Spreading Exponents Research Articles

Short-crestedness effect on the dynamic response of offshore floating wind turbines

ABSTRACT In practice, the ocean waves are short-crested and three-dimensional. The primary objective of the present research is to form a better understanding of the dynamics of offshore floating wind turbines in multi-directional waves. The short-crested waves are modelled using a spreading exponent function. The wave directionality effect on the dynamic performance of a semisubmersible offshore floating wind turbine is studied. In short-crested waves, the longitudinal response is reduced whereas the lateral response is amplified. The tower base fore-aft bending moment and the mooring line tension force are reduced. In the meanwhile, the fatigue damages of critical points at the tower base are also reduced. It is concluded that short-crestedness is beneficial to the structural integrity. The present research reveals the importance of wave short-crestedness effect on the performance of offshore floating wind turbines.

Study of early time dynamics of drop spreading in different surrounding pressure

The initial spreading phenomena of oil droplets on a partially wettable surface under various surrounding pressures was conducted through an experimental investigation outlined in this study. The gauge pressure of the surrounding medium was varied stepwise in the range from atmospheric pressure to 30 MPa. Upon contact with the surface, spreading alters the total energy of the system. The timescale for this process is very fast and the spreading involves the motion of the three-phase contact line established at the junction of the droplet, the substrate and the surrounding medium. In this study, the early time dynamics of different grades of oil drops spreading on PTFE substrates were examined utilizing high-speed imaging and drop shape analysis. Results show that the temporal evolution of the spreading radius closely resembles a power law where the empirically obtained exponent, α, was calculated for different surrounding pressures. Observations of instantaneous drop spreading reveal that spreading occurs through three distinct regimes: an initial spreading regime, a short transition regime and a viscous regime. In the inertial regime of the early time dynamics, spreading radius scales as r~tα where the spreading exponent, α, decreases with the increase of pressure. In addition, pressure influences the onset of the transition regime, the contact line speed, and the contact angle during the initial wetting process.

Dynamic spreading of a water nanodroplet on a nanostructured surface in the presence of an electric field

Molecular dynamics simulations are implemented to investigate the statics and dynamics of wetting for a water nanodroplet on a nanostructured surface in the presence of a vertical electric field. The results show that the electric field induces electro-stretching, electro-wettability, modified solid-liquid interfacial tension, and pinning at the triple line, and they jointly affect the spreading exponent and static contact angle of the nanodroplet. Under an upward electric field, the spreading is always hindered, and the static contact angle monotonously increases with the field strength. Interestingly, under a downward electric field, the spreading is first hindered and then is promoted as increasing the field strength, leading to a first increased and then decreased static contact angle. The increased solid-liquid interfacial tension and the enhanced pinning are found to be two main mechanisms for the slowing down of spreading and the increase in static contact angles for both electric fields at low field strengths. The same trends are observed at high field strengths under the upward electric field; however, exactly the reverse trends occur under the downward electric field, leading to the acceleration of spreading and the decrease in static contact angle at high field strengths. Moreover, it is found that the enhancement in intrinsic wettability of the surface can suppress the breaking of hydrogen bonds, thereby reducing the solid-liquid interfacial tension and accelerating the spreading. The enhancement in intrinsic wettability can also reduce the pinning at the triple line as well as the energy barrier of the Cassie-Wenzel transition, which contributes to the reduced static contact angle.

Energy Dissipation in Coronal Loops: Statistical Analysis of Intermittent Structures in Magnetohydrodynamic Turbulence

Abstract The power-law energy distribution observed in dissipation events ranging from flares down to nanoflares has been associated either to intermittent turbulence or to self-organized criticality. Despite the many studies conducted in recent years, it is unclear whether these two paradigms are mutually exclusive or they are complementary manifestations of the complexity of the system. We numerically integrate the magnetohydrodynamic equations to simulate the dynamics of coronal loops driven at their bases by footpoint motions. After a few photospheric turnover times, a stationary turbulent regime is reached, displaying a broadband power spectrum and a dissipation rate consistent with the cooling rates of the plasma confined in these loops. Our main goal is to determine whether the intermittent features observed in this turbulent flow can also be regarded as manifestations of self-organized criticality. A statistical analysis of the energy, area, and lifetime of the dissipative structures observed in these simulations displays robust scaling laws. We calculated the critical exponents characterizing the avalanche dynamics, and the spreading exponents that quantify the growth of these structures over time. In this work we also calculate the remaining critical exponents for several activity thresholds and verify that they satisfy the conservation relations predicted for self-organized critical systems. These results can therefore be regarded as a bona fide test supporting that the stationary turbulent regimes characterizing coronal loops also correspond to states of self-organized criticality.

Scaling of energy spreading in a disordered Ding-Dong lattice

We study numerical propagation of energy in a one-dimensional Ding-Dong lattice composed of linear oscillators with elastic collisions. Wave propagation is suppressed by breaking translational symmetry, and we consider three ways to do this: position disorder, mass disorder, and a dimer lattice with alternating distances between the units. In all cases the spreading of an initially localized wavepacket is irregular, due to the appearance of chaos, and subdiffusive. For a range of energies and of weak and moderate levels of disorder, we focus on the macroscopic statistical characterization of spreading. Guided by a nonlinear diffusion equation, we establish that the mean waiting times of spreading obey a scaling law in dependence of energy. Moreover, we show that the spreading exponents very weakly depend on the level of disorder.

CO2 wetting on pillar-nanostructured substrates

CO2 capture by dropwise CO2 condensation on cold solid surfaces is a promising technology. Understanding the role of the nanoscale surface and topographical features of CO2 droplet wetting characteristics is of importance for CO2 capture by this technology, but this remains unexplored as of yet. Here, using large-scale molecular dynamics (MD) simulations, the contact angle and wetting behaviors of CO2 droplets on pillar-structured Cu-like surfaces are investigated for the first time. Dynamic wetting simulations show that, by changing the strength of the solid–liquid attraction a smooth Cu-like surface offers a transition from CO2-philic to CO2-phobic. By periodically pillared roughening of the Cu-like surfaces, however, a higher contact angle and a smaller spreading exponent of a liquid CO2 droplet are realized. Particularly, a critical crossover of CO2-philic to CO2-phobic can appear. The wetting of the pillared surfaces by a liquid CO2 droplet proceeds non-uniformly. A liquid CO2 droplet is capable of exhibiting a transition from the Cassie state to the Wenzel state with increasing increasing inter-pillar distance, and increasing pillar width. The wetting morphologies of the metastable Wenzel state of a CO2 droplet are very different from each other. The findings will inform the ongoing design of CO2-phobic solid surfaces for practical dropwise condensation-based CO2 capture applications.

Multiscale flow characteristics of droplet spreading with microgravity conditions

In this paper, mesoscopic lattice–Boltzmann method (LBM) and microscopic molecular dynamics simulation method were used to simulate droplet dynamic wetting under microgravity. In terms of LBM, the wetting process of a droplet on a solid wall surface was simulated by introducing the fluid–fluid and solid–fluid interactions. In terms of molecular dynamics simulation, the spreading process of water on gold surface was simulated. Calculation results showed that two kinds of calculation methods were based on the microscopic molecular theory or mesoscopic kinetics theory, and such models could effectively overcome the contact line paradox issue, which results from the macro-continuum assumption and non-slip boundary condition assumption. The spreading exhibits two-stage behavior: fast spreading and slow spreading stages. For the two simulation methods, the ratio of fast spreading stage duration to slow spreading duration, spreading capacity (equilibrium contact radius/initial radius), and the spreading exponent of the rapid stage were very close. However, the predictive spreading index of the slow spreading stage was different, owing to the different spreading mechanisms between meso- and nanoscales.

Effects of wave directionality on extreme response for a long end-anchored floating bridge

Reliable design codes are of great importance when constructing new civil engineering concepts such as floating bridges. Previously only a scarce number of floating bridges have been built in rough wave conditions and only limited knowledge of the extreme environmental conditions and the associated extreme response exists. To form a better design basis an increased understanding of the sensitivity in the structural response towards changes in short-crested sea parameters is needed. Furthermore, acquiring the necessary accuracy in simulated extreme response is often a computationally expensive endeavour and the number of simulations needed is often based on experience. The present study investigates the wave-induced short-term extreme response of a simplified end-anchored floating bridge concept for several wave environments with a return period of 100 years. The study includes convergence of the coefficient of variation for the extreme response for different realization lengths as well as number of realizations. The sensitivity in the structural response towards different main wave directions and spreading exponents is investigated and includes both transverse and vertical displacement response spectra and extreme Von Mises stress in the bridge girder cross-section. The extreme response is based on an accuracy of 2% in the coefficient of variation equivalent to 40 3-h realizations and a low sensitivity in the response is found for natural occurring spreading exponents and for main wave directions within 15° from beam sea.

Directed percolation phase transition at the onset of STI in an inhomogeneous coupled map lattice

A model for inhomogeneously coupled logistic maps is considered to find some critical exponents in the transition from inhomogeneous steady state to spatiotemporal chaos through spatiotemporal intermittency. The laminar state in the model is described by inhomogeneous steady state with spatial period two. We obtain a complete set of static exponents which match with the corresponding directed percolation (DP) values in (1+1) dimension. We also find four nonuniversal spreading exponents in which three exponents are in agreement with DP values. The model in which absorbing state is inhomogeneous steady state, contributes a new example in evidence of Pomeau's [18] conjecture that the onset of STI in a deterministic system belongs to DP universality class.

Continuously variable spreading exponents in the absorbing Nagel–Schreckenberg model

I study the critical behavior of a traffic model with an absorbing state. The model is a variant of the Nagel–Schreckenberg (NS) model, in which drivers do not decelerate if their speed is smaller than their headway, the number of empty sites between them and the car ahead. This makes the free-flow state (i.e. all vehicles traveling at the maximum speed, vmax, and with all headways greater than vmax) absorbing; such states are possible for densities ρ smaller than a critical value . Drivers with nonzero velocity, and with headway equal to velocity, decelerate with probability p. This absorbing Nagel–Schreckenberg (ANS) model, introduced in Iannini and Dickman (2017 Phys. Rev. E 95 022106), exhibits a line of continuous absorbing-state phase transitions in the ρ-p plane. Here I study the propagation of activity from a localized seed, and find that the active cluster is compact, as is the active region at long times, starting from uniformly distributed activity. The critical exponents δ (governing the decay of the survival probability) and η (governing the growth of activity) vary continuously along the critical curve. The exponents satisfy a hyperscaling relation associated with compact growth.

A numerical model of superspreading surfactants on hydrophobic surface

Many contributions significantly on experimental and mathematical studies are made to understand the mechanism of superspreading. Only few numerical methods have been proposed which solve the system of equations with soluble and insoluble surfactants. Among them, we propose a computational fluid dynamics model, based on the volume of fluid technique, with the piecewise linear interface calculation method. Interface reconstruction is applied to simulate the time evolution of the dynamics of drop spreading of surfactants on a thin water layer. We have allowed the occurrence of both the regimes relating to a series of trisiloxane (M(D′EnOH)M), sodium dodecyl sulphate, and Tergitol NP10 surfactants drop on a thin water layer with the influence of Marangoni stress. The numerical data seem consistent with those experimental for both regimes. It validates predictions for the spreading exponent in which the law of the radius of the circular area covered by the surfactant grows as tα, where 0 < α < 1. The comparison of the numerical and experimental predictions by Lee et al. [“Spreading of trisiloxanes over thin aqueous layers,” Colloid J. 71, 365–369 (2009)] is well represented in both regimes. The numerical study confirms that the spreading rates during the first stage increase as the solubility increases. This finding suggests that the model is adequate for describing the spreading of surfactants on thin fluid layers.

Critical spreading dynamics of parity conserving annihilating random walks with power-law branching

We investigate the critical spreading of the parity conserving annihilating random walks model with Lévy-like branching. The random walks are considered to perform normal diffusion with probability p on the sites of a one-dimensional lattice, annihilating in pairs by contact. With probability 1−p, each particle can also produce two offspring which are placed at a distance r from the original site following a power-law Lévy-like distribution P(r)∝1∕rα. We perform numerical simulations starting from a single particle. A finite-time scaling analysis is employed to locate the critical diffusion probability pc below which a finite density of particles is developed in the long-time limit. Further, we estimate the spreading dynamical exponents related to the increase of the average number of particles at the critical point and its respective fluctuations. The critical exponents deviate from those of the counterpart model with short-range branching for small values of α. The numerical data suggest that continuously varying spreading exponents sets up while the branching process still results in a diffusive-like spreading.

Conserved Manna model on Barabasi–Albert scale-free network

In this paper, a conserved Manna model is constructed and studied on Barabasi–Albert scale-free network with degree exponent γ = 3. Numerically I show that the system undergoes an absorbing state phase transition when the particle density is varied. Such a phase transition is characterized by measuring several critical exponents associated with the critical behaviour of the model. It has been found that the critical exponents exhibit mean field values of directed percolation. At the critical point, the spreading exponents have also been estimated. They satisfy the usual scaling relations. The effect of various initial conditions has been investigated and the result found to be independent of initial conditions, contrary to the fact that critical behaviour of such model highly depends on initial conditions when studied on regular lattice. The study confirms that though the Manna model in the lower dimensions exhibits different critical behavior other than DP, in the scale-free network it exhibits similar mean field result of DP class.

Near-source attenuation of high-frequency body waves beneath the New Madrid Seismic Zone

Attenuation characteristics in the New Madrid Seismic Zone (NMSZ) are estimated from 157 local seismograph recordings out of 46 earthquakes of 2.6 ≤ M ≤ 4.1 with hypocentral distances up to 60 km and focal depths down to 25 km. Digital waveform seismograms were obtained from local earthquakes in the NMSZ recorded by the Center for Earthquake Research and Information (CERI) at the University of Memphis. Using the coda normalization method, we tried to determine Q values and geometrical spreading exponents at 13 center frequencies. The scatter of the data and trade-off between the geometrical spreading and the quality factor did not allow us to simultaneously derive both these parameters from inversion. Assuming 1/R 1.0 as the geometrical spreading function in the NMSZ, the Q P and Q S estimates increase with increasing frequency from 354 and 426 at 4 Hz to 729 and 1091 at 24 Hz, respectively. Fitting a power law equation to the Q estimates, we found the attenuation models for the P waves and S waves in the frequency range of 4 to 24 Hz as Q P = (115.80 ± 1.36) f (0.495 ± 0.129) and Q S = (161.34 ± 1.73) f (0.613 ± 0.067), respectively. We did not consider Q estimates from the coda normalization method for frequencies less than 4 Hz in the regression analysis since the decay of coda amplitude was not observed at most bandpass filtered seismograms for these frequencies. Q S/Q P > 1, for 4 ≤ f ≤ 24 Hz as well as strong intrinsic attenuation, suggest that the crust beneath the NMSZ is partially fluid-saturated. Further, high scattering attenuation indicates the presence of a high level of small-scale heterogeneities inside the crust in this region.

Topography- and topology-driven spreading of non-Newtonian power-law liquids on a flat and a spherical substrate.

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much larger than that of the roughness of substrate is considered. The equilibrium contact angle on a rough substrate is modeled by the Wenzel and the Cassie-Baxter model. Only the viscous energy dissipation within the droplet volume is considered, and that within the texture of substrate by imbibition is neglected. Then, the energy balance approach is adopted to derive the evolution equation of the contact angle. When the equilibrium contact angle vanishes, the relaxation of dynamic contact angle θ of a droplet obeys a power-law decay θ∼t^{-α} except for the Newtonian and the non-Newtonian shear-thinning liquid of the Wenzel model on a spherical substrate. The spreading exponent α of the non-Newtonian shear-thickening liquid of the Wenzel model on a spherical substrate is larger than others. The relaxation of the Newtonian liquid of the Wenzel model on a spherical substrate is even faster showing the exponential relaxation. The relaxation of the non-Newtonian shear-thinning liquid of Wenzel model on a spherical substrate is fastest and finishes within a finite time. Thus, the topography (roughness) and the topology (flat to spherical) of substrate accelerate the spreading of droplet.

Effects of Solid Fraction on Droplet Wetting and Vapor Condensation: A Molecular Dynamic Simulation Study.

Recently, numerous studies focused on the wetting process of droplets on various surfaces at a microscale level. However, there are a limited number of studies about the mechanism of condensation on patterned surfaces. The present study performed the dynamic wetting behavior of water droplets and condensation process of water molecules on substrates with different pillar structure parameters, through molecular dynamic simulation. The dynamic wetting results indicated that droplets exhibit Cassie state, PW state, and Wenzel state successively on textured surfaces with decreasing solid fraction. The droplets possess a higher static contact angle and a smaller spreading exponent on textured surfaces than those on smooth surfaces. The condensation processes, including the formation, growth, and coalescence of a nanodroplet, are simulated and quantitatively recorded, which are difficult to be observed by experiments. In addition, a wetting transition and a dewetting transition were observed and analyzed in condensation on textured surfaces. Combining these simulation results with previous theoretical and experimental studies will guide us to understand the hypostasis and mechanism of the condensation more clearly.

Attenuation of Lg waves in the New Madrid seismic zone of the central United States using the coda normalization method

Unique properties of coda waves are employed to evaluate the frequency dependent quality factor of Lg waves using the coda normalization method in the New Madrid seismic zone of the central United States. Instrument and site responses are eliminated and source functions are isolated to construct the inversion problem. For this purpose, we used 121 seismograms from 37 events with moment magnitudes, M, ranging from 2.5 to 5.2 and hypocentral distances from 120 to 440km recorded by 11 broadband stations.A singular value decomposition (SVD) algorithm is used to extract Q values from the data, while the geometric spreading exponent is assumed to be a constant. Inversion results are then fitted with a power law equation from 3 to 12Hz to derive the frequency dependent quality factor function. The final results of the analysis are QVLg (f)=(410±38) f0.49±0.05 for the vertical component and QHLg (f)=(390±26) f0.56±0.04 for the horizontal component, where the term after ± sign represents one standard error. For stations within the Mississippi embayment with an average sediment depth of 1 km around the Memphis metropolitan area, estimation of quality factor using the coda normalization method is not well-constrained at low frequencies (f<3Hz). There may be several reasons contributing to this issue, such as low frequency surface wave contamination, site effects, or even a change in coda wave scattering regime which can exacerbate the scatter of the data.

Transient super-ballistic spreading of wave packets with large spreading exponents in some hybrid ordered-quasiperiodic lattices

We consider the spreading of an initially localized wave packet in one-dimensional hybrid ordered-quasiperiodic lattices. We consider two diffrent kinds of quasiperiodic sequences, which are the Cantor and the period-doubling sequences. From numerical calculations based on the discrete Schrodinger equation, we demonstrate that hybrid ordered-quasiperiodic lattices can support the super-ballistic spreading of a wave packet with very large spreading exponents for certain transient time windows. Remarkably, in the case of the sublattice with the on-site potential obeying the period-doubling quasiperiodic sequence, we find that the super-ballistic exponent can be larger than six. We also point out that previous explanations of this phenomenon based on a generalized version of the point source model are incorrect.

Delocalization of two interacting particles in the 2D Harper model

We study the problem of two interacting particles in a two-dimensional quasiperiodic potential of the Harper model. We consider an amplitude of the quasiperiodic potential such that in absence of interactions all eigenstates are exponentially localized while the two interacting particles are delocalized showing anomalous subdiffusive spreading over the lattice with the spreading exponent $b \approx 0.5$ instead of a usual diffusion with $b=1$. This spreading is stronger than in the case of a correlated disorder potential with a one particle localization length as for the quasiperiodic potential. At the same time we do not find signatures of ballistic FIKS pairs existing for two interacting particles in the one-dimensional Harper model.

Kinetics of spreading of synergetic surfactant mixtures in the case of partial wetting

Spreading kinetics of mixtures of hydrocarbon surfactant, octaethylene glycol monododecyl ether, and fluoro-surfactant, Zonyl FSN-100, on highly hydrophobic substrate was experimentally studied. The mixtures reveal a synergism in their wetting properties with equilibrium contact angle of mixtures being 15–20° lower than that of individual surfactant solutions. The synergism is due to different affinity of the surfactants to the liquid/air and liquid/solid interface. Both individual surfactants and their mixtures demonstrate power law kinetics of spreading over the time span of tens of seconds. The spreading exponent is lower than that for pure liquids, but spreading exponent of mixtures is higher than that of individual solutions. The maximum in the spreading exponent is observed for the mixtures demonstrating the lowest equilibrium contact angles. For these mixtures the spreading exponent is close to that of pure liquids.