scholarly journals Buckling versus crystal expulsion controlled by deformation rate of particle-coated air bubbles in oil

Author(s):  
Saikat Saha ◽  
Francis Pagaud ◽  
Bernard P. Binks ◽  
Valeria Garbin

Oil foams stabilized by crystallizing agents exhibit outstanding stability and show promise for applications in consumer products. The stability and mechanics imparted by the interfacial layer of crystals underpin product shelf-life, as well as optimal processing conditions and performance in applications. Shelf-life is affected by the stability against bubble dissolution over a long time scale, which leads to slow compression of the interfacial layer. In processing flow conditions, the imposed deformation is characterized by much shorter time scales. In practical situations, the crystal layer is therefore subjected to deformation on extremely different time scales. Despite its importance, our understanding of the behavior of such interfacial layers at different time scales remains limited. To address this gap, here we investigate the dynamics of single, crystal-coated bubbles isolated from an oleofoam, at two extreme timescales: the diffusion-limited timescale characteristic of bubble dissolution 10,000 s, and a fast time scale characteristic of processing flow conditions, 0.001 s. In our experiments, slow deformation is obtained by bubble dissolution, and fast deformation in controlled conditions with real-time imaging is obtained using ultrasound-induced bubble oscillations. The experiments reveal that the fate of the interfacial layer is dramatically affected by the dynamics of deformation: after complete bubble dissolution, a continuous solid layer remains; while after fast, oscillatory deformation of the layer, small crystals are expelled from the layer. This observation shows promise towards developing stimuli-responsive systems, with sensitivity to deformation rate, in addition to the already known thermo- and photo-responsiveness of oleofoams.

1995 ◽  
Vol 03 (02) ◽  
pp. 591-602 ◽  
Author(s):  
PIERRE AUGER ◽  
JEAN-CHRISTOPHE POGGIALE

The aim of this work is to show that at the population level, emerging properties may occur as a result of the coupling between the fast micro-dynamics and the slow macrodynamics. We studied a prey-predator system with different time scales in a heterogeneous environment. A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to the growth and the interactions between the species. Preys go on the spatial patches on which some resources are located and can be caught by the predators on them. The efficiency of the predators to catch preys is patch-dependent. Preys can be more easily caught on some spatial patches than others. Perturbation theory is used in order to aggregate the initial system of ordinary differential equations for the patch sub-populations into a macro-system of two differential equations governing the total populations. Firstly, we study the case of a linear process of migration for which the aggregated system is formally identical to the slow part of the full system. Then, we study an example of a nonlinear process of migration. We show that under these conditions emerging properties appear at the population level.


2017 ◽  
Vol 74 (5) ◽  
pp. 1533-1547 ◽  
Author(s):  
William J. M. Seviour ◽  
Darryn W. Waugh ◽  
Richard K. Scott

Abstract The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising, since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here the stability of a Mars-like annular vortex is investigated using numerical integrations of the rotating shallow-water equations. The mode of instability and its growth rate is shown to depend upon the latitude and width of the annulus. By introducing thermal relaxation toward an annular equilibrium profile with a time scale similar to that of the instability, a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere can be simulated. This time scale, typically 0.5–2 sols, is similar to radiative relaxation time scales for Mars’s polar atmosphere. The persistence of an annular vortex is also shown to be robust to topographic forcing, as long as it is below a certain amplitude. It is therefore proposed that the persistence of this barotropically unstable annular vortex is permitted owing to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.


2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiping Lu ◽  
Ming Li ◽  
Wei Zhao

We investigate the stationarity property of the accumulated Ethernet traffic series. We applied several widely used stationarity and unit root tests, such as Dickey-Fuller test and its augmented version, Phillips-Perron test, as well as the Kwiatkowski-Phillips-Schmidt-Shin test and some of its generalizations, to the assessment of the stationarity of the traffic traces at the different time scales. The quantitative results in this research provide evidence that when the time scale increases, the accumulated traffic series are more stationary.


2021 ◽  
Vol 9 ◽  
Author(s):  
Peng Li ◽  
Fan Zhang ◽  
Xiyuan Ma ◽  
Senjing Yao ◽  
Zhuolin Zhong ◽  
...  

The park integrated energy system (PIES) plays an important role in realizing sustainable energy development and carbon neutral. Furthermore, its optimization dispatch can improve the energy utilization efficiency and reduce energy systems operation cost. However, the randomness and volatility of renewable energy and the instability of load all bring challenges to its optimal operation. An optimal dispatch framework of PIES is proposed, which constructs the operation models under three different time scales, including day-ahead, intra-day and real-time. Demand response is also divided into three levels considering its response characteristics and cost composition under different time scales. The example analysis shows that the multi-time scale optimization dispatch model can not only meet the supply and demand balance of PIES, diminish the fluctuation of renewable energy and flatten load curves, but also reduce the operation cost and improve the reliability of energy systems.


2019 ◽  
Vol 490 (1) ◽  
pp. 359-370 ◽  
Author(s):  
Ying Wang ◽  
Ji-lin Zhou ◽  
Fu-yao Liu ◽  
Wei Sun ◽  
Hui-Gen Liu ◽  
...  

ABSTRACT A type of compactly spaced and comparably sized multi-exoplanet system similar to TRAPPIST-1 has been discovered recently. The stability of these systems is an important issue, requiring further study. We examined how the initial inclinations influence the stability of multi-planet systems and derived an empirical formula describing the dependence of the instability time-scale on planetary mass, space separation and initial inclination. We find the following. (i) If space separations between planets are greater than 12RH (mutual Hill radius), coplanar multi-planet systems with 10−6 ≤ μ ≤ 10−3 (reduced planetary mass μ = m/M*) will remain stable within 1010Tin (the innermost orbital period). (ii) If initial inclinations of planets are smaller than 10° and space separations are greater than 10RH, multi-planet systems consisting of ≥5 planets with μ ≥ 10−5 will remain stable within 1010Tin. (iii) Initial inclinations in [0°, 10°] have inconsequential effects on the instability time-scales of massive multi-planet systems (μ ≥ 10−5), because eccentricities (excited during evolution) dominate the stability of these systems. (iv) If the initial inclinations are large enough (≥10°), sharp increases of instability time-scales in groups with 10−3 ≥ μ ≥ 10−5 will be moderated. This article presents a comprehensive study of the influence of inclination on the stability of multi-planet systems and discusses critical space separations for a multi-planet system becoming unstable.


2008 ◽  
Vol 26 (3) ◽  
pp. 441-446 ◽  
Author(s):  
J. L. Borkowski

Abstract. Solar UV radiation variability in the period 1976–2006 is discussed with respect to the relative changes in the solar global radiation, ozone content, and cloudiness. All the variables were decomposed into separate components, representing variations of different time scales, using wavelet multi-resolution decomposition. The response of the UV radiation to the changes in the solar global radiation, ozone content, and cloudiness depends on the time scale, therefore, it seems reasonable to model separately the relation between UV and explanatory variables at different time scales. The wavelet components of the UV series are modelled and summed to obtain the fit of observed series. The results show that the coarser time scale components can be modelled with greater accuracy than fine scale components and the fitted values calculated by this method are in better agreement with observed values than values calculated by the regression method, in which variables were not decomposed. The residual standard error in the case of modelling with the use of wavelets is reduced by 14% in comparison to the regression method without decomposition.


2021 ◽  
Author(s):  
Andrey Gavrilov ◽  
Aleksei Seleznev ◽  
Dmitry Mukhin ◽  
Alexander Feigin

<p>The problem of modeling interaction between processes with different time scales is very important in geoscience. In this report, we propose a new form of empirical evolution operator model based on the analysis of multiple time series representing processes with different time scales. We assume that the time series are given on the same time interval.</p><p>To construct the model, we extend the previously developed general form of nonlinear stochastic model based on artificial neural networks and designed for the case of time series with constant sampling interval [1]. This sampling interval is related to the main time scale of the process under consideration, which is described by the deterministic component of the model, while the faster time scales are modeled by its stochastic component, possibly depending on the system’s state. This model also includes slower processes in the form of weak time-dependence, as well as external forcing. The structure of the model is optimized using Bayesian approach [1]. The model has proven its efficiency in a number of applications [2-4].</p><p>The idea of modeling time series with different time scales is to formulate the above-described model individually for each time scale, and then to include the parameterized influence of the other time scales in it. Particularly, the influence of “slower” time series is included in the form of parameter trends, and the influence of “faster” time series is included by time-averaging their statistics. The algorithm and first results of comparison between the new model and the model without cross-interactions will be discussed.</p><p>The work was supported by the Russian Science Foundation (Grant No. 20-62-46056).</p><p>1. Gavrilov, A., Loskutov, E., & Mukhin, D. (2017). Bayesian optimization of empirical model with state-dependent stochastic forcing. Chaos, Solitons & Fractals, 104, 327–337. http://doi.org/10.1016/j.chaos.2017.08.032</p><p>2. Mukhin, D., Kondrashov, D., Loskutov, E., Gavrilov, A., Feigin, A., & Ghil, M. (2015). Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models. Journal of Climate, 28(5), 1962–1976. http://doi.org/10.1175/JCLI-D-14-00240.1</p><p>3. Gavrilov, A., Seleznev, A., Mukhin, D., Loskutov, E., Feigin, A., & Kurths, J. (2019). Linear dynamical modes as new variables for data-driven ENSO forecast. Climate Dynamics, 52(3–4), 2199–2216. http://doi.org/10.1007/s00382-018-4255-7</p><p>4. Mukhin, D., Gavrilov, A., Loskutov, E., Kurths, J., & Feigin, A. (2019). Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition. Scientific Reports, 9(1), 7328. http://doi.org/10.1038/s41598-019-43867-3</p>


2019 ◽  
Vol 491 (4) ◽  
pp. 5951-5965 ◽  
Author(s):  
G Hobbs ◽  
L Guo ◽  
R N Caballero ◽  
W Coles ◽  
K J Lee ◽  
...  

ABSTRACT We have constructed a new time-scale, TT(IPTA16), based on observations of radio pulsars presented in the first data release from the International Pulsar Timing Array (IPTA). We used two analysis techniques with independent estimates of the noise models for the pulsar observations and different algorithms for obtaining the pulsar time-scale. The two analyses agree within the estimated uncertainties and both agree with TT(BIPM17), a post-corrected time-scale produced by the Bureau International des Poids et Mesures (BIPM). We show that both methods could detect significant errors in TT(BIPM17) if they were present. We estimate the stability of the atomic clocks from which TT(BIPM17) is derived using observations of four rubidium fountain clocks at the US Naval Observatory. Comparing the power spectrum of TT(IPTA16) with that of these fountain clocks suggests that pulsar-based time-scales are unlikely to contribute to the stability of the best time-scales over the next decade, but they will remain a valuable independent check on atomic time-scales. We also find that the stability of the pulsar-based time-scale is likely to be limited by our knowledge of solar-system dynamics, and that errors in TT(BIPM17) will not be a limiting factor for the primary goal of the IPTA, which is to search for the signatures of nano-Hertz gravitational waves.


Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 101-139 ◽  
Author(s):  
Heinz-Otto Kreiss

In this section we discuss a very simple problem. Consider the scalar initial value problemHere ε > 0 is a small constant and a = a1 + ia2, a1, a2 real, is a complex number with |a| = 1. We can write down the solution of (1.1) explicity. It iswhereis the forced solution andis a solution of the homogeneous equationyS varies on the time scale ‘1’ while yF varies on the much faster scale 1/ε. We say that yS, yF vary on the slow and fast scale, respectively. We use also the phrase: yS and yF are the slow and the fast part of the solution, respectively.


2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Zhiping Lu ◽  
Ming Li ◽  
Wei Zhao

We contribute the quantitative descriptions of the large time scales for the Ethernet traffic to be Gaussian. We focus on the normality property of the accumulated traffic data under different time scales. The investigation is carried out graphically by the quantile-quantile (QQ) plots and numerically by statistical tests. The present results indicate that the larger the time scale, the more normal the Ethernet traffic.


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