Non-Newtonian natural convection flow along an isothermal horizontal circular cylinder using modified power-law model

Laminar two-dimensional natural convection boundary-layer flow of non-Newtonian fluids along an isothermal horizontal circular cylinder has been studied using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning as well as shear thickening fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively.

Testing for financial crashes using the Log Periodic Power Law model

Many papers claim that a Log Periodic Power Law (LPPL) model fitted to financial market bubbles that precede large market falls or 'crashes', contains parameters that are confined within certain ranges. Further, it is claimed that the underlying model is based on influence percolation and a martingale condition. This paper examines these claims and their validity for capturing large price falls in the Hang Seng stock market index over the period 1970 to 2008. The fitted LPPLs have parameter values within the ranges specified post hoc by Johansen and Sornette (2001) for only seven of these 11 crashes. Interestingly, the LPPL fit could have predicted the substantial fall in the Hang Seng index during the recent global downturn. Overall, the mechanism posited as underlying the LPPL model does not do so, and the data used to support the fit of the LPPL model to bubbles does so only partially. © 2013.

Nonlinear time series prediction based on a power-law noise model

In this paper we investigate the influence of a power-law noise model, also called noise, on the performance of a feed-forward neural network used to predict time series. We introduce an optimization procedure that optimizes the parameters the neural networks by maximizing the likelihood function based on the power-law model. We show that our optimization procedure minimizes the mean squared leading to an optimal prediction. Further, we present numerical results applying method to time series from the logistic map and the annual number of sunspots demonstrate that a power-law noise model gives better results than a Gaussian model.

Heat transfer to power-law fluids in thermal entrance region with viscous dissipation for constant heat flux conditions

An analytical solution of the heat transfer problem with viscous dissipation for non-Newtonian fluids with power-law model in the thermal entrance region of a circular pipe and two parallel plates under constant heat flux conditions is obtained using eigenvalue approach by suitably replacing one of the boundary conditions by total energy balance equation. Analytical expressions for the wall and the bulk temperatures and the local Nusselt number are presented. The results are in close agreement with those obtained by implicit finite-difference scheme. It is found that the role of viscous dissipation on heat transfer is completely different for heating and cooling conditions at the wall. The results for the case of cooling at the wall are of interest in the design of the oil pipe line.

Study of drag reduction by gas injection for power-law fluid flow in horizontal stratified and slug flow regimes

In this work, the drag reduction by gas injection for power-law fluid flow in stratified and slug flow regimes has been studied. Experimentswere conducted to measure the pressure gradient within air/CMC solutions in a horizontal Plexiglas pipe that had a diameter of 50mm and a length of 30 m. The drag reduction ratio in stratified flow regime was predicted using the two-fluid model. The results showed that the drag reduction should occur over the large range of the liquid holdup when the flow behaviour index remained at the low value. Furthermore, for turbulent gas-laminar liquid stratified flow, the drag reduction by gas injection for Newtonian fluid was more effective than that for shear-shinning fluid, when the dimensionless liquid height remained in the area of high value. The pressure gradient model for a gas/Newtonian liquid slug flow was extended to liquids possessing the Ostwald–de Waele power law model. The proposed model was validated against 340 experimental data point over a wide range of operating conditions, fluid characteristics and pipe diameters. The dimensionless pressure drop predicted was well inside the 20% deviation region for most of the experimental data. These results substantiated the general validity of the model presented for gas/non-Newtonian two-phase slug flows.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Friction losses in valves and fittings for power-law fluids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Testing of a Market Fraction Model and Power-law Behaviour in the DAX 30

This paper tests a simple market fraction asset pricing model with heterogeneous
agents. By selecting a set of structural parameters of the model through a systematic procedure, we show that the autocorrelations (of returns, absolute returns and squared returns) of the market fraction model share the same pattern as those of the DAX 30. By conducting econometric analysis via Monte Carlo simulations, we characterize these power-law behaviours and find that estimates of the power-law decay indices, the (FI)GARCH parameters, and the tail index of the selected market fraction model closely match those of the DAX 30. The results strongly support the explanatory power of the heterogeneous agent models.

Chaotic and power law states in the Portevin-Le Chatelier effect

Recent studies on the Portevin-Le Chatelier effect report an intriguing crossover phenomenon from low-dimensional chaotic to an infinite-dimensional scale-invariant power law regime in experiments on CuAl single crystals and AlMg polycrystals, as function of strain rate. We devise fully dynamical model which reproduces these results. At low and medium strain rates, the model is chaotic with the structure of the attractor resembling the reconstructed experimental attractor. At high strain rates, power law statistics for the magnitudes and durations of the stress drops emerge as in experiments and concomitantly, the largest Lyapunov exponent is zero.

Effect of catchment characteristics on the relationship between past discharge and the power law recession coefficient

This study concerns the relationship between the power law recession coefficient k (in - dQ/dt = kQ(alpha), Q being discharge at the basin outlet) and past average discharge Q(N) (where N is the temporal distance from the center of the selected time span in the past to the recession peak), which serves as a proxy for past storage state of the basin. The strength of the k-Q(N) relationship is characterized by the coefficient of determination R-N(2), which is expected to indicate the basin's ability to hold water for N days. The main objective of this study is to examine how R-N(2) value of a basin is related with its physical characteristics. For this purpose, we use streamflow data from 358 basins in the United States and selected 18 physical parameters for each basin. First, we transform the physical parameters into mutually independent principal components. Then we employ multiple linear regression method to construct a model of R-N(2) in terms of the principal components. Furthermore, we employ step-wise multiple linear regression method to identify the dominant catchment characteristics that influence R-N(2) and their directions of influence. Our results indicate that R-N(2) is appreciably related to catchment characteristics. Particularly, it is noteworthy that the coefficient of determination of the relationship between R-N(2) and the catchment characteristics is 0.643 for N = 45. We found that topographical characteristics of a basin are the most dominant factors in controlling the value of R-N(2). Our results may be suggesting that it is possible to tell about the water holding capacity of a basin by just knowing about a few of its physical characteristics. (C) 2015 Elsevier B.V. All rights reserved.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Nanoadhesion of a Power-Law Graded Elastic Material

The Dugdale-Barenblatt model is used to analyze the adhesion of graded elastic materials at the nanoscale with Young's modulus E varying with depth z according to a power law E = E-0(z/c(0))(k) (0 < k < 1) while Poisson's ratio v remains a constant, where E-0 is a referenced Young's modulus, k is the gradient exponent and c(0) is a characteristic length describing the variation rate of Young's modulus. We show that, when the size of a rigid punch becomes smaller than a critical length, the adhesive interface between the punch and the graded material detaches due to rupture with uniform stresses, rather than by crack propagation with stress concentration. The critical length can be reduced to the one for isotropic elastic materials only if the gradient exponent k vanishes.

Power law behavior of the isotope yield distributions in the multifragmentation regime of heavy ion reactions

Isotope yield distributions in the multifragmentation regime were studied with high-quality isotope identification, focusing on the intermediate mass fragments (IMFs) produced in semiviolent collisions. The yields were analyzed within the framework of a modified Fisher model. Using the ratio of the mass-dependent symmetry energy coefficient relative to the temperature, a(sym)/T, extracted in previous work and that of the pairing term, a(p)/T, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields were corrected for these effects. For a given I = N - Z value, the corrected yields of isotopes relative to the yield of C-12 show a power law distribution Y (N, Z)/Y(C-12) similar to A(-tau) in the mass range 1 <= A <= 30, and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted tau value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple deexcitation model, with which the power law distribution of the primary isotopes is determined to be tau(prim) = 2.4 +/- 0.2, suggesting that the disassembling system at the time of the fragment formation is indeed at, or very near, the critical point.

Exploring the Origin of Power Law Distribution in Single-Molecule Conformation Dynamics: Energy Landscape Perspectives

We explored the origin of power law distribution observed in single-molecule conformational dynamics experiments. By establishing a kinetic master equation approach to study statistically the microscopic state dynamics, we show that the underlying landscape with exponentially distributed density of states leads to power law distribution of kinetics. The exponential density of states emerges when the system becomes glassy and landscape becomes rough with significant trapping.