Search results for "Power-law"
showing 10 items of 23 documents
Variable power-law scaling of hillslope Hortonian rainfall–runoff processes
2019
Hydrological studies focused on Hortonian rainfall–run-off scaling have found that the run-off depth generally declines with the plot length in power-law scaling. Both the power-law proportional coefficient and the scaling exponent show great variability for specific conditions, but why and how they vary remain unclear. In the present study, the scaling of hillslope Hortonian rainfall–run-off processes is investigated for different rainfall, soil infiltration, and hillslope surface characteristics using the physically based cell-based rainfall-infiltration-run-off model. The results show that both temporally intermittent and steady rainfalls can result in prominent power-law scaling at the …
Fractional differential equations and related exact mechanical models
2013
Creep and relaxation tests, performed on various materials like polymers, rubbers and so on are well-fitted by power-laws with exponent β ∈ [0, 1] (Nutting (1921), Di Paola et al. (2011)). The consequence of this observation is that the stress-strain relation of hereditary materials is ruled by fractional operators (Scott Blair (1947), Slonimsky (1961)). A large amount of researches have been performed in the second part of the last century with the aim to connect constitutive fractional relations with some mechanical models by means of fractance trees and ladders (see Podlubny (1999)). Recently, Di Paola and Zingales (2012) proposed a mechanical model that corresponds to fractional stress-…
An exact thermodynamical model of power-law temperature time scaling
2016
In this paper a physical model for the anomalous temperature time evolution (decay) observed in complex thermodynamical system in presence of uniform heat source is provided. Measures involving temperatures T with power-law variation in time as T(t)∝tβ with β∈R shows a different evolution of the temperature time rate T(t) with respect to the temperature time-dependence T(t). Indeed the temperature evolution is a power-law increasing function whereas the temperature time rate is a power-law decreasing function of time. Such a behavior may be captured by a physical model that allows for a fast thermal energy diffusion close to the insulated location but must offer more resistance to the therm…
Thermally unstable throughflow of a power–law fluid in a vertical porous cylinder with arbitrary cross–section
2021
Abstract The present paper investigates how the cross–sectional shape of a vertical porous cylinder affects the onset of thermoconvective instability of the Rayleigh–Benard type. The fluid saturating the porous medium is assumed to be a non–Newtonian power–law fluid. A linear stability analysis of the vertical thorughflow is carried out. Three special shapes of the cylinder cross–section are analysed: square, circular and elliptical. The effect of changing the power–law index is investigated. The stability of a steady base state with vertical throughflow is analysed. The resulting stability problem is a differential eigenvalue problem that is solved numerically through the shooting method. …
Linear instability of the vertical throughflow in a horizontal porous layer saturated by a power-law fluid
2016
Abstract The effects of the vertical throughflow of a non-Newtonian power-law fluid on the onset of convective instability in a horizontal porous layer are investigated. The extended Darcy’s model of momentum diffusion is employed together with the Oberbeck–Boussinesq approximation. A stationary basic solution for the vertical throughflow is determined analytically. The basic velocity and temperature fields turn out to be independent of the non-Newtonian rheology. A linear stability analysis is carried out, leading to a fourth-order eigenvalue problem. A numerical solution of the eigenvalue problem is employed to obtain the neutral stability curves and the critical Rayleigh number for the o…
THE STATE OF FRACTIONAL HEREDITARY MATERIALS (FHM)
2014
The widespread interest on the hereditary behavior of biological and bioinspired materials motivates deeper studies on their macroscopic ``minimal" state. The resulting integral equations for the detected relaxation and creep power-laws, of exponent $\beta$, are characterized by fractional operators. Here strains in $SBV_{loc}$ are considered to account for time-like jumps. Consistently, starting from stresses in $L_{loc}^{r}$, $r\in [1,\beta^{-1}], \, \, \beta\in(0,1)$ we reconstruct the corresponding strain by extending a result in [42]. The ``minimal" state is explored by showing that different histories delivering the same response are such that the fractional derivative of their differ…
A generalized stage-discharge relationship for sharp-crested power-law weirs by dimensional analysis and self-similarity
2022
Weirs are characterized by a stage-discharge relationship which mainly depends on the shape and dimensions of the hydraulic structure. A weir with symmetrical power-law sides is a versatile weir that can produce some known weir types (rectangular, triangular, parabolic) as special cases. In this paper, the outflow process of sharp-crested power-law weirs is investigated using the dimensional analysis and the incomplete self-similarity theory. A new generalized theoretical stage-discharge relationship is proposed, and its applicability is tested using measurements available in the literature for different weir types.
Power laws and the market structure of tourism industry
2013
In this article, we use both graphical and analytical methods to investigate the market structure of one of the world’s fastest growing industries. For the German and Italian datasets, we show that the size distribution of tourism industry is heavy-tailed and consistent with a power-law behavior in its upper tail. Such a behavior seems quite persistent over the time horizon covered by our study, provided that during the period 2004–2009, the shape parameter is always in the vicinity of 2.5 for Germany and 2.6 for Italy. Size of the tourism industry has been proxied by the lodging capacity of hotel establishments: hotels, boarding houses, inns, lodging houses, motels, apartment hotels, touri…
Fractional calculus approach to the statistical characterization of random variables and vectors
2009
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. A…
A numerical assessment of the free energy function for fractional-order relaxation
2014
In this paper a novel method based on complex eigenanalysis in the state variables domain is proposed to uncouple the set of rational order fractional differential equations governing the dynamics of multi-degree-of-freedom system. The traditional complex eigenanalysis is appropriately modified to be applicable to the coupled fractional differential equations. This is done by expanding the dimension of the problem and solving the system in the state variable domain. Examples of applications are given pertaining to multi-degree-of-freedom systems under both deterministic and stochastic loads.