Sharp Wave Front Research Articles

Dynamic nonlocal metasurface for multifunctional integration via phase-change materials

Abstract Non-local metasurface supporting geometric phases at bound states in the continuum (BIC) simultaneously enables sharp spectral resonances and spatial wavefront shaping, thus providing a diversified optical platform for multifunctional devices. However, a static nonlocal metasurface cannot manipulate multiple degrees of freedom (DOFs), making it difficult to achieve multifunctional integration and be applied in different scenarios. Here, we presented and demonstrated phase-change non-local metasurfaces that can realize dynamic manipulation of multiple DOFs including resonant frequency, Q values, band, and spatial wavefront. Accordingly, a metasurface integrating multiple distinct functions is designed, as a proof-of-concept demonstration. Utilizing the geometry phase of quasi-BIC and the tunability of vanadium dioxide (VO2), a dynamic meta-lens is achieved by tailoring spatial light response at quasi-BIC in the temperature range from room temperature to 53 °C. Simultaneously, the sharp Fano resonance of quasi-BIC enables the metasurface to serve as an optical sensor in the mid-infrared band, yielding a sensitivity of 7.96 THz/RIU at room temperature. Furthermore, at the metallic state of VO2 (80 °C), the designed metasurface converts into a mid-infrared broadband absorber, achieving higher than 80 % absorptivity and an average absorption of 90 % from 28.62 THz to 37.56 THz. The proposed metasurface enabling multifunctional performances in different temperatures can effectively improve the availability of devices and find more new and complex scenarios in sensing, imaging, and communications.

Shockwave velocimetry using wave-based image processing to measure anisotropic shock emission

Noninvasive optical measurements of the shockwave propagation velocity using multiple pulse illumination allow deducing the shockwave pressure amplitude through Hugoniot relations and an appropriate equation of state of the medium. This technique is particularly useful for spatially resolved measurements near the shockwave emission site. Due to diffraction, however, a shockwave front can significantly change its morphology, rendering precise velocity measurements non-trivial. As solution we propose a wave front evolution (WaFE) velocimetry technique, which applies Huygens principle. We take a shadowgraph of the wave front at subsequent times as initial condition for the acoustic Helmholtz equation and numerically propagate the fronts in time. From the instance of time, when two subsequently taken wave front shadows numerically interfere and form one sharp wave front, the local shock velocity is obtained and the local shock pressure amplitude measured. With artificial test images, it is shown that this technique has excellent sub-pixel accuracy, robustness to noise, and can work with low contrast images and even overlapping and interfering wave fronts. The software is made available freely and can be applied to general shock front velocity measurements. We apply WaFE to determine the anisotropic shockwave emission from an elongated laser-induced plasma in water from shadowgraphs of the shockwave front imaged four times onto the same camera frame using multiple pulse illumination at a repetition rate of 60 MHz. The direction dependence of attenuation of the shockwave pressure amplitude is measured at distances of 50–300 μm to the plasma.

Quantum dynamics of dissipative Chern insulator

For open quantum systems, a short-time evolution is usually well described by the effective non-Hermitian Hamiltonians, while long-time dynamics requires the Lindblad master equation,in which the Liouvillian superoperators characterize the time evolution. In this paper, we constructed an open system by adding suitable gain and loss operators to the Chen insulator to investigate the time evolution of quantum states at long times by numerical simulations. Finally, we also propose a topolectrical circuits to realize the dissipative system for experimental observation. It is found that the opening and closing of the Liouvillian gap leads to different damping behaviours of the system and that the presence of non-Hermitian skin effects leads to a phenomenon of chiral damping with sharp wavefronts. Our study deepens the understanding of quantum dynamics of dissipative system.

Hyperbolic Conduction and Radiation Heat Transfer in Axisymmetric Cylinders with Variable Properties

This work investigates the combined mode of hyperbolic heat conduction and radiation transfer in a one-dimensional axisymmetric cylinder filled with absorbing, emitting, and scattering media. The volumetric radiation is investigated thanks to the semianalytic solution of the matrix formulation of the spherical harmonics equations PN. The governing hyperbolic energy equation is solved using the finite volume method (FVM) with Roe’s correction of interface fluxes in order to enhance the performances of the method, and the lattice Boltzmann method (LBM) has been designed for comparisons. The effects of the parameters such as constant and spatial-dependent scattering albedos, temperature-dependent thermal conductivity, heat-generated sources, extinction, and the conduction–radiation parameter on both the temperature and heat flux distributions for steady and transient states within the medium are examined. The results of the present work are in excellent agreement with those available in the literature. The PN−FVM results are also compared to those obtained with the PN−LBM combination, and excellent agreement is obtained. These results show that the mentioned parameters have a significant effect on both the temperature profiles and the hyperbolic sharp wave front. This study also shows that the proposed layered approach is an efficient, fast, and accurate solution method for radiative analysis in inhomogeneous media, whereas the Roe’s correction of interface fluxes in the FVM is suitable to accommodate a thermal wave front in non-Fourier analysis.

Centres of spiral waves can be detected as phase defect lines in optical voltage mapping data and numerical simulations

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): KU Leuven and FWO-Flanders Introduction To study the excitation patterns of spiral waves in two spatial dimensions over time, it is useful to abstract them to much simpler mathematical structures. Previously, those waves have been abstracted to phase singularities: single points around which spiral moves [1,2]. Recently, it was proposed to upgrade these points to phase defect lines [3,4]. The dynamics of either of these structures can then be studied in place of the spiral waves. Purpose To work with phase defects, firstly, we need a reliable method of locating them. Methods We recorded the transmembrane voltage over space and time in a numerical simulation of the mono-domain model as well as by using optical voltage mapping data of 10 cm² monolayers of conditionally immortalised human atrial myocytes [5]. Optical voltage mapping was performed with a sampling time of 6 ms and 100×100 square pixels of 0.25 mm width. The recorded intensity were smoothed and rescaled to get an estimate of the transmembrane voltages. Detailed protocols can be found in [5]. For the numerical simulations, we have implemented the linear-core tissue model by Bueno-Orovio, Cherry, and Fenton (2008) [6] with finite differences on a 1200×1200 rectangular grid with a grid size of 0.25 mm and a time step of 9 μs. We normalised the transmembrane voltage u such that zero corresponds to the resting state and one to the plateau of the action potential. A phase φ is an angle in radians which monotonously increases from zero to 2π during one action potential. Phases are defined in such a manner that, even for the sharp wave front of a cardiac action potential, this increase happens in a slow, gradual way. A phase can for instance be defined by using the local arrival time and the characteristic action potential duration [4]. At the centre of spiral waves, neighbouring parts of tissue have vastly different phase values φ. A phase singularity is a point where all phases meet. Phase defects are large jumps across space in phase. Phase defect lines can then be detected as lines in the phase defect field ρ with a value much larger than zero [7]. Results For the simulation, we can clearly see that the linear core of the Bueno-Orovio, Cherry, and Fenton (2008) [6] model is identified as a phase defect line of up to 100 mm in length (Fig.1). The spiral wave moves along it and turns at the end points. The same behaviour can be seen in vitro in the optical voltage mapping data (Fig.2). Multiple spirals can be observed, all of which revolve around phase defect lines of lengths of up to 4 mm. Conclusion In this study, we have shown that phase defect lines can be detected both in silico and in vitro. Their properties such as length, rotational frequency, and their dynamics can be used to gain additional insight into spiral waves in arrhythmias. We have introduced multiple methods to localise phase defects for which the code is publicly available.

A stable discontinuous Galerkin method for linear elastodynamics in 3D geometrically complex elastic solids using physics based numerical fluxes

Time-stable, high order accurate and explicit numerical methods are effective for hyperbolic wave propagation problems. As a result of the complexities of real geometries, internal interfaces and nonlinear boundary and interface conditions, discontinuities and sharp wave fronts may become fundamental features of the solution. Therefore, geometrically flexible and adaptive numerical algorithms are crucial for high fidelity and efficient simulations of wave phenomena in many applications. Adaptive curvilinear meshes hold promise to minimise the effort to represent complicated geometries or heterogeneous material data avoiding the bottleneck of feature-preserving meshing. To enable the design of stable DG methods on three space dimensional (3D) curvilinear elements we construct a structure preserving skew-symmetric coordinate transformation motivated by the underlying physics. Using a physics-based numerical penalty-flux, we develop a 3D provably energy-stable discontinuous Galerkin finite element approximation of the elastic wave equation in geometrically complex and heterogeneous media. By construction, our numerical flux is upwind and yields a discrete energy estimate analogous to the continuous energy estimate. The ability to treat conforming and non-conforming curvilinear elements allows for flexible adaptive mesh refinement strategies. The numerical scheme has been implemented in ExaHyPE, a simulation engine for parallel dynamically adaptive simulations of wave problems on adaptive Cartesian meshes. We present 3D numerical experiments of wave propagation in heterogeneous isotropic and anisotropic elastic solids demonstrating stability and high order accuracy. We demonstrate the potential of our approach for computational seismology in a regional wave propagation scenario in a geologically constrained 3D model including the geometrically complex free-surface topography of Mount Zugspitze, Germany.

A Reanalysis of the October 2016 “Meteotsunami” in British Columbia With Help of High-Frequency Radars and Autoregressive Modeling

On October 14, 2016, the coastal high-frequency radar system in Tofino (British Columbia, Canada) triggered an automatic tsunami warning based on the identification of abnormal surface current patterns. This occurred in the absence of any reported seismic event but coincided with a strong atmospheric perturbation, which qualified the event as meteotsunami. We reanalyze this case in the light of a new radar signal processing method, which was designed recently for inverting fast-varying sea surface currents from the complex voltage time series received on the antennas. This method, based on autoregressive modeling combined with a maximum entropy method, yields a dramatic improvement in both the signal-to-noise ratio and the quality of the surface current estimation for very short integration time. This makes it possible to evidence the propagation of a sharp wavefront of surface current during the event and to map its magnitude and arrival time over the radar coverage. We show that the amplitude and speed of the inferred residual current do not comply with a Proudman resonance mechanism but are consistent with the propagation of a low-pressure atmospheric front. This supports the hypothesis of a storm surge rather than a true meteotsunami to explain this event. Beyond this specific case, another outcome of the analysis is the promising use of HF radars as proxy’s for the characterization of atmospheric fronts.

Numerical Evaluation of Sonic Boom Deformation due to Atmospheric Turbulence

This paper presents the numerical studies on the effect of atmospheric turbulence on sonic boom signatures. The authors developed the SPnoise for Sonic Boom, which is a numerical analysis code to simulate the essential effect of atmospheric turbulence on sonic booms, i.e., fluctuation of the medium due to turbulence and focusing/defocusing of a sharp wavefront as a result of diffraction. Waveforms obtained from SPnoise for Sonic Boom are compared with those by sonic boom measurements from D-SEND#2, the second flight test of the Drop Test for Simplified Evaluation of Non-symmetrically Distributed Sonic Boom project, and fairly good agreement between simulated and measured waveforms is achieved.

Calculation of Waves in an Elastic-Plastic Body Based on ENO Modifications of the Godunov Method

The efficiency of two ENO modifications of the Godunov method for calculation axisymmetric problems of the dynamics of elastic-plastic bodies, namely a UNO scheme of the second-order of accuracy and a TVD scheme of the second order of accuracy outside the solution extremes where it decreases to the first order, has been numerically studied. The efficiency of the modifications is estimated by comparing the results of calculation of a number of problems on the propagation of spherical and cylindrical waves in a body with the results of reference solutions and the Godunov method. The exact and numerical solutions are used as reference solutions, the latter are obtained on fine grids. It is shown that for all the problems considered, the solutions by the TVD and UNO schemes are much closer to the reference ones than those by the Godunov method. The TVD and UNO schemes are characteristic of significantly less smearing of sharp wave fronts and a more accurate resolution of extrema. At the same time, the wave profiles and the extrema are reproduced by the UNO scheme somewhat better than by the TVD scheme.

Perturbative Traveling-Wave Solution for a Flux-Limited Reaction-Diffusion Morphogenesis Equation

In this study, we investigate a porous medium-type flux limited reaction--diffusion equation that arises in morphogenesis modeling. This nonlinear partial differential equation is an extension of the generalized Fisher--Kolmogorov--Petrovsky--Piskunov (Fisher-KPP) equation in one-dimensional space. The approximate analytical traveling wave solution is found by using a perturbation method. We show that the morphogen concentration propagates as a sharp wave front where the wave speed has a saturated value. The numerical solutions of this equation are also provided to compare them with the analytical predictions. Finally, we qualitatively compare our theoretical results with those obtained in experimental studies.

Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems.

One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely, that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wave front. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.

Analytical layered solution of radiation and non–Fourier conduction problems in optically complex media

The analytical layered solution for radiative transfer through participating optically complex media is developed. The angular processing of radiation is based on double spherical harmonics method (DPN) which split up the radiative intensity into two stream components before expanding in Legendre polynomial basis. The proposed layered radiative solution assumes that the optically complex media is a set of thin layers dealing with homogeneous properties. Therefore, the analytical solution for radiative transfer is performed and then coupled to the finite volume method (FVM), to solve the non – linear hyperbolic thermal conduction problems, formulated thanks to Cattaneo–Vernotte flux. In developing the FVM, the Roe′s corrections of interface fluxes is adopted in order to enhance the performances of the method. The accuracy of the proposed model for dealing with inhomogeneous radiation/conduction problems is investigated by considering participating media such as slab, solid or hollow spheres, with temperature – dependent thermal conductivity. The effects of different parameters, known as scattering albedo, graded index function, thermal conductivity, boundary emissivity and the conduction–radiation parameter on both temperature and heat flux distributions for purely radiation, steady and transient states are studied. Results of the present work compare well with those available in the literature with maximum relative error less than 1%. These results show that the listed parameters have a significant effect on both temperature profiles and hyperbolic sharp wave front. It also comes from this study that the proposed layered approach is an efficient, robust, and accurate method for radiative flow analysis in inhomogeneous media while the Roe′s correction of interface fluxes in FVM is suitable to accommodate thermal wave front in non – Fourier analysis.

Locality, Quantum Fluctuations, and Scrambling

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large N models exhibiting exponential growth of OTOCs and a sharp chaos wavefront and other random circuit models showing a diffusively broadened wavefront. In this paper we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wavefront. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a cross-over to a diffusively broadened wavefront. At small N we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively-broadened wavefront.

High accuracy modeling of sharp wave fronts for hyperbolic problems

In this paper, the arbitrary order derivative (ADER) schemes based on the generalized Riemann problem are proposed to capture shock waves and contact discontinuities by coupling ghost fluid method (GFM). The reconstruction technique for spatial derivatives at cell boundaries is presented by piece-wise smooth WENO interpolations which are used as initial states of the Riemann problems. A level set function is used to keep track of the location of wave fronts. The shock waves are pushed forward by shock speeds which are obtained by the Rankine–Hugoniot conditions, whereas the contact discontinuities are advanced by local fluid velocities. Numerical examples show that the presented scheme is suitable for capturing fine flow structures and has an accuracy comparable to other methods designed for traditional contact discontinuity.

An asynchronous spacetime discontinuous Galerkin finite element method for time domain electromagnetics

We present an asynchronous spacetime discontinuous Galerkin (aSDG) method for time domain electromagnetics in which space and time are directly discretized. By using differential forms we express Maxwell's equations and consequently their discontinuous Galerkin discretization for arbitrary domains in spacetime. The elements are discretized with electric and magnetic basis functions that are discontinuous across all inter-element boundaries and can have arbitrary high and per element spacetime orders. When restricted to unstructured grids that satisfy a specific causality constraint, the method has a local and asynchronous solution procedure with linear solution complexity in terms of the number of elements. We numerically investigate the convergence properties of the method for 1D to 3D uniform grids for energy dissipation, an error relative to the exact solution, and von Neumann dissipation and dispersion errors. Two dimensional simulations demonstrate the effectiveness of the method in resolving sharp wave fronts.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Laser pulse sharpening with electromagnetically induced transparency in plasma

We propose a laser-controlled plasma shutter technique to generate sharp laser pulses using a process analogous to electromagnetically induced transparency in atoms. The shutter is controlled by a laser with moderately strong intensity, which induces a transparency window below the cutoff frequency, and hence enables propagation of a low frequency laser pulse. Numerical simulations demonstrate that it is possible to generate a sharp pulse wavefront (sub-ps) using two broad pulses in high density plasma. The technique can work in a regime that is not accessible by plasma mirrors when the pulse pedestals are stronger than the ionization intensity.

On Traveling Wave Fronts in a Degenerate Nonlinear Parabolic System Modeling Bacterial Pattern Formation

In this paper we consider a degenerate nonlinear parabolic system which models spatio-temporal patterns generated by bacterial colonies. A three-dimensional phase space analysis of wave fronts in this model system is performed. The existence of a sharp wave front for a minimum speed in addition to smooth wave fronts for large speeds is shown. Further, an accurate numerical computation of such wave front solutions is presented.

Hyperbolic Conduction–Radiation in Participating and Inhomogeneous Slab With Double Spherical Harmonics and Lattice Boltzmann Methods

This work deals with the combined mode of non-Fourier conduction and radiation transfer in isotropically/anisotropically scattering, homogeneous, and inhomogeneous planar media with reflective boundaries subjected to the constant internal temperature of the medium and the externally isotropic diffuse incidence at one boundary. An analytical double spherical harmonics method (DPN) is proposed to solve the radiative problem. The non-Fourier conduction is described with the Cattaneo–Vernotte model, and the governing hyperbolic energy equation is solved using the lattice Boltzmann method (LBM). For radiative problems through the layer/layered media, the radiative heat fluxes, hemispherical radiative intensities, transmissivity, and reflectivity are found, while for coupled conduction and radiation, the temperature distributions are found for various optical thicknesses, space-dependent scattering albedo, conduction–radiation parameters, and boundary reflectivities. Results of the present work are in excellent agreement with those available in the literature. Moreover, these results demonstrate that the proposed analytical double spherical method is an efficient, robust, and accurate method for radiative transfer through inhomogeneous layer/layered planar media analysis. Furthermore, it is observed that space-dependent scattering albedo and boundary reflectivities have a very significant effect in the hyperbolic sharp wave front of non-Fourier conduction.

Moving mesh discontinuous Galerkin methods for PDEs with traveling waves

In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh strategy for one dimensional PDEs is based on the rezoning approach which decouples the solution of the PDE from the moving mesh equation. We show that the dG moving mesh method is able to resolve sharp wave fronts and wave speeds accurately for the optimal, arc-length and curvature monitor functions. Numerical results reveal the efficiency of the proposed moving mesh dG method for solving Burgers’, Burgers’–Fisher and Schlögl (Nagumo) equations.