Wavefront Dynamics Research Articles

Extended angular-spectrum modeling (EASM) of light energy transport in scattering media.

The exact modeling of light transport in scattering media is critical in biological imaging, free-space communication, and phosphor-converted lighting. Angular spectrum is proved to be a fast and effective approach to reconstructing the wavefront dynamics during the propagation in scattering media, however, finding it difficult in acquiring the wavefront and energy change simultaneously. Besides, conventional methods for energy tracing, such as the Monte Carlo method, are inefficient in speed and hard to simulate the wavefront change. Here, we propose an extended angular-spectrum modeling (EASM) approach using tenuous scattering approximate solutions to obtain a time-efficient and accurate method for reconstruction of energy and wavefront dynamics in various scattering media. The generality of our method is numerically simulated and experimentally verified with a set of scattering media with different properties. EASM has a time advantage under the guarantee of calculation accuracy, especially when calculating several thickness changes after the calculation model is established. Furthermore, multi-layered media can also be simulated by EASM with a good precision. The results suggest that EASM performs certain computations more efficiently than the conventional method and thus provides an effective and flexible calculation tool for scattering media.

Mechanisms of persistent atrial fibrillation and recurrences within 12 months post-ablation: Non-invasive mapping with electrocardiographic imaging.

Catheter ablation of persistent AF has not been consistently successful in terminating AF or preventing arrhythmia recurrences. Non-invasive Electrocardiographic Imaging (ECGI) can help to understand recurrences by mapping the mechanisms of pre-ablation AF and comparing them with the patterns of recurrent arrhythmias in the same patient. Seventeen persistent AF patients underwent ECGI before their first catheter ablation. Time-domain activation maps and phase progression maps were obtained on the bi-atrial epicardium. Location of arrhythmogenic drivers were annotated on the bi-atrial anatomy. Activation and phase movies were examined to understand the wavefront dynamics during AF. Eight patients recurred within 12 months of ablation and underwent a follow-up ECGI. Driver locations and movies were compared for pre- and post-ablation AF. A total of 243 focal drivers were mapped during pre-ablation AF. 62% of the drivers were mapped in the left atrium (LA). The pulmonary vein region harbored most of the drivers (43%). 35% of the drivers were mapped in the right atrium (RA). 59% (10/17) and 53% (9/17) of patients had repetitive sources in the left pulmonary veins (LPV) and left atrial appendage (LAA), and the lower half of RA, respectively. All patients had focal drivers. 29% (5/17) of patients had macro-reentry waves. 24% (4/17) of patients had rotors. Activation patterns during persistent AF varied from single macro-reentry to complex activity with multiple simultaneous wavefronts in both atria, resulting in frequent wave collisions. A total of 76 focal driver activities were mapped in 7/8 patients during recurrence. 59% of the post-ablation AF drivers were mapped in the LA. The pulmonary vein region harbored 50% of total drivers. 39% of sources were mapped in the RA. AF complexity remained similar post-ablation. 58% (44/76) of pre-ablation sources persisted during recurrence. 38% (3/8) of patients had macro-reentry and one patient had rotors. ECGI provides patient-specific information on mechanisms of persistent AF and recurrent arrhythmia. More than half pre-ablation sources repeated during post-ablation recurrence. This study provides direct evidence for drivers that persist days and months after the ablation procedure. Patient-tailored bi-atrial ablation is needed to successfully target persistent AF and prevent recurrence. ECGI can potentially predict recurrence and assist in choice of therapy.

Dynamic mode decomposition for aero-optic wavefront characterization

Aero-optical beam control relies on the development of low-latency forecasting techniques to quickly predict wavefronts aberrated by the turbulent boundary layer around an airborne optical system, and its study applies to a multidomain need from astronomy to microscopy for high-fidelity laser propagation. We leverage the forecasting capabilities of the dynamic mode decomposition (DMD) — an equation-free, data-driven method for identifying coherent flow structures and their associated spatiotemporal dynamics — to estimate future state wavefront phase aberrations to feed into an adaptive optic control loop. We specifically leverage the optimized DMD (opt-DMD) algorithm on a subset of the Airborne Aero-Optics Laboratory-Transonic experimental dataset, characterizing aberrated wavefront dynamics for 23 beam propagation directions via the spatiotemporal decomposition underlying DMD. Critically, we show that opt-DMD produces an optimally debiased eigenvalue spectrum with imaginary eigenvalues, allowing for arbitrarily long forecasting to produce a robust future state prediction, while exact DMD loses structural information due to modal decay rates.

Expansion of the Laser Beam Wavefront in Terms of Zernike Polynomials in the Problem of Turbulence Testing

The results of a study of the wavefront distortions of laser radiation caused by artificial turbulence obtained in laboratory conditions using a fan heater are presented. Decomposition of the wavefront in terms of Zernike polynomials is a standard procedure that traditionally is used to investigate the set of existing aberrations. In addition, the spectral analysis of the wavefront dynamics makes it possible to estimate the fraction of the energy distributed between different Zernike modes. It is shown that the fraction of energy related to the low-order polynomials is higher compared to the high-order polynomials. Also, one of the consequences of Taylor’s hypothesis is confirmed—low-order aberrations are slower compared to the higher-order ones.

Phyllotaxis-inspired nanosieves with multiplexed orbital angular momentum

Nanophotonic platforms such as metasurfaces, achieving arbitrary phase profiles within ultrathin thickness, emerge as miniaturized, ultracompact and kaleidoscopic optical vortex generators. However, it is often required to segment or interleave independent sub-array metasurfaces to multiplex optical vortices in a single nano-device, which in turn affects the device’s compactness and channel capacity. Here, inspired by phyllotaxis patterns in pine cones and sunflowers, we theoretically prove and experimentally report that multiple optical vortices can be produced in a single compact phyllotaxis nanosieve, both in free space and on a chip, where one meta-atom may contribute to many vortices simultaneously. The time-resolved dynamics of on-chip interference wavefronts between multiple plasmonic vortices was revealed by ultrafast time-resolved photoemission electron microscopy. Our nature-inspired optical vortex generator would facilitate various vortex-related optical applications, including structured wavefront shaping, free-space and plasmonic vortices, and high-capacity information metaphotonics.

The dynamics of 3-min wavefronts and their relation to sunspot magnetic fields.

We present a study of wave processes occurring in solar active region NOAA 11131 on 10 December 2010, captured by the Solar Dynamics Observatory in the 1600 Å, 304 Å and 171 Å channels. For spectral analysis, we employed pixelized wavelet filtering together with a developed digital technique based on empirical mode decomposition. We studied the ∼3-minute wave dynamics to obtain relationships with the magnetic structuring of the underlying sunspot. We found that during development of wave trains the motion path occurred along a preferential direction, and that the broadband wavefronts can be represented as a set of separate narrowband oscillation sources. These sources become visible as the waves pass through the umbral inhomogeneities caused by the differing magnetic field inclination angles. We found the spatial and frequency fragmentation of wavefronts, and deduced that the combination of narrowband spherical and linear parts of the wavefronts provide the observed spirality. Maps of the magnetic field inclination angles confirm this assumption. We detect the activation of umbral structures as the increasing of oscillations in the sources along the front ridge. Their temporal dynamics are associated with the occurrence of umbral flashes. Spatial localization of the sources is stable over time and depends on the oscillation period. We propose that these sources are the result of wave paths along the loops extending outwards from the magnetic bundles of the umbra. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.

Spatially resolved filament wavefront dynamics

Spatially resolved wavefront measurements are presented during nonlinear self-collapse and provide the first detailed characterization of wavefront evolution during filament formation. The wavefront dynamics of key nonlinear processes including Kerr self-focusing, ionization and plasma defocusing, and dynamic spatial replenishment are identified and resolved in both the filament core and reservoir regions. These results are analyzed and interpreted with respect to numerical simulations and provide insight into fundamental aspects of filamentation. They also inform applications based on phase manipulation, such as external beam guiding, and present a new method for measuring the nonlinear index of refraction, n2.

Traveling waves in delayed reaction-diffusion equations in biology.

This paper represents a literature review on traveling waves described by delayed reactiondiffusion (RD, for short) equations. It begins with the presentation of different types of equations arising in applications. The main results on wave existence and stability are presented for the equations satisfying the monotonicity condition that provides the applicability of the maximum and comparison principles. Other methods and results are described for the case where the monotonicity condition is not satisfied. The last two sections deal with delayed RD equations in mathematical immunology and in neuroscience. Existence, stability, and dynamics of wavefronts and of periodic waves are discussed.

Standardised Framework for Quantitative Analysis of Fibrillation Dynamics

The analysis of complex mechanisms underlying ventricular fibrillation (VF) and atrial fibrillation (AF) requires sophisticated tools for studying spatio-temporal action potential (AP) propagation dynamics. However, fibrillation analysis tools are often custom-made or proprietary, and vary between research groups. With no optimal standardised framework for analysis, results from different studies have led to disparate findings. Given the technical gap, here we present a comprehensive framework and set of principles for quantifying properties of wavefront dynamics in phase-processed data recorded during myocardial fibrillation with potentiometric dyes. Phase transformation of the fibrillatory data is particularly useful for identifying self-perpetuating spiral waves or rotational drivers (RDs) rotating around a phase singularity (PS). RDs have been implicated in sustaining fibrillation, and thus accurate localisation and quantification of RDs is crucial for understanding specific fibrillatory mechanisms. In this work, we assess how variation of analysis parameters and thresholds in the tracking of PSs and quantification of RDs could result in different interpretations of the underlying fibrillation mechanism. These techniques have been described and applied to experimental AF and VF data, and AF simulations, and examples are provided from each of these data sets to demonstrate the range of fibrillatory behaviours and adaptability of these tools. The presented methodologies are available as an open source software and offer an off-the-shelf research toolkit for quantifying and analysing fibrillatory mechanisms.

Curved surface geometry-induced topological change of an excitable planar wavefront.

On the curved surfaces of living and nonliving materials, planar excitable wavefronts frequently exhibit a directional change and subsequently undergo a discontinuous (topological) change; i.e., a series of wavefront dynamics from collision, annihilation to splitting. Theoretical studies have shown that excitable planar stable waves change their topology significantly depending on the initial conditions on flat surfaces, whereas the directional change of the waves occurs based on the geometry of curved surfaces. However, it is not clear if the geometry of curved surfaces induces this topological change. In this study, we first demonstrated that the curved surface geometry induces bending, collision, and splitting of a planar stable wavefront by numerically solving an excitable reaction-diffusion equation on a bell-shaped surface. We determined two necessary conditions for inducing the topological change: the characteristic length of the curved surface (i.e., the height of the bell-shaped structure) should be greater than the width of the wave, and the ratio of the height to the width of the bell shape should be greater than a threshold. As for the geometrical mechanism of the latter, we found that a bifurcation of the geodesics on the curved surface provides the alternative minimal paths of the wavefront, which circumvent the surface region with a high local curvature, thereby resulting in the topological change. These conditions imply that the topological change of the wavefront can be predicted on the basis of the curved surfaces, whose structures are larger than the wave width.

Time-evolution patterns of electrons in twisted bilayer graphene

We characterise the dynamics of electrons in twisted bilayer graphene by analysing the time-evolution of electron waves in the atomic lattice. We perform simulations based on a kernel polynomial technique using Chebyshev polynomial; this method does not requires any diagonalisation of the system Hamiltonian. Our simulations reveal that the inter-layer electronic coupling induces the exchange of waves between the two graphene layers. This wave transfer manifests as oscillations of the layer-integrated probability densities as a function of time. For the bilayer case, it also causes a difference in the wavefront dynamics compared to monolayer graphene. The intra-layer spreading of electron waves is irregular and progresses as a two-stage process. The first one characterised by a well-defined wavefront occurs in a short time | a wavefront forms instead during the second stage. The wavefront takes a hexagon-like shape with the vertices developing faster than the edges. Though the detail spreading form of waves depends on initial states, we observe localisation of waves in specific regions of the moir\'e zone. To characterise the electron dynamics, we also analyse the time auto-correlation functions. We show that these quantities shall exhibit the beating modulation when reducing the interlayer coupling.

Determinants of new wavefront locations in cholinergic atrial fibrillation.

AimsAtrial fibrillation (AF) wavefront dynamics are complex and difficult to interpret, contributing to uncertainty about the mechanisms that maintain AF. We aimed to investigate the interplay between rotors, wavelets, and focal sources during fibrillation.Methods and resultsArrhythmia wavefront dynamics were analysed for four optically mapped canine cholinergic AF preparations. A bilayer computer model was tuned to experimental preparations, and varied to have (i) fibrosis in both layers or the epicardium only, (ii) different spatial acetylcholine distributions, (iii) different intrinsic action potential duration between layers, and (iv) varied interlayer connectivity. Phase singularities (PSs) were identified and tracked over time to identify rotational drivers. New focal wavefronts were identified using phase contours. Phase singularity density and new wavefront locations were calculated during AF. There was a single dominant mechanism for sustaining AF in each of the preparations, either a rotational driver or repetitive new focal wavefronts. High-density PS sites existed preferentially around the pulmonary vein junctions. Three of the four preparations exhibited stable preferential sites of new wavefronts. Computational simulations predict that only a small number of connections are functionally important in sustaining AF, with new wavefront locations determined by the interplay between fibrosis distribution, acetylcholine concentration, and heterogeneity in repolarization within layers.ConclusionWe were able to identify preferential sites of new wavefront initiation and rotational activity, in order to determine the mechanisms sustaining AF. Electrical measurements should be interpreted differently according to whether they are endocardial or epicardial recordings.

Real-Time Rotational Activity Detection in Atrial Fibrillation.

Rotational activations, or spiral waves, are one of the proposed mechanisms for atrial fibrillation (AF) maintenance. We present a system for assessing the presence of rotational activity from intracardiac electrograms (EGMs). Our system is able to operate in real-time with multi-electrode catheters of different topologies in contact with the atrial wall, and it is based on new local activation time (LAT) estimation and rotational activity detection methods. The EGM LAT estimation method is based on the identification of the highest sustained negative slope of unipolar signals. The method is implemented as a linear filter whose output is interpolated on a regular grid to match any catheter topology. Its operation is illustrated on selected signals and compared to the classical Hilbert-Transform-based phase analysis. After the estimation of the LAT on the regular grid, the detection of rotational activity in the atrium is done by a novel method based on the optical flow of the wavefront dynamics, and a rotation pattern match. The methods have been validated using in silico and real AF signals.

Microorganism billiards in closed plane curves.

Recent experiments have shown that many species of microorganisms leave a solid surface at a fixed angle determined by steric interactions and near-field hydrodynamics. This angle is completely independent of the incoming angle. For several collisions in a closed body this determines a unique type of billiard system, an aspecular billiard in which the outgoing angle is fixed for all collisions. We analyze such a system using numerical simulation of this billiard for varying tables and outgoing angles, and also utilize the theory of one-dimensional maps and wavefront dynamics. When applicable we cite results from and compare our system to similar billiard systems in the literature. We focus on examples from three broad classes: the ellipse, the Bunimovich billiards, and the Sinai billiards. The effect of a noisy outgoing angle is also discussed.

Panoramic characterization of endocardial left atrial activation during human persistent AF: Insights from non-contact mapping

BackgroundThe relative importance of focal drivers, multiple wavelets, rotors and endocardial–epicardial circuits in the maintenance of persistent AF remains unclear. Our objective was to characterize AF wavefront (WF) dynamics during persistent AF. MethodsThe Ensite 3000 (St Jude Medical) non-contact mapping system was used to map the LA of 15 patients with persistent AF. Wavefronts were classified into planar WFs, rotors or focal WFs. For each new WF the site of origin, the unipolar electrogram, and propagation patterns were determined. ResultsAF was characterized by highly unstable patterns of activation with random combinations of 1–2 propagating planar wavefronts alternating with focal activations in a dynamic process. Stable reentry circuits and rotors were never seen. A total of 499 wavefront patterns were analyzed in this study (416 planar wavefronts and 83 focal wavefronts). In an individual patient planar WFs accounted for 67±35% of activations with lifespans of 98±86ms. Focal activations accounted for 29.7±33.5% of activations with lifespans of 76±95ms. The most common sites for new WF generation were the PVs (33%), LA roof (23%), anterior LA (15%), LAA (11%), and posterior LA (8%). The most common unipolar electrogram morphologies observed were QS pattern (34%), rS (29%), CFAE (26%), QR (7%) and Rs (4%), suggesting that WFs may originate from both the endocardial and epicardial surfaces. ConclusionHuman persistent AF is characterized by the formation of highly unstable WFs consisting of various combinations of one to two planar WFs and brief focal activations without any evidence of rotors or sustained focal sources.

Geometry and dynamics of fast magnetosonic wavefronts near magnetic null points

The behavior of two-dimensional fast magnetosonic waves in the vicinity of isolated points where the magnetic field vanishes is studied analytically. The geometry of rays and wavefronts is described, and the curvature of both is found using conformal mapping techniques. These results are applied to the formation of shock waves, obtaining that shock formation is guaranteed at a finite time for any initial condition of the perturbation when the wavefront is concave and the rays tend to focus, whereas otherwise shocks occur only for a certain range of initial conditions.

Variational principle for nonlinear wave propagation in dissipative systems.

The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.

Regulating wave front dynamics from the strongly discrete to the continuum limit in magnetically driven colloidal systems.

The emergence of wave fronts in dissipative driven systems is a fascinating phenomenon which can be found in a broad range of physical and biological disciplines. Here we report the direct experimental observation of discrete fronts propagating along chains of paramagnetic colloidal particles, the latter propelled above a traveling wave potential generated by a structured magnetic substrate. We develop a rigorously reduced theoretical framework and describe the dynamics of the system in terms of a generalized one-dimensional dissipative Frenkel-Kontorova model. The front dynamics is explored in a wide range of field parameters close to and far from depinning, where the discrete and continuum limits apply. We show how symmetry breaking and finite size of chains are used to control the direction of front propagation, a universal feature relevant to different systems and important for real applications.

ApproximateWeakly NonlinearModel of gas Dynamics EquationsWith Utilized Korobeinikov’s Chemical Reaction

The main purpose is to develop an analytic approach for investigating the wave front propagation on a surface of a cylinder that can be used a descriptor of a detonation engine. The analysis is based on a weakly nonlinear approximated gas dynamic equations with incorporated approximation of the Korobeinkov’s chemical reaction model that are used to describe the two-dimensional detonation field on a surface of a two-dimensional cylindrical chamber without thickness. We found that the wave fronts can be expressed analytically in explicit form for special classes of flow (e.g. isentropic gas flow). In more general cases, the dynamics of wave fronts can still be determined explicitly provided that the wave front is known at initial time and the exact solution, or its approximation is known a priori, e.g. from experimental or numerical analysis.

Multidimensional wave fronts propagation along the beams associated with thermodynamic model of a rotating detonation engine

The main purpose here is to develop an analytic approach for investigating the wave front propagation on a surface of a cylinder that can be used as a descriptor of a detonation engine. The analysis is based on a weakly nonlinear approximated gas dynamic equations with incorporated approximation of the Korobeinikov’s chemical reaction model that are used to describe the two-dimensional detonation field on a surface of a two-dimensional cylindrical chamber without thickness. We found that the wave fronts can be expressed analytically in explicit form for special classes of flow (e.g. isentropic gas flow). In more general cases, the dynamics of wave fronts can still be determined explicitly provided that the wave front is known at initial time and the exact solution is either known a priori, e.g. from experimental or numerical analysis.