Sum Of Modes Research Articles

Study of the solar flares effect on VLF radio signal propagating along NRK‐ALG path using LWPC code

AbstractThe X‐ray solar flare emissions penetrate down into the D region of the ionosphere (60–90 km of altitude) and affect the propagating very low frequency (VLF) radio signal. In this paper, we will present the effect of the solar flares on the signal mode composition of the NRK‐ALG path during the period from 2007 to 2013. In the Long Wave Propagating Capability (LWPC) code theory, the VLF signal is a sum of discrete modes that propagate to the receiver with different attenuation coefficients. Therefore, an interest is given to the behavior of these coefficients under solar flares. Effectively, from the simulation, we give more explanations about the role of the signal mode composition on the fading displacement since this later is a consequence of the destructive modes interferences. Thus, the sign (positive or negative) of the perturbed signal parameters (amplitude and phase) is found to be depending on the distance between the transmitter and the receiver. Finally, we give the Wait parameters and the electron density variations as a function of solar flares.

A Bayesian approach to simultaneously recover camera pose and non-rigid shape from monocular images

In this paper we bring the tools of the Simultaneous Localization and Map Building (SLAM) problem from a rigid to a deformable domain and use them to simultaneously recover the 3D shape of non-rigid surfaces and the sequence of poses of a moving camera. Under the assumption that the surface shape may be represented as a weighted sum of deformation modes, we show that the problem of estimating the modal weights along with the camera poses, can be probabilistically formulated as a maximum a posteriori estimate and solved using an iterative least squares optimization. In addition, the probabilistic formulation we propose is very general and allows introducing different constraints without requiring any extra complexity. As a proof of concept, we show that local inextensibility constraints that prevent the surface from stretching can be easily integrated.An extensive evaluation on synthetic and real data, demonstrates that our method has several advantages over current non-rigid shape from motion approaches. In particular, we show that our solution is robust to large amounts of noise and outliers and that it does not need to track points over the whole sequence nor to use an initialization close from the ground truth.

Free and forced Rossby normal modes in a rectangular gulf of arbitrary orientation

A free Rossby normal mode in a rectangular gulf of arbitrary orientation is constructed by considering the reflection of a Rossby mode in a channel at the head of the gulf. Therefore, it is the superposition of four Rossby waves in an otherwise unbounded ocean with the same frequency and wavenumbers perpendicular to the gulf axis whose difference is equal to 2mπ/W, where m is a positive integer and W the gulf's width. The lower (or higher) modes with small m (or large m) are oscillatory (evanescent) in the coordinate along the gulf; these are elucidated geometrically. However for oceanographically realistic parameter values, most of the modes are evanescent.When the gulf is forced at the mouth with a single Fourier component, the response is in general an infinite sum of modes that are needed to match the value of the streamfunction at the gulf's entrance. The dominant mode of the response is the resonant one, which corresponds to forcing with a frequency ω and wavenumber normal to the gulf axis η appropriate to a gulf mode: η=−βsinα/(2ω)±Mπ/W, where α is the angle between the gulf's axis and the eastern direction (+ve clockwise) and M the resonant's mode number. For zonal gulfs ω drops out of the resonance condition.For the special cases η=0 in which the free surface goes up and down at the mouth with no flow through it, or a flow with a sinusoidal profile, resonant modes can get excited for very specific frequencies (only for non-zonal gulfs in the η=0 case). The resonant mode is around the annual frequency for a wide range of gulf orientations α∈[40°, 130°] or α∈[220°, 310°] and gulf widths between 150 and 200km; these include the Gulf of California and the Adriatic Sea. If η is imaginary, i.e. a flow with an exponential profile, there is no resonance. In general less modes get excited if the gulf is zonally oriented.

Elementary Vectors and Conformal Sums in Polyhedral Geometry and their Relevance for Metabolic Pathway Analysis.

A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community. Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace is a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors). In this work, we extend the theorem, first to “subspace cones” and then to general polyhedral cones and polyhedra. Thereby, we refine Minkowski's and Carathéodory's theorems, two fundamental results in polyhedral geometry. We note that, in general, elementary vectors need not be support-minimal; in fact, they are conformally non-decomposable and form a unique minimal set of conformal generators. Our treatment is mathematically rigorous, but suitable for systems biologists, since we give self-contained proofs for our results and use concepts motivated by metabolic pathway analysis. In particular, we study cones defined by linear subspaces and nonnegativity conditions — like the flux cone — and use them to analyze general polyhedral cones and polyhedra. Finally, we review applications of elementary vectors and conformal sums in metabolic pathway analysis.

Travelling wave modes of a plane layered anelastic earth

Abstract : Incorporation of attenuation into the normal mode sum representations of seismic signals is commonlyeffected by applying perturbation theory. This is fine for weak attenuation, but problematic forstronger attenuation. In this work modes of the anelastic medium are represented as complexsuperpositions of elastic eigenfunctions. For the P-SV system a generalized eigenvalue equation for thecomplex eigenwavenumbers and complex coefficients used to construct the anelastic eigenfunctions isderived. The generalized eigenvalue problem for the P-SV problem is exactly linear in theeigenwavenumber at the expense of doubling the dimension. The SH problem is exactly linear in thesquare of the eigenwavenumber. This is in contrast to a similar standing wave problem for the earthfree oscillations (Tromp and Dahlen,1990). Attenuation is commonly incorporated into syntheticseismogram calculations by introduction of complex frequency dependent elastic moduli. The modulidepend nonlinearly on the frequency. The independent variable in the standing wave free oscillationproblem is the frequency, which makes the eigenvalue problem nonlinear. The choice of the wavenumber asthe independent variable for the traveling wave problem leads to a linear problem.

Suppression of the time-varying vibration of ball screws induced from the continuous movement of the nut using multiple tuned mass dampers

Considering the time-varying vibration characteristics of the ball screw caused by the continuous movement of the nut, this paper takes the form of a hollow screw shaft structure containing multiple tuned mass dampers (MTMD) to achieve the lateral multi-mode vibration control of the screw shaft. The screw shaft is modeled as an Euler–Bernoulli beam with elastic supports at both ends and the position of the nut. Each tuned mass damper (TMD) is connected to the screw shaft via an elastic spring and a viscous damping element. After establishment of the lateral dynamic model of the screw shaft which taking into account the changing positon of the nut and the multiple resonant responses of the shaft, the optimum design parameters of each TMD can be determined using a numerical optimization algorithm based on the mode summation method. The multiple resonant responses of the screw shaft installed with the optimally designed MTMD are analyzed to demonstrate the robust design of the MTMD for the lateral time-varying vibration control of the screw shaft. Theoretical studies and experimental results show that the proposed design method of the MTMD can remarkably improve the lateral dynamic stiffness of the screw shaft.

Decomposing a signal into short-time narrow-banded modes

An algorithm for nonparametric decomposition of a signal into the sum of short-time narrow-banded modes (components) is introduced. Specifically, the signal data is augmented with its Hilbert transform to obtain the analytic signal. Then the set of constituent amplitude and frequency modulated (AM–FM) analytic sinusoids, each with slowly varying amplitude and frequency, is sought. The method for obtaining the short-time narrow-banded modes is derived by minimizing an objective function comprised of three criteria: smoothness of the instantaneous amplitude envelope, smoothness of the instantaneous frequency and complete reconstruction of the signal data. A minimum of the objective function is approached using a sequence of suboptimal updates of amplitude and phase. The updates are intuitive, efficient and simple to implement. For a given mode, the amplitude and phase are extracted from the band-pass filtered residual (signal after the other modes are removed), where the band-pass filter is applied about the previous modal instantaneous frequency estimate. The method is demonstrated by application to random output-only vibration data and order tracking data. It is demonstrated that vibration modal responses can be estimated from single channel data and order tracking can be performed without measured tachometer data.

Publisher’s Note: Measurement of the lepton forward-backward asymmetry inB→Xsℓ+ℓ−decays with a sum of exclusive modes [Phys. Rev. D93, 032008 (2016)

We report the first measurement of the lepton forward-backward asymmetry AFB as a function of the squared four-momentum of the dilepton system, q2, for the electroweak penguin process B→Xsl+l- with a sum of exclusive final states, where l is an electron or a muon and Xs is a hadronic recoil system with an s quark. The results are based on a data sample containing 772×106 BB¯ pairs recorded at the ϒ(4S) resonance with the Belle detector at the KEKB e+e- collider. AFB for the inclusive B→Xsl+l- is extrapolated from the sum of 10 exclusive Xs states whose invariant mass is less than 2 GeV/c2. For q2>10.2 GeV2/c2, AFB<0 is excluded at the 2.3σ level, where σ is the standard deviation. For q2<4.3 GeV2/c2, the result is within 1.8σ of the standard model theoretical expectation.

Generalised Hermite–Gaussian beams and mode transformations

Generalised Hermite–Gaussian modes (gHG modes), an extended notion of Hermite–Gaussian modes (HG modes), are formed by the summation of normal HG modes with a characteristic function α, which can be used to unite conventional HG modes and Laguerre–Gaussian modes (LG modes). An infinite number of normalised orthogonal modes can thus be obtained by modulation of the function α. The gHG mode notion provides a useful tool in analysis of the deformation and transformation phenomena occurring in propagation of HG and LG modes with astigmatic perturbation.

Finite time-Lyapunov based approach for robust adaptive control of wind-induced oscillations in power transmission lines

Large amplitude oscillation of the power transmission lines, which is also known as galloping phenomenon, has hazardous consequences such as short circuiting and failure of transmission line. In this article, to suppress the undesirable vibrations of the transmission lines, first the governing equations of transmission line are derived via mode summation technique. Then, due to the occurrence of large amplitude vibrations, nonlinear quadratic and cubic terms are included in the derived linear equations. To suppress the vibrations, arbitrary number of the piezoelectric actuators is assumed to exert the actuation forces. Afterwards, a Lyapunov based approach is proposed for the robust adaptive suppression of the undesirable vibrations in the finite time. To compensate the supposed parametric uncertainties with unknown bands, proper adaption laws are introduced. To avoid the vibration devastating consequences as quickly as possible, appropriate control laws are designed. The vibration suppression in the finite time with supposed adaption and control laws is mathematically proved via Lyapunov finite time stability theory. Finally, to illustrate and validate the efficiency and robustness of the proposed finite time control scheme, a parametric case study with three piezoelectric actuators is performed. It is observed that the proposed active control strategy is more efficient and robust than the passive control methods.

Measurement of the lepton forward-backward asymmetry inB→Xsℓ+ℓ−decays with a sum of exclusive modes

We report the first measurement of the lepton forward-backward asymmetry ${\cal A}_{\rm FB}$ as a function of the squared four-momentum of the dilepton system, $q^2$, for the electroweak penguin process $B \rightarrow X_s \ell^+ \ell^-$ with a sum of exclusive final states, where $\ell$ is an electron or a muon and $X_s$ is a hadronic recoil system with an $s$ quark. The results are based on a data sample containing $772\times10^6$ $B\bar{B}$ pairs recorded at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+ e^-$ collider. ${\cal A}_{\rm FB}$ for the inclusive $B \rightarrow X_s \ell^+ \ell^-$ is extrapolated from the sum of 10 exclusive $X_s$ states whose invariant mass is less than 2 GeV/$c^2$. For $q^2 > 10.2$ GeV$^2$/$c^2$, ${\cal A}_{\rm FB} < 0$ is excluded at the 2.3$\sigma$ level, where $\sigma$ is the standard deviation. For $q^2 < 4.3$ GeV$^2$/$c^2$, the result is within 1.8$\sigma$ of the Standard Model theoretical expectation.

Efficient use of coherent X-rays in ptychography: Towards high-resolution and high-throughput observation of weak-phase objects

The efficient use of coherent X-rays is a crucial issue for ptychography at synchrotron facilities. We propose a method for optimizing the population of coherent modes for an optimal resolution. We show by a wave optical simulation that the intensity of a nearly diffraction-limited focusing X-ray beam can be described as an incoherent sum of a few orthogonal modes and that the first-mode flux significantly increases within a secondary source size by relaxing the requirement on the degree of coherence. We experimentally demonstrate it by means of multiple-mode ptychography with a synchrotron X-ray and achieve the high-resolution imaging of a weak-phase object. The present approach enables the high-resolution and high-throughput observation of weak-phase objects in materials science and biology.

A hybrid-mixed method for elasticity

This work presents a family of stable finite element methods for two- and three-dimensional linear elasticity models. The weak form posed on the skeleton of the partition is a byproduct of the primal hybridization of the elasticity problem. The unknowns are the piecewise rigid body modes and the Lagrange multipliers used to relax the continuity of displacements. They characterize the exact displacement through a direct sum of rigid body modes and solutions to local elasticity problems with Neumann boundary conditions driven by the multipliers. The local problems define basis functions which are in a one-to-one correspondence with the basis of the subspace of Lagrange multipliers used to discretize the problem. Under the assumption that such a basis is available exactly, we prove that the underlying method is well posed, and the stress and the displacement are super-convergent in natural norms driven by (high-order) interpolating multipliers. Also, a local post-processing computation yields strongly symmetric stress which is in local equilibrium and possesses continuous traction on faces. A face-based a posteriori estimator is shown to be locally efficient and reliable with respect to the natural norms of the error. Next, we propose a second level of discretization to approximate the basis functions. A two-level numerical analysis establishes sufficient conditions under which the well-posedness and super-convergent properties of the one-level method is preserved.

Jerks and conductivity anisotropy of lower mantle

Conductivity anisotropy of the lower mantle presumably caused by phase change of dielectric magnesiowustite at depths of 1500–2000 km is detectable from jerks. Jerks are induced by currents in the fluid outer core, propagate upward from the CMB through anisotropic conducting mantle, and appear on the Earth’s surface. The surface jerk patterns are studied theoretically from the potential of the geomagnetic field presented as a sum of magnetic and electric modes. Equations for the fields of both modes and their relationship in a weakly anisotropic earth are obtained by the perturbation method. The field potential is expanded into a series of spherical harmonics, and the equations are solved in the frequency and time domains. The surface jerk responses can be inverted to retrieve anisotropy parameters; the goal function in the inversion may correspond to misfit between the model and experimental values either along the horizontal or vertical components.

Diverse wave-particle interactions for energetic ions that traverse Alfvén eigenmodes on their first full orbit

Neutral-beam ions that are deflected onto loss orbits by Alfvén eigenmodes (AE) on their first bounce orbit and are detected by a fast-ion loss detector (FILD) satisfy the “local resonance” condition proposed by Zhang et al. [Nucl. Fusion 55, 22002 (2015)]. This theory qualitatively explains FILD observations for a wide variety of AE-particle interactions. When coherent losses are measured for multiple AE, oscillations at the sum and difference frequencies of the independent modes are often observed in the loss signal. The amplitudes of the sum and difference peaks correlate weakly with the amplitudes of the fundamental loss-signal amplitudes but do not correlate with the measured mode amplitudes. In contrast to a simple uniform-plasma theory of the interaction [Chen et al., Nucl. Fusion 54, 083005 (2014)], the loss-signal amplitude at the sum frequency is often larger than the loss-signal amplitude at the difference frequency, indicating a more detailed computation of the orbital trajectories through the mode eigenfunctions is needed.

A Dynamic Model for Double-Planet Planetary Gearsets

In this study, a two-dimensional (2D), steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of N number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.

Повышение топливной экономичности маневрового тепловоза при применении электронной системы управления впрыском топлива

When creating a new rolling stock or during its modernization it is important preliminarily to properly assess its operational efficiency, depending on the technical improvements. Changing the way of energy supply of traction is very important - for example, hybrid engines or two/three power units is used instead of one. The article proposes a new approach to the problem of assessing the effectiveness of operational work of shunting locomotives. Shunting operation is represented as the sum of random single modes, in which the processes in the power plant can be modeled with any degree of accuracy. Summation of performance indicators in individual modes according to the characteristics of random processes allows obtaining an overall assessment of technical and economic indicators of the locomotive in operation. The paper shows results of comparative assessment of the fuel economy of a diesel locomotive ChME3 in operating set of equipment and with installed electronic fuel injection control system (ESUVT. 02), obtained by modeling the working processes of the power plant and auxiliary equipment shunting locomotives in operation modes. Executed calculations show that in the operation of diesel locomotive ChME3 equipped with ESUVT. 02 system saves up to 10.2 % of fuel, particularly by reducing fuel consumption at idle. Application of a new methodology for assessing technical and economic indicators of locomotives in operation allows, in addition to fuel consumption, evaluating a number of other indicators.

Warping transform of the refractive normal mode in a shallow water waveguide

In a shallow water waveguide, the low-frequency acoustic field can be viewed as a sum of normal modes. Warping transform provides an effective tool to filter the normal modes from the received signal of a single hydrophone, which can be used for source ranging and geoacoustic inversion. However, it should be noted that the conventional warping operator h(t) = t2+tr2 is only valid for a signal consisting of reflection dominated modes, where r represents the source range. In a waveguide with a strong thermocline or a surface channel where refracted modes dominate the received sound field, the dispersive characteristics of the waveguide become different and the performance of the warping operator h(t) = t2+tr2 will be significantly degraded. In this paper, the dispersive characteristics and warping transform of the refractive normal modes in a waveguide with a linearly decreased sound speed profile are discussed. The formulae for the horizontal wavenumber, the phase in frequency domain and the instantaneous phase in time domain of the refractive mode are deduced. Based on these formulae, the time warping and frequency warping operators verified by the simulated data are presented. Through time-axis stretching or compression, the time warping operator h(t) =tr-t2, where tr= r/c(h) and c(h) represents the bottom sound speed, can transform the refracted modes into single-tone components of frequencies determined by source range, sound speed gradient of water, bottom sound speed and mode number. The frequency warping operator h(f) = Df3, where D is a constant, can transform the refracted modes into separable impulsive sequences through frequency-axis stretching or compression and the time delay of the impulsive sequences changes linearly with the source range. As the warped modes are separated in time domain or frequency domain, these two operators can be used for filtering the refracted normal modes from the received signal. The theories in this paper are also applicable for refractive modes in the waveguide with a linearly increased sound speed profile or a linear variation of the square of the index of refraction (n2-linear sound speed profile).

불균일 단면을 갖는 단순지지 보의 모달해석 및 실험

Beam-type structures with non-uniform cross sections are widely used in mechanical, architectural, and civil engineering fields. This paper deals with dynamic characteristics and vibration problems. Governing equations are first derived by using local coordinates. Their solutions are then assumed by using Galerkin's mode summation method. Bisection method is also applied in solving the determinant of the matrix which can provide natural frequencies. Whereas finite element methods adopt admissible functions satisfying only geometric boundary condition, in this study we apply Galerkin's mode summation method which uses eigen-functions satisfying both governing equations and boundary conditions. Modal analysis and experimental tests are finally performed using simply-supported beams with four different non-uniform cross-sections. Our analytical results then show good agreement with experimental ones.

Maxwell consideration of polaritonic quasi-particle Hamiltonians in multi-level systems

We address the problem of the correct description of light-matter coupling for excitons and cavity photons in the case of systems with multiple photon modes or excitons, respectively. In the literature, two different approaches for the phenomenological coupling Hamiltonian can be found: Either one single Hamiltonian with a basis whose dimension equals the sum of photonic modes and excitonic resonances is used. Or a set of independent Hamiltonians, one for each photon mode, is chosen. Both are usually used equivalently for the same kind of multi-photonic systems which cannot be correct. However, identifying the suitable Hamiltonian is difficult when modeling experimental data. By means of numerical transfer matrix calculations, we demonstrate the scope of application of each approach: The first one holds only for the coupling of a single photon state to several excitons, while in the case of multiple photon modes, separate Hamiltonians must be used for each photon mode.