu, C
2005-02-15
The Helmholtz machine provides what may be the best existing model for how the mammalian brain recognizes patterns. Based on the observation that the ''wake-sleep'' algorithm for training a Helmholtz machine is similar to the problem of finding the potential for a multi-channel Schrodinger equation, we propose that the construction of a Schrodinger potential using inverse scattering methods can serve as a model for how the mammalian brain learns to extract essential information from sensory data. In particular, inverse scattering theory provides a conceptual framework for imagining how one might use EEG and MEG observations of brain-waves together with sensory feedback to improve human learning and pattern recognition. Longer term, implementation of inverse scattering algorithms on a digital or optical computer could be a step towards mimicking the seamless information fusion of the mammalian brain.
Energy Technology Data Exchange (ETDEWEB)
Yao, Jie, E-mail: yjie2@uh.edu [Department of Mechanical Engineering, University of Houston, Houston, Texas 77204 (United States); Lesage, Anne-Cécile; Hussain, Fazle [Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas 79409 (United States); Bodmann, Bernhard G. [Department of Mathematics, University of Houston, Houston, Texas 77204 (United States); Kouri, Donald J. [Department of Physics, University of Houston, Houston, Texas 77204 (United States)
2014-12-15
The reversion of the Born-Neumann series of the Lippmann-Schwinger equation is one of the standard ways to solve the inverse acoustic scattering problem. One limitation of the current inversion methods based on the reversion of the Born-Neumann series is that the velocity potential should have compact support. However, this assumption cannot be satisfied in certain cases, especially in seismic inversion. Based on the idea of distorted wave scattering, we explore an inverse scattering method for velocity potentials without compact support. The strategy is to decompose the actual medium as a known single interface reference medium, which has the same asymptotic form as the actual medium and a perturbative scattering potential with compact support. After introducing the method to calculate the Green’s function for the known reference potential, the inverse scattering series and Volterra inverse scattering series are derived for the perturbative potential. Analytical and numerical examples demonstrate the feasibility and effectiveness of this method. Besides, to ensure stability of the numerical computation, the Lanczos averaging method is employed as a filter to reduce the Gibbs oscillations for the truncated discrete inverse Fourier transform of each order. Our method provides a rigorous mathematical framework for inverse acoustic scattering with a non-compact support velocity potential.
Inverse scattering of dispersive stratified structures
Skaar, Johannes
2012-01-01
We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown that the inverse scattering problem does not have a unique solution in general. When the dispersion is sufficiently small, such that the time-domain Fresnel reflections have durations less than the round-trip time in the layers, the solution is unique and can be found by layer peeling. Numerical examples with dispersive and lossy media are given, demonstrating the usefulness of the method for e.g. THz technology.
Inverse Scattering in a Multipath Environment
Directory of Open Access Journals (Sweden)
A. Cuccaro
2016-09-01
Full Text Available In this contribution an inverse scattering problem is ad- dressed in a multipath environment. In particular, multipath is created by known ”extra” point-like scatterers (passive elements expressely deployed between the scene under in- vestigation and the source/measurement domains. Through a back-projection imaging scheme, the role of the passive elements on the achievable performance is shown and com- pared to the free-space case.
Yu, XiaoChun; Bai, YuGuang; Cui, Miao; Gao, XiaoWei
2013-05-01
This paper presents a new inverse analysis approach to sensitivity analysis and material property identification in transient non-homogeneous and non-linear heat conduction Boundary Element Method (BEM) analysis based on Complex Variable Differentiation Method (CVDM). In this approach, the material properties are taken as the optimization variables, and the sensitivity coefficients are computed by CVDM. The advantages of using CVDM are that the computation of partial derivatives of an implicit function is reduced to function calculation in a complex domain, and the parameter sensitivity coefficients can be determined in a more accurate way than the traditional Finite Difference Method (FDM). Based on BEM and CVDM in evaluation of the sensitivity matrix of heat flux, the parameter such as thermal conductivity can be accurately identified. Six numerical examples are given to demonstrate the potential of the proposed approach. The results indicate that the presented method is efficient for identifying the thermal conductivity with single or multiple parameters.
Inverse obstacle scattering for elastic waves
Li, Peijun; Wang, Yuliang; Wang, Zewen; Zhao, Yue
2016-11-01
Consider the scattering of a time-harmonic plane wave by a rigid obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. An exact transparent boundary condition is introduced to reduce the scattering problem into a boundary value problem in a bounded domain. Given the incident field, the direct problem is to determine the displacement of the wave field from the known obstacle; the inverse problem is to determine the obstacle’s surface from the measurement of the displacement on an artificial boundary enclosing the obstacle. In this paper, we consider both the direct and inverse problems. The direct problem is shown to have a unique weak solution by examining its variational formulation. The domain derivative is derived for the displacement with respect to the variation of the surface. A continuation method with respect to the frequency is developed for the inverse problem. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.
Inverse potential scattering in duct acoustics.
Forbes, Barbara J; Pike, E Roy; Sharp, David B; Aktosun, Tuncay
2006-01-01
The inverse problem of the noninvasive measurement of the shape of an acoustical duct in which one-dimensional wave propagation can be assumed is examined within the theoretical framework of the governing Klein-Gordon equation. Previous deterministic methods developed over the last 40 years have all required direct measurement of the reflectance or input impedance but now, by application of the methods of inverse quantum scattering to the acoustical system, it is shown that the reflectance can be algorithmically derived from the radiated wave. The potential and area functions of the duct can subsequently be reconstructed. The results are discussed with particular reference to acoustic pulse reflectometry.
Linearized inversion of multiple scattering seismic energy
Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad
2014-05-01
Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. So, imaging seismic data with the single-scattering assumption does not locate multiple bounces events in their actual subsurface positions. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single scattering energy such as nearly vertical faults. Standard migration of these multiples provides subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. The resultant image obtained by the adjoint operator is a smoothed depiction of the true subsurface reflectivity model and is heavily masked by migration artifacts and the source wavelet fingerprint that needs to be properly deconvolved. Hence, we proposed a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. The proposed algorithm uses the least-square image based on single-scattering assumption as a constraint to invert for the part of the image that is illuminated by internal scattering energy. Then, we posed the problem of imaging double-scattering energy as a least-square minimization problem that requires solving the normal equation of the following form: GTGv = GTd, (1) where G is a linearized forward modeling operator that predicts double-scattered seismic data. Also, GT is a linearized adjoint operator that image double-scattered seismic data. Gradient-based optimization algorithms solve this linear system. Hence, we used a quasi-Newton optimization technique to find the least-square minimizer. In this approach, an estimate of the Hessian matrix that contains
INVERSE SCATTERING PROBLEMS BY SINGULAR SOURCE METHODS
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The inverse scattering problems are to detect the property of obstacles from the measurements outside the obstacles. One of important research areas in this topic is the recovery of boundary property for impenetrable obstacles. In this paper, we would like to give a brief review about the recently developed singular source methods. There are three different methods in this category, namely, linear sampling method, pointsource method and probe method. We also present some recent new results about the probe method.
Inverse scattering problem for quantum graph vertices
Cheon, Taksu; Turek, Ondrej
2011-01-01
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the scale invariant (or F\\"ul\\H{o}p-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.
Gamma ray vortices from nonlinear inverse Compton scattering of circularly polarized light
Taira, Yoshitaka; Katoh, Masahiro
2016-01-01
Inverse Compton scattering (ICS) is an elemental radiation process that produces high-energy photons both in nature and in the laboratory. Non-linear ICS is a process in which multiple photons are converted to a single high-energy photon. Here, we theoretically show that the photon produced by non-linear ICS of circularly polarized photons is a vortex, which means that it possesses a helical wave front and carries orbital angular momentum. Our work explains a recent experimental result regarding non-linear Compton scattering that clearly shows an annular intensity distribution as a remarkable feature of a vortex beam. Our work implies that gamma ray vortices should be produced in various situations in astrophysics in which high-energy electrons and intense circularly polarized light fields coexist. They should play a critical role in stellar nucleosynthesis. Non-linear ICS is the most promising radiation process for realizing a gamma ray vortex source based on currently available laser and accelerator technol...
Inverse scattering problem in turbulent magnetic fluctuations
Treumann, Rudolf A.; Baumjohann, Wolfgang; Narita, Yasuhito
2016-08-01
We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent response function, and reduce it to the solution of a special form of the famous Gelfand-Levitan-Marchenko equation of quantum mechanical scattering theory. The last of these applies to transmission and reflection in an active medium. The theory of turbulent magnetic fluctuations does not refer to such quantities. It requires a somewhat different formulation. We reduce the theory to the measurement of the low-frequency electromagnetic fluctuation spectrum, which is not the turbulent spectral energy density. The inverse theory in this form enables obtaining information about the turbulent response function of the medium. The dynamic causes of the electromagnetic fluctuations are implicit to it. Thus, it is of vital interest in low-frequency magnetic turbulence. The theory is developed until presentation of the equations in applicable form to observations of turbulent electromagnetic fluctuations as input from measurements. Solution of the final integral equation should be done by standard numerical methods based on iteration. We point to the possibility of treating power law fluctuation spectra as an example. Formulation of the problem to include observations of spectral power densities in turbulence is not attempted. This leads to severe mathematical problems and requires a reformulation of inverse scattering theory. One particular aspect of the present inverse theory of turbulent fluctuations is that its structure naturally leads to spatial information which is obtained from the temporal information that is inherent to the observation of time series. The Taylor assumption is not needed here. This is a consequence of Maxwell's equations, which couple space and time evolution. The inversion procedure takes advantage of a particular
Inverse problems and inverse scattering of plane waves
Ghosh Roy, Dilip N
2001-01-01
The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book''s primary focus.
A high-energy, high-flux source of gamma-rays from all-optical non-linear Thomson scattering
Corvan, D. J.; Zepf, M.; Sarri, G.
2016-09-01
γ-Ray sources are among the most fundamental experimental tools currently available to modern physics. As well as the obvious benefits to fundamental research, an ultra-bright source of γ-rays could form the foundation of scanning of shipping containers for special nuclear materials and provide the bases for new types of cancer therapy. However, for these applications to prove viable, γ-ray sources must become compact and relatively cheap to manufacture. In recent years, advances in laser technology have formed the cornerstone of optical sources of high energy electrons which already have been used to generate synchrotron radiation on a compact scale. Exploiting the scattering induced by a second laser, one can further enhance the energy and number of photons produced provided the problems of synchronisation and compact γ-ray detection are solved. Here, we report on the work that has been done in developing an all-optical and hence, compact non-linear Thomson scattering source, including the new methods of synchronisation and compact γ-ray detection. We present evidence of the generation of multi-MeV (maximum 16-18 MeV) and ultra-high brilliance (exceeding 1020 photons s-1mm-2mrad-2 0.1% BW at 15 MeV) γ-ray beams. These characteristics are appealing for the paramount practical applications mentioned above.
Phaseless tomographic inverse scattering in Banach spaces
Estatico, C.; Fedeli, A.; Pastorino, M.; Randazzo, A.; Tavanti, E.
2016-10-01
In conventional microwave imaging, a hidden dielectric object under test is illuminated by microwave incident waves and the field it scatters is measured in magnitude and phase in order to retrieve the dielectric properties by solving the related non-homogenous Helmholtz equation or its Lippmann-Schwinger integral formulation. Since the measurement of the phase of electromagnetic waves can be still considered expensive in real applications, in this paper only the magnitude of the scattering wave fields is measured in order to allow a reduction of the cost of the measurement apparatus. In this respect, we firstly analyse the properties of the phaseless scattering nonlinear forward modelling operator in its integral form and we provide an analytical expression for computing its Fréchet derivative. Then, we propose an inexact Newton method to solve the associated nonlinear inverse problems, where any linearized step is solved by a Lp Banach space iterative regularization method which acts on the dual space Lp* . Indeed, it is well known that regularization in special Banach spaces, such us Lp with 1 < p < 2, allows to promote sparsity and to reduce Gibbs phenomena and over-smoothness. Preliminary results concerning numerically computed field data are shown.
Inverse Scattering and the Geroch Group
Katsimpouri, Despoina; Virmani, Amitabh
2013-01-01
We study the integrability of gravity-matter systems in D=2 spatial dimensions with matter related to a symmetric space G/K using the well-known linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The linear system of BM makes the group structure of the Geroch group manifest and we analyse the relation of this group structure to the inverse scattering method of the BZ approach in general. Concrete solution generating methods are exhibited in the BM approach in the so-called soliton transformation sector where the analysis becomes purely algebraic. As a novel example we construct the Kerr-NUT solution by solving the appropriate purely algebraic Riemann-Hilbert problem in the BM approach.
A high-energy, high-flux source of gamma-rays from all-optical non-linear Thomson scattering
Energy Technology Data Exchange (ETDEWEB)
Corvan, D.J., E-mail: dcorvan01@qub.ac.uk; Zepf, M.; Sarri, G.
2016-09-01
γ-Ray sources are among the most fundamental experimental tools currently available to modern physics. As well as the obvious benefits to fundamental research, an ultra-bright source of γ-rays could form the foundation of scanning of shipping containers for special nuclear materials and provide the bases for new types of cancer therapy. However, for these applications to prove viable, γ-ray sources must become compact and relatively cheap to manufacture. In recent years, advances in laser technology have formed the cornerstone of optical sources of high energy electrons which already have been used to generate synchrotron radiation on a compact scale. Exploiting the scattering induced by a second laser, one can further enhance the energy and number of photons produced provided the problems of synchronisation and compact γ-ray detection are solved. Here, we report on the work that has been done in developing an all-optical and hence, compact non-linear Thomson scattering source, including the new methods of synchronisation and compact γ-ray detection. We present evidence of the generation of multi-MeV (maximum 16–18 MeV) and ultra-high brilliance (exceeding 10{sup 20} photons s{sup −1}mm{sup −2}mrad{sup −2} 0.1% BW at 15 MeV) γ-ray beams. These characteristics are appealing for the paramount practical applications mentioned above. - Highlights: • How synchrotron radiation can be produced in an all optical setting using laser-plasmas. • Generating high-energy, high-flux gamma ray beams. • Presenting results from a recent NLTS experimental campaign. • Reveal insight into the experimental techniques employed.
Crosta, Giovanni Franco; Pan, Yong-Le; Aptowicz, Kevin B.; Casati, Caterina; Pinnick, Ronald G.; Chang, Richard K.; Videen, Gorden W.
2013-12-01
Measurement of two-dimensional angle-resolved optical scattering (TAOS) patterns is an attractive technique for detecting and characterizing micron-sized airborne particles. In general, the interpretation of these patterns and the retrieval of the particle refractive index, shape or size alone, are difficult problems. By reformulating the problem in statistical learning terms, a solution is proposed herewith: rather than identifying airborne particles from their scattering patterns, TAOS patterns themselves are classified through a learning machine, where feature extraction interacts with multivariate statistical analysis. Feature extraction relies on spectrum enhancement, which includes the discrete cosine FOURIER transform and non-linear operations. Multivariate statistical analysis includes computation of the principal components and supervised training, based on the maximization of a suitable figure of merit. All algorithms have been combined together to analyze TAOS patterns, organize feature vectors, design classification experiments, carry out supervised training, assign unknown patterns to classes, and fuse information from different training and recognition experiments. The algorithms have been tested on a data set with more than 3000 TAOS patterns. The parameters that control the algorithms at different stages have been allowed to vary within suitable bounds and are optimized to some extent. Classification has been targeted at discriminating aerosolized Bacillus subtilis particles, a simulant of anthrax, from atmospheric aerosol particles and interfering particles, like diesel soot. By assuming that all training and recognition patterns come from the respective reference materials only, the most satisfactory classification result corresponds to 20% false negatives from B. subtilis particles and classification method may be adapted into a real-time operation technique, capable of detecting and characterizing micron-sized airborne particles.
Efficient Non Linear Loudspeakers
DEFF Research Database (Denmark)
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption....
Point sources and multipoles in inverse scattering theory
Potthast, Roland
2001-01-01
Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of applications, from medical imaging and radar to remote sensing and seismic exploration. Point Sources and Multipoles in Inverse Scattering Theory provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory. Focusing on methods developed over the last six years by Colton, Kirsch, and the author, this treatment uses point sources combined with several far-reaching techniques to obtain qualitative reconstruction methods. The author addresses questions of uniqueness, stability, and reconstructions for both two-and three-dimensional problems.With interest in extracting information about an object through scattered waves at an all-ti...
Efficient Non Linear Loudspeakers
DEFF Research Database (Denmark)
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption.......Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Inverse acoustic scattering problem in half-space with anisotropic random impedance
Helin, Tapio; Lassas, Matti; Päivärinta, Lassi
2017-02-01
We study an inverse acoustic scattering problem in half-space with a probabilistic impedance boundary value condition. The Robin coefficient (surface impedance) is assumed to be a Gaussian random function with a pseudodifferential operator describing the covariance. We measure the amplitude of the backscattered field averaged over the frequency band and assume that the data is generated by a single realization of λ. Our main result is to show that under certain conditions the principal symbol of the covariance operator of λ is uniquely determined. Most importantly, no approximations are needed and we can solve the full non-linear inverse problem. We concentrate on anisotropic models for the principal symbol, which leads to the analysis of a novel anisotropic spherical Radon transform and its invertibility.
A Recursive Born Approach to Nonlinear Inverse Scattering
Kamilov, Ulugbek S; Mansour, Hassan; Boufounos, Petros T
2016-01-01
The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails.
Multi-scattering inversion for low model wavenumbers
Alkhalifah, Tariq Ali
2015-08-19
A successful full wavenumber inversion (FWI) implementation updates the low wavenumber model components first for proper wavefield propagation description, and slowly adds the high-wavenumber potentially scattering parts of the model. The low-wavenumber components can be extracted from the transmission parts of the recorded data given by direct arrivals or the transmission parts of the single and double-scattering wave-fields developed from a predicted scatter field. We develop a combined inversion of data modeled from the source and those corresponding to single and double scattering to update both the velocity model and the component of the velocity (perturbation) responsible for the single and double scattering. The combined inversion helps us access most of the potential model wavenumber information that may be embedded in the data. A scattering angle filter is used to divide the gradient of the combined inversion so initially the high wavenumber (low scattering angle) components of the gradient is directed to the perturbation model and the low wavenumber (high scattering angle) components to the velocity model. As our background velocity matures, the scattering angle divide is slowly lowered to allow for more of the higher wavenumbers to contribute the velocity model.
A time domain sampling method for inverse acoustic scattering problems
Guo, Yukun; Hömberg, Dietmar; Hu, Guanghui; Li, Jingzhi; Liu, Hongyu
2016-06-01
This work concerns the inverse scattering problems of imaging unknown/inaccessible scatterers by transient acoustic near-field measurements. Based on the analysis of the migration method, we propose efficient and effective sampling schemes for imaging small and extended scatterers from knowledge of time-dependent scattered data due to incident impulsive point sources. Though the inverse scattering problems are known to be nonlinear and ill-posed, the proposed imaging algorithms are totally "direct" involving only integral calculations on the measurement surface. Theoretical justifications are presented and numerical experiments are conducted to demonstrate the effectiveness and robustness of our methods. In particular, the proposed static imaging functionals enhance the performance of the total focusing method (TFM) and the dynamic imaging functionals show analogous behavior to the time reversal inversion but without solving time-dependent wave equations.
Linearized inverse scattering based on seismic reverse time migration
op 't Root, T.J.P.M.; Stolk, C.C.; de Hoop, M.V.
2012-01-01
In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse time migration (RTM). In the process, the explicit evaluation of the so-called normal operator is avoided, while other different
Non-linear effects for cylindrical gravitational two-soliton
Tomizawa, Shinya
2015-01-01
Using a cylindrical soliton solution to the four-dimensional vacuum Einstein equation, we study non-linear effects of gravitational waves such as Faraday rotation and time shift phenomenon. In the previous work, we analyzed the single-soliton solution constructed by the Pomeransky's improved inverse scattering method. In this work, we construct a new two-soliton solution with complex conjugate poles, by which we can avoid light-cone singularities unavoidable in a single soliton case. In particular, we compute amplitudes of such non-linear gravitational waves and time-dependence of the polarizations. Furthermore, we consider the time shift phenomenon for soliton waves, which means that a wave packet can propagate at slower velocity than light.
Using inverse scattering methods to study inter-nucleus potentials
MacIntosh, R S
1998-01-01
It is now straightforward to carry out S-matrix to potential inversion over a very wide range of energies and for a wide range of projectile-target combinations. Inversion is possible in many cases involving spin. IP inversion also permits direct scattering data-to-potential inversion and furnishes powerful tools for the phenomenological analysis of nuclear scattering. The resulting single particle potentials exhibit various generic properties which challenge fundamental reaction theories as well as yield information on densities, provide input for reaction calculations. S-matrix to potential inversion is also a powerful tool for directly investigating theoretical processes which contribute to inter-nuclear potentials. Various studies have given insight into contributions to the dynamic polarisation potential (DPP) due to breakup processes and due to collective and reaction channel coupling and have also illuminated the role played by exchange processes in leading to non-locality and parity dependence of the ...
A direct sampling method for inverse electromagnetic medium scattering
Ito, Kazufumi
2013-09-01
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. It is applicable to a few incident fields and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence, it is strictly direct, computationally very efficient and highly robust to the presence of data noise. Two- and three-dimensional numerical experiments indicate that it can provide reliable support estimates for multiple scatterers in the case of both exact and highly noisy data. © 2013 IOP Publishing Ltd.
A direct sampling method to an inverse medium scattering problem
Ito, Kazufumi
2012-01-10
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when the measured data are only available for one or two incident directions. A mathematical derivation is provided for its validation. Two- and three-dimensional numerical simulations are presented, which show that the method is accurate even with a few sets of scattered field data, computationally efficient, and very robust with respect to noises in the data. © 2012 IOP Publishing Ltd.
Uniqueness in inverse elastic scattering with finitely many incident waves
Energy Technology Data Exchange (ETDEWEB)
Elschner, Johannes [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany); Yamamoto, Masahiro [Tokyo Univ. (Japan). Dept. of Mathematical Sciences
2009-07-01
We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation. (orig.)
A two-stage method for inverse medium scattering
Ito, Kazufumi
2013-03-01
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with nonsmooth mixed regularization. The first step is strictly direct and of sampling type, and it faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer size as well as intensities. The nonsmooth model can be efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the new approach is accurate, computationally efficient, and robust with respect to data noise. © 2012 Elsevier Inc.
Institute of Scientific and Technical Information of China (English)
LIU; Shaopu; HU; Xiaoli; LIU; Zhongfang
2006-01-01
The interaction between congo red (CR) and amikacin (AMK) was studied by resonance Rayleigh scattering (RRS), frequency doubling scattering (FDS) and second-order scattering (SOS) combining with absorption spectrum. In a weak acidic medium, CR combined with AMK to form an ion association complex with the composition ratio of 1∶1 by electrostatic interaction, hydrophobicity and charge transferring effect. As a result, the new spectra of RRS, FDS, and SOS appeared and their intensities were enhanced greatly. The maximum wavelengths of RRS, FDS and SOS were located at 563 nm, 475 nm and 940 nm, and the scattering intensities were proportional to the concentration of AMK. These three methods have very high sensitivities, and the detection limits were 4.0 ng·mL(1 for RRS, 3.6 ng·mL(1 for FDS and 1.9 ng·mL-1 for SOS, respectively. At the same time, the methods have better selectivity. A new method for the determination of trace amounts of AMK with congo red by resonance scattering technique has been developed. The recovery for the determination of AMK in blood serum and urine sample was between 95.5% and 105.5%. In this study, the properties, such as enthalpy of formation, charge distribution and mean polarizability, were calculated by AM1 quantum chemistry method. In addition, the reaction mechanism and the reasons for the enhancement of scattering spectra were discussed.
Inverse scattering from phaseless data in the freespace
Institute of Scientific and Technical Information of China (English)
ZHANG WenJi; LI LianLin; LI Fang
2009-01-01
In this paper a new approach for microwave imaging of unknown objects embedded in the freespace from phaseless data is presented. Firstly a cost functional is constructed by using the measured amplitude of the total field, which is the norm of the discrepancy between the measured amplitude and the calculated one. Then both the amplitude and phase of the scattered field are retrieved by minimizing the above cost functional. Finally, the geometrical and electrical parameters are reconstructed by using the retrieved scattered field. The phase retrieval process can be achieved in a very short time without adding any burden to the whole inverse scattering problem. The equivalent current density is introduced to reduce the nonlinearity of the inverse problem. The reconstruction of the non-radiating component of the equivalent current density improves the imaging quality. Experimental results are presented for the first time to show the feasibility of inverse scattering from phaseless data. The experimental results also show the validity and stability of the proposed method.
Kouri, Donald J; Vijay, Amrendra
2003-04-01
The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the frequency. By contrast, it is well known that the Born-Neumann series for the Volterra integral equations in quantum scattering are absolutely convergent, independent of the strength of the coupling characterizing the interaction. The transformation of the Lippmann-Schwinger equation from a Fredholm to a Volterra structure by renormalization has been considered previously for quantum scattering calculations and electromagnetic scattering. In this paper, we employ the renormalization technique to obtain a Volterra equation framework for the inverse acoustic scattering series, proving that this series also converges absolutely in the entire complex plane of coupling constant and frequency values. The present results are for acoustic scattering in one dimension, but the method is general. The approach is illustrated by applications to two simple one-dimensional models for acoustic scattering.
Stimulated Brillouin scattering enhancement in silicon inverse opal waveguides
Smith, M J A; de Sterke, C Martijn; Lapine, M; Kuhlmey, B T; Poulton, C G
2016-01-01
Silicon is an ideal material for on-chip applications, however its poor acoustic properties limit its performance for important optoacoustic applications, particularly for Stimulated Brillouin Scattering (SBS). We theoretically show that silicon inverse opals exhibit a strongly improved acoustic performance that enhances the bulk SBS gain coefficient by more than two orders of magnitude. We also design a waveguide that incorporates silicon inverse opals and which has SBS gain values that are comparable with chalcogenide glass waveguides. This research opens new directions for opto-acoustic applications in on-chip material systems.
Inverse Scattering and Locality in Integrable Quantum Field Theories
Alazzawi, Sabina
2016-01-01
We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix $S$ is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on $S$ that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the $O(N)$-invariant nonlinear $\\sigma$-models.
Inflationary Dynamics Reconstruction via Inverse-Scattering Theory
Mastache, Jorge; Kosowsky, Arthur
2016-01-01
The evolution of inflationary fluctuations can be recast as an inverse scattering problem. In this context, we employ the Gel'fand-Levitan method from inverse-scattering theory to reconstruct the evolution of both the inflaton field freeze-out horizon and the Hubble parameter during inflation. We demonstrate this reconstruction procedure numerically for a scenario of slow-roll inflation, as well as for a scenario which temporarily departs from slow-roll. The field freeze-out horizon is reconstructed from the accessible primordial scalar power spectrum alone, while the reconstruction of the Hubble parameter requires additional information from the tensor power spectrum. We briefly discuss the application of this technique to more realistic cases incorporating estimates of the primordial power spectra over limited ranges of scales and with specified uncertainties.
Scattering angle base filtering of the inversion gradients
Alkhalifah, Tariq Ali
2014-01-01
Full waveform inversion (FWI) requires a hierarchical approach based on the availability of low frequencies to maneuver the complex nonlinearity associated with the problem of velocity inversion. I develop a model gradient filter to help us access the parts of the gradient more suitable to combat this potential nonlinearity. The filter is based on representing the gradient in the time-lag normalized domain, in which low scattering angles of the gradient update are initially muted. The result are long-wavelength updates controlled by the ray component of the wavefield. In this case, even 10 Hz data can produce near zero wavelength updates suitable for a background correction of the model. Allowing smaller scattering angle to contribute provides higher resolution information to the model.
The possibilities of linearized inversion of internally scattered seismic data
Aldawood, Ali
2014-08-05
Least-square migration is an iterative linearized inversion scheme that tends to suppress the migration artifacts and enhance the spatial resolution of the migrated image. However, standard least-square migration, based on imaging single scattering energy, may not be able to enhance events that are mainly illuminated by internal multiples such as vertical and nearly vertical faults. To alleviate this problem, we propose a linearized inversion framework to migrate internally multiply scattered energy. We applied this least-square migration of internal multiples to image a vertical fault. Tests on synthetic data demonstrate the ability of the proposed method to resolve a vertical fault plane that is poorly resolved by least-square imaging using primaries only. We, also, demonstrate the robustness of the proposed scheme in the presence of white Gaussian random observational noise and in the case of imaging the fault plane using inaccurate migration velocities.
Relevance vector machine technique for the inverse scattering problem
Institute of Scientific and Technical Information of China (English)
Wang Fang-Fang; Zhang Ye-Rong
2012-01-01
A novel method based on the relevance vector machine(RVM)for the inverse scattering problem is presented in this paper.The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered.The nonlinearity is embodied in the relation between the scattered field and the target property,which can be obtained through the RVM training process.Besides,rather than utilizing regularization,the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output.Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy,convergence,robustness,generalization,and improved performance in terms of sparse property in comparison with the support vector machine(SVM)based approach.
Introduction to ground penetrating radar inverse scattering and data processing
Persico, Raffaele
2014-01-01
This book presents a comprehensive treatment of ground penetrating radar using both forward and inverse scattering mathematical techniques. Use of field data instead of laboratory data enables readers to envision real-life underground imaging; a full color insert further clarifies understanding. Along with considering the practical problem of achieving interpretable underground images, this book also features significant coverage of the problem's mathematical background. This twofold approach provides a resource that will appeal both to application oriented geologists and testing specialists,
Van Aert, S; Chen, J H; Van Dyck, D
2010-10-01
A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has
High resolution inverse scattering in two dimensions using recursive linearization
Borges, Carlos; Greengard, Leslie
2016-01-01
We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen's method of recursive linearization to reconstruct an unknown sound speed at resolutions of thousands of square wavelengths in a fully nonlinear regime. Despite the fact that the underlying optimization problem is formally ill-posed and non-convex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably band-limited approximation of the sound speed profile, each least squares calculation is well-conditioned and involves the solution of a large number of forward scattering problems, for which we employ a recently developed, spectrally accurate, fast direct solver. For the largest problems considered, involving 19,600 unknowns, approximately one million partial differential equations were ...
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, R.
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of {minus}100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k{sub p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
Efficient scattering angle filtering for Full waveform inversion
Alkhalifah, Tariq Ali
2015-08-19
Controlling the scattering angles between the state and the adjoint variables for the energy admitted into an inversion gradient or an image can help improve these functions for objectives in full waveform inversion (FWI) or seismic imaging. However, the access of the scattering angle information usually requires an axis extension that could be costly, especially in 3D. For the purpose of a scattering angle filter, I develop techniques that utilize the mapping nature (no domain extension) of the filter for constant-velocity background models to interpolate between such filtered gradients using the actual velocity. The concept has well known roots in the application of phase-shift-plus-interpolation utilized commonly in the downward continuation process. If the difference between the minimum and maximum velocity of the background medium is large, we obtain filtered gradients corresponding to more constant velocity backgrounds and use linear interpolation between such velocities. The accuracy of this approximation for the Marmousi model gradient demonstrates the e ectiveness of the approach.
Inverse scattering at fixed energy on asymptotically hyperbolic Liouville surfaces
Daudé, Thierry; Kamran, Niky; Nicoleau, Francois
2015-12-01
In this paper, we study an inverse scattering problem on Liouville surfaces having two asymptotically hyperbolic ends. The main property of Liouville surfaces consists of the complete separability of the Hamilton-Jacobi equations for the geodesic flow. An important related consequence is the fact that the stationary wave equation can be separated into a system of radial and angular ODEs. The full scattering matrix at fixed energy associated to a scalar wave equation on asymptotically hyperbolic Liouville surfaces can be thus simplified by considering its restrictions onto the generalized harmonics corresponding to the angular separated ODE. The resulting partial scattering matrices consists in a countable set of 2 × 2 matrices whose coefficients are the so called transmission and reflection coefficients. It is shown that the reflection coefficients are nothing but generalized Weyl-Titchmarsh (WT) functions for the radial ODE in which the generalized angular momentum is seen as the spectral parameter. Using the complex angular momentum method and recent results on 1D inverse problem from generalized WT functions, we show that the knowledge of the reflection operators at a fixed non-zero energy is enough to determine uniquely the metric of the asymptotically hyperbolic Liouville surface under consideration.
Pulsar high energy emission due to inverse Compton scattering
Energy Technology Data Exchange (ETDEWEB)
Lyutikov, Maxim
2013-06-15
We discuss growing evidence that pulsar high energy is emission is generated via Inverse Compton mechanism. We reproduce the broadband spectrum of Crab pulsar, from UV to very high energy gamma-rays - nearly ten decades in energy, within the framework of the cyclotron-self-Compton model. Emission is produced by two counter-streaming beams within the outer gaps, at distances above ∼ 20 NS radii. The outward moving beam produces UV-X-ray photons via Doppler-booster cyclotron emission, and GeV photons by Compton scattering the cyclotron photons produced by the inward going beam. The scattering occurs in the deep Klein-Nishina regime, whereby the IC component provides a direct measurement of particle distribution within the magnetosphere. The required plasma multiplicity is high, ∼10{sup 6} – 10{sup 7}, but is consistent with the average particle flux injected into the pulsar wind nebula.
Proton-proton hollowness at the LHC from inverse scattering
Arriola, Enrique Ruiz
2016-01-01
It is shown that the parametrizations of the NN scattering data at the LHC collision energies indicate a hollow in the inelasticity profile, with less absorption for head-on collisions than at a non-zero impact parameter. We show that some qualitatively unnoticed features may be unveiled by a judicious application of the inverse scattering problem in the eikonal approximation and within an optical potential model interpretation. The hollowness effect is magnified within a 3D picture of the optical potential, and will presumably be enhanced at higher energies. However, it sets in at much smaller energies than at the LHC. The hollowness feature of the experimental data precludes models, where inelasticity is obtained by folding of uncorrelated nucleon structures.
Non-linear dendrites can tune neurons
Directory of Open Access Journals (Sweden)
Romain Daniel Cazé
2014-03-01
Full Text Available A signature of visual, auditory, and motor cortices is the presence of neurons tuned to distinct features of the environment. While neuronal tuning can be observed in most brain areas, its origin remains enigmatic, and new calcium imaging data complicate this problem. Dendritic calcium signals, in a L2/3 neuron from the mouse visual cortex, display a wide range of tunings that could be different from the neuronal tuning (Jia et al 2010. To elucidate this observation we use multi-compartmental models of increasing complexity, from a binary to a realistic biophysical model of L2/3 neuron. These models possess non-linear dendritic subunits inside which the result of multiple excitatory inputs is smaller than their arithmetic sum. While dendritic non-linear subunits are ad-hoc in the binary model, non-linearities in the realistic model come from the passive saturation of synaptic currents. Because of these non-linearities our neuron models are scatter sensitive: the somatic membrane voltage is higher when presynaptic inputs target different dendrites than when they target a single dendrite. This spatial bias in synaptic integration is, in our models, the origin of neuronal tuning. Indeed, assemblies of presynaptic inputs encode the stimulus property through an increase in correlation or activity, and only the assembly that encodes the preferred stimulus targets different dendrites. Assemblies coding for the non-preferred stimuli target single dendrites, explaining the wide range of observed tunings and the possible difference between dendritic and somatic tuning. We thus propose, in accordance with the latest experimental observations, that non-linear integration in dendrites can generate neuronal tuning independently of the coding regime.
Quantum inverse scattering and the lambda deformed principal chiral model
Appadu, Calan; Hollowood, Timothy J.; Price, Dafydd
2017-07-01
The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current-current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard techniques of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an approach of Faddeev and Reshetikhin, we show that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz techniques. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.
Inverse geophysical and potential scattering on a small body
Energy Technology Data Exchange (ETDEWEB)
Katsevich, A.I.; Ramm, A.G.
1995-07-01
Simple and numerically stable approaches to approximate solution of inverse geophysical and potential scattering problems are described. The method we propose consists of two steps. Let {nu}(z) be the inhomogeneity (potential), and let D be its support, First, we find approximations to the zeroth moment (total intensity){integral}{sub D}{nu}(z)dz and the first moment (center of gravity) {integral}{sub D}z{nu}(z)/{integral}{sub D}{nu}(z)dz of the function {nu}(z). We call this step ``inhomogeneity localization``, because in many cases the center of gravity lies inside D or is located close to it. Second, we refine the above moments and find the tensor of the second central moments of {nu}(z). Using this information, we find an ellipsoid D and a real constant {nu}, such that the inhomogeneity (potential){nu}(z) = {nu}, z {epsilon} D, and {nu}(z) = 0, z {epsilon} D, fits best the scattering data and has the same zeroth, first, and second moments. We call this step ``approximate inversion``. The proposed method does not require any intensive computations, it is very simple to implement and it is relatively stable towards noise in the data.
Non-linear canonical correlation
van der Burg, Eeke; de Leeuw, Jan
1983-01-01
Non-linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An
DEFF Research Database (Denmark)
Andersen, Steffen; Harrison, Glenn W.; Hole, Arne Risa
2012-01-01
We develop an extension of the familiar linear mixed logit model to allow for the direct estimation of parametric non-linear functions defined over structural parameters. Classic applications include the estimation of coefficients of utility functions to characterize risk attitudes and discountin...
Electromagnetic Scattering and Inverse Scattering of Layered Media with a Slightly Rough Surface
Institute of Scientific and Technical Information of China (English)
LIN Zhi-Wei; XU Xin ZHANG Xiao-Juan; FANG Guang-You
2011-01-01
An electromagnetic (EM) scattering model for layered media covered by a 3D infinite rough surface and the corresponding inversion technique are investigated. The work aims at remote sensing the surface roughness and dielectric constant for different depths of bear soil through radar measurement data. The forward problem is carried out by the wave decomposition method. The small perturbation method (SPM) and EM boundary conditions are employed to solve the integral equations introduced by the wave decomposition method. The second-order SPM solution of the scattering field is involved in the computation of the forward problem for the first time. The backscattering coefficients of multiple frequencies, multiple angles and multiple polarizations are employed to create a nonlinear optimization problem. A genetic algorithm is introduced to help the inversion procedure approach to the global minimum of the cost function. Examples are carried out to validate the inversion technique. The inversion results show good agreement with the forward problem with given parameters and pose good tolerance to the input data with the additive white Gaussian noise.
Inverse Scattering Method and Soliton Solution Family for String Effective Action
Institute of Scientific and Technical Information of China (English)
GAO Ya-Jun
2009-01-01
A modified Hauser-Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and Kalb-Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained.
The Quantum Inverse Scattering Method for Hubbard-like Models
Martins, M J
1997-01-01
This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of the classical ``covering'' Hubbard model within the algebraic Bethe Ansatz framework. The fundamental commutation rules exhibit a hidden 6-vertex symmetry which plays a crucial role in the whole algebraic construction. Next we apply this formalism to study the SU(2) highest weights properties of the eigenvectors and the solution of a related coupled spin model with twisted boundary conditions. The machinery developed in this paper is applicable to many other models, and as an example we present the algebraic solution of the Bariev XY coupled model.
High duty cycle inverse Compton scattering X-ray source
Ovodenko, A.; Agustsson, R.; Babzien, M.; Campese, T.; Fedurin, M.; Murokh, A.; Pogorelsky, I.; Polyanskiy, M.; Rosenzweig, J.; Sakai, Y.; Shaftan, T.; Swinson, C.
2016-12-01
Inverse Compton Scattering (ICS) is an emerging compact X-ray source technology, where the small source size and high spectral brightness are of interest for multitude of applications. However, to satisfy the practical flux requirements, a high-repetition-rate ICS system needs to be developed. To this end, this paper reports the experimental demonstration of a high peak brightness ICS source operating in a burst mode at 40 MHz. A pulse train interaction has been achieved by recirculating a picosecond CO2 laser pulse inside an active optical cavity synchronized to the electron beam. The pulse train ICS performance has been characterized at 5- and 15- pulses per train and compared to a single pulse operation under the same operating conditions. With the observed near-linear X-ray photon yield gain due to recirculation, as well as noticeably higher operational reliability, the burst-mode ICS offers a great potential for practical scalability towards high duty cycles.
Symmetries in Non-Linear Mechanics
Aldaya, Victor; López-Ruiz, Francisco F; Cossío, Francisco
2014-01-01
In this paper we exploit the use of symmetries of a physical system so as to characterize the corresponding solution manifold by means of Noether invariants. This constitutes a necessary preliminary step towards the correct quantisation in non-linear cases, where the success of Canonical Quantisation is not guaranteed in general. To achieve this task "point symmetries" of the Lagrangian are generally not enough, and the notion of contact transformations is in order. The use of the Poincar\\'e-Cartan form permits finding both the symplectic structure on the solution manifold, through the Hamilton-Jacobi transformation, and the required symmetries, realized as Hamiltonian vector fields, associated with functions on the solution manifold (thus constituting an inverse of the Noether Theorem), lifted back to the evolution space through the inverse of this Hamilton-Jacobi mapping. In this framework, solutions and symmetries are somehow identified and this correspondence is also kept at a perturbative level. We prese...
Detection of inverse Compton scattering in plasma wakefield experiments
Energy Technology Data Exchange (ETDEWEB)
Bohlen, Simon
2016-12-15
Inverse Compton scattering (ICS) is the process of scattering of photons and electrons, where the photons gain a part of the electrons energy. In combination with plasma wakefield acceleration (PWA), ICS offers a compact MeV γ-ray source. A numerical study of ICS radiation produced in PWA experiments at FLASHForward was performed, using an ICS simulation code and the results from particle-in-cell modelling. The possibility of determining electron beam properties from measurements of the γ-ray source was explored for a wide range of experimental conditions. It was found that information about the electron divergence, the electron spectrum and longitudinal information can be obtained from measurements of the ICS beams for some cases. For the measurement of the ICS profile at FLASHForward, a CsI(Tl) scintillator array was chosen, similar to scintillators used in other ICS experiments. To find a suitable detector for spectrum measurements, an experimental test of a Compton spectrometer at the RAL was conducted. This test showed that a similar spectrometer could also be used at FLASHForward. However, changes to the spectrometer could be needed in order to use the pair production effect. In addition, further studies using Geant4 could lead to a better reconstruction of the obtained data. The studies presented here show that ICS is a promising method to analyse electron parameters from PWA experiments in further detail.
Inelastic Proton Scattering on 21Na in Inverse Kinematics
Austin, Roby
2009-10-01
R.A.E. Austin, R. Kanungo, S. Reeve, Saint Mary's University; D.G. Jenkins, C.Aa.Diget, A. Robinson, A.G. Tuff, O. Roberts, University of York, UK; P.J. Woods, T. Davinson, G. J. Lotay, University of Edinburgh; C.-Y. Wu, Lawrence Livermore National Laboratory; H. Al Falou, G.C. Ball, M. Djongolov, A. Garnsworthy, G. Hackman, J.N. Orce, C.J. Pearson, S. Triambak, S.J. Williams, TRIUMF; C. Andreiou, D.S. Cross, N. Galinski, R. Kshetri, Simon Fraser University; C. Sumithrarachchi, M.A. Schumaker, University of Guelph; M.P. Jones, S.V. Rigby, University of Liverpool; D. Cline, A. Hayes, University of Rochester; T.E. Drake, University of Toronto; We describe an experiment and associated technique [1] to measure resonances of interest in astrophysical reactions. At the TRIUMF ISAC-II radioactive beam accelerator facility in Canada, particles inelastically scattered in inverse kinematics are detected with Bambino, a δE-E silicon telescope spanning 15-40 degrees in the lab. We use the TIGRESS to detect gamma rays in coincidence with the charged particles to cleanly select inelastic scattering events. We measured resonances above the alpha threshold in ^22Mg of relevance to the rate of break-out from the hot-CNO cycle via the reaction ^ 18Ne(α,p)^21Na. [1] PJ Woods et al. Rex-ISOLDE proposal 424 Cern (2003).
Observation of redshifting and harmonic radiation in inverse Compton scattering
Sakai, Y.; Pogorelsky, I.; Williams, O.; O'Shea, F.; Barber, S.; Gadjev, I.; Duris, J.; Musumeci, P.; Fedurin, M.; Korostyshevsky, A.; Malone, B.; Swinson, C.; Stenby, G.; Kusche, K.; Babzien, M.; Montemagno, M.; Jacob, P.; Zhong, Z.; Polyanskiy, M.; Yakimenko, V.; Rosenzweig, J.
2015-06-01
Inverse Compton scattering of laser photons by ultrarelativistic electron beam provides polarized x- to γ -ray pulses due to the Doppler blueshifting. Nonlinear electrodynamics in the relativistically intense linearly polarized laser field changes the radiation kinetics established during the Compton interaction. These are due to the induced figure-8 motion, which introduces an overall redshift in the radiation spectrum, with the concomitant emission of higher order harmonics. To experimentally analyze the strong field physics associated with the nonlinear electron-laser interaction, clear modifications to the angular and wavelength distributions of x rays are observed. The relativistic photon wave field is provided by the ps CO2 laser of peak normalized vector potential of 0.5 laser [M. Babzien et al., Phys. Rev. Lett. 96, 054802 (2006)]. The angular spectral characteristics are revealed using K -, L -edge, and high energy attenuation filters. The observation indicates existence of the electrons' longitudinal motion through frequency redshifting understood as the mass shift effect. Thus, the 3rd harmonic radiation has been observed containing on-axis x-ray component that is directly associated with the induced figure-8 motion. These are further supported by an initial evidence of off-axis 2nd harmonic radiation produced in a circularly polarized laser wave field. Total x-ray photon number per pulse, scattered by 65 MeV electron beam of 0.3 nC, at the interaction point is measured to be approximately 109 .
DEFF Research Database (Denmark)
Du, Yigang
without iteration steps. The ASA is implemented in combination with Field II and extended to simulate the pulsed ultrasound fields. The simulated results from a linear array transducer are made by the ASA based on Field II, and by a released non-linear simulation program- Abersim, respectively....... The calculation speed of the ASA is increased approximately by a factor of 140. For the second harmonic point spread function the error of the full width is 1.5% at -6 dB and 6.4% at -12 dB compared to Abersim. To further investigate the linear and non-linear ultrasound fields, hydrophone measurements.......3% relative to the measurement from a 1 inch diameter transducer. A preliminary study for harmonic imaging using synthetic aperture sequential beamforming (SASB) has been demonstrated. A wire phantom underwater measurement is made by an experimental synthetic aperture real-time ultrasound scanner (SARUS...
Inverse scattering and GPR data processing: an Introduction
Persico, Raffaele
2014-05-01
Inverse scattering and GPR data processing: an Introduction Raffaele Persico This abstract is meant to propose a brief overview of the book "Introduction to Ground Penetrating Radar: Inverse scattering and data processing", edited by Wiley Press (ISBN 9781118305003). The reason why I propose this contribution is the fact that, in spite of the large relevant literature, to the best of my knowledge it is not very common to find a text entirely devoted to the physical-mathematical aspects (a part of them, of course) of GPR data processing. Also due to this, probably a sort of gap between the GPR practice and the underlying theory has been created, and indeed we can meet practitioners convinced that the quality of the achieved results is indefinitely improvable by making narrower the spatial step of the data, or that it is desirable to have extremely directive antennas because this would improve the resolution. In order to provide a work hopefully able to address these and other aspects and hopefully able to give a contribution to the correction of these imprecise beliefs, a dealing from the beginning has been proposed, i.e. a sequential, relatively plane, and as much as possible self consistent, dealing starting from the Maxwell's equations and reaching the most commonly exploited migration formulas and linear inversion algorithms, both within a 2D and a 3D framework. This follows the didactic aim to provide to the reader an insight about what can be reasonably achieved and what should be reasonably done in the field and during the processing phase in order to achieve satisfying results. In particular, the reader will be hopefully made aware not only of the mathematical passages, but also of the involved approximations, the needed assumptions and the physical limits of the final algorithms. The results have been also back-upped with numerical exercises and with some experimental tests, all of which conceived on purpose for this text, and some questions with the
Energy Technology Data Exchange (ETDEWEB)
Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
Bandoro, J.; Sica, R. J.; Argall, S.
2012-12-01
An important aspect of solar terrestrial relations is the coupling between the lower and upper atmosphere-ionosphere system. The coupling is evident in the general circulation of the atmosphere, where waves generate in the lower atmosphere play an important role in the dynamics of the upper atmosphere, which feeds back on the lower atmosphere's circulation. To address coupling problems requires measurements over the broadest range of heights possible. A recently developed retrieval method for temperature profiles from Rayleigh-scatter lidar measurements using an inversion approach allows the upward extension of the altitude range of temperature by 10 to 15 km over the conventional method, thus producing the equivalent of increasing the systems power-aperture product by 4 times [1]. The method requires no changes to the lidar's hardware and thus, can be applied to the body of existing measurements. In addition, since the uncertainties of the retrieved temperature profile are found by a Monte Carlo error analysis, it is possible to isolate systematic and random uncertainties to model the effect of each one on the final uncertainty product for the temperature profile. This unambiguous separation of uncertainties was not previously possible as only the propagation of the statistical uncertainties are typically reported. For the Purple Crow Lidar, corrections for saturation (e.g. non-linearity) in the photocount returns, ozone extinction and background removal all contribute to the overall systematic uncertainty. Results of individually varying each systematic correction and the effect on the final temperature uncertainty through Monte Carlo realizations are presented to determine the importance for each one. For example, it was found that treatment of the background correction as a systematic versus statistical uncertainty gave results in agreement with each other. This new method is then applied to measurements obtained by the Purple Crow lidar' Rayleigh-scatter
Internal gravity waves: Analysis using the periodic, inverse scattering transform
Directory of Open Access Journals (Sweden)
W. B. Zimmerman
1999-01-01
Full Text Available The discrete periodic inverse scattering transform (DPIST has been shown to provide the salient features of nonlinear Fourier analysis for surface shallow water waves whose dynamics are governed by the Korteweg-de Vries (KdV equation - (1 linear superposition of components with power spectra that are invariants of the motion of nonlinear dispersive waves and (2 nonlinear filtering. As it is well known that internal gravity waves also approximately satisfy the KdV equation in shallow stratified layers, this paper investigates the degree to which DPIST provides a useful nonlinear spectral analysis of internal waves by application to simulations and wave tank experiments of internal wave propagation from localized dense disturbances. It is found that DPIST analysis is sensitive to the quantity λ = (r/6s * (ε/μ2, where the first factor depends parametrically on the Richardson number and the background shear and density profiles and the second factor is the Ursell number-the ratio of the dimensionless wave amplitude to the dimensionless squared wavenumber. Each separate wave component of the decomposition of the initial disturbance can have a different value, and thus there is usually just one component which is an invariant of the motion found by DPIST analysis. However, as the physical applications, e.g. accidental toxic gas releases, are usually concerned with the propagation of the longest wavenumber disturbance, this is still useful information. In cases where only long, monochromatic solitary waves are triggered or selected by the waveguide, the entire DPIST spectral analysis is useful.
Non-linear Imaging using an Experimental Synthetic Aperture Real Time Ultrasound Scanner
DEFF Research Database (Denmark)
Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt
2011-01-01
This paper presents the first non-linear B-mode image of a wire phantom using pulse inversion attained via an experimental synthetic aperture real-time ultrasound scanner (SARUS). The purpose of this study is to implement and validate non-linear imaging on SARUS for the further development of new...... non-linear techniques. This study presents non-linear and linear B-mode images attained via SARUS and an existing ultrasound system as well as a Field II simulation. The non-linear image shows an improved spatial resolution and lower full width half max and -20 dB resolution values compared to linear...
de Jong, Roelof
2005-07-01
This program incorporates a number of tests to analyse the count rate dependent non-linearity seen in NICMOS spectro-photometric observations. In visit 1 we will observe a few fields with stars of a range in luminosity in NGC1850 with NICMOS in NIC1 in F090M, F110W and F160W and NIC2 F110W, F160W, and F180W. We will repeat the observations with flatfield lamp on, creating artificially high count-rates, allowing tests of NICMOS linearity as function of count rate. To access the effect of charge trapping and persistence, we first take darks {so there is not too much charge already trapped}, than take exposures with the lamp off, exposures with the lamp on, and repeat at the end with lamp off. Finally, we continue with taking darks during occultation. In visit 2 we will observe spectro-photometric standard P041C using the G096 and G141 grisms in NIC3, and repeat the lamp off/on/off test to artificially create a high background. In visits 3&4 we repeat photometry measurements of faint standard stars SNAP-2 and WD1657+343, on which the NICMOS non-linearity was originally discovered using grism observations. These measurements are repeated, because previous photometry was obtained with too short exposure times, hence substantially affected by charge trapping non-linearity. Measurements will be made with NIC1: Visit 5 forms the persistence test of the program. The bright star GL-390 {used in a previous persistence test} will iluminate the 3 NICMOS detectors in turn for a fixed time, saturating the center many times, after which a series of darks will be taken to measure the persistence {i.e. trapped electrons and the decay time of the traps}. To determine the wavelength dependence of the trap chance, exposures of the bright star in different filters will be taken, as well as one in the G096 grism with NIC3. Most exposures will be 128s long, but two exposures in the 3rd orbit will be 3x longer, to seperate the effects of count rate versus total counts of the trap
The algebraic method of the scattering inverse problem solution under untraditional statements
Popushnoj, M N
2001-01-01
The algebraic method of the scattering inverse problem solution under untraditional statements is proposed consistently in this review, in the framework of which some quantum theory od scattering charged particles problem were researched afterwards. The inverse problem of scattering theory of charged particles on the complex plane of the Coulomb coupling constant (CCC) is considered. A procedure of interaction potential restoration is established for the case when the energy, orbital moment quadrate and CCC are linearly dependent. The relation between one-parametric problems of the potential scattering of charged particles is investigated
Seismic inverse scattering in the downward continuation approach
Stolk, C.C.; Hoop, de M.V.
2006-01-01
Seismic data are commonly modeled by a linearization around a smooth background medium in combination with a high frequency approximation. The perturbation of the medium coefficient is assumed to contain the discontinuities. This leads to two inverse problems, first the linearized inverse problem fo
Constraint on Parameters of Inverse Compton Scattering Model for PSR B2319+60
Indian Academy of Sciences (India)
H. G. Wang; M. Lv
2011-03-01
Using the multifrequency radio profiles of pulsar PSR B2319+60, two parameters of inverse Compton scattering model, the initial Lorentz factor and the factor of energy loss of relativistic particles are constrained.
2010-02-28
illuminations. Inverse medium problems are encountered in acoustic, elastic, and electromagnetic wave propagation. We use a Lippmann- Schwinger formulation...Na. (5) This is a Born-approximation Lippmann- Schwinger scattering equation, where G(-, •;u) is the Green’s function (in the reference medium
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
Energy Technology Data Exchange (ETDEWEB)
Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)
2014-10-15
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.
Directory of Open Access Journals (Sweden)
Abel Palafox
2014-01-01
Full Text Available We address a prototype inverse scattering problem in the interface of applied mathematics, statistics, and scientific computing. We pose the acoustic inverse scattering problem in a Bayesian inference perspective and simulate from the posterior distribution using MCMC. The PDE forward map is implemented using high performance computing methods. We implement a standard Bayesian model selection method to estimate an effective number of Fourier coefficients that may be retrieved from noisy data within a standard formulation.
Review of the inverse scattering problem at fixed energy in quantum mechanics
Sabatier, P. C.
1972-01-01
Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.
Controlling ultrafast currents by the non-linear photogalvanic effect
Wachter, Georg; Lemell, Christoph; Tong, Xiao-Min; Yabana, Kazuhiro; Burgdörfer, Joachim
2015-01-01
We theoretically investigate the effect of broken inversion symmetry on the generation and control of ultrafast currents in a transparent dielectric (SiO2) by strong femto-second optical laser pulses. Ab-initio simulations based on time-dependent density functional theory predict ultrafast DC currents that can be viewed as a non-linear photogalvanic effect. Most surprisingly, the direction of the current undergoes a sudden reversal above a critical threshold value of laser intensity I_c ~ 3.8*10^13 W/cm2. We trace this switching to the transition from non-linear polarization currents to the tunneling excitation regime. We demonstrate control of the ultrafast currents by the time delay between two laser pulses. We find the ultrafast current control by the non-linear photogalvanic effect to be remarkably robust and insensitive to laser-pulse shape and carrier-envelope phase.
Kouri, Donald J.; Vijay, Amrendra; Zhang, Haiyan; Zhang, Jingfeng; Hoffman, David K.
2007-05-01
A method and system for solving the inverse acoustic scattering problem using an iterative approach with consideration of half-off-shell transition matrix elements (near-field) information, where the Volterra inverse series correctly predicts the first two moments of the interaction, while the Fredholm inverse series is correct only for the first moment and that the Volterra approach provides a method for exactly obtaining interactions which can be written as a sum of delta functions.
Estimating the location of a tunnel using correlation and inversion of Rayleigh wave scattering
Kasililar, A.; Harmankaya, U.; Wapenaar, C.P.A.; Draganov, D.S.
2013-01-01
The investigation of near-surface scatterers, such as cavities, tunnels, abandoned mine shafts, and buried objects, is important to mitigate geohazards and environmental hazards. By inversion of travel times of cross-correlated scattered waves, due to the incident Rayleigh waves, we estimate the loc
An Improved Hybrid Method for Inverse Obstacle Scattering Problems
Institute of Scientific and Technical Information of China (English)
LIU JUAN; MA FU-MING
2011-01-01
An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer.The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method,and it improves the hybrid method by introducing a general boundary condition.The numerical experiments show the feasibility of this method.
High-Power Laser Pulse Recirculation for Inverse Compton Scattering-Produced Gamma-Rays
Energy Technology Data Exchange (ETDEWEB)
Jovanovic, I; Shverdin, M; Gibson, D; Brown, C
2007-04-17
Inverse Compton scattering of high-power laser pulses on relativistic electron bunches represents an attractive method for high-brightness, quasi-monoenergetic {gamma}-ray production. The efficiency of {gamma}-ray generation via inverse Compton scattering is severely constrained by the small Thomson scattering cross section. Furthermore, repetition rates of high-energy short-pulse lasers are poorly matched with those available from electron accelerators, resulting in low repetition rates for generated {gamma}-rays. Laser recirculation has been proposed as a method to address those limitations, but has been limited to only small pulse energies and peak powers. Here we propose and experimentally demonstrate an alternative method for laser pulse recirculation that is uniquely capable of recirculating short pulses with energies exceeding 1 J. Inverse Compton scattering of recirculated Joule-level laser pulses has a potential to produce unprecedented peak and average {gamma}-ray brightness in the next generation of sources.
Cooper, S G; MacKintosh, R S; Pomerantsev, V N
2000-01-01
A practical S-matrix to potential inversion procedure which applies to coupled-channel scattering is presented. The inversion technique is described in the context of the problem of determining a tensor interaction T sub R which exactly reproduces non-diagonal S sup J sub l sub l sub ' for spin one projectiles. It also applies to spin-((1)/(2)) plus spin-((1)/(2)) scattering. The method is a generalization of the iterative-perturbative, IP, method. In this paper, spin-1 IP inversion is tested and evaluated and the variation of the potential is investigated for cases where there is insufficient information to define the potential uniquely. Since T sub P interactions must be presumed to be present in many applications, we examine the potentials which result when the S-matrix is generated from a T sub P interaction. The spin-1 IP algorithm can be incorporated within a direct observable-to-potential inversion procedure to provide an efficient alternative to standard phenomenology. We evaluate its application to f...
Nuclear applications of inverse scattering, present ... and future?
MacKintosh, R S
2005-01-01
There now exists a practical method (IP) for the routine inversion of $S$-matrix elements to produce the corresponding potential. It can be applied to spin-1/2 and spin-1 projectiles. We survey the ways that IP inversion can be applied in nuclear physics by inverting $S_{lj}$ derived from theory or from experiment. The IP inversion method can be extended to invert $S_{lj}(E)$ over a range of energies to produce a potential $V(r,E) + \\vect{l}\\vdot\\gvect{\\sigma} V_{\\rm ls}(r,E)$. It also yields parity-dependent potentials between pairs of light nuclei and can be convoluted with a direct search on the $S$-matrix to produce `direct data $\\to V$ inversion'. The last is an economical alternative form of optical model search to fit many observables (e.g. for polarized deuterons) for many energies, producing an energy-dependent potential with many parameters (e.g. $T_{\\rm R}$ for deuterons).
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
Institute of Scientific and Technical Information of China (English)
LI Chaokui; ZHU Qing; SONG Chengfang
2003-01-01
This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a nonlinear model. On the basis of the error definition, this paper puts forward a new adjustment criterion, SGPE.Last, this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
INVERSE CORRECTION OF FOURIER TRANSFORMS FOR ONE-DIMENSIONAL STRONGLY SCATTERING APERIODIC LATTICES
Directory of Open Access Journals (Sweden)
Y. F. Hsin
2016-05-01
Full Text Available The accuracy of the Fourier transform (FT, advantageous for the aperiodic lattice (AL design, is significantly improved for strongly scattering periodic lattices (PLs and ALs. The approach is to inversely obtain corrected parameters from an accurate transfer matrix method for the FT. We establish a corrected FT in order to improve the spectral inaccuracy of strongly scattering PLs by redefining wave numbers and reflective intensity. We further correct the FT for strongly scattering ALs by implementing improvements applied to strongly scattering PLs and then making detailed wave number adjustments in the main band spectral region. Silicon lattice simulations are presented.
Li, Xu; Chen, Zhigang; Gong, Jianmin; Taflove, Allen; Backman, Vadim
2004-06-01
Understanding light scattering by nonspherical particles is crucial in modeling the transport of light in realistic structures such as biological tissues. We report the application of novel analytical approaches based on modified Wentzel-Kramers-Brillouin and equiphase-sphere methods that facilitate accurate characterization of light scattering by a wide range of irregularly shaped dielectric particles. We also demonstrate that these approaches have the potential to address the inverse-scattering problem by means of a spectral analysis of the total scattering cross section of arbitrarily shaped particles.
Institute of Scientific and Technical Information of China (English)
代荣获; 张繁昌; 刘汉卿; 李灿灿
2014-01-01
Conventional three-term AVA inversion methods are based on the assumption thatγ (the ratio of S-wave velocity to P-wave velocity)is a constant value usually considered to be 0.5,whileγ is horizontally and vertically varied gradually in many cases.The estimated parameters of the inversion is bound to deviate from its true values with γ invariably being 0.5.and the selection γ needs to be reasonably.Based on Bayesian theory,we presents a nonlinear pre-stack seismic AVA inversion using successive iterative method,which considered the ratio’s initial background varying horizontally and vertically and being calculated by the-given initial model,and the nonlinear inversion problem was solved by successive iteration.The proposed method gived a reasonable solution for the selection of γ and solved the nonlinear problem caused by variable ratioγ.And the accuracy and stability of the three-term AVA inversion were improved.%常规 AVA 三参数反演方法均基于横波速度与纵波速度之比γ为常数这一假设条件,且常被近似地取为0.5。然而在许多情况下γ并不为常数,而是在横向与纵向都渐变。若一概假定γ等于0.5,反演出的岩性参数势必要偏离真实值,因此有必要合理地选择γ。笔者基于贝叶斯理论,提出逐次迭代非线性AVA 的反演方法。该方法把γ看成横向与纵向都渐变的反演初始背景,通过给定初始模型计算初始背景γ,并采用逐次迭代的策略求解该反演问题,解决了关于γ的选取问题以及由于引入变γ值而带来的非线性问题,提高了 AVA 三参数反演结果的精确度。
Advancing x-ray scattering metrology using inverse genetic algorithms
Hannon, Adam F.; Sunday, Daniel F.; Windover, Donald; Joseph Kline, R.
2016-07-01
We compare the speed and effectiveness of two genetic optimization algorithms to the results of statistical sampling via a Markov chain Monte Carlo algorithm to find which is the most robust method for determining real-space structure in periodic gratings measured using critical dimension small-angle x-ray scattering. Both a covariance matrix adaptation evolutionary strategy and differential evolution algorithm are implemented and compared using various objective functions. The algorithms and objective functions are used to minimize differences between diffraction simulations and measured diffraction data. These simulations are parameterized with an electron density model known to roughly correspond to the real-space structure of our nanogratings. The study shows that for x-ray scattering data, the covariance matrix adaptation coupled with a mean-absolute error log objective function is the most efficient combination of algorithm and goodness of fit criterion for finding structures with little foreknowledge about the underlying fine scale structure features of the nanograting.
Lemes, N. H. T.; Borges, E.; Sousa, R. V.; Braga, J. P.
Important physical and chemical information can be extracted from scattering experiments data. This kind of problem is usually ill-posed in the sense that one of the three conditions, existence, uniqueness, and continuity, is not satisfied. For example, the inversion of intermolecular potential functions from scattering data, such as experimental cross section, is an ill-posed problem which can be modeled as a Fredholm integral equation. In this work, an inversion method based on recursive neural networks is proposed to solve this inverse quantum scattering problem within the Born approximation. As physical example, the repulsive component of the potential function for the interaction Ar-Ar is obtained from differential cross-section data. The sensitivity of the potential energy function to be inverted, in relation to the differential cross-section data, is also analyzed. The present approach is simple, general, and numerically stable.
Adaptive eigenspace method for inverse scattering problems in the frequency domain
Grote, Marcus J.; Kray, Marie; Nahum, Uri
2017-02-01
A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.
On t-local solvability of inverse scattering problems in two-dimensional layered media
Baev, A. V.
2015-06-01
The solvability of two-dimensional inverse scattering problems for the Klein-Gordon equation and the Dirac system in a time-local formulation is analyzed in the framework of the Galerkin method. A necessary and sufficient condition for the unique solvability of these problems is obtained in the form of an energy conservation law. It is shown that the inverse problems are solvable only in the class of potentials for which the stationary Navier-Stokes equation is solvable.
Uniqueness and local stability for the inverse scattering problem of determining the cavity
Institute of Scientific and Technical Information of China (English)
FENG; Lixin; MA; Fuming
2005-01-01
Considering a time-harmonic electromagnetic plane wave incident on an arbitrarily shaped open cavity embedded in infinite ground plane, the physical process is modelled by Maxwell's equations. We investigate the inverse problem of determining the shape of the open cavity from the information of the measured scattered field. Results on the uniqueness and the local stability of the inverse problem in the 2-dimensional TM (transverse magnetic) polarization are proved in this paper.
Solution of an inverse scattering problem for the acoustic wave equation in three-dimensional media
Baev, A. V.
2016-12-01
A three-dimensional inverse scattering problem for the acoustic wave equation is studied. The task is to determine the density and acoustic impedance of a medium. A necessary and sufficient condition for the unique solvability of this problem is established in the form of an energy conservation law. The interpretation of the solution to the inverse problem and the construction of medium images are discussed.
Nucleon-alpha particle interactions from inversion of scattering phase shifts
Energy Technology Data Exchange (ETDEWEB)
Alexander, N.; Amos, K.; Apagyi, B.; Lun, D.R.
1996-03-01
Scattering amplitudes have been extracted from (elastic scattering) neutron-alpha (n-{alpha}) differential cross sections below threshold using the constraint that the scattering function is unitary. Real phase shifts have been obtained therefrom. A modification to the Newton iteration method has been used to solve the nonlinear equation that specifies the phase of the scattering amplitude in terms of the complete (0 to 180 deg) cross section since the condition for a unique and convergent solution by an exact iterated fixed point method, the `Martin` condition, is not satisfied. The results compare well with those found using standard optical model search procedures. Those optical model phase shifts, from both n - {alpha} and p - {alpha} (proton-alpha) calculations in which spin-orbit effects were included, were used in the second phase of this study, namely to determine the scattering potentials by inversion of that phase shift data. A modified Newton-Sabatier scheme to solve the inverse scattering problem has been used to obtain inversion potentials (both central and spin-orbit) for nucleon energies in the range 1 to 24 MeV. The inversion interactions differ noticeably from the Woods-Saxon forms used to give the input phase shifts. Not only do those inversion potentials when used in Schroedinger equations reproduce the starting phase shifts but they are also very smooth, decay rapidly, and are as feasible as the optical model potentials of others to be the local form for interactions deduced by folding realistic two-nucleon g matrices with the density matrix elements of the alpha particle. 23 refs., 8 tabs., 9 figs.
ON SOURCE ANALYSIS BY WAVE SPLITTING WITH APPLICATIONS IN INVERSE SCATTERING OF MULTIPLE OBSTACLES
Institute of Scientific and Technical Information of China (English)
Fahmi ben Hassen; Jijun Liu; Roland Potthast
2007-01-01
We study wave splitting procedures for acoustic or electromagnetic scattering problems. The idea of these procedures is to split some scattered field into a sum of fields coming from different spatial regions such that this information can be used either for inversion algorithms or for active noise control. Splitting algorithms can be based on general boundary layer potential representation or Green's representation formula. We will prove the unique decomposition of scattered wave outside the specified reference domain G and the unique decomposition of far-field pattern with respect to different reference domain G. Further, we employ the splitting technique for field reconstruction for a scatterer with two or more separate components, by combining it with the point source method for wave recovery. Using the decomposition of scattered wave as well as its far-field pattern, the wave splitting procedure proposed in this paper gives an efficient way to the computation of scattered wave near the obstacle, from which the multiple obstacles which cause the far-field pattern can be reconstructed separately. This considerably extends the range of the decomposition methods in the area of inverse scattering. Finally, we will provide numerical examples to demonstrate the feasibility of the splitting method.
Hardening of Thermal Photons Through Inverse Compton Scattering in Strong Magnetic Fields
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new spectrum function is obtained by use of the Compton scattering cross section in the laboratory frame derived earlier. This spectrum function, besides some modifications in the coefficients of the resonant term, contains also a non-resonant term which is inversely proportional to the square of the magnetic field. Based on this spectrum function, the hardening of thermal photons through inverse Compton scattering by relativistic electron beams on the surface of a strongly magnetized neutron star is investigated. Two new features are found. First, there is a maximum scattered photon energy for a given resonant scattering, beyond which resonance disappears. This maximum depends on the electron energy and the magnetic field, but is independent of the incident photon energy. Second, beyond each resonant scattering, there is a high-energy tail, resulting from non-resonant scattering. It is also found that all the tails have a common upper limit which is the highest scattered photon energy for the given incident photon and electron energies. These two new features are absent in the Monte Carlo simulations and therefore, may have physical implications for γγ-ray emissions.
Solution of a multiple-scattering inverse problem: electron diffraction from surfaces.
Saldin, D K; Seubert, A; Heinz, K
2002-03-18
We present a solution to the multiple-scattering inverse problem for low-energy electron diffraction that enables the determination of the three-dimensional atomic structure of an entire surface unit cell directly from measured data. The solution requires a knowledge of the structure of the underlying bulk crystal and is implemented by a maximum entropy algorithm.
von Schmid, M.; Bagchi, S.; Bonig, S.; Csatlos, M.; Dillmann, I.; Dimopoulou, C.; Egelhof, P.; Eremin, V.; Furuno, T.; Geissel, H.; Gernhaeuser, R.; Harakeh, M. N.; Hartig, A-L; Ilieva, S.; Kalantar-Nayestanaki, N.; Kiselev, O.; Kollmus, H.; Kozhuharov, C.; Krasznahorkay, A.; Kroell, T.; Kuilman, M.; Litvinov, S.; Litvinov, Yu A.; Mahjour-Shafiei, M.; Mutterer, M.; Nagae, D.; Najafi, M. A.; Nociforo, C.; Nolden, F.; Popp, U.; Rigollet, C.; Roy, S.; Scheidenberger, C.; Steck, M.; Streicher, B.; Stuhl, L.; Thuerauf, M.; Uesaka, T.; Weick, H.; Winfield, J. S.; Winters, D.; Woods, P. J.; Yamaguchi, T.; Yue, K.; Zamora, J. C.; Zenihiro, J.
2015-01-01
We have measured the nuclear-matter distribution of the doubly-magic N = Z nucleus Ni-56 by investigating elastic proton scattering in inverse kinematics. The radioactive beam of Ni-56 was injected and stored in the experimental storage ring (ESR, GSI) and interacted with an internal hydrogen gas-je
Narrowband inverse Compton scattering x-ray sources at high laser intensities
Seipt, D; Surzhykov, A; Fritzsche, S
2014-01-01
Narrowband x- and gamma-ray sources based on the inverse Compton scattering of laser pulses suffer from a limitation of the allowed laser intensity due to the onset of nonlinear effects that increase their bandwidth. It has been suggested that laser pulses with a suitable frequency modulation could compensate this ponderomotive broadening and reduce the bandwidth of the spectral lines, which would allow to operate narrowband Compton sources in the high-intensity regime. In this paper we, therefore, present the theory of nonlinear Compton scattering in a frequency modulated intense laser pulse. We systematically derive the optimal frequency modulation of the laser pulse from the scattering matrix element of nonlinear Compton scattering, taking into account the electron spin and recoil. We show that, for some particular scattering angle, an optimized frequency modulation completely cancels the ponderomotive broadening for all harmonics of the backscattered light. We also explore how sensitive this compensation ...
Forward and inverse models of electromagnetic scattering from layered media with rough interfaces
Tabatabaeenejad, Seyed Alireza
This work addresses the problem of electromagnetic scattering from layered dielectric structures with rough boundaries and the associated inverse problem of retrieving the subsurface parameters of the structure using the scattered field. To this end, a forward scattering model based on the Small Perturbation Method (SPM) is developed to calculate the first-order spectral-domain bistatic scattering coefficients of a two-layer rough surface structure. SPM requires the boundaries to be slightly rough compared to the wavelength, but to understand the range of applicability of this method in scattering from two-layer rough surfaces, its region of validity is investigated by comparing its output with that of a first principle solver that does not impose roughness restrictions. The Method of Moments (MoM) is used for this purpose. Finally, for retrieval of the model parameters of the layered structure using scattered field, an inversion scheme based on the Simulated Annealing method is investigated and a strategy is proposed to address convergence to local minimum.
Simulated scatter performance of an inverse-geometry dedicated breast CT system.
Bhagtani, Reema; Schmidt, Taly Gilat
2009-03-01
The purpose of this work was to quantify the effects of scatter for inverse-geometry dedicated breast CT compared to cone-beam breast CT through simulations. The inverse geometry was previously proposed as an alternative to cone-beam acquisition for volumetric CT. The inverse geometry consists of a large-area scanned-source opposite a detector array that is smaller in the transverse direction. While the gantry rotates, the x-ray beam is rapidly sequenced through an array of positions, acquiring a truncated projection image at each position. Inverse-geometry CT (IGCT) is expected to detect less scatter than cone-beam methods because only a fraction of the object is irradiated at any time and the fast detector isolates the measurements from sequential x-ray beams. An additional scatter benefit is the increased air gap due to the inverted geometry. In this study, we modeled inverse-geometry and cone-beam dedicated breast CT systems of equivalent resolution, field of view, and photon fluence. Monte Carlo simulations generated scatter and primary projections of three cylindrical phantoms of diameters 10, 14, and 18 cm composed of 50% adipose/50% glandular tissue. The scatter-to-primary ratio (SPR) was calculated for each breast diameter. Monte Carlo simulations were combined with analytical simulations to generate inverse-geometry and cone-beam images of breast phantoms embedded with tumors. Noise reprehenting the photon fluence of a realistic breast CT scan was added to the simulated projections. Cone-beam data were reconstructed with and without an ideal scatter correction. The CNR between breast tumor and background was compared for the inverse and cone-beam geometries for the three phantom diameters. Results demonstrated an order of magnitude reduction in SPR for the IGCT system compared to the cone-beam system. For example, the peak IGCT SPRs were 0.05 and 0.09 for the 14 and 18 cm phantoms, respectively, compared to 0.42 and 1 for the cone-beam system. For both
Non-Linear Relativity in Position Space
Kimberly, D; Medeiros-Neto, J F; Kimberly, Dagny; Magueijo, João; Medeiros, João
2003-01-01
We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear definition for the invariant contraction between momentum and position spaces. The second approach, instead, respects the linearity of the invariant contraction. This fully fixes the dual of momentum space and dictates a set of energy-dependent space-time Lorentz transformations. We discuss a variety of physical implications that would distinguish these two strategies. We also show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Non-linear (loop) quantum cosmology
Bojowald, Martin; Dantas, Christine C; Jaffe, Matthew; Simpson, David
2012-01-01
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.
Compressive inverse scattering: I. High-frequency SIMO/MISO and MIMO measurements
Fannjiang, Albert C.
2010-03-01
Inverse scattering from discrete targets with the single-input-multiple-output (SIMO), multiple-input-single-output (MISO) or multiple-input-multiple-output (MIMO) measurements is analyzed by compressed sensing theory with and without the Born approximation. High-frequency analysis of (probabilistic) recoverability by the L1-based minimization/regularization principles is presented. In the absence of noise, it is shown that the L1-based solution can recover exactly the target of sparsity up to the dimension of the data either with the MIMO measurement for the Born scattering or with the SIMO/MISO measurement for the exact scattering. The stability with respect to noisy data is proved for weak or widely separated scatterers. Reciprocity between the SIMO and MISO measurements is analyzed. Finally a coherence bound (and the resulting recoverability) is proved for diffraction tomography with high-frequency, few-view and limited-angle SIMO/MISO measurements.
Surface and Atmospheric Parameter Retrieval From AVIRIS Data: The Importance of Non-Linear Effects
Green Robert O.; Moreno, Jose F.
1996-01-01
AVIRIS data represent a new and important approach for the retrieval of atmospheric and surface parameters from optical remote sensing data. Not only as a test for future space systems, but also as an operational airborne remote sensing system, the development of algorithms to retrieve information from AVIRIS data is an important step to these new approaches and capabilities. Many things have been learned since AVIRIS became operational, and the successive technical improvements in the hardware and the more sophisticated calibration techniques employed have increased the quality of the data to the point of almost meeting optimum user requirements. However, the potential capabilities of imaging spectrometry over the standard multispectral techniques have still not been fully demonstrated. Reasons for this are the technical difficulties in handling the data, the critical aspect of calibration for advanced retrieval methods, and the lack of proper models with which to invert the measured AVIRIS radiances in all the spectral channels. To achieve the potential of imaging spectrometry, these issues must be addressed. In this paper, an algorithm to retrieve information about both atmospheric and surface parameters from AVIRIS data, by using model inversion techniques, is described. Emphasis is put on the derivation of the model itself as well as proper inversion techniques, robust to noise in the data and an inadequate ability of the model to describe natural variability in the data. The problem of non-linear effects is addressed, as it has been demonstrated to be a major source of error in the numerical values retrieved by more simple, linear-based approaches. Non-linear effects are especially critical for the retrieval of surface parameters where both scattering and absorption effects are coupled, as well as in the cases of significant multiple-scattering contributions. However, sophisticated modeling approaches can handle such non-linear effects, which are especially
Short- and long-term variations in non-linear dynamics of heart rate variability
DEFF Research Database (Denmark)
Kanters, J K; Højgaard, M V; Agner, E;
1996-01-01
OBJECTIVES: The purpose of the study was to investigate the short- and long-term variations in the non-linear dynamics of heart rate variability, and to determine the relationships between conventional time and frequency domain methods and the newer non-linear methods of characterizing heart rate...... variability. METHODS: Twelve healthy subjects were investigated by 3-h ambulatory ECG recordings repeated on 3 separate days. Correlation dimension, non-linear predictability, mean heart rate, and heart rate variability in the time and frequency domains were measured and compared with the results from...... corresponding surrogate time series. RESULTS: A small significant amount of non-linear dynamics exists in heart rate variability. Correlation dimensions and non-linear predictability are relatively specific parameters for each individual examined. The correlation dimension is inversely correlated to the heart...
An approximate factorization method for inverse medium scattering with unknown buried objects
Qu, Fenglong; Yang, Jiaqing; Zhang, Bo
2017-03-01
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous medium with different kinds of unknown buried objects inside. By constructing a sequence of operators which are small perturbations of the far-field operator in a suitable way, we prove that each operator in this sequence has a factorization satisfying the Range Identity. We then develop an approximate factorization method for recovering the support of the inhomogeneous medium from the far-field data. Finally, numerical examples are provided to illustrate the practicability of the inversion algorithm.
Influence on Atomic Inversion Evolution in Medium System from Compton Scattering
Institute of Scientific and Technical Information of China (English)
HAO Xiao-fei; HAO Dong-shan
2008-01-01
In Jaynes-Cummings model, by using the modulation of the coupling coefficient formed by the atom, medium and scattering optical, atomic inversion evolution of arbitrary forms has been worked out. Its feasibility has been proved, and the curvature of the atomic inversion evolution of the arbitrary forms is obtained. It announces that the atom and coupling medium system are to express the operators of the atom and optical field quantum in Jaynes-Cummings model. These operators can express arbitrary medium system. In these systems, the coupling coefficient can be changed and exactly controlled in the longer coherent times.
Non-linear Bayesian update of PCE coefficients
Litvinenko, Alexander
2014-01-06
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).
Buried Object Detection by an Inexact Newton Method Applied to Nonlinear Inverse Scattering
Directory of Open Access Journals (Sweden)
Matteo Pastorino
2012-01-01
Full Text Available An approach to reconstruct buried objects is proposed. It is based on the integral equations of the electromagnetic inverse scattering problem, written in terms of the Green’s function for half-space geometries. The full nonlinearity of the problem is exploited in order to inspect strong scatterers. After discretization of the continuous model, the resulting equations are solved in a regularization sense by means of a two-step inexact Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations.
Structured x-ray beams from twisted electrons by inverse Compton scattering of laser light
Seipt, D; Fritzsche, S
2014-01-01
The inverse Compton scattering of laser light on high-energetic twisted electrons is investigated with the aim to construct spatially structured x-ray beams. In particular, we analyze how the properties of the twisted electrons, such as the topological charge and aperture angle of the electron Bessel beam, affects the energy and angular distribution of scattered x-rays. We show that with suitably chosen initial twisted electron states one can synthesize tailor-made x-ray beam profiles with a well-defined spatial structure, in a way not possible with ordinary plane-wave electron beams.
Non linear system become linear system
Directory of Open Access Journals (Sweden)
Petre Bucur
2007-01-01
Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.
Oscillatons formed by non linear gravity
Obregón, O; Schunck, F E; Obregon, Octavio; Schunck, Franz E.
2004-01-01
Oscillatons are solutions of the coupled Einstein-Klein-Gordon (EKG) equations that are globally regular and asymptotically flat. By means of a Legendre transformation we are able to visualize the behaviour of the corresponding objects in non-linear gravity where the scalar field has been absorbed by means of the conformal mapping.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations betwee...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models.......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under...
Controller reconfiguration for non-linear systems
Kanev, S.; Verhaegen, M.
2000-01-01
This paper outlines an algorithm for controller reconfiguration for non-linear systems, based on a combination of a multiple model estimator and a generalized predictive controller. A set of models is constructed, each corresponding to a different operating condition of the system. The interacting m
Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories
Alazzawi, Sabina; Lechner, Gandalf
2017-09-01
We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix S is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on S that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the O( N)-invariant nonlinear {σ}-models.
Sarma, S. Das; Hwang, E. H.
1998-01-01
We calculate within the Boltzmann equation approach the charged impurity scattering limited low temperature electronic resistivity of low density $n$-type inversion layers in Si MOSFET structures. We find a rather sharp quantum to classical crossover in the transport behavior in the $0 - 5$K temperature range, with the low density, low temperature mobility showing a strikingly strong non-monotonic temperature dependence, which may qualitatively explain the recently observed anomalously strong...
Direct and Inverse Scattering Problem Associated with the Elliptic Sinh-Gordon Equation
1989-11-14
This paper describes how to generate the fundamental singular solutions of an integrable nonlinear elliptic PDE. 3. Coherent Structures in the Planar...Problems]) This paper describes how to peqerate the fundamental singular solutions of an integrable nonlinear elliptic PDE. 3. tbherent Structures in the...It is shown that the inverse scattering transform may be useful in the analysis of localized singular solutions . As an example, a cylindrically
Vacuum solutions of five dimensional Einstein equations generated by inverse scattering method
Tomizawa, S; Yasui, Y; Morisawa, Yoshiyuki; Tomizawa, Shinya; Yasui, Yukinori
2006-01-01
We study stationary and axially symmetric two solitonic solutions of five dimensional vacuum Einstein equations by using the inverse scattering method developed by Belinski and Zakharov. In this generation of the solutions, we use five dimensional Minkowski spacetime as a seed. It is shown that if we restrict ourselves to the case of one angular momentum component, the generated solution coincides with a black ring solution with a rotating two sphere which was found by Mishima and Iguchi recently.
Full waveform inversion based on scattering angle enrichment with application to real dataset
Wu, Zedong
2015-08-19
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI). However, the drawback of the existing RWI methods is inability to utilize diving waves and the extra sensitivity to the migrated image. We propose a combined FWI and RWI optimization problem through dividing the velocity into the background and perturbed components. We optimize both the background and perturbed components, as independent parameters. The new objective function is quadratic with respect to the perturbed component, which will reduce the nonlinearity of the optimization problem. Solving this optimization provides a true amplitude image and utilizes the diving waves to update the velocity of the shallow parts. To insure a proper wavenumber continuation, we use an efficient scattering angle filter to direct the inversion at the early stages to direct energy corresponding to large (smooth velocity) scattering angles to the background velocity update and the small (high wavenumber) scattering angles to the perturbed velocity update. This efficient implementation of the filter is fast and requires less memory than the conventional approach based on extended images. Thus, the new FWI procedure updates the background velocity mainly along the wavepath for both diving and reflected waves in the initial stages. At the same time, it updates the perturbation with mainly reflections (filtering out the diving waves). To demonstrate the capability of this method, we apply it to a real 2D marine dataset.
Solution of the nonlinear inverse scattering problem by T -matrix completion. II. Simulations
Levinson, Howard W.; Markel, Vadim A.
2016-10-01
This is Part II of the paper series on data-compatible T -matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043317 (2016), 10.1103/PhysRevE.94.043317] contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object, but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.
Institute of Scientific and Technical Information of China (English)
Yanmin Wang; Guobiao Liang; Zhidong Pan
2010-01-01
A modified regularization algorithm with a more proper operator was proposed for the inversion of partide size distribution(PSD)from light-scattering data in a laser particle sizer based on the Mie scattering principle.The Generalized Cross-Validation(GCV)method and the L-curve method were used for determining the regularization parameter.The Successive Over-Relaxation(SOR)iterative method was used to increase the exactness and stability of the converged result.The simulated results based on the modified algorithm are in a good agreement with the experimental data measured for nine standard particulate samples,their mixtures as well as three natural particulate materials with irregular shapes,indicating that this modified regularization method is not only feasible but also effective for the simulation of PSD from corresponding light-scattering data.
The Mathematical Basis of the Inverse Scattering Problem for Cracks from Near-Field Data
Directory of Open Access Journals (Sweden)
Yao Mao
2015-01-01
Full Text Available We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator’s mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator’s properties and modified linear sampling method, we reconstruct the shape and surface impedance.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Dobado, Antonio; Llanes-Estrada, Felipe J
2015-01-01
If new resonances of the electroweak symmetry breaking sector (longitudinal-gauge and Higgs) bosons are found in the 1-3 TeV region, the right tool to assess their properties and confront experimental data in a largely model-independent yet simple manner is Unitarized Effective Theory. Its ingredients are: 1) custodial symmetry and the Equivalence Theorem, that allow to approximate W_L and Z_L by an isospin-triplet of Goldstone bosons omega^a in the 1-TeV region. 2) The effective coupling of a generic, approximately massless scalar-isoscalar h to those Goldstone bosons, and the chiral Lagrangian describing them, valid up to about 3 TeV. 3) The Inverse Amplitude or other unitarization techniques that allow to extend the reach of perturbation theory to the first resonance in each partial wave. We highlight some of the parameter space that can give rise to 2-TeV resonances, for example a simultaneous scalar-isoscalar and a vector-isovector ones (motivated by the ATLAS excess) and also the potential importance of...
Non-Linear Dynamics and Fundamental Interactions
Khanna, Faqir
2006-01-01
The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.
Fliess, Michel; Join, Cédric; Sira-Ramirez, Hebertt
2008-01-01
International audience; Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line ...
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of three...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Fliess, Michel; Sira-Ramirez, Hebertt
2007-01-01
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.
Direct Waveform Inversion by Iterative Inverse Propagation
Schlottmann, R B
2009-01-01
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating these surface recordings to actual Earth properties is non-trivial. Tomographic techniques use only a small amount of the information contained in the full seismogram and result in relatively low resolution images. Other methods use a larger amount of the seismogram but are based on either linearization of the problem, an expensive statistical search over a limited range of models, or both. We present the development of a new approach to full waveform inversion, i.e., inversion which uses the complete seismogram. This new method, which falls under the general category of inverse scattering, is based on a highly non-linear Fredholm integral equation relating the Earth structure to itself and to the recorded seismograms. An iterative solution to this equation is proposed. The res...
Statistical flaw characterization through Bayesian shape inversion from scattered wave observations
McMahan, Jerry A.; Criner, Amanda K.
2016-02-01
A method is discussed to characterize the shape of a flaw from noisy far-field measurements of a scattered wave. The scattering model employed is a two-dimensional Helmholtz equation which quantifies scattering due to interrogating signals from various physical phenomena such as acoustics or electromagnetics. The well-known inherent ill-posedness of the inverse scattering problem is addressed via Bayesian regularization. The method is loosely related to the approach described in [1] which uses the framework of [2] to prove the well-posedness of the infinite-dimensional problem and derive estimates of the error for a particular discretization approach. The method computes the posterior probability density for the flaw shape from the scattered field observations, taking into account prior assumptions which are used to describe any a priori knowledge of the flaw. We describe the computational approach to the forward problem as well as the Markov chain Monte Carlo (MCMC) based approach to approximating the posterior. We present simulation results for some hypothetical flaw shapes with varying levels of observation error and arrangement of observation points. The results show how the posterior probability density can be used to visualize the shape of the flaw taking into account the quantitative confidence in the quality of the estimation and how various arrangements of the measurements and interrogating signals affect the estimation
Gharsalli, Leila; Ayasso, Hacheme; Duchêne, Bernard; Mohammad-Djafari, Ali
2014-11-01
In this paper, we deal with a nonlinear inverse scattering problem where the goal is to detect breast cancer from measurements of the scattered field that results from the interaction between the breast and a known interrogating wave in the microwave frequency range. Modeling of the wave-object (breast) interaction is tackled through a domain integral representation of the electric field in a 2D-TM configuration. The inverse problem is solved in a Bayesian framework where prior information, which consists in the fact that the object is supposed to be composed of compact homogeneous regions made of a restricted number of different materials, is introduced via a Gauss-Markov-Potts model. As an analytic expression for the joint maximum a posteriori (MAP) estimators yields an intractable solution, an approximation of the latter is proposed. This is done by means of a variational Bayesian approximation (VBA) technique that is adapted to complex-valued contrast and applied to compute the posterior estimators, and reconstruct maps of both permittivity and conductivity of the sought object. This leads to a joint semi-supervised estimation approach, which allows us to estimate the induced currents, the contrast and all of the parameters introduced in the prior model. The method is tested on two sets of synthetic data generated in different configurations and its performances are compared to that given by a contrast source inversion technique.
Ivanyshyn Yaman, Olha; Le Louër, Frédérique
2016-09-01
This paper deals with the material derivative analysis of the boundary integral operators arising from the scattering theory of time-harmonic electromagnetic waves and its application to inverse problems. We present new results using the Piola transform of the boundary parametrisation to transport the integral operators on a fixed reference boundary. The transported integral operators are infinitely differentiable with respect to the parametrisations and simplified expressions of the material derivatives are obtained. Using these results, we extend a nonlinear integral equations approach developed for solving acoustic inverse obstacle scattering problems to electromagnetism. The inverse problem is formulated as a pair of nonlinear and ill-posed integral equations for the unknown boundary representing the boundary condition and the measurements, for which the iteratively regularized Gauss-Newton method can be applied. The algorithm has the interesting feature that it avoids the numerous numerical solution of boundary value problems at each iteration step. Numerical experiments are presented in the special case of star-shaped obstacles.
Tsang, Leung; Chen, Zhengxiao; Oh, Seho; Marks, Robert J., II; Chang, A. T. C.
1992-01-01
Simultaneous inversion of the three parameters was performed which included mean-grain size of ice particles in snow, snow density, and snow temperatures from five brightness temperatures. Good results for the inversion of parameters were obtained using the neural network based on the simulated data computed from the dense media radiative transfer equation that takes into account the effects of multiple scattering.
The shifting zoom: new possibilities for inverse scattering on electrically large domains
Persico, Raffaele; Ludeno, Giovanni; Soldovieri, Francesco; De Coster, Alberic; Lambot, Sebastien
2017-04-01
Inverse scattering is a subject of great interest in diagnostic problems, which are in their turn of interest for many applicative problems as investigation of cultural heritage, characterization of foundations or subservices, identification of unexploded ordnances and so on [1-4]. In particular, GPR data are usually focused by means of migration algorithms, essentially based on a linear approximation of the scattering phenomenon. Migration algorithms are popular because they are computationally efficient and do not require the inversion of a matrix, neither the calculation of the elements of a matrix. In fact, they are essentially based on the adjoint of the linearised scattering operator, which allows in the end to write the inversion formula as a suitably weighted integral of the data [5]. In particular, this makes a migration algorithm more suitable than a linear microwave tomography inversion algorithm for the reconstruction of an electrically large investigation domain. However, this computational challenge can be overcome by making use of investigation domains joined side by side, as proposed e.g. in ref. [3]. This allows to apply a microwave tomography algorithm even to large investigation domains. However, the joining side by side of sequential investigation domains introduces a problem of limited (and asymmetric) maximum view angle with regard to the targets occurring close to the edges between two adjacent domains, or possibly crossing these edges. The shifting zoom is a method that allows to overcome this difficulty by means of overlapped investigation and observation domains [6-7]. It requires more sequential inversion with respect to adjacent investigation domains, but the really required extra-time is minimal because the matrix to be inverted is calculated ones and for all, as well as its singular value decomposition: what is repeated more time is only a fast matrix-vector multiplication. References [1] M. Pieraccini, L. Noferini, D. Mecatti, C
Spin 1 inversion a Majorana tensor force for deuteron alpha scattering
Cooper, S G; MacIntosh, R S; Pomerantsev, V N
1999-01-01
We demonstrate, for the first time, successful S-matrix to potential inversion for spin one projectiles with non-diagonal $S^j_{ll'}$ yielding a $T_{\\rm R}$ interaction. The method is a generalization of the iterative-perturbative, IP, method. We present a test case indicating the degree of uniqueness of the potential. The method is adapted, using established procedures, into direct observable to potential inversion, fitting $\\sigma$, ${\\rm i}T_{11}$, $T_{20}$, $T_{21}$ and $T_{22}$ for d + alpha scattering over a range of energies near 10 MeV. The $T_{\\rm R}$ interaction which we find is very different from that proposed elsewhere, both real and imaginary parts being very different for odd and even parity channels.
Non Linear Behaviour in Learning Processes
Manfredi, Paolo; Manfredi, Vicenzo Rosario
2003-01-01
This article is mainly based on R. E. Kahn's contribution to the book Non Linear Dynamics in Human Behavior. As stressed by Bronowski, both in art and in science, a person becomes creative by finding "a new unity" that is a link between things which were not thought alike before. Indeed the creative mind is a mind that looks for unexpected likeness finding a more profound unity, a pattern behind chaotic phenomena. In the context of scientific discovery, it can also be argued that creativi...
BRST structure of non-linear superalgebras
Asorey, M; Radchenko, O V; Sugamoto, A
2008-01-01
In this paper we analyse the structure of the BRST structure of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
Limits on Non-Linear Electrodynamics
Fouché, M; Rizzo, C
2016-01-01
In this paper we set a framework in which experiments whose goal is to test QED predictions can be used in a more general way to test non-linear electrodynamics (NLED) which contains low-energy QED as a special case. We review some of these experiments and we establish limits on the different free parameters by generalizing QED predictions in the framework of NLED. We finally discuss the implications of these limits on bound systems and isolated charged particles for which QED has been widely and successfully tested.
Chen, Xiang-Jun; Lam, Wa Kun
2004-06-01
An inverse scattering transform for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived by introducing an affine parameter to avoid constructing Riemann sheets. A one-soliton solution simpler than that in the literature is obtained, which is a breather and degenerates to a bright or dark soliton as the discrete eigenvalue becomes purely imaginary. The solution is mapped to that of the modified nonlinear Schrödinger equation by a gaugelike transformation, predicting some sub-picosecond solitons in optical fibers.
Interpreting Ulysses data using inverse scattering theory: Oblique Alfv\\'en waves
Wheeler, Harry R; Hamilton, R L
2015-01-01
Solitary wave structures observed by the Ulysses spacecraft in the solar wind were analyzed using both inverse scattering theory as well as direct numerical integration of the derivative nonlinear Schr\\"odinger (DNLS) equation. Several of these structures were found to be consistent with soliton solutions of the DNLS equation. Such solitary structures have been commonly observed in the space plasma environment and may, in fact, be long-lived solitons. While the generation of these solitons may be due to an instability mechanism, e.g., the mirror instability, they may be observable far from the source region due to their coherent nature.
A necessary condition for applying MUSIC algorithm in limited-view inverse scattering problem
Park, Taehoon; Park, Won-Kwang
2015-09-01
Throughout various results of numerical simulations, it is well-known that MUltiple SIgnal Classification (MUSIC) algorithm can be applied in the limited-view inverse scattering problems. However, the application is somehow heuristic. In this contribution, we identify a necessary condition of MUSIC for imaging of collection of small, perfectly conducting cracks. This is based on the fact that MUSIC imaging functional can be represented as an infinite series of Bessel function of integer order of the first kind. Numerical experiments from noisy synthetic data supports our investigation.
The Inverse Amplitude Method in $\\pi\\pi$ Scattering in Chiral Perturbation Theory to Two Loops
Nieves, J; Ruiz-Arriola, E
2002-01-01
The inverse amplitude method is used to unitarize the two loop $\\pi\\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\\bar b_{1,2,3,4,5,6} $ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.
Inverse freezing in {alpha}-cyclodextrin solutions probed by quasi elastic neutron scattering
Energy Technology Data Exchange (ETDEWEB)
Plazanet, M. [LENS, University of Florence, Via Nello Carrara 1, I-50019 Sesto-Fiorentino (Italy); INFM-CRS-Soft Matter (CNR), c/o Univ. la Sapienza, Piaz. A. Moro 2, I-00185 Roma (Italy); Institut Laue-Langevin, B.P. 156X, 38042 Grenoble Cx (France); Johnson, M.R. [Institut Laue-Langevin, B.P. 156X, 38042 Grenoble Cx (France); Schweins, R. [Institut Laue-Langevin, B.P. 156X, 38042 Grenoble Cx (France); Trommsdorff, H.P. [Institut Laue-Langevin, B.P. 156X, 38042 Grenoble Cx (France); Laboratoire de Spectrometrie Physique, Universite J. Fourier Grenoble - CNRS (UMR 5588), BP 87, 38402 St. Martin d' Heres Cx (France)], E-mail: trommsdorff@ill.fr
2006-12-11
Solutions of {alpha}-cyclodextrin, 4-methylpyridine and water undergo a reversible liquid-solid phase transition on heating ('inverse freezing'). In this paper quasi elastic neutron scattering (QENS) measurements are reported, from which the diffusive dynamics of different components in the liquid and solid phases is determined. Results imply that, in solution, {alpha}-cyclodextrin is contained in a solvation shell of 4-methylpyridine molecules, while in the crystal phase, the majority of the cell contents are immobilized on the nanosecond timescale. This information will be important in evaluating the entropy of the system in its different phases and in understanding the unusual phase transition.
Mature red blood cells: from optical model to inverse light-scattering problem.
Gilev, Konstantin V; Yurkin, Maxim A; Chernyshova, Ekaterina S; Strokotov, Dmitry I; Chernyshev, Andrei V; Maltsev, Valeri P
2016-04-01
We propose a method for characterization of mature red blood cells (RBCs) morphology, based on measurement of light-scattering patterns (LSPs) of individual RBCs with the scanning flow cytometer and on solution of the inverse light-scattering (ILS) problem for each LSP. We considered a RBC shape model, corresponding to the minimal bending energy of the membrane with isotropic elasticity, and constructed an analytical approximation, which allows rapid simulation of the shape, given the diameter and minimal and maximal thicknesses. The ILS problem was solved by the nearest-neighbor interpolation using a preliminary calculated database of 250,000 theoretical LSPs. For each RBC in blood sample we determined three abovementioned shape characteristics and refractive index, which also allows us to calculate volume, surface area, sphericity index, spontaneous curvature, hemoglobin concentration and content.
Doyuran, Adnan; Joshi, Chandrashekhar; Lim, Jae; Rosenzweig, James E; Tochitsky, Sergei Ya; Travish, Gil; Williams, Oliver
2005-01-01
An Inverse Compton Scattering (ICS) experiment investigating the polarized harmonic production in the nonlinear regime has begun which will utilize the existing terawatt CO2 laser system and 15 MeV photoinjector in the Neptune Laboratory at UCLA. A major motivation for a source of high brightness polarized x-rays is the production of polarized positrons for use in future linear collider experiments. Analytical calculations have been performed to predict the angular and frequency spectrums for various polarizations and different scattering angles. Currently, the experiment is running and we report the set-up and initial results. The advantages and limitations of using a high laser vector potential, ao, in an ICS-based polarized positron source are expected to be revealed with further measurement of the harmonic spectrum and angular characteristics.
A multifrequency MUSIC algorithm for locating small inhomogeneities in inverse scattering
Griesmaier, Roland; Schmiedecke, Christian
2017-03-01
We consider an inverse scattering problem for time-harmonic acoustic or electromagnetic waves with sparse multifrequency far field data-sets. The goal is to localize several small penetrable objects embedded inside an otherwise homogeneous background medium from observations of far fields of scattered waves corresponding to incident plane waves with one fixed incident direction but several different frequencies. We assume that the far field is measured at a few observation directions only. Taking advantage of the smallness of the scatterers with respect to wavelength we utilize an asymptotic representation formula for the far field to design and analyze a MUSIC-type reconstruction method for this setup. We establish lower bounds on the number of frequencies and receiver directions that are required to recover the number and the positions of an ensemble of scatterers from the given measurements. Furthermore we briefly sketch a possible application of the reconstruction method to the practically relevant case of multifrequency backscattering data. Numerical examples are presented to document the potentials and limitations of this approach.
Polarization effects in the non-linear Compton scattering
Ivanov, D Y; Serbo, V G
2005-01-01
We consider emission of a photon by an electron in the field of a strong laser wave. A probability of this process for circularly or linearly polarized laser photons and for arbitrary polarization of all other particles is calculated. We obtain the complete set of functions which describe such a probability in a compact invariant form. Besides, we discuss in some detail the polarization effects in the kinematics relevant to the problem of electron to photon conversion at photon-photon and electron-photon colliders.
Derkachov, G.; Jakubczyk, T.; Jakubczyk, D.; Archer, J.; Woźniak, M.
2017-07-01
Utilising Compute Unified Device Architecture (CUDA) platform for Graphics Processing Units (GPUs) enables significant reduction of computation time at a moderate cost, by means of parallel computing. In the paper [Jakubczyk et al., Opto-Electron. Rev., 2016] we reported using GPU for Mie scattering inverse problem solving (up to 800-fold speed-up). Here we report the development of two subroutines utilising GPU at data preprocessing stages for the inversion procedure: (i) A subroutine, based on ray tracing, for finding spherical aberration correction function. (ii) A subroutine performing the conversion of an image to a 1D distribution of light intensity versus azimuth angle (i.e. scattering diagram), fed from a movie-reading CPU subroutine running in parallel. All subroutines are incorporated in PikeReader application, which we make available on GitHub repository. PikeReader returns a sequence of intensity distributions versus a common azimuth angle vector, corresponding to the recorded movie. We obtained an overall ∼ 400 -fold speed-up of calculations at data preprocessing stages using CUDA codes running on GPU in comparison to single thread MATLAB-only code running on CPU.
Fouda, Ahmed E.
differential TR. This technique provides real-time tracking and exhibits superior clutter rejection at minimal processing costs. It also exploits the distinctive features of time-reversal such as statistical stability and superresolution. Next, we develop an UWB inverse scattering technique for extended targets, with continuous permittivity and/or conductivity fluctuations, based on Bayesian compressive sensing. Bayesian inversion provides means for estimating the confidence level of the inversion, and for adaptively optimizing subsequent measurements. This technique is applied to a wide range of problems of practical interest such as underground crosshole sensing, medical imaging, and rough surface reconstruction. Finally, we develop new TR-based wireless communication techniques for UWB multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) systems. We contrast relative strengths and limitations of those techniques for different scenarios of operation.
Non-Linear Dynamics of Saturn's Rings
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
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.
Novell, Anthony; Escoffre, Jean-Michel; Bouakaz, Ayache
2013-08-01
When insonified with suitable ultrasound excitation, contrast microbubbles generate various non-linear scattered components, such as the second harmonic (2H) and the subharmonic (SH). In this study, we exploit the wide frequency bandwidth of capacitive micromachined ultrasonic transducers (CMUTs) to enhance the response from ultrasound contrast agents by selective imaging of both the 2H and SH components simultaneously. To this end, contrast images using the pulse inversion method were recorded with a 64-element CMUT linear array connected to an open scanner. In comparison to imaging at 2H alone, the wideband imaging including both the 2H and SH contributions provided up to 130% and 180% increases in the signal-to-noise and contrast-to-tissue ratios, respectively. The wide-frequency band of CMUTs offers new opportunities for improved ultrasound contrast agent imaging.
Optimal non-linear health insurance.
Blomqvist, A
1997-06-01
Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.
Chaotic Discrimination and Non-Linear Dynamics
Directory of Open Access Journals (Sweden)
Partha Gangopadhyay
2005-01-01
Full Text Available This study examines a particular form of price discrimination, known as chaotic discrimination, which has the following features: sellers quote a common price but, in reality, they engage in secret and apparently unsystematic price discounts. It is widely held that such forms of price discrimination are seriously inconsistent with profit maximization by sellers.. However, there is no theoretical salience to support this kind of price discrimination. By straining the logic of non-linear dynamics this study explains why such secret discounts are chaotic in the sense that sellers fail to adopt profit-maximising price discounts. A model is developed to argue that such forms of discrimination may derive from the regions of instability of a dynamic model of price discounts.
Risks of non-linear climate change
Energy Technology Data Exchange (ETDEWEB)
Van Ham, J.; Van Beers, R.J.; Builtjes, P.J.H.; Koennen, G.P.; Oerlemans, J.; Roemer, M.G.M. [TNO-SCMO, Delft (Netherlands)
1995-12-31
Climate forcing as a result of increased concentrations of greenhouse gases has been primarily addressed as a problem of a possibly warmer climate. So far, such change has been obscured in observations, possibly as a result of natural climate variability and masking by aerosols. Consequently, projections of the effect of climate forcing have to be based on modelling, more specifically by applying Global Circulation Models GCMs. These GCMs do not cover all possible feedbacks; neither do they address all specific possible effects of climate forcing. The investigation reviews possible non-linear climate change which does not fall within the coverage of present GCMs. The review includes the potential relevance of changes in biogeochemical cycles, aerosol and cloud feedback, albedo instability, ice-flow instability, changes in the thermohaline circulation and changes resulting from stratospheric cooling. It is noted that these changes may have different time horizons. Three from the investigated issues provide indications for a possible non-linear change. On the decadal scale stratospheric cooling, which is the result of the enhanced greenhouse effect, in combination with a depleted ozone layer, could provide a positive feedback to further ozone depletion, in particular in the Arctic. Decreasing albedo on the Greenland ice sheet may enhance the runoff from this ice sheet significantly in case of warming on a timescale of a few centuries. Changes in ocean circulation in the North Atlantic could seasonally more than compensate a global warming of 3C in North-West Europe on a timescale of centuries to a millennium. 263 refs.
Compact FEL-driven inverse compton scattering gamma-ray source
Placidi, M.; Di Mitri, S.; Pellegrini, C.; Penn, G.
2017-05-01
Many research and applications areas require photon sources capable of producing gamma-ray beams in the multi-MeV energy range with reasonably high fluxes and compact footprints. Besides industrial, nuclear physics and security applications, a considerable interest comes from the possibility to assess the state of conservation of cultural assets like statues, columns etc., via visualization and analysis techniques using high energy photon beams. Computed Tomography scans, widely adopted in medicine at lower photon energies, presently provide high quality three-dimensional imaging in industry and museums. We explore the feasibility of a compact source of quasi-monochromatic, multi-MeV gamma-rays based on Inverse Compton Scattering (ICS) from a high intensity ultra-violet (UV) beam generated in a free-electron laser by the electron beam itself. This scheme introduces a stronger relationship between the energy of the scattered photons and that of the electron beam, resulting in a device much more compact than a classic ICS for a given scattered energy. The same electron beam is used to produce gamma-rays in the 10-20 MeV range and UV radiation in the 10-15 eV range, in a 4×22 m2 footprint system.
Zhang, Jin-Peng; Wu, Zhen-Sen; Zhao, Zhen-Wei; Zhang, Yu-Sheng; Wang, Bo
2012-10-01
The maritime tropospheric duct is a low-altitude anomalous refractivity structure over the ocean surface, and it can significantly affect the performance of many shore-based/shipboard radar and communication systems. We propose the idea that maritime tropospheric ducts can be retrieved from ocean forward-scattered low-elevation global positioning system (GPS) signals. Retrieval is accomplished by matching the measured power patterns of the signals to those predicted by the forward propagation model as a function of the modified refractivity profile. On the basis of a parabolic equation method and bistatic radar equation, we develop such a forward model for computing the trapped propagation characteristics of an ocean forward-scattered GPS signal within a tropospheric duct. A new GPS scattering initial field is defined for this model to start the propagation modeling. A preliminary test on the performance of this model is conducted using measured data obtained from a 2009-experiment in the South China Sea. Results demonstrate that this model can predict GPS propagation characteristics within maritime tropospheric ducts and serve as a forward model for duct inversion.
Institute of Scientific and Technical Information of China (English)
Zhang Jin-Peng; Wu Zhen-Sen; Zhao Zhen-Wei; Zhang Yu-Sheng; Wang Bo
2012-01-01
The maritime tropospheric duct is a low-altitude anomalous refractivity structure over the ocean surface,and it can significantly affect the performance of many shore-based/shipboard radar and communication systems. We propose the idea that maritime tropospheric ducts can be retrieved from ocean forward-scattered low-elevation global positioning system (GPS) signals.Retrieval is accomplished by matching the measured power patterns of the signals to those predicted by the forward propagation model as a function of the modified refractivity profile.On the basis of a parabolic equation method and bistatic radar equation,we develop such a forward model for computing the trapped propagation characteristics of an ocean forward-scattered GPS signal within a tropospheric duct.A new GPS scattering initial field is defined for this model to start the propagation modeling.A preliminary test on the performance of this model is conducted using measured data obtained from a 2009-experiment in the South China Sea.Results demonstrate that this model can predict GPS propagation characteristics within maritime tropospheric ducts and serve as a forward model for duct inversion.
Energy Technology Data Exchange (ETDEWEB)
Dixneuf, Sophie [Forschungszentrum Jülich GmbH IEK-8: Troposphere, 52425 Jülich (Germany); Rachet, Florent; Chrysos, Michael, E-mail: michel.chrysos@univ-angers.fr [LUNAM Université, Université d’Angers, CNRS UMR 6200, Laboratoire MOLTECH-Anjou, 2 Bd Lavoisier, 49045 Angers (France)
2015-02-28
Owing in part to the p orbitals of its filled L shell, neon has repeatedly come on stage for its peculiar properties. In the context of collision-induced Raman spectroscopy, in particular, we have shown, in a brief report published a few years ago [M. Chrysos et al., Phys. Rev. A 80, 054701 (2009)], that the room-temperature anisotropic Raman lineshape of Ne–Ne exhibits, in the far wing of the spectrum, a peculiar structure with an aspect other than a smooth wing (on a logarithmic plot) which contrasts with any of the existing studies, and whose explanation lies in the distinct way in which overlap and exchange interactions interfere with the classical electrostatic ones in making the polarizability anisotropy, α{sub ∥} − α{sub ⊥}. Here, we delve deeper into that study by reporting data for that spectrum up to 450 cm{sup −1} and for even- and odd-order spectral moments up to M{sub 6}, as well as quantum lineshapes, generated from SCF, CCSD, and CCSD(T) models for α{sub ∥} − α{sub ⊥}, which are critically compared with the experiment. On account of the knowledge of the spectrum over the augmented frequency domain, we show how the inverse scattering problem can be tackled both effectively and economically, and we report an analytic function for the anisotropy whose quantum lineshape faithfully reproduces our observations.
Dixneuf, Sophie; Rachet, Florent; Chrysos, Michael
2015-02-28
Owing in part to the p orbitals of its filled L shell, neon has repeatedly come on stage for its peculiar properties. In the context of collision-induced Raman spectroscopy, in particular, we have shown, in a brief report published a few years ago [M. Chrysos et al., Phys. Rev. A 80, 054701 (2009)], that the room-temperature anisotropic Raman lineshape of Ne-Ne exhibits, in the far wing of the spectrum, a peculiar structure with an aspect other than a smooth wing (on a logarithmic plot) which contrasts with any of the existing studies, and whose explanation lies in the distinct way in which overlap and exchange interactions interfere with the classical electrostatic ones in making the polarizability anisotropy, α∥ - α⊥. Here, we delve deeper into that study by reporting data for that spectrum up to 450 cm(-1) and for even- and odd-order spectral moments up to M6, as well as quantum lineshapes, generated from SCF, CCSD, and CCSD(T) models for α∥ - α⊥, which are critically compared with the experiment. On account of the knowledge of the spectrum over the augmented frequency domain, we show how the inverse scattering problem can be tackled both effectively and economically, and we report an analytic function for the anisotropy whose quantum lineshape faithfully reproduces our observations.
Weakly nonlinear models for internal waves: inverse scattering transform and solitary wave contents
Chen, Shengqian
2016-01-01
The time evolution emanating from ``internal dam-break'' initial conditions is studied for a class of models of stratified Euler fluids in configurations close to two-homogeneous layers separated by a thin diffused interface. Direct numerical simulations and experiments in wave tanks show that such initial conditions eventually give rise to coherent structures that are close to solitary-wave solutions moving ahead of a region of dispersive wave motion and turbulent mixing close to the location of the initial dam step. A priori theoretical predictions of the main features of these solitary waves, such as their amplitudes and speeds, appear to be unavailable, even for simplified models of wave evolution in stratified fluids. With the aim of providing estimates of the existence, amplitude and speed of such solitary waves, an approach based on Inverse Scattering Transform (IST) for completely integrable models is developed here and tested against direct numerical simulations of Euler fluids and some of their mode...
Qiao, G J; Zhang, B; Han, J L
2001-01-01
The shapes of pulse profiles, especially their variations with respect to observing frequencies, are very important to understand emission mechanisms of pulsars, while no previous attempt has been made in interpreting the complicated phenomenology. In this paper, we present theoretical simulations for the integrated pulse profiles and their frequency evolution within the framework of the inverse Compton scattering (ICS) model proposed by Qiao (1988) and Qiao & Lin (1998). Using the phase positions of the pulse components predicted by the ``beam-frequency figure'' of the ICS model, we present Gaussian fits to the multi-frequency pulse profiles for some pulsars. It is shown that the model can reproduce various types of the frequency evolution behaviors of pulse profiles observed.
Inverse Scattering Transform of the Coupled Sasa-Satsuma Equation by Riemann-Hilbert Approach
Wu, Jian-Ping; Geng, Xian-Guo
2017-05-01
The inverse scattering transform of a coupled Sasa-Satsuma equation is studied via Riemann-Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa-Satsuma equation, from which a Riemann-Hilbert problem is formulated. Then the Riemann-Hilbert problem corresponding to the reflection-less case is solved. As applications, multi-soliton solutions are obtained for the coupled Sasa-Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons. Supported by the National Natural Science Foundation of China under Project Nos. 11331008 and 11171312 and the Collaborative Innovation Center for Aviation Economy Development of Henan Province
Schwab, Hans-Martin; Beckmann, Martin F; Schmitz, Georg
2016-04-01
Photoacoustic imaging aims to visualize light absorption properties of biological tissue by receiving a sound wave that is generated inside the observed object as a result of the photoacoustic effect. In clinical applications, the strong light absorption in human skin is a major problem. When high amplitude photoacoustic waves that originate from skin absorption propagate into the tissue, they are reflected back by acoustical scatterers and the reflections contribute to the received signal. The artifacts associated with these reflected waves are referred to as clutter or skin echo and limit the applicability of photoacoustic imaging for medical applications severely. This study seeks to exploit the acoustic tissue information gained by plane wave ultrasound measurements with a linear array in order to correct for reflections in the photoacoustic image. By deriving a theory for clutter waves in k-space and a matching inversion approach, photoacoustic measurements compensated for clutter are shown to be recovered.
Desmal, Abdulla
2014-07-01
A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST algorithms minimize a cost function weighted between measurement-data misfit and a zeroth/first-norm penalty term and therefore promote "sharpness" in the solution. Consequently, when applied to domains with sharp variations, discontinuities, or sparse content, the proposed framework is more efficient and accurate than the "classical" BIM that minimizes a cost function with a second-norm penalty term. Indeed, numerical results demonstrate the superiority of the IST-BIM over the classical BIM when they are applied to sparse domains: Permittivity and conductivity profiles recovered using the IST-BIM are sharper and more accurate and converge faster. © 1963-2012 IEEE.
Structure of raft-model membrane by using the inverse contrast variation neutron scattering method
Energy Technology Data Exchange (ETDEWEB)
Hirai, Mitsuhiro [Department of Physics, Gunma University, Maebashi 371-8510 (Japan); Hirai, Harutaka [Department of Physics, Gunma University, Maebashi 371-8510 (Japan); Koizumi, Masaharu [Department of Physics, Gunma University, Maebashi 371-8510 (Japan); Kasahara, Kohji [Tokyo Metropolitan Institute of Medical Science, Tokyo 113-8613 (Japan); Yuyama, Kohei [Tokyo Metropolitan Institute of Medical Science, Tokyo 113-8613 (Japan); Suzuki, Naoko [Tokyo Metropolitan Institute of Medical Science, Tokyo 113-8613 (Japan)
2006-11-15
By means of the inverse contrast variation method in small-angle neutron scattering, we have studied the structure of a small unilamellar vesicle (SUV) composed of ganglioside, cholesterol and dipalmitoyl-phosphocholine. The SUV treated has a similar lipid composition as in a plasma membrane with microdomains, so-called rafts. The present results indicate an asymmetric distribution of lipid components within the bilayer of the vesicle, that is, a predominant distribution of ganglioside and cholesterol at the outer leaflet of the vesicle bilayer. The deviation from the linearity in a pseudo-Stuhrmannplot strongly suggests the presence of a large heterogeneity of lipid composition in a bilayer, namely a clustering of ganglioside and cholesterol molecules. This deviation is enhanced by temperature elevation, meaning that ganglioside-cholesterol clusters become larger with holding liquid-ordered (L{sub o}) phase.
Hansen, P. J.; Lonngren, K. E.
1993-01-01
A heuristic estimate for the soliton production rate by a pulse is verified for the Korteweg - de Vries equation using inverse scattering. An observation from this result, which is shown to hold for some other nonlinear equations and for the case of the 'forced' nonlinear Schroedinger equation, is that production is determined by quantities that are invariant under rescaling of the original nonlinear equations. We speculate that this result may be useful to the development of an inverse scattering theory for 'forced' nonlinear systems.
Exclusive measurements of quasi-free proton scattering reactions in inverse and complete kinematics
Directory of Open Access Journals (Sweden)
V. Panin
2016-02-01
Full Text Available Quasi-free scattering reactions of the type (p,2p were measured for the first time exclusively in complete and inverse kinematics, using a 12C beam at an energy of ∼400 MeV/u as a benchmark. This new technique has been developed to study the single-particle structure of exotic nuclei in experiments with radioactive-ion beams. The outgoing pair of protons and the fragments were measured simultaneously, enabling an unambiguous identification of the reaction channels and a redundant measurement of the kinematic observables. Both valence and deeply-bound nucleon orbits are probed, including those leading to unbound states of the daughter nucleus. Exclusive (p,2p cross sections of 15.8(18 mb, 1.9(2 mb and 1.5(2 mb to the low-lying 0p-hole states overlapping with the ground state (3/2− and with the bound excited states of 11B at 2.125 MeV (1/2− and 5.02 MeV (3/2−, respectively, were determined via γ-ray spectroscopy. Particle-unstable deep-hole states, corresponding to proton removal from the 0s-orbital, were studied via the invariant-mass technique. Cross sections and momentum distributions were extracted and compared to theoretical calculations employing the eikonal formalism. The obtained results are in a good agreement with this theory and with direct-kinematics experiments. The dependence of the proton–proton scattering kinematics on the internal momentum of the struck proton and on its separation energy was investigated for the first time in inverse kinematics employing a large-acceptance measurement.
Biondini, Gino; Fagerstrom, Emily; Prinari, Barbara
2016-10-01
We formulate the inverse scattering transform (IST) for the defocusing nonlinear Schrödinger (NLS) equation with fully asymmetric non-zero boundary conditions (i.e., when the limiting values of the solution at space infinities have different non-zero moduli). The theory is formulated without making use of Riemann surfaces, and instead by dealing explicitly with the branched nature of the eigenvalues of the associated scattering problem. For the direct problem, we give explicit single-valued definitions of the Jost eigenfunctions and scattering coefficients over the whole complex plane, and we characterize their discontinuous behavior across the branch cut arising from the square root behavior of the corresponding eigenvalues. We pose the inverse problem as a Riemann-Hilbert Problem on an open contour, and we reduce the problem to a standard set of linear integral equations. Finally, for comparison purposes, we present the single-sheet, branch cut formulation of the inverse scattering transform for the initial value problem with symmetric (equimodular) non-zero boundary conditions, as well as for the initial value problem with one-sided non-zero boundary conditions, and we also briefly describe the formulation of the inverse scattering transform when a different choice is made for the location of the branch cuts.
Non-Linear Sigma Model on Conifolds
Parthasarathy, R
2002-01-01
Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\\"{a}hler metrics on these manifolds. The K\\"{a}hler 2-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of 2-dimensional non-linear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the 'integration constants', arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be {\\it{non-singular}}. As the target space is Ricci flat, the perturbative 1-loop counter terms being absent, the model becomes topological. The inherent U(1) fibre over the base of the conifolds is shown to correspond to a gauge connection in the sigma model. The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action ...
Non-Linear Electrohydrodynamics in Microfluidic Devices
Directory of Open Access Journals (Sweden)
Jun Zeng
2011-03-01
Full Text Available 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.
Prinari, Barbara
2016-08-01
Soliton solutions of the focusing Ablowitz-Ladik equation with nonzero boundary conditions at infinity are derived within the framework of the inverse scattering transform (IST). After reviewing the relevant aspects of the direct and inverse problems, explicit soliton solutions are obtained which are the discrete analog of the Tajiri-Watanabe and Kuznetsov-Ma solutions to the focusing nonlinear Schrödinger equation on a finite background. Then, by performing suitable limits of the above solutions, discrete analogs of the celebrated Akhmediev and Peregrine solutions are also presented. The latter, which can be thought of as a discrete "rogue" wave, is expressed as a family of rational functions of the discrete spatial variable n ∈ ℤ and time τ ∈ ℝ, parametrically depending on the amplitude Qo of the background. These solutions, which had been recently derived by direct methods, are obtained for the first time within the framework of the IST, thus also providing a spectral characterization of the solutions and a description of the singular limit process.
Bürgel, Florian; Kazimierski, Kamil S.; Lechleiter, Armin
2017-06-01
We present a fast computational framework for the inverse medium problem in scattering, i.e. we look at discretization, reconstruction and numerical performance. The Helmholtz equation in two and three dimensions is used as a physical model of scattering including point sources and plane waves as incident fields as well as near and far field measurements. For the reconstruction of the medium, we set up a rapid variational regularization scheme and indicate favorable choices of the various parameters. The underlying paradigm is, roughly speaking, to minimize the discrepancy between the reconstruction and measured data while, at the same time, taking into account various structural a-priori information via suitable penalty terms. In particular, the involved penalty terms are designed to promote information expected in real-world environments. To this end, a combination of sparsity promoting terms, total variation, and physical bounds of the inhomogeneous medium, e.g. positivity constraints, is employed in the regularization penalty. A primal-dual algorithm is used to solve the minimization problem related to the variational regularization. The computational feasibility, performance and efficiency of the proposed approach is demonstrated for synthetic as well as experimentally measured data.
Analytical description of photon beam phase spaces in inverse Compton scattering sources
Directory of Open Access Journals (Sweden)
C. Curatolo
2017-08-01
Full Text Available We revisit the description of inverse Compton scattering sources and the photon beams generated therein, emphasizing the behavior of their phase space density distributions and how they depend upon those of the two colliding beams of electrons and photons. The main objective is to provide practical formulas for bandwidth, spectral density, brilliance, which are valid in general for any value of the recoil factor, i.e. both in the Thomson regime of negligible electron recoil, and in the deep Compton recoil dominated region, which is of interest for gamma-gamma colliders and Compton sources for the production of multi-GeV photon beams. We adopt a description based on the center of mass reference system of the electron-photon collision, in order to underline the role of the electron recoil and how it controls the relativistic Doppler/boost effect in various regimes. Using the center of mass reference frame greatly simplifies the treatment, allowing us to derive simple formulas expressed in terms of rms momenta of the two colliding beams (emittance, energy spread, etc. and the collimation angle in the laboratory system. Comparisons with Monte Carlo simulations of inverse Compton scattering in various scenarios are presented, showing very good agreement with the analytical formulas: in particular we find that the bandwidth dependence on the electron beam emittance, of paramount importance in Thomson regime, as it limits the amount of focusing imparted to the electron beam, becomes much less sensitive in deep Compton regime, allowing a stronger focusing of the electron beam to enhance luminosity without loss of mono-chromaticity. A similar effect occurs concerning the bandwidth dependence on the frequency spread of the incident photons: in deep recoil regime the bandwidth comes out to be much less dependent on the frequency spread. The set of formulas here derived are very helpful in designing inverse Compton sources in diverse regimes, giving a
Oh, Ju-Won
2016-07-04
Multiparameter full waveform inversion (FWI) applied to an elastic orthorhombic model description of the subsurface requires in theory a nine-parameter representation of each pixel of the model. Even with optimal acquisition on the Earth surface that includes large offsets, full azimuth, and multicomponent sensors, the potential for trade-off between the elastic orthorhombic parameters are large. The first step to understanding such trade-off is analysing the scattering potential of each parameter, and specifically, its scattering radiation patterns. We investigate such radiation patterns for diffraction and for scattering from a horizontal reflector considering a background isotropic model. The radiation patterns show considerable potential for trade-off between the parameters and the potentially limited resolution in their recovery. The radiation patterns of C11, C22, and C33 are well separated so that we expect to recover these parameters with limited trade-offs. However, the resolution of their recovery represented by recovered range of model wavenumbers varies between these parameters. We can only invert for the short wavelength components (reflection) of C33 while we can mainly invert for the long wavelength components (transmission) of the elastic coefficients C11 and C22 if we have large enough offsets. The elastic coefficients C13, C23, and C12 suffer from strong trade-offs with C55, C44, and C66, respectively. The trade-offs between C13 and C55, as well as C23 and C44, can be partially mitigated if we acquire P–SV and SV–SV waves. However, to reduce the trade-offs between C12 and C66, we require credible SH–SH waves. The analytical radiation patterns of the elastic constants are supported by numerical gradients of these parameters.
Nuclear-matter distributions of halo nuclei from elastic proton scattering in inverse kinematics
Energy Technology Data Exchange (ETDEWEB)
Egelhof, P.; Bauchet, A.; Fritz, S.; Geissel, H.; Gross, C.; Kraus, G.; Muenzenberg, G.; Neumaier, S.R.; Schaefer, T.; Scheidenberger, C. [Gesellschaft fuer Schwerionenforschung (GSI), D-64291 Darmstadt (Germany); Alkhazov, G.D.; Andronenko, M.N.; Gavrilov, G.E.; Khanzadeev, A.V.; Korolev, G.A.; Lobodenko, A.A.; Seliverstov, D.M.; Timofeev, N.A. [Petersburg Nuclear Physics Institute (PNPI), RU-188300 Gatchina (Russian Federation); Dobrovolsky, A.V. [Gesellschaft fuer Schwerionenforschung (GSI), D-64291 Darmstadt (Germany); Petersburg Nuclear Physics Institute (PNPI), RU-188300 Gatchina (Russian Federation); Mutterer, M. [Institut fuer Kernphysik (IKP), Technische Universitaet, D-64289 Darmstadt (Germany); Vorobyov, A.A.; Yatsoura, V.I.
2002-10-01
Proton-nucleus elastic scattering at intermediate energies, a well-established method for probing nuclear-matter density distributions of stable nuclei, was applied for the first time to exotic nuclei. This method is demonstrated to be an effective means for obtaining accurate and detailed information on the size and radial shape of halo nuclei. Absolute differential cross-sections for small-angle scattering were measured at energies near 700 MeV/u for the neutron-rich helium isotopes {sup 6}He and {sup 8}He, and more recently for the lithium isotopes {sup 6}Li, {sup 8}Li, {sup 9}Li and {sup 11}Li, using He and Li beams provided by the fragment separator FRS at GSI Darmstadt. Experiments were performed in inverse kinematics using the hydrogen-filled ionization chamber IKAR which served simultaneously as target and recoil-proton detector. For deducing nuclear-matter distributions, differential cross-sections calculated with the aid of the Glauber multiple-scattering theory, using various parametrizations for the nucleon density distributions as input, were fitted to the experimental cross-sections. The results on nuclear-matter radii and matter distributions are presented, and the significance of the data for a halo structure is discussed. Nuclear-matter distributions obtained for {sup 6}He and {sup 8}He conform with the concept that both nuclei compose of {alpha}-particle like cores and significant neutron halos. The matter distribution in {sup 11}Li exhibits, as expected from previous reaction cross-section studies with nuclear targets, the by far most extended halo component of all nuclei being investigated. In addition the present data allow a quantitative comparison of the structure of the He and Li isobars of either the mass number A=6 or A=8. The measured differential cross-sections have also been used for probing density distributions as predicted from various microscopic calculations. A few examples are presented. (orig.)
Non-linear Evolution of Rayleigh-Taylor Instability in a Radiation Supported Atmosphere
Jiang, Yan-Fei; Stone, James
2012-01-01
The non-linear regime of Rayleigh-Taylor instability (RTI) in a radiation supported atmosphere, consisting of two uniform fluids with different densities, is studied numerically. We perform simulations using our recently developed numerical algorithm for multi-dimensional radiation hydrodynamics based on a variable Eddington tensor as implemented in Athena, focusing on the regime where scattering opacity greatly exceeds absorption opacity. We find that the radiation field can reduce the growth and mixing rate of RTI, but this reduction is only significant when radiation pressure significantly exceeds gas pressure. Small scale structures are also suppressed in this case. In the non-linear regime, dense fingers sink faster than rarefied bubbles can rise, leading to asymmetric structures about the interface. By comparing the calculations that use a variable Eddington tensor (VET) versus the Eddington approximation, we demonstrate that anisotropy in the radiation field can affect the non-linear development of RTI...
Non-Linear Unit Root Properties of Crude Oil Production
Svetlana Maslyuk; Russell Smyth
2007-01-01
While there is good reason to expect crude oil production to be non-linear, previous studies that have examined the stochastic properties of crude oil production have assumed that crude oil production follows a linear process. If crude oil production is a non-linear process, conventional unit root tests, which assume linear and systematic adjustment, could interpret departure from linearity as permanent stochastic disturbances. The objective of this paper is to test for non-linearities and un...
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.
Non-linear vorticity upsurge in Burgers flow
Lam, F
2016-01-01
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initial data, modelling simple shears and wall boundary layers, are chosen for our computations. Most of the solutions are carried out well into the fully turbulent regime over finely-resolved scales in space and in time. It is found that an abrupt spatio-temporal concentration in shear constitutes an essential part during the flow evolution. The vorticity surge has been instigated by the non-linearity complying with instantaneous enstrophy production while ad hoc disturbances play no role in the process. In particular, the present method predicts the precipitous vorticity re-distribution and accumulation, predominantly over localised regions of minute dimension. The growth rate depends on viscosity and is a strong function of initial data. Nevertheless, the long-time energy decay is history-independent and is inversely proportional to ti...
Q-operators, Yangian invariance and the quantum inverse scattering method
Frassek, Rouven
2014-01-01
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with the Yang-Baxter equation which is the key relation in this systematic approach to study integrable models. Our main interest concerns rational integrable spin chains and lattice models. We recall the relation among them and how they can be solved using Bethe ansatz methods incorporating so-called Q-functions. In order to remind the reader how the Yangian emerges in this context, an overview of its so-called RTT-realization is provided. The main part is based on the author's original publications. Firstly, we construct Q-operators whose eigenvalues yield the Q-functions for rational homogeneous spin chains. The Q-operators are introduced as traces over certain monodromies of R-operators. Our construction allows us to derive the hierarchy of commuting Q-operators and the fun...
Directory of Open Access Journals (Sweden)
Y. Sakai
2017-06-01
Full Text Available Inverse Compton scattering (ICS is a unique mechanism for producing fast pulses—picosecond and below—of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by this source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K-edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.
Sakai, Y.; Gadjev, I.; Hoang, P.; Majernik, N.; Nause, A.; Fukasawa, A.; Williams, O.; Fedurin, M.; Malone, B.; Swinson, C.; Kusche, K.; Polyanskiy, M.; Babzien, M.; Montemagno, M.; Zhong, Z.; Siddons, P.; Pogorelsky, I.; Yakimenko, V.; Kumita, T.; Kamiya, Y.; Rosenzweig, J. B.
2017-06-01
Inverse Compton scattering (ICS) is a unique mechanism for producing fast pulses—picosecond and below—of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by this source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K -edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.
X-ray generation by inverse Compton scattering at the superconducting RF test facility
Energy Technology Data Exchange (ETDEWEB)
Shimizu, Hirotaka, E-mail: hirotaka@post.kek.jp [KEK, 1-1 Oho, Tsukuba 305-0801, Ibaraki (Japan); Akemoto, Mitsuo; Arai, Yasuo; Araki, Sakae; Aryshev, Alexander; Fukuda, Masafumi; Fukuda, Shigeki; Haba, Junji; Hara, Kazufumi; Hayano, Hitoshi; Higashi, Yasuo; Honda, Yosuke; Honma, Teruya; Kako, Eiji; Kojima, Yuji; Kondo, Yoshinari; Lekomtsev, Konstantin; Matsumoto, Toshihiro; Michizono, Shinichiro; Miyoshi, Toshinobu [KEK, 1-1 Oho, Tsukuba 305-0801, Ibaraki (Japan); and others
2015-02-01
Quasi-monochromatic X-rays with high brightness have a broad range of applications in fields such as life sciences, bio-, medical applications, and microlithography. One method for generating such X-rays is via inverse Compton scattering (ICS). X-ray generation experiments using ICS were carried out at the superconducting RF test facility (STF) accelerator at KEK. A new beam line, newly developed four-mirror optical cavity system, and new X-ray detector system were prepared for experiments downstream section of the STF electron accelerator. Amplified pulsed photons were accumulated into a four-mirror optical cavity and collided with an incoming 40 MeV electron beam. The generated X-rays were detected using a microchannel plate (MCP) detector for X-ray yield measurements and a new silicon-on-insulator (SOI) detector system for energy measurements. The detected X-ray yield by the MCP detector was 1756.8±272.2 photons/(244 electron bunches). To extrapolate this result to 1 ms train length under 5 Hz operations, 4.60×10{sup 5} photons/1%-bandwidth were obtained. The peak X-ray energy, which was confirmed by the SOI detector, was 29 keV, and this is consistent with ICS X-rays.
Na, Seong-Won; Kallivokas, Loukas F.
2008-03-01
In this article we discuss a formal framework for casting the inverse problem of detecting the location and shape of an insonified scatterer embedded within a two-dimensional homogeneous acoustic host, in terms of a partial-differential-equation-constrained optimization approach. We seek to satisfy the ensuing Karush-Kuhn-Tucker first-order optimality conditions using boundary integral equations. The treatment of evolving boundary shapes, which arise naturally during the search for the true shape, resides on the use of total derivatives, borrowing from recent work by Bonnet and Guzina [1-4] in elastodynamics. We consider incomplete information collected at stations sparsely spaced at the assumed obstacle’s backscattered region. To improve on the ability of the optimizer to arrive at the global optimum we: (a) favor an amplitude-based misfit functional; and (b) iterate over both the frequency- and wave-direction spaces through a sequence of problems. We report numerical results for sound-hard objects with shapes ranging from circles, to penny- and kite-shaped, including obstacles with arbitrarily shaped non-convex boundaries.
Inverse scattering problem for Sturm-Liouville operator on non-compact A-graph. Uniqueness result.
Directory of Open Access Journals (Sweden)
Mikhail Ignatyev
2015-12-01
Full Text Available We consider a connected metric graph with the following property: each two cycles can have at most one common point. Such graphs are called A-graphs. On noncompact A-graph we consider a scattering problem for Sturm--Liouville differential operator with standard matching conditions in the internal vertices. Transport, spectral and scattering problems for differential operators on graphs appear frequently in mathematics, natural sciences and engineering. In particular, direct and inverse problems for such operators are used to construct and study models in mechanics, nano-electronics, quantum computing and waveguides. The most complete results on (both direct and inverse spectral problems were achieved in the case of Sturm--Liouville operators on compact graphs, in the noncompact case there are no similar general results. In this paper, we establish some properties of the spectral characteristics and investigate the inverse problem of recovering the operator from the scattering data. A uniqueness theorem for such inverse problem is proved.
Non-linear BFKL dynamics: color screening vs. gluon fusion
Fiore, R; Zoller, V R
2012-01-01
A feasible mechanism of unitarization of amplitudes of deep inelastic scattering at small values of Bjorken $x$ is the gluon fusion. However, its efficiency depends crucially on the vacuum color screening effect which accompanies the multiplication and the diffusion of BFKL gluons from small to large distances. From the fits to lattice data on field strength correlators the propagation length of perturbative gluons is $R_c\\simeq 0.2-0.3$ fermi. The probability to find a perturbative gluon with short propagation length at large distances is suppressed exponentially. It changes the pattern of (dif)fusion dramatically. The magnitude of the fusion effect appears to be controlled by the new dimensionless parameter $\\sim R_c^2/8B$, with the diffraction cone slope $B$ standing for the characteristic size of the interaction region. It should slowly $\\propto 1/\\ln Q^2$ decrease at large $Q^2$. Smallness of the ratio $R_c^2/8B$ makes the non-linear effects rather weak even at lowest Bjorken $x$ available at HERA. We re...
Graphical and Analytical Analysis of the Non-Linear PLL
de Boer, Bjorn; Radovanovic, S.; Annema, Anne J.; Nauta, Bram
The fixed width control pulses from the Bang-Bang Phase Detector in non-linear PLLs allow for operation at higher data rates than the linear PLL. The high non-linearity of the Bang- Bang Phase Detector gives rise to unwanted effects, such as limit-cycles, not yet fully described. This paper
Non-linear stochastic response of a shallow cable
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2004-01-01
The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two-degrees-of-freedom...
Non-linear Frequency Scaling Algorithm for FMCW SAR Data
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
This paper presents a novel approach for processing data acquired with Frequency Modulated Continuous Wave (FMCW) dechirp-on-receive systems by using a non-linear frequency scaling algorithm. The range frequency non-linearity correction, the Doppler shift induced by the continuous motion and the ran
Non Linear Gauge Fixing for FeynArts
Gajdosik, Thomas
2007-01-01
We review the non-linear gauge-fixing for the Standard Model, proposed by F. Boudjema and E. Chopin, and present our implementation of this non-linear gauge-fixing to the Standard Model and to the minimal supersymmetric Standard Model in FeynArts.
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Indian Academy of Sciences (India)
I Ahmad; M R Arafah
2006-03-01
Elastic scattering of 800 MeV/c pions by 12C has been studied in the diffraction model with a view to determine pion optical potential by the method of inversion. Finding an earlier diffraction model analysis to be deficient in some respects, we propose a Glauber model based parametrization for the elastic -matrix and show that it provides an exceedingly good fit to the pion-carbon data. The proposed elastic -matrix gives a closed expression for the pion-12C optical potential by the method of inversion in the high energy approximation.
Rizzuti, G.; Gisolf, A.
2017-03-01
We study a reconstruction algorithm for the general inverse scattering problem based on the estimate of not only medium properties, as in more conventional approaches, but also wavefields propagating inside the computational domain. This extended set of unknowns is justified as a way to prevent local minimum stagnation, which is a common issue for standard methods. At each iteration of the algorithm, (i) the model parameters are obtained by solution of a convex problem, formulated from a special bilinear relationship of the data with respect to properties and wavefields (where the wavefield is kept fixed), and (ii) a better estimate of the wavefield is calculated, based on the previously reconstructed properties. The resulting scheme is computationally convenient since step (i) can greatly benefit from parallelization and the wavefield update (ii) requires modeling only in the known background model, which can be sped up considerably by factorization-based direct methods. The inversion method is successfully tested on synthetic elastic datasets.
Non-linear dynamics of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
by the rotation of the aerodynamic load and the curvature, as well as inertial induced non-linearities caused by the support point motion. The non-linear partial differential equations of motion in the moving frame of reference have been discretized, using the fixed base eigenmodes as a functional basis......The paper deals with the formulation of non-linear vibrations of a wind turbine wing described in a wing fixed moving coordinate system. The considered structural model is a Bernoulli-Euler beam with due consideration to axial twist. The theory includes geometrical non-linearities induced....... Important non-linear couplings between the fundamental blade mode and edgewise modes have been identified based on a resonance excitation of the wing, caused by a harmonically varying support point motion with the circular frequency omega. Assuming that the fundamental blade and edgewise eigenfrequencies...
Employment of CB models for non-linear dynamic analysis
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.
Non-linear dielectric monitoring of biological suspensions
Energy Technology Data Exchange (ETDEWEB)
Treo, E F; Felice, C J [Departamento de BioingenierIa, Universidad Nacional de Tucuman and Consejo Nacional de Investigaciones Cientificas y Tecnicas. CC327, CP4000, San Miguel de Tucuman (Argentina)
2007-11-15
Non-linear dielectric spectroscopy as a tool for in situ monitoring of enzyme assumes a non-linear behavior of the sample when a sinusoidal voltage is applied to it. Even many attempts have been made to improve the original experiments, all of them had limited success. In this paper we present upgrades made to a non-linear dielectric spectrometer developed and the results obtained when using different cells. We emphasized on the electrode surface, characterizing the grinding and polishing procedure. We found that the biological medium does not behave as expected, and the non-linear response is generated in the electrode-electrolyte interface. The electrochemistry of this interface can bias unpredictably the measured non-linear response.
DESIGN OF A GAMMA-RAY SOURCE BASED ON INVERSE COMPTON SCATTERING AT THE FAST SUPERCONDUCTING LINAC
Energy Technology Data Exchange (ETDEWEB)
Mihalcea, D. [NICADD, DeKalb; Jacobson, B. [RadiaBeam Tech.; Murokh, A. [Fermilab; Piot, P. [Fermilab; Ruan, J. [Fermilab
2016-10-10
A watt-level average-power gamma-ray source is currently under development at the Fermilab Accelerator Science & Technology (FAST) facility. The source is based on the Inverse Compton Scattering of a high-brightness 300-MeV beam against a high-power laser beam circulating in an optical cavity. The back scattered gamma rays are expected to have photon energies up to 1.5 MeV. This paper discusses the optimization of the source, its performances, and the main challenges ahead.
Quad-copter UAV BLDC Motor Control: Linear v/s non-linear control maps
Directory of Open Access Journals (Sweden)
Deep Parikh
2015-08-01
Full Text Available This paper presents some investigations and comparison of using linear versus non-linear static motor-control maps for the speed control of a BLDC (Brush Less Direct Current motors used in quad-copter UAV (Unmanned Aerial Vehicles. The motor-control map considered here is the inverse of the static map relating motor-speed output to motor-voltage input for a typical out-runner type Brushless DC Motors (BLDCM. Traditionally, quad-copter BLDC motor speed control uses simple linear motor-control map defined by the motor-constant specification. However, practical BLDC motors show non-linear characteristic, particularly when operated across wide operating speed-range as is commonly required in quad-copter UAV flight operations. In this paper, our investigations to compare performance of linear versus non-linear motor-control maps are presented. The investigations cover simulation-based and experimental study of BLDC motor speed control systems for quad-copter vehicle available. First the non-linear map relating rotor RPM to motor voltage for quad-copter BLDC motor is obtained experimentally using an optical speed encoder. The performance of the linear versus non-linear motor-control-maps for the speed control are studied. The investigations also cover study of time-responses for various standard test input-signals e.g. step, ramp and pulse inputs, applied as the reference speed-commands. Also, simple 2-degree of freedom test-bed is developed in our laboratory to help test the open-loop and closed-loop experimental investigations. The non-linear motor-control map is found to perform better in BLDC motor speed tracking control performance and thereby helping achieve better quad-copter roll-angle attitude control.
Development and characterization of a tunable ultrafast X-ray source via inverse-Compton-scattering
Energy Technology Data Exchange (ETDEWEB)
Jochmann, Axel
2014-07-01
will serve as a milestone and starting point for the scaling of the X-ray flux based on available interaction parameters of an ultrashort bright X-ray source at the ELBE center for high power radiation sources. The knowledge of the spatial and spectral distribution of photons from an inverse Compton scattering source is essential in designing future experiments as well as for tailoring the X-ray spectral properties to an experimental need.
Energy Technology Data Exchange (ETDEWEB)
Rijssel, Jos van; Kuipers, Bonny W.M.; Erné, Ben H., E-mail: B.H.Erne@uu.nl
2014-03-15
A numerical inversion method known from the analysis of light scattering by colloidal dispersions is now applied to magnetization curves of ferrofluids. The distribution of magnetic particle sizes or dipole moments is determined without assuming that the distribution is unimodal or of a particular shape. The inversion method enforces positive number densities via a non-negative least squares procedure. It is tested successfully on experimental and simulated data for ferrofluid samples with known multimodal size distributions. The created computer program MINORIM is made available on the web. - Highlights: • A method from light scattering is applied to analyze ferrofluid magnetization curves. • A magnetic size distribution is obtained without prior assumption of its shape. • The method is tested successfully on ferrofluids with a known size distribution. • The practical limits of the method are explored with simulated data including noise. • This method is implemented in the program MINORIM, freely available online.
Directory of Open Access Journals (Sweden)
S. Bagchi
2015-12-01
Full Text Available The Isoscalar Giant Monopole Resonance (ISGMR and the Isoscalar Giant Dipole Resonance (ISGDR compression modes have been studied in the doubly-magic unstable nucleus 56Ni. They were measured by inelastic α-particle scattering in inverse kinematics at 50 MeV/u with the MAYA active target at the GANIL facility. The centroid of the ISGMR has been obtained at Ex=19.1±0.5 MeV. Evidence for the low-lying part of the ISGDR has been found at Ex=17.4±0.7 MeV. The strength distribution for the dipole mode shows similarity with the prediction from the Hartree–Fock (HF based random-phase approximation (RPA [1]. These measurements confirm inelastic α-particle scattering as a suitable probe for exciting the ISGMR and the ISGDR modes in radioactive isotopes in inverse kinematics.
Music algorithm for imaging of a sound-hard arc in limited-view inverse scattering problem
Park, Won-Kwang
2017-07-01
MUltiple SIgnal Classification (MUSIC) algorithm for a non-iterative imaging of sound-hard arc in limited-view inverse scattering problem is considered. In order to discover mathematical structure of MUSIC, we derive a relationship between MUSIC and an infinite series of Bessel functions of integer order. This structure enables us to examine some properties of MUSIC in limited-view problem. Numerical simulations are performed to support the identified structure of MUSIC.
基于逆散射理论的地震波速度正则化反演%Regularized seismic velocity inversion based on inverse scattering theory
Institute of Scientific and Technical Information of China (English)
段晓亮; 王一博; 杨慧珠
2015-01-01
本文基于逆散射理论利用正则化有限差分对比源反演算法对地震波传播速度进行反演，该方法是基于波动方程的频率域波形反演算法，利用非线性共轭梯度法，通过最小化目标优化函数不断迭代更新速度模型。由于地球物理反演问题的病态性和不稳定性，通过基于反演参数总变差的正则化处理，使反演问题变为良性问题且算法具有较强的抗噪声干扰能力。反演过程中使用了频率-空间域9点差分正演算子以及PML吸收边界条件。与其他反演算法相比，由于背景模型在反演迭代过程中保持不变，可以避免在每次迭代过程中重新构造正演算子及矩阵分解等相关计算过程，使得该算法非常适合于大规模三维反演计算。此外，本文采用基于MPI的并行计算，进一步提高了反演计算的效率。二维CSEG模型反演结果表明该方法可以反演得到高分辨率的地震波速度重建结果，为地震勘探数据处理及解释提供准确的速度信息。%In this paper, the regularized finite difference contrast source inversion algorithm based on inverse scattering theory is utilized to invert the seismic velocity distribution in the underground medium, and this algorithm is a waveform inversion method in frequency domain based on wave equation. Velocity distribution is updated iteratively by minimizing the cost function using the nonlinear conjugate gradient method. The geophysical inversion problem has the characters of ill-posedness and instability, we handle this problem by adding an additional regularization item based on total variation of inversion parameter, making the inversion problem become a well-posed problem, and the algorithm has the ability of anti-noise interference. In the inversion process we use the frequency-space domain 9-point difference propagation operator under PML absorption boundary condition. Compared with other inversion algorithm
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
Energy Technology Data Exchange (ETDEWEB)
Romero, MarIa de los Angeles Sandoval; Weder, Ricardo [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-726, Mexico DF 01000 (Mexico)
2006-09-15
We consider nonlinear Schroedinger equations with a potential, and non-local nonlinearities, that are models in mesoscopic physics, for example of a quantum capacitor, and that are also models of molecular structure. We study in detail the initial value problem for these equations, in particular, existence and uniqueness of local and global solutions, continuous dependence on the initial data and regularity. We allow for a large class of unbounded potentials. We have no restriction on the growth at infinity of the positive part of the potential. We also construct the scattering operator in the case of potentials that go to zero at infinity. Furthermore, we give a method for the unique reconstruction of the potential from the small amplitude limit of the scattering operator. In the case of the quantum capacitor, our method allows us to uniquely reconstruct all the physical parameters from the small amplitude limit of the scattering operator.
Indian Academy of Sciences (India)
Manpreet Singh; Bhajan Singh; B S Sandhu
2008-01-01
An inverse response matrix converts the observed pulse-height distribution of a NaI(Tl) scintillation detector to a true photon spectrum. This also results in extraction of intensity and energy distributions of multiply scattered events originating from interactions of 279 keV photons with thick targets of bronze. The observed pulse-height distributions are a composite of singly and multiply scattered events in addition to bremmstrahlung originating from slowing down of Compton and photo-electrons in thick targets. To evaluate the contribution of multiply scattered events, the spectrum of singly scattered events contributing to inelastic Compton peak is reconstructed analytically. The optimum thickness (saturation depth), at which the number of multiply scattered events saturate, has been evaluated in different energy bin meshes chosen for scintillation detector response unfolding. Monte Carlo calculations based upon the package developed by Bauer and Pattison (Compton scattering experiments at the HMI (1981), HMI-B 364, pp. 1-106) supports the present experimental results.
Energy Technology Data Exchange (ETDEWEB)
Vladas Tvaskis; John Arrington; Michael Christy; Rolf Ent; Cynthia Keppel; Yongguang Liang; Grahame Vittorini
2006-01-26
The effects of two-photon exchange corrections, suggested to explain the difference between measurements of the proton elastic electromagnetic form factors using the polarization transfer and Rosenbluth techniques, have been studied in elastic and inelastic scattering data. Such corrections could introduce epsilon-dependent non-linearities in inelastic Rosenbluth separations, where epsilon is the virtual photon polarization parameter. It is concluded that such non-linear effects are consistent with zero for elastic, resonance, and deep-inelastic scattering for all Q{sup 2} and W{sup 2} values measured.
Frayer, C; Mykytyuk, Ya V; Perry, P A
2009-01-01
This is the first in a series of papers on scattering theory for one-dimensional Schr\\"odinger operators with highly singular potentials $q\\in H^{-1}(R)$. In this paper, we study Miura potentials $q$ associated to positive Schr\\"odinger operators that admit a Riccati representation $q=u'+u^2$ for a unique $u\\in L^1(R)\\cap L^2(R)$. Such potentials have a well-defined reflection coefficient $r(k)$ that satisfies $|r(k)|<1$ and determines $u$ uniquely. We show that the scattering map $S:u\\mapsto r$ is real-analytic with real-analytic inverse. To do so, we exploit a natural complexification of the scattering map associated with the ZS-AKNS system. In subsequent papers, we will consider larger classes of potentials including singular potentials with bound states.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
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.
NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS
Institute of Scientific and Technical Information of China (English)
Yang Xiaodong; Chen Li-Qun
2006-01-01
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
An Inverse Electromagnetic Scattering Method for One-Dimensional Inhomogeneous Media
Institute of Scientific and Technical Information of China (English)
LIN Zhi-Wei; XU Xin; ZHANG Xiao-Juan; FANG Guang-You
2011-01-01
A frequency-domain inversion scheme for reconstructing the permittivity profile of one-dimensional inhomogeneous media is proposed. The generalized reflection coefficients and the generalized transmission coefficients of the inhomogeneous media are used as the input data of the inverse model. A Newton-like iterative algorithm known as the generalized pulse-spectrum technique with the Tikhonov regularization is applied to solve the inverse problem. Novel boundary conditions are proposed for the inverse problem and therefore the permittivity at the boundary of the inhomogeneous media is not required as prior knowledge. The choice of frequency points of the frequency-domain method is also investigated. Numerical examples are carried out to validate the inversion technique. Good agreements between the reconstructed profiles and the true profiles are shown.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper presents a method on non-linear correction of broadband LFMCW signal utilizing its relativenonlinear error. The deriving procedure and the results simulated by a computer and tested by a practical system arealso introduced. The method has two obvious advantages compared with the previous methods: (1) Correction has norelation with delay time td and sweep bandwidth B; (2) The inherent non-linear error of VCO has no influence on thecorrection and its last results.
Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.
Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J
2016-10-03
Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods.
Non-linear Elasticity and Monitoring of Stress in the Focus of an Earthquake
Bakulin, V.; Bakulin, A.
2001-05-01
Non-linear elasticity proved to give comprehensive framework for relating seismic velocities in rocks to stress. This powerful theory allows attacking the problem of estimating stress state at the focus of earthquakes. Such idea has been proposed long time ago [Kostrov and Nikitin, 1968] however its implementation requires a-priori knowledge of non-linear rock properties. Three non-linear constants needed to describe variation of any velocity with stress are typically estimated from core measurements [Bakulin et al., 2000]. More reliable estimates can be obtained from multi-mode inversions of borehole acoustic data [Sinha, 1996]. Nevertheless database of non-linear formation constants is still very limited. More measurements are required to estimate non-linear rock properties on larger scale and with independent stress constraints. Such measurements can be done in mines [Bakulin and Bakulin, 1999] or in hydrocarbon reservoirs where time-dependent pressure measurements are available. Without knowledge of non-linear rock properties seismic waves can still bring information about directions of tectonic stresses. In particular, shear wave polarizations can deliver directions of principal stresses in the focus of an earthquake, provided the overburden effects were removed. If rock non-linear properties are independently derived then estimation of stress magnitudes becomes feasible. Such techniques were applied in mining environment [Bakulin and Bakulin, 1999]. They may become routine for monitoring stress state in the focus of earthquakes and therefore can be used for forecasting the seismic activity. Bakulin, A. V., Troyan, V. N., and Bakulin, V. N., 2000, Acoustoelasticity of rocks, St. Petersburg (in Russian). Bakulin, V. and Bakulin, A., 1999, Acoustopolarizational method of measuring stress in rock mass and determination of Murnaghan constants: 69th Annual Internat. Mtg., Soc. Expl. Geophys., 1971-1974. Kostrov, B.V., and Nikitin, L.V., 1968, Influence of initial
Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
Lee, Seungjin; Schlotterer, Oliver
2015-01-01
Recent progress on scattering amplitudes in super Yang--Mills and superstring theory benefitted from the use of multiparticle superfields. They universally capture tree-level subdiagrams, and their generating series solve the non-linear equations of ten-dimensional super Yang--Mills. We provide simplified recursions for multiparticle superfields and relate them to earlier representations through non-linear gauge transformations of their generating series. In this work we discuss the gauge transformations which enforce their Lie symmetries as suggested by the Bern--Carrasco--Johansson duality between color and kinematics. Another gauge transformation due to Harnad and Shnider is shown to streamline the theta-expansion of multiparticle superfields, bypassing the need to use their recursion relations beyond the lowest components. The findings of this work tremendously simplify the component extraction from kinematic factors in pure spinor superspace.
Sevick-Muraca, E M; Heintzelman, D L; Lee, J; Troy, T L; Paithankar, D Y
1997-12-01
From analytical and numerical solutions that predict the scattering of diffuse photon density waves and from experimental measurements of changes in phase shift theta and ac amplitude demodulation M caused by the presence of single and double cylindrical heterogeneities, we show that second- and higher-order perturbations can affect the prediction of the propagation characteristics of diffuse photon density waves. Our experimental results for perfect absorbers in a lossless medium suggest that the performance of fast inverse-imaging algorithms that use first-order Born or Rytov approximations might have inherent limitations compared with inverse solutions that use iterative solutions of a linear perturbation equation or numerical solutions of the diffusion equation.
Massive Neutrinos and the Non-linear Matter Power Spectrum
Bird, Simeon; Haehnelt, Martin G
2011-01-01
We perform an extensive suite of N-body simulations of the matter power spectrum, incorporating massive neutrinos in the range M = 0.15-0.6 eV, probing the non-linear regime at scales k < 10 hMpc-1 at z < 3. We extend the widely used HALOFIT approximation (Smith et al. 2003) to account for the effect of massive neutrinos on the power spectrum. In the strongly non-linear regime HALOFIT systematically over-predicts the suppression due to the free-streaming of the neutrinos. The maximal discrepancy occurs at k \\sim 1hMpc-1, and is at the level of 10% of the total suppression. Most published constraints on neutrino masses based on HALOFIT are not affected, as they rely on data probing the matter power spectrum in the linear or mildly non-linear regime. However, predictions for future galaxy, Lyman-alpha forest and weak lensing surveys extending to more non-linear scales will benefit from the improved approximation to the non-linear matter power spectrum we provide. Our approximation reproduces the induced n...
Analytical exact solution of the non-linear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica
2011-07-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
The Importance of Non-Linearity on Turbulent Fluxes
DEFF Research Database (Denmark)
Rokni, Masoud
2007-01-01
Two new non-linear models for the turbulent heat fluxes are derived and developed from the transport equation of the scalar passive flux. These models are called as non-linear eddy diffusivity and non-linear scalar flux. The structure of these models is compared with the exact solution which...... is derived from the Cayley-Hamilton theorem and contains a three term-basis plus a non-linear term due to scalar fluxes. In order to study the performance of the model itself, all other turbulent quantities are taken from a DNS channel flow data-base and thus the error source has been minimized. The results...... are compared with the DNS channel flow and good agreement is achieved. It has been shown that the non-linearity parts of the models are important to capture the true path of the streamwise scalar fluxes. It has also been shown that one of model constant should have negative sign rather than positive, which had...
Daudé, Thierry
2017-01-01
In this paper, the authors study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, they establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. The authors also use the miraculous property (quoting Chandrasekhar)-that the Dirac equation can be separated into radial and angular ordinary differential equations-to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, the authors use this expression of ...
Generalized non-linear strength theory and transformed stress space
Institute of Scientific and Technical Information of China (English)
YAO Yangping; LU Dechun; ZHOU Annan; ZOU Bo
2004-01-01
Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.
An algorithm for earthwork allocation considering non-linear factors
Institute of Scientific and Technical Information of China (English)
WANG Ren-chao; LIU Jin-fei
2008-01-01
For solving the optimization model of earthwork allocation considering non-linear factors, a hybrid al-gorithm combined with the ant algorithm (AA) and particle swarm optimization (PSO) is proposed in this pa-per. Then the proposed method and the LP method are used respectively in solving a linear allocation model of a high rockfill dam project. Results obtained by these two methods are compared each other. It can be conclu-ded that the solution got by the proposed method is extremely approximate to the analytic solution of LP method. The superiority of the proposed method over the LP method in solving a non-linear allocation model is illustrated by a non-linear case. Moreover, further researches on improvement of the algorithm and the allocation model are addressed.
Non-linear behaviour of large-area avalanche photodiodes
Fernandes, L M P; Monteiro, C M B; Santos, J M; Morgado, R E
2002-01-01
The characterisation of photodiodes used as photosensors requires a determination of the number of electron-hole pairs produced by scintillation light. One method involves comparing signals produced by X-ray absorptions occurring directly in the avalanche photodiode with the light signals. When the light is derived from light-emitting diodes in the 400-600 nm range, significant non-linear behaviour is reported. In the present work, we extend the study of the linear behaviour to large-area avalanche photodiodes, of Advanced Photonix, used as photosensors of the vacuum ultraviolet (VUV) scintillation light produced by argon (128 nm) and xenon (173 nm). We observed greater non-linearities in the avalanche photodiodes for the VUV scintillation light than reported previously for visible light, but considerably less than the non-linearities observed in other commercially available avalanche photodiodes.
Pattern formation due to non-linear vortex diffusion
Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.
Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.
Non-linear system identification in flow-induced vibration
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D.; Zeldin, B.A. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corp., Houston, TX (United States)
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
Non-linear Growth Models in Mplus and SAS.
Grimm, Kevin J; Ram, Nilam
2009-10-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included.
Change-Of-Bases Abstractions for Non-Linear Systems
Sankaranarayanan, Sriram
2012-01-01
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change-of-basis transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, the techniques developed here apply to continuous systems defined by Ordinary Differential Equations (ODEs), discrete systems defined by transition systems and hybrid systems that combine continuous as well as discrete subsystems. The techniques presented here allow us to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding an alge...
Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles
Shakra, Farah Abou
2012-01-01
Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering for a class of non star-shaped obstacles called illuminated from exterior. The main tool we use is the method of multipliers with weights that generalize the Morawetz multiplier to suit the geometry of the obstacle.
Non-linear growth and condensation in multiplex networks
Nicosia, Vincenzo; Latora, Vito; Barthelemy, Marc
2013-01-01
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which a single node connects to nearly all other nodes of a layer.
Realization of non-linear coherent states by photonic lattices
Directory of Open Access Journals (Sweden)
Shahram Dehdashti
2015-06-01
Full Text Available 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.
Comparison of Simulated and Measured Non-linear Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are rst compared with the linear...... simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound eld is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both...
Non-linear effects in bunch compressor of TARLA
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.
Foundations of the non-linear mechanics of continua
Sedov, L I
1966-01-01
International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable
Realization of non-linear coherent states by photonic lattices
Energy Technology Data Exchange (ETDEWEB)
Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn [State Key Laboratory of Modern Optical Instrumentations, Zhejiang University, Hangzhou 310027 (China); The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027 (China); Liu, Jiarui, E-mail: jrliu@zju.edu.cn; Yu, Faxin [School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027 (China)
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.
Daeichin, Verya; Bosch, Johan G; Needles, Andrew; Foster, F Stuart; van der Steen, Antonius; de Jong, Nico
2015-02-01
There is increasing use of ultrasound contrast agent in high-frequency ultrasound imaging. However, conventional contrast detection methods perform poorly at high frequencies. We performed systematic in vitro comparisons of subharmonic, non-linear fundamental and ultraharmonic imaging for different depths and ultrasound contrast agent concentrations (Vevo 2100 system with MS250 probe and MicroMarker ultrasound contrast agent, VisualSonics, Toronto, ON, Canada). We investigated 4-, 6- and 10-cycle bursts at three power levels with the following pulse sequences: B-mode, amplitude modulation, pulse inversion and combined pulse inversion/amplitude modulation. The contrast-to-tissue (CTR) and contrast-to-artifact (CAR) ratios were calculated. At a depth of 8 mm, subharmonic pulse-inversion imaging performed the best (CTR = 26 dB, CAR = 18 dB) and at 16 mm, non-linear amplitude modulation imaging was the best contrast imaging method (CTR = 10 dB). Ultraharmonic imaging did not result in acceptable CTRs and CARs. The best candidates from the in vitro study were tested in vivo in chicken embryo and mouse models, and the results were in a good agreement with the in vitro findings.
On form factors of the conjugated field in the non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2011-05-15
Izergin-Korepin's lattice discretization of the non-linear Schroedinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacing limit, to those of the conjugated field operator in the continuous model. We also compute the large-volume asymptotic behavior of such form factors in the continuous model. These are in particular characterized by Fredholm determinants of operators acting on closed contours. We provide a way of defining these Fredholm determinants in the case of generic paramaters. (orig.)
Quad-copter UAV BLDC Motor Control: Linear v/s non-linear control maps
Deep Parikh; Jignesh Patel; Jayesh Barve
2015-01-01
This paper presents some investigations and comparison of using linear versus non-linear static motor-control maps for the speed control of a BLDC (Brush Less Direct Current) motors used in quad-copter UAV (Unmanned Aerial Vehicles). The motor-control map considered here is the inverse of the static map relating motor-speed output to motor-voltage input for a typical out-runner type Brushless DC Motors (BLDCM). Traditionally, quad-copter BLDC motor speed control uses simple linear motor-cont...
DEFF Research Database (Denmark)
Garde, Henrik
2017-01-01
Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions, exactly characterize the inhomogeneities based on monotonicity....... For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method...
On form factors of the conjugated field in the non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2011-05-15
Izergin-Korepin's lattice discretization of the non-linear Schroedinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacing limit, to those of the conjugated field operator in the continuous model. We also compute the large-volume asymptotic behavior of such form factors in the continuous model. These are in particular characterized by Fredholm determinants of operators acting on closed contours. We provide a way of defining these Fredholm determinants in the case of generic paramaters. (orig.)
Canonical structure of evolution equations with non-linear dispersive terms
Indian Academy of Sciences (India)
B Talukdar; J Shamanna; S Ghosh
2003-07-01
The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The speciﬁc results presented refer to the third- and ﬁfth-order equations of the so-called distinguished subclass.
Non-linear magnetization effects within the Kosterlitz-Thouless theory
Benfatto, Lara; Castellani, Claudio; Giamarchi, Thierry
2008-03-01
Recent experiments in cuprate superconductors have attracted the attention on the role of vortex fluctuations. Measurements of the field-induced magnetization showed that the correlation length diverge exponentially, as predicted within the Kosterlitz-Thouless (KT) theory. However, it is somehow puzzling thepersistence of strong non-linear magnetization effects at low field. Here we address this issue by means of a new theoretical approach to the KT transition at finite magnetic field, based on the sine-Gordon model. This approach is particularly useful in two respects. First, it leads to a straightforward definition of the field-induced magnetization as a function of the external magnetic field H instead of the magnetic induction B, which is crucial to get a consistent description of the Meissner phase. Second, it allows us to identify the cross-over field Hcr from linear to non-linear magnetization both below and above the transition. Above TKT Hcr turns out to scale as the inverse correlation length, so that it decreases as the transition is approached. As a consequence, the fact that only the non-linear regime is accessible experimentally should be interpreted as a typical signature of the fast divergence of the correlation length within the KT theory. L.Benfatto, C.Castellani and T.Giamarchi, Phys. Rev. Lett. 99, 207002 (2007)
Schumacher, F.; Friederich, W.; Lamara, S.
2016-02-01
We present a new conceptual approach to scattering-integral-based seismic full waveform inversion (FWI) that allows a flexible, extendable, modular and both computationally and storage-efficient numerical implementation. To achieve maximum modularity and extendability, interactions between the three fundamental steps carried out sequentially in each iteration of the inversion procedure, namely, solving the forward problem, computing waveform sensitivity kernels and deriving a model update, are kept at an absolute minimum and are implemented by dedicated interfaces. To realize storage efficiency and maximum flexibility, the spatial discretization of the inverted earth model is allowed to be completely independent of the spatial discretization employed by the forward solver. For computational efficiency reasons, the inversion is done in the frequency domain. The benefits of our approach are as follows: (1) Each of the three stages of an iteration is realized by a stand-alone software program. In this way, we avoid the monolithic, unflexible and hard-to-modify codes that have often been written for solving inverse problems. (2) The solution of the forward problem, required for kernel computation, can be obtained by any wave propagation modelling code giving users maximum flexibility in choosing the forward modelling method. Both time-domain and frequency-domain approaches can be used. (3) Forward solvers typically demand spatial discretizations that are significantly denser than actually desired for the inverted model. Exploiting this fact by pre-integrating the kernels allows a dramatic reduction of disk space and makes kernel storage feasible. No assumptions are made on the spatial discretization scheme employed by the forward solver. (4) In addition, working in the frequency domain effectively reduces the amount of data, the number of kernels to be computed and the number of equations to be solved. (5) Updating the model by solving a large equation system can be
Numerical simulation of non-linear phenomena in geotechnical engineering
DEFF Research Database (Denmark)
Sørensen, Emil Smed
Geotechnical problems are often characterized by the non-linear behavior of soils and rock which are strongly linked to the inherent properties of the porous structure of the material as well as the presence and possible flow of any surrounding fluids. Dynamic problems involving such soil-fluid i...
Implementation of neural network based non-linear predictive control
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1999-01-01
of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...
Algorithms for non-linear M-estimation
DEFF Research Database (Denmark)
Madsen, Kaj; Edlund, O; Ekblom, H
1997-01-01
a sequence of estimation problems for linearized models is solved. In the testing we apply four estimators to ten non-linear data fitting problems. The test problems are also solved by the Generalized Levenberg-Marquardt method and standard optimization BFGS method. It turns out that the new method...
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found...
Range non-linearities correction in FMCW SAR
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
The limiting factor to the use of Frequency Modulated Continuous Wave (FMCW) technology with Synthetic Aperture Radar (SAR) techniques to produce lightweight, cost effective, low power consuming imaging sensors with high resolution, is the well known presence of non-linearities in the transmitted si
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially...
Non-Linear Interactive Stories in Computer Games
DEFF Research Database (Denmark)
Bangsø, Olav; Jensen, Ole Guttorm; Kocka, Tomas
2003-01-01
The paper introduces non-linear interactive stories (NOLIST) as a means to generate varied and interesting stories for computer games automatically. We give a compact representation of a NOLIST based on the specification of atomic stories, and show how to build an object-oriented Bayesian network...
Quantum-dot-based integrated non-linear sources
DEFF Research Database (Denmark)
Bernard, Alice; Mariani, Silvia; Andronico, Alessio
2015-01-01
The authors report on the design and the preliminary characterisation of two active non-linear sources in the terahertz and near-infrared range. The former is associated to difference-frequency generation between whispering gallery modes of an AlGaAs microring resonator, whereas the latter is gra...
Note About Hamiltonian Structure of Non-Linear Massive Gravity
Kluson, J
2011-01-01
We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.
Locally supersymmetric D=3 non-linear sigma models
Wit, B. de; Tollsten, A. K.; Nicolai, H.
1992-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it general
On the non-linearity of the subsidiary systems
Friedrich, H
2005-01-01
In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of generating catastrophic growth of gauge resp. constraint violations in numerical calculations.
Development and Control of a Non Linear Magnetic Levitation System
Directory of Open Access Journals (Sweden)
A Sanjeevi Gandhi
2013-06-01
Full Text Available Nowadays, studies to develop and control non linear systems is of great significance. Magnetic Levitation System has gained considerable interests due to its great practical importance in different engineering fields In this paper an electromagnetic levitation system was developed and mathematical model for the system was derived. The developed system was controlled manually.
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.;
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...... is studied. Both the Lebesgue and Hausdorff measures of this set are obtained....
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such d
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...
Surface wave scattering theory : with applications to forward and inverse problems in seismology
Snieder, R.K.
1987-01-01
Scattering of surface waves in a three dimensional layered elastic medium with embedded heterogeneities is described in this thesis with the Born approximation. The dyadic decomposition of the surface wave Green's function provides the crucial element for an efficient application of Born theory to s
Inverse scattering at fixed energy in de Sitter-Reissner-Nordstr\\"om black holes
Daudé, Thierry
2010-01-01
In this paper, we consider massless Dirac fields propagating in the outer region of de Sitter-Reissner-Nordstr\\"om black holes. We show that the metric of such black holes is uniquely determined by the partial knowledge of the corresponding scattering matrix $S(\\lambda)$ at a fixed energy $\\lambda \
A computerized implementation of a non-linear equation to predict barrier shielding requirements.
Chamberlain, A C; Strydom, W J
1997-04-01
A non-linear equation to predict barrier shielding thickness from the work function of x- and gamma-ray generators is presented. This equation is incorporated into a model that takes into account primary, scatter, and leakage radiation components to determine the amount of shielding necessary. The case of multiple wall materials is also considered. The equation accurately models the radiation attenuation curves given in NCRP 49 for concrete and lead, thus eliminating the necessity to use graphical or tabular methods to calculate shielding thickness, which can be inaccurate.
Inverse Scattering from a Sound-Hard Crack via Two-Step Method
Directory of Open Access Journals (Sweden)
Kuo-Ming Lee
2012-01-01
Full Text Available We present a two-step method for recovering an unknown sound-hard crack in ℝ2 from the measured far-field pattern. This method, based on a two-by-two system of nonlinear integral equations, splits the reconstruction into two consecutive steps which consists of a forward and an inverse problems. In this spirit, only the latter needs to be regularized.
Sparse frequencies data inversion and the role of multi-scattered energy
Alkhalifah, Tariq Ali
2017-05-26
In trying to extract a broad spectrum of model wavenumbers from the data, necessary to build a plausible model of the Earth, we are, in theory, bounded at the high end by the diffraction resolution limit, which is proportional to the highest usable frequency in the data. At the low end, and courtesy of our multi-dimensional acquisition, the principles behind diffraction tomography theoretically extend our range to zero-wavenumbers, mainly provided by transmissions like diving waves. Within certain regions of the subsurface (i.e. deep), we face the prospective of having a model wavenumber gap in representing the velocity. Here, I demonstrate that inverting for multi scattered energy, we can recover additional wavenumbers not provided by single scattering gradients, that may feed the high and low ends of the model wavenumber spectrum, as well as help us fill in the infamous intermediate wavenumber gap. Thus, I outline a scenario in which we acquire dedicated sparse frequency data, allowing for more time to inject more energy of those frequencies at a reduced cost. Such additional energy is necessary to the recording of more multi-scattered events. The objective of this new paradigm is a high resolution model of the Earth.
Thermodynamic analysis of non-linear Reissner-Nordstrom black holes
Cembranos, Jose A R; Jarillo, Javier
2015-01-01
In the present article we study the Inverse Electrodynamics Model. This model is a gauge and parity invariant non-linear Electrodynamics theory, which respects the conformal invariance of standard Electrodynamics. This modified Electrodynamics model, when minimally coupled to General Relativity, is compatible with static and spherically symmetric Reissner-Nordstrom-like black-hole solutions. However, these black-hole solutions present more complex thermodynamic properties than their Reissner-Nordstrom black-hole solutions counterparts in standard Electrodynamics. In particular, in the Inverse Model a new stability region, with both the heat capacity and the free energy negative, arises. Moreover, unlike the scenario in standard Electrodynamics, a sole transition phase is possible for a suitable choice in the set of parameters of these solutions.
Institute of Scientific and Technical Information of China (English)
Sisir Kumar Garai; Debojyati Samanta; Sourangshu Mukhopadhyay
2008-01-01
Optics has already been proved as a successful candidate for conducting parallel logic, arithmetic and algebraic operations. Several all-optical data processors were proposed since last few decades. To implement these systems, different data encoding decoding techniques such as polarization encoding, tristate, quartenary state, multivalued state, symbolic substitution technique etc. have already been proposed. All these are done to use optics in a suitable platform. We propose here a new concept of encoding data by adopting frequencies variation technique for conducting a inversion operation successfully.
Non-linear aeroelastic prediction for aircraft applications
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
Diagnostics for the optimization of an 11 keV inverse Compton scattering x-ray source
Energy Technology Data Exchange (ETDEWEB)
Chauchat, A.-S.; Brasile, J.-P [Thales Communications and Security, 4 avenue des Louvresses 92230 Gennevilliers (France); Le Flanchec, V.; Negre, J.-P.; Binet, A. [CEA DAM DIF, Bruyeres-le-Chatel 91290 Arpajon (France); Ortega, J.-M. [LCP Universite Paris-Sud, Bat. 201, 91405 Orsay (France)
2013-04-19
In a scope of a collaboration between Thales Communications and Security and CEA DAM DIF, 11 keV Xrays were produced by inverse Compton scattering on the ELSA facility. In this type of experiment, X-ray observation lies in the use of accurate electron and laser beam interaction diagnostics and on fitted X-ray detectors. The low interaction probability between < 100 {mu}m width, 12 ps [rms] length electron and photon pulses requires careful optimization of pulse spatial and temporal covering. Another issue was to observe 11 keV X-rays in the ambient radioactive noise of the linear accelerator. For that, we use a very sensitive detection scheme based on radio luminescent screens.
Xu, Yanping; Ren, Meiqi; Lu, Yang; Lu, Ping; Lu, Ping; Bao, Xiaoyi; Wang, Lixian; Messaddeq, Younès; LaRochelle, Sophie
2016-03-15
We propose a unique multi-parameter optical fiber sensor based on intramodal stimulated Brillouin scattering of higher-order acoustic modes in inverse-parabolic graded-index fiber (IPGIF) without a mode converter. Both optical modes and acoustic modes guided in the IPGIF are characterized and demonstrated theoretically and experimentally. Simulation analysis shows that the multi-peak feature in the Brillouin gain spectrum of the IPGIF is attributed to the couplings between the guided optical mode and the higher-order acoustic modes. Thanks to the distinct acoustic properties of the peaks induced by the sharp refractive index profile of the IPGIF, the different temperature and strain dependences of the first three Brillouin peaks enable the discrimination of the temperature and strain at an accuracy of 0.85°C and 17.4 με.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Directory of Open Access Journals (Sweden)
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Non-linear irreversible thermodynamics of single-molecule experiments
Santamaria-Holek, I; Hidalgo-Soria, M; Perez-Madrid, A
2015-01-01
Irreversible thermodynamics of single-molecule experiments subject to external constraining forces of a mechanical nature is presented. Extending Onsager's formalism to the non-linear case of systems under non-equilibrium external constraints, we are able to calculate the entropy production and the general non-linear kinetic equations for the variables involved. In particular, we analyze the case of RNA stretching protocols obtaining critical oscillations between di?erent con?gurational states when forced by external means to remain in the unstable region of its free-energy landscape, as observed in experiments. We also calculate the entropy produced during these hopping events, and show how resonant phenomena in stretching experiments of single RNA macromolecules may arise. We also calculate the hopping rates using Kramer's approach obtaining a good comparison with experiments.
The linear-non-linear frontier for the Goldstone Higgs
Gavela, M B; Machado, P A N; Saa, S
2016-01-01
The minimal $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $\\sigma$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic compl...
Non-linear Young's double-slit experiment.
San Roman, Julio; Ruiz, Camilo; Perez, Jose Antonio; Delgado, Diego; Mendez, Cruz; Plaja, Luis; Roso, Luis
2006-04-01
The Young's double slit experiment is recreated using intense and short laser pulses. Our experiment evidences the role of the non-linear Kerr effect in the formation of interference patterns. In particular, our results evidence a mixed mechanism in which the zeroth diffraction order of each slit are mainly affected by self-focusing and self-phase modulation, while the higher orders propagate linearly. Despite of the complexity of the general problem of non-linear propagation, we demonstrate that this experiment retains its simplicity and allows for a geometrical interpretation in terms of simple optical paths. In consequence, our results may provide key ideas on experiments on the formation of interference patterns with intense laser fields in Kerr media.
SSNN toolbox for non-linear system identification
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
A non-linear model of economic production processes
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.
Integration of non-linear cellular mechanisms regulating microvascular perfusion.
Griffith, T M; Edwards, D H
1999-01-01
It is becoming increasingly evident that interactions between the different cell types present in the vessel wall and the physical forces that result from blood flow are highly complex. This short article will review evidence that irregular fluctuations in vascular resistance are generated by non-linearity in the control mechanisms intrinsic to the smooth muscle cell and can be classified as chaotic. Non-linear systems theory has provided insights into the mechanisms involved at the cellular level by allowing the identification of dominant control variables and the construction of one-dimensional iterative maps to model vascular dynamics. Experiments with novel peptide inhibitors of gap junctions have shown that the coordination of aggregate responses depends on direct intercellular communication. The sensitivity of chaotic trajectories to perturbation may nevertheless generate a high degree of variability in the response to pharmacological interventions and altered perfusion conditions.
Parametric Analysis of Fiber Non-Linearity in Optical systems
Directory of Open Access Journals (Sweden)
Abhishek Anand
2013-06-01
Full Text Available With the advent of technology Wavelength Division Multiplexing (WDM is always an area of interest in the field of optical communication. When combined with Erbium Doped Fiber Amplifier (EDFA, it provides high data transmission rate and low attenuation. But due to fiber non-linearity such as Self Phase Modulation (SPM and Cross Phase Modulation (XPM the system performance has degraded. This non-linearity depends on different parameters of an optical system such as channel spacing, power of the channel and length of the fiber section. The degradation can be seen in terms of phase deviation and Bit Error Rate (BER performance. Even after dispersion compensation at the fiber end, residual pulse broadening still exists due to cross talk penalty.
Non-linear Behavior of Curved Sandwich Panels
DEFF Research Database (Denmark)
Berggreen, Carl Christian; Jolma, P.; Karjalainen, J. P.;
2003-01-01
In this paper the non-linear behavior of curved sandwich panels is investigated both numerically and experimentally. Focus is on various aspects of finite element modeling and calculation procedures. A simply supported, singly curved, CFRP/PVC sandwich panel is analyzed under uniform pressure load...... and results are compared to test data. A novel test arrangement utilizing a water filled cushion to create the uniform pressure load on curved panel specimen is used to obtain the experimental data. The panel is modeled with three different commercial finite element codes. Two implicit and one explicit code...... are used with various element types, modeling approaches and material models. The results show that the theoretical and experimental methods generally show fair agreement in panel non-linear behavior before collapse. It is also shown that special attention to detail has to be taken, because the predicted...
Non-Linear Aeroelastic Stability of Wind Turbines
DEFF Research Database (Denmark)
Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie;
2013-01-01
As wind turbines increase in magnitude without a proportional increase in stiffness, the risk of dynamic instability is believed to increase. Wind turbines are time dependent systems due to the coupling between degrees of freedom defined in the fixed and moving frames of reference, which may...... trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control...... and non-linear aero-elasticity into consideration. The stability of the wind turbine is determined by the maximum Lyapunov exponent of the system, which is operated directly on the non-linear state vector differential equations. Numerical examples show that this approach is promising for stability...
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
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.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
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. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Chatzidimitriou-Dreismann, C. A.; MacA Gray, E.; Blach, T. P.
2012-08-01
Nuclei and electrons in condensed matter and/or molecules are usually entangled, due to the prevailing (mainly electromagnetic) interactions. However, the "environment" of a microscopic scattering system (e.g. a proton) causes ultrafast decoherence, thus making atomic and/or nuclear entanglement effects not directly accessible to experiments. However, our neutron Compton scattering experiments from protons (H-atoms) in condensed systems and molecules have a characteristic collisional time about 100-1000 attoseconds. The quantum dynamics of an atom in this ultrashort, but finite, time window is governed by non-unitary time evolution due to the aforementioned decoherence. Unexpectedly, recent theoretical investigations have shown that decoherence can also have the following energetic consequences. Disentangling two subsystems A and B of a quantum system AB is tantamount to erasure of quantum phase relations between A and B. This erasure is widely believed to be an innocuous process, which e.g. does not affect the energies of A and B. However, two independent groups proved recently that disentangling two systems, within a sufficiently short time interval, causes increase of their energies. This is also derivable by the simplest Lindblad-type master equation of one particle being subject to pure decoherence. Our neutron-proton scattering experiments with H2 molecules provide for the first time experimental evidence of this effect. Our results reveal that the neutron-proton collision, leading to the cleavage of the H-H bond in the attosecond timescale, is accompanied by larger energy transfer (by about 2-3%) than conventional theory predicts. Preliminary results from current investigations show qualitatively the same effect in the neutron-deuteron Compton scattering from D2 molecules. We interpret the experimental findings by treating the neutron-proton (or neutron-deuteron) collisional system as an entangled open quantum system being subject to fast decoherence caused
Chakrabarti, Kisalaya; Cole, James B
2010-03-01
Inverse method has wide application on medical diagnosis where non-destructive evaluation is the key factor .Back scattered waves or echoes generated from the forward moving waves has information about its geometry, size and location. In this paper we have investigated how well different geometries of the object is determined from the back scattered waves by a high accuracy Non-Standard Finite Difference Time Inverse (NSFD-TI) Maxwell's algorithm and how the refractive index of the object plays a deterministic role on its size.
Defects in the discrete non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Doikou, Anastasia, E-mail: adoikou@upatras.gr [University of Patras, Department of Engineering Sciences, Physics Division, GR-26500 Patras (Greece)
2012-01-01
The discrete non-linear Schroedinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem....
Measuring the Non-Linear Effects of Monetary Policy
Christian Matthes; Regis Barnichon
2015-01-01
This paper proposes a method to identify the non-linear effects of structural shocks by using Gaussian basis functions to parametrize impulse response functions. We apply our approach to monetary policy and find that the effect of a monetary intervention depends strongly on (i) the sign of the intervention, (ii) the size of the intervention, and (iii) the state of the business cycle at the time of the intervention. A contractionary policy has a strong adverse effect on output, much stronger t...
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France); University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Markou, Chrysoula [Sorbonne Universites, UPMC Paris 6, LPTHE, UMR CNRS 7589, Paris (France)
2015-12-15
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R - λ){sup 2} = 0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories. (orig.)
The coupling of non-linear supersymmetry to supergravity
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios, E-mail: antoniad@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France); Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlestrasse 5, 3012, Bern (Switzerland); Markou, Chrysoula, E-mail: chrysoula@lpthe.jussieu.fr [LPTHE, UMR CNRS 7589, Sorbonne Universités, UPMC Paris 6, 75005, Paris (France)
2015-12-09
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R-λ){sup 2}=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
S Moolla; R Bharuthram; S V Singh; G S Lakhina
2003-12-01
Using ﬂuid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic ﬁeld in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric ﬁeld.
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
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 Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for no...... for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions....
Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
Adaptive spectral identification techniques in presence of undetected non linearities
Cella, G; Guidi, G M
2002-01-01
The standard procedure for detection of gravitational wave coalescing binaries signals is based on Wiener filtering with an appropriate bank of template filters. This is the optimal procedure in the hypothesis of addictive Gaussian and stationary noise. We study the possibility of improving the detection efficiency with a class of adaptive spectral identification techniques, analyzing their effect in presence of non stationarities and undetected non linearities in the noise
Likelihood inference for discretely observed non-linear diffusions
1998-01-01
This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the lat...
Non-linear dark matter collapse under diffusion
Velten, Hermano E S
2014-01-01
Diffusion is one of the physical processes allowed for describing the large scale dark matter dynamics. At the same time, it can be seen as a possible mechanism behind the interacting cosmologies. We study the non-linear spherical "top-hat" collapse of dark matter which undergoes velocity diffusion into a solvent dark energy field. We show constraints on the maximum magnitude allowed for the dark matter diffusion. Our results reinforce previous analysis concerning the linear perturbation theory.
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
Non-linear Higgs portal to Dark Matter
Bajo, Rocío del Rey
2016-01-01
The Higgs portal to scalar Dark Matter is considered in the context of non-linearly realised electroweak symmetry breaking. We determine the interactions of gauge bosons and the physical Higgs particle $h$ to a scalar singlet Dark Matter candidate $S$ in an effective description. The main phenomenological differences with respect to the standard scenario can be seen in the Dark Matter relic abundance, in direct/indirect searches and in signals at colliders.
Non-linear HRV indices under autonomic nervous system blockade.
Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel
2014-01-01
Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.
Non-linear polaronic conduction in magnetite nanowires
Energy Technology Data Exchange (ETDEWEB)
Singh, Pooja, E-mail: pooja7503@gmail.com [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Rout, P.K., E-mail: pkrout.phy@gmail.com [National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Husale, Sudhir; Gupta, Anurag [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Singh, Manju [National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Rakshit, R.K. [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); Dogra, Anjana, E-mail: anjanad@nplindia.org [Academy of Scientific and Innovative Research (AcSIR), CSIR-NPL Campus, Dr. K.S. Krishnan Marg, New Delhi 110012 (India); National Physical Laboratory, Council of Scientific and Industrial Research, Dr. K.S. Krishnan Marg, New Delhi 110012 (India)
2016-12-01
We report the temperature dependent current (I) – voltage (V) characteristics of Fe{sub 3}O{sub 4} nanowires with varying width (w) of 132, 358, and 709 nm. While the widest nanowire (w=709 nm) shows ohmic I (V) curves for all temperatures, those for w=132 and 358 nm show nonlinearity, which can be expressed by a combination of linear (V) and cubic (V{sup 3}) terms. The behaviour of conductance (linear bias component of current) and non-linearity in these nanowires is related to small polaron hopping related conduction. Moreover, we observed an anomalously large hopping lengths, which may be related to the size of percolation cluster and/or antiphase domain. Our study presents first experimental evidence for such non-linear polaronic conduction in magnetite nanowires. - Highlights: • Temperature dependent I–V measurements of FIB fabricated magnetite nanowires. • Small polaron based conduction in non-linear I–V curves. • Anomalously large hopping lengths due to percolation effect and/or antiphase domains.
Non-linear Q-clouds around Kerr black holes
Directory of Open Access Journals (Sweden)
Carlos Herdeiro
2014-12-01
Full Text Available Q-balls are regular extended ‘objects’ that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces – existence lines – of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.
Fitting and forecasting non-linear coupled dark energy
Casas, Santiago; Baldi, Marco; Pettorino, Valeria; Vollmer, Adrian
2015-01-01
We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range $z=0-1.6$ and wave modes below $k=10 \\text{h/Mpc}$. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and w...
Generalized Ghost Dark Energy with Non-Linear Interaction
Ebrahimi, E; Mehrabi, A; Movahed, S M S
2016-01-01
In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter. The functional form of dark energy density in the generalized ghost dark energy (GGDE) model is $\\rho_D\\equiv f(H, H^2)$ with coefficient of $H^2$ represented by $\\zeta$ and the model contains three free parameters as $\\Omega_D, \\zeta$ and $b^2$ (the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa, gamma-ray bursts, baryonic acoustic oscillation and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first non-linear interaction, the j...
Testing non-linear vacuum electrodynamics with Michelson interferometry
Schellstede, Gerold O; Lämmerzahl, Claus
2015-01-01
We discuss the theoretical foundations for testing non-linear vacuum electrodynamics with Michelson interferometry. Apart from some non-degeneracy conditions to be imposed, our discussion applies to all non-linear electrodynamical theories of the Pleba\\'nski class, i.e., to all Lagrangians that depend only on the two Lorentz-invariant scalars quadratic in the field strength. The main idea of the experiment proposed here is to use the fact that, according to non-linear electrodynamics, the phase velocity of light should depend on the strength and on the direction of an electromagnetic background field. There are two possible experimental set-ups for testing this prediction with Michelson interferometry. The first possibility is to apply a strong electromagnetic field to the beam in one arm of the interferometer and to compare the situation where the field is switched on with the situation where it is switched off. The second possibility is to place the whole interferometer in a strong electromagnetic field and...
Fabrication and characterization of non-linear parabolic microporous membranes.
Rajasekaran, Pradeep Ramiah; Sharifi, Payam; Wolff, Justin; Kohli, Punit
2015-01-01
Large scale fabrication of non-linear microporous membranes is of technological importance in many applications ranging from separation to microfluidics. However, their fabrication using traditional techniques is limited in scope. We report on fabrication and characterization of non-linear parabolic micropores (PMS) in polymer membranes by utilizing flow properties of fluids. The shape of the fabricated PMS corroborated well with simplified Navier-Stokes equation describing parabolic relationship of the form L - t(1/2). Here, L is a measure of the diameter of the fabricated micropores during flow time (t). The surface of PMS is smooth due to fluid surface tension at fluid-air interface. We demonstrate fabrication of PMS using curable polydimethylsiloxane (PDMS). The parabolic shape of micropores was a result of interplay between horizontal and vertical fluid movements due to capillary, viscoelastic, and gravitational forces. We also demonstrate fabrication of asymmetric "off-centered PMS" and an array of PMS membranes using this simple fabrication technique. PMS containing membranes with nanoscale dimensions are also possible by controlling the experimental conditions. The present method provides a simple, easy to adopt, and energy efficient way for fabricating non-linear parabolic shape pores at microscale. The prepared parabolic membranes may find applications in many areas including separation, parabolic optics, micro-nozzles / -valves / -pumps, and microfluidic and microelectronic delivery systems.
Schumacher, Florian; Friederich, Wolfgang
Due to increasing computational resources, the development of new numerically demanding methods and software for imaging Earth's interior remains of high interest in Earth sciences. Here, we give a description from a user's and programmer's perspective of the highly modular, flexible and extendable software package ASKI-Analysis of Sensitivity and Kernel Inversion-recently developed for iterative scattering-integral-based seismic full waveform inversion. In ASKI, the three fundamental steps of solving the seismic forward problem, computing waveform sensitivity kernels and deriving a model update are solved by independent software programs that interact via file output/input only. Furthermore, the spatial discretizations of the model space used for solving the seismic forward problem and for deriving model updates, respectively, are kept completely independent. For this reason, ASKI does not contain a specific forward solver but instead provides a general interface to established community wave propagation codes. Moreover, the third fundamental step of deriving a model update can be repeated at relatively low costs applying different kinds of model regularization or re-selecting/weighting the inverted dataset without need to re-solve the forward problem or re-compute the kernels. Additionally, ASKI offers the user sensitivity and resolution analysis tools based on the full sensitivity matrix and allows to compose customized workflows in a consistent computational environment. ASKI is written in modern Fortran and Python, it is well documented and freely available under terms of the GNU General Public License (http://www.rub.de/aski).
Kirczenow, George
2015-09-01
Valley currents and nonlocal resistances of graphene nanostructures with broken inversion symmetry are considered theoretically in the linear response regime. Scattering state wave functions of electrons entering the nanostructure from the contacts represented by groups of ideal leads are calculated by solving the Lippmann-Schwinger equation and are projected onto the valley state subspaces to obtain the valley velocity fields and total valley currents in the nanostructures. In the tunneling regime when the Fermi energy is in the spectral gap around the Dirac point energy, inversion symmetry breaking is found to result in strong enhancement of the nonlocal four-terminal Büttiker-Landauer resistance and in valley currents several times stronger than the conventional electric current. These strong valley currents are the direct result of the injection of electrons from a contact into the graphene in the tunneling regime. They are chiral and occur near contacts from which electrons are injected into the nanostructure whether or not a net electric current flows through the contact. It is also pointed out that enhanced nonlocal resistances in the linear response regime are not a signature of valley currents arising from the combined effect of the electric field and Berry curvature on the velocities of electrons.
Simulation of Forward and Inverse X-ray Scattering From Shocked Materials
Barber, John; Marksteiner, Quinn; Barnes, Cris
2012-02-01
The next generation of high-intensity, coherent light sources should generate sufficient brilliance to perform in-situ coherent x-ray diffraction imaging (CXDI) of shocked materials. In this work, we present beginning-to-end simulations of this process. This includes the calculation of the partially-coherent intensity profiles of self-amplified stimulated emission (SASE) x-ray free electron lasers (XFELs), as well as the use of simulated, shocked molecular-dynamics-based samples to predict the evolution of the resulting diffraction patterns. In addition, we will explore the corresponding inverse problem by performing iterative phase retrieval to generate reconstructed images of the simulated sample. The development of these methods in the context of materials under extreme conditions should provide crucial insights into the design and capabilities of shocked in-situ imaging experiments.
New technique for phase shift analysis multi-energy solution of inverse scattering problem
Cooper, S G; MacIntosh, R S; Kuznetsova, E V
1998-01-01
We demonstrate a new approach to the analysis of extensive multi-energy data. For the case of d + He-4, we produce a phase shift analysis covering for the energy range 3 to 11 MeV. The key idea is the use of iterative perturbative data-to-potential inversion which can produce potentials which reproduce the data simultaneously over a range of energies. It thus effectively regularizes the extraction of phase shifts from diverse, incomplete and possibly somewhat contradictory data sets. In doing so, it will provide guidance to experimentalists as to what further measurements should be made. This study is limited to vector spin observables and spin-orbit interactions. We discuss alternative ways in which the theory can be implemented and which provide insight into the ambiguity problems. We compare the extrapolation of these solutions to other energies. Majorana terms are presented for each potential component.
Ahn, Chi Young; Jeon, Kiwan; Park, Won-Kwang
2015-06-01
This study analyzes the well-known MUltiple SIgnal Classification (MUSIC) algorithm to identify unknown support of thin penetrable electromagnetic inhomogeneity from scattered field data collected within the so-called multi-static response matrix in limited-view inverse scattering problems. The mathematical theories of MUSIC are partially discovered, e.g., in the full-view problem, for an unknown target of dielectric contrast or a perfectly conducting crack with the Dirichlet boundary condition (Transverse Magnetic-TM polarization) and so on. Hence, we perform further research to analyze the MUSIC-type imaging functional and to certify some well-known but theoretically unexplained phenomena. For this purpose, we establish a relationship between the MUSIC imaging functional and an infinite series of Bessel functions of integer order of the first kind. This relationship is based on the rigorous asymptotic expansion formula in the existence of a thin inhomogeneity with a smooth supporting curve. Various results of numerical simulation are presented in order to support the identified structure of MUSIC. Although a priori information of the target is needed, we suggest a least condition of range of incident and observation directions to apply MUSIC in the limited-view problem.
Riley, L A; Baugher, T R; Bazin, D; Bowry, M; Cottle, P D; DeVone, F G; Gade, A; Glowacki, M T; Kemper, K W; Lunderberg, E; McPherson, D M; Noji, S; Recchia, F; Sadler, B V; Scott, M; Weisshaar, D; Zegers, R G T
2014-01-01
We have performed measurements of the $0_\\mathrm{g.s.}^+ \\rightarrow 2_1^+$ excitations in the neutron-rich isotopes $^{48,50}$Ca via inelastic proton scattering on a liquid hydrogen target, using the GRETINA $\\gamma$-ray tracking array. A comparison of the present results with those from previous measurements of the lifetimes of the $2_1^+$ states provides us the ratio of the neutron and proton matrix elements for the $0_\\mathrm{g.s.}^+ \\rightarrow 2_1^+$ transitions. These results allow the determination of the ratio of the proton and neutron effective charges to be used in shell model calculations of neutron-rich isotopes in the vicinity of $^{48}$Ca.
Long-term cavity closure in non-linear rocks
Cornet, Jan; Dabrowski, Marcin; Schmid, Daniel Walter
2017-08-01
The time dependent closure of pressurized cavities in viscous rocks due to far-field loads is a problem encountered in many applications like drilling, cavity abandonment and porosity closure. The non-linear nature of the flow of rocks prevents the use of simple solutions for hole closure and calls for the development of appropriate expressions reproducing all the dependencies observed in nature. An approximate solution is presented for the closure velocity of a pressurized cylindrical cavity in a non-linear viscous medium subjected to a combined pressure and shear stress load in the far field. The embedding medium is treated as homogeneous, isotropic, and incompressible and follows a Carreau viscosity model. We derive analytical solutions for the end-member cases of the pressure and shear loads. The exact analytical solution for pressure loads shows that the closure velocity vR is given by the implicit expression {Δ p}/{2{μ _0D_{II}^*}} = - 1/2B( {{v_R^2}/{RD_{II^* + v_R^2}};1/2, - 1/{2n}} ), where Δp is the pressure load, R is the hole radius, B is the incomplete beta function, and μ0, D_{II}^*, n are, respectively, the threshold viscosity, transition rate and stress exponent of the Carreau model. The closure velocity is dominated by the linear mechanism under pressure loads smaller than 1.8{μ _0}D_{II}^* and by the non-linear one under large pressure loads. In the non-linear regime, pressure variations support an increasing part of the load with increasing degree of non-linearity. The decay of the stress perturbation in the non-linear zone varies as r- 2/n where r is the radial distance to the hole. A solution for the maximum closure velocity at the cavity rim vRmax under far-field shear is given: v_{R\\max} = ( 1 + {\\overline {M_s}} ^{-1/2})R\\overline D_{II}, where \\overline {M_s} = (1 + {\\overline {D_{II}} }^2 \\big/ {nD{_{II}^*}^2}) \\big/ ( 1 + {\\overline {D_{II}}^2} \\big/ D{_{II}^*}^2) and \\overline {D_{II}} is the second invariant of the far
Non-linear absorption for concentrated solar energy transport
Energy Technology Data Exchange (ETDEWEB)
Jaramillo, O. A; Del Rio, J.A; Huelsz, G [Centro de Investigacion de Energia, UNAM, Temixco, Morelos (Mexico)
2000-07-01
In order to determine the maximum solar energy that can be transported using SiO{sub 2} optical fibers, analysis of non-linear absorption is required. In this work, we model the interaction between solar radiation and the SiO{sub 2} optical fiber core to determine the dependence of the absorption of the radioactive intensity. Using Maxwell's equations we obtain the relation between the refractive index and the electric susceptibility up to second order in terms of the electric field intensity. This is not enough to obtain an explicit expression for the non-linear absorption. Thus, to obtain the non-linear optical response, we develop a microscopic model of an harmonic driven oscillators with damp ing, based on the Drude-Lorentz theory. We solve this model using experimental information for the SiO{sub 2} optical fiber, and we determine the frequency-dependence of the non-linear absorption and the non-linear extinction of SiO{sub 2} optical fibers. Our results estimate that the average value over the solar spectrum for the non-linear extinction coefficient for SiO{sub 2} is k{sub 2}=10{sup -}29m{sup 2}V{sup -}2. With this result we conclude that the non-linear part of the absorption coefficient of SiO{sub 2} optical fibers during the transport of concentrated solar energy achieved by a circular concentrator is negligible, and therefore the use of optical fibers for solar applications is an actual option. [Spanish] Con el objeto de determinar la maxima energia solar que puede transportarse usando fibras opticas de SiO{sub 2} se requiere el analisis de absorcion no linear. En este trabajo modelamos la interaccion entre la radiacion solar y el nucleo de la fibra optica de SiO{sub 2} para determinar la dependencia de la absorcion de la intensidad radioactiva. Mediante el uso de las ecuaciones de Maxwell obtenemos la relacion entre el indice de refraccion y la susceptibilidad electrica hasta el segundo orden en terminos de intensidad del campo electrico. Esto no es
The non-linear evolution of edge localized modes
Energy Technology Data Exchange (ETDEWEB)
Wenninger, Ronald
2013-01-09
Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal
Polarization of x-gamma radiation produced by a Thomson and Compton inverse scattering
Petrillo, V.; Bacci, A.; Curatolo, C.; Drebot, I.; Giribono, A.; Maroli, C.; Rossi, A. R.; Serafini, L.; Tomassini, P.; Vaccarezza, C.; Variola, A.
2015-11-01
A systematic study of the polarization of x-gamma rays produced in Thomson and Compton scattering is presented, in both classical and quantum schemes. Numerical results and analytical considerations let us to establish the polarization level as a function of acceptance, bandwidth and energy. Few sources have been considered: the SPARC_LAB Thomson device, as an example of a x-ray Thomson source, ELI-NP, operating in the gamma range. Then, the typical parameters of a beam produced by a plasma accelerator has been analyzed. In the first case, with bandwidths up to 10%, a contained reduction (<10 % ) in the average polarization occurs. In the last case, for the nominal ELI-NP relative bandwidth of 5 ×1 0-3 , the polarization is always close to 1. For applications requiring larger bandwidth, however, a degradation of the polarization up to 30% must be taken into account. In addition, an all optical gamma source based on a plasma accelerated electron beam cannot guarantee narrow bandwidth and high polarization operational conditions required in nuclear photonics experiments.
Inverse scattering of 2d photonic structures by layer-stripping
Andresen, Marte P Hatlo; Skaar, Johannes
2011-01-01
Design and reconstruction of 2d and 3d photonic structures are usually carried out by forward simulations combined with optimization or intuition. Reconstruction by means of layer-stripping has been applied in seismic processing as well as in design and characterization of 1d photonic structures such as fiber Bragg gratings. Layer-stripping is based on causality, where the earliest scattered light is used to recover the structure layer-by-layer. Our set-up is a 2d layered nonmagnetic structure probed by plane polarized harmonic waves entering normal to the layers. It is assumed that the dielectric permittivity in each layer only varies orthogonal to the polarization. Based on obtained reflectance data covering a suitable frequency interval, time-localized pulse data are synthesized and applied to reconstruct the refractive index profile in the leftmost layer by identifying the local, time-domain Fresnel reflection at each point. Once the first layer is known, its impact on the reflectance data is stripped off...
Arahman, Nasrul; Maimun, Teuku; Mukramah, Syawaliah
2017-01-01
The composition of polymer solution and the methods of membrane preparation determine the solidification process of membrane. The formation of membrane structure prepared via non-solvent induced phase separation (NIPS) method is mostly determined by phase separation process between polymer, solvent, and non-solvent. This paper discusses the phase separation process of polymer solution containing Polyethersulfone (PES), N-methylpirrolidone (NMP), and surfactant Tetronic 1307 (Tet). Cloud point experiment is conducted to determine the amount of non-solvent needed on induced phase separation. Amount of water required as a non-solvent decreases by the addition of surfactant Tet. Kinetics of phase separation for such system is studied by the light scattering measurement. With the addition of Tet., the delayed phase separation is observed and the structure growth rate decreases. Moreover, the morphology of fabricated membrane from those polymer systems is analyzed by scanning electron microscopy (SEM). The images of both systems show the formation of finger-like macrovoids through the cross-section.
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.
Global non-linear effect of temperature on economic production
Burke, Marshall; Hsiang, Solomon M.; Miguel, Edward
2015-11-01
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate.
Non-linear DSGE Models and The Optimized Particle Filter
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper improves the accuracy and speed of particle filtering for non-linear DSGE models with potentially non-normal shocks. This is done by introducing a new proposal distribution which i) incorporates information from new observables and ii) has a small optimization step that minimizes...... the distance to the optimal proposal distribution. A particle filter with this proposal distribution is shown to deliver a high level of accuracy even with relatively few particles, and this filter is therefore much more efficient than the standard particle filter....
Non-linear feedback neural networks VLSI implementations and applications
Ansari, Mohd Samar
2014-01-01
This book aims to present a viable alternative to the Hopfield Neural Network (HNN) model for analog computation. It is well known that the standard HNN suffers from problems of convergence to local minima, and requirement of a large number of neurons and synaptic weights. Therefore, improved solutions are needed. The non-linear synapse neural network (NoSyNN) is one such possibility and is discussed in detail in this book. This book also discusses the applications in computationally intensive tasks like graph coloring, ranking, and linear as well as quadratic programming. The material in the book is useful to students, researchers and academician working in the area of analog computation.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
Linear and non-linear perturbations in dark energy models
Escamilla-Rivera, Celia; Fabris, Julio C; Alcaniz, Jailson S
2016-01-01
In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state $w(z)$. In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected $w(z)$ parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard $\\Lambda$CDM model.
Hans Hinterreiter’s non-linear transformations
DEFF Research Database (Denmark)
Makovicky, Emil
poster illustrates four different cases of this process, starting always with a plane-group pattern and showing both the application of non-linear transformations and coloured symmetry. In his more complex patterns, two of which are shown on the poster, Hinterreiter created domains of affinely...... of plane-group patterns onto curvilinear nets of different kinds, mostly combined with a skilful application of principles of dichroic or polychromatic symmetry. Unlike Escher, Hinterreiter strove to achieve the aesthetic ideal of a pure abstract form [2] with its inherent symmetries. His unique, two...
Studies for an alternative LHC non-linear collimation system
Lari, L; Boccone, V; Cerutti, F; Versaci, R; Vlachoudis, V; Mereghetti, A; Faus-Golfe, A; Resta-Lopez, J
2012-01-01
A LHC non-linear betatron cleaning collimation system would allow larger gap for the mechanical jaws, reducing as a consequence the collimator-induced impedance, which may limit the LHC beam intensity. In this paper, the performance of the proposed system is analyzed in terms of beam losses distribution around the LHC ring and cleaning efficiency in stable physics condition at 7TeV for Beam1. Moreover, the energy deposition distribution on the machine elements is compared to the present LHC Betatron cleaning collimation system in the Point 7 Insertion Region (IR).
Structure/property relationships in non-linear optical materials
Energy Technology Data Exchange (ETDEWEB)
Cole, J.M. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)]|[Durham Univ. (United Kingdom); Howard, J.A.K. [Durham Univ. (United Kingdom); McIntyre, G.J. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
The application of neutrons to the study of structure/property relationships in organic non-linear optical materials (NLOs) is described. In particular, charge-transfer effects and intermolecular interactions are investigated. Charge-transfer effects are studied by charge-density analysis and an example of one such investigation is given. The study of intermolecular interactions concentrates on the effects of hydrogen-bonding and an example is given of two structurally similar molecules with very disparate NLO properties, as a result of different types of hydrogen-bonding. (author). 3 refs.
Non-linear optical titanyl arsenates: Crystal growth and properties
Nordborg, Jenni Eva Louise
Crystals are appreciated not only for their appearance, but also for their unique physical properties which are utilized by the photonic industry in appliances that we come across every day. An important part of enabling the technical use of optical devices is the manufacture of crystals. This dissertation deals with a specific group of materials called the potassium titanyl phosphate (KIP) family, known for their non-linear optical and ferroelectric properties. The isomorphs vary in their linear optical and dielectric properties, which can be tuned to optimize device performance by forming solid solutions of the different materials. Titanyl arsenates have a wide range of near-infrared transmission which makes them useful for tunable infrared lasers. The isomorphs examined in the present work were primarily RbTiOASO4 (RTA) and CsTiOAsO4 (CTA) together with the mixtures RbxCs 1-xTiOAsO4 (RCTA). Large-scale crystals were grown by top seeding solution growth utilizing a three-zone furnace with excellent temperature control. Sufficiently slow cooling and constant upward lifting produced crystals with large volumes useable for technical applications. Optical quality RTA crystals up to 10 x 12 x 20 mm were grown. The greater difficulty in obtaining good crystals of CTA led to the use of mixed RCTA materials. The mixing of rubidium and cesium in RCTA is more favorable to crystal growth than the single components in pure RTA and CTA. Mixed crystals are rubidium-enriched and contain only 20-30% of the cesium concentration in the flux. The cesium atoms show a preference for the larger cation site. The network structure is very little affected by the cation substitution; consequently, the non-linear optical properties of the Rb-rich isomorphic mixtures of RTA and CTA can be expected to remain intact. Crystallographic methods utilizing conventional X-ray tubes, synchrotron radiation and neutron diffraction have been employed to investigate the properties of the atomic
Non-linear Calibration Leads to Improved Correspondence between Uncertainties
DEFF Research Database (Denmark)
Andersen, Jens Enevold Thaulov
2007-01-01
an investigation of an uncomplicated expression of the non-linear working curve that is well suited to an assessment of predicted uncertainties. At small concentrations, the working curve reduces to a straight line that corresponds to the conventional calibration line. If no interferences were disturbing...... limit theorem, an excellent correspondence was obtained between predicted uncertainties and measured uncertainties. In order to validate the method, experiments were applied of flame atomic absorption spectrometry (FAAS) for the analysis of Co and Pt, and experiments of electrothermal atomic absorption...
Non-Linear Dynamics of Saturn’s Rings
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
Non-linear dynamics in pulse combustor: A review
Indian Academy of Sciences (India)
Sirshendu Mondal; Achintya Kukhopadhyay; Swarnendu Sen
2015-03-01
The state of the art of non-linear dynamics applied to pulse combustor theoretically and experimentally is reviewed. Pulse combustors are a class of air-breathing engines in which pulsations in combustion are utilized to improve the performance. As no analytical solution can be obtained for most of the nonlinear systems, the whole set of solutions can be investigated with the help of dynamical system theory. Many studies have been carried out on pulse combustors whose dynamics include limit cycle behaviour, Hopf bifurcation and period-doubling bifurcation. The dynamic signature has also been used for early prediction of extinction.
A non-linear UAV altitude PSO-PD control
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.
Simulation of non-linear coaxial line using ferrite beads
Energy Technology Data Exchange (ETDEWEB)
Furuya, S.; Matsumoto, H.; Tachi, K.; Takano, S.; Irisawa, J. [Nagaoka Univ. of Technology, Niigata (Japan)
2002-06-01
A ferrite sharpener is a non-linear coaxial line using ferrite beads, which produces high-voltage, high-dV/dt pulses. We have been examining the characteristics of ferrite sharpeners experimentally, varying various parameters. Also we have made the simulation of the ferrite sharpener and compared the predictions with the experimental results in detail to analyze the characteristics of the sharpener. In this report, calculating the magnetization M of the ferrite bead, we divide the bead into n sections radially instead of adopting M at the average radius in the previous report. (author)
Hierarchical Non-linear Image Registration Integrating Deformable Segmentation
Institute of Scientific and Technical Information of China (English)
RAN Xin; QI Fei-hu
2005-01-01
A hierarchical non-linear method for image registration was presented, which integrates image segmentation and registration under a variational framework. An improved deformable model is used to simultaneously segment and register feature from multiple images. The objects in the image pair are segmented by evolving a single contour and meanwhile the parameters of affine registration transformation are found out. After that, a contour-constrained elastic registration is applied to register the images correctly. The experimental results indicate that the proposed approach is effective to segment and register medical images.
Utilization of non-linear converters for audio amplification
DEFF Research Database (Denmark)
Iversen, Niels Elkjær; Birch, Thomas; Knott, Arnold
2012-01-01
Class D amplifiers fits the automotive demands quite well. The traditional buck-based amplifier has reduced both the cost and size of amplifiers. However the buck topology is not without its limitations. The maximum peak AC output voltage produced by the power stage is only equal the supply voltage....... The introduction of non-linear converters for audio amplification defeats this limitation. A Cuk converter, designed to deliver an AC peak output voltage twice the supply voltage, is presented in this paper. A 3V prototype has been developed to prove the concept. The prototype shows that it is possible to achieve...
Non linear analyses of speech and prosody in Asperger's syndrome
DEFF Research Database (Denmark)
Fusaroli, Riccardo; Bang, Dan; Weed, Ethan
and explain this oddness of speech pattern. In this project, we quantify how the speech patterns of people with Asperger’s Syndrome (AS) differ from that of matched controls. To do so, we employed both traditional measures (pitch range and standard deviation, pause duration, and so on) and 2) non......-linear techniques measuring the structure (regularity and complexity) of verbal, prosodic and fluency behaviour. Our aims were (1) to achieve a more fine-grained understanding of the speech patterns in AS than has previously been achieved using traditional, linear measures of prosody and fluency, and (2) to employ...
Weak non-linear surface charging effects in electrolytic films
Dean, D. S.; Horgan, R. R.
2002-01-01
A simple model of soap films with nonionic surfactants stabilized by added electrolyte is studied. The model exhibits charge regularization due to the incorporation of a physical mechanism responsible for the formation of a surface charge. We use a Gaussian field theory in the film but the full non-linear surface terms which are then treated at a one-loop level by calculating the mean-field Poisson-Boltzmann solution and then the fluctuations about this solution. We carefully analyze the reno...
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...
Shea, Jacob D.; Kosmas, Panagiotis; Hagness, Susan C.; Van Veen, Barry D.
2010-01-01
Purpose: Breast density measurement has the potential to play an important role in individualized breast cancer risk assessment and prevention decisions. Routine evaluation of breast density will require the availability of a low-cost, nonionizing, three-dimensional (3-D) tomographic imaging modality that exploits a strong properties contrast between dense fibroglandular tissue and less dense adipose tissue. The purpose of this computational study is to investigate the performance of 3-D tomography using low-power microwaves to reconstruct the spatial distribution of breast tissue dielectric properties and to evaluate the modality for application to breast density characterization. Methods: State-of-the-art 3-D numerical breast phantoms that are realistic in both structural and dielectric properties are employed. The test phantoms include one sample from each of four classes of mammographic breast density. Since the properties of these phantoms are known exactly, these testbeds serve as a rigorous benchmark for the imaging results. The distorted Born iterative imaging method is applied to simulated array measurements of the numerical phantoms. The forward solver in the imaging algorithm employs the finite-difference time-domain method of solving the time-domain Maxwell’s equations, and the dielectric profiles are estimated using an integral equation form of the Helmholtz wave equation. A multiple-frequency, bound-constrained, vector field inverse scattering solution is implemented that enables practical inversion of the large-scale 3-D problem. Knowledge of the frequency-dependent characteristic of breast tissues at microwave frequencies is exploited to obtain a parametric reconstruction of the dispersive dielectric profile of the interior of the breast. Imaging is performed on a high-resolution voxel basis and the solution is bounded by a known range of dielectric properties of the constituent breast tissues. The imaging method is validated using a breast
On the formation of shocks of electromagnetic plane waves in non-linear crystals
Christodoulou, Demetrios
2015-01-01
An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global $C^2$-solution for small enough initial data. Inspired by recent work of D. Christodoulou, we revisit John's original proof and extract a more precise description of the behaviour of solutions at the time of shock. We show that John's singular first order quantity, when expressed in characteristic coordinates, remains bounded until the final time, which is then characterised by an inverse density of characteristics tending to zero in one point. Moreover, we study the derivatives of second order, showing again their boundedness when expressed in appropriate coordinates. We also recover John's upper bound for the time of shock formation and complement it with a lower bound. Finally, we apply these results to electromagnetic plane waves in a crystal with no magnetic properties and cubic electric non-linearity in the energy density...
On the formation of shocks of electromagnetic plane waves in non-linear crystals
Christodoulou, Demetrios; Perez, Daniel Raoul
2016-08-01
An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global C2-solution for small enough initial data. Inspired by recent work of D. Christodoulou, we revisit John's original proof and extract a more precise description of the behaviour of solutions at the time of shock. We show that John's singular first order quantity, when expressed in characteristic coordinates, remains bounded until the final time, which is then characterised by an inverse density of characteristics tending to zero in one point. Moreover, we study the derivatives of second order, showing again their boundedness when expressed in appropriate coordinates. We also recover John's upper bound for the time of shock formation and complement it with a lower bound. Finally, we apply these results to electromagnetic plane waves in a crystal with no magnetic properties and cubic electric non-linearity in the energy density, assuming no dispersion.
Parameter Scaling in Non-Linear Microwave Tomography
DEFF Research Database (Denmark)
Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar;
2012-01-01
Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....
Primordial black holes in linear and non-linear regimes
Allahyari, Alireza; Abolhasani, Ali Akbar
2016-01-01
Using the concept of apparent horizon for dynamical black holes, we revisit the formation of primordial black holes (PBH) in the early universe for both linear and non-linear regimes. First, we develop the perturbation theory for spherically symmetric spacetimes to study the formation of spherical PBHs in linear regime and we fix two gauges. We also introduce a well defined gauge invariant quantity for the expansion. Using this quantity, we argue that PBHs do not form in the linear regime. Finally, we study the non-linear regime. We adopt the spherical collapse picture by taking a closed FRW model in the radiation dominated era to investigate PBH formation. Taking the initial condition of the spherical collapse from the linear theory of perturbations, we allow for both density and velocity perturbations. Our model gives a constraint on the velocity perturbation. This model also predicts that the apparent horizon of PBHs forms when $\\delta > 3$. Applying the sound horizon constraint, we have shown the threshol...
Polycarbonate-Based Blends for Optical Non-linear Applications
Stanculescu, F.; Stanculescu, A.
2016-02-01
This paper presents some investigations on the optical and morphological properties of the polymer (matrix):monomer (inclusion) composite materials obtained from blends of bisphenol A polycarbonate and amidic monomers. For the preparation of the composite films, we have selected monomers characterised by a maleamic acid structure and synthesised them starting from maleic anhydride and aniline derivatives with -COOH, -NO2, -N(C2H5)2 functional groups attached to the benzene ring. The composite films have been deposited by spin coating using a mixture of two solutions, one containing the matrix and the other the inclusion, both components of the composite system being dissolved in the same solvent. The optical transmission and photoluminescence properties of the composite films have been investigated in correlation with the morphology of the films. The scanning electron microscopy and atomic force microscopy have revealed a non-uniform morphology characterised by the development of two distinct phases. We have also investigated the generation of some optical non-linear (ONL) phenomena in these composite systems. The composite films containing as inclusions monomers characterised by the presence of one -COOH or two -NO2 substituent groups to the aromatic nucleus have shown the most intense second-harmonic generation (SHG). The second-order optical non-linear coefficients have been evaluated for these films, and the effect of the laser power on the ONL behaviour of these materials has also been emphasised.
Non Linear Analysis of MPPT for Power Quality Improvement
Directory of Open Access Journals (Sweden)
S. Sankar
2015-08-01
Full Text Available In this study the conventional inverter interfacing renewable energy sources with the grid, without any additional hardware cost. Here, the main idea is the maximum utilization of inverter rating which is most of the time underutilized due to intermittent nature of RES. Based on the non-linear characteristics of PV, these thesis designs a VSS controller to realize the maximum power output of PV arrays. The output power from renewable energy sources fluctuates because of weather variations. This study proposes an effective power quality control strategy of renewable energy sources connected to power system using Photovoltaic (PV array. If the main controller used is a PR controller, any dc offset in a control loop will propagate through the system and the inverter terminal voltage will have a nonzero average value. In this strategy both load and inverter current sensing is required to compensate the load current harmonics. The non-linear load current harmonics may result in voltage harmonics and can create a serious PQ problem in the power system network.
A non-linear model of information seeking behaviour
Directory of Open Access Journals (Sweden)
Allen E. Foster
2005-01-01
Full Text Available The results of a qualitative, naturalistic, study of information seeking behaviour are reported in this paper. The study applied the methods recommended by Lincoln and Guba for maximising credibility, transferability, dependability, and confirmability in data collection and analysis. Sampling combined purposive and snowball methods, and led to a final sample of 45 inter-disciplinary researchers from the University of Sheffield. In-depth semi-structured interviews were used to elicit detailed examples of information seeking. Coding of interview transcripts took place in multiple iterations over time and used Atlas-ti software to support the process. The results of the study are represented in a non-linear Model of Information Seeking Behaviour. The model describes three core processes (Opening, Orientation, and Consolidation and three levels of contextual interaction (Internal Context, External Context, and Cognitive Approach, each composed of several individual activities and attributes. The interactivity and shifts described by the model show information seeking to be non-linear, dynamic, holistic, and flowing. The paper concludes by describing the whole model of behaviours as analogous to an artist's palette, in which activities remain available throughout information seeking. A summary of key implications of the model and directions for further research are included.
The Linear-Non-Linear Frontier for the Goldstone Higgs
Energy Technology Data Exchange (ETDEWEB)
Gavela, M. B. [Madrid, IFT; Kanshin, K. [Padua U.; Machado, P. A.N. [Madrid, IFT; Saa, S. [Madrid, IFT
2016-10-25
The minimal $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $\\sigma$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.
PV Degradation Curves: Non-Linearities and Failure Modes
Energy Technology Data Exchange (ETDEWEB)
Jordan, Dirk C.; Silverman, Timothy J.; Sekulic, Bill; Kurtz, Sarah R.
2016-09-03
Photovoltaic (PV) reliability and durability have seen increased interest in recent years. Historically, and as a preliminarily reasonable approximation, linear degradation rates have been used to quantify long-term module and system performance. The underlying assumption of linearity can be violated at the beginning of the life, as has been well documented, especially for thin-film technology. Additionally, non-linearities in the wear-out phase can have significant economic impact and appear to be linked to different failure modes. In addition, associating specific degradation and failure modes with specific time series behavior will aid in duplicating these degradation modes in accelerated tests and, eventually, in service life prediction. In this paper, we discuss different degradation modes and how some of these may cause approximately linear degradation within the measurement uncertainty (e.g., modules that were mainly affected by encapsulant discoloration) while other degradation modes lead to distinctly non-linear degradation (e.g., hot spots caused by cracked cells or solder bond failures and corrosion). The various behaviors are summarized with the goal of aiding in predictions of what may be seen in other systems.
Non-linear Plasma Wake Growth of Electron Holes
Hutchinson, I H; Zhou, C
2015-01-01
An object's wake in a plasma with small Debye length that drifts \\emph{across} the magnetic field is subject to electrostatic electron instabilities. Such situations include, for example, the moon in the solar wind wake 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...
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.
An Adaptive Non-Linear Map and Its Application
Institute of Scientific and Technical Information of China (English)
YAN Xuefeng
2006-01-01
A novel adaptive non-linear mapping (ANLM),integrating an adaptive mapping error (AME) with a chaosgenetic algorithm (CGA) including chaotic variable, was proposed to overcome the deficiencies of non-linear mapping (NLM). The value of AME weight factor is determined according to the relative deviation square of distance between the two mapping points and the corresponding original objects distance. The larger the relative deviation square between two distances is, the larger the value of the corresponding weight factor is. Due to chaotic mapping operator, the evolutional process of CGA makes the individuals of subgenerations distributed ergodically in the defined space and circumvents the premature of the individuals of subgenerations. The comparison results demonstrated that the whole performance of CGA is better than that of traditional genetic algorithm. Furthermore, a typical example of mapping eight-dimensional olive oil samples onto two-dimensional plane was employed to verify the effectiveness of ANLM. The results showed that the topology-preserving map obtained by ANLM can well represent the classification of original objects and is much better than that obtained by NLM.
Charged relativistic fluids and non-linear electrodynamics
Dereli, T.; Tucker, R. W.
2010-01-01
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these modified theories are tenable. However with the advent of high-intensity lasers and powerful laboratory magnetic fields this situation may be changing. We argue that an approach involving the self-consistent relativistic motion of a smooth fluid-like distribution of matter (composed of a large number of charged or neutral particles) in an electromagnetic field offers a viable theoretical framework in which to explore the experimental consequences of non-linear electrodynamics. We construct such a model based on the theory of Born and Infeld and suggest that a simple laboratory experiment involving the propagation of light in a static magnetic field could be used to place bounds on the fundamental coupling in that theory. Such a framework has many applications including a new description of the motion of particles in modern accelerators and plasmas as well as phenomena in astrophysical contexts such as in the environment of magnetars, quasars and gamma-ray bursts.
Non-linear leak currents affect mammalian neuron physiology
Directory of Open Access Journals (Sweden)
Shiwei eHuang
2015-11-01
Full Text Available 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.
Parameter Scaling in Non-Linear Microwave Tomography
DEFF Research Database (Denmark)
Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar
2012-01-01
Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....
Left-Right Non-Linear Dynamical Higgs
Shu, Jing; Yepes, Juan
2016-12-01
All the possible CP-conserving non-linear operators up to the p4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically, from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)L × SU(2)R × U(1)B-L. Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV-2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators. J. Y. also acknowledges KITPC financial support during the completion of this work
Non-linear plasma wake growth of electron holes
Hutchinson, I. H.; Haakonsen, C. B.; Zhou, C.
2015-03-01
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.
Huttunen, Jani; Kokkola, Harri; Mielonen, Tero; Esa Juhani Mononen, Mika; Lipponen, Antti; Reunanen, Juha; Vilhelm Lindfors, Anders; Mikkonen, Santtu; Erkki Juhani Lehtinen, Kari; Kouremeti, Natalia; Bais, Alkiviadis; Niska, Harri; Arola, Antti
2016-07-01
In order to have a good estimate of the current forcing by anthropogenic aerosols, knowledge on past aerosol levels is needed. Aerosol optical depth (AOD) is a good measure for aerosol loading. However, dedicated measurements of AOD are only available from the 1990s onward. One option to lengthen the AOD time series beyond the 1990s is to retrieve AOD from surface solar radiation (SSR) measurements taken with pyranometers. In this work, we have evaluated several inversion methods designed for this task. We compared a look-up table method based on radiative transfer modelling, a non-linear regression method and four machine learning methods (Gaussian process, neural network, random forest and support vector machine) with AOD observations carried out with a sun photometer at an Aerosol Robotic Network (AERONET) site in Thessaloniki, Greece. Our results show that most of the machine learning methods produce AOD estimates comparable to the look-up table and non-linear regression methods. All of the applied methods produced AOD values that corresponded well to the AERONET observations with the lowest correlation coefficient value being 0.87 for the random forest method. While many of the methods tended to slightly overestimate low AODs and underestimate high AODs, neural network and support vector machine showed overall better correspondence for the whole AOD range. The differences in producing both ends of the AOD range seem to be caused by differences in the aerosol composition. High AODs were in most cases those with high water vapour content which might affect the aerosol single scattering albedo (SSA) through uptake of water into aerosols. Our study indicates that machine learning methods benefit from the fact that they do not constrain the aerosol SSA in the retrieval, whereas the LUT method assumes a constant value for it. This would also mean that machine learning methods could have potential in reproducing AOD from SSR even though SSA would have changed during
Godziek, Agnieszka; Maciejowska, Anna; Sajewicz, Mieczysław; Kowalska, Teresa
2015-03-01
This is our new study in a series of publications devoted to exploration of applicability of high-performance liquid chromatography (HPLC) to providing answers to difficult questions from the area of the reaction kinetics and mechanisms with non-linear reactions. Although an excellent analytical performance of HPLC is an indisputable fact, so far its performance as a tool in the kinetic and mechanistic studies has been tested to a lesser extent. In our earlier studies, spontaneous peptidization dynamics of amino acids in solution was demonstrated by means of HPLC upon a few amino acid examples, and on that basis a theoretical model has been developed, anticipating an interdependence of dynamics on chemical structures of amino acids involved. In order to expand the spectrum of experimentally investigated amino acid cases, in this study we present the results valid for three novel amino acids of significant life sciences importance, which differ in terms of peptidization dynamics. Experimental evidence originates from the achiral HPLC with the evaporative light scattering detection and MS detection. A conclusion is drawn that different spontaneous peptidization dynamics of amino acids may significantly influence chemical composition of proteins encountered in living organisms. Hence, a need emerges for systematic physicochemical studies on spontaneous non-linear peptidization dynamics of proteinogenic amino acids in liquid abiotic (but also in the biotic) systems.
Ghosez, Philippe
2006-03-01
The non-linear response of infinite periodic solids to homogenous electric fields and cooperative atomic displacements will be discussed in the framework of density functional perturbation theory. The approach is based on the “2n + 1” theorem applied to an electric field dependent energy functional. We will focus on the non-linear optical susceptibilities, Raman scattering efficiencies and electrooptic coefficients. Different formulations of third-order energy derivatives will be examined and their convergence with respect to the k-point sampling will be discussed. The method will be applied to conventional semiconductors and to ferroelectric oxides. In the latter case, we will also describe how the first- principles results can be combined to an effective Hamiltonian approach in order to provide access to the temperature dependence of the optical properties. This work was done in collabration with M. Veithen and X. Gonze and was supported by the VolkwagenStiftung, FNRS-Belgium and the FAME-NoE.
DEFF Research Database (Denmark)
Ducrozet, Guillaume; Engsig-Karup, Allan Peter; Bingham, Harry B.;
2014-01-01
This paper deals with the development of an enhanced model for solving wave–wave and wave–structure interaction problems. We describe the application of a non-linear splitting method originally suggested by Di Mascio et al. [1], to the high-order finite difference model developed by Bingham et al....... [2] and extended by Engsig-Karup et al. [3] and [4]. The enhanced strategy is based on splitting all solution variables into incident and scattered fields, where the incident field is assumed to be known and only the scattered field needs to be computed by the numerical model. Although this splitting...
Short-time Lv transform and its application for non-linear FM signal detection
Institute of Scientific and Technical Information of China (English)
Shan Luo; Xiumei Li; Guoan Bi
2015-01-01
A new time-frequency transform, known as short-time Lv transform (STLVT), is proposed by applying the inverse Lv dis-tribution to process consecutive segments of long data sequence. Compared with other time-frequency representations, the STLVT is able to achieve better energy concentration in the time-frequency domain for signals containing multiple linear and/or non-linear frequency modulated components. The merits of the STLVT are demonstrated in terms of the effects of window length and overlap length between adjacent segments on signal energy concentra-tion in the time-frequency domain, and the required computational complexity. An application on the spectrum sensing for cognitive ratio (CR) by using a joint use of the STLVT and Hough transform (HT) is proposed and simulated.
Ishikawa, R; Belluzzi, L; Sainz, R Manso; Stepan, J; Bueno, J Trujillo; Goto, M; Tsuneta, S
2014-01-01
Magnetic field measurements in the upper chromosphere and above, where the gas-to-magnetic pressure ratio $\\beta$ is lower than unity, are essential for understanding the thermal structure and dynamical activity of the solar atmosphere. Recent developments in the theory and numerical modeling of polarization in spectral lines have suggested that information on the magnetic field of the chromosphere-corona transition region could be obtained by measuring the linear polarization of the solar disk radiation at the core of the hydrogen Lyman-$\\alpha$ line at 121.6~nm, which is produced by scattering processes and the Hanle effect. The Chromospheric Lyman-$\\alpha$ Spectropolarimeter (CLASP) sounding rocket experiment aims to measure the intensity (Stokes $I$) and the linear polarization profiles ($Q/I$ and $U/I$) of the hydrogen Lyman-$\\alpha$ line. In this paper we clarify the information that the Hanle effect can provide by applying a Stokes inversion technique based on a database search. The database contains a...
Kalmykov, S. Y.; Davoine, X.; Ghebregziabher, I.; Shadwick, B. A.
2016-09-01
Laser wakefield acceleration of electrons in the blowout regime can be controlled by tailoring the laser pulse phase and the plasma target. The 100 nm-scale bandwidth and negative frequency chirp of the optical driver compensate for the nonlinear frequency red-shift imparted by wakefield excitation. This mitigates pulse self-steepening and suppresses continuous injection. The plasma channel suppresses diffraction of the pulse leading edge, further reducing self-steepening, making injection even quieter. Besides, the channel destabilizes the pulse tail confined within the accelerator cavity (the electron density "bubble"), causing oscillations in the bubble size. The resulting periodic injection generates background-free comb-like beams - sequences of synchronized, low phase-space volume bunches. Controlling the number of bunches, their energy, and energy spacing by varying the channel radius and the pulse length (as permitted by the large bandwidth) enables the design of a tunable, all-optical source of polychromatic, pulsed γ-rays using the mechanism of inverse Thomson scattering. Such source may radiate ~107 quasi-monochromatic 10 MeV-scale photons per shot into a microsteradian-scale observation angle. The photon energy is distributed among several distinct bands, each having sub-25% energy spread dictated by the mrad-scale divergence of electron beam.
Dai, Z G; Liang, E W; Zhang, Bing
2006-01-01
The gamma-ray burst (GRB) 060218/SN 2006aj is a peculiar event, with the second lowest redshift, low luminosity, long duration, chromatic lightcurve features, and in particular, the presence of a thermal component in the X-ray and UV-optical spectra. Thanks to detailed temporal and spectral coverage of the {\\em Swift} observatory, the abundant data allow the GRB prompt emission to be modelled in great detail for the first time. The low flux of prompt UV/optical emission disfavors the conventional internal shock/synchrotron radiation models, which generally predict strong UV/optical emission. Here we show that the unusual prompt emission of GRB 060218 can be produced by inverse-Compton scattering of shock-accelerated relativistic electrons off the detected thermal photons. A pair of (forward plus reverse) shocks form when a relativistic outflow interacts with a preexisting slower shell. The observed gamma-ray emission and X-ray emission arise from the reverse-shocked and forward-shocked regions, respectively. ...
A three-body model for the analysis of quasi-free scattering reactions in inverse kinematics
Moro, Antonio M
2015-01-01
A new method to calculate cross sections for $(p,pn)$ and $(p,2p)$ reactions measured under inverse kinematics conditions is proposed. The method uses the prior form of the scattering transition amplitude, and replaces the exact three-body wave function appearing in this expression by an expansion in terms of $p$-$n$ or $p$-$p$ states, covering the physically relevant excitation energies and partial waves. A procedure of discretization, similar to that used in continuum-discretized coupled-channels calculations, is applied in order to make this expansion finite and numerically tractable. The proposed formalism is non-relativistic but several relativistic kinematical corrections are applied to extend its applicability to energies of current interest. The underlying optical potentials for the entrance and exit channels are generated microscopically, by folding an effective density-dependent G-matrix with the density of the composite nucleus. Numerical calculations for $^{12}$C($p$,$2p$), $^{12}$C($p$,$pn$) and ...
Non-linear dimensionality reduction of signaling networks
Directory of Open Access Journals (Sweden)
Ivakhno Sergii
2007-06-01
Full Text Available Abstract Background Systems wide modeling and analysis of signaling networks is essential for understanding complex cellular behaviors, such as the biphasic responses to different combinations of cytokines and growth factors. For example, tumor necrosis factor (TNF can act as a proapoptotic or prosurvival factor depending on its concentration, the current state of signaling network and the presence of other cytokines. To understand combinatorial regulation in such systems, new computational approaches are required that can take into account non-linear interactions in signaling networks and provide tools for clustering, visualization and predictive modeling. Results Here we extended and applied an unsupervised non-linear dimensionality reduction approach, Isomap, to find clusters of similar treatment conditions in two cell signaling networks: (I apoptosis signaling network in human epithelial cancer cells treated with different combinations of TNF, epidermal growth factor (EGF and insulin and (II combination of signal transduction pathways stimulated by 21 different ligands based on AfCS double ligand screen data. For the analysis of the apoptosis signaling network we used the Cytokine compendium dataset where activity and concentration of 19 intracellular signaling molecules were measured to characterise apoptotic response to TNF, EGF and insulin. By projecting the original 19-dimensional space of intracellular signals into a low-dimensional space, Isomap was able to reconstruct clusters corresponding to different cytokine treatments that were identified with graph-based clustering. In comparison, Principal Component Analysis (PCA and Partial Least Squares – Discriminant analysis (PLS-DA were unable to find biologically meaningful clusters. We also showed that by using Isomap components for supervised classification with k-nearest neighbor (k-NN and quadratic discriminant analysis (QDA, apoptosis intensity can be predicted for different
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
Tokluoglu, Erinc K.
fields generated by beam-plasma instabilities can be responsible for defocusing and distorting beams propagating in background plasma. This can be problematic in inertial fusion applications where the beam is intended to propagate ballistically as the background plasma neutralizes the beam space charge and current. We used particle-in-cell (PIC) code LSP to numerically investigate the defocusing effects in an ion beam propagating in background plasma experiences as it is exposed to the non-linear fields generated by Two-Stream instability between beam ions and plasma electrons. Supported by theory and benchmarked by the numerical solutions of governing E&M equations, the simulations were used to find and check scaling laws for the defocusing forces in the parameter space of beam and plasma density as well as the beam ion mass. A transition region where the defocusing fields peak has been identified, which should be avoided in the design of experimental devices. We further proposed a diagnostic tool to identify the presence of the two-stream instability in a system with parameters similar to the National Drift Compression Experiment II (NDCX-II) and conducted proof-of concept simulations. In the case of electron beam propagating in background plasma instability driven collisionless scattering and plasma heating is observed. 1-D simulations conducted in EDIPIC were benchmarked in LSP to study the excitation and time-evolution of electron-electron Two-Stream instability. Coupling of electron dynamics via non-linear ponderomotive force created by instability generated fields with ion cavities and Ion-Acoustic mode excitation was observed. Furthermore 2-D simulations of an electron-beam in a background plasma was performed. Many of the effects in observed in 1-D simulations were replicated. Morever generation of oblique modes with transverse wave numbers were observed in the simulations, which resulted in significant transverse scattering of beam electrons and the time
Brunetti, G
1999-01-01
The problem of the anisotropic Inverse Compton scattering between a monochromatic photon beam and relativistic electrons is revisited and formally solved without approximations. Solutions are given for the single scattering with an electron beam and with a population of electrons isotropically distributed, under the assumption that the energy distribution of the relativistic particles follows a simple power law as it is the case in many astrophysical applications. Both the Thomson approximation and the Klein-Nishina regime are considered for the scattering of an unpolarized photon beam. The equations are obtained without the ultra-relativistic approximation and are compared with the ultra-relativistic solutions given in the literature. The main characteristics of the power distribution and spectra of the scattered radiation are discussed for relevant examples. In the Thomson case for an isotropic electron population simple formulae holding down to mildly-relativistic energies are given. As an application the ...
New holographic dark energy model with non-linear interaction
Oliveros, A
2014-01-01
In this paper the cosmological evolution of a holographic dark energy model with a non-linear interaction between the dark energy and dark matter components in a FRW type flat universe is analysed. In this context, the deceleration parameter $q$ and the equation state $w_{\\Lambda}$ are obtained. We found that, as the square of the speed of sound remains positive, the model is stable under perturbations since early times; it also shows that the evolution of the matter and dark energy densities are of the same order for a long period of time, avoiding the so--called coincidence problem. We have also made the correspondence of the model with the dark energy densities and pressures for the quintessence and tachyon fields. From this correspondence we have reconstructed the potential of scalar fields and their dynamics.
Ferrite core non-linearity in coils for magnetic neurostimulation.
RamRakhyani, Anil Kumar; Lazzi, Gianluca
2014-10-01
The need to correctly predict the voltage across terminals of mm-sized coils, with ferrite core, to be employed for magnetic stimulation of the peripheral neural system is the motivation for this work. In such applications, which rely on a capacitive discharge on the coil to realise a transient voltage curve of duration and strength suitable for neural stimulation, the correct modelling of the non-linearity of the ferrite core is critical. A demonstration of how a finite-difference model of the considered coils, which include a model of the current-controlled inductance in the coil, can be used to correctly predict the time-domain voltage waveforms across the terminals of a test coil is presented. Five coils of different dimensions, loaded with ferrite cores, have been fabricated and tested: the measured magnitude and width of the induced pulse are within 10% of simulated values.
Non-Gaussianity vs. non-linearity of cosmological perturbations
Verde, L
2001-01-01
Following the discovery of the CMB, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us towards a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, non-linear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but these might not be faithful tr...
Hans Hinterreiter’s non-linear transformations
DEFF Research Database (Denmark)
Makovicky, Emil
Hans Hinterreiter (1902-1989) was a Swiss painter, belonging to the Constructivist movement, who spent most of his life in Ibiza, Spain. Since 1930 he occupied himself with the laws of form and colour. Parallel to Escher, he discovered laws of coloured symmetry before crystallographers started...... poster illustrates four different cases of this process, starting always with a plane-group pattern and showing both the application of non-linear transformations and coloured symmetry. In his more complex patterns, two of which are shown on the poster, Hinterreiter created domains of affinely......-step approach that combines plane group patterns with the principles of coloured symmetry and nonlinear transformations, his understanding of crystallographic and non-crystallographic symmetry and a meticulous application of these principles even to the most complex patterns produced a legacy close to the heart...
Non-linear Kalman filters for calibration in radio interferometry
Tasse, Cyril
2014-01-01
We present a new calibration scheme based on a non-linear version of Kalman filter that aims at estimating the physical terms appearing in the Radio Interferometry Measurement Equation (RIME). We enrich the filter's structure with a tunable data representation model, together with an augmented measurement model for regularization. We show using simulations that it can properly estimate the physical effects appearing in the RIME. We found that this approach is particularly useful in the most extreme cases such as when ionospheric and clock effects are simultaneously present. Combined with the ability to provide prior knowledge on the expected structure of the physical instrumental effects (expected physical state and dynamics), we obtain a fairly cheap algorithm that we believe to be robust, especially in low signal-to-noise regime. Potentially the use of filters and other similar methods can represent an improvement for calibration in radio interferometry, under the condition that the effects corrupting visib...
Hitting probabilities for non-linear systems of stochastic waves
Dalang, Robert C
2012-01-01
We consider a $d$-dimensional random field $u = \\{u(t,x)\\}$ that solves a non-linear system of stochastic wave equations in spatial dimensions $k \\in \\{1,2,3\\}$, driven by a spatially homogeneous Gaussian noise that is white in time. We mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent $\\beta$. Using Malliavin calculus, we establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of $\\IR^d$, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when $d(2-\\beta) > 2(k+1)$, points are polar for $u$. Conversely, in low dimensions $d$, points are not polar. There is however an interval in which the question of polarity of points remains open.
Predictability of extremes in non-linear hierarchically organized systems
Kossobokov, V. G.; Soloviev, A.
2011-12-01
Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare
Method and system for non-linear motion estimation
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.
Overall mass-transfer coefficients in non-linear chromatography
DEFF Research Database (Denmark)
Mollerup, Jørgen; Hansen, Ernst
1998-01-01
In case of mass transfer where concentration differences in both phases must be taken into account, one may define an over-all mass-transfer coefficient basd on the apparent over-all concentration difference. If the equilibrium relationship is linear, i.e. in cases where a Henry´s law relationship...... can be applied, the over-all mass-transfer coefficient will be concentration independent. However, in mass-transfer operations, a linear equilibrium relationship is in most cases not a valid approximation wherefore the over-all mass-transfer coefficient becomes strongly concentration dependent...... as shown in this paper. In this case one has to discard the use of over-all mass-transfer coefficients and calculate the rate of mass transfer from the two film theory using the appropriate non-linear relationship to calculate the equilibrium ratio at the interface between the two films....
Non-linear rheology in a model biological tissue
Matoz-Fernandez, D A; Barrat, Jean-Louis; Bertin, Eric; Martens, Kirsten
2016-01-01
Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model featuring random apoptosis and environment-dependent division rates, we evidence a crossover from linear flow to a shear-thinning regime with increasing shear rate. To rationalize this non-linear flow we derive a theoretical mean-field scenario that accounts for the interplay of mechanical and active noise in local stresses. These noises are respectively generated by the elastic response of the cell matrix to cell rearrangements and by the internal activity.
Realising traceable electrostatic forces despite non-linear balance motion
Stirling, Julian; Shaw, Gordon A.
2017-05-01
Direct realisation of force, traceable to fundamental constants via electromagnetic balances, is a key goal of the proposed redefinition of the international system of units (SI). This will allow small force metrology to be performed using an electrostatic force balance (EFB) rather than subdivision of larger forces. Such a balance uses the electrostatic force across a capacitor to balance an external force. In this paper we model the capacitance of a concentric cylinder EFB design as a function of the displacement of its free electrode, accounting for the arcuate motion produced by parallelogram linkages commonly used in EFB mechanisms. From this model we suggest new fitting procedures to reduce uncertainties arising from non-linear motion as well as methods to identify misalignment of the mechanism. Experimental studies on both a test capacitor and the NIST EFB validate the model.
The mathematics of non-linear metrics for nested networks
Wu, Rui-Jie; Shi, Gui-Yuan; Zhang, Yi-Cheng; Mariani, Manuel Sebastian
2016-10-01
Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness-complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness-complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness-complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.
Biometric Authentication System using Non-Linear Chaos
Directory of Open Access Journals (Sweden)
Dr.N.Krishnan
2010-08-01
Full Text Available A major concern nowadays for any Biometric Credential Management System is its potential vulnerability to protect its information sources; i.e. protecting a genuine user’s template from both internal and external threats. These days’ biometric authentication systems face various risks. One of the most serious threats is the ulnerability of the template's database. An attacker with access to a reference template could try to impersonate a legitimate user by reconstructing the biometric sample and by creating a physical spoof.Susceptibility of the database can have a disastrous impact on the whole authentication system. The potential disclosure of digitally stored biometric data raises serious concerns about privacy and data protection. Therefore, we propose a method which would integrate conventional cryptography techniques with biometrics. In this work, we present a biometric crypto system which encrypts the biometric template and the encryption is done by generating pseudo random numbers, based on non-linear dynamics.
Responding to non-linear internationalisation of public policy
DEFF Research Database (Denmark)
Daugbjerg, Carsten
2016-01-01
The transfer of regulatory authority to international organisations can initiate domestic policy reform. The internationalisation process can be a one-off transfer of authority to international institutions or an ongoing process. In the latter situation, the level of internationalisation may...... be gradually increased by expanding the regulatory scope of the regime or by deepening it. However, internationalisation processes may also involve stalemate or even reversal. How do domestic policy makers respond to such non-linear internationalisation? To answer this question, this paper analyzes...... the relationship between developments in the GATT and WTO farm trade negotiations and the reform trajectory of the EU's Common Agricultural Policy (CAP) from the early 1990s to 2013. Until 2008, the EU gradually changed the support instruments of the CAP to limit their trade distorting impact. After the Doha Round...
Computational models of signalling networks for non-linear control.
Fuente, Luis A; Lones, Michael A; Turner, Alexander P; Stepney, Susan; Caves, Leo S; Tyrrell, Andy M
2013-05-01
Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.
Linear and non-linear bias: predictions vs. measurements
Hoffmann, Kai; Gaztanaga, Enrique
2016-01-01
We study the linear and non-linear bias parameters which determine the mapping between the distributions of galaxies and the full matter density fields, comparing different measurements and predictions. Accociating galaxies with dark matter haloes in the MICE Grand Challenge N-body simulation we directly measure the bias parameters by comparing the smoothed density fluctuations of halos and matter in the same region at different positions as a function of smoothing scale. Alternatively we measure the bias parameters by matching the probablility distributions of halo and matter density fluctuations, which can be applied to observations. These direct bias measurements are compared to corresponding measurements from two-point and different third-order correlations, as well as predictions from the peak-background model, which we presented in previous articles using the same data. We find an overall variation of the linear bias measurements and predictions of $\\sim 5 \\%$ with respect to results from two-point corr...
Non linear prompt neutron kinetics in multigroup diffusion theory
Energy Technology Data Exchange (ETDEWEB)
Ghatak, Ajoy Kumar
1963-06-15
It is shown that in the usual point kinetics formulation of the Fuch's model the assumption that the basic quantity is the ratio of prompt negative temperature coefficient to prompt neutron lifetime is correct in the limit that the higher mode effects can be neglected. The criticality calculation needed to calculate this coefficient is defined. The effect on the Fuch's model when the heat capacity and temperature coefficient vary linearly with temperature and delayed neutrons are taken into account is considered. The higher mode contributions in the presence of temperature feed-back effects are estimated. A method for calculating the space-dependent effects in non-linear kinetics is outlined. An analysis of the transient behavior of the TREAT reactor is also given. (C.E.S.)
Non-linear Oscillations of Compact Stars and Gravitational Waves
Passamonti, A
2006-01-01
This thesis investigates in the time domain a particular class of second order perturbations of a perfect fluid non-rotating compact star: those arising from the coupling between first order radial and non-radial perturbations. This problem has been treated by developing a gauge invariant formalism based on the 2-parameter perturbation theory (Sopuerta, Bruni and Gualtieri, 2004) where the radial and non-radial perturbations have been separately parameterized. The non-linear perturbations obey inhomogeneous partial differential equations, where the structure of the differential operator is given by the previous perturbative orders and the source terms are quadratic in the first order perturbations. In the exterior spacetime the sources vanish, thus the gravitational wave properties are completely described by the second order Zerilli and Regge-Wheeler functions. As main initial configuration we have considered a first order differentially rotating and radially pulsating star. Although at first perturbative or...
An empirical evaluation of non-linear trading rules.
Directory of Open Access Journals (Sweden)
Sosvilla-Rivero, Simón
2003-01-01
Full Text Available In this paper we investigate the profitability of non-linear trading rules based on nearest neighbour (NN predictors. Applying this investment strategy to the New York Stock Exchange, our results suggest that, taking into account transaction costs, the NN-based trading rule is superior to both a riskadjusted buy-and-hold strategy and a linear ARIMA-based strategy in terms of returns for all of the years studied (1997-2002. Regarding other profitability measures, the NN-based trading rule yields higher Sharpe ratios than the ARIMA-based strategy for all of the years in the sample except for 2001. As for 2001, in 36 out of the 101 cases considered, the ARIMA-based strategy gives higher Sharpe ratios than those from the NN-trading rule, in 18 cases the opposite is true, and in the remaining 36 cases both strategies yield the same ratios.
Non-linear PIC simulation in a penning trap
Energy Technology Data Exchange (ETDEWEB)
Delzanno, G. L. (Gian L.); Lapenta, G. M. (Giovanni M.); Finn, J. M. (John M.)
2001-01-01
We study the non-linear dynamics of a Penning trap plasma, including the effect of the finite length and end curvature of the plasma column. A new cylindrical PIC code, called KANDINSKY, has been implemented by using a new interpolation scheme. The principal idea is to calculate the volume of each cell from a particle volume, in the same manner as it is done for the cell charge. With this new method, the density is conserved along streamlines and artificial sources of compressibility are avoided. The code has been validated with a reference Eulerian fluid code. We compare the dynamics of three different models: a model with compression effects, the standard Euler model and a geophysical fluid dynamics model. The results of our investigation prove that Penning traps can really be used to simulate geophysical fluids.
Robust C subroutines for non-linear optimization
DEFF Research Database (Denmark)
Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun
2004-01-01
This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems. The intention is that the routines should use the currently best algorithms available. All routines have standardized calls, and the user does not have...... by changing 1 to 0. The present report is a new and updated version of a previous report NI-91-03 with the same title, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated from Fortran to C. The reason for writing the present report is that some...... of the C subroutines have been replaced by more effective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modi ed to some extent. For a description of the original Fortran subroutines see the report [17]. The software...
Black Hole Hair Removal: Non-linear Analysis
Jatkar, Dileep P; Srivastava, Yogesh K
2009-01-01
BMPV black holes in flat transverse space and in Taub-NUT space have identical near horizon geometries but different microscopic degeneracies. It has been proposed that this difference can be accounted for by different contribution to the degeneracies of these black holes from hair modes, -- degrees of freedom living outside the horizon. In this paper we explicitly construct the hair modes of these two black holes as finite bosonic and fermionic deformations of the black hole solution satisfying the full non-linear equations of motion of supergravity and preserving the supersymmetry of the original solutions. Special care is taken to ensure that these solutions do not have any curvature singularity at the future horizon when viewed as the full ten dimensional geometry. We show that after removing the contribution due to the hair degrees of freedom from the microscopic partition function, the partition functions of the two black holes agree.
Black hole hair removal: non-linear analysis
Jatkar, Dileep P.; Sen, Ashoke; Srivastava, Yogesh K.
2010-02-01
BMPV black holes in flat transverse space and in Taub-NUT space have identical near horizon geometries but different microscopic degeneracies. It has been proposed that this difference can be accounted for by different contribution to the degeneracies of these black holes from hair modes, — degrees of freedom living outside the horizon. In this paper we explicitly construct the hair modes of these two black holes as finite bosonic and fermionic deformations of the black hole solution satisfying the full non-linear equations of motion of supergravity and preserving the supersymmetry of the original solutions. Special care is taken to ensure that these solutions do not have any curvature singularity at the future horizon when viewed as the full ten dimensional geometry. We show that after removing the contribution due to the hair degrees of freedom from the microscopic partition function, the partition functions of the two black holes agree.
Non Linear Lorentz Transformation and Doubly Special Relativity
Atehortua, A N; Mira, J M; Vanegas, N
2012-01-01
We generate non-linear representations of the Lorentz Group by unitary transformation over the Lorentz generators. To do that we use deformed scale transformations by introducing momentum-depending parameters. The momentum operator transformation is found to be equivalent to a particle momentum transformation. The configuration space transformation is found to depend on the old momentum operator and we show that this transformation generates models with two scales, one for the velocity ($c$) and another one for the energy. A Lagrangian formalism is proposed for these models and an effective metric for the deformed Minkowski space is found. We show that the Smolin model is one in a family of doubly special relativity. Finally we construct an ansatz for the quantization of such theories.
Non-linear scalable TFETI domain decomposition based contact algorithm
Dobiáš, J.; Pták, S.; Dostál, Z.; Vondrák, V.; Kozubek, T.
2010-06-01
The paper is concerned with the application of our original variant of the Finite Element Tearing and Interconnecting (FETI) domain decomposition method, called the Total FETI (TFETI), to solve solid mechanics problems exhibiting geometric, material, and contact non-linearities. The TFETI enforces the prescribed displacements by the Lagrange multipliers, so that all the subdomains are 'floating', the kernels of their stiffness matrices are known a priori, and the projector to the natural coarse grid is more effective. The basic theory and relationships of both FETI and TFETI are briefly reviewed and a new version of solution algorithm is presented. It is shown that application of TFETI methodology to the contact problems converts the original problem to the strictly convex quadratic programming problem with bound and equality constraints, so that the effective, in a sense optimal algorithms is to be applied. Numerical experiments show that the method exhibits both numerical and parallel scalabilities.
Considering Complexity: Toward A Strategy for Non-linear Analysis
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Ken Hatt
2009-01-01
Full Text Available This paper explores complexity and a strategy for non-linear analysis with a consistent ontological, epistemological and methodological orientation. Complexity is defined and approaches in the natural sciences, ecosystems research, discursive studies and the social sciences are reviewed. In social science, theoretical efforts associated with problems of social order (Luhmann, critical sociology (Byrne and post-structuralism (Cilliers as well as representative studies are examined. The review concludes that there is need for an approach that will address morphogenesis and facilitate analysis of multilateral mutual causal relations. The remainder of the paper approaches these matters by outlining Archer’s approach to morphogenesis, Maruyama’s morphogenetic casual-loop model of epistemology and illustrating Maruyama’s method for analysis which employs both positive and negative feedback loops. The result is a strategy based on morphogenetic causal loop models that can be used to analyze structuring and the connections through which structures may be reproduced or transformed.
Non-linear quantum dynamics in strong and short electromagnetic fields
Titov, Alexander I; Hosaka, Atsushi; Takabe, Hideaki
2016-01-01
In our contribution we give a brief overview of two widely discussed quantum processes: electron-positron pairs production off a probe photon propagating through a polarized short-pulsed electromagnetic (e.m.) (e.g.\\ laser) wave field or generalized Breit-Wheeler process and a single a photon emission off an electron interacting with the laser pules, so-called non-linear Compton scattering. We show that at small and moderate laser field intensities the shape and duration of the pulse are very important for the probability of considered processes. However, at high intensities the multi-photon interactions of the fermions with laser field are decisive and completely determined all aspects of subthreshold electron-positron pairs and photon production
A general derivation of the subharmonic threshold for non-linear bubble oscillations.
Prosperetti, Andrea
2013-06-01
The paper describes an approximate but rather general derivation of the acoustic threshold for a subharmonic component to be possible in the sound scattered by an insonified gas bubble. The general result is illustrated with several specific models for the mechanical behavior of the surface coating of bubbles used as acoustic contrast agents. The approximate results are found to be in satisfactory agreement with fully non-linear numerical results in the literature. The amplitude of the first harmonic is also found by the same method. A fundamental feature identified by the analysis is that the subharmonic threshold can be considerably lowered with respect to that of an uncoated free bubble if the mechanical response of the coating varies rapidly in the neighborhood of certain specific values of the bubble radius, e.g., because of buckling.
Non-linear collisionless damping of Weibel turbulence in relativistic blast waves
Lemoine, Martin
2014-01-01
The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the first-order non-linear terms associated to the diffusive nature of the particle trajectories. These corrections are found to systematically increase the damping rate, assuming that the scattering length remains larger than the coherence length of the magnetic fluctuations. The relevance of such corrections is discussed in a broader astrophysical perspective, in particular regarding the physics of the external relativistic ...
NOLB : Non-linear rigid block normal mode analysis method.
Hoffmann, Alexandre; Grudinin, Sergei
2017-04-05
We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy and topology analyses, and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes. A graphical user interfaces created for the SAMSON software platform will be made available at https: //www.samson-connect.net.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
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Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
Non-linear dynamics of a spur gear pair
Kahraman, A.; Singh, R.
1990-10-01
Non-linear frequency response characteristics of a spur gear pair with backlash are examined in this paper for both external and internal excitations. The internal excitation is of importance from the high frequency noise and vibration control viewpoint and it represents the overall kinematic or static transmission error. Such problems may be significantly different from the rattle problems associated with external, low frequency torque excitation. Two solution methods, namely the digital simulation technique and the method of harmonic balance, have been used to develop the steady state solutions for the internal sinusoidal excitation. Difficulties associated with the determination of the multiple solutions at a given frequency in the digital simulation technique have been resolved, as one must search the entire initial conditions map. Such solutions and the transition frequencies for various impact situations are easily found by the method of harmonic balance. Further, the principle of superposition can be employed to analyze the periodic transmission error excitation and/or combined excitation problems provided that the excitation frequencies are sufficiently apart from each other. Our analytical predictions match satisfactorily with the limited experimental data available in the literature. Using the digital simulation, we have also observed that the chaotic and subharmonic resonances may exist in a gear pair depending upon the mean or design load, mean to alternating force ratio, damping and backlash. Specifically, the mean load determines the conditions for no impacts, single-sided impacts and double-sided impacts. Our results are different from the frequency response characteristics of the conventional, single-degree-of-freedom, clearance type non-linear system. Our formulation should form the basis of further analytical and experimental work in the geared rotor dynamics area.
Non-linearities in Theory-of-Mind Development
Blijd-Hoogewys, Els M. A.; van Geert, Paul L. C.
2017-01-01
Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72–78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths. PMID:28101065
Baring, M G; Reynolds, S P; Grenier, I; Goret, P; Baring, Matthew G.; Ellison, Donald C.; Reynolds, Stephen P; Grenier, Isabelle; Goret, Philippe
1999-01-01
Supernova remnants (SNRs) are widely believed to be the principal source of galactic cosmic rays. Such energetic particles can produce gamma-rays and lower energy photons via interactions with the ambient plasma. In this paper, we present results from a Monte Carlo simulation of non-linear shock structure and acceleration coupled with photon emission in shell-like SNRs. These non-linearities are a by-product of the dynamical influence of the accelerated cosmic rays on the shocked plasma and result in distributions of cosmic rays which deviate from pure power-laws. Such deviations are crucial to acceleration efficiency and spectral considerations, producing GeV/TeV intensity ratios that are quite different from test particle predictions. The Sedov scaling solution for SNR expansions is used to estimate important shock parameters for input into the Monte Carlo simulation. We calculate ion and electron distributions that spawn neutral pion decay, bremsstrahlung, inverse Compton, and synchrotron emission, yieldin...
Keesman, K.J.
2006-01-01
In this short paper for the panel discussion on ¿Experience and challenges in identification of non-linear systems¿ some major issues with respect to identification of non-linear biochemical and environmental systems are presented.
State-variable analysis of non-linear circuits with a desk computer
Cohen, E.
1981-01-01
State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.
Discriminating Non-Linearity from Linearity: Its Cognitive Foundations in Five-Year-Olds
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…
The tanh-coth method combined with the Riccati equation for solving non-linear equation
Energy Technology Data Exchange (ETDEWEB)
Bekir, Ahmet [Dumlupinar University, Art-Science Faculty, Department of Mathematics, Kuetahya (Turkey)], E-mail: abekir@dumlupinar.edu.tr
2009-05-15
In this work, we established abundant travelling wave solutions for some non-linear evolution equations. This method was used to construct solitons and traveling wave solutions of non-linear evolution equations. The tanh-coth method combined with Riccati equation presents a wider applicability for handling non-linear wave equations.
Simonsen, Ingve; Kryvi, Jacob B; Maradudin, Alexei A
2015-01-01
An expression is obtained on the basis of phase perturbation theory for the contribution to the mean differential reflection coefficient from the in-plane co-polarized component of the light scattered diffusely from a two-dimensional randomly rough dielectric surface when the latter is illuminated by s-polarized light. This result forms the basis for an approach to inverting experimental light scattering data to obtain the normalized surface height autocorrelation function of the surface. Several parametrized forms of this correlation function, and the minimization of a cost function with respect to the parameters defining these representations, are used in the inversion scheme. This approach also yields the rms height of the surface roughness, and the dielectric constant of the dielectric substrate if it is not known in advance. The input data used in validating this inversion consists of computer simulation results for surfaces defined by exponential and Gaussian surface height correlation functions, withou...
Chaleil, A.; Le Flanchec, V.; Binet, A.; Nègre, J. P.; Devaux, J. F.; Jacob, V.; Millerioux, M.; Bayle, A.; Balleyguier, P.; Prazeres, R.
2016-12-01
An inverse Compton scattering source is under development at the ELSA linac of CEA, Bruyères-le-Châtel. Ultra-short X-ray pulses are produced by inverse Compton scattering of 30 ps-laser pulses by relativistic electron bunches. The source will be able to operate in single shot mode as well as in recurrent mode with 72.2 MHz pulse trains. Within this framework, an optical multipass system that multiplies the number of emitted X-ray photons in both regimes has been designed in 2014, then implemented and tested on ELSA facility in the course of 2015. The device is described from both geometrical and timing viewpoints. It is based on the idea of folding the laser optical path to pile-up laser pulses at the interaction point, thus increasing the interaction probability. The X-ray output gain measurements obtained using this system are presented and compared with calculated expectations.
Directory of Open Access Journals (Sweden)
Florian Schumacher
2016-01-01
Full Text Available Due to increasing computational resources, the development of new numerically demanding methods and software for imaging Earth’s interior remains of high interest in Earth sciences. Here, we give a description from a user’s and programmer’s perspective of the highly modular, flexible and extendable software package ASKI–Analysis of Sensitivity and Kernel Inversion–recently developed for iterative scattering-integral-based seismic full waveform inversion. In ASKI, the three fundamental steps of solving the seismic forward problem, computing waveform sensitivity kernels and deriving a model update are solved by independent software programs that interact via file output/input only. Furthermore, the spatial discretizations of the model space used for solving the seismic forward problem and for deriving model updates, respectively, are kept completely independent. For this reason, ASKI does not contain a specific forward solver but instead provides a general interface to established community wave propagation codes. Moreover, the third fundamental step of deriving a model update can be repeated at relatively low costs applying different kinds of model regularization or re-selecting/weighting the inverted dataset without need to re-solve the forward problem or re-compute the kernels. Additionally, ASKI offers the user sensitivity and resolution analysis tools based on the full sensitivity matrix and allows to compose customized workflows in a consistent computational environment. ASKI is written in modern Fortran and Python, it is well documented and freely available under terms of the GNU General Public License (http://www.rub.de/aski.
Non-linear evolution of the cosmic neutrino background
Energy Technology Data Exchange (ETDEWEB)
Villaescusa-Navarro, Francisco; Viel, Matteo [INAF/Osservatorio Astronomico di Trieste, Via Tiepolo 11, 34143, Trieste (Italy); Bird, Simeon [Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ, 08540 (United States); Peña-Garay, Carlos, E-mail: villaescusa@oats.inaf.it, E-mail: spb@ias.edu, E-mail: penya@ific.uv.es, E-mail: viel@oats.inaf.it [Instituto de Física Corpuscular, CSIC-UVEG, E-46071, Paterna, Valencia (Spain)
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
Non-linear controls on the persistence of La Nina
Di Nezio, P. N.; Deser, C.
2013-12-01
Non-linear controls on the persistence of La Nina Pedro DiNezio and Clara Deser Up to half of the observed La Nina events last for two years or more. Most El Nino events, in contrast, last no longer than one year. The physical processes causing this asymmetry in the duration of warm and cold ENSO events is unknown. The persistence of La Nina, not only exacerbates the climate impacts, especially in regions prone to drought, but also is highly unpredictable. In this talk we will explore the nonlinear processes that generate the persistence of La Nina in observations and in CCSM4 - a coupled climate model that simulates this feature realistically. First, we develop a non-linear delayed-oscillator model (nonlinDO) based on CCSM4's heat budget. All positive and negative feedbacks of nonlinDO capture the nonlinear and seasonal dependence exhibited by CCSM4. The nonlinear behavior is due to: 1) weaker atmospheric damping of cold events with respect to warm events, 2) stronger wind response for large warm events, and 3) weaker coupling between thermocline and sea-surface temperature anomalies when the thermocline deepens. We force the simple model with white Gaussian noise resulting in seasonal modulation of variance and skewness, and a spectral peak, that are in agreement with CCSM4. Sensitivity experiments with nonlinDO show that the thermocline nonlinearity (3) is the sole process controlling the duration of La Nina events. Linear ENSO theory indicates that La Nina events drive a delayed thermocline deepening that leads to their demise. However, the thermocline nonlinearity (3) renders this response ineffective as La Nina events become stronger. This diminishing of the delayed-thermocline feedback prevents the equatorial Pacific from returning to neutral or warm conditions and cold conditions persist for a second year. Observations show evidence for this thermocline nonlinearity suggesting that this process could be at work in the real world. Last, we show evidence that
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
Analyses of non-linear systems and their application to biology: a review.
Sato, S
1994-01-01
In this review article, Wiener's analyses of non-linear systems and other topics on non-linear noise and non-stationary signals are introduced. Firstly, application and limitation of linear aspects on a biological system and a background of introduction of the Wiener's theory to non-linear analysis are briefly mentioned. The practical applications, however, were not so successful for several reasons. We shall see how these problems are solved under collaboration between biologists and engineers who have a knowledge of the subject and utilizing computational facility. Several aspects of the methodology involving non-linear systems, non-linear noise and non-stationary signals are also reviewed.
NLHB : A Non-Linear Hopper Blum Protocol
Madhavan, Mukundan; Sankarasubramaniam, Yogesh; Viswanathan, Kapali
2010-01-01
In this paper, we propose a light-weight provably-secure authentication protocol called the NLHB protocol, which is a variant of the HB protocol. The HB protocol uses the complexity of decoding linear codes for security against passive attacks. In contrast, security for the NLHB protocol is proved by reducing passive attacks to the problem of decoding a class of non-linear codes\\footnote that are provably hard. We demonstrate that the existing passive attacks on the HB protocol family, which have contributed to considerable reduction in its effective key-size, are ineffective against the NLHB protocol. From the evidence, we conclude that smaller-key sizes are sufficient for the NLHB protocol to achieve the same level of passive attack security as the HB Protocol. Further, for this choice of parameters, we provide an implementation instance for the NLHB protocol for which the Prover/Verifier complexity is lower than the HB protocol, enabling authentication on very low-cost devices like RFID tags. Finally, in t...
Organic non-linear optics and opto-electronics
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.
Non-linear Dynamics of Speech in Schizophrenia
DEFF Research Database (Denmark)
Fusaroli, Riccardo; Simonsen, Arndis; Weed, Ethan
Background The speech of patients with schizophrenia is often described as monotonous, flat and without emotion. Distinctive speech patterns are qualitatively assessed in the diagnostic process and deeply impact the quality of everyday social interactions. In this project, we investigate and mode...... to the symptoms. Automated analysis of voice dynamics reveals potential for the assessment and monitoring of the disorder. Future work includes further validation of the approach, as well as more detailed investigation of the relation between speech patterns and other symptoms.......Background The speech of patients with schizophrenia is often described as monotonous, flat and without emotion. Distinctive speech patterns are qualitatively assessed in the diagnostic process and deeply impact the quality of everyday social interactions. In this project, we investigate and model...... speech patterns of people with schizophrenia contrasting them with matched controls and in relation to positive and negative symptoms. We employ both traditional measures (pitch mean and range, pause number and duration, speech rate, etc.) and 2) non-linear techniques measuring the temporal structure...
Non-linear and signal energy optimal asymptotic filter design
Directory of Open Access Journals (Sweden)
Josef Hrusak
2003-10-01
Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.
The weakly non-linear density-velocity relation
Chodorowski, Michal J.; Lokas, Ewa L.
1997-05-01
We rigorously derive up to third order in perturbation theory the weakly non-linear relation between the cosmic density and velocity fields. The density field is described by the mass density contrast, delta. The velocity field is described by the variable theta proportional to the velocity divergence, theta=-f (Omega)^-1H ^-1_0∇. v, where f (Omega)~=Omega^0.6, Omega is the cosmological density parameter and H_0 is the Hubble constant. Our calculations show that mean delta given theta is a third-order polynomial in theta, --_theta=a _1theta+a_2(theta ^2-sigma^2_theta)+ a_3theta^3. This result constitutes an extension of the formula --_theta=theta+a _2(theta^2-sigma^2 _theta) found by Bernardeau which involved second-order perturbative solutions. Third-order perturbative corrections introduce the cubic term. They also, however, cause the coefficient a_1 to depart from unity, in contrast with the linear theory prediction. We compute the values of the coefficients a_p for scale-free power spectra, as well as for standard cold dark matter (CDM), for Gaussian smoothing. The coefficients obey a hierarchy a_3Ganon et al. The results provide a method for breaking the Omega-bias degeneracy in comparisons of cosmic density and velocity fields such as IRAS-potent.
Non-linear modulation of short wavelength compressional Alfven eigenmodes
Energy Technology Data Exchange (ETDEWEB)
Fredrickson, E. D.; Gorelenkov, N. N.; Podesta, M.; Gerhardt, S. P.; Bell, R. E.; Diallo, A.; LeBlanc, B. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Bortolon, A. [University of California, Irvine, California 92697 (United States); Crocker, N. A. [University of California, Los Angeles, California 90095 (United States); Levinton, F. M.; Yuh, H. [Nova Photonics, Princeton, New Jersey 08543 (United States)
2013-04-15
Most Alfvenic activity in the frequency range between toroidal Alfven eigenmodes and roughly one half of the ion cyclotron frequency on National Spherical Torus eXperiment [Ono et al., Nucl. Fusion 40, 557 (2000)], that is, approximately 0.3 MHz up to Almost-Equal-To 1.2 MHz, are modes propagating counter to the neutral beam ions. These have been modeled as Compressional and Global Alfven Eigenmodes (CAE and GAE) and are excited through a Doppler-shifted cyclotron resonance with the beam ions. There is also a class of co-propagating modes at higher frequency than the counter-propagating CAE and GAE. These modes have been identified as CAE, and are seen mostly in the company of a low frequency, n = 1 kink-like mode. In this paper, we present measurements of the spectrum of these high frequency CAE (hfCAE) and their mode structure. We compare those measurements to a simple model of CAE and present a predator-prey type model of the curious non-linear coupling of the hfCAE and the low frequency kink-like mode.
Non-linear controllers in ship tracking control system
Institute of Scientific and Technical Information of China (English)
LESZEK M
2005-01-01
The cascade systems which stabilize the transverse deviation of the ship in relation to the set path is presented. The ship's path is determined as a broken line with specified coordinates of way points. Three controllers are used in the system. The main primary controller is the trajectory controller. The set value of heading for the course control system or angular velocity for the turning control system is generated. The course control system is used on the straight line of the set trajectory while the turning controller is used during a change of the set trajectory segment. The characteristics of the non-linear controllers are selected in such a way that the properties of the control system with the rate of turn controller are modelled by the first-order inertia, while the system with the course keeping controller is modelled by a second-order linear term. The presented control system is tested in computer simulation. Some results of simulation tests are presented and discussed.
Non-linear evolution of the cosmic neutrino background
Villaescusa-Navarro, Francisco; Peña-Garay, Carlos; Viel, Matteo
2012-01-01
We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size, high resolution N-body simulations. Our set of simulations explore the properties of neutrinos in a reference $\\Lambda$CDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass $10^{11}-10^{15}$ $h^{-1}$M$_{\\odot}$, 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. 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 ...
Non-linear optical microscopy sheds light on cardiovascular disease.
Directory of Open Access Journals (Sweden)
Valentina Caorsi
Full Text Available Many cardiac diseases have been associated with increased fibrosis and changes in the organization of fibrillar collagen. The degree of fibrosis is routinely analyzed with invasive histological and immunohistochemical methods, giving a limited and qualitative understanding of the tissue's morphological adaptation to disease. Our aim is to quantitatively evaluate the increase in fibrosis by three-dimensional imaging of the collagen network in the myocardium using the non-linear optical microscopy techniques Two-Photon Excitation microscopy (TPE and Second Harmonic signal Generation (SHG. No sample staining is needed because numerous endogenous fluorophores are excited by a two-photon mechanism and highly non-centrosymmetric structures such as collagen generate strong second harmonic signals. We propose for the first time a 3D quantitative analysis to carefully evaluate the increased fibrosis in tissue from a rat model of heart failure post myocardial infarction. We show how to measure changes in fibrosis from the backward SHG (B(SHG alone, as only backward-propagating SHG is accessible for true in vivo applications. A 5-fold increase in collagen I fibrosis is detected in the remote surviving myocardium measured 20 weeks after infarction. The spatial distribution is also shown to change markedly, providing insight into the morphology of disease progression.
Non-linear image scanning microscopy (Conference Presentation)
Gregor, Ingo; Ros, Robert; Enderlein, Jörg
2017-02-01
Nowadays, multiphoton microscopy can be considered as a routine method for the observation of living cells, organs, up to whole organisms. Second-harmonics generation (SHG) imaging has evolved to a powerful qualitative and label-free method for studying fibrillar structures, like collagen networks. However, examples of super-resolution non-linear microscopy are rare. So far, such approaches require complex setups and advanced synchronization of scanning elements limiting the image acquisition rates. We describe theory and realization of a super-resolution image scanning microscope [1, 2] using two-photon excited fluorescence as well as second-harmonic generation. It requires only minor modifications compared to a classical two-photon laser-scanning microscope and allows image acquisition at the high frame rates of a resonant galvo-scanner. We achieve excellent sensitivity and high frame-rate in combination with two-times improved lateral resolution. We applied this method to fixed cells, collagen hydrogels, as well as living fly embryos. Further, we proofed the excellent image quality of our setup for deep tissue imaging. 1. Müller C.B. and Enderlein J. (2010) Image scanning microscopy. Phys. Rev. Lett. 104(19), 198101. 2. Sheppard C.J.R. (1988) Super-resolution in confocal imaging. Optik (Stuttg) 80 53-54.
Non-linear Least Squares Fitting in IDL with MPFIT
Markwardt, Craig B
2009-01-01
MPFIT is a port to IDL of the non-linear least squares fitting program MINPACK-1. MPFIT inherits the robustness of the original FORTRAN version of MINPACK-1, but is optimized for performance and convenience in IDL. In addition to the main fitting engine, MPFIT, several specialized functions are provided to fit 1-D curves and 2-D images; 1-D and 2-D peaks; and interactive fitting from the IDL command line. Several constraints can be applied to model parameters, including fixed constraints, simple bounding constraints, and "tying" the value to another parameter. Several data weighting methods are allowed, and the parameter covariance matrix is computed. Extensive diagnostic capabilities are available during the fit, via a call-back subroutine, and after the fit is complete. Several different forms of documentation are provided, including a tutorial, reference pages, and frequently asked questions. The package has been translated to C and Python as well. The full IDL and C packages can be found at http://purl.co...
Non Linear Force Free Field Modeling for a Pseudostreamer
Karna, Nishu; Savcheva, Antonia; Gibson, Sarah; Tassev, Svetlin V.
2017-08-01
In this study we present a magnetic configuration of a pseudostreamer observed on April 18, 2015 on southern west limb embedding a filament cavity. We constructed Non Linear Force Free Field (NLFFF) model using the flux rope insertion method. The NLFFF model produces the three-dimensional coronal magnetic field constrained by observed coronal structures and photospheric magnetogram. SDO/HMI magnetogram was used as an input for the model. The high spatial and temporal resolution of the SDO/AIA allows us to select best-fit models that match the observations. The MLSO/CoMP observations provide full-Sun observations of the magnetic field in the corona. The primary observables of CoMP are the four Stokes parameters (I, Q, U, V). In addition, we perform a topology analysis of the models in order to determine the location of quasi-separatrix layers (QSLs). QSLs are used as a proxy to determine where the strong electric current sheets can develop in the corona and also provide important information about the connectivity in complicated magnetic field configuration. We present the major properties of the 3D QSL and FLEDGE maps and the evolution of 3D coronal structures during the magnetofrictional process. We produce FORWARD-modeled observables from our NLFFF models and compare to a toy MHD FORWARD model and the observations.
Non-linear equation: energy conservation and impact parameter dependence
Kormilitzin, Andrey
2010-01-01
In this paper we address two questions: how energy conservation affects the solution to the non-linear equation, and how impact parameter dependence influences the inclusive production. Answering the first question we solve the modified BK equation which takes into account energy conservation. In spite of the fact that we used the simplified kernel, we believe that the main result of the paper: the small ($\\leq 40%$) suppression of the inclusive productiondue to energy conservation, reflects a general feature. This result leads us to believe that the small value of the nuclear modification factor is of a non-perturbative nature. In the solution a new scale appears $Q_{fr} = Q_s \\exp(-1/(2 \\bas))$ and the production of dipoles with the size larger than $2/Q_{fr}$ is suppressed. Therefore, we can expect that the typical temperature for hadron production is about $Q_{fr}$ ($ T \\approx Q_{fr}$). The simplified equation allows us to obtain a solution to Balitsky-Kovchegov equation taking into account the impact pa...
Non-linear model for compression tests on articular cartilage.
Grillo, Alfio; Guaily, Amr; Giverso, Chiara; Federico, Salvatore
2015-07-01
Hydrated soft tissues, such as articular cartilage, are often modeled as biphasic systems with individually incompressible solid and fluid phases, and biphasic models are employed to fit experimental data in order to determine the mechanical and hydraulic properties of the tissues. Two of the most common experimental setups are confined and unconfined compression. Analytical solutions exist for the unconfined case with the linear, isotropic, homogeneous model of articular cartilage, and for the confined case with the non-linear, isotropic, homogeneous model. The aim of this contribution is to provide an easily implementable numerical tool to determine a solution to the governing differential equations of (homogeneous and isotropic) unconfined and (inhomogeneous and isotropic) confined compression under large deformations. The large-deformation governing equations are reduced to equivalent diffusive equations, which are then solved by means of finite difference (FD) methods. The solution strategy proposed here could be used to generate benchmark tests for validating complex user-defined material models within finite element (FE) implementations, and for determining the tissue's mechanical and hydraulic properties from experimental data.
Non-linear calibration models for near infrared spectroscopy.
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-02-27
Different calibration techniques are available for spectroscopic applications that show nonlinear behavior. This comprehensive comparative study presents a comparison of different nonlinear calibration techniques: kernel PLS (KPLS), support vector machines (SVM), least-squares SVM (LS-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS-SVM is also attractive due to its good predictive performance for both linear and nonlinear calibrations.
Are oil markets chaotic? A non-linear dynamic analysis
Energy Technology Data Exchange (ETDEWEB)
Panas, E.; Ninni, V. [Athens University of Economics and Business, Athens (Greece)
2000-10-01
The analysis of products' price behaviour continues to be an important empirical issue. This study contributes to the current literature on price dynamics of products by examining for the presence of chaos and non-linear dynamics in daily oil products for the Rotterdam and Mediterranean petroleum markets. Previous studies using only one invariant, such as the correlation dimension may not effectively determine the chaotic structure of the underlying time series. To obtain better information on the time series structure, a framework is developed, where both invariant and non-invariant quantities were also examined. In this paper various invariants for detecting a chaotic time series were analysed along with the associated Brock's theorem and Eckman-Ruelle condition, to return series for the prices of oil products. An additional non-invariant quantity, the BDS statistic, was also examined. The correlation dimension, entropies and Lyapunov exponents show strong evidence of chaos in a number of oil products considered. 30 refs.
Non-Linear Optical Microscopy Sheds Light on Cardiovascular Disease
Caorsi, Valentina; Toepfer, Christopher; Sikkel, Markus B.; Lyon, Alexander R.; MacLeod, Ken; Ferenczi, Mike A.
2013-01-01
Many cardiac diseases have been associated with increased fibrosis and changes in the organization of fibrillar collagen. The degree of fibrosis is routinely analyzed with invasive histological and immunohistochemical methods, giving a limited and qualitative understanding of the tissue's morphological adaptation to disease. Our aim is to quantitatively evaluate the increase in fibrosis by three-dimensional imaging of the collagen network in the myocardium using the non-linear optical microscopy techniques Two-Photon Excitation microscopy (TPE) and Second Harmonic signal Generation (SHG). No sample staining is needed because numerous endogenous fluorophores are excited by a two-photon mechanism and highly non-centrosymmetric structures such as collagen generate strong second harmonic signals. We propose for the first time a 3D quantitative analysis to carefully evaluate the increased fibrosis in tissue from a rat model of heart failure post myocardial infarction. We show how to measure changes in fibrosis from the backward SHG (BSHG) alone, as only backward-propagating SHG is accessible for true in vivo applications. A 5-fold increase in collagen I fibrosis is detected in the remote surviving myocardium measured 20 weeks after infarction. The spatial distribution is also shown to change markedly, providing insight into the morphology of disease progression. PMID:23409139
Non-linear Constitutive Model for the Oligocarbonate Polyurethane Material
Institute of Scientific and Technical Information of China (English)
Marek Pawlikowski
2014-01-01
The polyurethane,which was the subject of the constitutive research presented in the paper,was based on oligocarbonate diols Desmophen C2100 produced by Bayer@.The constitutive modelling was performed with a view to applying the material as the inlay of intervertebral disc prostheses.The polyurethane was assumed to be non-linearly viscohyperelastic,isotropic and incompressible.The constitutive equation was derived from the postulated strain energy function.The elastic and rheological constants were identified on the basis of experimental tests,i.e.relaxation tests and monotonic uniaxial tests at two different strain rates,i.e.λ =0.1 min-1 and λ =1.0 min-1.The stiffness tensor was derived and introduced to Abaqus@finite element (FE) software in order to numerically validate the constitutive model.The results of the constants identification and numerical implementation show that the derived constitutive equation is fully adequate to model stress-strain behavior of the polyurethane material.
Identification of a Non-Linear Landing Gear Model Using Nature-Inspired Optimization
Directory of Open Access Journals (Sweden)
Felipe A.C. Viana
2008-01-01
Full Text Available This work deals with the application of a nature-inspired optimization technique to solve an inverse problem represented by the identification of an aircraft landing gear model. The model is described in terms of the landing gear geometry, internal volumes and areas, shock absorber travel, tire type, and gas and oil characteristics of the shock absorber. The solution to this inverse problem can be obtained by using classical gradient-based optimization methods. However, this is a difficult task due to the existence of local minima in the design space and the requirement of an initial guess. These aspects have motivated the authors to explore a nature-inspired approach using a method known as LifeCycle Model. In the present formulation two nature-based methods, namely the Genetic Algorithms and the Particle Swarm Optimization were used. An optimization problem is formulated in which the objective function represents the difference between the measured characteristics of the system and its model counterpart. The polytropic coefficient of the gas and the damping parameter of the shock absorber are assumed as being unknown: they are considered as design variables. As an illustration, experimental drop test data, obtained under zero horizontal speed, were used in the non-linear landing gear model updating of a small aircraft.
Non-Linearity Analysis of Depth and Angular Indexes for Optimal Stereo SLAM
Directory of Open Access Journals (Sweden)
David Schleicher
2010-04-01
Full Text Available In this article, we present a real-time 6DoF egomotion estimation system for indoor environments using a wide-angle stereo camera as the only sensor. The stereo camera is carried in hand by a person walking at normal walking speeds 3–5 km/h. We present the basis for a vision-based system that would assist the navigation of the visually impaired by either providing information about their current position and orientation or guiding them to their destination through different sensing modalities. Our sensor combines two different types of feature parametrization: inverse depth and 3D in order to provide orientation and depth information at the same time. Natural landmarks are extracted from the image and are stored as 3D or inverse depth points, depending on a depth threshold. This depth threshold is used for switching between both parametrizations and it is computed by means of a non-linearity analysis of the stereo sensor. Main steps of our system approach are presented as well as an analysis about the optimal way to calculate the depth threshold. At the moment each landmark is initialized, the normal of the patch surface is computed using the information of the stereo pair. In order to improve long-term tracking, a patch warping is done considering the normal vector information. Some experimental results under indoor environments and conclusions are presented.
Kryvi, J. B.; Simonsen, I.; Maradudin, A. A.
2016-09-01
The contribution to the mean differential reflection coefficient from the in-plane, co-polarized scattering of p- polarized light from a two-dimensional randomly rough dielectric surface is used to invert scattering data to obtain the normalized surface height autocorrelation function of the surface. Within phase perturbation theory this contribution to the mean differential reflection coefficient possesses singularities (poles) when the polar scattering angle θs equals +/-θB= +/- tan-1√E, where E is the dielectric constant of the dielectric medium and θB is the Brewster angle. Nevertheless, we show in this paper that if the mean differential reflection coefficient is measured only in the angular range |θs| inversion scheme. This approach also yields the rms height of the surface roughness, and the dielectric constant of the scattering medium if it is not known in advance. The input data used in this minimization procedure consist of computer simulation results for surfaces defined by exponential and Gaussian surface height correlation functions, without and with the addition of multiplicative noise. The proposed inversion scheme is computationally efficient.
A non-Linear transport model for determining shale rock characteristics
Ali, Iftikhar; Malik, Nadeem
2016-04-01
Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007
An electromagnetic inverse scattering approac based on support vector machine%基于支持向量机的电磁逆散射方法
Institute of Scientific and Technical Information of China (English)
王芳芳; 张业荣
2012-01-01
为解决电磁逆散射问题，提出了一种实时逆散射方法，该方法利用支持向量机（SVM）将逆散射问题转化为一个回归估计问题．基于SVM的电磁逆散射方法成功地解决了逆散射问题中的非线性和不适定性．利用穿墙问题测试了该方法的可行性和有效性，测试结果表明，不论是无噪声还是有噪声的情况，该方法都能很好地对墙后目标进行探测与定位．此外，在穿墙环境下用SVM预测模型讨论了接收天线的采样位置数对预测结果的影响．最后对多源设置下的预测误差进行了分析和研究，研究表明，相比于单源情况多源设置有利于对墙后目标的识别．%In order to solve electromagnetic inverse scattering problem, a real-time inverse scattering method is proposed. This technique converts the inverse scattering problem into a regressed one using support vector machine （SVM）. Electromagnetic inverse scattering method based on the SVM deals with nonlinearity and ill-posedness inherent in the inverse scattering problem successfully. The feasibility and the validity are tested by making use of simulating through-wall problem, and the results demonstrate that this approach can detect and position the targets behind the wall, no matter whether there exists noise or not. In the through-wall scenario, the influence of the number of sampling positions of receiving antenna on the predicted results is discussed using the predicted model of SVM. In the end, the predicted errors are analyzed and investigated in the multiple source scenario. The results show that this kind of setting is helpful for target identification in through-wall problem.
Non-Linear Behaviour Of Gelatin Networks Reveals A Hierarchical Structure
Yang, Zhi
2015-12-14
We investigate the strain hardening behaviour of various gelatin networks - namely physically-crosslinked gelatin gel, chemically-crosslinked gelatin gels, and a hybrid gels made of a combination of the former two - under large shear deformations using the pre-stress, strain ramp, and large amplitude oscillation shear protocols. Further, the internal structures of physically-crosslinked gelatin gel and chemically-crosslinked gelatin gels were characterized by small angle neutron scattering (SANS) to enable their internal structures to be correlated with their nonlinear rheology. The Kratky plots of SANS data demonstrate the presence of small cross-linked aggregates within the chemically-crosslinked network, whereas in the physically-crosslinked gels a relatively homogeneous structure is observed. Through model fitting to the scattering data, we were able to obtain structural parameters, such as correlation length (ξ), cross-sectional polymer chain radius (Rc), and the fractal dimension (df) of the gel networks. The fractal dimension df obtained from the SANS data of the physically-crosslinked and chemically crosslinked gels is 1.31 and 1.53, respectively. These values are in excellent agreement with the ones obtained from a generalized non-linear elastic theory we used to fit our stress-strain curves. The chemical crosslinking that generates coils and aggregates hinders the free stretching of the triple helices bundles in the physically-crosslinked gels.
Directory of Open Access Journals (Sweden)
Atsuo Kuniba
2010-01-01
Full Text Available We study an integrable vertex model with a periodic boundary condition associated with U_q(A_n^{(1} at the crystallizing point q=0. It is an (n+1-state cellular automaton describing the factorized scattering of solitons. The dynamics originates in the commuting family of fusion transfer matrices and generalizes the ultradiscrete Toda/KP flow corresponding to the periodic box-ball system. Combining Bethe ansatz and crystal theory in quantum group, we develop an inverse scattering/spectral formalism and solve the initial value problem based on several conjectures. The action-angle variables are constructed representing the amplitudes and phases of solitons. By the direct and inverse scattering maps, separation of variables into solitons is achieved and nonlinear dynamics is transformed into a straight motion on a tropical analogue of the Jacobi variety. We decompose the level set into connected components under the commuting family of time evolutions and identify each of them with the set of integer points on a torus. The weight multiplicity formula derived from the q=0 Bethe equation acquires an elegant interpretation as the volume of the phase space expressed by the size and multiplicity of these tori. The dynamical period is determined as an explicit arithmetical function of the n-tuple of Young diagrams specifying the level set. The inverse map, i.e., tropical Jacobi inversion is expressed in terms of a tropical Riemann theta function associated with the Bethe ansatz data. As an application, time average of some local variable is calculated.
Non-linear pattern formation in bone growth and architecture.
Salmon, Phil
2014-01-01
The three-dimensional morphology of bone arises through adaptation to its required engineering performance. Genetically and adaptively bone travels along a complex spatiotemporal trajectory to acquire optimal architecture. On a cellular, micro-anatomical scale, what mechanisms coordinate the activity of osteoblasts and osteoclasts to produce complex and efficient bone architectures? One mechanism is examined here - chaotic non-linear pattern formation (NPF) - which underlies in a unifying way natural structures as disparate as trabecular bone, swarms of birds flying, island formation, fluid turbulence, and others. At the heart of NPF is the fact that simple rules operating between interacting elements, and Turing-like interaction between global and local signals, lead to complex and structured patterns. The study of "group intelligence" exhibited by swarming birds or shoaling fish has led to an embodiment of NPF called "particle swarm optimization" (PSO). This theoretical model could be applicable to the behavior of osteoblasts, osteoclasts, and osteocytes, seeing them operating "socially" in response simultaneously to both global and local signals (endocrine, cytokine, mechanical), resulting in their clustered activity at formation and resorption sites. This represents problem-solving by social intelligence, and could potentially add further realism to in silico computer simulation of bone modeling. What insights has NPF provided to bone biology? One example concerns the genetic disorder juvenile Pagets disease or idiopathic hyperphosphatasia, where the anomalous parallel trabecular architecture characteristic of this pathology is consistent with an NPF paradigm by analogy with known experimental NPF systems. Here, coupling or "feedback" between osteoblasts and osteoclasts is the critical element. This NPF paradigm implies a profound link between bone regulation and its architecture: in bone the architecture is the regulation. The former is the emergent
Linear and non-linear bias: predictions versus measurements
Hoffmann, K.; Bel, J.; Gaztañaga, E.
2017-02-01
We study the linear and non-linear bias parameters which determine the mapping between the distributions of galaxies and the full matter density fields, comparing different measurements and predictions. Associating galaxies with dark matter haloes in the Marenostrum Institut de Ciències de l'Espai (MICE) Grand Challenge N-body simulation, we directly measure the bias parameters by comparing the smoothed density fluctuations of haloes and matter in the same region at different positions as a function of smoothing scale. Alternatively, we measure the bias parameters by matching the probability distributions of halo and matter density fluctuations, which can be applied to observations. These direct bias measurements are compared to corresponding measurements from two-point and different third-order correlations, as well as predictions from the peak-background model, which we presented in previous papers using the same data. We find an overall variation of the linear bias measurements and predictions of ˜5 per cent with respect to results from two-point correlations for different halo samples with masses between ˜1012and1015 h-1 M⊙ at the redshifts z = 0.0 and 0.5. Variations between the second- and third-order bias parameters from the different methods show larger variations, but with consistent trends in mass and redshift. The various bias measurements reveal a tight relation between the linear and the quadratic bias parameters, which is consistent with results from the literature based on simulations with different cosmologies. Such a universal relation might improve constraints on cosmological models, derived from second-order clustering statistics at small scales or higher order clustering statistics.
Daudé, Thierry; Nicoleau, François
2016-10-01
We study inverse scattering problems at a fixed energy for radial Schr\\"{o}dinger operators on $\\R^n$, $n \\geq 2$. First, we consider the class $\\mathcal{A}$ of potentials $q(r)$ which can be extended analytically in $\\Re z \\geq 0$ such that $\\mid q(z)\\mid \\leq C \\ (1+ \\mid z \\mid )^{-\\rho}$, $\\rho \\textgreater{} \\frac{3}{2}$. If $q$ and $\\tilde{q}$ are two such potentials and if the corresponding phase shifts $\\delta\\_l$ and $\\tilde{\\delta}\\_l$ are super-exponentially close, then $q=\\tilde{q}$. Secondly, we study the class of potentials $q(r)$ which can be split into $q(r)=q\\_1(r) + q\\_2(r)$ such that $q\\_1(r)$ has compact support and $q\\_2 (r) \\in \\mathcal{A}$. If $q$ and $\\tilde{q}$ are two such potentials, we show that for any fixed $a\\textgreater{}0$, ${\\ds{\\delta\\_l - \\tilde{\\delta}\\_l \\ = \\ o \\left( \\frac{1}{l^{n-3}} \\ \\left( {\\frac{ae}{2l}}\\right)^{2l}\\right)}}$ when $l \\rightarrow +\\infty$ if and only if $q(r)=\\tilde{q}(r)$ for almost all $r \\geq a$. The proofs are close in spirit with the celebrated Borg-Marchenko uniqueness theorem, and rely heavily on the localization of the Regge poles that could be defined as the resonances in the complexified angular momentum plane. We show that for a non-zero super-exponentially decreasing potential, the number of Regge poles is always infinite and moreover, the Regge poles are not contained in any vertical strip in the right-half plane. For potentials with compact support, we are able to give explicitly their asymptotics. At last, for potentials which can be extended analytically in $\\Re z \\geq 0$ with $\\mid q(z)\\mid \\leq C \\ (1+ \\mid z \\mid )^{-\\rho}$, $\\rho \\textgreater{}1$ , we show that the Regge poles are confined in a vertical strip in the complex plane.
Bachelard, Nicolas; Sebbah, Patrick; Vanneste, Christian
2014-01-01
We use time-domain numerical simulations of a two-dimensional (2D) scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a small electric field intensity, we observe the strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a larger intensity induces non-linear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in non-linear Rabi oscillations. The transition between both regimes is observed and an analytical model is proposed which accurately describes our numerical observations.
Strubbe, David A.; Andrade, Xavier; Rubio, Angel; Louie, Steven G.
2010-03-01
Chloroform is often used as a solvent when measuring non-linear optical properties of organic molecules. We assess the influence of the solution environment on the molecular properties by calculating directly the non-linear susceptibilities of liquid chloroform at optical frequencies. We use the Sternheimer equation in time-dependent density-functional theory [J. Chem. Phys. 126, 184106 (2007)], on snapshots from ab initio molecular dynamics. We compare the results to those in the gas and solid phases, and to experimental values. We also calculate ab initio local-field factors, used to analyze electric-field-induced second-harmonic generation (EFISH) and hyper-Rayleigh scattering (HRS) experiments.
Chernavskaia, Olga; Heuke, Sandro; Vieth, Michael; Friedrich, Oliver; Schürmann, Sebastian; Atreya, Raja; Stallmach, Andreas; Neurath, Markus F.; Waldner, Maximilian; Petersen, Iver; Schmitt, Michael; Bocklitz, Thomas; Popp, Jürgen
2016-07-01
Assessing disease activity is a prerequisite for an adequate treatment of inflammatory bowel diseases (IBD) such as Crohn’s disease and ulcerative colitis. In addition to endoscopic mucosal healing, histologic remission poses a promising end-point of IBD therapy. However, evaluating histological remission harbors the risk for complications due to the acquisition of biopsies and results in a delay of diagnosis because of tissue processing procedures. In this regard, non-linear multimodal imaging techniques might serve as an unparalleled technique that allows the real-time evaluation of microscopic IBD activity in the endoscopy unit. In this study, tissue sections were investigated using the non-linear multimodal microscopy combination of coherent anti-Stokes Raman scattering (CARS), two-photon excited auto fluorescence (TPEF) and second-harmonic generation (SHG). After the measurement a gold-standard assessment of histological indexes was carried out based on a conventional H&E stain. Subsequently, various geometry and intensity related features were extracted from the multimodal images. An optimized feature set was utilized to predict histological index levels based on a linear classifier. Based on the automated prediction, the diagnosis time interval is decreased. Therefore, non-linear multimodal imaging may provide a real-time diagnosis of IBD activity suited to assist clinical decision making within the endoscopy unit.
Alabastri, A.
2013-10-25
In this paper, we review the principal theoretical models through which the dielectric function of metals can be described. Starting from the Drude assumptions for intraband transitions, we show how this model can be improved by including interband absorption and temperature effect in the damping coefficients. Electronic scattering processes are described and included in the dielectric function, showing their role in determining plasmon lifetime at resonance. Relationships among permittivity, electric conductivity and refractive index are examined. Finally, a temperature dependent permittivity model is presented and is employed to predict temperature and non-linear field intensity dependence on commonly used plasmonic geometries, such as nanospheres. 2013 by the authors; licensee MDPI, Basel, Switzerland.
Non-linear QCD dynamics and exclusive production
Machado, M V T; Meneses, A R
2010-01-01
In this contribution we analyse the cross sections for the exclusive vector meson production as well as the deeply virtual Compton scattering (DVCS) relying on the color dipole approach and considering the numerical solution of the Balitsky-Kovchegov equation including running coupling corrections. Comparisons to DESY-HERA data on exclusive processes and predictions to the Large Hadron Electron Collider, LHeC, are presented.
Generation of Long Waves using Non-Linear Digital Filters
DEFF Research Database (Denmark)
Høgedal, Michael; Frigaard, Peter; Christensen, Morten
1994-01-01
transform of the 1st order surface elevation and subsequently inverse Fourier transformed. Hence, the methods are unsuitable for real-time applications, for example where white noise are filtered digitally to obtain a wave spectrum with built-in stochastic variabillity. In the present paper an approximative...... method for including the correct 2nd order bound terms in such applications is presented. The technique utilizes non-liner digital filters fitted to the appropriate transfer function is derived only for bounded 2nd order subharmonics, as they laboratory experiments generally are considered the most...
Non-linearity parameter / of binary liquid mixtures at elevated pressures
Indian Academy of Sciences (India)
J D Pandey; J Chhabra; R Dey; V Sanguri; R Verma
2000-09-01
When sound waves of high amplitude propagate, several non-linear effects occur. Ultrasonic studies in liquid mixtures provide valuable information about structure and interaction in such systems. The present investigation comprises of theoretical evaluation of the acoustic non-linearity parameter / of four binary liquid mixtures using Tong and Dong equation at high pressures and = 303.15 K. Thermodynamic method has also been used to calculate the non-linearity parameter after making certain approximations.
2013-01-01
This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.
DEFF Research Database (Denmark)
Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik
2004-01-01
The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...... equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme...
Hadmack, Michael R; Madey, John M J; Kowalczyk, Jeremy M D
2014-01-01
The operation of an inverse-Compton scattering source of x-rays or gamma-rays requires the precision alignment and synchronization of highly focused electron bunches and laser pulses at the collision point. The arrival times of electron and laser pulses must be synchronized with picosecond precision. We have developed an RF synchronization technique that reduces the initial timing uncertainty from 350 ps to less than 2 ps, greatly reducing the parameter space to be optimized while commissioning the x-ray source. We describe the technique and present measurements of its performance.
A non-linear induced polarization effect on transient electromagnetic soundings
Hallbauer-Zadorozhnaya, Valeriya Yu.; Santarato, Giovanni; Abu Zeid, Nasser; Bignardi, Samuel
2016-10-01
In a TEM survey conducted for characterizing the subsurface for geothermal purposes, a strong induced polarization effect was recorded in all collected data. Surprisingly, anomalous decay curves were obtained in part of the sites, whose shape depended on the repetition frequency of the exciting square waveform, i.e. on current pulse length. The Cole-Cole model, besides being not directly related to physical parameters of rocks, was found inappropriate to model the observed distortion, due to induced polarization, because this model is linear, i.e. it cannot fit any dependence on current pulse. This phenomenon was investigated and explained as due to the presence of membrane polarization linked to constrictivity of (fresh) water-saturated pores. An algorithm for mathematical modeling of TEM data was then developed to fit this behavior. The case history is then discussed: 1D inversion, which accommodates non-linear effects, produced models that agree quite satisfactorily with resistivity and chargeability models obtained by an electrical resistivity tomography carried out for comparison.
Non-linear friction in reciprocating hydraulic rod seals: Simulation and measurement
Bullock, A. K.; Tilley, D. G.; Johnston, D. N.; Bowen, C. R.; Keogh, P. S.
2009-08-01
Non-linear seal friction can impede the performance of hydraulic actuation systems designed for high precision positioning with favourable dynamic response. Methods for predicting seal friction are required to help develop sealing systems for this type of application. Recent simulation techniques have claimed progress, although have yet to be validated experimentally. A conventional reciprocating rod seal is analysed using established elastohydrodynamic theory and the mixed lubrication Greenwood-Williamson-average Reynolds model. A test rig was used to assess the accuracy of the simulation results for both instroke and outstroke. Inverse hydrodynamic theory is shown to predict a U0.5 power law between rod speed and friction. Comparison with experimental data shows the theory to be qualitatively inaccurate and to predict friction levels an order of magnitude lower than those measured. It was not possible to model the regions very close to the inlet and outlet due to the high pressure gradients at the edges of the contact. The mixed lubrication model produces friction levels within the correct order of magnitude, although incorrectly predicts higher friction during instroke than outstroke. Previous experiments have reported higher friction during instroke than outstroke for rectangular seals, suggesting that the mixed lubrication model used could possibly be suitable for symmetric seals, although not for seal tribology in general.
Non-linear Vacuum Phenomena in Non-commutative QED
Alvarez-Gaumé, Luís
2001-01-01
We show that the classic results of Schwinger on the exact propagation of particles in the background of constant field-strengths and plane waves can be readily extended to the case of non-commutative QED. It is shown that non-perturbative effects on constant backgrounds are the same as their commutative counterparts, provided the on-shell gauge invariant dynamics is referred to a non-perturbatively related space-time frame. For the case of the plane wave background, we find evidence of the effective extended nature of non-commutative particles, producing retarded and advanced effects in scattering. Besides the known `dipolar' character of non-commutative neutral particles, we find that charged particles are also effectively extended, but they behave instead as `half-dipoles'.