Anderson Localization of Light in the Presence of Non-linear Effects
Bührer, Wolfgang
2012-01-01
The goal of the thesis presented here, was to further investigate the findings of Dr. Störzer in order to prove the wave nature of Anderson Localization. For this, two different approaches and setups were used.The first was a single photon counting Time-of-Flight setup, but with increased laser power and less noise in the detection part, where band pass filters were used as a crude spectrometer for analysing the spectral distribution of the photons travelling through highly turbid random medi...
Probing Anderson localization of light by weak non-linear effects
Breakdown of wave transport due to strong disorder is a universal phenomenon known as Anderson localization (AL). It occurs because of the macroscopic population of reciprocal multiple scattering paths, which in three dimensional systems happens at a critical scattering strength. Intensities on these random loops should thus be highly increased relative to those of a diffusive sample. In order to highlight localized modes of light, we exploit the optical nonlinearities of TiO2. Power dependent and spectrally resolved time of flight distribution measurements in transmission through slabs of TiO2 powders at various turbidities reveal that mostly long loops are affected by nonlinearities and that the deviations from diffusive transport observed at long times are due to these localized modes. Our data are a first step in the experimental investigation of the interplay between nonlinear effects and AL in 3D. (fast track communication)
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.
50 Years of Anderson Localization
Abrahams, Elihu
2010-01-01
In his groundbreaking paper Absence of diffusion in certain random lattices (1958), Philip W. Anderson originated, described and developed the physical principles underlying the phenomenon of the localization of quantum objects due to disorder. Anderson's 1977 Nobel Prize citation featured that paper, which was fundamental for many subsequent developments in condensed matter theory and technical applications. After more than a half century, the subject continues to be of fundamental importance. In particular, in the last 25 years, the phenomenon of localization has proved to be crucial for the
Wu, Tsan-Pei; Wang, Xiao-Qun; Guo, Guang-Yu; Anders, Frithjof; Chung, Chung-Hou
2016-05-01
The quantum criticality of the two-lead two-channel pseudogap Anderson impurity model is studied. Based on the non-crossing approximation (NCA) and numerical renormalization group (NRG) approaches, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, {ρ\\text{c}}(ω )\\propto |ω -{μ\\text{F}}{{|}r} (0 energy {μ\\text{F}} . At a fixed lead-impurity hybridization, a quantum phase transition from the two-channel Kondo (2CK) to the local moment (LM) phase is observed with increasing r from r = 0 to r={{r}\\text{c}}law scalings from the well-known \\sqrt{T} or \\sqrt{V} form is found. Moreover, novel power-law scalings in conductances at the 2CK-LM quantum critical point are identified. Clear distinctions are found on the critical exponents between linear and non-linear conductance at criticality. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed.
Anderson localization from classical trajectories
Brouwer, Piet W.; Altland, Alexander
2008-01-01
We show that Anderson localization in quasi-one dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron trajectories only. At large length scales, an exponential proliferation of trajectories of nearly identical classical action generates an abundance of interference terms, which eventually leads to a suppression of transport coefficients. We quantitatively descri...
The non-linear evolution of edge localized modes
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
The non-linear evolution of edge localized modes
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
Wu, Tsan-Pei; Wang, Xiao-Qun; Guo, Guang-Yu; Anders, Frithjof; Chung, Chung-Hou
2016-05-01
The quantum criticality of the two-lead two-channel pseudogap Anderson impurity model is studied. Based on the non-crossing approximation (NCA) and numerical renormalization group (NRG) approaches, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, [Formula: see text] (0 conductances at the 2CK-LM quantum critical point are identified. Clear distinctions are found on the critical exponents between linear and non-linear conductance at criticality. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed. PMID:27045815
Anderson localization in nonlocal nonlinear media
Folli, Viola; Conti, Claudio
2012-01-01
The effect of focusing and defocusing nonlinearities on Anderson localization in highly nonlocal media is theoretically and numerically investigated. A perturbative approach is developed to solve the nonlocal nonlinear Schroedinger equation in the presence of a random potential, showing that nonlocality stabilizes Anderson states.
Locally supersymmetric D=3 non-linear sigma models
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 Kaehler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it generally decomposes, into two separate quaternionic spaces, associated with inequivalent supermultiplets. For N=5, 6, 8 there is a unique (symmetric) space for any given number of supermultiplets. Beyond that there are only theories based on a single supermultiplet for N=9, 10, 12 and 16, associated with coset spaces with the exceptional isometry groups F4(-20), E6(-14), E7(-5) and E8(+8), respectively. For N=3 and N ≥ 5 the D=2 theories obtained by dimensional reduction are two-loop finite. (orig.)
Anderson localization in metallic nanoparticle arrays
Mai, Zhijie; Lin, Fang; Pang, Wei; Xu, Haitao; Tan, Suiyan; Fu, Shenhe; Li, Yongyao
2016-06-01
Anderson localization has been observed in various types of waves, such as matter waves, optical waves and acoustic waves. Here we reveal that the effect of Anderson localization can be also induced in metallic nonlinear nanoparticle arrays excited by a random electrically driving field. We find that the dipole-induced nonlinearity results in ballistic expansion of dipole intensity during evolution; while the randomness of the external driving field can suppress such an expansion. Increasing the strength of randomness above the threshold value, a localized pattern of dipole intensity can be generated in the metallic nanoparticle arrays. By means of statistics, the mean intensity distribution of the dipoles reveals the formation of Anderson localization. We further show that the generated Anderson localization is highly confined, with its size down to the scale of incident wavelength. The reported results might facilitate the manipulations of electromagnetic fields in the scale of wavelength.
Anderson localization in metallic nanoparticle arrays
Mai, Zhijie; Pang, Wei; Xu, Haitao; Tan, Suiyan; Fu, Shenhe; Li, Yongyao
2016-01-01
Anderson localization has been observed in various types of waves, such as matter waves, optical waves and acoustic waves. Here we reveal that the effect of Anderson localization can be also induced in metallic nonlinear nanoparticle arrays excited by a random electrically driving field. We find that the dipole-induced nonlinearity results in ballistic expansion of dipole intensity during evolution; while the randomness of the external driving field can suppress such an expansion. Increasing the strength of randomness above the threshold value, a localized pattern of dipole intensity can be generated in the metallic nanoparticle arrays. By means of statistics, the mean intensity distribution of the dipoles reveals the formation of Anderson localization. We further show that the generated Anderson localization is highly confined, with its size down to the scale of incident wavelength. The reported results might facilitate the manipulations of electromagnetic fields in the scale of wavelength.
Construction of local and non-local conservation laws for non-linear field equations
A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)
Random nanolasing in the Anderson localized regime
Liu, Jin; Garcia, P. D.; Ek, Sara;
2014-01-01
multiple scattering. The applicability of random lasers has been limited due to multidirectional emission, lack of tunability, and strong mode competition with chaotic fluctuations due to a weak mode confinement. The regime of Anderson localization of light has been proposed for obtaining stable multimode...... random lasing, and initial work concerned macroscopic one-dimensional layered media. Here, we demonstrate on-chip random nanolasers where the cavity feedback is provided by the intrinsic disorder. The strong confinement achieved by Anderson localization reduces the spatial overlap between lasing modes...
Universal mechanism for Anderson and weak localization.
Filoche, Marcel; Mayboroda, Svitlana
2012-09-11
Localization of stationary waves occurs in a large variety of vibrating systems, whether mechanical, acoustical, optical, or quantum. It is induced by the presence of an inhomogeneous medium, a complex geometry, or a quenched disorder. One of its most striking and famous manifestations is Anderson localization, responsible for instance for the metal-insulator transition in disordered alloys. Yet, despite an enormous body of related literature, a clear and unified picture of localization is still to be found, as well as the exact relationship between its many manifestations. In this paper, we demonstrate that both Anderson and weak localizations originate from the same universal mechanism, acting on any type of vibration, in any dimension, and for any domain shape. This mechanism partitions the system into weakly coupled subregions. The boundaries of these subregions correspond to the valleys of a hidden landscape that emerges from the interplay between the wave operator and the system geometry. The height of the landscape along its valleys determines the strength of the coupling between the subregions. The landscape and its impact on localization can be determined rigorously by solving one special boundary problem. This theory allows one to predict the localization properties, the confining regions, and to estimate the energy of the vibrational eigenmodes through the properties of one geometrical object. In particular, Anderson localization can be understood as a special case of weak localization in a very rough landscape. PMID:22927384
Effect of coulomb interaction on Anderson localization
We study the quantum mechanics of interacting particles in a disordered system, and in particular, what happens to Anderson localisation when interaction is taken into account. In the first part, one looks at the excited states of two particles in one dimension. For this model, it has been shown (Shepelyansky 1994) that a local repulsive interaction can partially destroy Anderson localisation. Here, we show that this model has similarities with the three-dimensional Anderson model at the metal-insulator transition. In particular, the maximum of rigidity obtained in the spectral statistics correspond to some intermediary statistics that cannot be described by random matrix theory neither by a Poisson statistics. The wave functions show a multifractal behaviour and the spreading of the center of mass of a wave packet is logarithmic in time. The second part deals with the ground state of a finite density of spinless fermions in two dimensions. After the scaling theory of localisation, it was commonly accepted that there was no metal in two dimensions. This idea has been challenged by the observation of a metal-insulator transition in low density electron gas (Kravchenko et al. 1994). We propose a scenario in which a metallic phase occurs between the Anderson insulator and the pinned Wigner crystal. This intermediate phase is characterized by an alignment of the local currents flowing in the system. (author)
Anderson localization of light with topological dislocations
Lobanov, Valery E; Vysloukh, Victor A; Torner, Lluis
2013-01-01
We predict Anderson localization of light with nested screw topological dislocations propagating in disordered two-dimensional arrays of hollow waveguides illuminated by vortex beams. The phenomenon manifests itself in the statistical presence of topological dislocations in ensemble-averaged output distributions accompanying standard disorder-induced localization of light spots. Remarkably, screw dislocations are captured by the light spots despite the fast and irregular transverse displacements and topological charge flipping undertaken by the dislocations due to the disorder. The statistical averaged modulus of the output local topological charge depends on the initial vorticity carried by the beam.
Probabilistic Numerical Methods for Fully Non-linear Non-local Parabolic PDEs
Fahim, Arash
2010-01-01
We introduce a probabilistic numerical method for the approximation of the solutions of fully non--linear parabolic non--local PDEs. The method is the generalization of the method in \\cite{ftw} for fully non--linear parabolic PDEs. As an independent result, we also introduce a Monte Carlo Quadrature method to approximate the integral with respect to L\\'evy measure which may appear inside the scheme. We consider the equations whose non--linearity is of the Hamilton--Jacobi--Belman type. We avoid the difficulties of infinite L\\'evy measures by truncation of the L\\'evy integral by some $\\kappa>0$ near $0$. The first result provides the convergence of the scheme for general parabolic non--linearities. The second result provides bounds on the rate of convergence for concave non--linearities from above and below. For both results, it is crucial to choose $\\kappa$ appropriately dependent on $h$.
Romero, María de los Ángeles Sandoval; Weder, Ricardo
2005-01-01
We consider non-linear Schr\\"odinger equations with a potential, and non-local non-linearities, that are models in mesoscopic physics, for example of a quantum capacitor, and that also are 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 ...
Distribution of critical temperature at Anderson localization
Gammag, Rayda; Kim, Ki-Seok
2016-05-01
Based on a local mean-field theory approach at Anderson localization, we find a distribution function of critical temperature from that of disorder. An essential point of this local mean-field theory approach is that the information of the wave-function multifractality is introduced. The distribution function of the Kondo temperature (TK) shows a power-law tail in the limit of TK→0 regardless of the Kondo coupling constant. We also find that the distribution function of the ferromagnetic transition temperature (Tc) gives a power-law behavior in the limit of Tc→0 when an interaction parameter for ferromagnetic instability lies below a critical value. However, the Tc distribution function stops the power-law increasing behavior in the Tc→0 limit and vanishes beyond the critical interaction parameter inside the ferromagnetic phase. These results imply that the typical Kondo temperature given by a geometric average always vanishes due to finite density of the distribution function in the TK→0 limit while the typical ferromagnetic transition temperature shows a phase transition at the critical interaction parameter. We propose that the typical transition temperature serves a criterion for quantum Griffiths phenomena vs smeared transitions: Quantum Griffiths phenomena occur above the typical value of the critical temperature while smeared phase transitions result at low temperatures below the typical transition temperature. We speculate that the ferromagnetic transition at Anderson localization shows the evolution from quantum Griffiths phenomena to smeared transitions around the critical interaction parameter at low temperatures.
The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum
Adcock, T. A. A.; Taylor, P. H. [Department of Engineering Science, University of Oxford, Oxford (United Kingdom)
2016-01-15
The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.
Adcock, T. A. A.; Taylor, P. H.
2016-01-01
The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.
Kolmogorov turbulence, Anderson localization and KAM integrability
Shepelyansky, D. L.
2012-06-01
The conditions for emergence of Kolmogorov turbulence, and related weak wave turbulence, in finite size systems are analyzed by analytical methods and numerical simulations of simple models. The analogy between Kolmogorov energy flow from large to small spacial scales and conductivity in disordered solid state systems is proposed. It is argued that the Anderson localization can stop such an energy flow. The effects of nonlinear wave interactions on such a localization are analyzed. The results obtained for finite size system models show the existence of an effective chaos border between the Kolmogorov-Arnold-Moser (KAM) integrability at weak nonlinearity, when energy does not flow to small scales, and developed chaos regime emerging above this border with the Kolmogorov turbulent energy flow from large to small scales.
Anderson localization and momentum-space entanglement
We consider Anderson localization and the associated metal–insulator transition for non-interacting fermions in D = 1, 2 space dimensions in the presence of spatially correlated on-site random potentials. To assess the nature of the wave function, we follow a recent proposal to study momentum-space entanglement. For a D = 1 model with long-range disorder correlations, both the entanglement spectrum and the entanglement entropy allow us to clearly distinguish between extended and localized states based upon a single realization of disorder. However, for other models, including the D = 2 case with long-range correlated disorder, we find that the method is not similarly successful. We analyze the reasons for its failure, concluding that the much desired generalization to higher dimensions may be problematic. (paper)
Controlling Anderson localization in disordered photonic crystal waveguides
Garcia-Fernández, David; Smolka, Stephan; Stobbe, Søren;
2010-01-01
In most experiments on Anderson localization so far, only completely random systems without any long-range correlation between the scattering sites have been used, meaning that the Anderson localized modes cannot be controlled. Strongly confined modes were recently observed in the slow-light regime...... of a disordered photonic crystal waveguide and attributed to Anderson localization. We have tested this hypothesis by measuring the light localization length, ξloc, in a disordered photonic crystal waveguide and checked explicitly the criterion of one dimensional Anderson localization that ξloc is...... shorter than the waveguide length LS. Our measurements demonstrate for the first time the close relation between light localization and density of states, which can be used ultimately for controlling Anderson localized modes....
Controlling Anderson localization in disordered photonic crystal waveguides
Garcia-Fernández, David; Smolka, Stephan; Stobbe, Søren; Lodahl, Peter
2010-01-01
In most experiments on Anderson localization so far, only completely random systems without any long-range correlation between the scattering sites have been used, meaning that the Anderson localized modes cannot be controlled. Strongly confined modes were recently observed in the slow-light regime...
Controlling Anderson localization in disordered photonic crystal waveguides
Smolka, Stephan; Garcia, Pedro D.; Lodahl, Peter
2010-01-01
We prove Anderson localization in the slow-light regime of a photonic crystal waveguide by measuring the ensemble-averaged localization length which is controlled by the dispersion of the disordered photonic crystal waveguide.......We prove Anderson localization in the slow-light regime of a photonic crystal waveguide by measuring the ensemble-averaged localization length which is controlled by the dispersion of the disordered photonic crystal waveguide....
Transverse Anderson localization of light: a tutorial review
Mafi, Arash
2015-01-01
This tutorial review gives an overview of the transverse Anderson localization of light in one and two transverse dimensions. A pedagogical approach is followed throughout the presentation, where many aspects of localization are illustrated by means of a few simple models. The tutorial starts with some basic aspects of random matrix theory, and light propagation through and reflection from a random stack of dielectric slabs. Transverse Anderson localization of light in one- and two-dimensiona...
Controlling Anderson localization in disordered photonic crystal waveguides
Garcia-Fernández, David; Smolka, Stephan; Stobbe, Søren;
structures [1,2]. Originally proposed for electrons by P. W. Anderson [3], only completely random systems without any long-range correlation between the scattering sites have been used so far, meaning that the Anderson-localized modes cannot be controlled. In disordered photonic crystals, these modes are...... predicted to appear at frequencies in or near a band gap [4] providing a possible way to control Anderson-localized modes. We have tested this hypothesis by measuring the light localization length, ξ, in a disordered photonic crystal waveguide (PCW) as a function of the dispersive slowdown factor of light...... of the waveguide. Our measurements demonstrate for the first time the close relation between light localization and density of states [5], which can be used ultimately for controlling the extension and spectral position of Anderson-localized modes....
Cavity quantum electrodynamics in the Anderson-localized regime
Sapienza, Luca; Nielsen, Henri Thyrrestrup; Stobbe, Søren;
2010-01-01
We experimentally measure, by means of time-resolved photoluminescence spectroscopy, a 15-fold enhancement of the spontaneous emission decay rate of single semiconductor quantum dots coupled to disorder-induced Anderson-localized modes with efficiencies reaching 94%....
Localization of non-linearly modeled autonomous mobile robots using out-of-sequence measurements.
Besada-Portas, Eva; Lopez-Orozco, Jose A; Lanillos, Pablo; de la Cruz, Jesus M
2012-01-01
This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS) measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors) and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost. PMID:22736962
Localization of Non-Linearly Modeled Autonomous Mobile Robots Using Out-of-Sequence Measurements
Jesus M. de la Cruz
2012-02-01
Full Text Available This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost.
Multiple-beam Propagation in an Anderson Localized Optical Fiber
Karbasi, Salman; Mafi, Arash
2012-01-01
We investigate the simultaneous propagation of multiple beams in a disordered Anderson localized optical fiber. The profiles of each beam fall off exponentially, enabling multiple channels at high-density. We examine the influence of fiber bends on the movement of the beam positions, which we refer to as drift. We investigate the extent of the drift of localized beams induced by macro-bending and show that it is possible to design Anderson localized optical fibers which can be used for practical beam-multiplexing applications.
Absence of Anderson localization in certain random lattices
Choi, Wonjun; Yin, Cheng; Hooper, Ian R.; Bernes, William L.; Bertolotti, Jacopo
2016-01-01
We report on the transition between an Anderson localized regime and a conductive regime in a 1D scattering system with correlated disorder. We show experimentally that when long-range correlations, in the form of a power-law spectral density with power larger than 2, are introduced the localization length becomes much bigger than the sample size and the transmission peaks typical of an Anderson localized system merge into a pass band. As other forms of long-range correlations are known to ha...
Probing the statistical properties of Anderson localization with quantum emitters
Smolka, Stephan; Nielsen, Henri Thyrrestrup; Sapienza, Luca;
2011-01-01
embedded in disordered photonic crystal waveguides as light sources. Anderson-localized modes are efficiently excited and the analysis of the photoluminescence spectra allows us to explore their statistical properties, for example the localization length and average loss length. With increasing the amount...
Interplay of Anderson localization and strong interaction in disordered systems
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbard-gapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose-Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered. (orig.)
Interplay of Anderson localization and strong interaction in disordered systems
Henseler, Peter
2010-01-15
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length {xi}, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of {xi} for small and intermediate disorders and a strong reduction of {xi} due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbard-gapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of {xi} as a function of decreasing interaction, which we assume to persist until the superfluid Bose-Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered. (orig.)
A Probabilistic Scheme for Fully Non-linear Non-local Parabolic PDEs with singular Levy measures
Fahim, Arash
2011-01-01
We introduce a Monte Carlo scheme for the approximation of the solutions of fully non--linear parabolic non--local PDEs. The method is the generalization of the method proposed by [Fahim-Touzi-Warin,2011] for fully non--linear parabolic PDEs. As an independent result, we also introduce a Monte Carlo Quadrature method to approximate the integral with respect to Lévy measure which may appear inside the scheme. We consider the equations whose non--linearity is of the Hamilton--Jacobi--Belman typ...
Controlling Anderson localization in disordered photonic crystal waveguides
Garcia-Fernández, David; Smolka, Stephan; Stobbe, Søren; Lodahl, Peter
Quantum optics and quantum information technologies require enhancement of light-matter interaction by, for example, confining light in a small volume. A very recently demonstrated route towards light confinement makes use of multiple scattering of light and wave interference in disordered photonic...... structures [1,2]. Originally proposed for electrons by P. W. Anderson [3], only completely random systems without any long-range correlation between the scattering sites have been used so far, meaning that the Anderson-localized modes cannot be controlled. In disordered photonic crystals, these modes are...
Cavity quantum electrodynamics with Anderson-localized modes
Sapienza, Luca; Nielsen, Henri Thyrrestrup; Stobbe, Søren;
2010-01-01
factor of 15 on resonance with the Anderson-localized mode, and 94% of the emitted single photons coupled to the mode. Disordered photonic media thus provide an efficient platform for quantum electrodynamics, offering an approach to inherently disorder-robust quantum information devices....
Transverse Anderson localization of light: a tutorial review
Mafi, Arash
2015-01-01
This tutorial review gives an overview of the transverse Anderson localization of light in one and two transverse dimensions. A pedagogical approach is followed throughout the presentation, where many aspects of localization are illustrated by means of a few simple models. The tutorial starts with some basic aspects of random matrix theory, and light propagation through and reflection from a random stack of dielectric slabs. Transverse Anderson localization of light in one- and two-dimensional coupled waveguide arrays is subsequently established and discussed. Recent experimental observations of localization and image transport in disordered optical fibers are discussed. More advanced topics, such as hyper-transport in longitudinally varying disordered waveguides, the impact of nonlinearity, and propagation of partially coherent and quantum light, are also examined.
Absence of Anderson localization in certain random lattices
Choi, Wonjun; Hooper, Ian R; Bernes, William L; Bertolotti, Jacopo
2016-01-01
We report on the transition between an Anderson localized regime and a conductive regime in a 1D scattering system with correlated disorder. We show experimentally that when long-range correlations, in the form of a power-law spectral density with power larger than 2, are introduced the localization length becomes much bigger than the sample size and the transmission peaks typical of an Anderson localized system merge into a pass band. As other forms of long-range correlations are known to have the opposite effect, i.e. to enhance localization, our results show that care is needed when discussing the effects of correlations, as different kinds of long-range correlations can give rise to very different behavior.
Photon transport enhanced by transverse Anderson localization in disordered superlattices
Hsieh, Pin-Chun; McMillan, James; Tsai, Min-An; Lu, Ming; Panoiu, Nicolae; Wong, Chee Wei
2014-01-01
One of the daunting challenges in optical physics is to accurately control the flow of light at the subwavelength scale, by patterning the optical medium one can design anisotropic media. The light transport can also be significantly affected by Anderson localization, namely the wave localization in a disordered medium, a ubiquitous phenomenon in wave physics. Here we report the photon transport and collimation enhanced by transverse Anderson localization in chip-scale dispersion engineered anisotropic media. We demonstrate a new type of anisotropic photonic structure in which diffraction is nearly completely arrested by cascaded resonant tunneling through transverse guided resonances. By perturbing the shape of more than 4,000 scatterers in these superlattices we add structural disordered in a controlled manner and uncover the mechanism of disorder-induced transverse localization at the chip-scale. Arrested spatial divergence is captured in the power-law scaling, along with exponential asymmetric mode profil...
Many-body Anderson localization in one-dimensional systems
Delande, Dominique; Sacha, Krzysztof; Płodzień, Marcin; Avazbaev, Sanat K.; Zakrzewski, Jakub
2013-04-01
We show, using quasi-exact numerical simulations, that Anderson localization in a disordered one-dimensional potential survives in the presence of attractive interaction between particles. The localization length of the particles' center of mass—computed analytically for weak disorder—is in good agreement with the quasi-exact numerical observations using the time evolving block decimation algorithm. Our approach allows for simulation of the entire experiment including the final measurement of all atom positions.
Brambila, Danilo
2012-01-01
We have theoretically studied Anderson localization in a 2D+1 nonlinear kicked rotor model. The system shows a very rich dynamical behavior, where the Anderson localization is suppressed and soliton wave-particles undergo a superdiffusive motion.
Multi-Scale Jacobi Method for Anderson Localization
Imbrie, John Z.
2015-11-01
A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale analysis of exponential decay of the eigenfunction correlator (this implies strong dynamical localization). The method has been used in recent work on many-body localization (Imbrie in On many-body localization for quantum spin chains, arXiv:1403.7837 URL"/> , 2014).
Non-linear Heat Transport Modelling with Edge Localized Modes and Plasma Edge Control in Tokamaks
Becoulet, M.; Huysmans, G.; Thomas, P.; Ghendrih, P.; Grosman, A.; Monier-Garbet, P.; Garbet, X.; Zwingman, W.; Nardon, E. [Euratom-CEA, Centre d' Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee; Moyer, R. [California Univ., San Diego, La Jolla CA (United States); Evans, T.; Leonard, A. [General Atomics, San Diego, CA (United States)
2004-07-01
The paper presents a new approach for the modelling of the pedestal energy transport in the presence of Type I ELMs (edge localized mode) based on the linear ideal MHD code MISHKA coupled with the non-linear energy transport code TELM in a realistic tokamak geometry. The main mechanism of increased transport through the External Transport Barrier (ETB) in this model of ELMs is the increased convective flux due to the MHD velocity perturbation and an additional conductive flux due the radial perturbation of the magnetic field leading to a flattening of the pressure profile in the unstable zone. The typical Type I ELM time-cycle including the destabilization of the ballooning modes leading to the fast (200 {mu}s) collapse of the pedestal pressure followed by the edge pressure profile re-building on a diffusive time scale was reproduced numerically. The possible mechanism of Type I ELMs control using a stochastic plasma boundary created by external coils is modelled in the paper. In the stochastic layer the transverse transport is effectively increased by the magnetic field line diffusion. The modelling results for DIII-D experiment on Type I ELM suppression using the external perturbation from the I-coils demonstrated the possibility to decrease the edge pressure gradient just under the ideal ballooning limit, leading to the high confinement regime without Type I ELMs. (authors)
Quasiperiodic driving of Anderson localized waves in one dimension
Hatami, H.; Danieli, C.; Bodyfelt, J. D.; Flach, S
2016-01-01
We consider a quantum particle in a one-dimensional disordered lattice with Anderson localization, in the presence of multi-frequency perturbations of the onsite energies. Using the Floquet representation, we transform the eigenvalue problem into a Wannier-Stark basis. Each frequency component contributes either to a single channel or a multi-channel connectivity along the lattice, depending on the control parameters. The single channel regime is essentially equivalent to the undriven case. T...
Floß, Johannes
2011-01-01
We demonstrate that the current laser technology used for field-free molecular alignment via a cascade of Raman rotational transitions allows for observing long-discussed non-linear quantum phenomena in the dynamics of the periodically kicked rotor. This includes the scaling of the absorbed energy near the conditions of quantum resonance and Anderson-like localization in the angular momentum. Based on these findings, we suggest a novel approach to tunable selective rotational excitation and alignment in a molecular mixture, using trains of short laser pulses. We demonstrate the efficiency of this approach by applying it to a mixture of two nitrogen isotopologues (14N2 and 15N2), and show that strong selectivity is possible even at room temperature.
Quasiperiodic driving of Anderson localized waves in one dimension
Hatami, H.; Danieli, C.; Bodyfelt, J. D.; Flach, S.
2016-06-01
We consider a quantum particle in a one-dimensional disordered lattice with Anderson localization in the presence of multifrequency perturbations of the onsite energies. Using the Floquet representation, we transform the eigenvalue problem into a Wannier-Stark basis. Each frequency component contributes either to a single channel or a multichannel connectivity along the lattice, depending on the control parameters. The single-channel regime is essentially equivalent to the undriven case. The multichannel driving increases substantially the localization length for slow driving, showing two different scaling regimes of weak and strong driving, yet the localization length stays finite for a finite number of frequency components.
Signatures of Anderson localization excited by an optical frequency comb
Gentilini, S.
2010-01-25
We investigate Anderson localization of light as occurring in ultrashort excitations. A theory based on time dependent coupled-mode equations predicts universal features in the spectrum of the transmitted pulse. In particular, the process of strong localization of light is shown to correspond to the formation of peaks in both the amplitude and in the group delay of the transmitted pulse. Parallel ab initio simulations made with finite-difference time-domain codes and molecular dynamics confirm theoretical predictions, while showing that there exists an optimal degree of disorder for the strong localization. © 2010 The American Physical Society.
Integrals of motion for one-dimensional Anderson localized systems
Modak, Ranjan; Mukerjee, Subroto; Yuzbashyan, Emil A.; Shastry, B. Sriram
2016-03-01
Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess ‘additional’ integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.
On the structure on non-local conservation laws in the two-dimensional non-linear sigma-model
The non-local conserved charges are supposed to satisfy a special multiplicative law in the space of asymptotic states of the non-linear sigma-model. This supposition leads to factorization equations for two-particle scattering matrix elements and determines to some extent the action of these charges in the asymptotic space. Their conservation turns out to be consistent with the factorized S-matrix of the non-linear sigma-model. It is shown also that the factorized sine-Gordon S-matrix is consistent with a similar family of conservation laws
Defect-controlled Anderson localization of light in photonic lattices
The transverse localization of light in a disordered photonic lattice with a central defect is analyzed numerically. The effect of different input beam widths on various regimes of Anderson localization is investigated. The inclusion of a defect enhances the localization of both narrow and broad beams, as compared to the lattice with no defect. But, in the case of a broad beam a higher disorder level is needed to reach the same localization as for a narrow input beam. It is also investigated how the transverse localization of light in such geometries depends on both the strength of disorder and the strength of nonlinearity in the system. While in the linear regime the localization is most pronounced in the lattice with the defect, in the nonlinear regime this is not the case. (paper)
Transversal Anderson localization of sound in acoustic waveguide arrays
We present designs of one-dimensional acoustic waveguide arrays and investigate wave propagation inside. Under the condition of single identical waveguide mode and weak coupling, the acoustic wave motion in waveguide arrays can be modeled with a discrete mode-coupling theory. The coupling constants can be retrieved from simulations or experiments as the function of neighboring waveguide separations. Sound injected into periodic arrays gives rise to the discrete diffraction, exhibiting ballistic or extended transport in transversal direction. But sound injected into randomized waveguide arrays readily leads to Anderson localization transversally. The experimental results show good agreement with simulations and theoretical predictions. (paper)
Invariant-imbedding approach to localization. II. Non-linear random media
Doucot, B.; Rammal, R.
1987-01-01
By employing an invariant-imbedding method a partial differential equation is derived for the complex reflection amplitude R (L ) of a one-dimensional non-linear random medium of length L. The method of characteristics reduces this equation to a dynamical system. Averaging of the perturbation of orbits by weak disorder is used to investigate the probability distribution of R (L). Two different situations are considered : fixed output w 0 (Problem A) and fixed input (Problem B). For a large cl...
Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor
Manai, Isam; Clément, Jean-François; Chicireanu, Radu; Hainaut, Clément; Garreau, Jean Claude; Szriftgiser, Pascal; Delande, Dominique
2015-01-01
Dimension 2 is expected to be the lower critical dimension for Anderson localization in a time-reversal-invariant disordered quantum system: the dynamics is generically localized in dimension lower than 2, while it presents a transition from a diffusive regime at weak disorder to a localized regime at strong disorder in dimension larger than 2. We use an atomic quasiperiodically kicked rotor – equivalent to a two-dimensional Anderson-like model – to experimentally study Anderson localization ...
Anderson localization in metamaterials and other complex media
Gredeskul, Sergey A; Asatrian, Ara A; Bliokh, Konstantin Y; Bliokh, Yuri P; Freilikher, Valentin D; Shadrivov, Ilya V
2012-01-01
We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magneto-active optical structures, (iii) graphene superlattices, and (iv) nonlinear dielectric media. First, we demonstrate that left-handed metamaterials can significantly suppress localization of light and lead to an anomalously enhanced transmission. This suppression is essential at the long-wavelength limit in the case of normal incidence, at specific angles of oblique incidence (Brewster anomaly), and in the vicinity of the zero-epsilon or zero-mu frequencies for dispersive metamaterials. Remarkably, in disordered samples comprised of alternating normal and left-handed metamaterials, the reciprocal Lyapunov exponent and reciprocal transmittance increment can differ from each other. Second, we study magneto-active multilayered structures, which exhibit nonreciprocal localization of light depending on the direction of propagation ...
Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor.
Manai, Isam; Clément, Jean-François; Chicireanu, Radu; Hainaut, Clément; Garreau, Jean Claude; Szriftgiser, Pascal; Delande, Dominique
2015-12-11
Dimension 2 is expected to be the lower critical dimension for Anderson localization in a time-reversal-invariant disordered quantum system. Using an atomic quasiperiodic kicked rotor-equivalent to a two-dimensional Anderson-like model-we experimentally study Anderson localization in dimension 2 and we observe localized wave function dynamics. We also show that the localization length depends exponentially on the disorder strength and anisotropy and is in quantitative agreement with the predictions of the self-consistent theory for the 2D Anderson localization. PMID:26705619
Breteaux, Sébastien
2014-01-01
We introduce a one parameter family of non-linear, non-local integro-differential equations and its limit equation. These equations originate from a derivation of the linear Boltzmann equation using the framework of bosonic quantum field theory. We show the existence and uniqueness of strong global solutions for these equations, and a result of uniform convergence on every compact interval of the solutions of the one parameter family towards the solution of the limit equation.
Density of states controls Anderson localization in disordered photonic crystal waveguides
Garcia-Fernández, David; Smolka, Stephan; Stobbe, Søren;
2010-01-01
We prove Anderson localization in a disordered photonic crystal waveguide by measuring the ensemble-averaged extinction mean-free path, ℓe, which is controlled by the dispersion in the photon density of states (DOS) of the photonic crystal waveguide. Except for the very low DOS case, where out...... demonstrates the close relation between Anderson localization and the DOS in disordered photonic crystals, which opens a promising route to controlling and exploiting Anderson-localized modes for efficient light confinement....
All-solid-state cavity QED using Anderson-localized modes in disordered photonic crystal waveguides
Lodahl, Peter; Sapienza, Luca; Nielsen, Henri Thyrrestrup;
2010-01-01
We employ Anderson-localized modes in deliberately disordered photonic crystal waveguides to confine light and enhance the interaction with matter. A 15-fold enhancement of the decay rate of a single quantum dot is observed meaning that 94% of the emitted single photons are coupled to an Anderson...
Kojima, Kotaro [Department of Architecture and Architectural Engineering, Kyoto University, Kyoto 615-8540 (Japan); Kamagata, Shuichi [Nuclear Power Department, Kajima Corporation, Tokyo 107-8348 (Japan); Takewaki, Izuru, E-mail: takewaki@archi.kyoto-u.ac.jp [Department of Architecture and Architectural Engineering, Kyoto University, Kyoto 615-8540 (Japan)
2014-07-01
Highlights: • A new interpretation of large earthquake accelerations is provided. • Non-linear interaction between an embedded building and its surrounding soil is a key. • A bi-linear restoring-force characteristic with a gap-slip process is used for analysis. • Ricker wavelet and a continuous sweep sinusoidal wave are adopted as input. • The amplification is induced by a higher mode due to the change of a support condition. - Abstract: A new interpretation of large amplitude earthquake accelerations recorded at the Kashiwazaki-Kariwa nuclear power station during the Niigata-ken Chuetsu-oki earthquake in 2007 is provided from the viewpoint of non-linear local interaction between an embedded building and its surrounding soil. An occurrence mechanism is investigated by the dynamic response analysis in which a bi-linear restoring-force characteristic with a gap-slip process is used. The Ricker wavelet and the continuous sweep sinusoidal wave are adopted as an input. The amplification is explained to be induced by an additional higher mode due to the change of a support condition, such as a gap between an embedded building and its surrounding soil.
Highlights: • A new interpretation of large earthquake accelerations is provided. • Non-linear interaction between an embedded building and its surrounding soil is a key. • A bi-linear restoring-force characteristic with a gap-slip process is used for analysis. • Ricker wavelet and a continuous sweep sinusoidal wave are adopted as input. • The amplification is induced by a higher mode due to the change of a support condition. - Abstract: A new interpretation of large amplitude earthquake accelerations recorded at the Kashiwazaki-Kariwa nuclear power station during the Niigata-ken Chuetsu-oki earthquake in 2007 is provided from the viewpoint of non-linear local interaction between an embedded building and its surrounding soil. An occurrence mechanism is investigated by the dynamic response analysis in which a bi-linear restoring-force characteristic with a gap-slip process is used. The Ricker wavelet and the continuous sweep sinusoidal wave are adopted as an input. The amplification is explained to be induced by an additional higher mode due to the change of a support condition, such as a gap between an embedded building and its surrounding soil
Linearized versus non-linear inverse methods for seismic localization of underground sources
Oh, Geok Lian; Jacobsen, Finn
2013-01-01
the Bayes nonlinear inversion method. The travel times used in the beamformer are derived from solving the Eikonal equation. In the linearized inversion method, we assume that the elastic waves are predominantly acoustic waves, and the acoustic approximation is applied. For the nonlinear inverse......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, and...... 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....
Non-linear non-local molecular electrodynamics with nano-optical fields.
Chernyak, Vladimir Y; Saurabh, Prasoon; Mukamel, Shaul
2015-10-28
The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields may vary appreciably across the molecular length scale. Rather than incrementally adding higher multipoles, it is advantageous and more physically transparent to describe the optical process using non-local response functions that intrinsically include all multipoles. We present a semi-classical approach for calculating non-local response functions based on the minimal coupling Hamiltonian. The first, second, and third order response functions are expressed in terms of correlation functions of the charge and the current densities. This approach is based on the gauge invariant current rather than the polarization, and on the vector potential rather than the electric and magnetic fields. PMID:26520498
Two-photon Anderson localization in a disordered quadratic waveguide array
We theoretically investigate two-photon Anderson localization in a χ (2) waveguide array with off-diagonal disorder. The nonlinear parametric down-conversion process would enhance both the single-photon and the two-photon Anderson localization. In the strong disorder regime, the two-photon position correlation exhibits a bunching distribution around the pumped waveguides, which is independent of pumping conditions and geometrical structures of waveguide arrays. Quadratic nonlinearity can be supplied as a new ingredient for Anderson localization. Also, our results pave the way for engineering quantum states through nonlinear quantum walks. (paper)
Schulte, T.; Drenkelforth, S.; Kruse, J.; Ertmer, W.; Arlt, J.; Sacha, K.; Zakrzewski, J.; Lewenstein, M.
2005-10-01
We investigate, both experimentally and theoretically, possible routes towards Anderson-like localization of Bose-Einstein condensates in disordered potentials. The dependence of this quantum interference effect on the nonlinear interactions and the shape of the disorder potential is investigated. Experiments with an optical lattice and a superimposed disordered potential reveal the lack of Anderson localization. A theoretical analysis shows that this absence is due to the large length scale of the disorder potential as well as its screening by the nonlinear interactions. Further analysis shows that incommensurable superlattices should allow for the observation of the crossover from the nonlinear screening regime to the Anderson localized case within realistic experimental parameters.
We investigate, both experimentally and theoretically, possible routes towards Anderson-like localization of Bose-Einstein condensates in disordered potentials. The dependence of this quantum interference effect on the nonlinear interactions and the shape of the disorder potential is investigated. Experiments with an optical lattice and a superimposed disordered potential reveal the lack of Anderson localization. A theoretical analysis shows that this absence is due to the large length scale of the disorder potential as well as its screening by the nonlinear interactions. Further analysis shows that incommensurable superlattices should allow for the observation of the crossover from the nonlinear screening regime to the Anderson localized case within realistic experimental parameters
Jessamine P Winer
Full Text Available Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning.
Cosmic flows and the expansion of the local Universe from non-linear phase-space reconstructions
Heß, Steffen; Kitaura, Francisco-Shu
2016-03-01
In this work, we investigate the impact of cosmic flows and density perturbations on Hubble constant H0 measurements using non-linear phase-space reconstructions of the Local Universe (LU). In particular, we rely on a set of 25 precise constrained N-body simulations based on Bayesian initial conditions reconstructions of the LU using the Two-Micron Redshift Survey galaxy sample within distances of about 90 h-1 Mpc. These have been randomly extended up to volumes enclosing distances of 360 h-1 Mpc with augmented Lagrangian perturbation theory (750 simulations in total), accounting in this way for gravitational mode coupling from larger scales, correcting for periodic boundary effects, and estimating systematics of missing attractors (σlarge = 134 s-1 km). We report on Local Group (LG) speed reconstructions, which for the first time are compatible with those derived from cosmic microwave background-dipole measurements: |vLG| = 685 ± 137 s-1 km. The direction (l, b) = (260.5° ± 13.3°, 39.1 ± 10.4°) is found to be compatible with the observations after considering the variance of large scales. Considering this effect of large scales, our local bulk flow estimations assuming a Λ cold dark matter model are compatible with the most recent estimates based on velocity data derived from the Tully-Fisher relation. We focus on low-redshift supernova measurements out to 0.01 positive bias in H0. Taking these effects into account yields a correction of ΔH0 = -1.76 ± 0.21 s- 1 km Mpc- 1, thereby reducing the tension between local probes and more distant probes. Effectively H0 is lower by about 2 per cent.
Image transport through a disordered optical fiber mediated by transverse Anderson localization
Karbasi, Salman; Koch, Karl W; Hawkins, Thomas; Ballato, John; Mafi, Arash
2013-01-01
Transverse Anderson localization of light allows localized optical-beam-transport through a transversely-disordered and longitudinally-invariant medium. Its successful implementation in disordered optical fibers recently resulted in the simultaneous propagation of multiple beams in a single strand of an optical fiber, suggesting potential applications for spatial beam multiplexing and image transport. We present what is, to the best of our knowledge, the first demonstration of optical image transport using transverse Anderson localization of light. The image transport quality obtained in the polymer disordered optical fiber is comparable with or better than some of the best commercially available multicore imaging fibers with less pixelation and higher contrast. A proof-of-concept glass version is also evaluated and further optimization is discussed. Our results open the way to device-level implementation of the transverse Anderson localization of light with potential applications in biological and medical im...
Transverse Anderson localization of light near Dirac points of photonic nanostructures
Deng, Hanying; Malomed, Boris A; Panoiu, Nicolae C; Ye, Fangwei
2015-01-01
We perform a comparative study of the Anderson localization of light beams in disordered layered photonic nanostructures that, in the limit of periodic layer distribution, possess either a Dirac point or a Bragg gap in the spectrum of the wavevectors. In particular, we demonstrate that the localization length of the Anderson modes increases when the width of the Bragg gap decreases, such that in the vanishingly small bandgap limit, namely when a Dirac point is formed, even extremely high levels of disorders are unable to localize the optical modes located near the Dirac point. A comparative analysis of the key features of the propagation of Anderson modes formed in the Bragg gap or near the Dirac point is also presented. Our findings could provide valuable guidelines in assessing the influence of structural disorder on the functionality of a broad array of optical nanodevices.
Anderson localization of spinons in a spin-1/2 antiferromagnetic Heisenberg chain
Pan, B. Y.; Zhou, S. Y.; Hong, X. C.; Qiu, X; Li, S. Y.
2012-01-01
Anderson localization is a general phenomenon of wave physics, which stems from the interference between multiple scattering paths1,2. It was originally proposed for electrons in a crystal, but later was also observed for light3-5, microwaves6, ultrasound7,8, and ultracold atoms9-12. Actually, in a crystal, besides electrons there may exist other quasiparticles such as magnons and spinons. However the search for Anderson localization of these magnetic excitations is rare so far. Here we repor...
A modal perspective on the transverse Anderson localization of light in disordered optical lattices
Karbasi, Salman; Mafi, Arash
2013-01-01
We frame the transverse Anderson localization of light in a one-dimensional disordered optical lattice in the language of localized propagating eigenmodes. The modal analysis allows us to explore localization behavior of a disordered lattice independent of the properties of the external excitation. Various localization-related phenomena, such as the periodic revival of a propagating Anderson-localized beam are easily explained in modal language. We characterize the localization strength by the average width of the guided modes and carry out a detailed analysis of localization behavior as a function of the optical and geometrical parameters of the disordered lattice. We also show that in order to obtain a minimum average mode width, the average width of the individual random sites in the disordered lattice must be larger than the wavelength of the light by approximately a factor of two or more, and the optimum site width for the maximum localization depends on the design parameters of the disordered lattice.
Observation of migrating transverse Anderson localizations of light in nonlocal media
Leonetti, Marco; Mafi, Arash; Conti, Claudio
2014-01-01
We report the experimental observation of the interaction and attraction of many localized modes in a two dimensional (2D) system realized by a disordered optical fiber supporting transverse Anderson localization. We show that a nonlocal optically nonlinear response of thermal origin alters the localization length by an amount determined by the optical power and also induces an action at a distance between the localized modes and their spatial migration. Evidence of a collective and strongly interacting regime is given.
Spectral statistics for the discrete Anderson model in the localized regime
Germinet, François
2010-01-01
We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at sufficiently large coupling, the limit of the level spacing distribution is that of i.i.d. random variables distributed according to the density of states of the random Hamiltonian. This text is a contribution to the proceedings of the conference "Spectra of Random Operators and Related Topics" held at Kyoto University, 02-04/12/09 organized by N. Minami and N. Ueki.
Single-ion-pair fluorescence ratios in ruby and Anderson localization
Chu, S.; Gibbs, H. M.; Passner, A.
1981-12-01
The experiment of Koo, Walker, and Geschwind (KWG) presenting evidence for a mobility edge separating localized and extended states has been repeated and extended. Although some of the features reported by KWG were seen, there are notable qualitative and quantitative differences in our work. We conclude that there is no compelling evidence for an Anderson transition in ruby.
Anderson localization through Polyakov loops: lattice evidence and Random matrix model
Bruckmann, Falk; Kovács, Tamás G.; Schierenberg, Sebastian
2011-01-01
We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find stron...
Experimental observation of Anderson localization in laser-kicked molecular rotors
Bitter, Martin
2016-01-01
We observe and study the phenomenon of Anderson localization in a system of true quantum kicked rotors. Nitrogen molecules in a supersonic molecular jet are cooled down to 27~K and are rotationally excited by a periodic train of 24~high-intensity femtosecond pulses. Exponential distribution of the molecular angular momentum - the most unambiguous signature of Anderson localization - is measured directly by means of coherent Raman scattering. We demonstrate the suppressed growth of the molecular rotational energy with the number of laser kicks and study the dependence of the localization length on the kick strength. Both timing and amplitude noise in the pulse train is shown to destroy the localization and revive the diffusive growth of angular momentum.
We calculated numerically the localization length of one-dimensional Anderson model with diagonal disorder. For weak disorder, we showed that the localization length changes continuously as the energy changes from the band center to the boundary of the anomalous region near the band edge. We found that all the localization lengths for different disorder strengths and different energies collapse onto a single curve, which can be fitted by a simple equation. Thus the description of the perturbation theory and the band center anomaly were unified into this equation. -- Highlights: → We study the band center anomaly of one-dimensional Anderson localization. → We study numerically the Lyapunov exponent through a parametrization method of the transfer matrix. → We give a unified equation to describe the band center anomaly and perturbation theory.
Scaling analysis of transverse Anderson localization in a disordered optical waveguide
Abaie, Behnam
2016-01-01
The intention of this manuscript is twofold. First, the mode-width probability density function (PDF) is introduced as a powerful statistical tool to study and compare the transverse Anderson localization properties of a disordered one dimensional optical waveguide. Second, by analyzing the scaling properties of the mode-width PDF with the transverse size of the waveguide, it is shown that the mode-width PDF gradually converges to a terminal configuration. Therefore, it may not be necessary to study a real-sized disordered structure in order to obtain its statistical localization properties and the same PDF can be obtained for a substantially smaller structure. This observation is important because it can reduce the often demanding computational effort that is required to study the statistical properties of Anderson localization in disordered waveguides. Using the mode-width PDF, substantial information about the impact of the waveguide parameters on its localization properties is extracted. This information ...
Controlling Anderson localization in disordered heterostrctures with Lévy-type distribution
In this paper, we propose a disordered heterostructure in which the distribution of the refractive index of one of its constituents follows a Lévy-type distribution characterized by the exponent α. For the normal and oblique incidences, the effect of α variation on the localization length is investigated in different frequency ranges. As a result, the controllability of Anderson localization can be achieved by changing the exponent α in the disordered structure having heavy tailed distribution. (paper)
Damkilde, Lars; Pedersen, Ronnie
2012-01-01
has been tested on a standard linear test such as Cook’s panel, and is shown as expected to be somewhat more flexible than the LST-element and the compatible quadratic strain element (QST). The extended element has also been applied to material non-linear geotechnical problems. Geotechnical problems......This paper describes a new triangular plane element which can be considered as a linear strain triangular element (LST) extended with incompatible displacement modes. The extended element will have a full cubic interpolation of strains and stresses. The extended LST-element is connected with other...... elements similar to the LST-element i.e. through three corner nodes and three mid-side nodes. The incompatible modes are associated with two displacement gradients at each mid-side node and displacements in the central node. The element passes the patch test and converges to the exact solution. The element...
Anderson localization through Polyakov loops: Lattice evidence and random matrix model
We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such ''wrong'' Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.
Anderson localization through Polyakov loops: Lattice evidence and random matrix model
Bruckmann, Falk; Kovács, Tamás G.; Schierenberg, Sebastian
2011-08-01
We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such “wrong” Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.
Anderson localization through Polyakov loops: lattice evidence and Random matrix model
Bruckmann, Falk; Schierenberg, Sebastian
2011-01-01
We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.
Transverse Anderson Localization in Disordered Glass Optical Fibers: A Review
Arash Mafi
2014-07-01
Full Text Available Disordered optical fibers show novel waveguiding properties that can be used for various device applications, such as beam-multiplexed optical communications and endoscopic image transport. The strong transverse scattering from the transversely disordered optical fibers results in transversely confined beams that can freely propagate in the longitudinal direction, similar to conventional optical fibers, with the advantage that any point in the cross section of the fiber can be used for beam transport. For beam multiplexing and imaging applications, it is highly desirable to make the localized beam radius as small as possible. This requires large refractive index differences between the materials that define the random features in the disordered fiber. Here, disordered glass-air fibers are briefly reviewed, where randomly placed airholes in a glass matrix provide the sufficiently large refractive index difference of 0.5 for strong random transverse scattering. The main future challenge for the fabrication of an optimally disordered glass-air fibers is to increase the fill-fraction of airholes to nearly 50% for maximum beam confinement.
Waintal, X
1999-09-10
We study the quantum mechanics of interacting particles in a disordered system, and in particular, what happens to Anderson localisation when interaction is taken into account. In the first part,one looks at the excited states of two particles in one dimension. For this model, it has been shown (Shepelyansky 1994) that a local repulsive interaction can partially destroy Anderson localisation. Here, we show that this model has similarities with the three-dimensional Anderson model at the metal-insulator transition. In particular, the maximum of rigidity obtained in the spectral statistics correspond to some intermediary statistics that cannot be described by random matrix theory neither by a Poisson statistics. The wave functions show a multifractal behaviour and the spreading of the center of mass of a wave packet is logarithmic in time. The second part deals with the ground state of a finite density of spinless fermions in two dimensions. After the scaling theory of localisation, it was commonly accepted that there was no metal in two dimensions. This idea has been challenged by the observation of a metal-insulator transition in low density electron gas (Kravchenko et al. 1994). We propose a scenario in which a metallic phase occurs between the Anderson insulator and the pinned Wigner crystal. This intermediate phase is characterized by an alignment of the local currents flowing in the system. (author)
Levy, Daniel; Roos, Jason; Robinson, Jace; Carpenter, William; Martin, Richard; Taylor, Clark; Sugrue, Joseph; Terzuoli, Andrew
2016-06-01
Multiple sensors are used in a variety of geolocation systems. Many use Time Difference of Arrival (TDOA) or Received Signal Strength (RSS) measurements to estimate the most likely location of a signal. When an object does not emit an RF signal, Angle of Arrival (AOA) measurements using optical or infrared frequencies become more feasible than TDOA or RSS measurements. AOA measurements can be created from any sensor platform with any sort of optical sensor, location and attitude knowledge to track passive objects. Previous work has created a non-linear optimization (NLO) method for calculating the most likely estimate from AOA measurements. Two new modifications to the NLO algorithm are created and shown to correct AOA measurement errors by estimating the inherent bias and time-drift in the Inertial Measurement Unit (IMU) of the AOA sensing platform. One method corrects the sensor bias in post processing while treating the NLO method as a module. The other method directly corrects the sensor bias within the NLO algorithm by incorporating the bias parameters as a state vector in the estimation process. These two methods are analyzed using various Monte-Carlo simulations to check the general performance of the two modifications in comparison to the original NLO algorithm.
Efficient Non Linear Loudspeakers
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....
Anderson localization of electrons in single crystals: Li (x) Fe(7)Se(8).
Ying, Tianping; Gu, Yueqiang; Chen, Xiao; Wang, Xinbo; Jin, Shifeng; Zhao, Linlin; Zhang, Wei; Chen, Xiaolong
2016-02-01
Anderson (disorder-induced) localization, proposed more than half a century ago, has inspired numerous efforts to explore the absence of wave diffusions in disordered media. However, the proposed disorder-induced metal-insulator transition (MIT), associated with the nonpropagative electron waves, has hardly been observed in three-dimensional (3D) crystalline materials, let alone single crystals. We report the observation of an MIT in centimeter-size single crystals of Li x Fe7Se8 induced by lattice disorder. Both specific heat and infrared reflectance measurements reveal the presence of considerable electronic states in the vicinity of the Fermi level when the MIT occurs, suggesting that the transition is not due to Coulomb repulsion mechanism. The 3D variable range hopping regime evidenced by electrical transport measurements at low temperatures indicates the localized nature of the electronic states on the Fermi level. Quantitative analyses of carrier concentration, carrier mobility, and simulated density of states (DOS) fully support that Li x Fe7Se8 is an Anderson insulator. On the basis of these results, we provide a unified DOS picture to explain all the experimental results, and a schematic diagram for finding other potential Anderson insulators. This material will thus serve as a rich playground for both theoretical and experimental investigations on MITs and disorder-induced phenomena. PMID:26989781
Simulation of Anderson localization in two-dimensional ultracold gases for pointlike disorder
Morong, W.; DeMarco, B.
2015-08-01
Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold gases has been elusive. We show that a cause of this difficulty is the relatively high percolation threshold of a speckle potential in two dimensions, resulting in strong classical localization. We propose a realistic pointlike disorder potential that circumvents this percolation limit with localization lengths that are experimentally observable. The percolation threshold is evaluated for experimentally realistic parameters, and a regime of negligible classical trapping is identified. Localization lengths are determined via scaling theory, using both exact scattering cross sections and the Born approximation, and by direct simulation of the time-dependent Schrödinger equation. We show that the Born approximation can underestimate the localization length by four orders of magnitude at low energies, while exact cross sections and scaling theory provide an upper bound. Achievable experimental parameters for observing localization in this system are proposed.
Coalescence of Anderson-localized modes at an exceptional point in 2D random media
Bachelard, Nicolas; Arlandis, Julien; Touzani, Rachid; Sebbah, Patrick
2014-01-01
In non-hermitian systems, the particular position at which two eigenstates coalesce under a variation of a parameter in the complex plane is called an exceptional point. A non-perturbative theory is proposed which describes the evolution of modes in 2D open dielectric systems when permittivity distribution is modified. We successfully test this theory in a 2D disordered system to predict the position in the parameter space of the exceptional point between two Anderson-localized states. We observe that the accuracy of the prediction depends on the number of localized states accounted for. Such an exceptional point is experimentally accessible in practically relevant disordered photonic systems
A general detailed analysis for the nonlinear generation of localized fields, due to the existence of a strong pump field inside the non-uniform plasma, has been considered. We have taken into account the effects of relativistic and non-local nonlinearities on the structure of plasma resonance region. The nonlinear Schroedinger equation describing the localized fields is investigated. Besides, the generalized dispersion relation is obtained to study the modulational instabilities in different cases. (author)
Efficient Non Linear Loudspeakers
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...
Natale, Joseph; Hentschel, George
Firing-rate networks offer a coarse model of signal propagation in the brain. Here we analyze sparse, 2D planar firing-rate networks with no synapses beyond a certain cutoff distance. Additionally, we impose Dale's Principle to ensure that each neuron makes only or inhibitory outgoing connections. Using spectral methods, we find that the number of neurons participating in excitations of the network becomes insignificant whenever the connectivity cutoff is tuned to a value near or below the average interneuron separation. Further, neural activations exceeding a certain threshold stay confined to a small region of space. This behavior is an instance of Anderson localization, a disorder-induced phase transition by which an information channel is rendered unable to transmit signals. We discuss several potential implications of localization for both local and long-range computation in the brain. This work was supported in part by Grants JSMF/ 220020321 and NSF/IOS/1208126.
Cossu, Guido
2016-01-01
We investigate the properties of the background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures. We compute the eigenmodes of the M\\"obius domain-wall fermion operator on configurations generated for the $SU(3)$ gauge theory with two flavors of fermions, in the temperature range $[0.9,1.9]T_c$. We identify the source of localization of the eigenmodes with gauge configurations that are self-dual and support negative fluctuations of the Polyakov loop $P_L$, in the high temperature sea of $P_L\\sim 1$. The dependence of these observations on the boundary conditions of the valence operator is studied. We also investigate the spatial overlap of the left-handed and right-handed projected eigenmodes in correlation with the localization and the corresponding eigenvalue. We discuss an interpretation of the results in terms of monopole-instanton structures.
Cossu, Guido; Hashimoto, Shoji
2016-06-01
We investigate the properties of the background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures. We compute the eigenmodes of the Möbius domain-wall fermion operator on configurations generated for the SU(3) gauge theory with two flavors of fermions, in the temperature range [0.9, 1.9]T c . We identify the source of localization of the eigenmodes with gauge configurations that are self-dual and support negative fluctuations of the Polyakov loop P L , in the high temperature sea of P L ˜ 1. The dependence of these observations on the boundary conditions of the valence operator is studied. We also investigate the spatial overlap of the left-handed and right-handed projected eigenmodes in correlation with the localization and the corresponding eigenvalue. We discuss an interpretation of the results in terms of monopole-instanton structures.
Investigation of Anderson localization in disordered heterostructures irradiated by a Gaussian beam
Ardakani, Abbas Ghasempour
2016-02-01
The propagation of a Gaussian beam through a one-dimensional disordered media is studied. By employing the transfer matrix method, the localization length as a function of frequency is calculated for different values of transverse coordinate r. It is demonstrated that the localization length significantly depends on r in different frequency ranges. This result is in contrast to those reported for a plane wave incident on disordered structures in which the localization length is transversely constant. For some frequency regions, the peak of localization length is red-shifted and becomes smaller with increasing the transverse coordinate. At some frequencies, the system is in the localized state for particular values of r, while at other r values the system is in the extend regime at the same frequencies. It is observed that the quality of localization at each frequency depends on r. To quantify the localization behavior of the whole Gaussian beam, a modified localization length is defined in terms of the input and output powers of the Gaussian beam where the dependence of Anderson localization on the transverse coordinate is considered. It is suggested that this modified localization length is used in experiments performed for study of wave propagation in one-dimensional random media under illumination of laser beams.
Suppression of Anderson localization in a graphene sheet applied by a random voltage pattern
We theoretically study the transport of electronic waves through a graphene sheet applied by a random voltage pattern in which the magnitudes and/or the widths of the voltages are random. When the magnitudes of the voltages exceed the electronic energy, the applied region can be considered as left-handed (LH) layers. Compared to the disordered structures with right-handed (RH) layers only, the spectra of the (average) density of states and the localization lengths in mixed random structures with RH and LH layers all show the suppression of Anderson localization, owing to the phase compensation effect of LH layers that reduces the long-range interference in the random system.
Efficient Localization Bounds in a Continuous N-Particle Anderson Model with Long-Range Interaction
Chulaevsky, Victor
2016-04-01
We establish strong dynamical and exponential spectral localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the mathematical literature, the uniform decay bounds on the eigenfunction correlators (EFCs) at low energies are proved, in the multi-particle continuous configuration space, in the (symmetrized) norm-distance, which is a natural distance in the multi-particle configuration space, and not in the Hausdorff distance. This results in uniform bounds on the EFCs in arbitrarily large but bounded domains in the physical configuration space, and not only in the actually infinite space, as in prior works on multi-particle localization in Euclidean spaces.
On the question of possible experimental observation of Anderson localization of the neutron
A possible experiment for observation of the Anderson localization of the neutron is discussed. It is shown that the localized state may be formed in the process of inelastic downscattering of thermal or cold neutrons in a highly disordered substance with low neutron capture and upscattering cross sections. According to the sense of localization of the particle, its probability density exponentially decays outside a certain region of localization. Localized particles have exponentially small chances of running away from a random system. Any particle outside the localized energy band has an exponentially small probability of getting inside a random system. Neutrons localized in this way may be captured or inelastically upscattered to the thermal (cold) energy range with a time constant dependent on the corresponding cross sections. The most convenient substances for realizing such experiments are strong coherent neutron scatters with low capture and upscattering cross sections at low temperatures. These are Be, BeO, C, D2, D2O and CO2. The lifetime of trapped (localized) neutrons in the sample is measured by counting the upscattered neutrons with neutron counter surrounding the sample. Estimations of experimental parameters relevant to such an experiment are given
Javadi, Alisa; Sapienza, Luca; Thyrrestrup, Henri; Lodahl, Peter
2013-01-01
Optical nanostructures have proven to be meritorious for tailoring the emission properties of quantum emitters. However, unavoidable fabrication imperfections may represent a nuisance. Quite remarkably, disorder offers new opportunities since light can be efficiently confined by random multiple scattering leading to Anderson localization. Here we investigate the effect of such disorder-induced cavities on the emission dynamics of single quantum dots embedded in disordered photonic-crystal waveguides. We present time-resolved measurements of both the total emission from Anderson-localized cavities and from single emitters that are coupled to the cavities. We observe both strongly inhibited and enhanced decay rates relative to the rate of spontaneous emission in a homogeneous medium. From a statistical analysis, we report an average Purcell factor of 2 in without any control on the quantum dot - cavity detuning. By spectrally tuning individual quantum dots into resonance with Anderson-localized modes, a maximum...
Monthus, Cécile
2016-03-01
The generalization of the Dyson Brownian motion approach of random matrices to Anderson localization (AL) models (Chalker et al 1996 Phys. Rev. Lett. 77 554) and to many-body localization (MBL) Hamiltonians (Serbyn and Moore 2015 arXiv:1508.07293) is revisited to extract the level repulsion exponent β, where β =1 in the delocalized phase governed by the Wigner-Dyson statistics, β =0 , in the localized phase governed by the Poisson statistics, and 0 {{|}2} for the same eigenstate m = n and for consecutive eigenstates m = n + 1. For the Anderson localization tight-binding Hamiltonian with random on-site energies h i , we find β =2{{Y}n,n+1}(N)/≤ft({{Y}n,n}(N)-{{Y}n,n+1}(N)\\right) in terms of the density correlation matrix {{Y}nm}(N)\\equiv {\\sum}i=1N| {{|}2}| {{|}2} for consecutive eigenstates m = n + 1, while the diagonal element m = n corresponds to the inverse participation ratio {{Y}nn}(N)\\equiv {\\sum}i=1N| {{|}4} of the eigenstate |{φn}> .
This paper proposes a one-dimensional random structure composed of three types of alternating layers of dielectric and magnetized plasma materials. By employing the transfer matrix method, the localization lengths of the waves propagating in opposite directions are calculated. The numerical results demonstrate that nonreciprocal features appear in the averaged localization length and individual transmission resonances. However, in the short wavelength regime, the nonreciprocal behavior of the averaged localization length disappears, and the maximum of differential transmission decreases. The author investigates the effects of the external magnetic field, incident angle, collision frequency, and plasma density of the plasma layer on the reciprocal properties. The frequencies at which nonreciprocity occurs depend on the external magnetic field. Thus, it is possible to realize a photonic diode that is tunable with the external magnetic field. Also found is that for small angles of incidence no significant difference exists between the localization lengths of the forward and backward waves. There is a lower limit for the plasma density of the magnetized plasma layers to obtain nonreciprocal Anderson localization. As the collision frequency increases, the nonreciprocal features of the proposed random system survive. (papers)
coexist in waveguide-like systems with randomly corrugated boundaries, specifically, the entropic localization and the one-dimensional Anderson (disorder-driven) localization. If the particular mode propagates across the rough segment ballistically, the Fabry–Pérot-type oscillations should be observed in the conductance, which are suppressed for the mode transferred in the Anderson-localized regime
Highlights: → Statistics of normalized eigenfunctions in one-dimensional Anderson localization at E = 0 is studied. → Moments of inverse participation ratio are calculated. → Equation for generating function is derived at E = 0. → An exact solution for generating function at E = 0 is obtained. → Relation of the generating function to the phase distribution function is established. - Abstract: The one-dimensional (1d) Anderson model (AM), i.e. a tight-binding chain with random uncorrelated on-site energies, has statistical anomalies at any rational point f=(2a)/(λE) , where a is the lattice constant and λE is the de Broglie wavelength. We develop a regular approach to anomalous statistics of normalized eigenfunctions ψ(r) at such commensurability points. The approach is based on an exact integral transfer-matrix equation for a generating function Φr(u, φ) (u and φ have a meaning of the squared amplitude and phase of eigenfunctions, r is the position of the observation point). This generating function can be used to compute local statistics of eigenfunctions of 1d AM at any disorder and to address the problem of higher-order anomalies at f=p/q with q > 2. The descender of the generating function Pr(φ)≡Φr(u=0,φ) is shown to be the distribution function of phase which determines the Lyapunov exponent and the local density of states. In the leading order in the small disorder we derived a second-order partial differential equation for the r-independent ('zero-mode') component Φ(u, φ) at the E = 0 (f=1/2 ) anomaly. This equation is nonseparable in variables u and φ. Yet, we show that due to a hidden symmetry, it is integrable and we construct an exact solution for Φ(u, φ) explicitly in quadratures. Using this solution we computed moments Im = N2m> (m ≥ 1) for a chain of the length N → ∞ and found an essential difference between their m-behavior in the center-of-band anomaly and for energies outside this anomaly. Outside the anomaly the
Hewson, Alex C.; Bauer, Johannes
2010-01-01
We show that information on the probability density of local fluctuations can be obtained from a numerical renormalisation group calculation of a reduced density matrix. We apply this approach to the Anderson-Holstein impurity model to calculate the ground state probability density $\\rho(x)$ for the displacement $x$ of the local oscillator. From this density we can deduce an effective local potential for the oscillator and compare its form with that obtained from a semiclassical approximation...
The experiments described in this paper show that there are two types of non-linear three-wave processes: A. Disintegration of an electron plasma wave. In a plasma column of a density of 108 to 109 electrons/cm3, an electron temperature of the order of several eV, a length of 60 cm, a radius of 1 cm, which is confined by a magnetic field of 2500 G, a monochromatic electron plasma wave of frequency f1 is excited. A noise spectrum in a frequency band always below f1 due to the disintegration of this wave is observed. The resonance relations are verified. The threshold level and the energy transfer lengths are measured. The results of measurement show that the mechanism of disintegration should be interpreted without making use of the random-phase hypothesis. The shape of the spectrum is explained by varying the interaction coefficient as a function of the different phase velocities. In the same way, the parameter amplification of a wave pre-excited at one of the disintegration spectrum frequencies is studied. B. Non-linear generation of an electromagnetic wave. In a plasma with an electron density between 109 and 1011 electrons/cm3, which is confined by a magnetic field of the order of 4000 G and generated by a stationary high-frequency discharge, the interaction of two microwave beams propagated perpendicularly to the confining magnetic field and polarized both according to ordinary and extraordinary modes is brought about. The intersection of these beams defines the volume of interaction in which the third wave is generated. Two processes were studied, depending on the polarization of the two primary waves: (OX.O') and (OO', X). The measurements show that the conditions of resonance imposed on the frequencies and propagation vectors are satisfied. The power released is compared with the theoretical value. The polarization of the generated wave is in accordance with that expected from the structure of the interaction matrix. (author)
Anderson localization at the edge of a 2D topological insulator
Khalaf, Eslam; Ostrovsky, Pavel
We study transport via edge modes in a disordered 2D topological insulator allowing for the presence of non-protected diffusive channels in addition to the topologically protected edge channels. This scenario can be realized at the interface between two quantum Hall system, in a Weyl semimetal in a magnetic field or at the edge of a quantum spin Hall system. The edge transport is described by a one-dimensional field theory in the form of a supersymmetric non-linear sigma model with a topological term. The transfer-matrix formalism is employed to map the problem to the problem of finding the eigenfunctions of a certain operator on a symmetric superspace. The latter problem is solved exactly for all symmetry classes, enabling us to obtain the full counting statistics and mesoscopic conductance fluctuations in the system. Our main finding is that disorder is much more effective in localizing the diffusive (non-protected) channels in the presence of topologically protected ones. This manifests itself as a suppression of the shot noise and conductance fluctuations at scales much shorter than the localization length.
Pietracaprina, Francesca; Ros, Valentina; Scardicchio, Antonello
2016-02-01
In this paper we analyze the predictions of the forward approximation in some models which exhibit an Anderson (single-body) or many-body localized phase. This approximation, which consists of summing over the amplitudes of only the shortest paths in the locator expansion, is known to overestimate the critical value of the disorder which determines the onset of the localized phase. Nevertheless, the results provided by the approximation become more and more accurate as the local coordination (dimensionality) of the graph, defined by the hopping matrix, is made larger. In this sense, the forward approximation can be regarded as a mean-field theory for the Anderson transition in infinite dimensions. The sum can be efficiently computed using transfer matrix techniques, and the results are compared with the most precise exact diagonalization results available. For the Anderson problem, we find a critical value of the disorder which is 0.9 % off the most precise available numerical value already in 5 spatial dimensions, while for the many-body localized phase of the Heisenberg model with random fields the critical disorder hc=4.0 ±0.3 is strikingly close to the most recent results obtained by exact diagonalization. In both cases we obtain a critical exponent ν =1 . In the Anderson case, the latter does not show dependence on the dimensionality, as it is common within mean-field approximations. We discuss the relevance of the correlations between the shortest paths for both the single- and many-body problems, and comment on the connections of our results with the problem of directed polymers in random medium.
Milde, Frank; R{ö}mer, Rudolf A.
1998-01-01
Recently, a metal-insulator transition (MIT) was found in the anisotropic Anderson model of localization by transfer-matrix methods (TMM). This MIT has been also investigated by multifractal analysis (MFA) and the same critical disorders $W_c$ have been obtained within the accuracy of the data. We now employ energy level statistics (ELS) to further characterize the MIT. We find a crossover of the nearest-neighbor level spacing distribution $P(s)$ from GOE statistics at small disorder indicati...
Du, Yigang
The theory for modeling non-linear acoustic propagation is addressed in the dissertation. The solutions to both the linear and non-linear wave equations have been found by an angular spectrum approach (ASA), in which an analytical expression can be derived. This makes the calculation complete...... 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 are...
Daley, P; Wortis, R
2016-05-01
Non-interacting systems with bounded disorder have been shown to exhibit sharp density of state peaks at the band edge which coincide with an energy range of abruptly suppressed localization. Recent work has shown that these features also occur in the presence of on-site interactions in ensembles of two-site Anderson-Hubbard systems at half filling. Here we demonstrate that this effect in interacting systems persists away from half filling, and moreover that energy regions with suppressed localization continue to appear in ensembles of larger systems despite a loss of sharp features in the density of states. PMID:27022884
Modelling Loudspeaker Non-Linearities
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...
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 discounting...
The galactic fluid, in the early epochs of the Universe is treated, as a non-linear Stokesian fluid. Some general comments on fluids with viscosity are made. Then, an exact solution is examined and a qualitative analysis is given for Bianchi type-I cosmological model generated by a fluid with quadratic viscosity dependence on the deformation tensor. (Author)
Processing of nuclear medicine images is generally performed by essentially linear methods with the non-negativity condition being applied as the only non-linear process. The various methods used: matrix methods in signal space and Fourier or Hadamard transforms in frequency or sequency space are essentially equivalent. Further improvement in images can be obtained by the use of inherently non-linear methods. The recent development of an approximation to a least-difference method (as opposed to a least-square method) has led to an appreciation of the effects of data bounding and to the development of a more powerful process. Data bounding (modification of statistically improbable data values) is an inherently non-linear method with considerable promise. Strong bounding depending on two-dimensional least-squares fitting yields a reduction of mottling (buttermilk effect) not attainable with linear processes. A pre-bounding process removing very bad points is used to protect the strong bounding process from incorrectly modifying data points due to the weight of an extreme but yet unbounded point as the fitting area approaches it
Gomes, Anderson S L; Pincheira, Pablo I R; Moura, André L; Gagné, Mathieu; Kashyap, Raman; Raposo, Ernesto P; de Araújo, Cid B
2016-01-01
The analogue of the paramagnetic to spin-glass phase transition in disordered magnetic systems, leading to the phenomenon of replica symmetry breaking, has been recently demonstrated in a two-dimensional random laser consisting of an organic-based amorphous solid-state thin film. We report here the first demonstration of replica symmetry breaking in a one-dimensional photonic system consisting of an erbium-doped random fiber laser operating in the continuous-wave regime based on a unique random fiber grating system, which plays the role of the random scatterers and operates in the Anderson localization regime. The clear transition from a photonic paramagnetic to a photonic spin glass phase, characterized by the probability distribution function of the Parisi overlap, was verified and characterized. In this unique system, the radiation field interacts only with the gain medium, and the fiber grating, which provides the disordered feedback mechanism, does not interfere with the pump.
Steinigeweg, Robin [Institut fuer Theoretische Physik, Technische Universitaet Braunschweig, Mendelsohnstrasse 3, D-38106 Braunschweig (Germany); Niemeyer, Hendrik; Gemmer, Jochen, E-mail: r.steinigeweg@tu-bs.d, E-mail: jgemmer@uos.d [Fachbereich Physik, Universitaet Osnabrueck, Barbarastrasse 7, D-49069 Osnabrueck (Germany)
2010-11-15
Single-particle transport in disordered potentials is investigated at scales below the localization length. The dynamics at those scales is concretely analyzed for the three-dimensional Anderson model with Gaussian on-site disorder. This analysis particularly includes the dependence of characteristic transport quantities on the amount of disorder and the energy interval, e.g. the mean free path that separates ballistic and diffusive transport regimes. For these regimes mean velocities and diffusion constants are quantitatively given. Using the Boltzmann equation in the limit of weak disorder, we reveal the known energy dependences of transport quantities. By the application of the time-convolutionless projection operator technique in the limit of strong disorder, we obtain evidence for much less pronounced energy dependences. All our results are partially confirmed by the numerically exact solution of the time-dependent Schroedinger equation or by approximative numerical integrators. A comparison with other findings in the literature is also provided.
Non-linear constitutive equations for gravitoelectromagnetism
Duplij, Steven; Di Grezia, Elisabetta; Esposito, Giampiero; Kotvytskiy, Albert
2013-01-01
This paper studies non-linear constitutive equations for gravitoelectromagnetism. Eventually, the problem is solved of finding, for a given particular solution of the gravity-Maxwell equations, the exact form of the corresponding non-linear constitutive equations.
Corrections to scaling at the Anderson transition
Slevin, Keith; Ohtsuki, Tomi
1998-01-01
We report a numerical analysis of corrections to finite size scaling at the Anderson transition due to irrelevant scaling variables and non-linearities of the scaling variables. By taking proper account of these corrections, the universality of the critical exponent for the orthogonal universality class for three different distributions of the random potential is convincingly demonstrated.
Penyajian Integral dari Operator Non Linear
Budiman, Herdi; Sunusi, Nurtiti
2004-01-01
Fungsional linear kontinu pada suatu ruang fungsi dapat disajikan dengan suatu integral dan biasanya linear. Pada papaer ini akan diberikan penyajian integral dari suatu operator non linear, dengan cara mengkonstruksi integral non linear Henstock Kurzweil, fungsi f:[0,1] ---------> X, dengan X merupakan ruang Banach, dilanjutkan dengan penyajian integral dari operator non linear pada ruang C=C([0,1],X).
Anderson localization of light in a colloidal suspension (TiO2@silica).
Jimenez-Villar, Ernesto; da Silva, Iran F; Mestre, Valdeci; de Oliveira, Paulo C; Faustino, Wagner M; de Sá, Gilberto F
2016-06-01
In recent years, there has been dramatic progress in the photonics field in disordered media, ranging from applications in solar collectors, photocatalyzers, random lasing, and other novel photonic functions, to investigations into fundamental topics, such as light confinement and other phenomena involving photon interactions. This paper reports several pieces of experimental evidence of localization transition in a strongly disordered scattering medium composed of a colloidal suspension of core-shell nanoparticles (TiO2@silica) in ethanol solution. We demonstrate the crossover from a diffusive transport to a localization transition regime as the nanoparticle concentration is increased, and that an enhanced absorption effect arises at localization transition. PMID:26804337
Anderson localization of light in a colloidal suspension (TiO2@silica)
Jimenez-Villar, Ernesto; da Silva, Iran F.; Mestre, Valdeci; de Oliveira, Paulo C.; Faustino, Wagner M.; de Sá, Gilberto F.
2016-05-01
In recent years, there has been dramatic progress in the photonics field in disordered media, ranging from applications in solar collectors, photocatalyzers, random lasing, and other novel photonic functions, to investigations into fundamental topics, such as light confinement and other phenomena involving photon interactions. This paper reports several pieces of experimental evidence of localization transition in a strongly disordered scattering medium composed of a colloidal suspension of core-shell nanoparticles (TiO2@silica) in ethanol solution. We demonstrate the crossover from a diffusive transport to a localization transition regime as the nanoparticle concentration is increased, and that an enhanced absorption effect arises at localization transition.In recent years, there has been dramatic progress in the photonics field in disordered media, ranging from applications in solar collectors, photocatalyzers, random lasing, and other novel photonic functions, to investigations into fundamental topics, such as light confinement and other phenomena involving photon interactions. This paper reports several pieces of experimental evidence of localization transition in a strongly disordered scattering medium composed of a colloidal suspension of core-shell nanoparticles (TiO2@silica) in ethanol solution. We demonstrate the crossover from a diffusive transport to a localization transition regime as the nanoparticle concentration is increased, and that an enhanced absorption effect arises at localization transition. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr07540h
Simulation of non-linear ultrasound fields
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...... 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...
Anderson localization and its ramifications disorder, phase coherence and electron correlations
Kettemann, S
2003-01-01
The phenomenon of localization of the electronic wave function in a random medium can be regarded as the key manifestation of quantum coherence in a condensed matter system. As one of the most remarkable phenomena in condensed matter physics discovered in the 20th century, the localization problem is an indispensable part of the theory of the quantum Hall effects and rivals superconductivity in its significance as a manifestation of quantum coherence at a macroscopic scale. The present volume, written by some of the leading experts in the field, is intended to highlight some of the recent progress in the field of localization, with particular emphasis on the effect of interactions on quantum coherence. The chapters are written in textbook style and should serve as a reliable and thorough introduction for advanced students or researchers already working in the field of mesoscopic physics.
Measurement-induced disturbance near Anderson localization in one-dimensional systems
We study the localization transition in several typical one-dimensional single-particle systems by means of measurement-induced disturbance (MID). The results show that the MID presents a rapid drop around the boundary between the localized state and extended ones, and the corresponding first-order derivative exhibits a behavior of divergence around the critical point for deterministic on-site potential systems (e.g. the quasi-periodic model). These characteristics can capture a phase diagram as well as the traditional method. For the non-deterministic on-site systems (e.g. the random dimer model), the states around the resonant energies possess relatively large values for MID, which means that they are extended. In addition, as the random potential ϵ b exceeds the critical value, the states possessing a large MID vanish completely. These results show that MID can be useful in detecting localization transition in these typical one-dimensional systems. (paper)
Non-linear models: applications in economics
Albu, Lucian-Liviu
2006-01-01
The study concentrated on demonstrating how non-linear modelling can be useful to investigate the behavioural of dynamic economic systems. Using some adequate non-linear models could be a good way to find more refined solutions to actually unsolved problems or ambiguities in economics. Beginning with a short presentation of the simplest non-linear models, then we are demonstrating how the dynamics of complex systems, as the economic system is, could be explained on the base of some more advan...
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
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 identification applied to PWR steam generators
For the precise industrial purpose of PWR nuclear power plant steam generator water level control, a natural method is developed where classical techniques seem not to be efficient enough. From this essentially non-linear practical problem, an input-output identification of dynamic systems is proposed. Through Homodynamic Systems, characterized by a regularity property which can be found in most industrial processes with balance set, state form realizations are built, which resolve the exact joining of local dynamic behaviors, in both discrete and continuous time cases, avoiding any load parameter. Specifically non-linear modelling analytical means, which have no influence on local joined behaviors, are also pointed out. Non-linear autoregressive realizations allow us to perform indirect adaptive control under constraint of an admissible given dynamic family
Neural Networks for Non-linear Control
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....
Modelling Loudspeaker Non-Linearities
Agerkvist, Finn T.
2007-01-01
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...... property of the suspension is studied and it demonstrated that significant part of the variation can be predicted from the dissipated power....
Non-linear sigma models with generalized geometry
In this paper it is shown that the bosonic non-linear sigma model with algebraically extended world-sheet geometry is locally equivalent to the usual theory, but differs from the latter globally in that world-sheet instantons do not destabilize axions and in that it has a different critical dimension
Non-linear finite element modeling
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 of the...... Southern Denmark and in Medicine and Technology at the Technical University of Denmark. The note focus on the applicability to actually code routines with the purpose to analyze a geometrically or material non-linear problem. The note is tried to be kept on so brief a form as possible, with the main focus...
Optimal Stopping for Non-linear Expectations
Erhan Bayraktar; Song Yao
2009-01-01
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
Stability of non-linear integrable accelerator
Batalov, I.; Valishev, A.
2012-01-01
The stability of non-linear Integrable Optics Test Accelerator (IOTA) model was tested. The area of the stable region in transverse coordinates and the maximum attainable tune spread were found as a function of non-linear lens strength. Particle loss as a function of turn number was analyzed to determine whether a dynamic aperture limitation present in the system. The system was also tested with sextupoles included in the machine for chromaticity compensation. A method of evaluation of the be...
Non-linear analysis of concrete structures
Work in progress on the inelastic analysis of concrete structures using the finite element method is described. The study serves two objectives, the working stress design and the ultimate load analysis. The distribution of temperature, of particular importance in nuclear structures, is studied. The basis for the non linear analysis of instantaneous deformations is given, based in plasticity theory. Linear and non linear viscoelasticity based in the state variables approach are studied. Several numerical examples are presented. (Author)
Non-Linear Electrohydrodynamics in Microfluidic Devices
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.
Non-linear cluster lens reconstruction
Kaiser, N
1994-01-01
We develop a method for general non-linear cluster lens reconstruction using the observable distortion of background galaxies. The distortion measures the combination \\gamma/(1-\\kappa) of shear \\gamma and surface density \\kappa. From this we obtain an expression for the gradient of \\log (1 - \\kappa) in terms of directly measurable quantities. This allows one to reconstruct 1 - \\kappa up to an arbitrary constant multiplier. Recent work has emphasised an ambiguity in the relation between the distortion and \\gamma/(1-\\kappa). Here we show that the functional relation depends only on the parity of the images, so if one has data extending to large radii, and if the critical lines can be visually identified (as lines along which the distortion diverges), this ambiguity is resolved. Moreover, we show that for a generic 2-dimensional lens it is possible to locally determine the parity from the distortion. The arbitrary multiplier, which may in fact take a different value in each region bounded by the contour \\kappa =...
Physically and geometrically non-linear vibrations of thin rectangular plates
Breslavsky, Ivan; Amabili, Marco; Legrand, Mathias
2013-01-01
International audience Static deflection as well as free and forced large-amplitude vibrations of thin rectangular rubber plates under uniformly distributed pressure are investigated. Both physical, through a neo-Hookean constitutive law to describe the non-linear elastic deformation of the material, and geometrical non-linearities are accounted for. The deflections of a thin initially flat plate are described by the von Karman non-linear plate theory. A method for building a local model, ...
Non-linear dynamic of rotor-stator system with non-linear bearing clearance
Sinou, Jean-Jacques
2008-01-01
The study deals with a rotor-stator contact inducing vibration in rotating machinery. A numerical rotor-stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of this system, non-linear dynamic equations can be integrated numerically. However, this procedure is both time consuming and costly to perform. The aim of this Note is to apply the Alternate Frequency/Time Method and the 'path following continuation' in order to obtain the non-linear responses to this problem. Then the orbits of rotor and stator responses at various speeds are investigated.
Macroscopic and non-linear quantum games
Full text: We consider two models of quantum games. The first one is Marinatto and Weber's 'restricted' quantum game in which only the identity and the spin-flip operators are used. We show that this quantum game allows macroscopic mechanistic realization with the use of a version of the 'macroscopic quantum machine' described by Aerts already in 1980s. In the second model we use non-linear quantum state transformations which operate on points of spin-1/2 on the Bloch sphere and which can be used to distinguish optimally between two non-orthogonal states. We show that efficiency of these non-linear strategies out-perform any linear ones. Some hints on the possible theory of non-linear quantum games are given. (author)
Correlations and Non-Linear Probability Models
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 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...... 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....
Neighborhood approximations for non-linear voter models
Schweitzer, Frank
2016-01-01
Non-linear voter models assume that the opinion of an agent depends on the opinions of its neighbors in a non-linear manner. This allows for voting rules different from majority voting. While the linear voter model is known to reach consensus, non-linear voter models can result in the coexistence of opposite opinions. Our aim is to derive approximations to correctly predict the time dependent dynamics, or at least the asymptotic outcome, of such local interactions. Emphasis is on a probabilistic approach to decompose the opinion distribution in a second-order neighborhood into lower-order probability distributions. This is compared with an analytic pair approximation for the expected value of the global fraction of opinions and a mean-field approximation. Our reference case are averaged stochastic simulations of a one-dimensional cellular automaton. We find that the probabilistic second-order approach captures the dynamics of the reference case very well for different non-linearities, i.e for both majority an...
NICE: Non-linear Independent Components Estimation
Dinh, Laurent; Krueger, David; Bengio, Yoshua
2014-01-01
We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution that is easy to model. For this purpose, a non-linear deterministic transformation of the data is learned that maps it to a latent space so as to make the transformed data conform to a factorized distribution, i.e., resulting in independent latent variables....
Light focusing in the Anderson Regime
Leonetti, Marco; Mafi, Arash; Conti, Claudio
2014-01-01
Anderson localization is a regime in which diffusion is inhibited and waves (also electromagnetic waves) get localized. Here we exploit adaptive optics to achieve focusing in disordered optical fibers in the Anderson regime. By wavefront shaping and optimization, we observe the generation of a propagation invariant beam, where light is trapped transversally by disorder, and show that Anderson localizations can be also excited by extended speckled beams. We demonstrate that disordered fibers allow a more efficient focusing action with respect to standard fibers in a way independent of their length, because of the propagation invariant features and cooperative action of transverse localizations.
Non-linear thermoelectrics of molecular junctions with vibrational coupling
Leijnse, M.; Wegewijs, M.R.; Flensberg, K
2010-01-01
We present a detailed study of the nonlinear thermoelectric properties of a molecular junction, represented by a dissipative Anderson-Holstein model. A single-orbital level with strong Coulomb interaction is coupled to a localized vibrational mode and we account for both electron and phonon exchange with both electrodes, investigating how these contribute to the heat and charge transports. We calculate the efficiency and power output of the device operated as a heat to electric power converte...
Conjugate Gradient Acceleration of Non-Linear Smoothing Filters
Knyazev, Andrew; Malyshev, Alexander,
2015-01-01
The most efficient signal edge-preserving smoothing filters, e.g., for denoising, are non-linear. Thus, their acceleration is challenging and is often performed in practice by tuning filter parameters, such as by increasing the width of the local smoothing neighborhood, resulting in more aggressive smoothing of a single sweep at the cost of increased edge blurring. We propose an alternative technology, accelerating the original filters without tuning, by running them through a special conjuga...
Fixed Charge Capacitated Non-Linear Transportation Problem
Das, Atanu; Basu, Manjusri; Acharya, Debiprasad
2013-01-01
The fixed charge (fixed cost) may present the cost of renting a vehicle, landing fees in an airport, setup cost for machines in a manufacturing environment, etc. In this paper, we discuss fixed charge capacitated in a non-linear transportation problem. Thereby, we establish local optimum condition of this problem. Next we establish an algorithm for solving this transportation problem. Also, we illustrate a numerical example to support this algorithm
Non linearity between finance and growth
L. Deidda; B. Fattouh
2001-01-01
We present a simple model which establishes a non linear and possibly non monotonic relationship between financial development and economic growth. Applying a threshold regression model to King and Levine™s (1993) data set, we find evidence that is consistent with the main implications stemming from the theoretical model.
Non-linear Loudspeaker Unit Modelling
Pedersen, Bo Rohde; Agerkvist, Finn
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...
Dark Energy and Non-linear Perturbations
BRUCK, C.; Mota, D. F.
2005-01-01
Dark energy might have an influence on the formation of non--linear structures during the cosmic history. For example, in models in which dark energy couples to dark matter, it will be non--homogeneous and will influence the collapse of a dark matter overdensity. We use the spherical collapse model to estimate how much influence dark energy might have.
Non-linear wave equations:Mathematical techniques
An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author)
Generalized non-linear Schroedinger hierarchy
The importance in studying the completely integrable models have became evident in the last years due to the fact that those models present an algebraic structure extremely rich, providing the natural scenery for solitons description. Those models can be described through non-linear differential equations, pseudo-linear operators (Lax formulation), or a matrix formulation. The integrability implies in the existence of a conservation law associated to each of degree of freedom. Each conserved charge Qi can be associated to a Hamiltonian, defining a time evolution related to to a time ti through the Hamilton equation ∂A/∂ti=[A,Qi]. Particularly, for a two-dimensions field theory, infinite degree of freedom exist, and consequently infinite conservation laws describing the time evolution in space of infinite times. The Hamilton equation defines a hierarchy of models which present a infinite set of conservation laws. This paper studies the generalized non-linear Schroedinger hierarchy
无
2007-01-01
@@ Design Concept: "Wuhan Blue Prototype" A highlight of the concept is its integration with the local neighbourhood.The building and site planning will be coordinated with the existing planned facilities with a great lawn leading up from the community entrance toward a community gym and shopping centre. The Blue Sky Prototype itself is planned as an open-air network of pedestrian streets and public gardens at ground level winding up to vertical floor plates. The front doors of each unit will open to wide open-air streets and the sky.
Non-linear phase dispersion spectroscopy
Robles, Francisco E.; Satterwhite, Lisa L.; Wax, Adam
2011-01-01
Non-linear phase dispersion spectroscopy (NLDS) is introduced as a means to retrieve wide-band, high spectral resolution profiles of the wavelength-dependent, real part of the refractive index. The method is based on detecting dispersion effects imparted to a light field with low coherence transmitted through a thin sample and detected interferometrically in the spectral domain. The same sampled signal is also processed to yield quantitative phase maps and spectral information regarding the t...
Non--Linear Evolution of Cosmological Perturbations
Matarrese, Sabino
1996-01-01
In these lecture notes I review the theory of the non--linear evolution of cosmological perturbations in a self--gravitating collisionless medium, with vanishing vorticity. The problem is first analyzed in the context of the Newtonian approximation, where the basic properties of the Zel'dovich, frozen--flow and adhesion algorithms are introduced. An exact general relativistic formalism is then presented and it is shown how the Newtonian limit, both in Lagrangian and Eulerian coordinates, can ...
Superconformal mechanics and non-linear realizations
de Azcárraga, J A; Bueno, J C P; Townsend, P K
1999-01-01
We use the method of non-linear realizations to recover the superspace action of the SU(1,1|1)-invariant superconformal mechanics, and the field equations of its SU(1,1|2)-invariant extension. The coefficient of the superpotential term can be interpreted as the orbital angular momentum of a particle near the horizon of an extreme Reissner-Nordstrom black hole.
Farakos, Fotis
2012-01-01
We present a non-linear MSSM with non-standard Higgs sector and goldstino field. Non-linear supersymmetry for the goldstino couplings is described by the constrained chiral superfield and, as usual, the Standard Model sector is encompassed in suitable chiral and vector supermultiplets. Two models are presented. In the first model (non-linear MSSM$3 1/2$), the second Higgs is replaced by a new supermultiplet of half-family with only a new generation of leptons (or quarks). In the second model, for anomaly cancellation purposes, the second Higgs is retained as a spectator superfield by imposing a discrete symmetry. Both models do not have a $\\mu$-problem as a $\\mu$-term is forbidden by the discrete symmetry in the case of a spectator second Higgs or not existing at all in the case of a single Higgs. Moreover, the tree level relation between the Higgs mass and the hidden sector SUSY breaking scale $\\sqrt{f}$ is derived. Finally, we point out a relative suppression by $m_{soft}/\\Lambda$ of the bottom and tau Yuka...
Useful tools for non-linear systems: Several non-linear integral inequalities
Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.
2013-01-01
Roč. 49, č. 1 (2013), s. 73-80. ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf
Abaie, Behnam; Hosseini, Seyed Rasoul; Karbasi, Salman; Mafi, Arash
2016-04-01
Impact of the boundaries on transversely localized modes of a truncated one-dimensional disordered optical lattice is numerically studied. The results show lower modal number density near the boundaries compared with the bulk, while the average decay rate of the tail of localized modes is the same near the boundaries as in the bulk. It is suggested that the perceived suppressed localization near the boundaries is due to a lower mode density: on average, it is less probable to excite a localized mode near the boundaries; however, once it is excited, its localization is with the same exponential decay rate as any other localized mode.
Schreurs, D; Verspecht, J.; Acciari, G; Colantonio, P.; Giannini, F; Limiti, E.; Leuzzi, G.
2001-01-01
The Non-Linear Scattering Functions have been theoretically defined and experimentally measured for the linear-equivalent design of non-linear circuits in arbitrary large signal conditions. Non-linear measures and simulations have been compared, with good agreement. Linear CAD concepts can therefore be extended to non-linear circuits in a rigorous way.
Limits on Non-Linear Electrodynamics
Fouché, M.; Battesti, R.; 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...
Interpolation of compact non-linear operators
Bento AJG
2000-01-01
Let and be two Banach couples and let be a continuous map such that is a Lipschitz compact operator and is a Lipschitz operator. We prove that if is also compact or is continuously embedded in or is continuously embedded in , then is also a compact operator when and . We also investigate the behaviour of the measure of non-compactness under real interpolation and obtain best possible compactness results of Lions–Peetre type for non-linear operators. A two-sided compactness r...
Non-Linear Dynamics of Saturn's Rings
Esposito, L. W.
2015-10-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Results of driven N-body systems by Stuart Robbins: Even unforced rings show large variations; Forcing triggers aggregation; Some limit cycles and phase lags seen, but not always as predicted by predator-prey model. Summary of Halo Results: A predatorprey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw'. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon
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.
Non-linear statistical downscaling of present and LGM precipitation and temperatures over Europe
Vrac, M.; Marbaix, P.; Paillard, D.; Naveau, P.
2007-01-01
Local-scale climate information is increasingly needed for the study of past, present and future climate changes. In this study we develop a non-linear statistical downscaling method to generate local temperatures and precipitation values from large-scale variables of a Earth System Model of Intermediate Complexity (here CLIMBER). Our statistical downscaling scheme is based on the concept of Generalized Additive Models (GAMs), capturing non-linearities via non-parametric techniques. Our GAMs ...
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 Beam Dynamics Studies at SPEAR
The frequency map analysis of a Hamiltonian system recently introduced to accelerators physics in combination with turn-by-turn phase space measurements opens new experimental opportunities for studying non linear dynamic in storage rings. In this paper we report on the experimental program at SPEAR having the goal of measuring the frequency map of the machine. In this paper we discuss the accuracy of the instantaneous tune extraction from experimental data and demonstrate the possibility of the frequency map measurement. The instantaneous tune extraction technique can be applied to experimental tracking data with reasonable accuracy. Frequency map can be experimentally determined using the existing turn-by-turn phase space measurement techniques and NAFF instantaneous tune extraction.
Non-linear Fields in Generalized Cosmologies
Fasiello, Matteo
2016-01-01
The perturbative approach to structure formation has recently received a lot of attention in the literature. In such setups the final predictions for observables like the power spectrum is often derived under additional approximations such as a simplified time dependence. Here we provide all-order perturbative integral solutions for density and velocity fields in generalized cosmologies. We go beyond the standard results based on extending the EdS-like approximations. As an illustrative example, we apply our findings to the calculation of the one-loop power spectrum. We find corrections close to $1\\%$ in the mildly non-linear regime of $\\Lambda$CDM cosmologies for the density power spectrum, while in the case of the density-momentum power spectrum effects can reach up to $1.5\\%$ for $k\\sim 0.2h/$Mpc.
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...
Chaotic Discrimination and Non-Linear Dynamics
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.
Non-linear time heteronymous dymping in non-linear parametric planetary systems
Hortel, Milan; Škuderová, Alena
Prague : Institute of Thermomechanics AS CR, v. v. i., 2011 - (Fuis, V.), s. 203-206 ISBN 978-80-87012-33-8. [Engineering Mechanics 2011 /17./. Svratka (CZ), 09.05.2011-12.05.2011] Institutional research plan: CEZ:AV0Z20760514 Keywords : non-linear dynamics * time variable damping * planetary systems Subject RIV: BI - Acoustics
Carlos A Bustamante Chaverra
2013-03-01
Full Text Available Un método sin malla es desarrollado para solucionar una versión genérica de la ecuación no lineal de convección-difusión-reacción en dominios bidimensionales. El método de Interpolación Local Hermítica (LHI es empleado para la discretización espacial, y diferentes estrategias son implementadas para solucionar el sistema de ecuaciones no lineales resultante, entre estas iteración de Picard, método de Newton-Raphson y el Método de Homotopía truncado (HAM. En el método LHI las Funciones de Base Radial (RBFs son empleadas para construir una función de interpolación. A diferencia del Método de Kansa, el LHI es aplicado localmente y los operadores diferenciales de las condiciones de frontera y la ecuación gobernante son utilizados para construir la función de interpolación, obteniéndose una matriz de colocación simétrica. El método de Newton-Rapshon se implementa con matriz Jacobiana analítica y numérica, y las derivadas de la ecuación gobernante con respecto al paramétro de homotopía son obtenidas analíticamente. El esquema numérico es veriﬁcado mediante la comparación de resultados con las soluciones analíticas de las ecuaciones de Burgers en una dimensión y Richards en dos dimensiones. Similares resultados son obtenidos para todos los solucionadores que se probaron, pero mejores ratas de convergencia son logradas con el método de Newton-Raphson en doble iteración.A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diﬀusion-reaction equation in two-dim-ensional domains. The Local Hermitian Interpolation (LHI method is employed for the spatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM. The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs
Non-linear flow response and reaction plane correlations
Teaney, Derek; Yan, Li
2012-01-01
We apply the non-linear flow response formalism to the recently measured event plane correlations. We find that as a result of the combined effects of linear and non-linear flow response, the observed event plane correlations can be understood as an effective average of the 'linear limit' and 'non-linear limit'.
K-Exponential Stability of Non-Linear Delay Systems
ZHANG Yi; Banks, S. P.
1990-01-01
In this paper we introduce a new concept of k-exponential stability. The k-exponential stability of non-linear delay systems is investigated via the non-linear variation of parameters formula and non-linear inequality analysis.
Global non-linear effect of temperature on economic production.
Burke, Marshall; Hsiang, Solomon M; Miguel, Edward
2015-11-12
Growing evidence demonstrates that climatic conditions can have a profound impact on the functioning of modern human societies, but effects on economic activity appear inconsistent. Fundamental productive elements of modern economies, such as workers and crops, exhibit highly non-linear responses to local temperature even in wealthy countries. In contrast, aggregate macroeconomic productivity of entire wealthy countries is reported not to respond to temperature, while poor countries respond only linearly. Resolving this conflict between micro and macro observations is critical to understanding the role of wealth in coupled human-natural systems and to anticipating the global impact of climate change. Here we unify these seemingly contradictory results by accounting for non-linearity at the macro scale. We show that overall economic productivity is non-linear in temperature for all countries, with productivity peaking at an annual average temperature of 13 °C and declining strongly at higher temperatures. The relationship is globally generalizable, unchanged since 1960, and apparent for agricultural and non-agricultural activity in both rich and poor countries. These results provide the first evidence that economic activity in all regions is coupled to the global climate and establish a new empirical foundation for modelling economic loss in response to climate change, with important implications. If future adaptation mimics past adaptation, unmitigated warming is expected to reshape the global economy by reducing average global incomes roughly 23% by 2100 and widening global income inequality, relative to scenarios without climate change. In contrast to prior estimates, expected global losses are approximately linear in global mean temperature, with median losses many times larger than leading models indicate. PMID:26503051
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.
Raj, S; Hashimoto, D; Matsui, H; Souma, S; Sato, T; Takahashi, T; Sarma, D D; Mahadevan, Priya; Oishi, S
2006-04-14
The electronic structure of the insulating sodium tungsten bronze, Na(0.025)WO(3), is investigated by high-resolution angle-resolved photoemission spectroscopy. We find that near-E(F) states are localized due to the strong disorder arising from random distribution of Na+ ions in the WO(3) lattice, which makes the system insulating. The temperature dependence of photoemission spectra provides direct evidence for polaron formation. The remnant Fermi surface of the insulator is found to be the replica of the real Fermi surface in the metallic system. PMID:16712121
Purpose: To evaluate the rates of tumor downstaging after preoperative chemoradiation for locally advanced rectal cancer. Materials and Methods: Preoperative chemoradiotherapy (CTX/XRT) that delivered 45 Gy in 25 fractions over 5 weeks with continuous infusion 5-fluorouracil (300 mg/m2/day) was given to 117 patients. The pretreatment stage distribution, as determined by endorectal ultrasound (u), included uT2N0 in 2%, uT3N0 in 47%, uT3N1 in 49%, and uT4N0 in 2% of cases; endorectal ultrasound was not performed in 13% of cases (15 patients). Approximately 6 weeks after completion of CTX/XRT, surgery was performed. Results: The pathological tumor stages were Tis-2N0 in 26%, T2N1 in 5%, T3N0 in 21%, T3N1 in 15%, T4N0 in 5%, and T4N1 in 1%; a complete response (CR) to preoperative CTX/XRT was pathologically confirmed in 32 (27%) of patients. Tumor downstaging occurred in 72 (62%) cases. Only 3% of cases had pathologic evidence of progressive disease. Pretreatment tumor size (1 T-stage level was accomplished in 45% of those downstaged. Overall, a sphincter-saving (SP) procedure was possible in 59% of patients and an abdominoperineal resection (APR) was required in 41% of cases. Factors predictive of SP included downstaging (p 40 years (p 6 cm from the anal verge, SP was performed in 14 of the 15 (93%) patients with a CR and 32 of 33 (97%) of patients with residual disease (p < 0.00004). Conclusions: Significant tumor downstaging results from preoperative chemoradiation allowing sphincter sparing surgery in over 40% of patients whose tumors were located < 6 cm from the anal verge and who otherwise would have required colostomy
Non-Linear Pricing in Imperfectly Competitive Markets
Reggiani, Carlo
2009-01-01
This thesis is dedicated to the analysis of non-linear pricing in oligopoly. Non-linear pricing is a fairly predominant practice in most real markets, mostly characterized by some amount of competition. The sophistication of pricing practices has increased in the latest decades due to the technological advances that have allowed companies to gather more and more data on consumers preferences. The first essay of the thesis highlights the main characteristics of oligopolistic non-linear ...
Pulse Propagation in a Non-Linear Medium
Edah Gaston; Adanhounmè Villévo; Kanfon Antonin; Guédjé François; Hounkonnou Mahouton Norbert
2015-01-01
This paper considers a novel approach to solving the general propagation equation of optical pulses in an arbitrary non-linear medium. Using a suitable change of variable and applying the Adomian decomposition method to the non-linear Schrödinger equation, an analytical solution can be obtained which takes into accountparameters such as attenuation factor, the second order dispersive parameter, the third order dispersive parameter and the non-linear Kerr effect coeffic...
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.
Robust, data-driven inference in non-linear cosmostatistics
Wandelt, Benjamin D; Lavaux, Guilhem
2012-01-01
We discuss two projects in non-linear cosmostatistics applicable to very large surveys of galaxies. The first is a Bayesian reconstruction of galaxy redshifts and their number density distribution from approximate, photometric redshift data. The second focuses on cosmic voids and uses them to construct cosmic spheres that allow reconstructing the expansion history of the Universe using the Alcock-Paczynski test. In both cases we find that non-linearities enable the methods or enhance the results: non-linear gravitational evolution creates voids and our photo-z reconstruction works best in the highest density (and hence most non-linear) portions of our simulations.
Pulse Propagation in a Non-Linear Medium
Edah, Gaston; Adanhounmè, Villévo; Kanfon, Antonin; Guédjé, François; Hounkonnou, Mahouton Norbert
2015-02-01
This paper considers a novel approach to solving the general propagation equation of optical pulses in an arbitrary non-linear medium. Using a suitable change of variable and applying the Adomian decomposition method to the non-linear Schrödinger equation, an analytical solution can be obtained which takes into accountparameters such as attenuation factor, the second order dispersive parameter, the third order dispersive parameter and the non-linear Kerr effect coefficient. By analysing the solution, this paper establishes that this method is suitable for the study of light pulse propagation in a non-linear optical medium.
A comparison of equivalent linear and non-linear approaches for site amplification studies
The specification of the seismic design criteria for a nuclear installation requires that the effect of the local soil conditions at the site on seismic motion is assessed. The local soil conditions, in particular the material properties of the different soil strata, will affect both the frequency content and peak ground acceleration of seismic motion at the surface. Two main approaches which are used to account for the non-linear behavior of the soil are the equivalent linear approach and the non-linear incremental approach (Desai, 1976). In this paper the non-linear seismic response of a typical site characterized by shallow weak, horizontal soil layers overlying firm rock is examined using both these approaches. The results are compared and the extent of applicability of the equivalent linear approach is determined. The results are compared also with the results obtained from a linear analysis in order to examine the conservatisms inherent in such an analysis
Non-linear wave packet dynamics of coherent states
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.
Identification of Non-Linear Structures using Recurrent Neural Networks
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
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....
Algorithms for non-linear M-estimation
Madsen, Kaj; Edlund, O; Ekblom, H
1997-01-01
In non-linear regression, the least squares method is most often used. Since this estimator is highly sensitive to outliers in the data, alternatives have became increasingly popular during the last decades. We present algorithms for non-linear M-estimation. A trust region approach is used, where...
Non-linear dynamics of wind turbine wings
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
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 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....... 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.
Option pricing with linear market impact and non-linear Black and Scholes equations
Gregoire Loeper
2013-01-01
We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a non-linear Black-Scholes Equation that provides an exact replication strategy. This equation is fully non-linear and singular, but we show that it is well posed, and we prove existence of smooth solutions for a large class of final payoffs, both for constant and local volatility. To obtain regularity of the solutions, we develop an original method based on Lege...
Adaptive non-linear predictive control of a simulated flotation cell
This work illustrates the non-linear modelling and control of a flotation cell using a predictive strategy. A non-linear predictive model, based on local linear models, is used to represent the predictions of the system output and to calculate the control signal. This model is directly identified, using the available input-output data, and then used to calculate the control signal. Simulated results show not only the advantages of using simple models to approximate complex phenomenological models, but also the performance of the proposed predictive control approach. (author)
Adaptive Kronrod-Patterson integration of non-linear finite-element matrices
Janssen, Hans
2010-01-01
inappropriate discretization. In response, this article develops adaptive integration, based on nested Kronrod-Patterson-Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non-linearity. Adaptive integration is developed based on a standard infiltration...
Identification of non-linear models of neural activity in bold fmri
Jacobsen, Daniel Jakup; Madsen, Kristoffer Hougaard; Hansen, Lars Kai
2006-01-01
Non-linear hemodynamic models express the BOLD signal as a nonlinear, parametric functional of the temporal sequence of local neural activity. Several models have been proposed for this neural activity. We identify one such parametric model by estimating the distribution of its parameters. These...
Towards non-linear simulations of full ELM crashes in ASDEX upgrade
Lessig, Alexander; Hoelzl, Matthias; Lackner, Karl; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Boltzmannstrasse 2, 85748 Garching (Germany)
2014-07-01
Edge localized modes (ELMs) of large size are a severe concern for the operation of ITER due to the large transient heat loads on divertor targets and wall structures. Using the non-linear MHD code JOREK, we have performed first simulations of full ELM crashes in ASDEX upgrade, taking into account a large number of toroidal Fourier harmonics. The evolution of the toroidal Fourier spectrum and the drop of pedestal gradients are studied. In particular, we confirm a previously introduced quadratic mode coupling model for the early non-linear evolution of the mode structure and present first results concerning the evolution in the fully non-linear phase. Eventually, we aim to identify different ELM types in our simulations as observed in experiments and to compare the results to experimental observations, e.g., regarding the pedestal evolution and the heat deposition patterns. Work is ongoing to increase poloidal resolution and include diamagnetic stabilization of high mode numbers.
Non-linear simulations of ELMs in ASDEX Upgrade including diamagnetic drift effects
Lessig, Alexander; Hoelzl, Matthias; Krebs, Isabel; Franck, Emmanuel; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, Boltzmannstrasse 2, 85748 Garching (Germany); Orain, Francois; Morales, Jorge; Becoulet, Marina [CEA-IRFM, Cadarache, 13108 Saint-Paul-Lez-Durance (France); Huysmans, Guido [ITER Organization, 13067 Saint-Paul-Lez-Durance (France)
2015-05-01
Large edge localized modes (ELMs) are a severe concern for ITER due to high transient heat loads on divertor targets and wall structures. Using the non-linear MHD code JOREK, we have performed ELM simulations for ASDEX Upgrade (AUG) including diamagnetic drift effects. The influence of diamagnetic terms onto the evolution of the toroidal mode spectrum for different AUG equilibria and the non-linear interaction of the toroidal harmonics are investigated. In particular, we confirm the diamagnetic stabilization of high mode numbers and present new features of a previously introduced quadratic mode coupling model for the early non-linear evolution of the mode structure. Preliminary comparisons of full ELM crashes with experimental observations are shown aiming at code validation and the understanding of different ELM types. Work is ongoing to include toroidal and neoclassical poloidal rotation in our simulations.
Non-Linear Aeroelastic Stability of Wind Turbines
Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie;
2013-01-01
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...... identification of the non-linear wind turbine system.......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...
Working group 3 : Identification of non-linear systems
GOLINVAL, JC; G. Kerschen; V. Lenaerts; Thouverez, F.; Argoul, P.
2003-01-01
Researchers in structural dynamics have long recognised the importance of diagnosing and modelling non-linearity. The last 20 years have witnessed a shift in emphasis from single degree-of-freedom (sdof) to multi-degree-of-freedom (mdof) non-linear structural dynamics. The main feature of the program of COST F3 Working Group 3 was to identify the behaviour of a structure which exhibits a localised non-linear component. Inside this working group, two benchmarks were defined and studied intensi...
Non-linear conductivity and quantum interference in disordered metals
Leadbeater, M.; Raimondi, R.; Schwab, P.; Castellani, C.
1999-01-01
We report on a novel non-linear electric field effect in the conductivity of disordered conductors. We find that an electric field gives rise to dephasing in the particle-hole channel, which depresses the interference effects due to disorder and interaction and leads to a non-linear conductivity. This non-linear effect introduces a field dependent temperature scale $T_E$ and provides a microscopic mechanism for electric field scaling at the metal-insulator transition. We also study the magnet...
Computer modeling of batteries from non-linear circuit elements
Waaben, S.; Federico, J.; Moskowitz, I.
1983-01-01
A simple non-linear circuit model for battery behavior is given. It is based on time-dependent features of the well-known PIN change storage diode, whose behavior is described by equations similar to those associated with electrochemical cells. The circuit simulation computer program ADVICE was used to predict non-linear response from a topological description of the battery analog built from advice components. By a reasonable choice of one set of parameters, the circuit accurately simulates a wide spectrum of measured non-linear battery responses to within a few millivolts.
Analysis of non-linearity in differential wavefront sensing technique.
Duan, Hui-Zong; Liang, Yu-Rong; Yeh, Hsien-Chi
2016-03-01
An analytical model of a differential wavefront sensing (DWS) technique based on Gaussian Beam propagation has been derived. Compared with the result of the interference signals detected by quadrant photodiode, which is calculated by using the numerical method, the analytical model has been verified. Both the analytical model and numerical simulation show milli-radians level non-linearity effect of DWS detection. In addition, the beam clipping has strong influence on the non-linearity of DWS. The larger the beam clipping is, the smaller the non-linearity is. However, the beam walking effect hardly has influence on DWS. Thus, it can be ignored in laser interferometer. PMID:26974079
NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS
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.
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.
A new conformal-invariant non-linear spinor equation
We propose a new model for a spinor particle, based on a non-linear Dirac equation. We invoke group invariance and use symmetry reduction in order to obtain a multiparameter family of exact solutions of the proposed equation. (authors)
Linear and non-linear optics of condensed matter
Part I - Linear optics: 1. General introduction. 2. Frequency dependence of epsilon(ω, k vector). 3. Wave-vector dependence of epsilon(ω, k vector). 4. Tensor character of epsilon(ω, k vector). Part II - Non-linear optics: 5. Introduction. 6. A classical theory of non-linear response in one dimension. 7. The generalization to three dimensions. 8. General properties of the polarizability tensors. 9. The phase-matching condition. 10. Propagation in a non-linear dielectric. 11. Second harmonic generation. 12. Coupling of three waves. 13. Materials and their non-linearities. 14. Processes involving energy exchange with the medium. 15. Two-photon absorption. 16. Stimulated Raman effect. 17. Electro-optic effects. 18. Limitations of the approach presented here. (author)
Fluidelastic instability of a flexible weir: non linear analysis
A new type of fluidelastic instability was discovered during the hot tests of Super Phenix LMFBR. This instability is due to the fluid discharge, over a flexible weir shell which separates two thin fluid sheets (the feeding and restitution collectors). An analytical non-linear model was realized. The flow and force sources at the top of the collectors are described and projected on the modal basis of the system formed by the collectors and the weir shell. This model is used to estimate the vibratory level when a steady-state is reached by the effect of non-linearities. The influence of the different non-linear relations implied by the weir discharge is discussed. Comparisons of the steady-state amplitudes and behaviour in time, between calculation and measurement on the reactor are made. They demonstrate that the model is relevant for such non-linear analysis
On a non linear third - order parabolic equation
De Angelis, Monica
2012-01-01
Aim of this paper is the qualitative analysis of the solution of a boundary value problem for a third-order non linear parabolic equation which describes several dissipative models. When the source term is linear, the problem is explictly solved by means of a Fourier series with properties of rapid convergence. In the non linear case,appropriate estimates of this series allow to deduce the asymptotic behaviour of the solution.
Graphical and Analytical Analysis of the Non-Linear PLL
Boer, de, F.R.; Radovanović, Saša; Annema, Anne Johan; Nauta, Bram
2003-01-01
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 introduces an analysis for accurate prediction of these effects and design alterations to lower its influence on the phase error.
Non-linear transformations of the Schwartz distributions
The problem of non-linear transformations of the variables of the Schwartz distributions with point support is treated by means of the generalized asymptotic functions. To this aim, a variant of the latter functions for the case of many variables is presented and the existence of asymptotic analogues of the point distributions, consistent with the linear operations, is shown. In this scheme some results concerning the non-linear transformations of the point distributions are obtained. (author). 11 refs
Non-linear analysis of multilayer composite structures
Kroflič, Aleš
2012-01-01
A new mathematical model for non-linear static analysis of multilayer composite structures with deformable connection is presented. Doctoral thesis is divided into two parts. In the first part a new mathematical model for analysis of plane multilayer frames is presented. Each layer of composite frame is modelled with geometrically exact Reissner model of plane beam. An important novelty of the model is the introduction of a new constitutive law for connection. Arbitrary non-linear relationshi...
Non-Linear Seismic Analysis of Masonry Buildings
Parisi, Fulvio
2010-01-01
Non-linear analysis is the most viable tool to get accurate predictions of the actual response of masonry structures under earthquake loading. Analytical methods based on the idealisation of masonry walls with openings as systems of macro-elements allow not only to capture the main failure modes observed after past earthquakes, but also to ensure a limited computational demand in engineering practice. The present thesis deals with non-linear incremental static (pushover) analysis on mason...
NON-LINEAR SOIL MODELS FOR PIPELINE AND RISER ANALYSIS
Irman, Arifian Agusta
2015-01-01
This thesis describes the development and application of non-linear soil models in pipeline and riser design. A non-linear soil model is typically employed when investigating a complex pipe-soil interaction problem. Two main pipe-soil interactions are frequently studied: the vertical pipe-soil interaction at the touchdown point of the steel catenary riser (SCR) during cyclic heave motion, and the lateral pipe-soil interaction during the pipeline s lateral buckling. Mathematical models for...
Non-linear corrections to inflationary power spectrum
Gong, Jinn-Ouk(Asia Pacific Center for Theoretical Physics, 67 Cheongam-ro, Pohang, 790-784, Korea); Noh, Hyerim; Hwang, Jai-chan
2010-01-01
We study non-linear contributions to the power spectrum of the curvature perturbation on super-horizon scales, produced during slow-roll inflation driven by a canonical single scalar field. We find that on large scales the linear power spectrum completely dominates and leading non-linear corrections remain totally negligible, indicating that we can safely rely on linear perturbation theory to study inflationary power spectrum. We also briefly comment on the infrared and ultraviolet behaviour ...
Non-linear normal modes in dynamics - discrete systems
Náprstek, Jiří; Fischer, Cyril
Vol. 821. Zürich: Trans Tech Publications, 2016 - (Fischer, C.), s. 254-265 ISBN 978-3-03835-700-1. [Engineering mechanics 2015 /21./. Svratka (CZ), 11.05.2015-14.05.2015] R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : non-linear dynamical systems * non-linear normal modes * discretization * multi-scale method Subject RIV: JM - Building Engineering
Rotorcraft trajectory tracking by non linear inverse control
Drouin, Antoine; Brandao-Ramos, Alexandre Carlos; Miquel, Thierry; Mora-Camino, Félix
2007-01-01
The purpose of this communication is to investigate the usefulness of the non linear inverse control approach to solve the trajectory tracking problem for a four rotor aircraft. After introducing simplifying assumptions, the flight dynamics equations for the four rotor aircraft are considered. A trajectory tracking control structure based on a two layer non linear inverse approach is then proposed. A supervision level is introduced to take into account the actuator limitations.
Risk Assessment Under a Non-linear Fiscal Rule.
Christos Shiamptanis
2012-01-01
In the aftermath of the recent financial crisis and recession, governments' actions around the world suggest a non-linear responsiveness of fiscal policy to debt. Additionally, governments are realizing that they face fiscal limits on the size of debt that they can repay. The fiscal limits arise due to distortionary taxation and political will. This paper explores the implications of a non-linear fiscal rule coupled with fiscal limits on solvency crisis. We derive the restrictions on the non-...
Non-linear Integrated Sachs-Wolfe Effect
Cooray, A R
2002-01-01
We discuss the non-linear extension to the integrated Sachs-Wolfe effect (ISW) resulting from the divergence of the large scale structure momentum density field. The non-linear ISW effect leads to an increase in the total ISW contribution by roughly two orders of magnitude at l ~ 1000. This increase, however, is still below the cosmic variance limit of the primary anisotropies; at further small angular scales, secondary effects such as gravitational lensing and the kinetic Sunyaev-Zel'dovich (SZ) effect dominates the non-linear ISW power spectrum. We show this second-order non-linear ISW contribution is effectively same as the contribution previously described as a lensing effect due to the transverse motion of gravitational lenses and well known as the Kaiser-Stebbins effect under the context of cosmic strings. Due to geometrical considerations, there is no significant three point correlation function, or a bispectrum, between the linear ISW effects and its non-linear extension. The non-linear ISW contributi...
Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
Barles, Guy; Chasseigne, Emmanuel; Imbert, Cyril
2011-01-01
This paper is concerned with Hölder regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we assume that, at each point of the domain, either the equation is strictly elliptic in the classical fully non-linear sense, or (and this is the most original part of our work) the equation is strictly elliptic in a non-local non-linear sense we make precise. Next we impose some regularity and growth c...
Interview with Philip W. Anderson
Phil Anderson, Professor of Physics at Princeton University, has devoted his career to research in theoretical physics. He is a member of the National Academy of Science and the American Academy of Arts and Sciences, a foreign member of the Royal Society, and a foreign associate of the Accademia Lincei in Rome. The Americal Physical Society awarded him the Oliver E. Buckley Solid State Physics Prize in 1964. In 1977 he won the Nobel Prize in Physics with J.H. van Vleck and N.F. Mott. His work has encompassed a broad range of subjects: quantum theory of condensed matter, broken symmetry, transport theory and localization, random statistical systems, spectral line broadening, superfluidity in helium and neutron stars, magnetism, and superconductivity. His avocations include ''hiking, the game of GO, Romanesque architecture, and the human condition.'' In this interview he explains his RVB theory of the oxide superconductors and its historical context
We consider, in a 1+3 space time, arbitrary (finite) systems of nonlinear Klein-Gordon equations (respectively Schroedinger equations) with an arbitrary local and analytic non-linearity in the unknown and its first and second order space-time (respectively first order space) derivatives, having no constant or linear terms. No restriction is given on the frequency sign of the initial data. In the case of non-linear Klein-Gordon equations all masses are supposed to be different from zero. We prove, for such systems, that the wave operator (from t=infinite to t=0) exists on a domain of small entire test functions of exponential type and that the analytic Cauchy problem, in R+ x R3, has a unique solution for each initial condition (at t=0) being in the image of the wave operator. The decay properties of such solutions are discussed in detail. (orig.)
The object of the paper is to present a numerical method of determining the dynamic response at characteristic points of the building taking into account the non-linear behaviour of locally impacted cracked damaged concrete. The method is based on the determination of a verified load function (VLF) which, applied to a linear elastic model of the structure, leads to the same response of the building (far from the impact point) as that due to the RLF impact force applied to a more realistic non-linear model of the reinforced concrete building. The practical advantage of using this procedure is that it avoids long and costly non-linear time integration of a full structural model. In order to obtain the VLF one only performs non-linear explicit calculations locally which include the main physical phenomenon occuring in an impacted reinforced concrete structure. (orig./HP)
Non-linear statistical downscaling of present and LGM precipitation and temperatures over Europe
Vrac, M.; Paillard, D.; Naveau, P.
2007-01-01
The needs of small-scale climate information have become prevalent to study the impacts of future climate change as well as for paleoclimate researches where the reconstructions from proxies are obviously local. In this study we develop a non-linear statistical downscaling method to generate local temperatures and precipitation values from large-scale variables (e.g. Global Circulation Model – GCM – outputs), through Generalized Additive Models (GAMs) calibrated on the pre...
Non-linear statistical downscaling of present and LGM precipitation and temperatures over Europe
Vrac, M.; Paillard, D.; Naveau, P.
2007-01-01
International audience The needs of small-scale climate information have become prevalent to study the impacts of future climate change as well as for paleoclimate researches where the reconstructions from proxies are obviously local. In this study we develop a non-linear statistical downscaling method to generate local temperatures and precipitation values from large-scale variables (e.g. Global Circulation Model – GCM – outputs), through Generalized Additive Models (GAMs) calibrated on t...
Anderson, Karl F.
1994-01-01
Four-wire-probe concept applied to electrical-resistance transducers. Anderson current loop is excitation-and-signal-conditioning circuit suitable for use with strain gauges, resistance thermometers, and other electrical-resistance transducers mounted in harsh environments. Used as alternative to Wheatstone bridge. Simplifies signal-conditioning problem, enabling precise measurement of small changes in resistance of transducer. Eliminates some uncertainties in Wheatstone-bridge resistance-change measurements in flight research. Current loop configuration makes effects of lead-wire and contact resistances insignificantly small. Also provides output voltage that varies linearly with change in gauge resistance, and does so at double sensitivity of Wheatstone bridge.
Non-linear coupling of quantum theory and classical gravity
The possibility that the non-linear evolution proposed earlier for a relativistic quantum field theory may be related to its coupling to a classical gravitational field is discussed. Formally, in the Schroedinger picture, it is shown how both the Schroedinger equation and Einstein's equations (with the expectation value of the energy-momentum tensor on the right) can be derived from a variational principle. This yields a non-linear quantum evolution. Other terms can be added to the action integral to incorporate explicit non-linearities of the type discussed previously. The possibility of giving a meaning to the resulting equation in a Heisenberg or interaction-like picture, is briefly discussed. (author)
Theoretical studies for novel non-linear optical crystals
Wu, Kechen; Chen, Chuangtian
1996-09-01
To fulfil the "molecular engineering" of non-linear optical crystals, two theoretical models suitable respectively for the studies of the absorption edge and birefringence of a non-linear optical crystal have been set up. Molecular quantum chemical methods have been adopted in the systematic calculations of some typical crystals. DV-SCM-X α methods have been used to calculate the absorption edge on the UV side of BBO, LBO, KB5, KDP, Na 2SbF 5, Ba 2TiSi 2O 8, iodate and NaNO 2 crystals. Ab initio methods have been adopted to study the birefringence of NaNO 2, BBO, LiIO 3 and urea crystals. All the theoretical results agreed well with the experimental values. The relationship between structure and properties has been discussed. The results will be helpful to the search for novel non-linear optical crystals.
Asymtotics of M-estmation in Non-linear Regression
Ying YANG
2004-01-01
Consider the standard non-linear regression model yi = g(xi,θo) +εi, i = 1,..., n where g(x,θ) is a continuous function on a bounded closed region X × , θo is the unknown parameter vector in Rp, {x1, x2, ... ,xn} is a deterministic design of experiment and {ε1, ε2 ,εn} is a sequence of independent random variables. This paper establishes the existences of M-estimates and the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are independent and identically distributed. This result is then used to obtain the asymptotic distribution of a class of M-estimators for a large class of non-linear regression models. At the same time, we point out that Theorem 2 of Wang (1995) (J. of Multivariate Analysis, vol. 54, pp. 227-238, Corrigenda. vol. 55, p. 350) is not correct.
Non-linear system identification in flow-induced vibration
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.
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.
Ghost Dark Energy with Non-Linear Interaction Term
Ebrahimi, E.
2016-06-01
Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w D = p/ ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω D ). We find that in one case, w D cross the phantom line ( w D < -1). However in two other classes w D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w D , q. We study squared sound speed {vs2}, and find that for one case of non-linear interaction term {vs2} can achieves positive values at late time of evolution.
Neural network modelling of non-linear hydrological relationships
Abrahart, R. J.; See, L. M.
2007-09-01
Two recent studies have suggested that neural network modelling offers no worthwhile improvements in comparison to the application of weighted linear transfer functions for capturing the non-linear nature of hydrological relationships. The potential of an artificial neural network to perform simple non-linear hydrological transformations under controlled conditions is examined in this paper. Eight neural network models were developed: four full or partial emulations of a recognised non-linear hydrological rainfall-runoff model; four solutions developed on an identical set of inputs and a calculated runoff coefficient output. The use of different input combinations enabled the competencies of solutions developed on a reduced number of parameters to be assessed. The selected hydrological model had a limited number of inputs and contained no temporal component. The modelling process was based on a set of random inputs that had a uniform distribution and spanned a modest range of possibilities. The initial cloning operations permitted a direct comparison to be performed with the equation-based relationship. It also provided more general information about the power of a neural network to replicate mathematical equations and model modest non-linear relationships. The second group of experiments explored a different relationship that is of hydrological interest; the target surface contained a stronger set of non-linear properties and was more challenging. Linear modelling comparisons were performed against traditional least squares multiple linear regression solutions developed on identical datasets. The reported results demonstrate that neural networks are capable of modelling non-linear hydrological processes and are therefore appropriate tools for hydrological modelling.
Arithmetic coding as a non-linear dynamical system
Nagaraj, Nithin; Vaidya, Prabhakar G.; Bhat, Kishor G.
2009-04-01
In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luröth Series (GLS). GLS achieves Shannon's entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.
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.
Non-linear optics of ultrastrongly coupled cavity polaritons
Crescimanno, Michael; Liu, Bin; McMaster, Michael; Singer, Kenneth
2016-05-01
Experiments at CWRU have developed organic cavity polaritons that display world-record vacuum Rabi splittings of more than an eV. This ultrastrongly coupled polaritonic matter is a new regime for exploring non-linear optical effects. We apply quantum optics theory to quantitatively determine various non-linear optical effects including types of low harmonic generation (SHG and THG) in single and double cavity polariton systems. Ultrastrongly coupled photon-matter systems such as these may be the foundation for technologies including low-power optical switching and computing.
Non-Linear Fibres for Widely Tunable Femtosecond Fibre Lasers
Pedersen, Martin Erland Vestergaard
theoretically and numerically. For the intermodal four-wave mixing experiment an alternative version of the Generalised Non-Linear Schrödinger Equation is derived, which includes the correct dispersion of the transverse field. It is observed that the alternative version of the Generalised Non-Linear Schrödinger...... Equation, as opposed to the commonly used version, is able to reproduce the intermodal four-wave mixing experiment. The relation between the intramodal self-phase modulation and the intramodal Raman effect is determined from experimental measurements on a number of step-index fibres. The Raman fraction is...
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
Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators
Taleghani, Barmac K.; Campbell, Joel F.
1999-01-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
The Importance of Non-Linearity on Turbulent Fluxes
Rokni, Masoud
2007-01-01
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...
Mathematical problems in non-linear Physics: some results
The basic results presented in this report are the following: 1) Characterization of the range and Kernel of the variational derivative. 2) Determination of general conservation laws in linear evolution equations, as well as bounds for the number of polynomial conserved densities in non-linear evolution equations in two independent variables of even order. 3) Construction of the most general evolution equation which has a given family of conserved densities. 4) Regularity conditions for the validity of the Lie invariance method. 5) A simple class of perturbations in non-linear wave equations. 6) Soliton solutions in generalized KdV equations. (author)
Sparse PDF maps for non-linear multi-resolution image operations
Hadwiger, Markus
2012-11-01
We introduce a new type of multi-resolution image pyramid for high-resolution images called sparse pdf maps (sPDF-maps). Each pyramid level consists of a sparse encoding of continuous probability density functions (pdfs) of pixel neighborhoods in the original image. The encoded pdfs enable the accurate computation of non-linear image operations directly in any pyramid level with proper pre-filtering for anti-aliasing, without accessing higher or lower resolutions. The sparsity of sPDF-maps makes them feasible for gigapixel images, while enabling direct evaluation of a variety of non-linear operators from the same representation. We illustrate this versatility for antialiased color mapping, O(n) local Laplacian filters, smoothed local histogram filters (e.g., median or mode filters), and bilateral filters. © 2012 ACM.
We have carried out numerical investigations of transmittance fluctuations in disordered chains in the presence of external electric fields. We have obtained an almost constant fluctuation in a length scale smaller than the localization length. However, the value of the fluctuation in the plateau region is dependent on the external electric field and strength of disorder. We have also studied the transmittance autocorrelation as a function of external electric field to probe non-linearity in transmittance. (author). 26 refs, 4 figs
LINEAR AND NON-LINEAR CAMERA CALIBRATION TECHNIQUES
Manoj Gupta
2011-01-01
This Paper deals with calibrate a camera to find out the intrinsic and extrinsic camera parameters which are necessary to recover the depth estimation of an object in stereovision system. Keywords: Camera Calibration, Tsai’s algorithm, Stereovision, Linear Calibration, Non-Linear Calibration, Depth estimation
Characterising dynamic non-linearity in floating wind turbines
Fully coupled aero-hydro-control-elastic codes are being developed to cope with the new modelling challenges presented by floating wind turbines, but there is also a place for more efficient methods of analysis. One option is linearisation and analysis in the frequency domain. For this to be an effective method, the non-linearities in the system must be well understood. The present study focusses on understanding the dynamic response of the rotor to the overall platform motion, as would arise from wave loading, by using a simple model of a floating wind turbine with a rigid tower and flexible rotor (represented by hinged rigid blades). First, an equation of motion of the blade is derived and an approximate solution for the blade response is found using the perturbation method. Secondly, the full non-linear solution is found by time- domain simulation. The response is found to be linear at lower platform pitching frequencies, becoming non-linear at higher frequencies, with the approximate solution giving good results for weakly non-linear behaviour. Higher rotor speeds have a stabilising effect on the response. In the context of typical floating turbine parameters, it is concluded that the blade flapwise response is likely to be linear
Non-linear duality invariant partially massless models?
Cherney, D.; Deser, S.; Waldron, A; Zahariade, G.
2016-01-01
We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Our models mimic Dirac–Born–Infeld theory but it is unclear whether they are Lagrangian.