Steady-state Wave Research Articles

Tracing shock type with chemical diagnostics

Aims.The physical structure of a shock wave may take a form unique to its shock type, implying that the chemistry of each shock type is unique as well. We aim to investigate the different chemistries of J-type and C-type shocks in order to identify unique molecular tracers of both shock types. We apply these diagnostics to the protostellar outflow L1157 to establish whether the B2 clump could host shocks exhibiting type-specific behaviour. Of particular interest is the L1157-B2 clump, which has been shown to exhibit bright emission in S-bearing species and HNCO.Methods.We simulate, using a parameterised approach, a planar, steady-state J-type shock wave using UCLCHEM. We compute a grid of models using both C-type and J-type shock models to determine the chemical abundance of shock-tracing species as a function of distance through the shock and apply it to the L1157 outflow. We focus on known shock-tracing molecules such as H2O, HCN, and CH3OH.Results.We find that a range of molecules including H2O and HCN have unique behaviour specific to a J-type shock, but that such differences in behaviour are only evident at lowvsand lownH. We find that CH3OH is enhanced by shocks and is a reliable probe of the pre-shock gas density. However, we find no difference between its gas-phase abundance in C-type and J-type shocks. Finally, from our application to L1157, we find that the fractional abundances within the B2 region are consistent with both C-type and J-type shock emission.

Direct electron transfer-type bioelectrocatalysis of FAD-dependent glucose dehydrogenase using porous gold electrodes and enzymatically implanted platinum nanoclusters

The direct electron transfer (DET)-type bioelectrocatalysis of flavin adenine dinucleotide (FAD)-dependent glucose dehydrogenase (GDH) from Aspergillus terreus (AtGDH) was carried out using porous gold (Au) electrodes and enzymatically implanted platinum nanoclusters (PtNCs). The porous Au electrodes were prepared by anodization of planar Au electrodes in a phosphate buffer containing glucose as a reductant. Moreover, PtNCs were generated into AtGDH by an enzymatic reduction of hexachloroplatinate (IV) ion. The modification was confirmed by native polyacrylamide gel electrophoresis and sodium dodecyl sulfate polyacrylamide gel electrophoresis analyses. The AtGDH-adsorbed porous Au electrode showed a DET-type bioelectrocatalytic wave both in the presence and absence of PtNCs; however, the current density with PtNCs (~1 mA cm−2 at 0 V vs. Ag|AgCl|sat. KCl) was considerably higher than that without PtNCs. The kinetic and thermodynamic analysis of the steady-state catalytic wave indicated that inner PtNCs shortened the distance between the catalytic center of AtGDH (=FAD) and the conductive material, and improved the heterogeneous electron transfer kinetics between them.

Transient wave diffraction around cylinders by a novel boundary element method based on Fourier-Laguerre expansions

ABSTRACT A novel boundary element method based on series expansion is developed for wave diffraction by a vertical circular cylinder in the time domain. Unlike traditional potential flow boundary element methods in which velocity potentials are evaluated on each panel, both the velocity potential and its normal derivative are expanded by Laguerre functions in the vertical direction and Fourier series along the circumference of cylinder, respectively. A boundary integral equation is therefore established associated with expansion coefficients in the sense of Galerkin collocation. Free-surface Green function in the time domain is no longer explicitly computed but its integration involving Fourier-Laguerre basis functions on the whole cylindrical surface is evaluated. Incoming waves are transient with wavefronts, which are more general than steady-state plane progressive waves. Results obtained by using the present method are compared with those from existing time-domain analysing method.

Nonlinear Waves at the Interface between a Dielectric and a Topological Insulator

A system of equations for two components of the electric field of a surface wave propagating along the interface between a nonlinear dielectric and topological insulator is derived, based on the dispersion relation for a nonlinear mode. The system is used to show that small disturbances of a steady-state surface wave neither attenuate nor increase over time.

Dynamic stress state around shallow-buried cavity under transient P wave loads in different conditions

The failure of underground structure is always caused by local stress redistribution resulted from transient impact loads. An analytical model is established and solved by using the complex variable function method to illustrate the dynamic stress concentration around a shallow-buried cavity under transient P wave loads. The transient wave response is attained as an integration of steady-state wave response in circular frequency domain. By adopting a Butterworth filter, the jump points in the dynamic stress concentration factor (DSCF) curve which is not in line with the overall trend is filtered out to obtain more reasonable results. The convergence and accuracy of the solutions are verified and discussed in detail. DSCF distributions of high wavenumber incidences differ from that of low wavenumber incidences significantly in amplitudes and distribution patterns. The effects of the cavity depth, incidence angle and position of wave peak on DSCF distributions are illustrated.

On collinear steady-state gravity waves with an infinite number of exact resonances

In this paper, we investigate the nonlinear interaction of two primary progressive waves traveling in the same/opposite direction. Without loss of generality, two cases are considered: waves traveling in the same direction and waves traveling in the opposite direction. There exist an infinite number of resonant wave components in each case, corresponding to an infinite number of singularities in mathematical terms. Resonant wave systems with an infinite number of singularities are rather difficult to solve by means of traditional analytic approaches such as perturbation methods. However, this mathematical obstacle is easily cleared by means of the homotopy analysis method (HAM): the infinite number of singularities can be completely avoided by choosing an appropriate auxiliary linear operator in the frame of the HAM. In this way, we successfully gain steady-state systems with an infinite number of resonant components, consisting of the nonlinear interaction of the two primary waves traveling in the same/opposite direction. In physics, this indicates the general existence of so-called steady-state resonant waves, even in the case of an infinite number of resonant components. In mathematics, it illustrates the validity and potential of the HAM to be applied to rather complicated nonlinear problems that may have an infinite number of singularities.

Analytical solutions for the interfacial viscous capillary-gravity waves due to an oscillating Stokeslet

The fundamental solutions of the Stokes/Oseen equations due to a point force in an unbounded viscous fluid are referred to as the Stokeslet/Oseenlet, for which a systematic derivation are analytically presented here in terms of a uniform expression. By means of integral transforms, the closed-form solutions are explicitly deduced in a formula which involves the Hamiltonian, Hessian, and Laplacian operators, and elementary functions. Secondly, interfacial viscous capillary-gravity waves between two semi-infinite fluids due to oscillating singularities, including a simple source in the upper inviscid fluid and a Stokeslet in the low viscous fluid, were analytically studied by the Laplace-Fourier integral transform and asymptotic analysis. The dynamics responses consist of the transient and steady-state components, which are dealt with by the method of stationary phase and the Cauchy residue theorem, respectively. The transient response is made up of one short capillarity-dominated and one long gravity-dominated wave with the former riding on the latter. The steady-state wave has the same frequency as that of oscillating singularities. Asymptotic solutions for the wave profiles and the exact solution for the wave number are analytically derived, which show the combined effects of fluid viscosity, surface capillarity and an upper layer fluid.

Fundamentals and Applications of Redox Enzyme-functionalized Electrode Reactions

Electrochemical coupling of redox enzyme reactions, called bioelectrocatalysis, has been attracting great attention over the last four decades. It has become an important technology that can be applied to a wide range of bioelectrochemical devices including biosensors, biofuel cells, and bioreactors. This article presents an overview of the basic concepts of steady-state catalytic waves of mediated- and direct electron transfer (DET)-type bioelectrocatalysis. Several equations that can be used for the analysis of steady-state waves are introduced. The analysis may provide important thermodynamic and kinetic parameters that can be used not only for performance evaluation of the devices but also for fundamental research on the enzymes. Important progress made on how to tune electrode surfaces and enzymes for DET-type reactions are presented. Applications to bioelectrochemical devices are also summarized with emphasis on the achievements recorded in our research group.

Structure and phase composition of SHS products in titanium, carbon and aluminum reactive mixtures

The TiC + Al binder metal matrix composites were obtained by self-propagating high-temperature synthesis (SHS) in the reactive powder mixtures of titanium, carbon (carbon black) and aluminum. It was found that a steady-state wave combustion occurs when the aluminum powder content in reactive mixtures does not exceed 50 wt.%. Loose SHS cakes obtained during synthesis were crashed and screened to get lumpy, nearly equlaxial composite powders favorable to good flowability necessary for powder application in cladding and spraying of wear-resistant coatings. The synthesis products were studied by scanning electron microscopy, X-ray diffraction (XRD) and local energy-dispersive X-ray spectroscopy (EDX). It was found that the average size of carbide inclusions in the composite structure depends on the content of thermally inert aluminum powder in the reaction mixtures. The titanium carbide lattice parameter determined by XRD turned out to be slightly below the known values for equiatomic titanium carbide. However, no any dependence of the lattice parameter on the aluminum content in composites was found. TiC inclusions in the composite structure were investigated by EDX spectroscopy. Titanium content in the carbide was close to that in equiatomic titanium carbide. Titanium carbide contains up to 2.5 wt.% aluminum in addition to titanium and carbon. Aluminum dissolution in the carbide lattice can influence the lattice parameter.

Fast Ignition by a Proton Beam and Burning of a DT Cylindrical Shell Target

Edge ignition of a cylindrical shell target by a proton beam with a small mass heating depth of about 0.5 g/cm2 is analyzed for two values of the initial mass density of the DT fuel, $${{\rho }_{0}} \approx 110$$ and 22 g/cm3, and given beam parameters (the intensity $$J \propto {{\rho }_{0}}$$ and impact time $$\Delta {{t}_{{{\text{pr}}}}} \propto \rho _{0}^{{ - 1}}$$ ). By comparing results obtained using different models of heat transfer through the fuel–shell interface, it is shown that application of a strong magnetic field that suppresses heat transfer but does not affect the trajectories of the α-particles produced in the DT reaction reduces the ignition energy by only about 10%. The unsteady detonation wave generated in the course of ignition transforms into a steady-state fast shockless burning wave, in which the cold fuel is heated by α-particles. The wave parameters depend on the deposited energy. As the wave propagates through the fuel, the α-particles escaping from the fuel volume carry away about one-half of their initial power. For one of the simulation versions, the target length H is determined ( $${{\rho }_{0}}H \approx 10$$ g/cm2) at which the gain reaches a value of $$G = 1250$$ . An approximate formula is derived that relates the slope of the pressure profile in a steady-state wave to the wave velocity and the heating power per unit mass of the fuel near the wave front. The applicability of the formulas relating the pressure and velocity at the Chapman–Jouguet point to the propagation velocity of a strong detonation wave is demonstrated.

Application research on surface wave technique in crack depth detection of hydraulic concrete

Crack has a strong influence on the integrity, impermeable property, durability and bearing capacity of hydraulic concrete buildings. Although ultrasound is the main nondestructive testing method of concrete crack depth at present, a large amount of engineering applications demonstrate that it is not suitable for the crack depth detection of the hydraulic structure concrete. This paper illustrated the basic principle of detection of concrete crack depth by surface wave technique and verified the feasibility of surface wave technique to detect crack depth by two engineering examples, including steady-state surface wave method and transient-state surface wave method. The practical results show that surface wave is a rapid and effective nondestructive testing method in the detection of crack depth of concrete, which will have a good application prospect.

On the near resonances of collinear steady-state wave groups in finite water depth

In this paper, the role nearly resonant components play in collinear steady-state wave groups in finite water depth is investigated theoretically. Fully nonlinear water wave equations are solved when the resonance conditions are nearly satisfied. Convergent solutions are obtained for steady-state wave groups with multiple near resonances. Spectra analysis shows that, as water depth decreases from deep water to finite water depth, the four-wave nearly resonant interactions play a dominant role in nonlinear steady-state wave groups. Meanwhile the dispersion relation changes with the water depth and some low and high frequency components appear in the spectrum due to the three-wave nearly resonant interactions. Comparison between the linear and nonlinear wave groups are made in finite water depth when the mean rates of mass, momentum and energy fluxes are almost conserved. It is found that wave energy in nonlinear wave groups is redistributed as more components join the resonance when the nonlinearity increases. Besides, both the wave group steepness and magnitude of water particle horizontal velocities near the crests and troughs in nonlinear wave groups increase more rapidly with the nonlinearity. The significance of near resonances in finite water depth for collinear steady-state wave groups is demonstrated.

An optimized, parameter-free PML-FEM for wave scattering problems in the ocean and coastal environment

Water-wave propagation in nearshore regions and hydroacoustic scattering problems, in the presence of structures, are fundamental to ocean and coastal engineering. Efficient modelling of these phenomena can be achieved using the Helmholtz equation with spatially varying coefficients to which mild-slope models are reducible. Despite the relatively simple forms of these models, geometric and medium inhomogeneities and inclusions, yield complex wavefield solutions that can only be numerically approximated. However, the numerical treatment of such problems in infinite domains requires the truncation of the computational region. In this work, an optimal, parameter-free Perfectly Matched Layer (PML) model is implemented in a Finite Element scheme. The fundamental similarities between the governing equations for steady-state water wave and hydroacoustic scattering problems allow for a joint analysis of the proposed PML-FEM solution strategy. Excellent convergence characteristics are verified through comparisons against benchmark solutions. Water-wave propagation solutions for an uneven seabed featuring an elliptic shoal are compared with available experimental data. Also, wave diffraction by vertical cylinders in regions of variable bathymetry, and scattering by an elliptically shaped body in the ocean-acoustic waveguide, are studied. The proposed numerical scheme is found to be an efficient means to tackle challenging wave-seabed-body interaction problems in large spatial domains.

Finite-amplitude steady-state wave groups with multiple near-resonances in finite water depth

Finite-amplitude wave groups with multiple near-resonances are investigated to extend the existing results due to Liu et al. (J. Fluid Mech., vol. 835, 2018, pp. 624–653) from steady-state wave groups in deep water to steady-state wave groups in finite water depth. The slow convergence rate of the series solution in the homotopy analysis method and extra unpredictable high-frequency components in finite water depth make it hard to obtain finite-amplitude wave groups accurately. To overcome these difficulties, a solution procedure that combines the homotopy analysis method-based analytical approach and Galerkin method-based numerical approaches has been used. For weakly nonlinear wave groups, the continuum of steady-state resonance from deep water to finite water depth is established. As nonlinearity increases, the frequency bands broaden and more steady-state wave groups are obtained. Finite-amplitude wave groups with steepness no less than $0.20$ are obtained and the resonant sets configuration of steady-state wave groups are analysed in different water depths. For waves in deep water, the majority of non-trivial components appear around the primary ones due to four-wave, six-wave, eight-wave or even ten-wave resonant interactions. The dominant role of four-wave resonant interactions for steady-state wave groups in deep water is demonstrated. For waves in finite water depth, additional non-trivial high-frequency components appear in the spectra due to three-wave, four-wave, five-wave or even six-wave resonant interactions with the components around the primary ones. The amplitude of these high-frequency components increases further as the water depth decreases. Resonances composed by components only around the primary ones are suppressed while resonances composed by components around the primary ones and from the high-frequency domain are enhanced. The spectrum of steady-state resonant wave groups changes with the water depth and the significant role of three-wave resonant interactions in finite water depth is demonstrated.

An inviscid analysis of the Prandtl azimuthal mass transport during swirl-type sloshing

An inviscid analytical theory of a slow steady liquid mass rotation during the swirl-type sloshing in a vertical circular cylindrical tank with a fairly deep depth is proposed by utilising the asymptotic steady-state wave solution by Faltinsen et al. (J. Fluid Mech., vol. 804, 2016, pp. 608–645). The tank performs a periodic horizontal motion with the forcing frequency close to the lowest natural sloshing frequency. The azimuthal mass transport (first observed in experiments by Prandtl (Z. Angew. Math. Mech., vol. 29(1/2), 1949, pp. 8–9)) is associated with the summarised effect of a vortical Eulerian-mean flow, which, as we show, is governed by the inviscid Craik–Leibovich equation, and an azimuthal non-Eulerian mean. Suggesting the mass-transport velocity tends to zero when approaching the vertical wall (supported by existing experiments) leads to a unique non-trivial solution of the Craik–Leibovich boundary problem and, thereby, gives an analytical expression for the summarised mass-transport velocity within the framework of the inviscid hydrodynamic model. The analytical solution is validated by comparing it with suitable experimental data.

Вимушені усталені коливання рідини в баці з квадратним перерізом

The paper conducts a series of analytical studies on the resonant steady-state sloshing in a rigid square base container, which have been originated by Faltinsen & Timokha who derived and applied the Narimanov-Moiseev—type nonlinear modal equations for investigation in the sloshing problem. The modal equations, which consist on nine-dimensional system of ordinary differential equations, should be applicable for sway/pitch/surge/roll periodic excitations but, due to, basically, mathematical difficulties, the previous papers exclusively concentrated on the reciprocating (longitudinal, oblique and diagonal) motions of the container. This article is showed that the steady-state waves caused by this kind of forcing are asymptotically identical to those occurring when the tank performs horizontal orbital motions. We generalize the previous results by Faltinsen & Timokha to classify the steady-state wave regimes versus the semi-axes ratio of the forcing ellipse in the tank which is filled by a liquid with a finite depth.

МОДЕЛИРОВАНИЕ УПРУГОПЛАСТИЧЕСКОГО ДЕФОРМИРОВАНИЯ ЭЛЕМЕНТОВ ПРОСТРАНСТВЕННЫХ КОНСТРУКЦИЙ ПРИ ИМПУЛЬСНОМ ВЗАИМОДЕЙСТВИИ С ЖИДКОСТЬЮ НА ОСНОВЕ МЕТОДА ГОДУНОВА ПОВЫШЕННОЙ ТОЧНОСТИ

The spatial problem of internal explosive loading of an elastoplastic cylindrical container filled with water in Eulerian - Lagrangian variables using multigrid algorithms is considered. A defining system of three-dimensional equations of the dynamics of gas, fluid, and elastoplastic medium is presented. For numerical modeling, a modification of S.K. Godunov scheme of the increased accuracy for both detonation products and liquids, and elastoplastic container is used. At the moving contact boundaries “detonation products - liquid”, “liquid - deformable body”, the exact solution of the Riemann's problem is used. A time dependent model is used to describe the propagation of steady-state detonation wave through an explosive from an initiation region. In both cases, the initiation of detonation occurs at the center of the charge. Two problems have been solved: the first task for the aisymmetric position of the charge, the second for the charge shifted relative to the axis of symmetry. In the first task, the processes are two-dimensional axisymmetric in nature, in the second task, the processes are essentially three-dimensional. A comparison is made of the results of calculations of the first problem using a three-dimensional method with a solution using a previously developed two-dimensional axisymmetric method and experimental data. Good agreement is observed between the numerical results for the maximum velocities and circumferential strains obtained by various methods and experimental data. There is good agreement between the numerical results obtained by various methods and the known experimental data. Comparison of the results of solving the first and second problems shows a significant effect of the position of the charge on the wave processes in the liquid, the processes of loading the container and its elastoplastic deformation. The dynamic behavior of a gas bubble with detonation products is analyzed. A significant deviation of the bubble shape from the spherical one, caused by the action of shock waves reflected from the structure, is shown. Comparison of the results of solving the first and second problems showed a significant effect of the charge position on wave processes in a liquid, the processes of loading a container and its elastoplastic deformation. In particular, in the second problem, shock waves of higher amplitude are observed in the liquid when reflected from the walls of the container.

МОДЕЛИРОВАНИЕ УПРУГОПЛАСТИЧЕСКОГО ДЕФОРМИРОВАНИЯ ЭЛЕМЕНТОВ ПРОСТРАНСТВЕННЫХ КОНСТРУКЦИЙ ПРИ ИМПУЛЬСНОМ ВЗАИМОДЕЙСТВИИ С ЖИДКОСТЬЮ НА ОСНОВЕ МЕТОДА ГОДУНОВА ПОВЫШЕННОЙ ТОЧНОСТИ

The spatial problem of internal explosive loading of an elastoplastic cylindrical container filled with water in Eulerian - Lagrangian variables using multigrid algorithms is considered. A defining system of three-dimensional equations of the dynamics of gas, fluid, and elastoplastic medium is presented. For numerical modeling, a modification of S.K. Godunov scheme of the increased accuracy for both detonation products and liquids, and elastoplastic container is used. At the moving contact boundaries “detonation products - liquid”, “liquid - deformable body”, the exact solution of the Riemann's problem is used. A time dependent model is used to describe the propagation of steady-state detonation wave through an explosive from an initiation region. In both cases, the initiation of detonation occurs at the center of the charge. Two problems have been solved: the first task for the aisymmetric position of the charge, the second for the charge shifted relative to the axis of symmetry. In the first task, the processes are two-dimensional axisymmetric in nature, in the second task, the processes are essentially three-dimensional. A comparison is made of the results of calculations of the first problem using a three-dimensional method with a solution using a previously developed two-dimensional axisymmetric method and experimental data. Good agreement is observed between the numerical results for the maximum velocities and circumferential strains obtained by various methods and experimental data. There is good agreement between the numerical results obtained by various methods and the known experimental data. Comparison of the results of solving the first and second problems shows a significant effect of the position of the charge on the wave processes in the liquid, the processes of loading the container and its elastoplastic deformation. The dynamic behavior of a gas bubble with detonation products is analyzed. A significant deviation of the bubble shape from the spherical one, caused by the action of shock waves reflected from the structure, is shown. Comparison of the results of solving the first and second problems showed a significant effect of the charge position on wave processes in a liquid, the processes of loading a container and its elastoplastic deformation. In particular, in the second problem, shock waves of higher amplitude are observed in the liquid when reflected from the walls of the container.

Applying dynamically updated nearshore bathymetry estimates to operational nearshore wave modeling

Abstract: Simulations of nearshore waves using the Steady-State Spectral Wave (STWAVE) Model with temporally-varying bathymetric boundary conditions were undertaken for a period of 11 months at the U.S. Army Corps of Engineers Field Research Facility in Duck, NC. Five sets of bathymetry were tested, two of which were derived from survey data (one evolving with each monthly bathymetric survey, one static) and three were derived from the depth inversion algorithm, cBathy, using Argus optical imagery data updated every half hour. The standard cBathy half-hourly Kalman filtered product was used along with two modified versions that filter depth estimates during large waves prior to being assimilated by the Kalman filter using an offshore wave height threshold or an optically derived wave breaking threshold to reduce bottom boundary condition errors. Bathymetry derived from the modified Kalman filter methods were first validated using continuous in-situ sonic altimeter data, and were found to improve RMSEs relative to the original cBathy bathymetry from an average of about 0.09 m and about 0.15 m offshore and onshore of the sandbar, respectively. Wave model results over the five bathymetric boundary conditions show that the thresholded cBathy bathymetry performs similarly (and slightly better in places) to simulations using an evolving bathymetry as new measurements are available. The wave height predictions using the static bathymetry were approximately equivalent in performance (if not, slightly better in places) to that of the original cBathy, while the evolving surveyed bathymetry had similar performance to the thresholded cBathy method.

Improved direct electron transfer-type bioelectrocatalysis of bilirubin oxidase using thiol-modified gold nanoparticles on mesoporous carbon electrode

Ketjen Black (KB), a mesoporous carbon material, was modified with gold nanoparticles (AuNPs) and 4-mercaptobenzoic acid (MBA). The MBA/AuNP-modified KB was utilized as an effective scaffold for the direct electron transfer (DET)-type bioelectrocatalytic reduction of dioxygen by bilirubin oxidase from Myrothecium verrucaria (BOD). Owing to the MBA/AuNP modification, the limiting current density of the steady-state catalytic wave was doubled and the half-wave potential of the catalytic wave was shifted to the positive direction by 140mV. The kinetic analysis of the steady-state catalytic wave indicated that the modification narrowed the orientation distribution of the adsorbed BOD and shortened the mean length between the redox copper site of BOD and the electrode surface. The electrostatic attraction and π–π interactions between BOD and MBA are likely responsible for the favorable orientation of the enzyme.