Nonstandard Wave Research Articles

Exact and Numerical Solutions of the Riemann Problem for a Conservative Model of Compressible Two-Phase Flows

In this work we study the solution of the Riemann problem for the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) two-phase flow model introduced in Romenski et al. (J Sci Comput 42(1):68, 2009, Quart Appl Math 65(2):259–279, 2007). All characteristic fields are carefully studied and explicit expressions are derived for the Riemann invariants and the Rankine–Hugoniot conditions. Due to the presence of multiple characteristics in the system under consideration, non-standard wave phenomena can occur. Therefore we briefly review admissibility conditions for discontinuities and then discuss possible wave interactions. In particular we will show that overlapping rarefaction waves are possible and moreover we may have shocks that lie inside a rarefaction wave. In contrast to nonconservative two phase flow models, such as the Baer–Nunziato system, we can use the advantage of the conservative form of the model under consideration. Furthermore, we show the relation between the considered conservative SHTC system and the corresponding barotropic version of the nonconservative Baer–Nunziato model. Additionally, we derive the reduced four equation Kapila system for the case of instantaneous relaxation, which is the common limit system of both, the conservative SHTC model and the non-conservative Baer–Nunziato model. Finally, we compare exact solutions of the Riemann problem with numerical results obtained for the conservative two-phase flow model under consideration, for the non-conservative Baer–Nunziato system and for the Kapila limit. The examples underline the previous analysis of the different wave phenomena, as well as differences and similarities of the three systems.

Reconstruction Algorithms for Photoacoustic Tomography in Heterogeneous Damping Media

In this article, we study several reconstruction methods for the inverse source problem of photoacoustic tomography with spatially variable sound speed and damping. The backbone of these methods is the adjoint operators, which we thoroughly analyze in both the $$L^2$$ - and $$H^1$$ -settings. They are casted in the form of a nonstandard wave equation. We derive the well posedness of the aforementioned wave equation in a natural functional space and also prove the finite speed of propagation. Under the uniqueness and visibility condition, our formulations of the standard iterative reconstruction methods, such as Landweber’s and conjugate gradients (CG), achieve a linear rate of convergence in either $$L^2$$ - or $$H^1$$ -norm. When the visibility condition is not satisfied, the problem is severely ill posed and one must apply a regularization technique to stabilize the solutions. To that end, we study two classes of regularization methods: (i) iterative and (ii) variational regularization. In the case of full data, our simulations show that the CG method works best; it is very fast and robust. In the ill-posed case, the CG method behaves unstably. Total variation regularization method (TV), in this case, significantly improves the reconstruction quality.

Generation of single photons with highly tunable wave shape from a cold atomic ensemble.

The generation of ultra-narrowband, pure and storable single photons with widely tunable wave shape is an enabling step toward hybrid quantum networks requiring interconnection of remote disparate quantum systems. It allows interaction of quantum light with several material systems, including photonic quantum memories, single trapped ions and opto-mechanical systems. Previous approaches have offered a limited tuning range of the photon duration of at most one order of magnitude. Here we report on a heralded single photon source with controllable emission time based on a cold atomic ensemble, which can generate photons with temporal durations varying over three orders of magnitude up to 10 μs without a significant change of the readout efficiency. We prove the nonclassicality of the emitted photons, show that they are emitted in a pure state, and demonstrate that ultra-long photons with nonstandard wave shape can be generated, which are ideally suited for several quantum information tasks.

Lightning Performance and its Prevention for Quadruple-circuit Transmission Line with 220kV/110kV Voltage in a Tower

According to the physical process of discharge development of insulator that is struck by lightning, the lightning flashover model for quadruple-circuit transmission line with dual voltage 220kV/110kV in same tower is established basing on EMTP. The actual evaluation index of lightning protection performance is adopted with the consideration of influence of system voltage. The characteristics of multi-circuit trip-out simultaneously for mixed-voltage lines in same tower is studied, and the distinctions of lightning protection performance caused by differentiated configuration mode of lightning protection measures including phase sequence arrangement, coupling ground wire and so on. The results indicate that the lightning withstand level fluctuates approximately with the phase angle in the form of non-standard sinusoidal wave. The lightning withstand level emerges as optimum performance under the completely reversed phase sequence. The effect of coupling ground wire on top of tower is superior to that on bottom. DOI: http://dx.doi.org/10.11591/telkomnika.v11i10.3413

A nonstandard wave decomposition to ensure the convergence of Debye series for modeling wave propagation in an immersed anisotropic elastic plate

When ultrasonic guided waves in an immersed plate are expressed as Debye series, they are considered as the result of successive reflections from the plate walls. Against all expectations, the Debye series can diverge for any geometry if inhomogeneous waves are involved in the problem. For an anisotropic elastic plate immersed in a fluid, this is the case if the incidence angle is greater than the first critical angle.Physically, this divergence can be explained by the energy coupling between two inhomogeneous waves of same kind of polarization, which are expressed by conjugate wavenumbers. Each of these latter inhomogeneous waves does not transfer energy but a linear combination of them can do it. Mathematically, this is due to the fact that inhomogeneous waves do not constitute a basis orthogonal in the sense of energy, contrarily to homogeneous waves. To avoid that difficulty, an orthogonalization of these inhomogeneous waves is required. Doing so, nonstandard upgoing and downgoing waves in the plate are introduced to ensure the convergence of the new Debye series written in the basis formed by these latter waves.The case of an aluminum plate immersed in water illustrates this study by giving numerical results and a detailed description of the latter nonstandard waves. The different reflection and refraction coefficients at each plate interface are analyzed in terms of Debye series convergence and of distribution of energy fluxes between the waves in the plate. From that investigation, an interesting physical phenomenon is described for one specific pair “angle of incidence/frequency”. For this condition, the quasi-energy brought by the incident harmonic plane wave crosses the plate without any conversion to reflected waves either at the first interface or at the second interface. In this zone, there is a perfect impedance matching between the fluid and the plate.

Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation

We study the properties of a novel discontinuous Petrov Galerkin (DPG) method for acoustic wave propagation. The method yields Hermitian positive definite matrices and has good pre-asymptotic stability properties. Numerically, we find that the method exhibits negligible phase errors (otherwise known as pollution errors) even in the lowest order case. Theoretically, we are able to prove error estimates that explicitly show the dependencies with respect to the wavenumber ω, the mesh size h, and the polynomial degree p. But the current state of the theory does not fully explain the remarkably good numerical phase errors. Theoretically, comparisons are made with several other recent works that gave wave number explicit estimates. Numerically, comparisons are made with the standard finite element method and its recent modification for wave propagation with clever quadratures. The new DPG method is designed following the previously established principles of optimal test functions. In addition to the nonstandard test functions, in this work, we also use a nonstandard wave number dependent norm on both the test and trial space to obtain our error estimates.

Resonant behavior of EHV transformer windings under system originated oscillatory transient over voltages

Grid connected EHV transformers experience various terminal disturbances when in service. The present work attempts to investigate the voltage stresses that may develop on the transformer insulations under a variety of terminal disturbances. A number of standard and non-standard wave shapes like lightning impulse, chopped lightning impulse, steep-front long tail switching surge and oscillatory transient over voltages have been simulated and impressed on the terminals of a 400 kV EHV power transformer operating in the Indian power grid to ascertain how the winding insulations are stressed under these disturbances. Relevant section of the Indian power grid and the transformer has been modeled using Alternative Transient Program (ATP). It has been established that oscillatory system transients can trigger natural resonate frequencies of the transformers causing high voltage stresses on the insulations. Short Time Fourier Transform (STFT) analysis of the oscillatory voltage response of the windings confirmed the presence of resonant frequencies indicating forced resonance. Some remedial measures involving winding design modifications have been suggested in the paper to overcome the problem.

Scattering in Flatland: Efficient Representations via Wave Atoms

This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by thresholding the small coefficients to zero. This phenomenon was perhaps first observed in 1993 by Bradie, Coifman, and Grossman, in the context of local Fourier bases (Bradie et al. in Appl. Comput. Harmon. Anal. 1:94–99, 1993). Their results have since then been extended in various ways. The purpose of this paper is to bridge a theoretical gap and prove that a well-chosen fixed expansion, the non-standard wave atom form, provides a compression of the acoustic single- and double-layer potentials with wave number k as O(k)-by-O(k) matrices with C e δ k 1+δ non-negligible entries, with δ>0 arbitrarily small, and e the desired accuracy. The argument assumes smooth, separated, and not necessarily convex scatterers in two dimensions. The essential features of wave atoms that allow this result to be written as a theorem are a sharp time-frequency localization that wavelet packets do not obey, and a parabolic scaling (wavelength of the wave packet) ∼ (essential diameter)2. Numerical experiments support the estimate and show that this wave atom representation may be of interest for applications where the same scattering problem needs to be solved for many boundary conditions, for example, the computation of radar cross sections.

Simulation and Prediction of Weather Radar Clutter Using a Wave Propagator on High Resolution NWP Data

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Weather radars are essential sensors for observation of precipitation in the troposphere and play a major part in weather forecasting and hydrological modelling. Clutter caused by non-standard wave propagation is a common problem in weather radar applications, and in this paper a method for prediction of this type of weather radar clutter is presented. The method uses a wave propagator to identify areas of potential non-standard propagation. The wave propagator uses a three dimensional refractivity field derived from the geophysical parameters: temperature, humidity, and pressure obtained from a high-resolution Numerical Weather Prediction (NWP) model. The wave propagator is based on the parabolic equation approximation to the electromagnetic wave equation. The parabolic equation is solved using the well-known Fourier split-step method. Finally, the radar clutter prediction technique is used in two cases of superrefraction propagation and the feasibility for detection and removal of clutter echoes while preserving precipitation echoes is illustrated. </para>

Dissipative issue of high-order shock capturing schemes with non-convex equations of state

It is well known that, closed with a non-convex equation of state (EOS), the Riemann problem for the Euler equations allows non-standard waves, such as split shocks, sonic isentropic compressions or rarefaction shocks, to occur. Loss of convexity then leads to non-uniqueness of entropic or Lax solutions, which can only be resolved via the Liu-Oleinik criterion (equivalent to the existence of viscous profiles for all admissible shock waves). This suggests that in order to capture the physical solution, a numerical scheme must provide an appropriate level of dissipation. A legitimate question then concerns the ability of high-order shock capturing schemes to naturally select such a solution. To investigate this question and evaluate modern as well as future high-order numerical schemes, there is therefore a crucial need for well-documented benchmarks. A thermodynamically consistent C ∞ non-convex EOS that can be easily introduced in Eulerian as well as Lagrangian hydrocodes for test purposes is here proposed, along with a reference solution for an initial value problem exhibiting a complex composite wave pattern (the Bizarrium test problem). Two standard Lagrangian numerical approaches, both based on a finite volume method, are then reviewed (vNR and Godunov-type schemes) and evaluated on this Riemann problem. In particular, a complete description of several state-of-the-art high-order Godunov-type schemes applicable to general EOSs is provided. We show that this particular test problem reveals quite severe when working on high-order schemes, and recommend it as a benchmark for devising new limiters and/or next-generation highly accurate schemes.

A Description of Seismic Acoustic Wave Propagation in Porous Media via Homogenization

We consider a linear system of differential equations describing the joint motion of an elastic porous body and a fluid occupying the porous space. A rigorous justification is performed for the homogenization procedures under various conditions imposed on the physical parameters as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic and the process's characteristic time is sufficiently small. Such models describe the propagation of seismic acoustic waves. In the present paper, we derive the homogenized equations, which are different types of nonstandard wave equations depending on the relations between the physical parameters. The proofs are based on Nguetseng's two-scale convergence method of homogenization in periodic structures.

The geometry of sets of parameters of wave packet frames

We study wave packet systems WP ( ψ , M ) ; that is, countable collections of dilations, translations, and modulations of a single function ψ ∈ L 2 ( R ) . The parameters of these unitary actions form a discrete subset M ⊂ R + × R × R . We introduce analogues of the notion of Beurling density, adapted to the geometry of discrete subsets of R + × R × R , and notions of lower and upper dimensions associated with these densities. Our goal is to describe completeness properties of wave packet systems via geometric properties of the sets of their parameters. In particular, we show necessary conditions for WP ( ψ , M ) to be a Bessel system, and we construct multiple examples of non-standard wave packet frames with prescribed dimensions.

Identification strategy in the presence of corrupted measurements

– To propose and develop an identification method of material parameters from dynamics test in the presence of extensively corrupted measurements., – The method we propose, which is based on the use of the error in constitutive relation for identification problems in the framework of transient dynamics, leads to nonstandard wave propagation problems. For solving this numerical difficulty, we used the transition matrix method for short‐duration tests and the combined Riccati constant/transition matrix approach for long‐duration tests., – A numerical strategy adapted to the problem. Results obtained appears to be insensitive to perturbation of measurements up to a very high level of perturbation., – Only simple case of elastic bar have been treated so far., – Without any a priori information on the level of perturbation, this method is robust with respect to the perturbation. A coupling of two resolution methods allows to deal with problem of arbitrary duration.

A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description.

A nonstandard wave equation, established by Galbrun in 1931, is used to study sound propagation in nonuniform flows. Galbrun's equation describes exactly the same physical phenomenon as the linearized Euler's equations (LEE) but is derived from an Eulerian-Lagrangian description and written only in term of the Lagrangian perturbation of the displacement. This equation has interesting properties and may be a good alternative to the LEE: only acoustic displacement is involved (even in nonhomentropic cases), it provides exact expressions of acoustic intensity and energy, and boundary conditions are easily expressed because acoustic displacement whose normal component is continuous appears explicitly. In this paper, Galbrun's equation is solved using a finite element method in the axisymmetric case. With standard finite elements, the direct displacement-based variational formulation gives some corrupted results. Instead, a mixed finite element satisfying the inf-sup condition is proposed to avoid this problem. A first set of results is compared with semianalytical solutions for a straight duct containing a sheared flow (obtained from Pridmore-Brown's equation). A second set of results concerns a more complex duct geometry with a potential flow and is compared to results obtained from a multiple-scale method (which is an adaptation for the incompressible case of Rienstra's recent work).

Electron velocity space hole modes

In space plasmas the local electron distribution is formed by ballistic motion from different source regions. Since electrons with positive and negative parallel (υ∥) velocities have different sources and experience different interactions with the large‐scale electromagnetic fields, the electron distribution function near υ∥ = 0 should possess considerable structure, including the possibility of velocity space holes, i.e., regions where the phase space density is zero, and sharp discontinuities. A particular hole distribution, which may occur upstream of slow shocks in the distant geomagnetic tail, is shown to support a nonstandard plasma wave mode with frequencies between the ion and electron plasma frequencies and parallel phase speed above the ion, but well below the electron, thermal speed. The hole mode can be destabilized by a positive slope in the low parallel velocity electron distribution, and the growth rate is strongly enhanced if the electron parallel temperature exceeds the perpendicular temperature; the mode can also be excited by a hot, fast ion beam. The hole modes exist only for a narrow range of propagation angles about the magnetic field direction. A discontinuity in the integrated parallel distribution function also supports a nonstandard wave mode which is unstable if the value of the distribution function increases across the discontinuity.

Riccati-coupled similarity shock wave solutions for multispeed discrete Boltzmann models

We study nonstandard shock wave similarity solutions for three multispeed discrete Boltzmann models: (1) the square 8Νi, model with speeds 1 and √2 with thex axis along one median, (2) the Cabannes cubic 14Νi model with speeds 1 and √3 and thex axis perpendicular to one face, and (3) another 14Νi, model with speeds 1 and √2. These models have five independent densities and two nonlinear Riccati-coupled equations. The standard similarity shock waves, solutions of scalar Riccati equations, are monotonic and the same behavior holds for the conservative macroscopic quantities. First, we determine exact similarity shock-wave solutions of coupled Riccati equations and we observe nonmonotonic behavior for one density and a smaller effect for one conservative macroscopic quantity when we allow a violation of the microreversibility. Second, we obtain new results on the Whitham weak shock wave propagation. Third, we solve numerically the corresponding dynamical system, with microreversibility satisfied or not, and we also observe the analogous nonmonotonic behavior.

The generalized integration method for predicting impulse volt-time characteristics for non-standard wave shapes-a theoretical basis

A theoretical basis for the integration method of predicting the strength of insulation subjected to impulses of nonstandard wave shapes is presented. Two theoretical approaches are developed for a general physical model of impulse breakdown applicable to gaseous, liquid, and solid insulation, and from an energy-balance model applied to an incipient breakdown channel in a general dielectric. It is therefore not surprising to find that the integration method is reasonably successful as a tool for predicting nonstandard wave-shape insulation strengths, using as input the data derived from tests with standard-wave-shape impulses. Numerical results are presented that provide an understanding of the shape of volt-time curves. An energy balance model has also been used to derive the resistance of the channel after breakdown has occurred.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Growth and Uniqueness Theorems for an Abstract Nonstandard Wave Equation

A uniqueness theorem is proved for a solution to an abstract, nonstandard wave equation (see (1.1)). Growth estimates for a weighted norm of the solution and its kinetic energy are also given. It is then shown that solutions to the linearized equations of Cauchy elasticity, which are a special case of the abstract equation considered, are unstable for certain types of elasticities.

Lightning Protection in Multi-Line Stations

Improved characteristics of modern arresters have substantially increased permissible separation distances and flexibility of arrester location in the protection of station and equipment against lightning overvoltages. This was demonstrated by investigations on representative station arrangements for 138-, 230-, and 345-kV system voltages using methods developed for evaluating the effective severity of a large variety of nonstandard wave shapes upon the different types of insulation structures.