Scaling Properties of Flood Peaks

The scaling behavior of flood peak distributions is examined using a statistical model of the spatio-temporal distribution of rainfall and a hydrological model that describes the transformation of rainfall to discharge within a drainage network. Of particular interest is the empirical observation made by a number of investigators that the coefficient of variation (CV) of annual flood peaks for a region increases with drainage area up to drainage areas of approximately 100 km², and decreases with drainage area for larger drainage basins. This observation is neither consistent with simple scaling models, in which the coefficient of variation does not vary with drainage area, nor multiscaling models, in which the coefficient of variation decreases monotonically with drainage area. Model analyses illustrate that knowledge of the spatial and temporal organization of the rainfall, together with the details of the network structure of the drainage basin, is sufficient information with which to explain the observed behavior of sample CV. The interaction between the temporal variability of rainfall, relative to basin size, and the network structure is shown to be of particular importance.     

Bifurcations of basins of attraction from the view point of prime ends

In dynamical systems examples are common in which two or more attractors coexist, and in such cases the basin boundary is nonempty and the basins often have fractal basin boundaries. The purpose of this paper is to describe the structure and properties of unbounded basins and their boundaries for two-dimensional diffeomorphisms. Frequently, if not always, there is a periodic saddle on the boundary that is accessible from the basin. Carathéodory and many others developed an approach in which an open set (in our case a basin) is compactified using so-called prime end theory. Under the prime end compactification of the basin, boundary points of the basin (prime ends) can be characterized as either type 1, 2, 3, or 4. In all well-known examples, most points are of type 1. Many two-dimensional basins have a basin cell, that is, a trapping region whose boundary consists of pieces of the stable and unstable manifolds of a well chosen periodic orbit. Then the basin consists of a central body (the basin cell) and a finite number of channels attached to it, and the basin boundary is fractal. We present a result that says {a basin has a basin cell} if and only if {every prime end that is defined by a chain of unbounded regions (in the basin) is a prime end of type 3 and furthermore all other prime ends are of type 1}. We also prove as a parameter is varied, the basin cell for a basin B is created (or destroyed) if and only if either there is a saddle node bifurcation or the basin B has a prime end that is defined by a chain of unbounded regions and is a prime end of either type 2 or type 4.     

Influence of the multiplicity of the roots on the basins of attraction of Newton’s method

In this work, we develop and implement two algorithms for plotting and computing the measure of the basins of attraction of rational maps defined on the Riemann sphere. These algorithms are based on the subdivisions of a cubical decomposition of a sphere and they have been made by using different computational environments. As an application, we study the basins of attraction of the fixed points of the rational functions obtained when Newton’s method is applied to a polynomial with two roots of multiplicities m and n. We focus our attention on the analysis of the influence of the multiplicities m and n on the measure of the two basins of attraction. As a consequence of the numerical results given in this work, we conclude that, if m > n, the probability that a point in the Riemann Sphere belongs to the basin of the root with multiplicity m is bigger than the other case. In addition, if n is fixed and m tends to infinity, the probability of reaching the root with multiplicity n tends to zero.     

Study of Saudi Arabian climatic conditions using Hurst exponent and climatic predictability index

This paper utilizes Hurst exponent to study the persistency of meteorological parameters individually and dependency of rainfall/precipitation on pressure and temperature using climate predictability index. For the purpose, daily averages of surface pressure and temperature and daily total rainfall data for a period of 7 years for three locations and 14 years for seven locations has been utilized. The Hurst exponents (H) for above mentioned meteorological parameters were calculated using rescaled range analysis (R/S) and absolute moments methods. These H values were used to calculate the fractal dimension D for pressure, temperature and rainfall data. Finally, these D’s were used to calculate the climate predictability index PI_C in terms of pressure predictability index (PI_P), temperature predictability index (PI_T) and rainfall predictability index (PI_R). The Hurst exponent analysis showed that H values for rainfall, relative humidity and wind speed time series data for all the stations were >0.5 which is indicative of persistence behavior of the parameters on the previous values while for pressure and temperature H values were <0.5 means anti-persistence behavior. The climate predictability index showed that in most of the cases the rainfall was dependent on both pressure and temperature predictability indices. In some cases it was more dependent on pressure index than the temperature and in some cases otherwise. In Saudi Arabia there is no prevalent or established rainy season and the present analysis could not result into concrete results. It is therefore recommended to analyze the data by breaking the entire data set into seasons and further into different years.     

Specific surface area of mercuric sulphide

The specific surface area of mercuric sulphide (a) has been determined by three methods: (a) gas adsorption method (N₂ adsorption), (b) air permeability method and (c) microscopic method. The area values are compared. In the gas adsorption method, the effect of degassing temperature on the surface area of solid was studied. In the permeability method the porosity range over which the specific surface area remains constant was also determined.     

Multifractal rainfall extremes: Theoretical analysis and practical estimation

We study the extremes generated by a multifractal model of temporal rainfall and propose a practical method to estimate the Intensity–Duration–Frequency (IDF) curves. The model assumes that rainfall is a sequence of independent and identically distributed multiplicative cascades of the beta-lognormal type, with common duration D. When properly fitted to data, this simple model was found to produce accurate IDF results [Langousis A, Veneziano D. Intensity–duration–frequency curves from scaling representations of rainfall. Water Resour Res 2007;43. doi:10.1029/2006WR005245]. Previous studies also showed that the IDF values from multifractal representations of rainfall scale with duration d and return period T under either d → 0 or T → ∞, with different scaling exponents in the two cases. We determine the regions of the (d, T)-plane in which each asymptotic scaling behavior applies in good approximation, find expressions for the IDF values in the scaling and non-scaling regimes, and quantify the bias when estimating the asymptotic power-law tail of rainfall intensity from finite-duration records, as was often done in the past. Numerically calculated exact IDF curves are compared to several analytic approximations. The approximations are found to be accurate and are used to propose a practical IDF estimation procedure.     

Centralized and decentralized management of groundwater with multiple users

In this work, we investigate two groundwater inventory management schemes with multiple users in a dynamic game-theoretic structure: (i) under the centralized management scheme, users are allowed to pump water from a common aquifer with the supervision of a social planner, and (ii) under the decentralized management scheme, each user is allowed to pump water from a common aquifer making usage decisions individually in a non-cooperative fashion. This work is motivated by the work of Saak and Peterson [14], which considers a model with two identical users sharing a common aquifer over a two-period planning horizon. In our work, the model and results of Saak and Peterson [14] are generalized in several directions. We first build on and extend their work to the case of n non-identical users distributed over a common aquifer region. Furthermore, we consider two different geometric configurations overlying the aquifer, namely, the strip and the ring configurations. In each configuration, general analytical results of the optimal groundwater usage are obtained and numerical examples are discussed for both centralized and decentralized problems.     

Application of the asymptotic solution to EM field scattering problem for creation of media with prescribed permeability

Scattering of electromagnetic (EM) waves by many small impedance particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a→0, where a is the characteristic size of a particle and the number M(a) of the particles tends to infinity at a suitable rate. The proposed theory allows one to create a medium with a desirable spatially inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability μ(x) of the limiting medium. The computational results confirm a possibility to create the media with various distributions of μ(x).     

A comparison between iterative methods by using the basins of attraction

There exists a real competition between authors to construct improved iterative methods for solving nonlinear equations. In this paper, by using computer experiment, we study the basins of attraction for some of the iterative methods for solving the equation P(z) = 0, where P:C→C is a complex coefficients polynomial, and this allows us to compare their performances (the area of convergence and theirs speed). The beauty fractal pictures generated by these methods are presented too.     

Learning networks in rainfall estimation

This paper utilizes Artificial Neural Networks (ANNs), standard Support Vector Regression (SVR), Least-Squares Support Vector Regression (LS-SVR), linear regression (LR) and a rain rate (RR) formula that meteorologists use, to estimate rainfall. A unique source of ground truth rainfall data is the Oklahoma Mesonet. With the advent of the WSR-88D network of radars data mining is feasible for this study. The reflectivity measurements from the radar are used as inputs for the techniques tested. LS-SVR generalizes better than ANNs, linear regression and a rain rate formula in rainfall estimation and for rainfall detection, SVR has a better performance than the other techniques.Mathematics Subject Classification: 30C40     

Hydrogeochemical modeling for groundwater management in arid and semiarid regions using MODFLOW and MT3DMS: A case study of the Jeffara of Medenine coastal aquifer,South-Eastern Tunisia

The study of water quality and the quantification of reserves and their variations according to natural and anthropogenic forcing is necessary to establish an adequate management plan for groundwater resources. For this purpose, a modeling approach is a useful tool that allows, after calibration phase and verification of simulation, and under different scenarios of forcing and operational changes, to estimate and control the groundwater quantity and quality. The main objective of this study is to collect all available data in a model that simulates the Jeffara of Medenine coastal aquifer system functioning. To achieve this goal, a conceptual model was constructed based on previous studies and hydrogeological investigations. The regional groundwater numerical flow model for the Jeffara aquifer was developed using MODFLOW working under steady-state and transient conditions. Groundwater elevations measured from the piezometric wells distributed throughout the study area in 1973 were selected as the target water levels for steady state (head) model calibration. A transient simulation was undertaken for the 42 years from 1973 to 2015. The historical transient model calibration was satisfactory, consistent with the continuous piezometric decline in response to the increase in groundwater abstraction. The developed numerical model was used to study the system's behavior over the next 35 years under various constraints. Two scenarios for potential groundwater extraction for the period 2015–2050 are presented. The predictive simulations show the effect of the increase of the exploitation on the piezometric levels. To study the phenomenon of salinization, which is one of the most severe and widespread groundwater contamination problems, especially in coastal regions, a solute transport model has been constructed by using MT3DMS software coupled with the groundwater flow model. The best calibration results are obtained when the connection with the overlying superficial aquifer is considered suggesting that groundwater contamination originates from this aquifer. Recommendations for water resource managers

• The results of this study show that Groundwater resources of Jeffara of Medenine coastal aquifer in Tunisia are under immense pressure from multiple stresses.
• The water resources manager must consider the impact of economic and demographic development in groundwater management to avoid the intrusion of saline water.
• The results obtained presented some reference information that can serve as a basis for water resources planning.
• The model runs to provide information that managers can use to regulate and adequately control the Jeffara of Medenine water resources.

     

The threshold method for estimating total rainfall

The threshold method estimates the total rainfall F _G in a region G using the area B _G of the subregion where rainfall intensity exceeds a certain threshold value c. We model the rainfall in a region by a marked spatial point process and derive a correlation formula between F _G and B _G. This correlation depends not only on the rainfall distribution but also on the variation of number of raining sites, showing the importance of taking account of the spatial character of rainfall. In the extreme case where the variation of number of raining sites is dominant, the threshold method may work regardless of rainfall distributions and even regardless of threshold values. We use the lattice gas model from statistical physics to model raining sites and show a huge variation in the number of raining sites is theoretically possible if a phase transition occurs, that is, physically different states coexist. Also, we show by radar observation datasets that there are huge variations of raining sites actually.     

Exceedance probability of the integral of a stochastic process

Let X={X(s)}_s∈S be an almost sure continuous stochastic process (S compact subset of R^d) in the domain of attraction of some max-stable process, with index function constant over S. We study the tail distribution of ∫_SX(s)ds, which turns out to be of Generalized Pareto type with an extra ‘spatial’ parameter (the areal coefficient from Coles and Tawn (1996) [3]). Moreover, we discuss how to estimate the tail probability P(∫_SX(s)ds>x) for some high value x, based on independent and identically distributed copies of X. In the course we also give an estimator for the areal coefficient. We prove consistency of the proposed estimators. Our methods are applied to the total rainfall in the North Holland area; i.e. X represents in this case the rainfall over the region for which we have observations, and its integral amounts to total rainfall.The paper has two main purposes: first to formalize and justify the results of Coles and Tawn (1996) [3]; further we treat the problem in a non-parametric way as opposed to their fully parametric methods.     

Topologie locale des méthodes de Newton cubiques: plan dynamique

For a cubic Newton map N, we obtain the following theorems: 1) The boundary of the immediate basin of each fixed critical point is locally connected. 2) The Julia set J(N) is locally connected provided either N has no irrational indifferent periodic point or N has no Siegel disc and the orbit of the non-fixed critical point doesn 't accumulate on the boundary of the fixed immediate basins. In particular, in contrast with Julia sets of polynomials, J(N) can be locally connected even if N has a periodic Cremer point.The proofs rely on the construction of articulated rays which are very special simple arcs landing on J(N).     

Revealing the Escape Dynamics in a Hamiltonian System with Five Exits

The scope of this work is to reveal, by means of numerical methods, the escape process in a Hamiltonian system with five exits which describes the problem of rearrangement multichannel scattering. For determining the influence of the energy on the nature of the orbits we classify starting conditions of orbits in planes of two dimensions. All the complex basins of escape, associated with the five escape channels of the system, are illustrated by using color-coded diagrams. The distribution of time of the escape is correlated with the corresponding escape basins. The uncertainty (fractal) dimension along with the (boundary) basin entropy are computed for quantifying the degree of fractality of the dynamical system.     

Third- to fourth-grade students’ conceptions of multiplication and area measurement

In this study, 34 children were evaluated in order to elucidate their multiplicative thinking and interpretation of the area formula of a rectangle, and to determine what roles these factors play in solving area measurement problems. One-on-one interviews and problem-solving tasks were employed to explore the problem-solving skills of the children regarding these two concepts. This study also explored how the associations changed throughout two consecutive phases, from the third to the fourth grades. The results indicated that in the third grade, multiplicative thinking was associated with the solving of area measurement problems. Third-grade children who understood the meaning of the multiplication symbol “p × q” in models (e.g., the set model and arrays) outperformed children who understood only partial multiplicative concepts or additive thinking; however, the association between multiplicative thinking and solving area measurement problems was not significant in the fourth grade. In contrast, children’s ability to interpret the area formula of a rectangle was associated with their performance at solving area measurement problems throughout the third and fourth grades. The way of interpreting the area formula was associated with the extent to which the children understood multiplication, area measurement, and the spatial concepts embedded in rectangular figures. The instructional implications of the study are discussed in terms of developing child abilities to solve area measurement problems by connecting multiplication and area measurement.     

Global dynamics in a non-linear model of the equity ratio

A model for firms' financial conditions is proposed, which ultimately reduces to a two-dimensional non-invertible map in the variables mean and variance of the equity ratio. The possible dynamics of the model and the global behaviour are investigated. We describe the mechanism of bifurcations leading to fractalization of the basins and/or fractalization of their boundaries, showing how a locally stable attractor may be almost globally unstable. Multistability is also investigated. Two, three or four co-existing attractors have been found and we describe the mechanism of bifurcations leading their basins to become chaotically intermingled, and thus to unpredictability of the asymptotic state in a wide region. The knowledge of such regimes, besides those associated with simple dynamics, may be of help for the operators. While the use of the technical tools we propose to study the global dynamics and bifurcations may be of help for further investigations.     

Controlling unpredictability in the randomly driven Hénon–Heiles system

Noisy scattering dynamics in the randomly driven Hénon–Heiles system is investigated in the range of initial energies where the motion is unbounded. In this paper we study, with the help of the exit basins and the escape time distributions, how an external perturbation, be it dissipation or periodic forcing with a random phase, can enhance or mitigate the unpredictability of a system that exhibit chaotic scattering. In fact, if basin boundaries have the Wada property, predictability becomes very complicated, since the basin boundaries start to intermingle, what means that there are points of different basins close to each other. The main responsible of this unpredictability is the external forcing with random phase, while the dissipation can recompose the basin boundaries and turn the system more predictable. Therefore, we do the necessary simulations to find out the values of dissipation and external forcing for which the exit basins present the Wada property. Through these numerical simulations, we show that the presence of the Wada basins have a specific relation with the damping, the forcing amplitude and the energy value. Our approach consists on investigating the dynamics of the system in order to gain knowledge able to control the unpredictability due to the Wada basins.     

Stokes flow of an assemblage of porous particles: stress jump condition

The present article investigates the overall bed permeability of an assemblage of porous particles. For the bed of porous particles, the fluid-particle system is represented as an assemblage of uniform porous spheres fixed in space. Each sphere, with a surrounding envelope of fluid, is uncoupled from the system and considered separately. This model is popularly known as cell model. Stokes equations are employed inside the fluid envelope and Brinkman equations are used inside the porous region. The stress jump boundary condition is used at the porous-liquid interface together with the continuity of normal stress and continuity of velocity components. On the surface of the fluid envelope, three different possible boundary conditions are tested. The obtained expression for the drag force is used to estimate the overall bed permeability of the assemblage of porous particles and the behavior of overall bed permeability is analyzed with various parameters like modified Darcy number (Da*), stress jump coefficient (??), volume fraction (??), and effective viscosity.