Harmonic Surface Research Articles

Effect of a harmonic surface pressure on wave propagation over a beach

The objective is to study the harmonic forced wave motion over a beach by a finite Fourier transform technique. The constructed approximate solution has a logarithmic singularity at the shoreline. It accounts for reflexion and local perturbations. Trapping of waves may take place for particular choices of the applied surface pressure excess. The case of a wave incident against a cliff with horizontal bottom is solved exactly. The method deals invariably with a variety of bottom shapes, including the case where there is an additional corrugation of the bottom on a finite interval. Other bottom boundary conditions than impermeability can be treated as well. The results may be of interest in several practical applications, in particular the evaluation of the reflected wave. Numerical applications for a plane sloping beach, a parabolic-type beach and a shelf-type beach are presented and the systems of streamlines have been drawn over and in the proximity of the beach.

Three-dimensional numerical simulation of a cylindrical oscillating water column (OWC) device placed in a wave flume

A three-dimensional computational fluid dynamic (CFD) model is developed for simulating a cylindrical Oscillating Water Column (OWC) device for harvesting wave energy. The single-phase CFD model solves the Reynolds-Averaged Navier-Stokes (RANS) equations using the finite element method for simulating the wave motion and uses an aerodynamic model to simulate the flow through the air turbine. The model is implemented to simulate wave energy harvesting of a cylindrical OWC device. Through harmonic decomposition, it is found that the first harmonic wave surface elevation oscillates like a piston in the OWC chamber. However, both the amplitude and phase of the second harmonic wave surface elevation vary significantly along the wave direction in the OWC chamber, demonstrating a sloshing mode of the second harmonic. This study further proved the reduction of the capture width ratio caused by the transverse sloshing mode when the wavelength is the same as the wave flume width. The effect of the width of the wave flume on the peak CWR is found to be negligibly small when the wave flume width is three times the OWC diameter.

A Weierstrass Representation Formula for Discrete Harmonic Surfaces

A discrete harmonic surface is a trivalent graph which satisfies the balancing condition in the 3-dimensional Euclidean space and achieves energy minimizing under local deformations. Given a topological trivalent graph, a holomorphic function, and an associated discrete holomorphic quadratic form, a version of the Weierstrass representation formula for discrete harmonic surfaces in the 3-dimensional Euclidean space is proposed. By using the formula, a smooth converging sequence of discrete harmonic surfaces is constructed, and its limit is a classical minimal surface defined with the same holomorphic data. As an application, we have a discrete approximation of the Enneper surface.

Excitation of third harmonic terahertz surface plasmon over a rippled graphene-free space interface

We examined the third harmonic (TH) terahertz (THz) surface plasmon waves (SPWs) generation over a graphene surface deposited on a rippled dielectric substrate (SiO2) by obliquely incidenting a p-polarized laser beam on a graphene surface with frequency ω0 and wave numbers k0x and k0z at an incident angle θ. Laser beam exerts ponderomotive force on free electrons of the graphene surface and produce nonlinear second harmonic (SH) oscillatory velocity v→2ω0 at frequency 2ω0. SH oscillatory velocity couples with perturbed ripple electron density to produce TH nonlinear current density J→3ω0nl at frequency 3ω0. Ripple wave number (q) provides an extra wave number to develop resonant TH THz SPWs at frequency 3ω0 and wave number kz=3k0z+q. The required ripple wave number for the excitation of THz TH SPWs is lower for the higher Fermi energy of the graphene sheet as compared to lower Fermi energy. Graphene sheet’s Fermi energy and angle of incidence laser beam significantly modify the amplitude of TH THz SPWs.

Generation of second harmonic terahertz surface plasmon wave over a rippled graphene surface

Abstract We propose a mechanism for the generation of second harmonic terahertz surface plasmon waves by incident terahertz electromagnetic radiation (ω, k 0) over a graphene surface deposited on the rippled dielectric substrate (SiO2). A p-polarized THz radiation incident obliquely on the graphene surface exerts a nonlinear ponderomotive force on free electrons in the rippled regime. This nonlinear ponderomotive force imparts oscillatory velocity to the electrons at frequency 2ω. Second harmonic oscillatory velocity couples with the modulated electron density and generates a nonlinear current density that drives second harmonic terahertz surface plasmon waves. Rippled surface provides an extra wave number for the phase matching condition to produce resonantly second harmonic at frequency 2ω and wavenumber (2k 0z + q). We examine the tunable response of second harmonic terahertz surface plasmon waves with respect to change in Fermi energy of graphene and laser incident angle. Second harmonic amplitude gets higher values by lowering the Fermi energy (E F) and increasing incident angle.

A new construction for harmonic evolute surfaces of quasi tangent surfaces with quasi frame

In this paper, we study a harmonic evolute surface of quasi tangent surface associated with quasi frame. We construct quasi tangent surface with first and second fundamental forms. Moreover, we determine harmonic evolute surface of quasi tangent surface by using these fundamental forms. Finally, we obtain some new results about these new surfaces.

Hybrid Quantum-Classical Boson Sampling Algorithm for Molecular Vibrationally Resolved Electronic Spectroscopy with Duschinsky Rotation and Anharmonicity.

Using a photonic quantum computer for boson sampling has demonstrated a tremendous advantage over classical supercomputers. It is highly desirable to develop boson sampling algorithms for realistic scientific problems. In this work, we propose a hybrid quantum-classical sampling (HQCS) algorithm to calculate the optical spectrum for complex molecules considering Duschinsky rotation effects and anharmonicity. The classical sum-over-states method for this problem has a computational complexity that exponentially increases with system size. The HQCS algorithm creates an intermediate harmonic potential energy surface (PES) to bridge the initial and final PESs. The magnitude and sign of the overlap between the initial and the intermediate state are estimated by boson sampling and classical algorithms, respectively. The overlap between the intermediate and the final state is efficiently evaluated by classical algorithms. The feasibility of HQCS is demonstrated in calculations of the emission spectrum of a Morse model as well as the pyridine molecule.

Identifying the influence of surface texture waveforms on colors of polished surfaces using an explainable AI approach

An explainable artificial intelligence approach based on consolidating the Local Interpretable and Model-agnostic Explanation (LIME) model outputs was devised to discern the influence of the surface morphology on the colors exhibited by stainless-steel 304 parts polished with a Magnetic Abrasive Finishing (MAF) process. The MAF polishing process was used to create two regions, each appearing either blue or red to the naked eye. The color distribution was microscopically heterogeneous, i.e., some red microscale patches were dispersed in blue regions, and vice versa. The surface morphology was represented in the frequency domain (using a 2D Fourier transform) to capture the harmonic surface patterns, such as the feed and lay marks from the polishing process. A Convolutional Neural Network (CNN) was employed to identify the color of the region from the frequency characteristics of the surface morphology. The CNN was able to predict the observed colors with test accuracies exceeding 99%, suggesting that the frequency characteristics of the surface morphology of the red regions are distinctly different from those of the blue regions. A LIME model was constructed around each small segment within each region of the surface to identify the frequency features that are influential for differentiating between the colors. To deal with the effect of heterogeneity, an algorithm based on the query by experts was used to reconcile the local influences and gather the global explanations of the frequency characteristics that inform the blue versus red regions. We found that the dominant morphological features in the red regions are those that capture the polishing lay patterns underlying surface structure, whereas those in the blue regions capture the non-uniform and high-frequency waveform patterns, such as those result when oxide films form due to the intense polishing conditions.

Microflow multi-layer diffraction optical element processed by hybrid manufacturing technology.

Traditional planar diffractive optical elements (DOEs) are challenged in imaging systems due to diffraction efficiency and chromatic dispersion. In this paper, we have designed a microfluidic diffractive optical element (MFDOE), which is processed by digital micromirror device (DMD) maskless lithography (DMDML) assisted femtosecond laser direct writing (FsLDW). MFDOE is a combination of photoresist-based multi-layer harmonic diffraction surface and liquid, realizing diffraction efficiency of more than 90% in the visible band. And it shows achromatic characteristics in the two bands of 469 nm (±20 nm) and 625 nm (±20 nm). These results show that MFDOE has good imaging performance.

Droplet motion induced by superposition of shear flow and horizontal surface vibration

The directional motion of sessile droplets can be induced by vibration, a shear flow or a combination of both mechanisms. This study investigates the latter case. To be more precise, the influence of superimposed horizontal surface vibration on the critical inflow velocity is analyzed. A rectangular Plexiglas channel is used for the experiments. The harmonic surface vibration is induced in horizontal plane. Two cases of vibration direction superimposed to the incident flow are considered. Case I: the surface vibration acts in the direction of the incident flow. Case II: the surface vibration acts perpendicular to the direction of flow. The working fluids are air flow and droplets made of distilled water. The substrate is polymethylmethacrylate (PMMA), which provides moderate static contact angles (74.4∘ for water). Droplet volumes of 7.8–39.9 μl are used. The frequency and the excitation acceleration are varied. The investigations show that the critical inflow velocity associated with the onset of droplet motion can be significantly reduced by superimposing a harmonic oscillation. A decrease of the critical velocity can be observed for both excitation directions. The decrease is particularly noticeable at surface vibration in the range of the first and third eigenfrequency of the droplet. In contrast, the second and fourth eigenfrequencies only have a weak effect. A strong correlation between the droplet deformation, given by the excitation of the surface vibration and the decrease of the critical inflow velocity can be detected.

Direct observation of ferroelectricity in two-dimensional MoS2

Recent theoretical predictions of ferroelectricity in two-dimensional (2D) van der Waals materials reveal exciting possibilities for their use in scalable low-power electronic devices with polarization-dependent functionalities. These prospects have been further invigorated by the experimental evidence of the polarization response in some transition metal chalcogenides (TMCs)—a group of narrow-band semiconductors and semimetals with a wealth of application potential. Among the TMCs, molybdenum disulfide (MoS2) is known as one of the most promising and robust 2D electronic materials. However, in spite of theoretical predictions, no ferroelectricity has been experimentally detected in MoS2, while the emergence of this property could enhance its potential for electronics applications. Here, we report the experimental observation of a stable room-temperature out-of-plane polarization ordering in 2D MoS2 layers, where polarization switching is realized by mechanical pressure induced by a tip of a scanning probe microscope. Using this approach, we create the bi-domain polarization states, which exhibit different piezoelectric activity, second harmonic generation, surface potential, and conductivity. Ferroelectric MoS2 belongs to the distorted trigonal structural 1T” phase, where a spontaneous polarization is inferred by its P3m1 space-group symmetry and corroborated by theoretical modeling. Experiments on the flipped flakes reveal that the 1T”-MoS2 samples consist of the monolayers with randomly alternating polarization orientation, which form stable but switchable “antipolar” head-to-head or tail-to-tail dipole configurations. Mechanically written domains are remarkably stable facilitating the application of 1T”-MoS2 in flexible memory and electromechanical devices.

HSMA: An O(N) electrostatics package implemented in LAMMPS

We implement two recently developed fast Coulomb solvers, HSMA3D (Zhao et al. (2018) [49]) and HSMA2D (Liang et al. (2020) [50]), into a new user package HSMA for the molecular dynamics simulation engine LAMMPS. The HSMA package is designed for efficient and accurate modeling of electrostatic interactions in 3D and 2D periodic systems with dielectric effects at O(N) cost. The implementation is hybrid MPI and OpenMP parallelized and compatible with existing LAMMPS functionalities. The vectorization technique following AVX512 instructions is adopted for acceleration. To establish the validity of our implementation, we have presented extensive comparisons to the widely used particle-particle particle-mesh (PPPM) algorithm in LAMMPS and other dielectric solvers. With the proper choice of algorithm parameters and parallelization setup, the package enables calculations of electrostatic interactions that is efficient especially for systems with dielectric mismatch. Program summaryProgram Title: HSMACPC Library link to program files:https://doi.org/10.17632/z39zyh573s.1Developer's repository link:https://github.com/LiangJiuyang/HSMA-Harmonic-surface-mapping-algorithm-in-LAMMPSLicensing provisions: GPLv3Programming language: C++Nature of problem: Evaluation of long-range electrostatic interactions for charged system with fully periodic condition or confined by planar dielectric interfaces.Solution method: We implement the Harmonic Surface Mapping algorithm (HSMA), which combines the image-charge method with the harmonic surface mapping and converts the contribution of infinite images into a finite number of surface charges on an auxiliary sphere, into simulation package LAMMPS. The HSMA package works for both fully periodic systems and partially periodic systems with planar dielectric interfaces, achieving truly linear O(N) complexity by employing fast multipole method. Our package can be applied to general all-atom simulations and a broad range of charged complex fluids under dielectric confinement.Additional comments including restrictions and unusual features: Hybrid MPI plus OpenMP parallelization is used in HSMA package for high-performance computing. We provide vector optimization by using the AVX512 instructions and Intel MKL library for further acceleration. The Intel Parallel Studio is required for these techniques.

Key technologies of 18 MeV self-extraction cyclotron

In this work, an 18 MeV self extraction high current cyclotron is designed, which provides a feasible design scheme for the self extraction system. For the main magnet, it is designed by restricting the parameter change of the main magnetic field through “three judgments”. For the self extraction system, the phase space suitable for particle extraction is scanned by injecting the phase space, and the gradient correction magnet is used to increase the acceptance of the extracted beam. For the harmonic coil, through the second harmonic change of the magnetic field, the beam characteristics are analyzed and the position of the harmonic coil is determined. Under the condition of scanning different harmonic coil surface currents, the extraction of the beam is obtained, and then the phase space of the beam is pushed to the acceptance. In order to match the radial dimension and the axial dimension of the target beam and obtain a stronger beam, the magnetic channel of the double structure is selected and the related design idea is given. The final beam size is 30.5 mm × 12.9 mm, the particles that can be extracted account for 82.62% of the successfully accelerated particles.

Second-order perturbation solution and analysis of nonlinear surface waves

The properties of ultrasonic nonlinear surface wave in the quasilinear region are investigated. In this work the governing equation of particle displacement potential is employed for surface wave in isotropic elastic solid with quadratic nonlinearity. Then, the quasilinear solution of the nonlinear surface wave is obtained by the perturbation method, and the absolute nonlinear parameter of the surface wave is derived. Subsequently, the main components of the second harmonic surface wave solution are discussed. A finite element model for the propagating nonlinear surface wave is developed, and simulation results of the nonlinear surface wave displacements agree well with the theoretical solutions, which indicates that the proposed theory is effective. Finally, the properties of wave propagation and the characteristic of the nonlinear parameter for the surface wave are analyzed based on the theoretical solutions. It is found that the second harmonic surface wave consists of cumulative and non-cumulative displacement terms. The cumulative displacement term is related to the self-interaction of the longitudinal wave component of the surface wave. However, its amplitude is larger than that of the pure longitudinal wave when the initial excitation conditions and propagation distances are the same. The nonlinear parameters for surface and longitudinal waves are related to each other, and an explicit relationship is found, which can be determined by the second-order elastic coefficients of the material. The propagation properties of nonlinear surface waves and the measurement method of absolute nonlinear parameters are also discussed, which will benefit the practical application of nonlinear surface waves.

Harmonic Evolute Surface of Tubular Surfaces via B -Darboux Frame in Euclidean 3-Space

In this article, we look at a surface associated with real-valued functions. The surface is known as a harmonic surface, and its unit normal vector and mean curvature have been used to characterize it. We use the Bishop-Darboux frame ( B -Darboux frame) in Euclidean 3-space E 3 to study and explain the geometric characteristics of the harmonic evolute surfaces of tubular surfaces. The characterizations of the harmonic evolute surface’s ϱ and ς parameter curves are evaluated, and then, they are compared. Finally, an example of a tubular surface’s harmonic evolute surface is presented, along with visuals of these surfaces.

The analysis of structural magnetic resonance imaging manifestation of hippocampus based on voxel and spherical harmonic surface morphometry in mesial temporal lobe epilepsy

Objective: To compare the hippocampal volume and local surface morphology changes in patients with mesial temporal lobe (mTLE) using the voxel-based morphometry and spherical harmonic methods respectively. Methods: A total of 66 patients (31 males and 35 females, age range from 17 to 48 (28±8) years) with mTLE and 80 age-and gender-matched controls (38 males and 42 females, age range from 19 to 46 (27±7) years) were retrospectively collected from July 2009 to February 2019 at Jinling hospital.. High resolution structural MRI of the whole brain, three-dimensional T1-weighted data(3DT1) were acquired from each subject. The changes of hippocampal volume and surface morphology were evaluated between mTLE groups and controls for observing the hippocampal atrophy pattern by using voxel-based morphometry and spherical harmonic shape descriptions point distribution model respectively. Pearson correlation analysis was conducted for observing the relationship between the morphological changes of hippocampus and disease duration. Results: Compared with the controls, hippocampal volume on the affected side in patients with mTLE was significantly reduced (Z-score:-1.55±0.57 vs 0.38±0.58, P<0.001) and negatively correlated with disease duration (r=-0.297, P=0.016). Furthermore, surface morphology analysis subtly showed that the atrophy of the affected hippocampus in patients with mTLE mainly located in the head, mesial lateral part and posterior tail of the hippocampus. Their displacement values were negatively correlated with disease duration (r=-0.336, P=0.006) and positively associated with the hippocampal grey matter volume (r=0.336, P=0.006). Conclusions: Voxel-based morphometry analysis reveals a global reduction in hippocampal volume, while the morphological measurement method based on surface shape can describe the local morphological changes of hippocampal atrophy.

Nonlinear ultrasonic testing for evaluation of fracture toughness in 4130 steel

An estimation of plane strain fracture toughness [endif]--&gt; is essential to assess the operational safety of fracture-critical systems; loss of [endif]--&gt;can lead to catastrophic failure. However, it is not possible to quantify [endif]--&gt;in situ; the laboratory testing to determine [endif]--&gt;is destructive. Here, we investigate nonlinear ultrasonic testing as a nondestructive method to evaluate [endif]--&gt;. This is based on a hypothesized correlation between the nonlinear ultrasonic parameters and [endif]--&gt;characteristics of a material given their mutual dependence on microstructure. Using Second Harmonic Generation (SHG), surface and bulk waves are used to measure the (relative) nonlinearity parameter for tempered 4130 steel samples. Coupons made of the same materials are also tested for their [endif]--&gt;characteristics using Charpy V-Notch testing, providing a direct comparison between destructive and nondestructive measures. Our results show correlations between ultrasonic parameters and [endif]--&gt;characteristics of 4130 steel samples, but different relations are observed for bulk and surface waves. The observed differences are possibly due to sample heterogeneity and different wave structures of the two wave modes and should be further investigated. We demonstrate the potential of nonlinear ultrasonic testing for [endif]--&gt;estimation. The ultimate goal is developing a nondestructive method to assess [endif]--&gt; in situ.

Principles of modeling the fluorescence spectral dynamics of dye molecules in solutions

FSDS is Fluorescence Spectral Dynamics Simulator, designed to investigate photoinduced charge transfer and its manifestations in time-resolved fluorescence spectra of a dye in a solvent. The project is implemented in C, using the MPI library. The computer model simulates stationary absorption and fluorescence spectra, as well as the time evolution of population distributions along the solvent reaction coordinate, to calculate spectral dynamics. Excitation and relaxation of intramolecular high-frequency vibrations are described at the quantum level. FSDS can fit the physical parameters of the dyes to experimental data. The dye excitation is consistently described accounting for the finite duration of the pump pulse. The program code implements two evolutionary models: a spin-boson model within the harmonic potential and a stochastic model based on the Smoluchowski diffusion operator for an arbitrary free energy surface. Computer simulation shows the numerical coincidence of the calculations performed in the framework of these models for the harmonic free energy surface. The detail description of the code and numerical schemes are presented. Program summaryProgram Title: Fluorescence Spectral Dynamics Simulator (FSDS)CPC Library link to program files:https://doi.org/10.17632/d39rrrkvhr.1Code Ocean capsule:https://codeocean.com/capsule/6544976Licensing provisions: GPLv3Programming language: CSupplementary material: Sample configuration files, User ManualNature of problem: The time-resolved spectra contain reach information about photochemical processes. However, the chemically important information about separate elementary processes is entangled due to they proceed in parallel. Time-resolved spectra modeling allows extracting information about these processes. The presented program code makes it possible to determine the relaxation characteristics of the solvent and the times of intramolecular relaxation.Solution method: Finite-difference time-domain and Brownian dynamics simulation methods.

Проявления неустойчивости при схлопывании металлических облицовок кумулятивных зарядов и в родственных струйных течениях динамически деформируемых профилированных тел

The paper briefly analyzes a number of published works devoted to cumulative explosion under conditions of the possible development of surface instability of the collapsing liner of a shaped charge. Most studies stated that surface instability was initially initiated by harmonic surface disturbances or disturbances in the parameters of a given load simulating an explosive one. The instability manifested itself in the form of the development of surface disturbances over time; the absence or limited growth was considered as the preservation of the stability of the deformable shell. In addition to the influence of instability on cumulative processes, related jet flows were also investigated. This is the so-called explosive dispersion (dusting), which occurs both under the influence of the interference of shock waves and unloading waves, and in the presence of initial disturbances of the surface shape. The analysis is built within the framework of the phenomenological approach — both the main results of the experiments and their mathematical descriptions were considered, which in most cases were carried out from the positions established in the mechanics of continuous media, as well as with the help of numerical modeling. Based on the results, conclusions were formulated about the reasons and forms of manifestation of surface instability of collapsing metal liners of shaped charges, the nature of the development and parameters of functioning of such charges, as well as about the features and laws of this process.

ON THE HARMONIC EVOLUTE SURFACES OF TUBULAR SURFACES IN EUCLIDEAN 3-SPACE

The aim of this study is to investigate and interpret the geometric properties of the harmonic evolute surfaces of the tubular surfaces in Euclidean 3-space. For this purpose, the harmonic evolute surface is defined by considering the definitions and theorems for the tubular surface constructed in the Euclidean 3-space. The characterizations of the s and ψ parameter curves of the harmonic evolute surface obtained are examined, and then parameter curves of the tubular surface and harmonic evolute surface are compared. Finally, the harmonic evolute surface of a tubular surface is given an example and the graphics of these surfaces are drawn.