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1.
This study focuses on the prediction of the porosity of nonuniform sediment mixtures,considering the effects of particle packing.A random particle packing model has been developed for the porosity of bimodal mixtures by extending the existing random particle filling theory.Coefficients in the developed model are calibrated by fitting the model to measured data for a variety of bimodal mixtures,including spherical glass particles,rounded quarry grains,and natural sediments.The model coefficients ...  相似文献   

2.
During an explosive volcanic eruption, tephra fall out from the umbrella region of the eruption cloud to the ground surface. We investigated the effect of the intensity of turbulence in the umbrella cloud on dispersion and sedimentation of tephra by performing a series of laboratory experiments and three dimensional (3-D) numerical simulations. In the laboratory experiments, spherical glass-bead particles are mixed in stirred water with various intensities of turbulence, and the spatial distribution and the temporal evolution of the particle concentration are measured. The experimental results show that, when the root-mean-square of velocity fluctuation in the fluid (Wrms) is much greater than the particle terminal velocity (vt), the particles are homogeneously distributed in the fluid, and settle at their terminal velocities at the base of the fluid where turbulence diminishes. On the other hand, when Wrms is as small as or smaller than vt, the particle concentration increases toward the base of the fluid during settling, which substantially increases the rate of particle settling. The results of the 3-D simulations of eruption cloud indicate that Wrms is up to 40 m/s in most of the umbrella cloud even during a large scale plinian eruption with a magma discharge rate of 109 kg/s. These results suggest that relatively coarse pyroclasts (more than a few mm in diameter) tend to concentrate around the base of the umbrella cloud, whereas fine pyroclasts (less than 1/8 mm in diameter) may be distributed homogeneously throughout the umbrella cloud during tephra dispersion. The effect of the gradient of particle concentration in the umbrella cloud explains the granulometric data of the Pinatubo 1991 plinian deposits.  相似文献   

3.
The dependency on relative humidity of the settling velocity of aerosol particles in stagnant air and of the diffusion coefficient due to Brownian motion of aerosol particles was computed for six aerosol types and different particles sizes in dry state. The computations are based (1) on mean bulk densities of dry aerosol particles obtained from measurements or from the knowledge of the chemical composition of the particles, (2) on micro-balance measurements of the water uptake per unit mass of dry aerosol substance versus water activity at thermodynamic equilibrium, and (3) on measurements of the equilibrium water activity of aqueous sea salt solutions. The results show a significant dependence of the settling velocity and Brownian diffusion of aerosol particles on relative humidity and on the particle's chemical composition.Nomenclature A surface parameter of a particle - B surface parameter of a particle - c L velocity of sound in moist air - C 1+Kn[A+Qexp(–B/Kn]=slip correction - D diffusion coefficient of a particle - D 1 D(=1)=diffusion coefficient of a spherical particle - f P w /P we (T,P)=relative humidity (f=0 dry air,f=1 saturated air) - g acceleration due to gravity - g |g| - k 1.3804×10–16 erg/°K=Boltzmann constant - Kn L /r=Knudsen number of a particle - Kn 0 0L /r 0=Knudsen number of a dry particle - m 4r 3/3=mass of a particle - m L 4r 3 L /3=mass of the moist air displaced by a particle - M mobility of a particle - M 0 molar mass of dry air - M w molar mass of water - Ma |u–u L |/c L =Mach number of the particles motion relative to the ambient air - n particle number per unit volume of air - P P 0+P w =pressure of the moist air - P 0 partial pressure of the dry air - P w partial pressure of the water vapour - P we P we (T,P)=equilibrium partial water vapour pressure over a plane surface of water saturated with air - Q surface parameter of a particle - r equivalent radius of a particle (radius of a sphere with the particles volume) - r 0 equivalent radius of a particle in dry state - R 1+0.13Re 0.85=inertia correction - R 0 specific gas constant of dry air - R w specific gas constant of water - Re 2r L uu L / L =Reynolds number of the particles motion relative to the ambient air - t time - T absolute temperature - u velocity of a particle - u (amount of the) settling velocity of a particle in stagnant air - u 1 u(=1)=(amount of the) settling velocity of a spherical particle in stagnant air - u L velocity of the ambient moist air (far enough from the particle where the flow pattern remains undistorted) - W drag coefficient of a particles equivalent sphere - empirical parameter in equation (3.1) - dynamic viscosity of a particles liquid cover - L dynamic viscosity of moist air - 0L dynamic viscosity of dry air (at the same pressure and temperature like the moist air) - celsius temperature - dynamic shape factor of a particle (=1 for a sphere) - 0 dynamic shape factor of a dry particle - L mean free path of the molecules in moist air - 0L mean free path of the molecules in dry air (at the same pressure and temperature like the moist air) - Po mean free path of the molecules in dry air at the pressureP 0 of the dry air and the temperature given - factor of solid to liquid change-over (=1 for a solid particle) - mean bulk density of a particle - L density of the moist air - 0L density of the dry air at the same pressure and temperature like the moist air - 0 mean bulk density of a dry particle - 0 mean diameter of the molecules of dry air - w diameter of water molecules - relaxation time of a particle - gradient operation - 3.141593  相似文献   

4.
Single bed load particle impacts were experimentally investigated in supercritical open channel flow over a fixed planar bed of low relative roughness height simulating high‐gradient non‐alluvial mountain streams as well as hydraulic structures. Particle impact characteristics (impact velocity, impact angle, Stokes number, restitution and dynamic friction coefficients) were determined for a wide range of hydraulic parameters and particle properties. Particle impact velocity scaled with the particle velocity, and the vertical particle impact velocity increased with excess transport stage. Particle impact and rebound angles were low and decreased with transport stage. Analysis of the particle impacts with the bed revealed almost no viscous damping effects with high normal restitution coefficients exceeding unity. The normal and resultant Stokes numbers were high and above critical thresholds for viscous damping. These results are attributed to the coherent turbulent structures near the wall region, i.e. bursting motion with ejection and sweep events responsible for turbulence generation and particle transport. The tangential restitution coefficients were slightly below unity and the dynamic friction coefficients were lower than for alluvial bed data, revealing that only a small amount of horizontal energy was transferred to the bed. The abrasion prediction model formed by Sklar and Dietrich in 2004 was revised based on the new equations on vertical impact velocity and hop length covering various bed configurations. The abrasion coefficient kv was found to be vary around kv ~ 105 for hard materials (tensile strength ft > 1 MPa), one order of magnitude lower than the value assumed so far for Sklar and Dietrich's model. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

5.
Fluvial suspended sediment typically consists of a variety of complex, composite particles referred to as flocs. Floc characteristics are determined by factors such as the source, size and geochemical properties of the primary particles, chemical and biological coagulation processes in the water column and shear stress and turbulence levels in the stream. Studies of floc morphology have used two contrasting methods of sampling and analysis. In the first method, particles settle on a microscope slide and are observed from below using an inverted microscope. The second method uses filtration at no or low vacuum and particles deposited on the filter are observed with a microscope. Floc morphology can be quantified using fractal dimensions. The aims of the present study were to examine the effect of the two sampling methods on the fractal dimensions of particle populations, and to evaluate for each method how well the fractal dimensions at the various sampling sites reflect basin conditions. Suspended solids were collected in triplicate on inverted microscope slides and on 0·45 μm Millipore HA filters in two southern Ontario streams with contrasting riparian zones during a minor runoff event resulting from the melt of a freshly fallen snowpack. An image analysis system was used to determine area, longest axis and perimeter of particles. The morphology of the particle population of each sample was characterized using four fractal dimensions (D, D1, D2 and DK). Systematic differences in fractal dimensions obtained with the two methods were observed. For the settling method, outlines of larger particles were frequently blurred because of the distance between the focal plane (the top of the inverted microscope slides) and the plane of the particle outline. In this method, the blurring of large particles can cause an increase in the projected area and length of the particle. The effect on the particle perimeter is unpredictable because it depends on the amount of detail lost through blurring and its effect on the apparent increase in particle size. Because of blurring, D and D1 tend to be systematically lower for the settling method, whereas the net effect on D2 is unpredictable. Particle size distributions derived from settling are typically coarser because small, low density particles may remain in the water column and all particles may not deposit on the slides. This loss of fines results in systematically lower DK values for the settling method compared with the filtration method. Fractal dimensions and particle size distributions obtained with the filtration method were sensitive to and clearly indicated differences between drainage basins and between sites within each basin. These differences were explained by basin characteristics and conditions. Fractal dimensions and particle size distributions obtained with the settling method were less sensitive to drainage basin characteristics and conditions, which limits their usefulness as process indicators. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

6.
从新疆乌鲁木齐市2004—2015年得到的841个钻孔中选择深度达30 m以下且钻孔资料记录完整的有效钻孔123个,通过计算5~30 m范围内不同深度的等效剪切波速,分别利用线性拟合、二次拟合和三次拟合对各深度vSd)及其vS30进行拟合。通过对比发现,三个方程的拟合误差都随深度的增加而减少,且三次拟合方程的误差始终小于同深度的线性拟合和二次拟合方程,因此推荐使用三次拟合方程来估计新疆乌鲁木齐市钻孔的vS30值。同时将此结果和Boore的结果进行比较后发现,不同深度处的等效剪切波速vSd)和vS30具有地域差异性;Boore得到的结果在钻孔深度小于20 m时明显高估vS30值,拟合曲线偏离实际数据点较远,所以本文拟合结果更适用于新疆乌鲁木齐市。综合比较可知,三次拟合得到的研究结果可以为新疆乌鲁木齐市钻孔深度不足30 m的地区求解vS30值提供参考。最后,利用新疆克拉玛依市2004—2015年钻孔资料检验三个拟合公式对克拉玛依市的适用性,发现深度越接近30 m,误差越小;线性模型和二次模型相对来说比较可靠,平均误差接近于0,并且对深度大于10 m的钻孔有高估现象;三次模型相对来说误差比较大,并且几乎在所有深度都有低估现象。  相似文献   

7.
Equilibrium water uptake and the sizes of atmospheric aerosol particles have for the first time been determined for high relative humidities, i.e., for humidities above 95 percent, as a function of the particles chemical composition. For that purpose a new treatment of the osmotic coefficient has been developed and experimentally confirmed. It is shown that the equilibrium water uptake and the equilibrium sizes of atmospheric aerosol particles at large relative humidities are significantly dependent on their chemical composition.List of symbols A proportionality factor - a w activity of water in a solution - c p v specific heat of water vapour at constant pressure - c w specific heat of liquid water - f relative humidity - l w specific heat of evaporation of water - M i molar mass of solute speciesi - M s mean molar mass of all the solute species in a solution - M w molar mass of water - m 0 mass of an aerosol particle in dry state - m i mass of solute speciesi - m s mass of solute - m w mass of water taken up by an aerosol particle in equilibrium state - m total molality=number of mols of solute species in 1000 g of water - m i molality of solute speciesi - m k total molality of a pure electrolytek - O(m 2) remaining terms being of the second and of higher powers ofm - p + standard pressure - p total pressure of the gas phase - p pressure within a droplet - p 1,p 2,p 3 coefficients in the expansion of M - p 1i, p2i, p3i specific parameters of ioni - p s saturation vapour pressure - p w water vapour pressure - R w individual gas constant of water - r radius of a droplet - r 0 equivalent volume radius of an aerosol particle in dry state - T temperature - T 0 standard temperature - T 1 temperature of the pure water drop in the osmometer - v w specific volume of pure water - z i valence of ioni - i relativenumber concentration of ioni in a solution - correction term due to the adsorption of ions at liquid-solid interfaces - activity coefficient of solute speciesi in a solution, related to molalities - I bridge current - T temperature difference between solution and pure water drop in the osmometer - exponential mass increase coefficient - w specific chemical potential of water vapour - w specific chemical potential of water - 0 w specific chemical potential of pure water vapour - 0 w specific chemical potential of pure water - 0 density of an aerosol particle in dry state - w density of pure water - surface tension of a droplet - 0 surface tension of pure water, i.e., at infinite dilution of the solute - osmotic coefficient - k osmotic coefficient of a solution of a pure electrolytek - k osmotic coefficient of a solution of a mixed solute - M fugacity coefficient of water vapour - s i=1 i z 2 i This work is part of a Ph.D. thesis carried out at the Meteorological Institute of the Johannes Gutenberg-Universität, Mainz.  相似文献   

8.
Summary The principle of the sampling method of submicron aerosols with the Aerosol Spectrometer is briefly described and the analytic procedures for deriving the frequency-size distributionC d (d) from photo-micrographic particle counts and microphotometric light scattering measurementsS d (d) of identical areas of the particle deposit.After initial analysis the deposits were exposed to elevated temperature (80° C) for several hours and re-analyzed. Four representative aerosol types, originating from the high sea, the shore, vegetation, and metropolitan smog are analyzed in this manner for the range (0.2 d1.3 ). All show a very marked decrease, even disappearance of the smaller particles (d<0.5 ) and shrinkage of the larger particles (d<1 ). By far the largest effect is observed for the smog aerosols.This volatility appears to be caused by either evaporation of the particle substace or by the gradual oxidation of its organic components into more volatile products (CO2, H2O).  相似文献   

9.
In this paper, we present a complete morphological characterization of the ash particles erupted on 18 December 2002 from Etna volcano, Italy. The work is based on the acquisition and processing of bidimensional digital images carried out by scanning electron microscopy (SEM) to obtain shape parameters by image analysis. We measure aspect ratio (AR), form factor (FF), compactness (CC), and rectangularity (RT) of 2065 ash particles with size between 0.026 and 1.122 mm. We evaluate the variation of these parameters as a function of the grain-size. Ash particles with a diameter of <0.125 mm vary from mostly equant to very equant, ash particles between 0.125 and 0.250 mm have an intermediate shape, and particles with diameters >0.250 mm are subelongate. We find that, on average, particles with a diameter of <0.250 mm are subrounded, particles between 0.250 and 0.50 mm are subangular, and particles >0.50 mm are angular. Using this morphological analysis and an empirical relation between the drag coefficient (C D) and Reynolds number (R e) of Wilson and Huang (Earth Planet Sci Lett 44:311–324, 1979), we calculate the terminal settling velocities (V WH). The comparisons between these velocities and those calculated with the formula of Kunii and Levenspiel (Fluidization engineering. Wiley, New York, pp 97, 1969) (V KL), which considers ash particles as spheres, show that V KL are in average 1.28 greater than V WH. Hence, we quantify the systematic error on the spatial distribution of the mass computed around the volcano carried out by tephra dispersal models when the particles are assumed to be spherical.  相似文献   

10.
11.
Particle selectivity plays an important role in clarifying sediment transport processes in vegetative filter strips (VFS). 10-m long grass strips at slopes of 5° and 15° were subjected to a series of sediment-laden inflows experiments with different particle sizes to investigate the sediment transport and its response to overland flow hydraulics. The inflow sediments came from local soil, river-bed sand, and mixed, with median particle size d50 of 39.9, 207.9 and 77.4 μm, respectively. Three independent repeated experiments were carried for each treatment. The results show that when the sediment trapping lasted for a certain length of time, the re-entrainment of some small-sized particles was greater than the deposition; that is, net loss occurred, which was not erosion of the original soil. Net loss of particles is mainly determined by the particle diameter. The coarser the inflow sediment particles and/or the steeper the slope, the coarser the particles can be net lost. Deposited sediment causes the VFS bed surface to become smooth and hydraulic resistance decrease exponentially. Unit stream power P is more suitable than shear stress τ of overland flow to be used to describe the process of sediment particle transport in VFS. The relationship between P and d50 of outflow sediment is very consistent with the form of power function with a constant term. These results are helpful to understand the physical process of sediment transport on vegetation hillslopes.  相似文献   

12.
Two year measurements of aerosol concentration and size distribution (0.25 μm < d < 30 μm) in the atmospheric surface layer, collected in L’Aquila (Italy) with an optical particle counter, are reported and analysed for the different modes of the particle size distribution. A different seasonal behaviour is shown for fine mode aerosols (largely produced by anthropogenic combustion), coarse mode and large-sized aerosols, whose abundance is regulated not only by anthropogenic local production, but also by remote natural sources (via large scale atmospheric transport) and by local sources of primary biogenic aerosols. The observed total abundance of large particles with diameter larger than 10 μm is compared with a statistical counting of primary biogenic particles, made with an independent technique. Results of these two observational approaches are analysed and compared to each other, with the help of a box model driven by observed meteorological parameters and validated with measurements of fine and coarse mode aerosols and of an atmospheric primary pollutant of anthropogenic origin (NOx). Except in winter months, primary biogenic particles in the L’Aquila measurement site are shown to dominate the atmospheric boundary layer population of large aerosol particles with diameter larger than 10 μm (about 80 % of the total during summer months), with a pronounced seasonal cycle, contrary to fine mode aerosols of anthropogenic origin. In order to explain these findings, the main mechanisms controlling the abundance and variability of particulate matter tracers in the atmospheric surface layer are analysed with the numerical box-model.  相似文献   

13.
Particulate matter suspended in the River Severn (Shropshire, UK) consists chiefly of clay-sized mineral particles, together with living and dead micro-organisms (algae and bacteria). Its concentration depends strongly on discharge, but the particle size distribution shows no systematic variability. For most samples, the particle volume is log-normally distributed with respect to diameter, the mean diameter being ca. 9 μm. The particles are mainly aggregates, including some with linear dimensions of the order of tens or hundreds of micrometres. Particle density depends appreciably on size, decreasing from ca. 2.5 × 106 g m?3 at a diameter of 2.5 μm to ca. 1.3 × 106 g m ?3 at 20 μm. The collision efficiency factor for particle aggregation is estimated to be 0.01–0.03. At low discharge, the ‘dead zone’ in the River Severn at Leighton is a well defined region of stagnant water behind a gravel bar. The rate of deposition of fine particles on its bed is of the order of tens of grams per square metre per day. Resuspension requires a critical bed shear velocity of 0.03–0.04 m s?1, which occurs at main river discharges greater than about 150 m3 s?1. Under such conditions the gravel bar is underwater and the dead zone is a region of highly turbulent return flow. A simple mechanistic model of particle dynamics in the dead zone accounts reasonably well for particle accumulation rates when run with parameter values based on measured particle and hydraulic properties. Calculations with the model suggest that most of the sedimentation flux to the dead zone bed is due to particles with equivalent sphere diameters in the range 30–240 μm. Simulations indicate that deposition proceeded continuously during spring and summer, whereas repeated deposition and resuspension occurred in autumn and winter.  相似文献   

14.
GeneratinggroundmotionbytwonewtechniquesofaddingharmonicwaveinthetimedomainandapproximatingtoresponsespectrumasawholeCHANG...  相似文献   

15.
This paper deals with steel moment frames combined with hysteretic dampers. Specifically, it examines the strength of dampers required to minimize damage to moment frames under earthquake loading. The important structural variables are the ratio of the dampers' shear strength to the maximum resistance, termed β in this study, and the relative stiffness between the damper and the main frame, termed k. The equivalent viscous damping ratio of the entire structural system is affected by the quantities β and k and the ductility ratio of the main frame. The optimum dampers' strength ratio (βopt), which maximizes the equivalent viscous damping ratio, was formulated as a function of k, and it was found that βopt is independent of the ductility ratio of the main frame. Earthquake response analysis confirmed that damage to the main frame can be significantly reduced by hysteretic dampers and minimized at the value of βopt. © 1998 John Wiley & Sons, Ltd.  相似文献   

16.
Depth filtration is still one of the most important water treatment processes. It remains difficult to model mathematically because of the complexity of the process and the impact of numerous suspension parameters. The shape of the grains and suspension particles or flocs are among these parameters. The results of theoretical calculations suggest their visible impact on filtration. The shape of the media grain is relatively easy to measure. The shapes of the flocs or suspension particles, which are commonly not perfectly spherical, are much more difficult to predict. However, a few apparatuses developed lasting recent years make this possible. The FPIA 3000, manufactured by Malvern Instruments, uses flow particle image analysis method to measure 26 shape parameters of the suspension particles. Experimental measurement of suspension particle shape after flocculation and after depth filtration has allowed us to answer the question regarding the possible application of this measuring technique in water filtration technology. The experiments have also provided us with detailed information about the shape of flocs and suspension particles in filtered water. High number of particles characterized by circularity lower than 0.8 was detected in flocculated water inflowing to the filter. The particles remained in the outflow was characterized by visibly higher circularity than the particles inflowing to the filter. The results revealed much better removal of the particles characterized by lower circularity during filtration, whereas relation between convexity of the particles and their removal efficiency was not so evident.  相似文献   

17.
The catalog of Kamchatka earthquakes is represented as a probability space of three objects {Ω, $ \tilde F $ \tilde F P}. Each earthquake is treated as an outcome ω i in the space of elementary events Ω whose cardinality for the period under consideration is given by the number of events. In turn, ω i is characterized by a system of random variables, viz., energy class ki, latitude φ i , longitude λ i , and depth h i . The time of an outcome has been eliminated from this system in this study. The random variables make up subsets in the set $ \tilde F $ \tilde F and are defined by multivariate distributions, either by the distribution function $ \tilde F $ \tilde F (φ, λ, h, k) or by the probability density f(φ, λ, h, k) based on the earthquake catalog in hand. The probabilities P are treated in the frequency interpretation. Taking the example of a recurrence relation (RR) written down in the form of a power law for probability density f(k), where the initial value of the distribution function f(k 0) is the basic data [Bogdanov, 2006] rather than the seismic activity A 0, we proceed to show that for different intervals of coordinates and time the distribution f elim(k) of an earthquake catalog with the aftershocks eliminated is identical to the distribution f full(k), which corresponds to the full catalog. It follows from our calculations that f 0(k) takes on nearly identical numeral values for different initial values of energy class k 0 (8 ≤ k 0 ≤ 12) f(k 0). The difference decreases with an increasing number of events. We put forward the hypothesis that the values of f(k 0) tend to cluster around the value 2/3 as the number of events increases. The Kolmogorov test is used to test the hypothesis that statistical recurrence laws are consistent with the analytical form of the probabilistic RR based on a distribution function with the initial value f(k 0) = 2/3. We discuss statistical distributions of earthquake hypocenters over depth and the epicenters over various areas for several periods  相似文献   

18.
As part of the multinational Lake Owens Dust Experiment (LODE), we have studied the generation of dust storms on the south sand sheet of Owens (dry) Lake, California, an anthropogenically desiccated playa reported to be the single greatest source of particulate matter in North America. During March 1993, we performed an intensive field study including eight significant dust storms, building on our prior work (1978–1984) and preliminary studies (1991–1992). We studied sources and magnitude of coarse saltating particles, the meteorological conditions that allow them to become mobile across the flat playa of Owens (dry) Lake, and how the motion of saltating particles across different types of playa surfaces results in the generation of PM10 dusts (aerosol particles smaller than 10 μm aerodynamic diameter). Saltating grains of lacustrine sand and broken crust abrade and disaggregate the playa surface into fine aerosols, and the resulting PM10 concentrations recorded during major dust storms are among the highest ever recorded in North America. On 23 March 1993, we measured a 2 h concentration on the playa of 40 620 μg m−3, as far as we can determine the highest ambient PM10 value ever recorded in the U.S.A. Abrasion of salt-silt-clay crusts by saltation is shown to be responsible for all but a small part of one dust storm. The quantity ‘sand run’, saltating particle transport multiplied by wind run, is shown to be very closely correlated with dust aerosol concentration. Finally, we have established that on-lake bed studies are essential for quantitative prediction of dust events on the Owens (dry) Lake bed, despite the difficult conditions encountered.  相似文献   

19.
A novel and efficient protocol optimising deep‐bed filtration of surface water was developed. The innovation lies in ballasted‐flocculation filtration and an intermediate downwash. The approach is based on the assumption that kaolin particles with a partial positive charge may adsorb onto the surface of C. parvum oocysts and neutralize their negative charge. Application of this technology enhanced removal of inorganic particles and Cryptosporidium parvum oocysts by approximately 30 % and shortened the ripening stage of the filtration process from 1 h to about 10 min.  相似文献   

20.
A control strategy is proposed for variable damping elements (VDEs) used together with auxiliary stiffness elements (ASEs) that compose a time‐varying non‐linear Maxwell (NMW) element, considering near‐future excitation influence. The strategy first composes a state equation for the structural dynamics and the mechanical balance in the NMW elements. Next, it establishes a cost function for estimating future responses by the weighted quadratic norms of the state vector, the controlled force and the VDEs' damping coefficients. Then, the Euler equations for the optimum values are introduced, and also approximated by the first‐order terms under the autoregressive (AR) model of excitation information. Thus, at each moment tk, the strategy conducts the following steps: (1) identify the obtained seismic excitation information to an AR model, and convert it to a state equation; and (2) determine VDEs' damping coefficients under the initial conditions at tk and the final state at tk+L, using the first‐order approximation of the Euler equations. The control effects are examined by numerical experiments. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

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