Periodic Wavefronts Research Articles

Mitigation of atmospheric turbulence effect by light beams carrying self-rotating wavefront.

We propose an approach against the turbulence-induced degradation by using laser beam with self-rotating wavefront. Such laser beam, generated by the coherent combination of vortex beams with different helical charges and central angular frequencies, can introduce coupling of its wavefront in spatial and temporal domain, that is, periodic wavefront rotation. When the wavefront rotation is faster than the airflow, the laser beam can travel through the inhomogeneity and anisotropy of air in the azimuthal direction within the time interval of airflow. The wavefront distortion caused by the turbulent atmosphere is therefore rotated and gradually smoothed as the laser beam travels. After the laser propagating through the turbulent atmosphere, the total wavefront distortion becomes centrosymmetric with lower peak-to-valley (PV) value. Such smoothed wavefront distortion can dramatically eliminate the turbulence-induced degradation of laser beams, especially beam centroid drift. We believe that this approach can lead to new trend in remote sensing, free-space optical communication, lidar, etc.

Periodic traveling wavefronts of a multi-type SIS epidemic model with seasonality

This paper is concerned with a time-periodic and nonlocal system arising from the spread of a deterministic epidemic in multi-types of population by incorporating a seasonal variation. The existence of the critical wave speed of the periodic traveling wavefronts and its coincidence with the spreading speed were proved in Wu et al. (J Math Anal Appl 463:111–133, 2018). In this paper, we prove the uniqueness and stability of all non-critical periodic wavefronts. Of particular interest is the influences of time-periodicity on the spreading speed in one-dimensional case. It turns out that, in comparison with the autonomous case, the periodicity of the infection rate increases the spreading speed, while the periodicity of the combined death/emigration/recovery rate for infectious individuals decreases the spreading speed. We also find that the contact distribution increases the spreading speed.

Adapted numerical modelling of the Belousov–Zhabotinsky reaction

Adapted numerical schemes for the integration of differential equations generating periodic wavefronts have reported benefits in terms of accuracy and stability. This work is focused on differential equations modelling chemical phenomena which are characterized by an oscillatory dynamics. The adaptation is carried out through the exponential fitting technique, which is specially suitable to follow the apriori known qualitative behavior of the solution. In particular, we have merged this strategy with the information coming from existing theoretical studies and especially the observation of time series. Numerical tests will be provided to show the effectiveness of this problem-oriented approach.

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction–diffusion problems

In this paper, an adapted numerical scheme for reaction–diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit–explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

Adapted numerical methods for advection–reaction–diffusion problems generating periodic wavefronts

The paper presents an adapted numerical integration for advection–reaction–diffusion problems. The numerical scheme, exploiting the a-priori knowledge of the qualitative behaviour of the solution, gains advantages in terms of efficiency and accuracy with respect to classic schemes already known in literature. The adaptation is here carried out through the so-called trigonometrical fitting technique for the discretization in space, giving rise to a system of ODEs whose vector field contains both stiff and non-stiff terms. Due to this mixed nature of the vector field, an Implicit–Explicit (IMEX) method is here employed for the integration in time, based on the first order forward–backward Euler method. The coefficients of the method here introduced rely on unknown parameters which have to be properly estimated. In this work, such an estimate is performed by minimizing the leading term of the local truncation error. The effectiveness of this problem-oriented approach is shown through a rigorous theoretical analysis and some numerical experiments.

Vortex-antivortex proliferation from an obstacle in thin film ferromagnets

Magnetization dynamics in thin film ferromagnets can be studied using a dispersive hydrodynamic formulation. The equations describing the magnetodynamics map to a compressible fluid with broken Galilean invariance parametrized by the longitudinal spin density and a magnetic analog of the fluid velocity that define spin-density waves. A direct consequence of these equations is the determination of a magnetic Mach number. Micromagnetic simulations reveal nucleation of nonlinear structures from an impenetrable object realized by an applied magnetic field spot or a defect. In this work, micromagnetic simulations demonstrate vortex-antivortex pair nucleation from an obstacle. Their interaction establishes either ordered or irregular vortex-antivortex complexes. Furthermore, when the magnetic Mach number exceeds unity (supersonic flow), a Mach cone and periodic wavefronts are observed, which can be well-described by solutions of the steady, linearized equations. These results are reminiscent of theoretical and experimental observations in Bose-Einstein condensates, and further supports the analogy between the magnetodynamics of a thin film ferromagnet and compressible fluids. The nucleation of nonlinear structures and vortex-antivortex complexes using this approach enables the study of their interactions and effects on the stability of spin-density waves.

Robust path planning by propagating rhythmic spiking activity in a hippocampal network model

It is believed that humans and animals like rodents and bats navigate in a familiar environment using a cognitive map. Yet, how maps are previously learned when exploring a novel environment and then used to plan routes to specific goals remains unclear. We propose here a biologically inspired method, called Multiwave, with two main ingredients: (i) a symmetric spike-timing dependent plasticity rule that compels the connectivity to map the environment, and (ii) periodic wavefronts propagating through the network to direct the agent towards the goal and increase robustness to noise. The modeling involves a detailed neural network for biological plausibility and a simplified equivalent network, better suited for robotic implementation. Using both simulations and robotic experiments, we show the efficiency of Multiwave for path planning. Multiwave is relevant not only to neuroscience, as the detailed model is biologically grounded, but also to robotic applications, as the simplified model is suitable for analog implementation on neuromorphic hardware.

Fractional Fourier transform-based description of the Talbot effect: application to analog signal processing

The Talbot effect, or self-imaging, is a fascinating feature of Fresnel diffraction, where an input periodic wavefront is periodically recovered after specific propagation distances through free space. Interestingly, the Fresnel propagator shows a great similarity to the fractional Fourier transform (FrFT). In this paper, we provide an interpretation of the Talbot effect in the frame of the FrFT and derive simple summation formulas between the FrFT of a function and the function itself. In particular, we show that both the FrFT and the Fourier transform (FT) of any input function can be generated by coherent addition of spatially shifted replicas of the function itself, multiplied by a quadratic phase term. Transposed into the temporal domain, these results may have important applications for real-time analog computation of the FrFT/FT of arbitrary signals.

The impact of the wavelet propagation distribution on SEIRS modeling with delay.

Previous models of disease spread involving delay have used basic SIR (susceptible – infectious – recovery) formulae and approaches. This paper demonstrates how time-varying SEIRS (S – exposed – I – R – S) models can be extended with delay to produce wave propagations that simulate periodic wave fronts of disease spread in the context of population movements. The model also takes into account the natural mortality associated with the disease spread. Understanding the delay of an infectious disease is critical when attempting to predict where and how fast the disease will propagate. We use cellular automata to model the delay and its effect on the spread of infectious diseases where population movement occurs. We illustrate an approach using wavelet transform analysis to understand the impact of the delay on the spread of infectious diseases. The results indicate that including delay provides novel ways to understand the effects of migration and population movement on disease spread.

The James Webb Space Telescope

The James Webb Space Telescope (JWST) is a large (6.6 m), cold (<50 K), infrared (IR)-optimized space observatory that will be launched early in the next decade into orbit around the second Earth–Sun Lagrange point. The observatory will have four instruments: a near-IR camera, a near-IR multiobject spectrograph, and a tunable filter imager will cover the wavelength range, 0.6 < ; < 5.0 μ m, while the mid-IR instrument will do both imaging and spectroscopy from 5.0 < ; < 29 μ m. The JWST science goals are divided into four themes. The key objective of The End of the Dark Ages: First Light and Reionization theme is to identify the first luminous sources to form and to determine the ionization history of the early universe. The key objective of The Assembly of Galaxies theme is to determine how galaxies and the dark matter, gas, stars, metals, morphological structures, and active nuclei within them evolved from the epoch of reionization to the present day. The key objective of The Birth of Stars and Protoplanetary Systems theme is to unravel the birth and early evolution of stars, from infall on to dust-enshrouded protostars to the genesis of planetary systems. The key objective of the Planetary Systems and the Origins of Life theme is to determine the physical and chemical properties of planetary systems including our own, and investigate the potential for the origins of life in those systems. Within these themes and objectives, we have derived representative astronomical observations. To enable these observations, JWST consists of a telescope, an instrument package, a spacecraft, and a sunshield. The telescope consists of 18 beryllium segments, some of which are deployed. The segments will be brought into optical alignment on-orbit through a process of periodic wavefront sensing and control. The instrument package contains the four science instruments and a fine guidance sensor. The spacecraft provides pointing, orbit maintenance, and communications. The sunshield provides passive thermal control. The JWST operations plan is based on that used for previous space observatories, and the majority of JWST observing time will be allocated to the international astronomical community through annual peer-reviewed proposal opportunities.

Design of Talbot array illuminators for three-dimensional intensity distributions

The self-imaging phenomenon is investigated as the basis for designing diffractive optical elements to generate three-dimensional diffraction patterns. The phase-only diffractive element is related to the intensity distribution at a finite and discrete set of Fresnel diffraction planes by use of the matrix formalism of the fractional Talbot effect. This description provides a framework to determine the degrees of freedom which can be exploited for design. It also helps to identify inherent symmetries of periodic wavefronts, which limit the set of intensity patterns that can be implemented. A simulated annealing algorithm is used to exploit the design freedom. Our discussion includes an example to illustrate observations.

Sildenafil-nitric oxide donor combination promotes ventricular tachyarrhythmias in the swine right ventricle.

We tested the hypothesis that sildenafil, singly or in combination with nitric oxide (NO) donors, promotes ventricular tachycardia (VT) and ventricular fibrillation (VF). Vulnerability to VT/VF was tested by rapid pacing in eight isolated normal swine right ventricles (RV). The endocardial activation was optically mapped, and the dynamic action potential duration (APD) restitution curves were constructed with metal microelectrodes. At baseline, no VT/VF could be induced. Sildenafil (0.2 microg/ml) or NO donor singly or in combination did not alter VT/VF vulnerability. However, when 2 microg/ml sildenafil was combined with NO donors, the incidence of VT and VF rose significantly (P < 0.01). VT with a single periodic wavefront was induced in five of eight RVs, and VF with multiple wavefronts was induced in all eight RVs. The sildenafil-NO donor pro-VT/VF combination significantly increased the maximum slope of the APD restitution curve and the amplitude of the APD alternans. The pro-VT/VF effects of sildenafil were reversible after drug-free Tyrode solution perfusion. We conclude that a sildenafil (2 microg/ml) and NO donor combination increases VT/VF vulnerability in the normal RV by a mechanism compatible with the restitution hypothesis.

Image of the Optical Grating Modulated by the Signal and Its Application to the Measurement of Strain Distribution

A treatment is given for obtaining the image from a modulated object in a projection system. A diffraction grating put on the object plane converts the entering plane wavefront from a light source into a periodic wavefront, which gives a carrier wave, and the signal to be projected is given on the carrier as an amplitude, phase, or frequency modulation. The modulated carrier wave forms its spectrum on the entrance pupil of the projection lens. The signal appears as side bands of each carrier spectrum. A narrow opaque mask put on the plane of the spectra acts as a detector, which cuts off some spectral components, and the residual spectra reveal the image of the signal on a screen. A mask whose transmittance varies as a function of position, that is, a frequency selective filter, is used to detect the signal from a frequency-modulated carrier. The method is shown to be useful to analyze the image from an object pattern composed of scanning lines or mesh points, to detect the defects of optical gratings, and to measure the strain distribution of materials under test.