Spatial Waves Research Articles

Dynamic zonation of liver polyploidy.

The liver is a polyploid organ, consisting of hepatocytes with one or two nuclei each containing 2, 4, 8 or more haploid chromosome sets. The dynamic changes in the spatial distributions of polyploid classes across the liver lobule, its repeating anatomical unit, have not been characterized. Identifying these spatial patterns is important for understanding liver homeostatic and regenerative turnover, as well as potential division of labor among ploidy classes. Here, we use single molecule-based tissue imaging to reconstruct the spatial zonation profiles of liver polyploid classes in mice of different ages. We find that liver polyploidy proceeds in spatial waves, advancing more rapidly in the mid-lobule zone compared to the periportal and perivenous zones. We also measure the spatial zonation profiles of S-phase entry at different ages and identify more rapid S-phase entry in the mid-lobule zone at older ages. Our findings reveal fundamental features of liver spatial heterogeneity and highlight their dynamic changes during development and aging.

Light-Induced Waveguides in Nematic Liquid Crystals

Spatial optical solitary waves in media with nonlinear refractive index are self-localized beams as well as waveguides induced by light. We review their guiding features in reorientational birefringent soft matter, namely nematic liquid crystals, for which a highly “nonlocal” response enhances the confinement, stabilization, and robustness of the generated optical solitary waves, termed “nematicons.” The waveguiding properties of the spatial solitons in nematic liquid crystals are illustrated through the confinement of low-power signals and other solitary waves, as well as optical vortices.

Stereo wave imaging from moving vessels: Practical use and applications

Stereo wave imaging of the sea surface elevation has become an effective instrumentation to gather small- and medium-range 3-D wind wave data. Indeed, fruitful applications of stereo techniques have provided new insights into directional wave spectra, space–time distributions of wave maxima, and small-scale wave statistics. So far, however, stereo systems have been deployed mainly on fixed structures (e.g. oceanographic platforms or lighthouses) in order to simplify the installation and maintenance procedures. Nonetheless, advances in stereo calibration and processing suggest that stereo deployments are also feasible onboard moving vessels, thus broadening the impact of these observations on the study of wind waves. In this context, this study aims at discussing how the stereo processing designed to gather reliable wave data from fixed structures should be managed to operate on a moving structure. In particular, estimate of stereo cameras orientation and position with respect to the mean sea plane is of utmost importance. We discuss this aspect by using a synthetic sea state and stereo data collected during an oceanographic campaign onboard a research vessel. Results suggest that, without complementary data sources for ship motion compensation, the sea surface elevation field should include at least about sixteen spatial (2-D) waves to gather a robust estimate of the mean sea plane and consequently realistic wave parameters (e.g. the significant wave height). In this respect, our results provide also insight into the uncertainty of estimates in case of a limited number of 2-D waves is collected by the stereo system. Finally, applications of stereo wave imaging on a moving structure are discussed, with particular emphasis on the collection of space–time wave fields for assessment of numerical models and operational wave observation onboard vessels.

Direct Radiations of Surface Plasmon Polariton Waves by Gradient Groove Depth and Flaring Metal Structure

An efficient method to radiate surface plasmon polaritons (SPPs) directly using metallic corrugated strip with gradient grooves and flaring structure has been proposed, in which the gradient grooves are used to overcome the big mismatch of wavenumbers between SPP modes and radiated spatial waves while the flaring structure provides impedance matching in wide frequency band. Both numerical simulations and measurement results suggest good direct radiation performance of the proposed structure in a wide frequency band from 5 to 20 GHz, in which the measured radiation patterns show a high gain level of 9.9 dBi on average, and the average efficiency can achieve 92%. The proposed direct radiation structure is of great application values in communication systems and integrated circuits.

Dual-channel near-field control by polarizations using isotropic and inhomogeneous metasurface.

We propose a method for dual-channel near-field manipulations by designing isotropic but inhomogeneous metasurfaces. As example, we present a dual-channel near-field focusing metasurface device. When the device is driven by surface waves from different channels on the metasurface, the near fields will be focused at the same spatial point with different polarizations. Conversely, if a linearly polarized source is radiated at the spatial focal point, different channels will be evoked on the metasurface controlled by polarization. We fabricated and measured the metasurface device in the microwave frequency. Well agreements between the simulation and measurement results are observed. The proposed method exhibits great flexibility in controlling the surface waves and spatial waves simultaneously. It is expected that the proposed method and dual-channel device will facilitate the manipulation of near electromagnetic or optical waves in different frequency regimes.

Spatial Rogue Waves in Photorefractive Ferroelectrics.

Rogue waves are observed as light propagates in the extreme nonlinear regime that occurs when a photorefractive ferroelectric crystal is undergoing a structural phase transition. The transmitted spatial light distribution contains bright localized spots of anomalously large intensity that follow a signature long-tail statistics that disappears as the nonlinearity is weakened. The isolated wave events form as out-of-equilibrium response and disorder enhance the Kerr-saturated nonlinearity at the critical point. Self-similarity associable to the individual observed filaments and numerical simulations of the generalized nonlinear Schrödinger equation suggests that dynamics of soliton fusions and scale invariance can microscopically play an important role in the observed rogue intensities and statistics.

The rhythms of steady posture: Motor commands as spatially organized oscillation patterns

Beta-band (15–30Hz) oscillations in motor cortex have been implicated in voluntary movement and postural control. Yet the mechanisms linking those oscillations to function remains elusive. Recently, spatial waves of synchronized beta oscillations have been observed in primary and pre-motor cortex during delayed-reaching movements. Here we propose that the motor cortex may exploit differences in the morphological properties of spatial oscillation patterns to encode motor commands. Furthermore, we argue that the descending motor pathways spatially filter those patterns to selectively shape the motor drive to the muscles. The ensuing motor drive need not be overtly rhythmic despite the oscillatory nature of the neural coding scheme. We demonstrate this principle using a model of the descending motor system in which oscillatory cortical patterns govern steady postures in a simulated biomechanical joint. The cortex was represented by a sheet of coupled oscillators operating in the beta-band. Lateral inhibition between the oscillators induced spatially synchronized beta waves. The spatial orientation of those waves was governed by the dominant direction of lateral inhibition, which we manipulated. The descending motor tracts that emanated from the cortex were tuned such that specific muscles responded selectively to cortical waves with a given orientation. A range of steady joint postures could thus be achieved by manipulating the dominant direction of the lateral coupling. The model thereby demonstrates the proposed mechanism by which oscillatory patterns in cortex are translated into steady motor postures. The model also reproduces some oscillatory aspects of motor physiology. In particular, it replicates the general reduction of cortical beta power at the onset of movement and the weak but significant levels of corticomuscular coherence observed during steady motor output.

Quantitative characterization of spurious numerical oscillations in 48 CMIP5 models

AbstractSpurious numerical oscillations (SNOs) (e.g., Gibbs oscillations) can appear as unrealistic spatial waves near discontinuities or sharp gradients in global model fields (e.g., orography) and have been a known problem in global models for decades. Multiple methods of oscillation reduction exist; consequently, the oscillations are presumed small in modern climate models and hence are rarely addressed in recent literature. Here we use two metrics to quantify SNOs in 13 variables from 48 Coupled Model Intercomparison Project Phase 5 models along a Pacific ocean transect near the Andes. Results show that 48% of nonspectral models and 95% of spectral models have at least one variable with SNO amplitude as large as, or greater than, atmospheric interannual variability. The impact of SNOs on climate simulations should be thoroughly evaluated and further efforts to substantially reduce SNOs in climate models are urgently needed.

A method for lowering the level of the backward radiation of a microwave horn radiator

A method for lowering the level of the backward electromagnetic radiation arising at the edge of the output aperture of a microwave horn radiator is proposed and developed. The method is based on excitation of slow surface electromagnetic waves on the exterior side of the aperture edge of the horn radiator and subsequent transformation of these waves into spatial electromagnetic waves traveling in the antiphase with electromagnetic waves of the backward radiation. The method was tested by the example of a pyramidal horn radiator with curvilinear walls of a combined shape. Computer simulation of such a radiator was performed.

Spatial optical solitons in highly nonlocal media

We theoretically investigate the propagation of bright spatial solitary waves in highly nonlocal media possessing radial symmetry in a three-dimensional cylindrical geometry. Focusing on a thermal nonlinearity, modeled by a Poisson equation, we show how the profile of the light-induced waveguide strongly depends on the extension of the nonlinear medium in the propagation direction as compared to the beamwidth. We demonstrate that self-trapped beams undergo oscillations in size, either periodically or aperiodically, depending on the input waist and power. The---usually neglected---role of the longitudinal nonlocality as well as the detrimental effect of absorptive losses are addressed.

A nearshore long-term infragravity wave analysis for open harbours

This study presents a comprehensive methodology for the reanalysis, characterization and propagation of wave bound infragravity waves (1/300Hz to 1/30Hz) in the nearshore. A deep water short wave reanalysis has been modified analytically to include the energy input associated with infragravity waves (full spectrum), through the decomposition and energy balance of the radiation stress of waves in deep water. A hybrid clustering-numerical wave propagation downscaling technique was used, forced by the modified full wave spectra previously obtained, resulting in hourly series of high spatial resolution nearshore ocean waves, including short and bound long waves. The methodology has been applied to the northern coast of Spain and validated by comparing buoy and pressure gauge records in the coast, for short wave (agitation) and infragravity wave (resonance) responses in open harbours, with very satisfactory results.

In-Plane Vibration Response of the Periodic Viaduct on Saturated Soil under Rayleigh Surface Wave

In this study, the in-plane vibration response of the periodic viaduct on saturated soil under Rayleigh surface wave is studied. The Floquet transform method is used to decompose Rayleigh surface wave into a set of spatial harmonic waves. Considering the periodic condition of the viaduct, the wave number domain dynamic response of the periodic viaduct on saturated soil subjected to Rayleigh surface wave excitation is obtained by the transfer matrix method. Then the space domain dynamic response is retrieved by means of the inverse Floquet transform. Numerical results show that when the periodic viaduct is undergoing in-plane vibration, there exist three kinds of characteristic waves corresponding to axial compression, transverse shear, and bending vibration. Furthermore, when the frequency of Rayleigh wave is within the pass band of the periodic viaduct, the disturbance propagates over a very long distance and the attenuation of the wave motion far from the source is determined by the characteristic wave with the smallest attenuation, while the vibration attenuates rapidly and propagates in a short distance when the frequency of excitation source is in the range of band gap of periodic structure.

Drag Reduction in Turbulent Boundary Layers with Half Wave Wall Oscillations

Spatial square waves with positive cycle are used as steady forcing technique to study drag reduction effects on a turbulent boundary layer flow. Pseudospectral method is used for performing direct numerical simulations on very high resolution grids. A smooth step function is employed to prevent Gibbs phenomenon at the sharp discontinuities of a square wave. The idea behind keeping only the positive cycle of the spatial forcing is to reduce the power consumption to boost net power savings. For some spatial frequency of the oscillations with half waves, it is possible to prevent recovery of skin friction back to the reference case values. A set of wall oscillation parameters is numerically simulated to study its effect on the power budget.

Spatial trigger waves: positive feedback gets you a long way.

Trigger waves are a recurring biological phenomenon involved in transmitting information quickly and reliably over large distances. Well-characterized examples include action potentials propagating along the axon of a neuron, calcium waves in various tissues, and mitotic waves in Xenopus eggs. Here we use the FitzHugh-Nagumo model, a simple model inspired by the action potential that is widely used in physics and theoretical biology, to examine different types of trigger waves—spatial switches, pulses, and oscillations—and to show how they arise.

Numerical Algorithm for Computing Acoustic and Vortical Spatial Instability Waves

Local linear stability is often invoked in computational aeroacoustics to predict Mach wave radiation or to prescribe inflow conditions in order to drive turbulent transition in large-eddy simulations. In this work, the governing equations are reformulated for the nonoscillatory part of eigenfunctions. Boundary conditions can thus be explicitly enforced and, moreover, the numerical cost is drastically reduced regardless of the method chosen to solve this problem. An efficient method based on a matrix formulation is proposed in this study. One single, small collocation domain is used, even for computing the stability of supersonic flows. Vortical and acoustic instability waves of supersonic plane jets are briefly revisited to demonstrate the efficiency of this new approach.

Spatial rogue waves in a photorefractive pattern-forming system.

We have experimentally analyzed pattern formation in an optical system composed of a bulk photorefractive crystal subjected to a single optical feedback. In a highly nonlinear regime far above the modulational instability threshold, we are reporting on turbulent spatiotemporal dynamics that leads to rare, intense localized optical peaks. We have proven that the statistics and features of those peaks correspond to the signatures of two-dimensional spatial rogue events. These optical rogue waves occur erratically in space and time and live typically the same amount of time as the response time of the photorefractive material.

Critical travelling waves for general heterogeneous one-dimensional reaction–diffusion equations

This paper investigates time-global wave-like solutions of heterogeneous reaction–diffusion equations: ∂tu−a(x)∂xxu−b(x)∂xu=f(x,u) in R×R, where the coefficients a, ax, axx, 1/a, b, bx and f are only assumed to be measurable and bounded in x∈R and the nonlinearity f is Lipschitz-continuous in u∈[0,1], with f(x,0)=f(x,1)=0 for all x∈R. In this general framework, the notion of spatial transition wave has been introduced by Berestycki and Hamel [4]. Such waves always exist for one-dimensional ignition-type equations [22,27], but not for monostable ones [26]. We introduce in the present paper a new notion of wave-like solutions, called critical travelling waves since their definition relies on a geometrical comparison in the class of time-global solutions trapped between 0 and 1. Critical travelling waves always exist, whatever the nonlinearity of the equation is, are monotonic in time and unique up to normalization. They are spatial transition waves if such waves exist. Moreover, if the equation is of monostable type, for example if b≡0 and f(x,u)=c(x)u(1−u), with infR⁡c>0, then critical travelling waves have minimum least mean speed. If the coefficients are homogeneous/periodic, then we recover the classical notion of planar/pulsating travelling wave. If the heterogeneity of the coefficients is compactly supported, then critical transition waves are either a spatial transition wave with minimal global mean speed or bump-like solutions if spatial transition does not exist. In the bistable framework, the nature of the critical travelling waves depends on the existence of non-trivial steady states. Hence, the notion of critical travelling wave provides a unifying framework to earlier scattered existence results for wave-like solutions. We conclude by proving that in the monostable framework, critical travelling waves attract, in a sense and under additional assumptions, the solution of the Cauchy problem associated with a Heaviside initial datum.

Colloidal solitary waves with temperature dependent compressibility

Spatial solitary waves which form in colloidal suspensions of dielectric nanoparticles are considered. The interactions, or compressibility, of the colloidal particles, is modelled using a series in the particle density, or packing fraction, where the virial, or series, coefficients depend on the type of particle interaction model. Both the theoretical hard disk and sphere repulsive models, and a model with temperature dependent compressibility, are considered. Experimental results show that particle interactions can be temperature dependent and either repulsive or attractive in nature, so we model the second virial coefficient using a physically realistic temperature power law. One- and two-dimensional semi-analytical colloidal solitary wave solutions are found. Trial functions, based on the form of the nonlinear Schrödinger equation soliton, are used, together with averaging, to develop the semi-analytical solutions. When the background packing fraction is low, the one-dimensional solitary waves have three solutions branches (with a bistable regime) while the two-dimensional solitary waves have two solution branches, with a single stable branch. The temperature dependent second virial coefficient results in changes to the solitary wave properties and the parameter space, in which multiple solutions branches occur. An excellent comparison is found between the semi-analytical and numerical solutions.

Surface electromagnetic waves in a metal

Microwave surface electromagnetic waves are observed on a plane metal/dielectric interface in a frequency range of 0.5–20 GHz. The problem of separation of surface and spatial waves simultaneously excited by a source located on the medium interface is solved.

Propulsion at low Reynolds numbers by multiple traveling waves

Microorganisms or micro-robotic swimmers employ traveling waves as a common swimming mechanism involving time-irreversible deformations of their outer surface. Normally, the deforming surfaces constitute of multiple spatial waves, some standing and others propagating forward or backward. A unique technique is developed here to experimentally decompose a waving surface into its spatial wavelengths in each time instance by processing a sequence of photographs. This information is curve fitted to yield the phase velocity, frequency, and amplitudes of the propagating and receding waves of each component. The significance of the harmonic decomposition is demonstrated using an experimental macro-scale swimmer that utilizes small amplitude circumferential waves. A numerical image processing and curve-fitting procedure is shown and a theoretical model is also developed to account for the hydrodynamic effects of multiple wavelengths. The theoretical results fit well with the experimental data at low speeds, although the contribution of higher harmonics was small in experiment, but the higher harmonics are clearly visible and successfully identified. Still, the importance of the multiharmonics analysis for swimmers, which utilize traveling waves mechanisms, found both in nature and in man-made machines, was formulated and partially verified.