Time-averaged Energy Research Articles

Ray Theory Results and Ray Wavefront Diagrams for the Hyperbolic Cosine Propagation Sound-Speed Profile

In this paper, we provide a complete geometrical treatment of classical rays emanating from an underwater point source and propagating in an unbounded medium where the speed of sound has a hyperbolic cosine dependence on the depth coordinate $(z)$ . General results are derived exclusively from Snell's law and are not limited to the case in which the ray emitting source is located at a point on the minimum propagation speed plane. Explicit relations are provided for the following: 1) the ray depth coordinate $(z)$ expressed as a function of the ray horizontal range $(\rho)$ and the ray source angle $(\theta_0)$ ; 2) all the relations among the ray source angle $(\theta_0)$ , the ray receiver angle $(\theta)$ , and the travel time $(\tau)$ to reach an arbitrary position of the receiver from an arbitrary position of the source; and 3) the classical wavefront coordinates $(\rho,z)$ along a ray expressed as a function of the ray source angle $(\theta_0)$ and travel time $(\tau)$ . From the wavefront coordinates $(\rho,z)$ , we construct and display ray/wavefront diagrams for a varying source depth $(z_0)$ relative to the minimum propagation speed plane. We also derive the time-averaged acoustic energy flux carried along classical ray tubes.

Direct detection signatures of self-interacting dark matter with a light mediator

Self-interacting dark matter (SIDM) is a simple and well-motivated scenario that could explain long-standing puzzles in structure formation on small scales. If the required self-interaction arises through a light mediator (with mass ∼ 10 MeV) in the dark sector, this new particle must be unstable to avoid overclosing the universe. The decay of the light mediator could happen due to a weak coupling of the hidden and visible sectors, providing new signatures for direct detection experiments. The SIDM nuclear recoil spectrum is more peaked towards low energies compared to the usual case of contact interactions, because the mediator mass is comparable to the momentum transfer of nuclear recoils. We show that the SIDM signal could be distinguished from that of DM particles with contact interactions by considering the time-average energy spectrum in experiments employing different target materials, or the average and modulated spectra in a single experiment. Using current limits from LUX and SuperCDMS, we also derive strong bounds on the mixing parameter between hidden and visible sector.

General relation for optical group delay

A general applicable theory is presented for group delay (GD) in nonabsorbing photonic structures, for which the structural boundaries consist of longitudinally invariant waveguides. It is shown that the sum of the GDs of the various outgoing modes weighted by their transmittances is, in general, approximately equal to the ratio of time-averaged optical energy and time-averaged input power. It is further demonstrated that exact equality is obtained by taking into account interference effects of modes that have spatial overlap at the structural boundary. A detailed theory is presented, discussed, and elucidated via a simple example.

Prediction of Scattered Broadband Shock-Associated Noise

A mathematical model is developed for the prediction of broadband shock-associated noise in the presence of an airframe body. Model arguments are dependent on the vector Green’s function of the linearized Euler equations, steady Reynolds-averaged Navier–Stokes solutions, and the two-point cross-correlation of the equivalent source. The equivalent source is dependent on steady Reynolds-averaged Navier–Stokes solutions of the jet flow that capture the nozzle and airframe geometry. Contours of the time-averaged streamwise velocity component and turbulent kinetic energy are examined with varying airframe position relative to the nozzle exit. Propagation effects are incorporated by approximating the vector Green’s function of the linearized Euler equations. This approximation involves the use of ray theory and an assumption that broadband shock-associated noise is relatively unaffected by the refraction of the jet shear layer. A nondimensional parameter is proposed that quantifies the changes of the broadband shock-associated noise source with varying jet operating condition and airframe position. Scattered broadband shock-associated noise possesses a second set of broadband lobes that are due to the effect of scattering. Presented predictions from an overexpanded jet demonstrate relatively good agreement compared to a wide variety of measurements.

Solution to the Klein–Gordon equation for the study of time‐domain waveguide fields and accompanying energetic processes

In electromagnetics, power flow and energy densities are associated with time-varying electromagnetic fields. For time-harmonic waves, such quadratic characteristics are derived using the complex-valued spatial forms of field vectors resulting in time-averaged power flow and energy densities. Hence, the opportunity to study dynamic processes of the quadratic characteristics is lost in the time-harmonic electromagnetics. To overcome this drawback, the authors consider the problem of a waveform propagation in a hollow waveguide via solving the system of Maxwell's equations with time derivative in an energetic space of ‘real-valued’ functions. The transverse electric and transverse magnetic modal field components are presented as the products of modal basis elements and the modal amplitudes. The vector basis elements are obtained with required physical dimensions, volt per metre and ampere per metre. Thereby, the modal amplitudes are dimension-free scalar functions. The system of evolutionary equations for the modal amplitudes is derived and solved explicitly. The Klein–Gordon equation (KGE) plays a central role herein. A novel set of real-valued solutions to the KGE is obtained and applied for analysis of the energetic processes pertinent to the time-domain signal propagation. The velocity of transportation of the modal field energy is obtained and energetic exchange between the transverse and longitudinal field components is discussed.

Identification of dominant modes in random dynamical and aeroelastic systems

Identification of dominant modes is an important step in studying linearly vibrating systems, including flow-induced vibrations. In the presence of uncertainty, when some of the system parameters and the external excitation are modeled as random quantities, this step becomes more difficult. This work is aimed at giving a systematic treatment to this end. The ability to capture the time-averaged kinetic energy is chosen as the primary criterion for selection of modes. Accordingly, a methodology is proposed based on the overlap of probability density functions (pdf) of the natural and excitation frequencies, proximity of the natural frequencies of the mean or baseline system, modal participation factor, and stochastic variation of mode shapes in terms of the modes of the baseline system — termed here as statistical modal overlapping. The probabilistic descriptors of the natural frequencies and mode shapes are found by solving a random eigenvalue problem. Three distinct vibration scenarios are considered: (i) undamped and damped free vibrations of a bladed disk assembly, (ii) forced vibration of a building, and (iii) flutter of a bridge model. Through numerical studies, it is observed that the proposed methodology gives an accurate selection of modes.

Convection Heat Transfer Enhancement on Recirculating Flows in a Backward Facing Step: The Effects of a Small Square Turbulence Promoter

This work addresses the numerical simulation of incompressible turbulent recirculating channel flows in a backward-facing step. The effects of a small square turbulence promoter on convection heat transfer are evaluated through a parametric study. The governing equations comprise the time-averaged mass, linear momentum, and energy conservation principles in conjunction with the two-equation k–epsilon turbulence model. The study is focused on the assessment of the local and global Nusselt numbers at the channel stepped wall. The main results indicate that a maximum increment around 15% on the average Nusselt number can be achieved by using a small turbulence promoter to disturb the flow. Furthermore, it was found that the peak of the local Nusselt number on the stepped wall is located in the region where the turbulent diffusion is maximum in the near wall region.

Energy flow, energy density of Timoshenko beam and wave mode incoherence

Time-averaged energy flow and energy density are of significance in vibration analysis. The wave decomposition method is more fruitful and global in physical sense than the state variables depicted point by point. By wave approach, the Timoshenko beam vibration field is decomposed into two distinct modes: travelling and evanescent waves. Consequently, the power and energy functions defined on these waves’ amplitude and phase need to be established. However, such formulas on Timoshenko beam are hardly found in literatures. Furthermore, the incoherence between these two modes is of theoretical and practical significance. This characteristic guarantees that the resultant power or energy of a superposed wave field is equal to the sum of the power or energy that each wave mode would generate individually. Unlike Euler–Bernoulli beam, such incoherence in the Timoshenko beam case has not been theoretically proved so far. Initially, the power and energy formulas based on wave approach and the corresponding incoherence proof are achieved by present work, both in theoretical and numerical ways. Fortunately, the theoretical and numerical results show that the travelling and evanescent wave modes are incoherent with each other both on power and energy functions. Notably, the energy function is unconventional and self-defined in order to obtain the incoherence. Some remarkable power transmission characteristics of the evanescent wave are also illustrated meanwhile.

Simulation of Low-Intensity Ultrasound Propagating in a Beagle Dog Dentoalveolar Structure to Investigate the Relations between Ultrasonic Parameters and Cementum Regeneration

The therapeutic effect of low-intensity pulsed ultrasound on orthodontically induced inflammatory root resorption is believed to be brought about through mechanical signals induced by the low-intensity pulsed ultrasound. However, the stimulatory mechanism triggering dental cell response has not been clearly identified yet. The aim of this study was to evaluate possible relations between the amounts of new cementum regeneration and ultrasonic parameters such as pressure amplitude and time-averaged energy density. We used the finite-element method to simulate the previously published experiment on ultrasonic wave propagation in the dentoalveolar structure of beagle dogs. Qualitative relations between the thickness of the regenerated cementum in the experiment and the ultrasonic parameters were observed. Our results indicated that the areas of the root surface with greater ultrasonic pressure were associated with larger amounts of cementum regeneration. However, the establishment of reliable quantitative correlations between ultrasound parameters and cementum regeneration requires more experimental data and simulations.

Proposed stochastic parameterisations of subgrid turbulence in large eddy simulations of turbulent channel flow

Stochastic and deterministic subgrid parameterisations are developed for the large eddy simulation (LES) of a turbulent channel flow with friction-velocity-based Reynolds number of Reτ = 950 and centreline-based Reynolds number of Re0 = 20,580. The subgrid model coefficients (eddy viscosities) are determined from the statistics of truncated reference direct numerical simulations (DNSs). The stochastic subgrid model consists of a mean-field shift, a drain eddy viscosity acting on the resolved field and a stochastic backscatter force of variance proportional to the backscatter eddy viscosity. The deterministic variant consists of a net eddy viscosity acting on the resolved field, which represents the net effect of the drain and backscatter. LES adopting the stochastic and deterministic models is shown to reproduce the time-averaged kinetic energy spectra of the DNS within the resolved scales.

Energy flux streamlines versus acoustic rays for modeling an acoustic lens: Testing and refinement

As an extension of recently published experimental work [Cleon E. Dean and Kendez Parker, “A ray model of sound focusing with a balloon lens: An experiment for high school students,” J. Acoust. Soc. Am. 131, 2459–2462 (2012)], preliminary results comparing energy flux streamlines [David M. F. Chapman, “Using streamlines to visualize acoustic energy flow across boundaries,” J. Acoust. Soc. Am. 124, 48–56 (2008)] versus acoustic rays for visualizing the energy flow inside and in the focal region of an acoustic lens in the form of a carbon dioxide filled balloon in air were presented. The sound field was expanded in the usual Legendre polynomials and spherical Bessel functions, and the energy flux vectors at points throughout the regions of interest were calculated [J. Adin Mann III, et al., “Instantaneous and time-averaged energy transfer in acoustic fields,” J. Acoust. Soc. Am. 82, 17–30 (1987)]. Deficiencies in the streamline plotting routines used in this earlier version of Mathematica and subtle differences between acoustic rays and acoustic energy flux streamlines lent itself to an inaccurate perception of the results. This talk uses Mathematica 10 routines to revisit these results and concentrates on testing and verification of the conclusions from the previous work.

Turbulence flow field around two eccentric circular piers in scour hole

ABSTRACTFlow pattern at single pier has been extensively studied by several investigators, but scanty work is available on turbulent flow pattern around piers placed in close proximity. The work explained in this research is concerned with an experimental study of the horseshoe vortex flow pattern and characteristics in a local equilibrium scour hole around two identical circular piers placed in the longitudinal direction to the flow with an eccentricity (transverse distance). Instantaneous three-dimensional velocities were measured by using an acoustic Doppler Velocimeter (ADV). The contours and distributions of the time-averaged velocity components, turbulence intensities and turbulence kinetic energy are presented at different azimuthal planes: 0°, 45°, −45°, 90° and −90°. Velocity vectors obtained from time-averaged velocity fields are used to show further flow features. The vorticity and circulation of the horseshoe vortex are determined by using a forward difference technique of computational hydrodynamics and the Stokes theorem, respectively. The eccentric pier arrangement and the interference between the piers play an important role in the creation and formation of the greater scour depth at the eccentric rear pier. Vortex strength of the eccentric rear pier is found higher than the front pier.

Electron energy distributions and electron impact source functions in Ar/N2 inductively coupled plasmas using pulsed power

In plasma materials processing, such as plasma etching, control of the time-averaged electron energy distributions (EEDs) in the plasma allows for control of the time-averaged electron impact source functions of reactive species in the plasma and their fluxes to surfaces. One potential method for refining the control of EEDs is through the use of pulsed power. Inductively coupled plasmas (ICPs) are attractive for using pulsed power in this manner because the EEDs are dominantly controlled by the ICP power as opposed to the bias power applied to the substrate. In this paper, we discuss results from a computational investigation of EEDs and electron impact source functions in low pressure (5–50 mTorr) ICPs sustained in Ar/N2 for various duty cycles. We find there is an ability to control EEDs, and thus source functions, by pulsing the ICP power, with the greatest variability of the EEDs located within the skin depth of the electromagnetic field. The transit time of hot electrons produced in the skin depth at the onset of pulse power produces a delay in the response of the EEDs as a function of distance from the coils. The choice of ICP pressure has a large impact on the dynamics of the EEDs, whereas duty cycle has a small influence on time-averaged EEDs and source functions.

Rigorous theory of molecular orientational nonlinear optics

Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955)] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO) through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1) the derivation of rigorous tensorial components of the effective molecular hyperpolarizabilities, (2) the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect), optical Kerr effect (OKE), dc electric field induced second harmonic generation (EFISH), degenerate four wave mixing (DFWM) and third harmonic generation (THG). We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR), Pockels effect and difference frequency generation (DFG) are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR), dc electric field induced difference frequency generation (EFIDFG) and pump-probe transmission are presented.

Wireless-Uplinks-Based Energy-Efficient Scheduling in Mobile Cloud Computing

Mobile cloud computing (MCC) combines cloud computing and mobile internet to improve the computational capabilities of resource-constrained mobile devices (MDs). In MCC, mobile users could not only improve the computational capability of MDs but also save operation consumption by offloading the mobile applications to the cloud. However, MCC faces the problem of energy efficiency because of time-varying channels when the offloading is being executed. In this paper, we address the issue of energy-efficient scheduling for wireless uplink in MCC. By introducing Lyapunov optimization, we first propose a scheduling algorithm that can dynamically choose channel to transmit data based on queue backlog and channel statistics. Then, we show that the proposed scheduling algorithm can make a tradeoff between queue backlog and energy consumption in a channel-aware MCC system. Simulation results show that the proposed scheduling algorithm can reduce the time average energy consumption for offloading compared to the existing algorithm.

Turbulent heat transport and its anisotropy in an impinging jet

The turbulent heat transport is anisotropic in many cases as reported by several researchers. RANS- based turbulence models use the turbulent viscosity when expressing the turbulent heat flux in the energy balance (analogy of the Reynolds stresses in the momentum balance). The turbulent (eddy) viscosity calculation comes from the Boussinesq analogy mainly and it represents just a scalar value, hence a possible anisotropy in the turbulent flow field cannot be simply transferred to the temperature field. The computational cost of a LES-based approach can be too prohibitive in complex cases, therefore simpler explicit algebraic heat flux models describing the turbulent heat flux in the time-averaged energy equation could be used to get more accurate CFD results. This paper compares several turbulence models for the case of a turbulent impinging jet and deals with a methodology of implementing a user-defined function describing the anisotropic turbulent heat flux in a CFD code.

Characteristics and seasonal variability of internal tides in the southern South China Sea

Two sets of current mooring records at the same location are used to investigate the generation and temporal variation of internal tides (ITs) near reefs in the southern South China Sea (SCS). The total records covered more than 900 days. ITs in this region are dominated by mode-1 diurnal motions, which are mainly composed of O1, P1 and K1 constituents. The major axes of both diurnal barotropic and baroclinic tidal ellipses are oriented in the northeast-southwest direction. The ITs over the entire observation period clearly show an approximately 14-day spring-neap cycle. Meanwhile, the diurnal ITs also displayed an evident seasonal change: their energy was higher in summer and winter than in spring and autumn. The modal decomposition of diurnal motion shows that their time-averaged kinetic energy in summer and winter was about 1.2kJ/m2, which was approximately 60% higher than the values in spring and autumn. The same seasonal variation also occurred at the diurnal barotropic tides with prominent O1, P1 and K1 constituents. Because stratification does not show a significant seasonal variation in the southern SCS, the enhanced diurnal ITs in winter and summer can be attributed to the barotropic forcing with the semi-annual cycle caused by the modulation of diurnal P1 and K1.

Study of turbulent energy dissipation rate of fluid flow in the vicinity of dispersed phase boundary using spatiotemporal tree model.

The hierarchical shell models of turbulence including a spatial dimension, namely, spatiotemporal tree models, reproduce the intermittent behavior of Navier-Stokes equations in both space and time dimensions corresponding to high Reynolds number turbulent flows. This model is used, for the first time in this paper, in a one-dimensional flow zone containing a dispersed-phase particle that can be used in the study of dispersed-phase flows. In this paper, a straightforward method has been used to introduce discrete phase into the spatiotemporal tree model that leads to an increased amount of turbulent energy dissipation rate in the vicinity of the discrete phase. The effects of particle insertion and particle size on the turbulent energy dissipation rate are demonstrated. Moreover, the space-scale behavior of the time-averaged turbulent energy dissipation rate in the presence of dispersed phase is demonstrated by means of continuous wavelet transform.

Numerical Modeling of Surf Zone Hydrodynamics over Movable Bed

Shin, S.; Cox, D., and Yoon, H.D., 2014. Numerical modeling of surf zone hydrodynamics over movable bed.Understanding of hydrodynamics over moveable bed is crucial for predicting rip current generation. The capability of a numerical model based on Reynolds-averaged Navier–Stokes equations, COBRAS (COrnell BReaking waves And Structures), to simulate hydrodynamics over a movable barred beach was verified. The numerical simulation results were validated with the data collected from a large-scale two-dimensional experiment, which was conducted at the Hinsdale Wave Research Laboratory at Oregon State University. In this study, numerical model results were compared with the experimental results in terms of significant wave heights, wave setup, time-averaged horizontal velocities, and turbulent kinetic energy in different cross-shore locations. The COBRAS model successfully predicted the significant wave heights and setup from the offshore boundary to the vicinity of the bar location, but it slightly overestimated the significant wave heights when broken waves propagated to the shoreline. The numerical simulation was able to predict time-averaged horizontal velocities and turbulent kinetic energy well for all measurement locations. Overestimation of the turbulent kinetic energy at bar trough is because of the limitation of the turbulence closure scheme. Overall, based on the results of this study, the COBRAS model can be used to predict hydrodynamics in barred beaches, but improvement of the turbulence closure scheme is still required.

Toward transcoding as a service: energy-efficient offloading policy for green mobile cloud

In this article we investigate energy-efficient offloading policy for transcoding as a service (TaaS) in a generic mobile cloud system. Computation on mobile devices can be offloaded to a mobile cloud system that consists of a dispatcher at the front end and a set of service engines at the back end. Particularly, a transcoding task can be executed on the mobile device (i.e. mobile execution) or offloaded and scheduled by the dispatcher to one of the service engines in the cloud (i.e. cloud execution). We aim to minimize the energy consumption of transcoding on the mobile device and service engines in the cloud while achieving low delay. For the mobile device, we formulate its offloading policy under delay deadline as a constrained optimization problem. We find an operational region on which execution mode, that is, mobile execution or cloud execution, is more energy efficient for the mobile device. For the cloud, we propose an online algorithm to dispatch transcoding tasks to service engines, with an objective to reduce energy consumption while achieving queue stability. By appropriately choosing the control variable, the proposed algorithm outperforms alternative algorithms, with lower time average energy consumption and time average queue length on the service engines. The proposed offloading policy can reduce energy consumption on both mobile devices and the cloud jointly, which provides guidelines for the design of green mobile cloud.