Large Wave Numbers Research Articles

Statistics of Travelling Ionospheric Disturbances Observed Using the LOFAR Radio Telescope

A climatology of Travelling Ionospheric Disturbances (TIDs) observed using the LOw Frequency ARray (LOFAR) has been created based on 2,723 hours of astronomical observations. Radio telescopes such as LOFAR must contend with many causes of signal distortions, including the ionosphere. To produce accurate astronomical images, calibration solutions are derived to mitigate these distortions as much as possible. These calibration solutions provide extremely precise measurements of ionospheric variations across the LOFAR network, enabling TIDs to be detected which may be inaccessible to more traditional techniques. Waves are detected by LOFAR under all observing conditions, with no clear dependence on solar or geomagnetic activity. The vast majority of the observed waves travel in the opposite direction to the climatological thermospheric winds, suggesting that they are caused by upward propagating atmospheric gravity waves which are filtered by the wind. Waves of different periods display slightly different propagation directions, with waves of shorter periods consistent with the winds at lower altitudes within the thermosphere ($\SI{180}{\kilo\metre}$ for $10-\SI{15}{\minute}$ periods compared to $\SI{220}{\kilo\metre}$ for $20-\SI{27}{\minute}$ periods). This suggests that either the shorter period waves are being detected at lower altitudes or that they are simply more sensitive to the winds at lower altitudes. This indicates that observations made using LOFAR may enable the investigation of vertical coupling within the neutral atmosphere. The shortest period waves in the dataset ($<\sim\SI{10}{\minute}$) display distinct characteristics, suggesting they may be from a distinct population such as previously reported disturbances in the plasmasphere. The short period waves are compared to previous observations using other radio telescopes, showing that plasmaspheric disturbances likely account for some of the shortest period waves ($<\sim\SI{5}{\min}$) but there are still a large number of waves at these periods which are of uncertain origin.

Mechanisms underlying how free surfaces influence very-large-scale motions in turbulent plane open channel flows based on linear non-modal analysis

Linear non-modal analyses are performed to study the mechanism of how deformable free surfaces influence very-large-scale motions (VLSMs) in turbulent open channel flows. The mean velocity and eddy viscosity profiles obtained from direct numerical simulations are used in the generalised Orr–Sommerfeld and Squire equations to represent background turbulence effects. Solutions of surface-wave eigenmodes and shear eigenmodes are obtained. The results indicate that at high Froude numbers, free surfaces enhance the maximum transient growth rate of VLSMs through surface-wave eigenmodes. We then analyse the energy budget equation to reveal the underlying mechanism. For streamwise-uniform motions, the energy growth rate is enhanced by an energy production term associated with the correlation between the streamwise velocity, which is generated by the lifting-up effect of streamwise vortices composed of shear eigenmodes, and the vertical velocity, which is induced by a spanwise standing wave composed of surface-wave eigenmodes. For streamwise-varying motions, the energy growth rate is enhanced by a standing wave moving with a pair of vortices that travel at a speed approximately equal to the projection of the mean surface velocity along the wavenumber vector direction. Finally, an analytical expression of the energy production term is derived to provide the initial conditions for the maximum transient growth and explain the weak free-surface effect observed at large spanwise wavenumbers and low Froude numbers. The results demonstrate a linear non-modal mechanism in interactions between free surfaces and VLSMs in open channel flows.

Stability of finite-length collapsible channel flow to spanwise perturbations

We consider flow through a finite-length flexible-walled channel formed by removing a portion from one wall of a wide rigid channel and replacing by a pre-tensioned hyperelastic sheet of finite thickness. The flow is driven by a prescribed upstream flow rate which is uniform along the channel inlet, and so with periodic boundary conditions in the transverse direction the system admits a steady state with a wall profile which is deformed in the streamwise direction but spatially uniform in the spanwise direction. Identical to the planar case, this system exhibits two stable static configurations: an upper branch where the flexible wall is mostly inflated and a lower branch where the wall is highly collapsed. We consider the stability of these steady states to spanwise perturbations, showing that both can become unstable to distinct families of self-excited oscillations. In particular, for large spanwise wavenumbers, these steady states are unstable to oscillatory normal modes where the perturbation wall profile has a single oscillating hump in the streamwise direction, not previously seen in collapsible channel flows driven by fixed upstream flux. Furthermore, for sufficiently large wavenumbers and no wall pre-tension in the spanwise direction, this system is always unstable to a new spanwise non-uniform static configuration, which arises due to the merging of a pair of unstable oscillatory normal modes. However, with non-zero spanwise wall pre-tension, there is always a region of parameter space where the spanwise uniform steady state is stable for all wavenumbers.

Core Payload of the Space Gravitational Wave Observatory: Inertial Sensor and Its Critical Technologies.

Since Einstein's prediction regarding the existence of gravitational waves was directly verified by the ground-based detector Advanced LIGO, research on gravitational wave detection has garnered increasing attention. To overcome limitations imposed by ground vibrations and interference at arm's length, a space-based gravitational wave detection initiative was proposed, which focuses on analyzing a large number of waves within the frequency range below 1 Hz. Due to the weak signal intensity, the TMs must move along their geodesic orbit with a residual acceleration less than 10-15 m/s2/Hz1/2. Consequently, the core payload-inertial sensor was designed to shield against stray force noise while maintaining the high-precision motion of the test mass through a drag-free control system, providing an ultra-stable inertial reference for laser interferometry. To meet these requirements, the inertial sensor integrates a series of unit settings and innovative designs, involving numerous subsystems and technologies. This article provides a comprehensive overview of these critical technologies used in the development of inertial sensors for space gravitational wave detection and discusses future trends and potential applications for these sensors.

Integrating structural and seismic properties for enhanced seismic response prediction of building structures via artificial neural network

This study presents a machine learning-based method to predict seismic responses for building structures by integrating structural and seismic properties. In the presented method, seismic intensity measures (SIMs) representing the characteristics of seismic waves are introduced to predict seismic responses. These SIMs include indicators that represent the time domain information, frequency domain information, and energy characteristics of seismic waves, and are used as the inputs of an artificial neural network (ANN) for response prediction. To reflect the structural response characteristics to seismic waves with various frequency properties in the ANN model, the structural properties are also incorporated as the input information in the prediction model. The maximum inter-story drift ratio of the structure is selected as the target seismic response and set as the output of the prediction model. Separate ANN models are built for linear and nonlinear systems, respectively. To train prediction models, datasets are generated via analysis of a large number of seismic waves for numerous linear and nonlinear systems with various characteristics. Then, the prediction performance of ANN models is evaluated using datasets that consist of the SIMs, the structural properties, and the corresponding seismic response. In addition, response prediction performance is comparatively examined according to changes in the types of properties used as the inputs of the prediction model. Furthermore, response prediction performance according to ANN architecture configuration changes is also investigated in detail.

Isotropic tensor fields in amorphous solids: Correlation functions of displacement and strain tensor fields.

Generalizing recent work on isotropic tensor fields in isotropic and achiral condensed matter systems from two to arbitrary dimensions we address both mathematical aspects assuming perfectly isotropic systems and applications focusing on correlation functions of displacement and strain field components in amorphous solids where isotropy may not hold. Various general points are exemplified using simulated polydisperse Lennard-Jones particles. It is shown that the strain components in reciprocal space have essentially a complex circularly symmetric Gaussian distribution albeit weak non-Gaussianity effects become visible for large wave numbers q where also anisotropy effects become relevant. The dynamical strain correlation functions are strongly nonmonotonic with respect to q with a minimum roughly at the breakdown of the continuum limit.

Turbulent cascade arrests and the formation of intermediate-scale condensates.

Energy cascades lie at the heart of the dynamics of turbulent flows. In a recent study of turbulence in fluids with odd viscosity X.M. de Wit et al. [Nature (London) 627, 515 (2024)0028-083610.1038/s41586-024-07074-z], the two dimensionalization of the flow at small scales leads to the arrest of the energy cascade and selection of an intermediate scale, between the forcing and the viscous scales. To demonstrate the generality of the phenomenon and its existence for a wide class of turbulent systems, we study a shell model that is carefully constructed to have three-dimensional turbulent dynamics at small wave numbers and two-dimensional turbulent dynamics at large wave numbers. The large scale separation that we can achieve in our shell model allows us to examine clearly the interplay between these dynamics, which leads to an arrest of the energy cascade at a transitional wave number and an associated accumulation of energy at the same scale. Such pile-up of energy around the transitional wave number is reminiscent of the formation of condensates in two-dimensional turbulence, but, in contrast, it occurs at intermediate wave numbers instead of the smallest wave number.

Box Constraints and Weighted Sparsity Regularization for Identifying Sources in Elliptic PDEs

We explore the possibility for using boundary data to identify sources in elliptic PDEs. Even though the associated forward operator has a large null space, it turns out that box constraints, combined with weighted sparsity regularization, can enable rather accurate recovery of sources with constant magnitude/strength. In addition, for sources with varying strength, the support of the inverse solution will be a subset of the support of the true source. We present both an analysis of the problem and a series of numerical experiments. Our work only addresses discretized problems. The reason for introducing the weighting procedure is that standard (unweighted) sparsity regularization fails to provide adequate results for the source identification task considered in this paper. This investigation is also motivated by applications, e.g. recovering mass distributions from measurements of gravitational fields and inverse scattering. We develop the methodology and the analysis in terms of Euclidean spaces, and our results can therefore be applied to many problems. For example, the results are equally applicable to models involving the screened Poisson equation as to models using the Helmholtz equation, with both large and small wave numbers.

Hydrodynamic energy flux in a many-particle system

In this letter, we demonstrate energy transfers and thermalization in an isolated ensemble of realistic gas particles. We perform a grid-free classical molecular dynamics simulation of two-dimensional Lenard-Jones gas. We start our simulation with a large-scale vortex akin to a hydrodynamic flow and study its non-equilibrium behavior till it attains thermal equilibrium. In the intermediate phases, small wavenumbers (k) exhibit E(k)∝k−3 kinetic energy spectrum, whereas large wavenumbers exhibit E(k)∝k spectrum. Asymptotically, E(k)∝k for the whole range of k, thus indicating thermalization. These results are akin to those of Euler turbulence despite complex collisions and interactions among the particles.

Bayesian inversion of a fractional elliptic system derived from seismic exploration

In this paper, we concentrate on the Bayesian inversion of a dispersion‐dominated fractional Helmholtz (DDFH) equation, which has been introduced in studies concerning seismic exploration. To establish the inversion theory, we meticulously examine the DDFH equation. We transform it into a system comprising both fractional‐ and integer‐order elliptic equations, extending the conventional definition of the spectral fractional Laplace operator to accommodate non‐homogeneous boundary conditions. Subsequently, we establish the well‐posedness theory for scenarios involving both small and large wavenumbers. Our proof hinges upon the regularity attributes of select fractional elliptic equations and capitalizes fully on the structural peculiarities of the elliptic system, which distinguish it from classical cases. Thereafter, we focus on the inverse medium scattering problem pertinent to the DDFH equation, framed within the Bayesian statistical framework. We address two scenarios: one devoid of model reduction errors and another characterized by such errors—arising from the implementation of certain absorbing boundary conditions. More precisely, based on the properties of the forward operator, well‐posedness of the posterior measures have been proved in both cases, which provide an opportunity to quantify the uncertainties of this problem.

Faraday instability of viscous liquid films on a heated substrate with Maxwell–Cattaneo heat flux

Faraday instability of viscous liquid films with Maxwell–Cattaneo (MC) heat flux on an infinite, heated horizontal substrate subject to vertical time-varying periodic vibration is investigated theoretically. The MC effect means that the response of the heat flux to a temperature gradient obeys a relaxation time law rather than a classical Fourier time law. Applying the classic Floquet theory to linear analysis, a recursive relation is obtained. When considering the MC effect, a new phenomenon appears at a large wave number k. The neutral stability curves branch new tongues that turn left rather than right as before, but the tongues still move up and right as the wave number increases. Furthermore, typical harmonic (H) and subharmonic (SH) alternation behavior continues to exist. Interestingly, the first tongue of a branch is H or SH, implying that there is a transition following the branches. However, near the critical wave number kc of a branch, the SH and H almost overlap. As Cattaneo number C increases, the tongue-like unstable zones of branches become wider, and the critical wave number kc of the appeared branch becomes small. As the driving frequency ω decreases, the branch tongues become elongated and the critical wave number kc of the appeared branch becomes small.

A study on the pressure‐driven flow of magnetized non‐Newtonian Casson fluid between two corrugated curved walls of an arbitrary phase difference

AbstractPressure‐driven movement is a fundamental concept with numerous applications in various industries, scientific disciplines, and fields of engineering. Its proper execution is vital for promoting revolutionary innovations and providing solutions in numerous sectors. Therefore, this article scrutinizes the pressure‐driven flow of magnetized Casson fluid between two curved corrugated walls. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity field and volumetric flow rate, taking the corrugation amplitude as the perturbation parameter. The results show that the peak of the velocity increases with the radius of curvature and the width of the channel for a constant pressure gradient. The velocity exhibited a declining trend due to an increase in the Casson fluid parameter. For a sufficiently large corrugation wavenumber, the flow rate decreases, and the phase difference becomes irrelevant. However, the reduction in flow can be minimized by decreasing the channel radius of curvature. In general, a smooth curved channel will give the maximum flow rate for a large corrugation wavenumber. The model can be used to simulate blood flow in arteries with varying geometries and magnetic fields, aiding in the study of cardiovascular diseases and the design of medical devices like stents.

Stability of plane Couette flow under anisotropic superhydrophobic effects

We study the linear stability of plane Couette flow subject to an anisotropic slip boundary condition that models the slip effect of parallel microgrooves with a misalignment about the direction of the wall motion. This boundary condition has been reported to be able to destabilize channel flow far below the critical Reynolds number of the no-slip case. Unlike channel flow, the no-slip plane Couette flow is known to be linearly stable at arbitrary Reynolds numbers. Nevertheless, the results show that the slip can cause linear instability at finite Reynolds numbers also. The misalignment angle of the microgrooves that maximizes the destabilizing effect is nearly π/4, and the unstable modes are of small streamwise wavenumbers and relatively large spanwise wavenumbers. The flow is always more destabilized by two slippery walls compared to a single slippery wall. These observations are in qualitative agreement with the slippery channel flow with the same boundary condition, indicating that such an anisotropic superhydrophobic effect has a rather general destabilizing effect in shear flows regardless of the profile of the base flow. The absence of the Tollmien–Schlichting instability allows us to reveal the inverse relationship between the critical Reynolds number and the slip length as well as the misalignment in the small-parameter regime. The results suggest that arbitrary nonvanishing slip length and misalignment, with arbitrarily weak anisotropy, may suffice to destabilize plane Couette flow.

Theoretical study of short-range exchange interaction based on semiconductor dielectric function model toward time-dependent dielectric density functional theory

This study explores various models of semiconductor dielectric functions, with a specific emphasis on the large wavenumber spectrum and the derivation of the screened exchange interaction. Particularly, we discuss the short-range effect of the screened exchange potential. Our investigation reveals that the short-range effect originating from the high wavenumber spectrum is contingent upon the dielectric constant of the targeted system. To incorporate dielectric-dependent behaviors concerning the short-range aspect into the dielectric density functional theory (DFT) framework, we utilize the local Slater term and the Yukawa-type term, adjusting the ratio between these terms based on the dielectric constant. Additionally, we demonstrate the efficacy of the time-dependent dielectric DFT method in accurately characterizing the electronic structure of excited states in dyes and functional molecules. Several theoretical approaches have incorporated parameters dependent on the system to elucidate short-range exchange interactions. Our theoretical analysis and discussions will be useful for those studies.

Wavenumber-explicit stability and convergence analysis of ℎ𝑝 finite element discretizations of Helmholtz problems in piecewise smooth media

We present a wavenumber-explicit convergence analysis of the h p hp Finite Element Method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber k k . Our analysis covers the heterogeneous Helmholtz equation with Robin, exact Dirichlet-to-Neumann, and second order absorbing boundary conditions, as well as perfectly matched layers.

Properties of X-ray diffraction and Raman scattering in PbSe, PbS and PbS0,5Se0,5 thin films

Structural properties of PbSe, PbS and PbS0.5Se0.5 thin films and mechanisms of combinational scattering of light from phonons were studied by X-ray diffraction and Raman spectroscopy methods. The results of X-ray diffraction show that the crystallite sizes found in the thin layers of the studied substances are in the order of nanometers and vary in the interval d~10.7 ÷ 30.8 nm. It was determined that the scattering bands of the PbSe0.5S0.5 sample with large nanoparticle sizes shift to the region of large wave numbers compared to the scattering bands observed in the region of low wave numbers.

In situ reduction of copper nanoparticles in porous carbonized wood for efficiently enhancing electromagnetic interference shielding performance

In this study, porous carbonized wood was used as the substrate, and a multi-layer composite of copper/carbonized wood/copper (Cu/CW/Cu) layer with light weight, flame retardancy, and efficient electromagnetic shielding effectiveness was prepared by electroless copper method. The results showed that the copper particles can be filled in the layered porous structure of the carbonized wood. The metal Cu layer was evenly covered on the surface of the whole carbonized wood, and the average surface roughness was 7.62 µm. The absorption peak at 2340 cm−1 was significantly enhanced, which proved that the increase of the number of electroless Cu on the carbonized wood surface promoted the improvement of Cu autocatalytic ability. After three depositions of Cu, the conductivity of the composite material reached 1154 S/cm, showing good electrical properties. The shielding effectiveness in the X-band from 8.2 to 12.4 GHz was up to 55.97 dB at low density (0.27 g/cm3). Specific shielding effectiveness SSE/t was as high as 581.69 dB cm2 g−1. Through the “absorption–reflection–absorption” path, high absorption and low reflection are achieved, shielding a large number of incident electromagnetic waves.

The second data release from the European Pulsar Timing Array

The European Pulsar Timing Array (EPTA) and Indian Pulsar Timing Array (InPTA) collaborations have measured a low-frequency common signal in the combination of their second and first data releases, respectively, with the correlation properties of a gravitational wave background (GWB). Such a signal may have its origin in a number of physical processes including a cosmic population of inspiralling supermassive black hole binaries (SMBHBs); inflation, phase transitions, cosmic strings, and tensor mode generation by the non-linear evolution of scalar perturbations in the early Universe; and oscillations of the Galactic potential in the presence of ultra-light dark matter (ULDM). At the current stage of emerging evidence, it is impossible to discriminate among the different origins. Therefore, for this paper, we consider each process separately, and investigated the implications of the signal under the hypothesis that it is generated by that specific process. We find that the signal is consistent with a cosmic population of inspiralling SMBHBs, and its relatively high amplitude can be used to place constraints on binary merger timescales and the SMBH-host galaxy scaling relations. If this origin is confirmed, this would be the first direct evidence that SMBHBs merge in nature, adding an important observational piece to the puzzle of structure formation and galaxy evolution. As for early Universe processes, the measurement would place tight constraints on the cosmic string tension and on the level of turbulence developed by first-order phase transitions. Other processes would require non-standard scenarios, such as a blue-tilted inflationary spectrum or an excess in the primordial spectrum of scalar perturbations at large wavenumbers. Finally, a ULDM origin of the detected signal is disfavoured, which leads to direct constraints on the abundance of ULDM in our Galaxy.

Polytropic spherical astrocosmic fluid stability in the EiBI gravity with strong collective correlative effects

We herein present a dynamical analysis of the Jeans (gravitational) instability in a viscoelastic polytropic astrocloud within the Eddington-inspired Born-Infeld (EiBI) gravity framework in spherical geometry. The zeroth-order material density curvature corrections to the effective self-gravitational potential are properly incorporated. The applied spherical normal mode analysis yields a unique form of monic cubic dispersion relation with multiparametric coefficients dependent on the diverse equilibrium astrofluidic conditions without invoking any kind of traditional quasi-classic approximation. It is seen that the positive EiBI gravity parameter (χ>0) acts as a stabilizing agent and a negative EiBI gravity parameter (χ<0) acts as a destabilizing agent against the inward non-local self-gravity action. Additionally, we find that larger astroclouds are more prone to gravitational collapse, irrespective of the χ-polarity, and vice-versa. It is further investigated that the cloud temperature plays a stabilizing role at larger wavenumbers and destabilizing at smaller wavenumbers for χ>0. However, for χ<0, the fluid temperature consistently exhibits a destabilizing effect. The viscoelastic relaxation time stabilizes the astrofluid against the self-gravity irrespective of the χ-polarity. The fluid density acts as a stabilizer for χ>0, destabilizer for χ<0, and so forth. This study could be potentially applicable in the EiBI-modified gravitational theory in exploring gravity-driven large-scale astrocosmic phenomena towards structure formation mechanism via the canonical Jeans condensation in diverse astrocosmic conditions.

A phase velocity preserving fourth-order finite difference scheme for the Helmholtz equation with variable wavenumber

Numerically solving the Helmholtz equation with large wavenumbers can be challenging due to the highly oscillatory nature of the solution. This paper proposes a 3-point finite difference scheme for numerically solving the 1D Helmholtz equation with variable wavenumber. The proposed scheme preserves the phase velocity, making it well-suited for problems with large wavenumbers. Convergence analysis shows that the proposed scheme is guaranteed to have fourth-order accuracy. Numerical results demonstrate that the proposed scheme maintains high accuracy even for problems with large wavenumbers.