Short-Time Dynamics of Partial Wetting
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Abstract:
When a liquid drop contacts a wettable surface, the liquid spreads over the solid to minimize the total surface energy. The first moments of spreading tend to be rapid. For example, a millimeter-sized water droplet will wet an area having the same diameter as the drop within a millisecond. For perfectly wetting systems, this spreading is inertially dominated. Here we identify that even in the presence of a contact line, the initial wetting is dominated by inertia rather than viscosity. We find that the spreading radius follows a power-law scaling in time where the exponent depends on the equilibrium contact angle. We propose a model, consistent with the experimental results, in which the surface spreading is regulated by the generation of capillary waves.Keywords:
Millisecond
Wetting transition
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Capillary wave
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Linear low-density polyethylene
Gel point
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A probabilistic fragmentation model is introduced and analyzed. We show that, under very general conditions, an effective power law for the mass distribution arises with a realistic exponent. The exponent has a universal limit, but, in practice, the effective exponent depends on the detailed breaking mechanism and the initial conditions. This dependence is in fair agreement with experimental results.
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Fragmentation
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Hertz
Dynamics
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Urban agglomeration
Plot (graphics)
Rank (graph theory)
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A model is discussed which gives rise to the widely used power law for creep under constant load, namely, dl/dt = Ωt-n, where l is the strain, t the time, Ω a function dependent on temperature and load and n an exponent which may have any value between 0 and 1. In this model, the exponent n is interpreted as a function of the number of "flow units" which must be activated simultaneously before flow can take place.
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Constant (computer programming)
Power function
Strain (injury)
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The origin of the nontrivial power-law relationships between atomic packing density and the related structural properties is considered to be a key puzzle in understanding the nature of glasses. Here, we report the direct link between the medium-range structural evolution and elastic heterogeneity by systematically investigating the packing-density-dependent properties of various glasses based on extensive large-scale molecular dynamics simulations. It is shown that the power exponent of the peaks corresponding to the medium-range orders on the pair correlation function converges to the exponent of the first diffraction peak rather than the Euclidean dimension. This exponent can be regarded as an indicator of heterogeneous mechanical properties. The global power-law relationship results from intrinsic mechanical heterogeneity, with the nontrivial power-law response being a local feature. Our finding provides a different perspective on order in disordered materials and sheds some light on the structural-property relationship in glasses.
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On the basis of theoretical analysis and the statistics of actual production data, we find out the exponential relationship between the concentration of polymer solution and the distance to injection well. Combining the exponential relationship between the power law exponent and the concentration of polymer solution, we can get the expression to determine the power law exponent of polymer solution. Compared to trial method used in explanation of well testing, this method can save expanation time, it is feasible.
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Polymer solution
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A cellular automaton model called the Firm Dynamics Model (FDM) is introduced to simulate the dynamics of firms within an economy. The model includes the growth of firms and their mergers and exits. The main objective is to compare the size-frequency distributions in the model with the empirical firm size distributions of several countries (USA, UK, Spain and Sweden). The empirical size distributions were assembled from business censuses and additional information on the country’s largest companies in terms of the number of employees. For the four datasets analyzed here, the firm size distribution is compatible with a power law of the Pareto type with an exponent of close to two (for the probability density). For its part, the model delivers two different size-frequency distributions depending on the type of merger that firms can undergo: the friendly-merger version gives rise to subcritical distributions with an exponential tail, whereas the aggressive-merger version produces power-law distributions. The simulation model was run with underlying lattices in one, two and three dimensions in order to compare the simulated power-law exponent with the empirical one. The best agreement was obtained with the two-dimensional aggressive-merger model version, for which the power-law exponent is [Formula: see text], as compared with an empirical exponent of [Formula: see text] (average over the four datasets). Further simulations with the model on a Bethe lattice confirm that the two-dimensional model provides the best fit to the empirical exponent.
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Econophysics
Lattice (music)
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고도에 따른 풍속변화를 의미하는 Wind shear는 풍력발전기의 에너지 생산량에 직접적으로 영향을 미치는 중요한 요소이다. 풍속을 보정하는 방법으로는 멱법칙(Power Law)이 사용되는데, 일반적으로 쓰이는 0.143(1/7)의 멱지수(Power Law exponent) 값을 이용한 보정식을 1/7th 멱법칙이라 한다. 하지만 멱지수는 해당 지역의 대기 안정도, 지표면의 상태 등에 의해 많은 영향을 받으므로, 실제 정확한 풍력에너지 예측을 위해서는 관심지역의 멱지수의 정확한 계산이 필요하다. 본 연구에서는 제주도 북동부 연안지역 3곳에 Met-mast를 설치하여 풍력자원을 측정하였고, 이를 바탕으로 제주도 북동부 지역에 적합한 멱지수를 계산하여 제안하였다. 제주도 북동부 연안지역의 멱지수를 계산한 결과, 한동 0.141, 평대 0.138, 우도 0.1254의 값을 얻었다. 0.143(1/7)의 멱지수 값, 제안한 멱지수 값을 적용하여 계산한 연간에너지생산량과 실제 측정된 풍황자료를 이용하여 계산한 연간에너지생산량을 비교한 결과, 세 지역 모두 제안한 멱지수 값을 적용하여 계산한 연간에너지생산량이 실제 측정된 풍황자료를 이용하여 계산한 연간에너지생산량과 유사한 결과를 보였고, 따라서 제안한 멱지수 값의 적용이 가능하다고 판단된다.
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Cubic crystal system
Cubic function
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