scholarly journals Interaction of cavitation bubbles with the interface of two immiscible fluids on multiple time scales

2021 ◽  
Vol 932 ◽  
Author(s):  
Rui Han ◽  
A-Man Zhang ◽  
Sichao Tan ◽  
Shuai Li
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Cavitation Bubble ◽  
High Speed ◽  
Bubble Dynamics ◽  
Immiscible Fluids ◽  
Multiple Time Scales ◽  
Liquid Jet ◽  
Short Time Scale ◽  
Multiple Time

We experimentally, numerically and theoretically investigate the nonlinear interaction between a cavitation bubble and the interface of two immiscible fluids (oil and water) on multiple time scales. The underwater electric discharge method is utilized to generate a cavitation bubble near or at the interface. Both the bubble dynamics on a short time scale and the interface evolution on a much longer time scale are recorded via high-speed photography. Two mechanisms are found to contribute to the fluid mixing in our system. First, when a bubble is initiated in the oil phase or at the interface, an inertia-dominated high-speed liquid jet generated from the collapsing bubble penetrates the water–oil interface, and consequently transports fine oil droplets into the water. The critical standoff parameter for jet penetration is found to be highly dependent on the density ratio of the two fluids. Furthermore, the pinch-off of an interface jet produced long after the bubble dynamics stage is reckoned as the second mechanism, carrying water droplets into the oil bulk. The dependence of the bubble jetting behaviours and interface jet dynamics on the governing parameters is systematically studied via experiments and boundary integral simulations. Particularly, we quantitatively demonstrate the respective roles of surface tension and viscosity in interface jet dynamics. As for a bubble initiated at the interface, an extended Rayleigh–Plesset model is proposed that well predicts the asymmetric dynamics of the bubble, which accounts for a faster contraction of the bubble top and a downward liquid jet.

Time-scale dependent mechanism of atmospheric CO2 concentration drivers of watershed water-energy balance

2021 ◽  
Author(s):  
Jing Zhao
Keyword(s):  
Energy Balance ◽  
River Basin ◽  
Time Scales ◽  
Time Scale ◽  
Hydrological Processes ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
The Wei River Basin ◽  
Balance Dynamics ◽  
The Impact

<p>The elevated atmospheric carbon dioxide concentration (CO<sub>2</sub>), as a key variable linking human activities and climate change, seriously affects the watershed hydrological processes. However, whether and how atmospheric CO<sub>2</sub> influences the watershed water-energy balance dynamics at multiple time scales have not been revealed. Based on long-term hydrometeorological data, the variation of non-stationary parameter n series in the Choudhury's equation in the mainstream of the Wei River Basin (WRB), the Jing River Basin (JRB) and Beiluo River Basin (BLRB), three typical Loess Plateau regions in China, was examined. Subsequently, the Empirical Mode Decomposition method was applied to explore the impact of CO<sub>2</sub> on watershed water-energy balance dynamics at multiple time scales. Results indicate that (1) in the context of warming and drying condition, annual n series in the WRB displays a significantly increasing trend, while that in the JRB and BLRB presents non-significantly decreasing trends; (2) the non-stationary n series was divided into 3-, 7-, 18-, exceeding 18-year time scale oscillations and a trend residual. In the WRB and BLRB, the overall variation of n was dominated by the residual, whereas in the JRB it was dominated by the 7-year time scale oscillation; (3) the relationship between CO<sub>2 </sub>concentration and n series was significant in the WRB except for 3-year time scale. In the JRB, CO<sub>2 </sub>concentration and n series were significantly correlated on the 7- and exceeding 7-year time scales, while in the BLRB, such a significant relationship existed only on the 18- and exceeding 18-year time scales. (4) CO<sub>2</sub>-driven temperature rise and vegetation greening elevated the aridity index and evaporation ratio, thus impacting watershed water-energy balance dynamics. This study provided a deeper explanation for the possible impact of CO<sub>2</sub> concentration on the watershed hydrological processes.</p>

Modeling IP Traffic Behavior through Markovian Models

2008 ◽  
pp. 305-315
Author(s):  
Antóniol Nogueira ◽  
Paulo Salvador ◽  
Rui Valadas ◽  
António Pacheco
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Marginal Distribution ◽  
Arrival Process ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Markovian Models ◽  
Fitting Procedure ◽  
Packet Arrival ◽  
Traffic Behavior

This article addresses the use of Markovian models, based on discrete time MMPPs (dMMPPs), for modeling IP traffic. In order to describe the packet arrival process, we will present three traffic models that were designed to capture self-similar behavior over multiple time scales. The first model is based on a parameter fitting procedure that matches both the autocovariance and marginal distribution of the counting process (Salvador 2003). The dMMPP is constructed as a superposition of two-state dMMPPs (2-dMMPPs), designed to match the autocovariance function, and one designed to match the marginal distribution. The second model is a superposition of MMPPs, each one describing a different time scale (Nogueira 2003a). The third model is obtained as the equivalent to a hierarchical construction process that, starting at the coarsest time scale, successively decomposes MMPP states into new MMPPs to incorporate the characteristics offered by finer time scales (Nogueira 2003b). These two models are constructed by fitting the distribution of packet counts in a given number of time scales.

Watershed water-energy balance dynamics and their association with diverse influencing factors at multiple time scales

2020 ◽  
Author(s):  
Shengzhi Huang ◽  
Jing Zhao ◽  
Kang Ren
Keyword(s):  
Energy Balance ◽  
Influencing Factors ◽  
River Basin ◽  
Time Scales ◽  
Time Scale ◽  
Dynamic Change ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Plateau Region ◽  
Balance Dynamics

<p>The Budyko curve is an effective tool for estimating how precipitation (P) partition into evapotranspiration (E) and streamflow (Q). Controlling the shape of the Budyko curve, the Budyko parameter represents the superimposed impact of various periodic factors (including climatic factors, catchment characteristics, teleconnection factors and anthropogenic activities) on the watershed water-energy balance dynamics, and such superimposed impact is not conducive to identifying the driving factors of the dynamic change of Budyko parameter at different time scales, and thus affect the parameter estimation. Here we obtain the dynamic change of Budyko parameter for the Wei River Basin (WRB)-a typical Loess Plateau region in China based on a 11-years moving window, and then adopt the Empirical Mode Decomposition (EMD) method to reveal the relationships between influencing factors and Budyko parameter series at multiple time scales by considering the interplay among different influencing factors. Results indicate that (1) Budyko parameter series are decomposed into 4-, 12-, 20-, exceeding 20-year time scale oscillations and a residual component with an significantly increasing trend in the upstream of the WRB (UWR) and the middle and lower reaches of the WRB (MDWR), a non-significantly decreasing trend in the Jing River Basin (JRB) and Beiluo River Basin (BLRB); (2) by analyzing the residual trend component, evaporation ratio (E/P), soil moisture (SM) and effective irrigated area (EIA) are found to induce the significant increase of parameter in the UWR, whereas that in the MDWR is dominated by baseflow (BF) and Niño 3.4; (3) parameter dynamics at the 4-year time scale is dominated by E/P, aridity index (E<sub>P</sub>/P), BF and SM; BF, PDO and sunspots attribute to the dynamics at 12-year time scale; all the factors except BF and SM contribute to the dynamics at 20- or exceeding 20-year time scales. The results of this study will help identify the connection between watershed water-energy balance dynamics and changing environment at multiple time scales, and also be beneficial for guiding water resources management and ecological development planning on the Loess Plateau region.</p>

Multiscale Joint Symbolic Transfer Entropy for Quantification of Causal Interactions Between Heart Rate and Blood Pressure Variability Under Postural Stress

2015 ◽  
Vol 14 (03) ◽  
pp. 1550031 ◽  
Author(s):  
A. Singh ◽  
B. S. Saini ◽  
D. Singh
Keyword(s):  
Blood Pressure ◽  
Time Delay ◽  
Time Scales ◽  
Frequency Band ◽  
Supine Position ◽  
Time Scale ◽  
Upright Position ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Symbolic Transfer Entropy

In this paper, joint symbolic transfer entropy (JSTE) is explored to quantify causal interactions between systolic blood pressure (SBP) and RR intervals (peak-to-peak distance between consecutive R-peaks) at multiple time scales. SBP→RR coupling (C s-r ) and RR→SBP coupling (C r-s ) coupling is analyzed at multiple time scales and delays. The ability of the approach based on JSTE to detect SBP–RR causal coupling is tested on 42 healthy subjects in supine and upright position along with 21 subjects of EUROBAVAR dataset. In addition, lack of causal coupling from SBP to RR was assessed on 20 post-acute myocardial infarction (AMI) patients. Results demonstrate that (i) standard deviation (SD) of RR interval series and SBP series decreases with time scale τ = 1 to 10 for all types of subjects. (ii) SD in supine is more than that of upright position at each time scale irrespective of types of subjects. (iii) JSTE decreases with time delay for healthy and AMI patients but does not follow decreasing trend for baroflex sensitivity BRS failure patients. (iv) JSTE in supine position is more than that of upright position irrespective of time delay. (v) JSTE decreases with time scale for healthy and AMI patients but does not follow decreasing trend for BRS failure patients. (vi) JSTE in supine position is more than that of upright position only at finer scales. (vii) Enhanced feed-forward (FF) coupling and suppressed feedback (FB) coupling found at supine position within low frequency band (0.04–0.15 Hz) as well as high frequency band (0.151–0.4 Hz) indicated prevalence on non-baroreflex mechanisms. (viii) FB coupling recovered in the upright position which was stronger than FF coupling. Upon comparison with cross conditional entropy (CCE), it is found that JSTE provides more significant differences between supine and upright position.

scholarly journals On Estimating Survival and Hazard Ratios Using One Time-Scale When Cohort Data Have Multiple Time-Scales: A Simulation Study

2021 ◽  
Author(s):  
Nurgul Batyrbekova ◽  
Hannah Bower ◽  
Paul Dickman ◽  
Robert Szulkin ◽  
Paul C. Lambert ◽  
...  
Keyword(s):  
Time Scales ◽  
Simulation Study ◽  
Time Scale ◽  
Proportional Hazards ◽  
Survival Models ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Cohort Data ◽  
Hazard Ratios ◽  
The One

Abstract Background: When estimating survival functions and hazard ratios during theanalysis of cohort data, we often choose one time-scale, such as time-on-study, asthe primary time-scale, and include a xed covariate, such as age at entry, in themodel. However, we rarely consider the possibility of simultaneous effects ofmultiple time-scales on the hazard function. Methods: In a simulation study, within the framework of exible parametricmodels, we investigate whether relying on one time-scale and xed covariate asproxy for the second time-scale is sucient in capturing the true survivalfunctions and hazard ratios when there are actually two underlying time-scales. Result: We demonstrate that the one-time-scale survival models appeared toapproximate well the survival proportions, however, large bias was observed in thelog hazard ratios if the covariate of interest had interactions with the secondtime-scale or with both time-scales. Conclusion: We recommend to exercise caution and encourage tting modelswith multiple time-scales if it is suspected that the cohort data have underlyingnon-proportional hazards on the second time-scale or both time-scales.

scholarly journals A Multivariate Quantile-Matching Bias Correction Approach with Auto- and Cross-Dependence across Multiple Time Scales: Implications for Downscaling

2016 ◽  
Vol 29 (10) ◽  
pp. 3519-3539 ◽  
Author(s):  
Rajeshwar Mehrotra ◽  
Ashish Sharma
Keyword(s):  
Water Resources ◽  
Time Scales ◽  
Bias Correction ◽  
Time Scale ◽  
General Circulation ◽  
Circulation Model ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Multiple Variables ◽  
Multivariate Quantile

Abstract A novel multivariate quantile-matching nesting bias correction approach is developed to remove systematic biases in general circulation model (GCM) outputs over multiple time scales. This is a significant advancement over typical quantile-matching alternatives available for bias correction, as they implicitly assume that correction of individual variable attributes will lead to correction of dependence biases between multiple variables. Furthermore, existing approaches perform bias correction at a given time scale (e.g., daily), whereas applications often require biases to be addressed at more than one time scale (such as annual in the case of most water resources planning projects). The proposed approach addresses all these issues, and additionally attempts to correct for lag-1 dependence (and cross-dependence) attributes across multiple time scales. The approach is called multivariate recursive quantile nesting bias correction (MRQNBC). The fidelity of the approach is demonstrated by applying it to a vector of CSIRO Mk3 GCM atmospheric variables and comparing the results with the commonly used quantile-matching approach. Following this, the implications of the approach in hydrology- and water resources–related applications are demonstrated by feeding the bias-corrected data to a rainfall downscaling model and comparing the downscaled rainfall attributes for current and future climate. The proposed approach is shown to represent the variability and persistence related attributes better and can thus be expected to have important consequences for the simulation of occurrence and intensity of extreme events such as floods and droughts in downscaled simulations, of importance in various climate impact assessment applications.

scholarly journals The multiple time scales of sleep dynamics as a challenge for modelling the sleeping brain

2011 ◽  
Vol 369 (1952) ◽  
pp. 3884-3901 ◽  
Author(s):  
Eckehard Olbrich ◽  
Jens Christian Claussen ◽  
Peter Achermann
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Computational Models ◽  
Multiple Time Scales ◽  
Sleep Stages ◽  
Multiple Time ◽  
Sleep Regulation ◽  
Typical Time ◽  
Electroencephalogram Eeg ◽  
Different Time Scales

A particular property of the sleeping brain is that it exhibits dynamics on very different time scales ranging from the typical sleep oscillations such as sleep spindles and slow waves that can be observed in electroencephalogram (EEG) segments of several seconds duration over the transitions between the different sleep stages on a time scale of minutes to the dynamical processes involved in sleep regulation with typical time constants in the range of hours. There is an increasing body of work on mathematical and computational models addressing these different dynamics, however, usually considering only processes on a single time scale. In this paper, we review and present a new analysis of the dynamics of human sleep EEG at the different time scales and relate the findings to recent modelling efforts pointing out both the achievements and remaining challenges.

scholarly journals Multi-time scale data assimilation for atmosphere–ocean state estimates

2015 ◽  
Vol 11 (4) ◽  
pp. 3729-3757 ◽  
Author(s):  
N. Steiger ◽  
G. Hakim
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Time Scales ◽  
Time Scale ◽  
Low Frequency ◽  
Climate System ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Proxy Data ◽  
Frequency Components

Abstract. Paleoclimate proxy data span seasonal to millennial time scales, and Earth's climate system has both high- and low-frequency components. Yet it is currently unclear how best to incorporate multiple time scales of proxy data into a single reconstruction framework and to also capture both high- and low-frequency components of reconstructed variables. Here we present a data assimilation algorithm that can explicitly incorporate proxy data at arbitrary time scales. Through a series of pseudoproxy experiments, we find that atmosphere–ocean states are most skilfully reconstructed by incorporating proxies across multiple time scales compared to using proxies at short (annual) or long (~ decadal) time scales alone. Additionally, reconstructions that incorporate long time-scale pseudoproxies improve the low-frequency components of the reconstructions relative to using only high-resolution pseudoproxies. We argue that this is because time averaging high-resolution observations improves their covariance relationship with the slowly-varying components of the coupled-climate system, which the data assimilation algorithm can exploit. These results are insensitive to the choice of climate model, despite the model variables having very different spectral characteristics. Our results also suggest that it may be possible to reconstruct features of the oceanic meridional overturning circulation based solely on atmospheric surface temperature proxies.

scholarly journals Standardized Water Budget Index and Validation in Drought Estimation of Haihe River Basin, North China

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Shaohua Liu ◽  
Denghua Yan ◽  
Hao Wang ◽  
Chuanzhe Li ◽  
Baisha Weng ◽  
...  
Keyword(s):  
River Basin ◽  
Time Scales ◽  
Time Scale ◽  
Water Budget ◽  
Drought Index ◽  
Multiple Time Scales ◽  
Haihe River Basin ◽  
Drought Indices ◽  
Multiple Time ◽  
Haihe River

The physical-based drought indices such as the self-calibrated Palmer Drought Severity Index (sc-PDSI) with the fixed time scale is inadequate for the multiscalar drought assessment, and the multiscalar drought indices including Standardized Precipitation Index (SPI), Reconnaissance Drought Index (RDI), and Standardized Precipitation Evapotranspiration Index (SPEI) based on the meteorological factors are lack of physical mechanism and cannot depict the actual water budget. To fill this gap, the Standardized Water Budget Index (SWBI) is constructed based on the difference between areal precipitation and actual evapotranspiration (AET), which can describe the actual water budget but also assess the drought at multiple time scales. Then, sc-PDSI was taken as the reference drought index to compare with multiscalar drought indices at different time scale in Haihe River basin. The result shows that SWBI correlates better with sc-PDSI and the RMSE of SWBI is less than other multiscalar drought indices. In addition, all of drought indices show a decreasing trend in Haihe River Basin, possibly due to the decreasing precipitation from 1961 to 2010. The decreasing trends of SWBI were significant and consistent at all the time scales, while the decreasing trends of other multiscalar drought indices are insignificant at time scale less than 3 months.

scholarly journals COMPUTATIONAL MODELING OF DYNAMICAL SYSTEMS

2005 ◽  
Vol 15 (03) ◽  
pp. 471-481 ◽  
Author(s):  
JOHAN JANSSON ◽  
CLAES JOHNSON ◽  
ANDERS LOGG
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Computational Modeling ◽  
Time Scales ◽  
Time Scale ◽  
Short Note ◽  
Multiple Time Scales ◽  
Time Interval ◽  
Multiple Time ◽  
Fast Time

In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be very costly. By resolving the fast time scales in a short time simulation, a model for the effect of the small time scale variation on large time scales can be determined, making solution possible on a long time interval. This process of computational modeling can be completely automated. Two examples are presented, including a simple model problem oscillating at a time scale of 10–9 computed over the time interval [0,100], and a lattice consisting of large and small point masses.

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