On the transport of energy in water waves

Theory is developed and utilized for the calculation of the separate transport of kinetic, gravity potential, and surface-tension energies within sinusoidal surface waves in water of arbitrary depth. In Sect. 2 it is shown that each of these three types of energy constituting the wave travel at different speeds, and that the group velocity, c _g , is the energy-weighted average of these speeds, depth- and time-averaged in the case of the kinetic energy. It is shown that the time-averaged kinetic energy travels at every depth horizontally either with (deep water), or faster than the wave itself, and that the propagation of a sinusoidal wave is made possible by the vertical transport of kinetic energy to the free surface, where it provides the oscillating balance in surface energy just necessary to allow the propagation of the wave.The propagation speed along the surface of the gravity potential energy is null, while the surface-tension energy travels forward along the wave surface everywhere at twice the wave velocity, c. The flux of kinetic energy, when viewed traveling with a wave, provides a pattern of steady flux lines which originate and end on the free surface after making vertical excursions into the wave, even to the bottom, and these are calculated. The pictures produced in this way provide immediate insight into the basic mechanisms of wave motion. In Sect. 3 the modulated gravity wave is considered in deep water and the balance of terms involved in the propagation of the energy in the wave group is determined; it is shown again that vertical transport of kinetic energy to the surface is fundamental in allowing the propagation of the modulation, and in determining the well-known speed of the modulation envelope, c _g . Dedicated to Professor J.N. Newman in recollection of his many significant contributions to the theory and computation of waves and floating bodies and to the founding of the IWWWFB.     

Effects of momentum transfer on particle dispersions of dense gas–particle two-phase turbulent flows

A modified momentum transfer coefficient of dense gas–particle two-phase turbulent flows is developed and its effect on particle dispersion characteristics in high particle concentration turbulent downer flows has been numerically simulated incorporating into a second-order moment (USM) two-phase turbulent model and the kinetic theory of granular flow (KTGF) to consider particle–particle collisions. The particle fractions, the time-averaged axial particle velocity, the particle velocities fluctuation, and their correlations between gas and particle phases based on the anisotropic behaviors and the particle collision frequency are obtained and compared using traditional momentum transfer coefficients proposed by Wen (1966), Difelice (1985), Lu (2003) and Beetstra (2007). Predicted results of presented model are in good agreement with experimental measurement by Wang et al. (1992). The particle fluctuation velocity and its fluctuation velocity correlations along axial–axial and radial–radial directions have stronger anisotropic behaviors. Furthermore, the presented model is in a better accordance with Lu’s model in light of particle axial velocity fluctuation, particle temperature, particle kinetic energy and correlations of particle–gas axial–axial velocity fluctuation. Also, they are larger than those of other models. Beetstra’s model is not suitable for this downer simulation due to the relative lower particle volume fraction, particle collision and particle kinetic energy.     

Analytical modelling of high velocity impacts of cylindrical projectiles on carbon/epoxy laminates

In this work an analytical model has been developed in order to predict the residual velocity of a cylindrical steel projectile, after impacting into a woven carbon/epoxy thin laminate. The model is based in an energy balance, in which the kinetic projectile energy is absorbed by the laminate through three different mechanisms: linear momentum transfer, fiber failure and laminate crushing. This last mechanism needs the quantification of the through-thickness compressive strength, which has been evaluated by means of quasi-static punch tests. Finally, high velocity impact tests have been accomplished in a wide range of velocities, to validate the model.     

Two interactional solitary waves propagating in two-dimensional hexagonal packing granular system

We investigate the wave propagation in the two-dimensional (2D) hexagonal packing of spheres in a rectangular region using numerical simulations and theoretical analyses. The impact excitations are resolved into two distinct solitary waves with the same wave amplitude and front velocity. A universal relation between the wave front velocity and the force amplitude is obtained. One-dimensional chain models of the 2D packing are generated. The transfer of energy and momentum leads to the phenomenon of an energy equipartition in the 2D homogeneous hexagonal packed system. Moreover, the solitary wave train containing solitary waves with a decreasing amplitude is also noted. We apply conservation of energy and momentum to the collision process between spheres to predict the amplitude of the solitary wave train. Our analytical results are in good agreement with the numerical simulations.     

基于二元指数后退的电子标签防碰撞算法

为解决目前现有电子标签防碰撞算法在电子标签数量较大时,读取效率低且耗时较长的问题,提出了一种基于二元指数后退的时隙选择算法,当碰撞发生时,改进算法以二进制指数方式进行时隙的增加,并随机选择时隙发送数据,重复这个过程直到所有标签被正确读出。仿真试验表明,在电子标签数量急剧增加时,改进算法的读取效率较高,电子标签读取所需时隙基本不增加。     

Universal theorems for total energy of the dynamics of linearly elastic heterogeneous solids

In this paper we consider a sample of a linearly elastic heterogeneous composite in elastodynamic equilibrium and present universal theorems which provide lower bounds for the total elastic strain energy plus the kinetic energy, and the total complementary elastic energy plus the kinetic energy. For a general heterogeneous sample which undergoes harmonic motion at a single frequency, we show that, among all consistent boundary data which produce the same average strain, the uniform-stress boundary data render the total elastic strain energy plus the kinetic energy an absolute minimum. We also show that, among all consistent boundary data which produce the same average momentum in the sample, the uniform velocity boundary data render the total complementary elastic energy plus the kinetic energy an absolute minimum. We do not assume statistical homogeneity or material isotropy in our treatment, although they are not excluded. These universal theorems are the dynamic equivalent of the universal theorems already known for the static case [Nemat-Nasser and Hori, 1993] and [Nemat-Nasser and Hori, 1995]. It is envisaged that the bounds on the total energy presented in this paper will be used to formulate computable bounds on the overall dynamic properties of linearly elastic heterogeneous composites with arbitrary microstructures.     

Hypervelocity penetration modeling: momentum vs. energy and energy transfer mechanisms

Analytic penetration modeling usually relies on either a momentum balance or an energy-rate balance to predict depth of penetration by a penetrator based on initial geometry and impact velocity. In recent years, fairly sophisticated models of penetration have arisen that develop the three-dimensional flow field within a target. Based on the flow field and constitutive assumptions, it is then possible to derive a momentum or an energy-rate balance. This paper examines the use of assumed flow fields within a target created by impact and then examines the resulting predicted behavior based on either momentum conservation or energy conservation. It is shown that for the energy-rate balance to work, the details of the energy transfer mechanisms must be included in the model. In particular, how the projectile energy is initially transferred into target kinetic energy and elastic compression energy must be included. As impact velocity increases, more and more energy during the penetration event is temporarily deposited within the target as elastic compression and target kinetic energy. This energy will be dissipated by the target at a later time, but at the time of penetration it is this transfer of energy that defines the forces acting on the projectile. Thus, for an energy rate balance approach to successfully model penetration, it must include the transfer of energy into kinetic energy within the target and the storage of energy by elastic compression. Understanding the role of energy dissipation in the target clarifies the various terms in analytic models and identifies their origin in terms of the fundamental physics. Understanding the modes of energy transfer also assists in understanding the hypervelocity result that penetration depth only slowly increases with increasing velocity even though the kinetic energy increases as the square of the velocity.     

Forward/Backward Switching of Plasmonic Wave Propagation Using Sign‐Reversal Coupling

Backward waves with wave‐front propagation opposite in direction to that of energy flow have attracted considerable interest in the context of photonic metamaterials. However, switching between forward and backward waves in the same frequency range has remained a challenge. Here, on a platform of coupled designer surface plasmon resonators in the microwave regime, multiband forward/backward switching of plasmonic wave propagation is demonstrated. This approach makes use of sign‐reversal coupling that occurs when switching the coupling configuration between tightly confined photonic modes. Direct experimental measurements of plasmon dispersion curves confirm the forward/backward propagation of plasmonic waves in the same frequency range. This study provides a solution to forward/backward switching of subwavelength plasmonic wave propagation, and may find potential applications in photonic integrated systems.     

NUMERICAL SIMULATION OF GRANULAR COUETTE FLOWS BETWEEN TWO ROUGH PARALLEL PLATES

This paper presents a numerical method for calculating the granular Couette flows between two parallel plates. A kinetic model which includes the frictional energy loss effects is employed, and the equations of motion are solved using a numerical iterative method. The boundary conditions are satisfied by ensuring the balance of momentum and energy at such boundaries. The mean velocity, the fluctuation kinetic energy and the solid volume fraction profiles are evaluated under a variety of conditions. The mean velocity profiles are compared with the molecular dynamic simulation results, and good agreement is observed. The study shows that the slip velocity may vary considerably depending on the surface roughness, coefficient of restitution and friction coefficient.     

Quantization of coupled modes propagation in integrated optical waveguides

Abstract

A quantum mechanical analysis of the propagation of coupled modes in integrated optical waveguides is given. The modal orthonormalization property on a cross-section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry are taken into account to derive the quantum momentum operator and Heisenberg's equations giving a quantum-consistent formulation of the coupled mode propagation as a function of forward and backward creation and annihilation operators.     

Automated dynamic fracture procedure for modelling mixed-mode crack propagation using explicit time integration brick finite elements

Several fracture codes have been developed in recent years to perform analyses of dynamic crack propagation in arbitrary directions. However, general-purpose, commercial finite-element software which have capabilities to do fracture analyses are still limited in their use to stationary cracks and crack propagation along trajectories known a priori . In this paper, we present an automated fracture procedure implemented in the large-scale, nonlinear, explicit, finite-element code DYNA3D which can be used to simulate dynamic crack propagation in arbitrary directions. The model can be used to perform both generation- and application-phase simulations of self-similar as well as non-self-similar dynamic crack propagation in linear elastic structures without user intervention. It is developed based on dynamic fracture mechanics concepts and implemented for three-dimensional solid elements. Energy approach is used in the model to check for crack initiation/propagation. Dynamic energy release rate and stress intensity factors are determined from far-field finite-element field solutions using finite-domain integrals. Fracture toughness is input as a function of crack-tip velocity, and when the criterion for crack growth is satisfied, an element deletion-and-replacement re-meshing procedure is used along with a gradual nodal release technique to update the crack geometry and model the crack propagation. Direction of crack propagation is determined using the maximum circumferential stress criterion. Numerical simulations of experiments involving non-self-similar crack propagation are performed, and results are presented as verification examples.     

A simple kinetic theory for granular flow of binary mixtures of smooth,inelastic, spherical particles

Summary Following the approach of the kinetic theory for mixtures of dense gases, the general conservation equations for the rapid flow of a binary mixture of smooth, inelastic, spherical granular particles are derived. Explicit constitutive relations for stress and rate of energy dissipation are obtained by making simple approximations for the particle velocity distribution functions. These approximations are appropriate for cases where collisional interactions are the dominant mechanism for momentum and energy exchange in the system. The theory is applied to the case of simple shear flow. In general, the theory predicts that stresses decrease with increasing concentration of the small particles and decreasing diameter ratio of small to large particles. Theoretical predictions of stresses are compared with experimental results and reasonable agreement is found.With 9 Figures     

Wave propagation in elasto-plastic granular systems

Due to the nonlinear nature of the inter-particle contact, granular chains made of elastic spheres are known to transmit solitary waves under impulse loading. However, the localized contact between spherical granules leads to stress concentration, resulting in plastic behavior even for small forces. In this work, we investigate the effects of plasticity in wave propagation in elasto-plastic granular systems. In the first part of this work, a force–displacement law between contacting elastic-perfectly plastic spheres is developed using a nonlinear finite element analysis. In the second part, this force–displacement law is used to simulate wave propagation in one-dimensional granular chains. In elasto-plastic chains, energy dissipation leads to the formation and merging of wave trains, which have characteristics very different from those of elastic chains. Scaling laws for peak force at each contact point along the chain, velocity of the leading wave, local contact and total dissipation are developed.     

Deformation and fracture of a long-rod projectile induced by an oblique moving plate: Experimental tests

The influence of projectile length to diameter ratio (15, 30 and 45), plate thickness (0.5, 1 and 2 projectile diameters), projectile velocity (1500, 2000 and 2500 m/s) and plate velocity (−300 to 300 m/s) on the interaction between long-rod tungsten projectiles and oblique steel plates (obliquity 60°) was studied experimentally in small-scale reverse impact tests. The residual projectiles and their motions were characterised in terms of changes in length, velocity, angular momentum, linear momentum and kinetic energy. The parameters found to have the largest influence on the disturbance of the projectile were the plate velocity, in particular its direction, and the thickness of the plate. In the ranges studied, the influence of length to diameter ratio and of projectile velocity were found to be less important.     

筒形件反旋工艺塑性流动刚塑性有限元分析

建立了筒形件反旋工艺平面变形刚塑性有限元分析的力学模型，比较了把反旋工艺视为正挤和本文力学模型条件下的速度场，有限元分析结果与反旋实际条件相符。     

Kinetic theory and dynamic structure factor of a condensate in the random phase approximation

No Heading We present the microscopic kinetic theory of a homogeneous dilute Bose condensed gas in the generalized random phase approximation (GRPA), which satisfies the following requirements: 1) the mass, momentum and energy conservation laws; 2) the H-theorem; 3) the superfluidity property and 4) the recovery of the Bogoliubov theory at zero temperature ¹. In this approach, the condensate influences the binary collisional process between two normal atoms, in the sense that their interaction force results from the mediation of a Bogoliubov collective excitation traveling throughout the condensate. Furthermore, as long as the Bose gas is stable, no collision happens between condensed and normal atoms. In this paper, we show how the kinetic theory in the GRPA allows to calculate the dynamic structure factor at finite temperature and when the normal and superfluid are in a relative motion. The obtained spectrum for this factor provides a prediction which, compared to the experimental results, allows to validate the GRPA.PACS numbers:03.75.Hh, 03.75.Kk, 05.30.–d     

Explosion propagation in inert porous media

Porous media are often used in flame arresters because of the high surface area to volume ratio that is required for flame quenching. However, if the flame is not quenched, the flow obstruction within the porous media can promote explosion escalation, which is a well-known phenomenon in obstacle-laden channels. There are many parallels between explosion propagation through porous media and obstacle-laden channels. In both cases, the obstructions play a duel role. On the one hand, the obstruction enhances explosion propagation through an early shear-driven turbulence production mechanism and then later by shock-flame interactions that occur from lead shock reflections. On the other hand, the presence of an obstruction can suppress explosion propagation through momentum and heat losses, which both impede the unburned gas flow and extract energy from the expanding combustion products. In obstacle-laden channels, there are well-defined propagation regimes that are easily distinguished by abrupt changes in velocity. In porous media, the propagation regimes are not as distinguishable. In porous media the entire flamefront is affected, and the effects of heat loss, turbulence and compressibility are smoothly blended over most of the propagation velocity range. At low subsonic propagation speeds, heat loss to the porous media dominates, whereas at higher supersonic speeds turbulence and compressibility are important. This blending of the important phenomena results in no clear transition in propagation mechanism that is characterized by an abrupt change in propagation velocity. This is especially true for propagation velocities above the speed of sound where many experiments performed with fuel-air mixtures show a smooth increase in the propagation velocity with mixture reactivity up to the theoretical detonation wave velocity.     

Phase–field model for solidification of Fe–C alloys

The phase–field model for binary alloys by Kim et al. is briefly introduced and the main difference in the definition of free energy density in interface region between the models by Kim et al. and by Wheeler et al. is di cussed. The governing equations for a dilute binary alloy are derived and the phase-field parameters are obtained at a thin interface limit. The examples of the phase–field simulation on Ostwald ripening, isothermal dendrite growth and particle/interface interaction for Fe–C alloys are demonstrated. In Ostwald ripening, it is shown that small solid particles preferably melt out and then large particles agglomerate. In isothermal dendrite growth, the kinetic coefficient dependence on growth rate is examined for both the phase-field model and the dendrite growth model by Lipton et al. The growth rate by the dendrite model shows strong kinetic coefficient dependence, though that by the phase–field model is not sensitive to it. The particle pushing and engulfment by interface are successfully reproduced and the critical velocity for the pushing/engulfment transition is estimated. Through the simulation, it is shown that the phase-field model correctly reproduces the local equilibrium condition and has the wide potentiality to the applications on solidification.     

Fully coupled 3D modeling of plasma-particle interactions in a plasma jet

A three-dimensional model is developed to clarify two-way interactions of energy, momentum and turbulence between plasma and particles. The plasma-particle two-way interactions are modeled by coupling a Lagrangian approach for particle behavior with a Eulerian approach for plasma flow. The effect of each two-way interaction on energy and momentum transfers, and turbulence modulation is clarified by numerical simulation. The local deformations of the plasma jet kinetic energy and its dissipation rate fields are caused by the presence of the particle in the plasma jet. Plasma-particle interactions are very complex and effect of each interaction on another is evident. Net loss from plasma jet parameters decreases with increasing particle size. Particle temperature and velocity distributions are decreased due to the turbulence modulation. The effect of the number of particles used in the simulation on energy and momentum transfers, and turbulence modulation is significant.     

Spiraling elliptic breathers in nonlocal nonlinear media with linear anisotropy

The dynamical properties of spiraling elliptic breathers in nonlocal nonlinear media with linear anisotropy are analytically discussed. Using a two-dimensional asynchronous fractional Fourier transform, the exact analytical solutions of spiraling elliptic breathers are obtained to the nonlocal nonlinear Schrödinger equation with unequal diffraction coefficients in the highly nonlocal limit. It is found that the spiraling elliptic breathers exhibit a kind of molecule-like libration due to the combined effects of the linear anisotropy and the orbital angular momentum. The angular velocity of the spiraling elliptic breathers is discussed, which can be controlled by the linear anisotropy parameter. In the media with linear anisotropy such as uniaxial crystals, the angular velocity of the spiraling elliptic breathers can be controlled by changing the propagation directions of optical beams. Furthermore, the nonlinearity of media is found to enhance the rotation effect of spiraling elliptic breathers.