Small Wave Numbers Research Articles

Crack detection in ultrahigh-performance concrete using robust principal component analysis and characteristic evaluation in the frequency domain

Studying the crack propagation of ultrahigh-performance concrete (UHPC) helps us understand its mechanical mechanism and assess its structural performance. A novel method for crack separation and its characteristic evaluation was developed in this work. The proposed method introduces robust principal component analysis (RPCA) to decompose a data matrix from video streams stacked into a low-rank matrix and a sparse matrix, in which the sparse matrix represents the crack information. Compared with the cracks in a binary image, the obtained sparse matrix preserves rich crack information that can be used to quantify crack characteristics. The statistical characteristics of the crack area, the major and minor axes of the equivalent ellipse for crack regions, and the power spectral density are investigated and compared continuously. The proposed method is demonstrated by the crack development of UHPC under tensile loading. The analysis results indicate that RPCA can accurately separate cracks from the background. In the frequency domain by performing the Fourier transform of the sparse matrix, cracks are concentrated at small wavenumbers and the magnitude of small wavenumbers increases with an increase in the crack width. The relationship between the crack propagation and the stress–strain is also discussed. This work provides insight into the crack propagation of UHPC and an accumulated crack database for predicting the damage evolution of UHPC.

The effect of side walls on the stability of falling films

We study the influence of side walls on the stability of falling liquid films. We combine a temporal biglobal stability analysis based on the linearised Navier–Stokes equations with experiments measuring the spatial growth rate of sinusoidal waves flowing downstream an inclined channel. Very good agreement was found when comparing the theoretical and experimental results. Strong lateral confinement of the channel stabilises the flow. In the wavenumber-Reynolds number space, the instability region experiences a fragmentation due to selective damping of moderate wavenumbers. For this range of parameters, the three-dimensional confined problem shows several prominent stability modes which are classified into two categories, the well-known Kapitza hydrodynamic instability mode (H-mode) and a new unstable mode, we refer to it as wall-mode (W-mode). The two mode types are stabilised differently, where the H-modes are stabilised at small wavenumbers, while the W-modes experience stabilisation at high wavenumbers, and at sufficiently small channel widths, only the W-mode is observed. The reason behind the unique H-modes stabilisation is that they become analogous to waveguide modes, which can not propagate below a certain cut-off wavenumber. The spatial structure of the eigenmodes experiences significant restructuring at wavenumbers smaller than the most damped wavenumber. The mode switching preserves the spatial symmetry of the unstable mode.

Emergent structural correlations in dense liquids.

The complete quantitative description of the structure of dense and supercooled liquids remains a notoriously difficult problem in statistical physics. Most studies to date focus solely on two-body structural correlations, and only a handful of papers have sought to consider additional three-body correlations. Here, we go beyond the state of the art by extracting many-body static structure factors from molecular dynamics simulations and by deriving accurate approximations up to the six-body structure factor via density functional theory. We find that supercooling manifestly increases four-body correlations, akin to the two- and three-body case. However, at small wave numbers, we observe that the four-point structure of a liquid drastically changes upon supercooling, both qualitatively and quantitatively, which is not the case in two-point structural correlations. This indicates that theories of the structure or dynamics of dense liquids should incorporate many-body correlations beyond the two-particle level to fully capture their intricate behavior.

Sound characteristics of disordered granular disks: effects of contact damping

We investigate numerically the sound properties of disordered dense granular packings in two dimensions. Employing linear equations of motion and excluding contact changes from our simulations, we demonstrate time evolution of sinusoidal standing waves of granular disks. We varied the strength of normal and tangential viscous forces between the disks in contact to explore the dependence of sound characteristics such as dispersion relations, attenuation coefficients, and sound speeds on the contact damping. For small wave numbers, the dispersion relations and sound speeds of acoustic modes are quite insensitive to the damping. However, a small dip in the phase speed of the transverse mode decreases as the viscous force in normal direction increases. In addition, the dispersion relation of the rotational mode differs qualitatively from the theoretical prediction for granular crystals. Therefore, disordered configurations with energy dissipation play a prominent role in sound properties of granular materials. Furthermore, we report how attenuation coefficients depend on the contact damping and quantify how they differ from the prediction of lattice theory. These improved relations, based on our numerical results, can in future be compared to advanced theories and experiments.

Boundary-Layer Disruption and Heat-Transfer Enhancement in Convection Turbulence by Oscillating Deformations of Boundary.

In this Letter, we propose a novel strategy for significantly enhancing the heat transfer in convection turbulence. By introducing a boundary deformation of the standing-wave type, flow modulation can be realized when the amplitude is comparable or larger than the boundary-layer thickness. For a fixed moderate frequency, the entire fluid layer follows the boundary motion at small wave numbers, while only the near-wall regions are affected by the boundary deformation at large wave numbers. The heat-flux enhancement happens for the latter. For a fixed wave number and gradually increasing frequency, the vortical flows inside the wave valleys exhibit nonlinear transition and alter the distribution of boundary heat flux, and the global heat flux increases significantly at large enough frequencies. The current findings suggest that oscillating deformations of boundary can efficiently break the boundary layers, which serves as the bottleneck of global heat transfer, and open a new venue for modulating the convection turbulence.

Role of dual breakwaters and trenches on efficiency of an oscillating water column

In this paper, the effects of double-submerged breakwaters and trenches on the hydrodynamic performance of an oscillating water column (OWC) are investigated. The multi-domain boundary element method is used to tackle the physical problem of wave scattering and radiation from the device. The role of the height of the breakwaters, depth of the trenches, width of the breakwaters and trenches, spacing between the structures, length of the OWC chamber, and other wave and structural parameters is investigated on the efficiency of OWC. The study reveals that there is an oscillating pattern of the efficiency curve in the presence of single or double breakwater/trenches; this pattern is absent when the bottom is flat. Moreover, compared to single or no breakwaters/trenches, the occurrence of full OWC efficiency is higher in the presence of double breakwaters/trenches. Furthermore, the amplitude of the oscillating pattern in the efficiency curve increases with an increase in the height and depth of the breakwaters and trenches, respectively. For some particular wave and structural parameters, zero OWC efficiency occurs nearly k0h=3.4 within 0<k0h<5 (k0 wave number and h water depth). This zero efficiency moves toward small wave numbers as the spacing between OWC and rigid breakwater/trench increases. The radiation conductance of OWC decreases with an increase in the barrier height. The findings outline the structural criteria that can be employed to build and deploy an effective OWC device.

The Extrinsic Enriched Finite Element Method with Appropriate Enrichment Functions for the Helmholtz Equation

The traditional finite element method (FEM) could only provide acceptable numerical solutions for the Helmholtz equation in the relatively small wave number range due to numerical dispersion errors. For the relatively large wave numbers, the corresponding FE solutions are never adequately reliable. With the aim to enhance the numerical performance of the FEM in tackling the Helmholtz equation, in this work an extrinsic enriched FEM (EFEM) is proposed to reduce the inherent numerical dispersion errors in the standard FEM solutions. In this extrinsic EFEM, the standard linear approximation space in the linear FEM is enriched extrinsically by using the polynomial and trigonometric functions. The construction of this enriched approximation space is realized based on the partition of unity concept and the highly oscillating features of the Helmholtz equation in relatively large wave numbers can be effectively captured by the employed specially-designed enrichment functions. A number of typical numerical examples are considered to examine the ability of this extrinsic EFEM to control the dispersion error for solving Helmholtz problems. From the obtained numerical results, it is found that this extrinsic EFEM behaves much better than the standard FEM in suppressing the numerical dispersion effects and could provide much more accurate numerical results. In addition, this extrinsic EFEM also possesses higher convergence rate than the conventional FEM. More importantly, the formulation of this extrinsic EFEM can be formulated quite easily without adding the extra nodes. Therefore, the present extrinsic EFEM can be regarded as a competitive alternative to the traditional finite element approach in dealing with the Helmholtz equation in relatively high frequency ranges.

Synthesis of Ni doped-TiO2 Thin Film Photocatalysts on Glass Surfaces

Thin film of TiO2 modified Ni2+ cationic (Ni doped-TiO2) thin films were synthesized from titanium tetraisopropoxide (TTIP) and Ni(NO3)2.6H2O using the combined sol-gel and dip coating method followed by calcination at 500oC for an hour. This study aims to determine the concentration of Ni2+ and the optimum number of layers for application as self-cleaning. Frontier transform infrared (FTIR) spectrophotometric analysis observed a shift in the vibration absorption peak of Ti-O towards a smaller wave number as an indication that the Ni2+ cationic have incorporated in the TiO2matrix in forming Ni-TiO2. Based on the of x-ray diffraction (XRD) it is known that Ni-TiO2 has anatase crystalline phase with a crystallite size of 149.20 nm. Diffuse reflectance ultraviolet-visible (DRSUV-Vis) spectrophotometry showed a decrease in the bandgap energy (3.2 eV to 2.22 eV). Surface morphological by scanning electron microscopy (SEM) method showed that the addition of polyethylene glycol (PEG) resulted in a more homogeneous distribution of particles than thin films without PEG. The self-cleaning activity of Ni-TiO2 was tested for surface hydrophilic properties by measuring the contact angle of water and oil droplets under visible light illumination.

Experiments on Marangoni spreading – evidence of a new type of interfacial instability

Marangoni spreading on thin films is widely observed in nature and applied in industry. It has serious implications for airway drug delivery, especially in surfactant displacement therapy. This paper reports the results of experimental investigations of a surfactant-laden droplet spreading on films made of more viscous Newtonian fluids as well as on films made of viscoelastic fluids. The experiments used particle seeding, the transmission-speckle method and particle tracking velocimetry (PTV) to determine the deformation of the film–droplet interface and to measure velocity fields. Radially aligned patterns were observed on Newtonian films. Similar patterns, but with much smaller wavenumber, were observed on viscoelastic films in combination with rapid azimuthal variations of the film thickness. The Saffman–Taylor instability at the film–droplet interface explains the formation of patterns on a more viscous Newtonian film, and their onset requires exceeding the critical capillary number. The pattern formation on viscoelastic films is correlated with an instability at the film–droplet–air contact line when the liquid is expelled radially by the spreading droplet. PTV revealed azimuthal variations of the velocity field in the vicinity of the contact line. The observed contact line instability is different from previously reported fingering instabilities of Newtonian thin films. A simple scaling law accounting for the Marangoni-stress-induced elastic shear deformation is proposed to describe the flow field in the patterns formed in the viscoelastic films.

Combining Multi-Dimensional SAR Parameters to Improve RVoG Model for Coniferous Forest Height Inversion Using ALOS-2 Data

This paper considers extinction coefficient changes with height caused by the inhomogeneous distribution of scatterers in heterogeneous forests and uses the InSAR phase center height histogram and Gaussian function to fit the normalized extinction coefficient curve so as to reflect the vertical structure of the heterogeneous forest. Combining polarization decomposition based on the physical model and the PolInSAR parameter inversion method, the ground and volume coherence matrices can be separated based on the polarization characteristics and interference coherence diversity. By combining the new abovementioned parameters, the semi-empirical improved RVoG inversion model can be used to both quantify the effects of temporal decorrelation on coherence and phase errors and avoid the effects of small vertical wavenumbers on the large temporal baseline of spaceborne data. The model provided robust inversion for the height of the coniferous forest and enhanced the parameter estimation of the forest structure. This study addressed the influence of vertical structure differences on the extinction coefficient, though the coherence of the ground and volume in sparse vegetation areas could not be accurately estimated, and the oversensitivity of temporal decorrelation caused by inappropriate vertical wavenumbers. According to this method we used spaceborne L-band ALOS-2 PALSAR data on the Saihanba forest in Hebei Province acquired in 2020 for the purpose of height inversion, with a temporal baseline range of 14–70 days and the vertical wavenumber range of 0.01–0.03 rad/m. The results are further validated using sample data, with R2 reaching 0.67.

Hopf instability of a Rayleigh–Taylor unstable thin film heated from the gas side

A thin liquid film located on the underside of a horizontal solid substrate can be stabilized by the Marangoni effect if the liquid is heated at its free surface. Applying long-wave approximation and projecting the velocity and temperature fields onto a basis of low-order polynomials, we derive a dimension-reduced set of three coupled evolution equations where nonlinearities of both the Navier–Stokes and the heat equation are included. We find that in a certain range of fluid parameters and layer depth, the first bifurcation from the motionless state is oscillatory which sets in with a finite but small wave number. The oscillatory branch is determined using a linear stability analysis of the long-wave model, but also by solving the linearized original hydrodynamic equations. Finally, numerical solutions of the reduced nonlinear model equations in three spatial dimensions are presented.

Chitosan or Cyclodextrin Grafted with Oleic Acid Self-Assemble into Stabilized Polymeric Micelles with Potential of Drug Carriers

Polymeric micelles combining the advantages of biocompatible poly- and oligosaccharides with classical micellar amphiphilic systems represent a promising class of drug carriers. In this work, micelles based on chitosan (or cyclodextrin) and oleic acid with various modification degrees were synthesized-the most optimal grafting degree is 15-30% in terms of CMC. According to NTA data, micelles have a hydrodynamic diameter of the main fraction of 60-100 nm. The inclusion of the antibacterial agents: moxifloxacin or rifampicin in micelles was studied by FTIR spectroscopy and fluorescence spectroscopy using a pyrene label (using monomer-excimer approach). When aromatic molecules are incorporated into micelles, the absorption bands of C-H bonds of the fatty tails of micelles shift towards smaller wavenumbers, indicating a stabilization of the micelles structure, and the microenvironment of the drug molecule changes according to the low frequencies shift and intensity changes in oscillation frequencies of 1450 cm-1 corresponding to aromatic fragment. Loading of moxifloxacin and rifampicin into micelles leads to a change in the fluorescent properties: a shift of the maximum of fluorescence emission to the long-wavelength region and an increase in the fluorescence anisotropy due to a drastic increase in the hydrodynamic volume of the fluorophore-containing rotating fragment. Using the pyrene label, the critical micelle concentrations were determined: from 4 to 30 nM depending on the polymer composition. Micellar systems enhance the effect of the antibiotic by increasing the penetration into bacterial cells and storing the drug in a protective coat. As a part of the supramolecular structure, the antibiotic remains active for more than four days, while in free form, the activity decreases after two days. In pharmacokinetic experiments, in vivo moxifloxacin in micellar systems show 1.7 times more efficiency compared to free form; moreover, two times higher maximal concentration in the blood is achieved. The advantage of polymer micellar systems in comparison with simple cyclodextrins and chitosan, which do not so significantly contribute to the antibacterial and pharmacokinetic parameters, was shown. Thus, polymeric micelles are one of the key approaches to improving the effectiveness of antibacterial drugs and solving the problems of resistant bacterial infections and multidrug resistance.

Microscopic Depictions of Vanishing Shampoo Foam Examined by Time-of-Flight Small-Angle Neutron Scattering

A novel surfactant of N–dodecanoyl–N–(2-hydroxyethyl)–β–alanine (coded as C12–EtOH–βAla) was synthesized by modifying the methyl group of N–dodecanoyl–N–methyl–β–alanine (coded as C12–Me–βAla). Amino-acid-type surfactants (C12–EtOH–βAla and C12–Me–βAla) are more healthy and environmentally friendly compared to sodium dodecyl sulfate (SDS). To investigate the microstructures of these new surfactants, we employed a method of time-of-flight small-angle neutron scattering (TOF SANS) at a pulsed neutron source, Tokai Japan (J–PARC). The advances in TOF SANS enable simultaneous multiscale observations without changing the detector positions, which is usually necessary for SANS at the reactor or small-angle X-ray scattering. We performed in situ and real-time observations of microstructures of collapsing shampoo foam covering over a wide range of length scales from 100 to 0.1 nm. After starting an air pump, we obtained time-resolved SANS from smaller wave number, small-angle scattering attributed to (1) a single bimolecular layer with a disk shape, (2) micelles in a bimolecular layer, and (3) incoherent scattering due to the hydrogen atoms of surfactants. The micelle in the foam film was the same size as the micelle found in the solution before foaming. The film thickness (~27 nm) was stable for a long time (<3600 s), and we simultaneously found a Newton black film of 6 nm thickness at a long time limit (~1000 s). The incoherent scattering obtained with different contrasts using protonated and deuterated water was crucial to determining the water content in the foam film, which was about 10~5 wt%.

A preliminary depth-integrated model for tsunamis propagation including water compressibility and seafloor elasticity

A model for tsunamis propagation is derived by coupling a weakly compressible liquid layer, standing for the ocean, to a viscoelastic solid layer of constant depth, representing the upper layer of the Earth. Below this layer, the Earth is assumed to be perfectly rigid. The resulting equations are averaged over the depth of the water layer for the liquid part and are integrated over the thickness of the solid layer for the solid part. The obtained system of equations is hyperbolic and admits an exact equation of energy conservation. The model is dispersive and includes an elastic branch, an acoustic branch and a gravity branch. The elasticity of the solid layer entails: (1) a reverse dispersion effect i.e. the phase velocity of the gravity branch decreases for small wave numbers if the wave number decreases; (2) an arrival time delay of the tsunami and (3) a leading negative phase i.e. a negative water elevation before the arrival of the main wave. All these effects are absent if the sea floor is assumed to be perfectly rigid. The arrival time delay due to elasticity comes in addition to the delay due to seawater compressibility. These effects are in agreement with previous works on tsunamis propagation. This preliminary model is a promising alternative approach for tsunamis propagation due to its ability to capture the main physical effects with a relatively simple mathematical structure of equations, which is easy to solve numerically.

Triggering of Whistler‐Mode Rising and Falling Tone Emissions in a Homogeneous Magnetic Field

AbstractWe perform a self‐consistent one‐dimensional electromagnetic particle simulation with a uniform magnetic field and open boundaries. The plasma environment consists of cold isotropic electrons, energetic electrons, and immobile ions. The energetic electrons are initialized with a subtracted‐Maxwellian distribution with temperature anisotropy. By oscillating external currents with a constant frequency 0.2 fce, where fce is the electron cyclotron frequency, a whistler‐mode wave is injected as a triggering wave from the center of the simulation system, and we investigated the process of interactions between the triggering wave and energetic electrons. We find that both rising‐tone and falling‐tone emissions are triggered through the formation of an electron hole and an electron hill in the velocity phase space consisting of a parallel velocity and the gyro‐phase angle of the perpendicular velocities. The rising‐tone emission varies from 0.2 fce to 0.4 fce, while the falling‐tone varies from 0.2 fce to 0.15 fce. The generation region of the rising‐tone triggered emission starts near the injection point of the triggering wave and moves upstream generating new subpackets. The generation region of the falling‐tone triggered emission also moves upstream generating new subpackets. The simultaneous formation of the electron hole and hill is identified by separating small and large wavenumber components corresponding to lower and higher frequencies, respectively, by applying the discrete Fourier transformation to the waveforms in space. Based on the simulation results of the whistler‐mode triggered emissions, we conclude that the mechanism of frequency variation of whistler‐mode chorus emissions works even in a uniform magnetic field.

The Oblique Alfvén Ion Beam Instability in the Earth's Ion Foreshock

How ions evolve in the Earth’s ion foreshock is a basic problem in the heliosphere community, and the ion beam instability is usually proposed to be one major mechanism affecting the ion dynamics therein. This work will perform comprehensive analyses of the oblique ion beam instability in the Earth’s ion foreshock. We show that in addition to two well-known parallel instabilities (i.e., the parallel fast-magnetosonic whistler instability and the parallel Alfvén ion cyclotron instability), the oblique Alfvén ion beam (OA/IB) instability can also be triggered by free energy relating to the relative drift dV between the solar wind proton and reflected proton populations. For slow dV (e.g., dV ≲ 2.2V A , where V A denotes the Alfvén speed), it only triggers the OA/IB instability. When dV ≳ 2.2V A , the growth rate in the OA/IB instability can be about 0.6 times the maximum growth rate in parallel instabilities. Moreover, this work finds the existence of two types of OA/IB instabilities. The first one appears at slow dV and in the small wavenumber region at fast dV, and this instability can be described by the cold fluid model. The second one arises in large wavenumber regions at fast dV, and this instability only appears in warm plasmas. Furthermore, through the energy transfer rate method, we propose that the OA/IB instability is driven by the competition among the Landau and cyclotron wave-particle interactions of beam protons, the cyclotron wave-particle interaction of core protons, and the Landau wave-particle interaction of electrons. Because oblique waves can experience significant damping, the importance of the OA/IB instability may be the effective heating of ions in the Earth’s foreshock.

Bendocapillary instability of liquid in a flexible-walled channel

We study the bendocapillary instability of a liquid droplet that part fills a flexible walled channel. Inspired by experiments in which a periodic pattern emerges as droplets of liquid are condensed slowly into deformable microchannels, we develop a mathematical model of this instability. We describe equilibria of the system, and use a combination of numerical methods and asymptotic analysis in the limit of small channel wall deflections, to elucidate the key features of this instability. We find that configurations are unstable to perturbations of sufficiently small wavenumber regardless of parameter values, that the growth rate of the instability is highly sensitive to the volume of liquid in the channel, and that both wetting and non-wetting configurations are susceptible to the instability in the same channel. Insight into novel interfacial instabilities opens the possibility for their control and thus exploitation in processes such as microfabrication.

Long-wavelength electromagnetic waves of surface type in circular metal waveguides partially filled by plasma in presence of an axial static magnetic field

The method of successive approximations is applied to solve the Maxwell equations in cylindrical plasma waveguide geometry for electromagnetic waves with arbitrary azimuthal wave index and small axial wavenumber. The theory of surface flute waves is used as zeroth approximation. This study generalizes previous investigations whose results are utilized for verification of newly obtained conclusions. The influences of several plasma waveguide parameters such as magnitude and sign of the azimuthal wave index, the width of the dielectric layer between a plasma and a waveguide wall and the magnitude of its dielectric constant, the radii of the plasma column and the metal wall, and the external axial static magnetic field on the wave dispersion properties are analyzed.

Effective Hamiltonian for the system of the electromagnetic field and charged particles

A classical system of point charged particles and electromagnetic field is investigated in the general formulation, in which there is no direct interaction of the particles with each other. Particles are assumed to be non-relativistic for research simplicity. The point of view is defended that gauge choice determines the physical picture of processes in the system. The idea of extended gauge, in which scalar φk and longitudinal part Alnk of the vector potentials transform separately for large and small wave numbers, is proposed. Moreover, in the new gauge φk ≠ 0 only when k ≥ k0 and Alnk ≠ 0 only when k ≤ k0 , where k0 is a certain wave number. This greatly simplifies the study of the system dynamics, in which the transversecomponents Atnk of the vector potential are taken into account and do not change at the gauge transformation. Basing on the extended gauge idea, it is established that the system has a massive oscillatory mode described by a transverse potential Atnk and an oscillatory mod described by a longitudinal potential Alnk with the laws of dispersion (ωk2 + ω02 )1/2 і ω0, respectively (ωk = ck is the dispersion law for electromagnetic waves in vacuum, and ω0 is the plasma frequency). These modes can be called electromagnetic and plasma ones. At the same time, effective interaction between charged particles is introduced, which describes the screening effect. A connection of our work with Bohm and Pines investigations related to the presence of plasma modes in a Coulomb system, in which they do not use idea of gauge transformations, is analyzed.

Simulación numérica de la cascada de energía en fluidos turbulentos

Transfer of energy from large to small scales in turbulent flows is described as a flux of energy from small wave numbers to large wave numbers in the spectral representation of the Navier-Stokes equation. The problem of resolving the relevant scales in the flow corresponds in the spectral representation to determining the spectral truncation at large wave numbers. The effective number of degrees of freedom in the flow depends on the Reynolds number and a numerical simulation of the Navier Stokes equation for high Reynolds numbers is impractical without some sort of reduction of the number of degrees of freedom. The shell models are constructed to obey the same conservation laws and symmetries as the Navier Stokes equation as an alternative. In this work we present the Sabra shell model for the study of the energy cascade of turbulence and we will show numerically that the energy dissipation is approximately -1/3 which is in agreement with the theory K41.