scholarly journals Contact lines over random topographical substrates. Part 2. Dynamics

2011 ◽  
Vol 672 ◽  
pp. 384-410 ◽  
Author(s):  
NIKOS SAVVA ◽  
GRIGORIOS A. PAVLIOTIS ◽  
SERAFIM KALLIADASIS
Keyword(s):  
White Noise ◽  
Statistical Properties ◽  
Substrate Roughness ◽  
Droplet Spreading ◽  
Contact Points ◽  
Spreading Dynamics ◽  
Theoretical Predictions ◽  
Long Time ◽  
Band Limited ◽  
System Of Integrodifferential Equations

We examine the dynamics of a two-dimensional droplet spreading over a random topographical substrate. Our analysis is based on the formalism developed in Part 1 of this study, where a random substrate was modelled as band-limited white noise. The system of integrodifferential equations for the motion of the contact points over deterministic substrates derived by Savva and Kalliadasis (Phys. Fluids, vol. 21, 2009, 092102) is applicable to the case of random substrates as well. This system is linearized for small substrate amplitudes to obtain stochastic differential equations for the droplet shift and contact line fluctuations in the limit of shallow and slowly varying topographies. Our theoretical predictions for the time evolution of the statistical properties of these quantities are verified by numerical experiments. Considering the statistics of the dynamics allows us to fully address the influence of the substrate variations on wetting. For example, we demonstrate that the droplet wets the substrate less as the substrate roughness increases, illustrating also the possibility of a substrate-induced hysteresis effect. Finally, the analysis of the long-time limit of spreading dynamics for a substrate represented by a band-limited white noise is extended to arbitrary substrate representations. It is shown that the statistics of spreading is independent of the characteristic length scales that naturally arise from the statistical properties of a substrate representation.

Model Reduction of Piezoelectric Energy Harvesters Subject to Band-Limited, Stochastic Base Excitation

2012 ◽  
Author(s):  
Adam M. Wickenheiser
Keyword(s):  
White Noise ◽  
Design Optimization ◽  
Broadband Noise ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Energy Harvesters ◽  
White Noise Excitation ◽  
Single Degree ◽  
Piezoelectric Energy ◽  
Band Limited

In many scenarios where vibration energy harvesting can be utilized — particularly those involving bio-motions or environmental disturbances — energy sources are broadband and non-stationary. On the other hand, design procedures have been predominantly developed for harmonic or white noise excitation, specifically for single degree of freedom approximations of the transducer. In this paper, a general approach for design optimization of cantilevered, piezoelectric energy harvesters in the presence of band-limited, white-noise excitation is outlined. For this study, human and vehicular motions are considered; these complex waveforms are distilled into a small set of dominant features with regard to their impact on the power output of the device. Criteria based on modal participation factors, including pre-filtering of the disturbance, are used in guiding the reduction of the input and plant degrees of freedom in order to make the design optimization problem tractable. This process determines the error in assuming a low-order model for the transducer in the presence of broadband noise that may excite multiple modes of vibration. Furthermore, this study considers the quantitative impact of charge cancellation in higher modes and the benefits of inserting multiple electrodes along the length. To illustrate these methods, energy harvesters are designed for acceleration data collected from walking and car idling. It is shown that a simple method that is a generalization of naïve approaches that assume harmonic or white noise excitation and a single degree of freedom can determine which simplifications are appropriate and the inaccuracies that can be expected from them.

Relationship between temporal and spatial averages in grid turbulence

2013 ◽  
Vol 730 ◽  
pp. 593-606 ◽  
Author(s):  
L. Djenidi ◽  
S. F. Tardu ◽  
R. A. Antonia
Keyword(s):  
Strong Support ◽  
Statistical Properties ◽  
Grid Turbulence ◽  
Mean Flow ◽  
Lateral Direction ◽  
Ergodic Hypothesis ◽  
Long Time ◽  
The Mean ◽  
Temporal And Spatial ◽  
Boltzmann Method

AbstractA long-time direct numerical simulation (DNS) based on the lattice Boltzmann method is carried out for grid turbulence with the view to compare spatially averaged statistical properties in planes perpendicular to the mean flow with their temporal counterparts. The results show that the two averages become equal a short distance downstream of the grid. This equality indicates that the flow has become homogeneous in a plane perpendicular to the mean flow. This is an important result, since it confirms that hot-wire measurements are appropriate for testing theoretical results based on spatially averaged statistics. It is equally important in the context of DNS of grid turbulence, since it justifies the use of spatial averaging along a lateral direction and over several realizations for determining various statistical properties. Finally, the very good agreement between temporal and spatial averages validates the comparison between temporal (experiments) and spatial (DNS) statistical properties. The results are also interesting because, since the flow is stationary in time and spatially homogeneous along lateral directions, the equality between the two types of averaging provides strong support for the ergodic hypothesis in grid turbulence in planes perpendicular to the mean flow.

scholarly journals Triadic resonances in precessing rapidly rotating cylinder flows

2015 ◽  
Vol 778 ◽  
Author(s):  
T. Albrecht ◽  
H. M. Blackburn ◽  
J. M. Lopez ◽  
R. Manasseh ◽  
P. Meunier
Keyword(s):  
Rotating Cylinder ◽  
Direct Numerical Simulations ◽  
Mode Shapes ◽  
Resonance Model ◽  
Rapid Rotation ◽  
Nutation Angle ◽  
Resonant Instability ◽  
Theoretical Predictions ◽  
Long Time ◽  
Good Agreement

Direct numerical simulations of flows in cylinders subjected to both rapid rotation and axial precession are presented and analysed in the context of a stability theory based on the triadic resonance of Kelvin modes. For a case that was chosen to provide a finely tuned resonant instability with a small nutation angle, the simulations are in good agreement with the theory and previous experiments in terms of mode shapes and dynamics, including long-time-scale regularization of the flow and recurrent collapses. Cases not tuned to the most unstable triad, but with the nutation angle still small, are also in quite good agreement with theoretical predictions, showing that the presence of viscosity makes the physics of the triadic-resonance model robust to detuning. Finally, for a case with $45^{\circ }$ nutation angle for which it has been suggested that resonance does not occur, the simulations show that a slowly growing triadic resonance predicted by theory is in fact observed if sufficient evolution time is allowed.

scholarly journals Signal-to-noise ratio in the membrane potential of the owl's auditory coincidence detectors

2012 ◽  
Vol 108 (10) ◽  
pp. 2837-2845 ◽  
Author(s):  
Go Ashida ◽  
Kazuo Funabiki ◽  
Paula T. Kuokkanen ◽  
Richard Kempter ◽  
Catherine E. Carr
Keyword(s):  
Neural Circuit ◽  
Signal To Noise Ratio ◽  
Phase Locking ◽  
Low Frequency ◽  
Membrane Potentials ◽  
Signal To Noise ◽  
Theoretical Predictions ◽  
Noise Ratio ◽  
Band Limited

Owls use interaural time differences (ITDs) to locate a sound source. They compute ITD in a specialized neural circuit that consists of axonal delay lines from the cochlear nucleus magnocellularis (NM) and coincidence detectors in the nucleus laminaris (NL). Recent physiological recordings have shown that tonal stimuli induce oscillatory membrane potentials in NL neurons (Funabiki K, Ashida G, Konishi M. J Neurosci 31: 15245–15256, 2011). The amplitude of these oscillations varies with ITD and is strongly correlated to the firing rate. The oscillation, termed the sound analog potential, has the same frequency as the stimulus tone and is presumed to originate from phase-locked synaptic inputs from NM fibers. To investigate how these oscillatory membrane potentials are generated, we applied recently developed signal-to-noise ratio (SNR) analysis techniques (Kuokkanen PT, Wagner H, Ashida G, Carr CE, Kempter R. J Neurophysiol 104: 2274–2290, 2010) to the intracellular waveforms obtained in vivo. Our theoretical prediction of the band-limited SNRs agreed with experimental data for mid- to high-frequency (>2 kHz) NL neurons. For low-frequency (≤2 kHz) NL neurons, however, measured SNRs were lower than theoretical predictions. These results suggest that the number of independent NM fibers converging onto each NL neuron and/or the population-averaged degree of phase-locking of the NM fibers could be significantly smaller in the low-frequency NL region than estimated for higher best-frequency NL.

scholarly journals A new metric for statistical properties of long time behaviors

2020 ◽  
Vol 269 (4) ◽  
pp. 2741-2773
Author(s):  
Liqi Zheng ◽  
Zuohuan Zheng
Keyword(s):  
Statistical Properties ◽  
Long Time

Stationary random vibration of a viscoelastic Timoshenko cantilever beam under diverse random processes

2019 ◽  
Vol 234 (4) ◽  
pp. 849-861
Author(s):  
Qingzhao Zhou ◽  
David He ◽  
Yaping Zhao
Keyword(s):  
White Noise ◽  
Cantilever Beam ◽  
Time Correlation ◽  
Random Excitation ◽  
Transverse Displacement ◽  
Mean Square ◽  
Concentrated Force ◽  
The Mean ◽  
Definite Integration ◽  
Band Limited

In this paper, the stochastic properties of a uniform Timoshenko cantilever beam are investigated systematically. Based on the external viscous damping and Kelvin–Voigt viscoelastic damping, the partial differential equations of the Timoshenko beam subjected to random excitation are derived. The applied load is the concentrated force, and the excitation related to includes the ideal white noise, the band-limited white noise, and the exponential noise. Expressions are obtained for the space–time correlation functions and the space–frequency power spectral density functions of the transverse displacement response. The evident improvement is that the infinite integral and the definite integration in the mean square responses are worked out by means of the residue integral method and the integration by partial fraction, and the exact solutions of the mean square response are obtained in the form of an infinite series finally. This improvement provides a basis for both the mode truncation and the modal cross-spectral densities whether which can be ignored. Providing the numerical example, the numerical results obtained show the effectiveness of the theoretical analysis.

scholarly journals X-Ray Observations of Elliptical Galaxies by ASCA Satellite

1996 ◽  
Vol 171 ◽  
pp. 412-412
Author(s):  
K. Matsushita ◽  
K. Makishima
Keyword(s):  
Low Temperature ◽  
Mass Loss ◽  
Elliptical Galaxies ◽  
Stellar Mass ◽  
Plasma Emission ◽  
X Ray ◽  
Theoretical Predictions ◽  
Long Time ◽  
Temperature Component ◽  
Hubble Time

Using ASCA, we have confirmed that the ISM of X-ray bright elliptical galaxies are surprisingly metal poor, as compared to the theoretical predictions. In fact the exact values of the derived metallicity depend considerably on the plasma emission codes. However, the overall metallicity cannot be larger than ∼ 1 solar. For low LX/LB galaxies, all the available plasma codes suggest abundances less than half a solar. The ASCA spectra may be compatible with somewhat higher metallicity if we assume there is an additional low-temperature component (e.g. kTe ∼ 0.3 keV). However, the derived abundance can not be over 1 solar. In particular, the Si abundance turns out to be < 1.5 solar, confirming the metal-poor nature of the ISM. These ASCA results are in severe contradiction with most of the SN Ia rate, particularly that of Tammann (1982). Considering further that a fairly long time (109–10yr) is needed for the stellar mass loss to accumulates into the ISM, it is suggested that the SN Ia rate has remained quite low throughout Hubble time.

scholarly journals Exact statistical properties of the Burgers equation

2000 ◽  
Vol 417 ◽  
pp. 323-349 ◽  
Author(s):  
L. FRACHEBOURG ◽  
Ph. A. MARTIN
Keyword(s):  
White Noise ◽  
Large Distance ◽  
Burgers Equation ◽  
Higher Order ◽  
Statistical Properties ◽  
Inviscid Limit ◽  
Initial Condition ◽  
Spatial Correlations ◽  
One Dimensional ◽  
The One

The one-dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed analytical forms. In particular, the large distance behaviour of spatial correlations of the field is determined. Since higher-order distributions factorize in terms of the one- and two- point functions, our analysis provides an explicit and complete statistical description of this problem.

Simulation of Spreading Dynamics of a EWOD Droplet With Dynamic Contact Angle and Contact Angle Hysteresis

2009 ◽  
Author(s):  
Fangjun Hong ◽  
Ping Cheng ◽  
Zhen Sun ◽  
Huiying Wu
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Low Voltage ◽  
Contact Angle Hysteresis ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Dielectric Surface ◽  
Contact Radius ◽  
Droplet Spreading ◽  
Spreading Dynamics

In this paper, the electrowetting dynamics of a droplet on a dielectric surface was investigated numerically by a mathematical model including dynamic contact angle and contact angle hysteresis. The fluid flow is described by laminar N-S equation, the free surface of the droplet is modeled by the Volume of Fluid (VOF) method, and the electrowetting force is incorporated by exerting an electrical force on the cells at the contact line. The Kilster’s model that can deal with both receding and advancing contact angle is adopted. Numerical results indicate that there is overshooting and oscillation of contact radius in droplet spreading process before it ceases the movement when the excitation voltage is high; while the overshooting is not observed for low voltage. The explanation for the contact line overshooting and some special characteristics of variation of contact radius with time were also conducted.

Numerical Investigation of a Liquid Droplet Impinging on a Heated Surface

2009 ◽  
Author(s):  
Andres Diaz ◽  
Alfonso Ortega ◽  
Ryan Anderson
Keyword(s):  
Heat Transfer ◽  
Numerical Investigation ◽  
Fundamental Problem ◽  
Water Drop ◽  
Liquid Droplet ◽  
Heated Surface ◽  
Heat Removal ◽  
Droplet Spreading ◽  
Droplet Shape ◽  
Spreading Dynamics

Previous studies, most of them experimental, reveal that the cooling effectiveness of a water drop impinging on a heated surface depends on the wall temperature, droplet shape and velocity. All previous studies focus on the behavior of a droplet falling in a quiescent environment, such as still air. Evidence in the literature also shows that gas assisted droplet sprays, in which a gas phase propels the droplets, are more efficient in heat removal than sprays consisting of droplets alone. It is conjectured that this is due to an increase in the maximum droplet spreading diameter upon impact, a thinner film, and consequently an increase in the overall heat transfer coefficient. Recent experiments in the author’s group [1, 2] show that the carrier gas jet strongly influences droplet spreading dynamics by imposing normal and shear forces on the liquid surface. The heat transfer is greatly augmented in the process, compared to a free falling droplet. To date, there has been no fundamental investigation of the physics of gas assisted spray cooling. To begin to understand the complicated process, this paper reports on a fundamental problem of a single liquid droplet that impinges on a heated surface. This paper contributes a numerical investigation of the problem using the volume of fluid (VOF) technique to capture droplet spreading dynamics and heat transfer in a single drop event. The fluid mechanics is investigated and compared to the experimental data. The greatest uncertainty in the simulation is in the specification of the contact angle of the advancing or receding liquid front, and in capturing the onset of the three-dimensional fingering phenomena.

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