Statistical models for spatial patterns of heavy particles in turbulence

The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations have demonstrated that heavy particles respond in intricate ways to turbulent fluctuations of the carrying fluid: non-interacting particles may cluster together and form spatial patterns even though the fluid is incompressible, and the relative speeds of nearby particles can fluctuate strongly. Both phenomena depend sensitively on the parameters of the system. This parameter dependence is difficult to model from first principles since turbulence plays an essential role. Laboratory experiments are also very difficult, precisely since they must refer to a turbulent environment. But in recent years it has become clear that important aspects of the dynamics of heavy particles in turbulence can be understood in terms of statistical models where the turbulent fluctuations are approximated by Gaussian random functions with appropriate correlation functions. In this review, we summarise how such statistical-model calculations have led to a detailed understanding of the factors that determine heavy-particle dynamics in turbulence. We concentrate on spatial clustering of heavy particles in turbulence. This is an important question because spatial clustering affects the collision rate between the particles and thus the long-term fate of the system.     

Liesegang patterns: Complex formation of precipitate in an electric field

Formation of 1D Liesegang patterns was studied numerically in precipitation and reversible complex formation of precipitate scenarios in an electric field. The Ostwald’s supersaturation model reported by Buki, Kárpáti-Smidróczki and Zrínyi (BKZ model) was extended further. In the presence of an electric field the position of the first and the last bands (X _n) measured from the junction point of the outer and the inner electrolytes can be described by the functionX _n =a ₁τ _n ^1/2 +a ₂τ_n +a ₃, where τ_n is the time elapsed until the nth band formation,a ₁,a ₂ anda ₃ are constants. The variation of the total number of bands with different electric field strengths (ε) has a maximum. For higher ε one can observe a moving precipitation zone that becomes wider due to precipitation and reversible complex formation.     

Development of band patterns in surface films: A simple theory

Semiconductor technology often employs thin films deposited on crystal surfaces, and in some cases these films can self-organize into band, ring or spiral patterns during annealing. A simple theory is proposed which predicts the stability or instability of such films and, in the case of instability, the band spacing, which depends upon bulk, surface and interfacial free energies. This information could be of use in self-assembly techniques. In some cases, bands condense into particle arrays upon further annealing, and a theoretical model is developed to predict the subsequent evolution of circular band patterns by diffusion, which causes the regular disappearance of alternate bands.     

The shape of the past in the World Wide Web: Scale-free patterns and dynamics

Human societies accumulate a great deal of information about past events. People make reference to things that happened in time in different ways and record them in multiple media. We have studied the current use of this information by analysing the frequency of occurrence of numbers associated with years in the World Wide Web (WWW). We found a consistent scale-free reduction in the number of web pages referencing events occurred in increasingly older years. This was found for the entire WWW and separately for web pages written in 12 different languages. From year 2005 to 2006 the increase on the number of web pages associated to each year also decayed as a power-law from recent to old years. Such general pattern reveals that time elapsed to present is the best predictor of the interest or the amount of information on a particular year in the WWW. Moreover, the power-law increase from one year to the next shows that the scale-free shape of past in the WWW is dynamically maintained.     

Insights into the sonochemical decomposition of Fe(CO)5: theoretical and experimental understanding of the role of molar concentration and power density on the reaction yield

The present work analyses, in detail, the optimization of a sonochemical process with respect to concentration of precursor and power supplied in a system. This is due to that even a small change in power dramatically changes the high-energy conditions created with the bubble collapse. A model reaction that has been considered for this purpose involves the decomposition of Fe(CO)₅ in decalin solvent as this reaction is strongly influenced by the cavitation conditions. Sonochemical treatment of this carbonyl results in the formation of amorphous Fe₂O₃, which on heat treatment gives nanocrystalline Fe₂O₃. It has been observed that concentration and power density parameters play an important role to obtain higher decomposition of Fe(CO)₅ and hence higher yield of the amorphous Fe₂O₃ product. Also, using the experimentally observed results, a correlation (polynomial) has been developed.     

Insights into the novel application of Fe-MOFs in ultrasound-assisted heterogeneous Fenton system: Efficiency,kinetics and mechanism

In this work, as a new strategy, ultrasound/H₂O₂/MOF system was firstly applied by environmental-benign Fe-MOFs (MIL-53, MIL-88B and MIL-101) for tetracycline hydrochloride removal. The synthetic Fe-MOFs were characterized by XRD, FTIR, SEM, XPS, N₂ sorption-desorption isotherms and CO-FTIR. MIL-88B demonstrated the best catalytic performance because of its highest amount of Lewis acid sites. Influencing factors, contrast experiment, and corresponding dynamics were carried out to obtain the best experimental conditions and reaction system. Under optimal conditions ([Tetracycline hydrochloride] = 10 mg/L, [MIL-88B] = 0.3 g/L, [H₂O₂] = 44 mM, [ultrasound power] = 60 W, and pH = 5.0), the-first-order kinetic rate constant k was calculated to be 0.226 min⁻¹, higher than the simple combination of the ultrasound system (0.004) and MIL-88B/H₂O₂ system (0.163), indicating the importance of synergistic effect between ultrasound and Fenton reaction. EPR test and quenching experiment proved that ·OH is mainly responsible for tetracycline hydrochloride removal. The major reaction path is the adsorption and decomposition of H₂O₂ by coordinative unsaturated iron sites on Fe-MOF, but it is not the only path. The direct decomposition of H₂O₂ and the cavitation effect caused by ultrasound also contribute to the generation of OH.     

二元Ni-Al合金极端条件下的弹性和热力学性能：全电子准谐波近似 cited: 1)

通过在原子尺度上建模来研究Al、NiAl和Ni₃Al合金在极端高温和高压下的点阵常数、弹性常数、弹性模量、泊松比和弹性各向异性因子等性质．计算得到的弹性常数均满足相应的力学稳定条件．由于NiAl和Ni₃Al具有较高的B=G值,在0～30 GPa内都属于延展性材料．通过包含电子热运动对体系吉布斯自由能贡献的全电子准谐近似方法,得到了高温高压下Al、NiAl和Ni₃Al合金的热膨胀系数、体积模量、热容和熵等．计算值与已有的实验值和理论值符合较好     

Insights into ultrasound-promoted degradation of naphthenic acid compounds in oil sands process affected water. Part I: Accelerated H-abstraction and decarboxylation of aromatic and alicyclic compounds

Propelled by enormous increase in demand for fuel sources, Canadian oil sands are becoming increasingly important as a fuel source due to their abundance and upgrading capability. However, extraction of bitumen, a high acid crude (HAC) oil, requires 2–3 units of water per unit of oil resulting in naphthenic acid (NA)-rich oil sands process affected water (OSPW) collected in effluent ponds. This study illustrates the role of sonochemistry in the accelerated degradation through H-abstraction and subsequent decarboxylation of aromatic and alicyclic naphthenic acid model compounds. Benzoic acid and 3-methylcyclohexane carboxylic acid were selected as model NA compounds to investigate the mechanism of hydroxyl radical (OH^•) initiated carboxylic acid degradation in 378 KHz sonochemical reactor. Established FTIR methods with low resolution LCMS spectroscopy confirmation were applied to determine the extent of carboxylic acid degradation and identify the formation of products. FTIR monitoring showed a non-linear degradation of carboxylic acids with formation of many intermediates highlighting the shift from cyclic carboxylic acids to cyclic alcohols during BA degradation. Subsequent decrease in carboxylic acid groups signifies scission of cyclic structures before complete mineralization. This is confirmed with the LCMS identification of products such as: 3-hydroxybenzoic acid and phenol. This study postulated new breakdown pathways for degradation of benzoic acid with complete mineralization at a sonochemical reaction time (SRT) of 4 h. A radical quenching process was also inferred through the formation of conglomerates during sonochemical degradation of BA. Extension of the study to 3-methylcyclohexane carboxylic acid (3mCHA) shows similar non-linearity with an increase in carboxylic acid groups indicating H-abstraction followed by ring-opened compounds. However, due to the complex nature of 3mCHA’s ring-opened compounds, complete mineralization is not achieved. The putative role of sonochemistry is a promising and sustainable degradation method for mitigating NAs in OSPW, but sonication periods need to be considered carefully to ensure adequate mineralization of their constituents and combinatorial methods with other advanced oxidation methods may be needed to enhance industrial application.In Part II, an in silico screening approach using first principles is reported to identify the breakdown of the organic compounds and determine molecular rates of reaction to confirm the mechanistic origins of the compounds formed.     

Analysis of the real estate market in Las Vegas: Bubble, seasonal patterns, and prediction of the CSW indices

We analyze 27 house price indices of Las Vegas from June 1983 to March 2005, corresponding to 27 different zip codes. These analyses confirm the existence of a real estate bubble, defined as a price acceleration faster than exponential, which is found, however, to be confined to a rather limited time interval in the recent past from approximately 2003 to mid-2004 and has progressively transformed into a more normal growth rate comparable to pre-bubble levels in 2005. There has been no bubble till 2002 except for a medium-sized surge in 1990. In addition, we have identified a strong yearly periodicity which provides a good potential for fine-tuned prediction from month to month. A monthly monitoring using a model that we have developed could confirm, by testing the intra-year structure, if indeed the market has returned to “normal” or if more turbulence is expected ahead. We predict the evolution of the indices one year ahead, which is validated with new data up to September 2006. The present analysis demonstrates the existence of very significant variations at the local scale, in the sense that the bubble in Las Vegas seems to have preceded the more global USA bubble and has ended approximately two years earlier (mid-2004 for Las Vegas compared with mid-2006 for the whole of the USA).     

Strongly nonlinear beats in the dynamics of an elastic system with a strong local stiffness nonlinearity: Analysis and identification

We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong nonlinear stiffness at its free end.