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To quantify variations in seismic hazard assessment, a large number of scenario earthquake shaking maps (hereafter referred to as s-EQ maps for short) are required. In this article, we propose a method to easily generate a large number of s-EQ maps by combining modal decomposition and empirical copula. First, by applying modal decomposition to a set of existing s-EQ maps, we identify a scenario set with a parameter space to reduce the dimensionality of models. Next, we model a probability distribution of the modal coordinates, which we regard as random variables to allow us to induce a probability measure on the parameter space. By applying an empirical copula for modeling the probability distributions, the dependence structure between modal coordinates and the probability distribution of an individual modal coordinate can be discussed independently. Some simulations show that the dependence structure between modal coordinates is important to not distort the seismic hazard assessment. The proposed method can be applied to actual existing s-EQ maps to easily generate a large number of new s-EQ maps that follow the original probability distribution. We also show that variations can be added to the newly generated s-EQ maps by adjusting the empirical copula. Furthermore, we give a generalization of the proposed method to cases with nonequal probabilities of occurrence of existing scenarios.

Symmetries are widespread in physical, technological, biological, and social systems and networks, including power grids. The swing equation is a classic model for the dynamics of powergrid networks. The main goal of this paper is to explain how network symmetries affect the swing equation transient and steady state dynamics. We introduce a modal decomposition that allows us to study transient effects, such as the presence of overshoots in the system response. This modal decomposition provides insight into the peak flows within the network lines and allows a rigorous characterization of the effects of symmetries in the network topology on the dynamics. Our work applies to both cases of homogeneous and heterogeneous parameters. Further, the model is used to show how small perturbations propagate in networks with symmetries. Finally, we present an application of our approach to a large power grid network that displays symmetries., 13 Pages including references, 8 Figures. Accepted for publishing in IEEE TNSE

This paper presents an in-depth investigation of the unsteady flows through two-stage high-pressure (hp) axial turbine with analyses of the rotor-stator interaction effects on the aerothermodynamic performance. The unsteady flow structures are characterized by the formation and convection of the tip leakage vortex and the hub corner vortices from the first stage blade-row through the second stage nozzle guide vanes (NGV) and blade-row. The modal decomposition of the circumferential distributions of static pressure depicts the modulation of the potential effect in the form of lobed structure propagating in both sides. Moreover, the blade pressure field shows that the first blade-row is exposed to a periodic overpressure induced by the first NGV while in the second blade-row the linear combination of both potential effects is dominant and results in a complex unsteady blade loading. FFT analyses of unsteady turbine performance for two-stage and part stages reveal that the total-to-total isentropic efficiency, torque-based efficiency and pressure ratio of the first stage depend strongly on the first blade-row passing frequency (BPF), whereas the total-to-total isentropic efficiency in second stage and two-stage turbine is related to the second blade-row BPF while the pressure ratio and the torque-based efficiency depend on the two rotors BPFs. Finally, the torque oscillations are mainly associated with the combination of frequencies of first stage NGV with that of second stage NGV. Furthermore, the obtained results show that Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations are essential in analyzing the complex wakes and vortical structures through the two-stage turbine components and may produce better estimation of the performance.

Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and scientific applications, often require a large number of linear modes to obtain a small representation error. This difficulty, even for the most simple transports, originates from the inappropriateness of the decomposition structure in time dependent amplitudes of purely spatial modes. In this article an approach is discussed, which decomposes a flow field into several fields of co-moving frames, where each one can be approximated by a few modes. The method of decomposition is formulated as an optimization problem. Different singular-value-based objective functions are discussed and connected to former formulations. A boundary treatment is provided. The decomposition is applied to generic cases and to a technically relevant flow configuration of combustion physics.

The mode-2 internal solitary waves (ISWs) generated by mode-2 internal tide (IT) are identified by mooring observations in the northern South China Sea (SCS) from 2016 to 2017. Two mode-2 ISWs with a re-appearance period of 24.9 h observed on 29 and 30 July 2016 are characterized by type-b ISWs. They occurred when the isotherms compressed obviously in the vertical direction. Modal decomposition of IT horizontal currents shows that the vertical compression of the isotherms is mainly caused by diurnal mode-2 IT. The analysis of the role of the density stratification reveals that a deeper and thinner pycnocline is favorable for generation of mode-2 ISWs rather than pycnocline intensity. By comparing the mode-2 nonlinear, dispersion coefficients and the Ursell numbers calculated based on the stratification associated with different kinds of ITs with the observation results, it is shown that the diurnal mode-2 IT plays a crucial role in the generation of the mode-2 ISWs. When the diurnal mode-2 IT interacts with the semidiurnal IT and causes a deeper and thinner pycnocline, the mode-2 ISWs are easily excited.

A new acoustic sensing capability, consisting of a flexible high-density linear piezoelectric sensor array coupled to a high-bandwidth interrogation device, is developed and applied to in situ wavenumber–frequency modal decomposition of acoustic emissions in plates. An experimental assessment of the capability is undertaken using acoustic emissions generated by a ball-drop impact on aluminium and composite panels. A new method for acoustic source localisation based on this new sensor array is described, and it is shown to be more accurate than a conventional multilateration technique using single-point piezoelectric receivers. The potential of this new capability for acoustic emission detection, location and possible quantification is discussed.

The wake produced by a utility-scale wind turbine invested by a laminar, uniform inflow is analyzed by means of two different modal decompositions, the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), in its sparsity-promoting variant. The turbine considered is the NREL-5MW at tip-speed ratio λ=7 and a diameter-based Reynolds number of the order 108. The flow is simulated through large eddy simulation, where the forces exerted by the blades are modeled using the actuator line method, whereas tower and nacelle are modeled employing the immersed boundary method. The main flow structures identified by both modal decompositions are compared and some differences emerge that can be of great importance for the formulation of a reduced-order model. In particular, a high-frequency mode directly related to the tip vortices is found using both methods, but it is ranked differently. The other dominant modes are composed by large-scale low-frequency structures, but with different frequency content and spatial structure. The most energetic 200 POD modes account for ≈20% only of the flow kinetic energy. While using the same number of DMD modes, it is possible to reconstruct the flow field to within 80% accuracy. Despite the similarities between the set of modes, the comparison between these modal-decomposition techniques points out that an energy-based criterion such as that used in the POD may not be suitable for formulating a reduced-order model of wind turbine wakes, while the sparsity-promoting DMD appears able to perform well in reconstructing the flow field with only a few modes.

High-frequency motions in the southeastern South China Sea (SCS) have rarely been investigated due to sparse field observations. The vertical distribution and temporal variation of internal tides (ITs) and near-inertial waves (NIWs) near the Nansha area in the southeastern SCS were studied using a mooring current dataset from December 2018 to June 2019 in this study. Results showed that ITs were mainly dominated by O1, K1, and M2. Tidal energy analysis indicates that the diurnal ITs were the most energetic components, followed by the semidiurnal ITs. Modal decomposition reveals that diurnal ITs were dominated by mode-3, rather than mode-1, as reported by previous studies. The horizontal kinetic energy (HKE) of diurnal ITs fluctuated within a limited range, almost unaffected by the background field. However, the HKE of semidiurnal ITs was dominated by mode-1 and more affected by the background field, especially at the end of March. Most observations showed the phase of the NIWs propagating upward and the energy propagating downward. During the northeast monsoon period, the near-inertial energy had a large magnitude due to strong wind forcing. In addition, the near-inertial energy peaked from the middle of March to the beginning of April because of the input of NIWs from afar. Overall, near-inertial energy was found concentrated above a 500–600 m depth in the southeastern SCS.

We propose a globally optimized stochastic parallel gradient descent (SPGD) algorithm to analyze the modal content of laser beams with high precision. Modal decomposition (MD) based on conventional SPGD algorithms often falls to a local minimum when a laser beam consists of six or more fiber eigenmodes, which results in a false combination of modes. While keeping the simplicity and speed advantages of the SPGD algorithm, we adopted several optimization techniques to discern the global minimum from local minima and achieve better accuracy. The enhanced SPGD algorithm includes the annealing of the learning rates, identifying and escaping of local minima with large perturbations, and comparing of the transient error function with a reference value. We were able to exactly analyze the modal content of beams from six-mode optical fibers with high precision in seconds. Calculation of the modal weight and phase percentage errors, as well as simulations of far-field evolution images, confirmed the importance of finding the global minimum in improving the accuracy and real-time analysis of MD. The simple structure of the enhanced algorithm and its global optimization ability in multimode fibers will accelerate numerical MD in diverse laser applications.

The paper presents four ensembles of numerical experiments that compare the response to monopole and dipole heating perturbations resembling different phases of the Madden–Julian oscillation (MJO). The results quantify the Rossby and inertio-gravity (IG) wave response using the normal-mode function decomposition. The day 3 response is characterized by about 60% variance in the IG modes, with about 85% of it belonging to the Kelvin waves. On day 14, only 10% of the response variance is due to the Kelvin waves. Although the n = 1 Rossby mode is the main contributor to the Rossby variance at all time scales, the n > 1 Rossby modes contribute over 50% of the balanced response to the MJO heating. In the short range, dipole perturbations produce a response with the maximal variance in zonal wavenumbers k = 2–3 whereas in the medium range the response maximizes at k = 1 in all experiments. Furthermore, the medium-range response to the heating perturbation mimicking MJO phase 6 is found also over Europe.

This paper presents a new technique for the extraction of high-order wave-damage interaction coefficients (WDIC) through modal decomposition. The frequency and direction dependent complex-valued WDIC are used to model the scattering and mode conversion phenomena of guided wave interaction with damage. These coefficients are extracted from the harmonic analysis of local finite element model (FEM) mesh with non-reflective boundaries (NRB) and they are capable of describing the amplitude and phase of the scattered waves as a function of frequency and direction. To extract the WDIC of each wave mode, all the possible propagating wave modes are considered to be scattered simultaneously from the damage and propagate independently. Formulated in frequency domain, the proposed method is highly efficient, providing an overdetermined equation system for the calculation of mode participation factors, i.e., WDIC of each mode. Case studies in a 6-mm aluminum plate were carried out to validate the WDIC of: (1) a through-thickness hole and (2) a sub-surface crack. At higher frequency, scattered waves of high-order modes will appear and their WDIC can be successfully extracted through the modal decomposition.

Modal decomposition techniques have become important mathematical methodologies in analysing complex flow physics. The data-driven methods, such as proper orthogonal decomposition and dynamic mode decomposition are used to extract coherent structures in the form of spatial modes. These methods can be applied to both numerical and experimental data to identify the characteristic dynamics of the system. However, the classical data-driven modal decomposition methods are only applicable to problems with a fixed shape and are not suitable for systems with fluid–structure interaction or systems with shape-changing geometries. In this paper we propose a novel method utilizing a conformal mapping technique to solve this issue. Through different examples with deforming geometry, the capability of the method to accurately capture the flow features is demonstrated. The proposed method is found to be suitable for a wide range of applications and a possible candidate for reduced-order flow modelling of complex shape-changing systems.

By including the additional variable, degree of coherence (DOC) in stochastic parallel gradient descent (SPGD) algorithm, we could improve the accuracy of modal decomposition which satisfies both measured near-field and far-field laser beams.

This article concerns numerical simulations of glass plates loaded by a force impulse caused by a low velocity impact. Three types of numerical models of different complexity – the spring-mass system, the modal decomposition based model, and the conventional finite element method – all exploiting the Hertz contact law are compared and their advantages and limitations are discussed. Their performance is verified against the results provided by the commercial software LS-DYNA and validated by two full scale experiments. It is observed that the accuracy of the spring-based model decreases with increasing dimension of the plate and increasing stiffness of the impactor. Nevertheless, the models based on modal decomposition and finite element methods deliver results reasonably close to experimental measurements.

Ultrasonic guided waves are used extensively when checking for defects in petrochemical and other industries and are mostly generated using piezoelectric transducers on an angled wedge or electromagnetic acoustic transducers (EMATs) in different configurations. Low-frequency inspection allows for long-distance propagation, but it is best suited for detecting relatively large defects, while at higher frequencies, the presence of multiple wave modes limit defect detectability, so achieving practical single Lamb mode excitation via careful transduction is very beneficial. This paper investigates the relative ability of angled piezoelectric and meander coil EMAT probes to produce single-mode transduction in the medium (~1–5 MHz-mm) and high (>5 MHz-mm) frequency-thickness regions of the dispersion curves. The nature of each transducer is studied analytically by simulating the corresponding surface forces, followed by the use of a Fourier transform in time and space (2-D fast Fourier transform) to highlight the excitation region in the wavenumber–frequency space. With angled wedge excitation there is a linear relationship between the excitation frequency and the wavenumber which means that the excitation tends to track typical dispersion curves, allowing for easier pure mode generation. In contrast, the EMAT controls frequency and wavenumber separately which makes it more difficult to generate a pure mode when dispersion curves are close together; however, by narrowing the frequency bandwidth via a large number of cycles in the excitation signal, pure mode generation via an EMAT was shown to be possible even in areas of closely spaced modes. As example cases, analytical results, backed up by experiments, showed that signals dominated by the A0 mode at 1.5 MHz-mm and also the A1 mode at 18 MHz-mm can be generated with both angled piezoelectric and EMAT probes.

In vibrating mechanical systems, the targeted energy transfer mechanism (TET) of nonlinear energy sinks (NES) is employed as an alternative to linear tuned mass dampers (TMD) as passive vibrations absorbers for transient vibrations. The major advantages a NES has over a linear TMD are (1) an increased robustness to detuning and (2) the ability to dissipate multiple frequencies with only a single NES through so-called resonance capture cascading (RCC). The performance, especially the speed, of TET and RCC has rarely been a topic of research. In this research, algebraic performance measures for the speed of both TET and RCC are derived, called the pumping time and the cascading time, respectively. It shows that cascading time can be seen as a sum of single-mode pumping times, by introducing a novel modal decomposition. The strength of both measures is that they do not require numerical simulations, allowing easy optimization of the NES. The influence of different nonlinearities on the TET and RCC performance is investigated. Actual numerical simulations presented in the study validate the merit of both the pumping time and cascading time.

[EN] In this paper, the unsteady behaviour of a compression-ignited (CI) engine combustion chamber is studied by analysing the results of a Computational Fluid Dynamics (CFD) model through the application of different flow decomposition techniques, aiming to resolve the underlying modal structure of the process. Experimental validation for the combustion simulation is provided, and a methodology for extracting coherent pressure information is proposed in order to provide a suitable input for different analysis methods. These range from straightforward Fourier transform techniques to more sophisticated modal decomposition approaches. In particular Proper Orthogonal Decomposition (POD) is shown to provide valuable insight into the time-spatial structure of the combustion flow field, allowing the establishment of correlations between pressure modes and physical parameters of the combustion, such as the injection timing or the chamber geometry. Dynamic Mode Decomposition (DMD) on the other hand is proven to successfully highlight the link between the frequency of the unsteady energy components and their spatial distribution within the chamber. Advantage is then taken of the modal characterization of the unsteady behaviour in the chamber to showcase how physical parameters such as the spray angle can be modified to optimize the acoustic signature of the combustion process, helping CI internal combustion engines reduce their acoustic environmental impact (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved., The equipment used in this work has been partially supported by FEDER project funds "Dotacidn de infraestructuras cientifico tecnicas para el Centro Integral de Mejora Energetica y Medioambiental de Sistemas de Transporte (CiMeT)" [grant number FEDER-ICTS-2012-06], framed in the operational program of unique scientific and technical infrastructure of the Spanish Government.

International audience; We study the propagation of elastic waves in the time-harmonic regime in a waveguide which is unbounded in one direction and bounded in the two other (transverse) directions. We assume that the waveguide is thin in one of these transverse directions, which leads us to consider a Kirchhoff-Love plate model in a locally perturbed 2D strip. For time harmonic scattering problems in unbounded domains, well-posedness does not hold in a classical setting and it is necessary to prescribe the behaviour of the solution at infinity. This is challenging for the model that we consider and constitutes our main contribution. Two types of boundary conditions are considered: either the strip is simply supported or the strip is clamped. The two boundary conditions are treated with two different methods. For the simply supported problem, the analysis is based on a result of Hilbert basis in the transverse section. For the clamped problem, this property does not hold. Instead we adopt the Kondratiev's approach, based on the use of the Fourier transform in the unbounded direction, together with techniques of weighted Sobolev spaces with detached asymptotics. After introducing radiation conditions, the corresponding scattering problems are shown to be well-posed in the Fredholm sense. We also show that the solutions are the physical (outgoing) solutions in the sense of the limiting absorption principle.

The following article has been submitted to The Journal of Acoustical Society of America on May 17, 2019. If and after it is published, it will be found at http://asa.scitation.org/journal/jas; An induct modal decomposition technique is described. The basis for the technique is to consider the decomposition as an inference problem. Using transfer function measurements at the duct walls, a Bayesian inference is conducted to evaluate the acoustic modal coecients in the presence of uncertainties. These uncertainties encompass model errors, microphone measurements error, and uncertainty on the ow prole. The formalism of the direct problem of modal decomposition in a ducted shear ow is rst developed. The case of a circular cross-section duct is then treated without and with a ow, using synthetic noisy signals for the inference problem.

[EN] The operation of compressor at lower mass flow rates is limited by surge which is marked by large fluctuations in operational variables and accompanied by significant increase in noise. Ported shroud casing treatment is a widely used method to control the flow near unstable conditions in order to obtain a stable operation and enhance deep surge margin. The research on the acoustic effects of the ported shroud design is limited. Therefore, this paper numerically characterises the acoustic features of a turbocharger compressor with ported shroud design operating at marginal or soft surge conditions and investigates the correlation between acoustic characteristics and the spatial flow structures. The acoustic and the flow field features are analysed using spectral signatures obtained from an experimentally validated numerical model using both performance and acoustic measurements. Propagation of the frequency content through the ducts has been estimated with the aid of the beamforming and method of characteristics to enhance the content coming from the compressor. Expected acoustic phenomena such as rotating order tones and blade passing peaks are correctly identified in the modelled spectrum with the limitation to capture the specific broadband features. Hence, the numerical model can be used to further the research encompassing the impact these flow enhancement solutions have on the noise emission of the turbocharger. Inspection of the flow field shows radially exiting fluid at the ported shroud slot leading to the formation of the high-speed jets exiting the ported shroud cavity. Circumferential propagation of the stall cells is also identified in the impeller. Further inspection of the pressure field through modal decomposition implies the localisation of the energetic noise sources in the impeller downstream components. The influence of the ported shroud cavity on the acoustic characteristic of the compressor is not significant and is limited to the propagation of the tonal noise in the direction of impeller upstream. (C) 2019 Elsevier Ltd. All rights reserved., The project is sponsored and supported by BorgWarner Turbo Systems and the Regional Growth Fund (RGF Grant Award 01.09.07.01/1789C). The authors would like to thank BorgWarner Turbo Systems for permission to publish the results presented in this paper. The support of the HPC group at the University of Huddersfield is gratefully acknowledged.

International audience

This paper presents a way to obtain angle-dependent reflection, transmission and absorption coefficients of a sample based on the modal decomposition method in a rectangular waveguide. Microphone locations are optimized to ensure that the modal decomposition can be applied. The method is subsequently validated both numerically and experimentally.

This work is focused on high-speed multimode link for short haul communication by adopting hybrid optical add/drop multiplexing and mode division multiplexing schemes. 4× 10 GBps are successfully transported over 1 km multimode link by using Hermite Gaussian (HG) modes at 850 and 850.5 nm. Moreover, mode decomposition at receiver side is also reported for each channel. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:1613–1617, 2016

Coherent and incoherent internal tides (CITs and ICITs) in the southern South China Sea were investigated from two sets of 18-month mooring current records. The CITs were mainly composed of diurnal Q 1, O 1, P 1 and K 1 and semidiurnal M 2. The observed diurnal internal tides (ITs) were more coherent than the semidiurnal constituents. Coherent diurnal variance accounted for approximately 58% of the diurnal motion, whereas semidiurnal tides contained a much smaller fraction (35%) of coherent motion. The ICITs mainly consisted of motion at non-tidal harmonic frequencies around the tidal frequency, and showed clear intermittency. The modal decomposition of CITs and ICITs showed that CITs were dominated by mode- 1, whereas mode-1 and higher modes in ICITs signals showed comparable amplitudes. CITs and ICITs accounted for approximately 64% and 36% of the total kinetic energy of internal tides, respectively.

Guided wave inspection is used extensively in petrochemical plants to check for defects such as corrosion. Long-range low-frequency inspection can be used to detect relatively large defects, while higher frequency inspection provides improved sensitivity to small defects, but the presence of multiple dispersive modes makes it difficult to implement. This paper investigates the possibility of exciting a single-mode Lamb wave with low dispersion at a frequency thickness of around 20 MHz-mm. It is shown by finite element (FE) analysis backed up by experiments that a signal dominated by the A1 mode can be generated, even in a region where many modes have similar phase velocities. The A1 mode has relatively little motion at the plate surface which means that only a small reflection is generated at features such as T-joints; this is verified numerically. It is also expected that it will be relatively unaffected by surface roughness or attenuative coatings. These features are very similar to those of the higher order mode cluster (HOMC) reported by other authors, and it is shown that the A1 mode shape is very similar to the deflected shape reported in HOMC.

In this paper, we propose a measurement technique based on local strain measurements to perform real-time reconstruction of the overall structural deformation and the distributed stress field produced by the impact of a body on a water free surface. In particular, we seek establishing a measurement chain capable of acquiring and elaborating the signals at high frequency, so that it can be utilized to study rapidly varying strain fields, such as those occurring in impulsive events. Fiber Bragg gratings are utilized to sense the local structural deformation. Experiments are conducted on flexible plastic wedges with variable deadrise angles impacting on a quiescent fluid surface. The experimental tests are performed in free fall and we explore variations of the entry velocity by varying the drop height. The structural deformation is reconstructed from point-wise strain measurements utilizing a modal reconstruction methodology. The impact dynamics are analysed through accelerometers and linear position sensors. Results show that the impact behaviour of the flexible body is characterized by a main overall deformation where the structure is distorted in the direction of the loading, whereby marked vibrations, whose amplitude increase with the entry velocity, dominate the dynamic response. The influence of the mode shapes considered in the present analysis on the accuracy of the results is also observed. The proposed methodology allows for a fairly high acquisition frequency, which translates into a real-time structural reconstruction technique. Results show that the proposed methodology can be a valuable tool for the live monitoring of structures undergoing impact events.

Basing on the relationship of joint production, we take lead-bismuth, lead-selenium, zinc-cadmium, and zinc-germanium as examples to study the nonlinear Granger causal relationship between the prices of main-byproduct metal pairs. The price relationship between the main metal and byproduct metal is nonlinear and varies with the time scales. Therefore, we use an Ensemble Empirical Modal Decomposition method (EEMD) to break down the price series of the main metals and byproduct metals into different frequency bands, and then test these different frequency bands for nonlinear Granger causality. The results show that a two-way nonlinear Granger causal relationship exists between the prices of the main metals and byproduct metals, and this nonlinear Granger causal relationship is reflected primarily in the short- and medium-term time scales. Moreover, the effect of the main metal price on the price of the byproduct metal is not as significant as previously thought, and the influence of the byproduct metal price on the main metal price has been previously underestimated.

Rotating machinery such as fans feature a variety of sound generating mechanisms. In addition to stationary sound sources and sources moving synchronously to the measured object, sources rotating at different speeds can occur. This paper presents a method for detecting different rotational speeds of multiple dominant sources present in one data set. It is based on modal decomposition and processing of data measured with a circular microphone array. The method is applied to data sets with simulated point sources as well as measurement data of an axial fan with forward-skewed blades at two different operating points.

The Humboldt and the Benguela upwelling systems are connected to the equatorial variability through the coastal waveguide, so that a large variance of the coastal sea level and current variability can be described as an infinite sum of orthonormal free Coastal-Trapped Wave (CTW) modes. The objective of this study is to infer the CTW mode contributions to the coastal variability in both systems at subseasonal timescales (

The paper addresses the classical problem of time-harmonic forced vibrations of a fluid-filled cylindrical shell considered as a multi-modal waveguide carrying infinitely many waves. The forced vibration problem is solved using tailored Green's matrices formulated in terms of eigenfunction expansions. The formulation of Green's matrix is based on special (bi-)orthogonality relations between the eigenfunctions, which are derived here for the fluid-filled shell. Further, the relations are generalised to any multi-modal symmetric waveguide. Using the orthogonality relations the transcendental equation system is converted into algebraic modal equations that can be solved analytically. Upon formulation of Green's matrices the solution space is studied in terms of completeness and convergence (uniformity and rate). Special features and findings exposed only through this modal decomposition method are elaborated and the physical interpretation of the bi-orthogonality relation is discussed in relation to the total energy flow which leads to derivation of simplified equations for the energy flow components.

The wake behind a sphere, rotating about an axis aligned with the streamwise direction, has been experimentally investigated in a low-velocity water tunnel using LIF visualizations and PIV measurements. The measurements focused on the evolution of the flow regimes that appear depending on two control parameters, namely the Reynolds number $Re$ and the dimensionless rotation or swirl rate $\Omega$, which is the ratio of the maximum azimuthal velocity of the body to the free stream velocity. In the present investigation, we cover the range of $Re$ smaller than 400 and $\Omega$ from 0 and 4. Different wakes regimes such as an axisymmetric flow, a low helical state and a high helical mode are represented in the ($Re$, $\Omega$) parameter plane.

Bloom, Fokkink & van Glabbeek (2004) presented a method to decompose formulas from Hennessy-Milner logic with regard to a structural operational semantics specification. A term in the corresponding process algebra satisfies a Hennessy-Milner formula if and only if its subterms satisfy certain formulas, obtained by decomposing the original formula. They used this decomposition method to derive congruence formats in the realm of structural operational semantics. In this paper it is shown how this framework can be extended to specifications that include bounded lookahead in their premises. This extension is used in the derivation of a congruence format for the partial trace preorder.

We implement digital holograms for the creation and detection of the spatial modes of light. We make use of modal decomposition theory to determine the numerous properties of light, from the modal content of laser beams to decoding the information stored in optical fields carrying orbital angular momentum. We demonstrate the versatility of these techniques to characterize both structured and vector fields with static and propagating optical fields. Finally, we show a holographic technique to realise a communication link using a densely packed spatial mode set where we experimentally multiplex and de-multiplex over 100 spatial modes.

International audience; This paper presents a new application of the normal mode decomposition to measure the reflection and absorption coefficients of a low growing living plant in a large 300 × 300 mm impedance tube. In this way the higher frequency limit can be extended by a factor of 3 in comparison to that suggested by the standard ISO 10534-2 method for this type of an impedance tube. The adopted method (Prisutova et al., 2014) is based on minimising the difference between the spatial Fourier transform of the measured sound pressure at a range of closely spaced positions along the impedance tube and the predicted transform arising from the normal mode decomposition method. The angular and frequency dependent complex reflection coefficients for the first 5 normal modes are recovered. The acoustical properties of three plants specimen, Pelargonium hortorum, Begonia benariensis and Hedera helix, are measured with the adopted method. These properties are related to the plant morphology through an equivalent fluid model. It is shown that in some cases the predicted and measured data are in close agreement. However, there are cases when the agreement between these data is poor. The possible reasons for this discrepancy are proposed and discussed. This work paves the way for a better understanding of the relations between the plant morphology and its acoustical properties.

Radio over Free Space (Ro-FSO) is promising candidate for providing ubiquitous digital services especially in rural areas. This work investigates the performance of MDM of two 5Gbps-10GHz data channels over FSO link using LP 01 and LP 02 modes under the effect of atmospheric turbulences. The signal to noise ratio (SNR), total received power, modal decomposition at receiver at the receiver is also reported. The reported result shows the successful transmission of two channels with acceptable SNR over FSO link under atmospheric turbulences.

International audience; This paper presents a new approach for proving that the presence of a bounded defect in a uniform open waveguide cannot produce trapped modes, contrary to the case of a closed waveguide. The originality of the proof lies in the fact that it relies on a modal decomposition. It shows in particular that the absence of trapped modes results from a strong connection between the various modal components of the field. The case of the three-dimensional scalar wave equation is considered.

Methods to design test-procedures for acoustic multi-ports in ducts with a focus on pressure sampling positions for accurate modal decomposition are demonstrated. Acoustic fields up- and downstream of an in-duct acoustic element are excited by external sources and decomposed into transmitted and reflected aeroacoustic modal pres- sure amplitudes in order to first determine the acoustic scattering of the element. Secondly, the determination of the element source strength requires tests with no external sources, but with known terminations and scattering data. Unfavourable source and sensor positions lead to mode coupling and to ill-conditioned or even singular decomposition matrices, which results in high amplifications of uncertainties within the wave decomposition. An unoptimised but over-determined assembly is compared with a setup containing a minimum of sensors but with optimised positions. Lower uncertainty amplification, despite the usage of fewer sensors, is achieved for most frequencies, especially after the cut-on of t he higher order acoustic modes. A genetic algorithm (GA) is used to achieve this optimised setup by minimising the condition number of the decomposition matrix, which is a multi-dimensional optimisation problem with numerous local minima. To estimate the stability of the optimised configuration, a Monte-Carlo Method (MCM) is deployed to introduce normal distributed complex pressure un- certainties into the decomposition. In order to estimate the wave number, different approaches are compared - namely the classical non-dissipative wav e number estimate, an extended Kirchhoff method for viscous-thermal damping and an eigenvalue solution of the Linearised Navier Stokes Equations by Dokumaci. The presented de- composition method is not only applicable to measurement data but is equally useful to post-process results from numerical computation. QC 20160916 IDEAL VENT

cited By 0; Conference of ICU International Congress on Ultrasonics, ICU 2015 ; Conference Date: 11 May 2015 Through 14 May 2015; International audience; The guided wave field generated by finite size transducers in a composite plate is studied. For isotropic plates, Fraunhofer-like approximations can be found in the literature. Similar approximations fail when the plate is anisotropic. A new calculation method is proposed. Based on a modal decomposition, its principle is to integrate over the transducer surface as seen in energy directions from the calculation point. Special care is taken when dealing with energy paths in direction of caustics. To validate this method, some comparisons are made between our results and those obtained using a full integration over the surface of the source.

The operational requirements for naval and research vessels have seen an increasing demand for quieter ships either to comply the ship operational requirements or to minimize the influence of shipping noise on marine life. To estimate the future radiated noise of a ship, scale measurements are realized in cavitation tunnel. DGA Hydrodynamics operates its cavitation tunnel with low background noise which allows such measurements. Understanding acoustic propagation in cavitation tunnel remains a challenge. The success of an accurate acoustic measurement depends both on a realistic propagation model and also on an efficient control of acoustic sensor characteristics. This short communication presents the results of experiments performed in GTH (Large Cavitation Tunnel) at DGA Hydrodynamics. An acoustic source radiates pure sine wave at the entrance of the test section and generates an acoustic field measured with flush mounted hydrophones. A modal decomposition is then performed to fit measurements. Complex ...

Cascaded optical cavities appear in various quantum information processing schemes in which atomic qubits are sitting in separate cavities interconnected by photons as flying qubits. The usual theoretical description relies on a coupled-mode Hamiltonian approach. Here we investigate the system of cascaded cavities without modal decomposition by using a scattering model approach and determine the validity regime of the coupled-mode models.

International audience; It is now well established that linear and nonlinear instability waves play a significant role in the noise generation process for a wide variety of shear flows such as jets or mixing layers. In that context, the problem of acoustic radiation generated by spatially growing instability waves of two-dimensional subsonic and supersonic mixing layers are revisited in a global point of view, i.e., without any assumption about the base flow, in both a linear and a nonlinear framework by using global and Koopman mode decompositions. In that respect, a timestepping technique based on disturbance equations is employed to extract the most dynamically relevant coherent structures for both linear and nonlinear regimes. The present analysis proposes thus a general strategy for analysing the near-field coherent structures which are responsible for the acoustic noise in these configurations. In particular, we illustrate the failure of linear global modes to describe the noise generation mechanism associated with the vortex pairing for the subsonic regime whereas they appropriately explain the Mach wave radiation of instability waves in the supersonic regime. By contrast, the Dynamic Mode Decomposition (DMD) analysis captures both the near-field dynamics and the far-field acoustics with a few number of modes for both configurations. In addition, the combination of DMD and linear global modes analyses provides new insight about the influence on the radiated noise of nonlinear interactions and saturation of instability waves as well as their interaction with the mean flow.

In previous publications, qualitative agreement between studies of surface plasmon excitations in nanoparticles by near field light scattering and electron energy-loss spectroscopy (EELS) has been found for experiments and simulations. Here, we present a quantitative method for the comparison of light scattering and EELS for surface plasmons in metal spheres. Defining the Fourier transform of the modal component of the scattered electric field along the equivalent electron trajectory enables a direct evaluation of the relative weighting factor for light- and electron-excited surface plasmon modes. This common quantity for light scattering and EELS is examined for size, composition, and trajectory dependencies, facilitating the analysis of key differences between light and electron excitation. A single functional dependence on Drude model plasmon energies is identified to explain the relative modal weighting factors for light scattering and EELS. This method represents an important step toward the complete spectral and spatial reconstruction of EELS maps from near field light scattering calculations.

We employ a novel combination of a Fresnel lens and a diffuser for x-ray ptychography. The setup uses increased flux by enlarging the width of the coherence-defining slits upstream of the experimental station. In the reconstruction algorithm, modal decomposition is used to account for the resulting partial coherence in the beam. We show that if the object has sparse feactures and large areas of flat contrast, the diffuser facilitates a better reconstruction and the extra diversity in the data also allows cleaner separation of the constituent modes in the illumination. The setup also allows a quick, real-time measure of the beam coherence.

International audience; This work concerns the numerical finite element computation, in the frequency domain, of the diffracted wave produced by a defect (crack, inclusion, perturbation of the boundaries, etc.) located in a 3D infinite elastic waveguide. The objective is to use modal representations to build transparent conditions on some artificial boundaries of the computational domain. This cannot be achieved in a classical way, due to non-standard properties of elastic modes. However, a biorthogonality relation allows us to build an operator, relating hybrid displacement/stress vectors. An original mixed formulation is then derived and implemented, whose unknowns are the displacement field in the bounded domain and the normal component of the normal stresses on the artificial boundaries. Numerical validations are presented in the 2D case.

International audience; This paper presents an experimental, numerical and analytical study of the effect of open roof on acoustic propagation along a 3D urban canyon. The experimental study is led by means of a street scale model. The numerical results are performed with a 2D Finite Difference in Time Domain approach adapted to take into account the acoustic radiation losses due to the street open roof. An analytical model, based on the modal decomposition of the pressure field in a horizontal plane mixed with a 2D image sources model to describe the attenuation along the street, is also proposed. Results are given for several frequencies in the low frequency domain (1000-2500 Hz). The comparison of the three approaches shows a good agreement until f=100 Hz at full scale, the analytical model and the 2D numerical simulation adapted to 3D permit to modelize the acoustic propagation along a street. For higher frequency, experimental results show that the leakeage, due to the street open roof, is not anymore uniformly distributed on all modes of the street. The notion of leaky modes must be introduced to modelize the acoustic propagation in a street canyon.

cote interne IRCAM: Helie08a; None / None; International audience; This paper proposes to solve and simulate various Kirchhoff models of nonlinear strings using Volterra series. Two nonlinearities are studied: the string tension is supposed to depend either on the global elongation of the string (first model), or on the local strain located at $x$ (second, and more precise, model). The boundary conditions are simple Dirichlet homogeneous ones or general dynamic conditions (allowing the string to be connected to any system; typically a bridge). For each model, a Volterra series is used to represent the displacement as a functional of excitation forces. The Volterra kernels are solved using a modal decomposition: the first kernel of the series yields the standard modes of the linearized problem while the next kernels introduce the nonlinear dynamics. As a last step, systematic identification of the kernels lead to a structure composed of linear filters, sums, and products which are well-suited to the sound synthesis, using standard signal processing techniques. The nonlinear dynamic introduced through this simulation is significant and perceptible in sound results for sufficiently large excitations.

This article presents a method to estimate flow variables for an open channel network governed by the linearized Saint-Venant equations and subject to periodic forcing. The discharge at the upstream end of the system and the stage at the downstream end of the system are defined as the model inputs; the flow properties at selected internal locations, as well as the other external boundary conditions, are defined as the outputs. Both inputs and outputs are affected by noise and we use the model to improve the data quality. A spatially dependent transfer matrix in the frequency domain is constructed to relate the model input and output using modal decomposition. A data reconciliation technique is used to incorporate the error in the measured data and results in a set of reconciliated external boundary conditions; subsequently, the flow properties at any location in the system can be accurately estimated from the input measurements. The applicability and effectiveness of the method is demonstrated with a case study of the river flow subject to tidal forcing in the Sacramento-San Joaquin Delta, in California. We used existing USGS sensors in place in the Delta as measurement points, and deployed our own sensors at selected locations to produce data used for the validation. The proposed method gives an accurate estimation of the flow properties at intermediate locations within the channel network.

The aim of this work is to explain the vibrational behaviour of several plate sauctures whose plates are joined at different angles, having same widths but different lengths. An analytical formulation using a semi modal decomposition along the junction direction and a wave formulation along the perpendicular one is developed. This approach is very powerful because its numerical implementation is not too heavy (contrary to FEM) and because it's very versatile. Basic vibrational control parameters such as the quadratic velocity and the transfert mobility are shown. The simplest structure considered in this study is made of twin plates connected at any angle. It is shown that in some particular configuration, the vibrational behaviour of the structure can be highly sensitive to slight modifications of a geometrical parameter, particularly the angle between the plates. A statistical way is used to illustrate this phenomenon currently encountered in industrial applications. This formulation can also deal with periodic structures such as corrugated plates

This paper presents a methods to predict the Noise Reduction through cylindrical shells, when the external pressure is known by experimental mesures. We use the FFT to calculate the modal decomposition the predicted NR is compared with theoritical examples