Wind resource modelling in complex terrain using different mesoscale–microscale coupling techniques

Wind resource evaluation in two sites located in Portugal was performed using the mesoscale modelling system Weather Research and Forecasting (WRF) and the wind resource analysis tool commonly used within the wind power industry, the Wind Atlas Analysis and Application Program (WAsP) microscale model. Wind measurement campaigns were conducted in the selected sites, allowing for a comparison between in situ measurements and simulated wind, in terms of flow characteristics and energy yields estimates. Three different methodologies were tested, aiming to provide an overview of the benefits and limitations of these methodologies for wind resource estimation. In the first methodology the mesoscale model acts like “virtual” wind measuring stations, where wind data was computed by WRF for both sites and inserted directly as input in WAsP. In the second approach, the same procedure was followed but here the terrain influences induced by the mesoscale model low resolution terrain data were removed from the simulated wind data. In the third methodology, the simulated wind data is extracted at the top of the planetary boundary layer height for both sites, aiming to assess if the use of geostrophic winds (which, by definition, are not influenced by the local terrain) can bring any improvement in the models performance. The obtained results for the abovementioned methodologies were compared with those resulting from in situ measurements, in terms of mean wind speed, Weibull probability density function parameters and production estimates, considering the installation of one wind turbine in each site. Results showed that the second tested approach is the one that produces values closest to the measured ones, and fairly acceptable deviations were found using this coupling technique in terms of estimated annual production. However, mesoscale output should not be used directly in wind farm sitting projects, mainly due to the mesoscale model terrain data poor resolution. Instead, the use of mesoscale output in microscale models should be seen as a valid alternative to in situ data mainly for preliminary wind resource assessments, although the application of mesoscale and microscale coupling in areas with complex topography should be done with extreme caution.

Coherent structures in open channel flows with bed load transport over an hydraulically rough bed

Dissertação para obtenção do Grau de Mestre em Engenharia Civil – Perfil de Estruturas

On square permutations

Severini and Mansour introduced in [4]square polygons, as graphical representations of square permutations, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.

Optimal latent period in a bacteriophage population model structured by infection-age

We study the lysis timing of a bacteriophage population by means of a continuously infection-age-structured population dynamics model. The features of the model are the infection process of bacteria, the natural death process, and the lysis process which means the replication of bacteriophage viruses inside bacteria and the destruction of them. We consider that the length of the lysis timing (or latent period) is distributed according to a general probability distribution function. We have carried out an optimization procedure and we have found the latent period corresponding to the maximal fitness (i.e. maximal growth rate) of the bacteriophage population.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

Conditioning of stochastic 3-D fracture networks to hydrological and geophysical data

The geometry and connectivity of fractures exert a strong influence on the flow and transport properties of fracture networks. We present a novel approach to stochastically generate three-dimensional discrete networks of connected fractures that are conditioned to hydrological and geophysical data. A hierarchical rejection sampling algorithm is used to draw realizations from the posterior probability density function at different conditioning levels. The method is applied to a well-studied granitic formation using data acquired within two boreholes located 6 m apart. The prior models include 27 fractures with their geometry (position and orientation) bounded by information derived from single-hole ground-penetrating radar (GPR) data acquired during saline tracer tests and optical televiewer logs. Eleven cross-hole hydraulic connections between fractures in neighboring boreholes and the order in which the tracer arrives at different fractures are used for conditioning. Furthermore, the networks are conditioned to the observed relative hydraulic importance of the different hydraulic connections by numerically simulating the flow response. Among the conditioning data considered, constraints on the relative flow contributions were the most effective in determining the variability among the network realizations. Nevertheless, we find that the posterior model space is strongly determined by the imposed prior bounds. Strong prior bounds were derived from GPR measurements and helped to make the approach computationally feasible. We analyze a set of 230 posterior realizations that reproduce all data given their uncertainties assuming the same uniform transmissivity in all fractures. The posterior models provide valuable statistics on length scales and density of connected fractures, as well as their connectivity. In an additional analysis, effective transmissivity estimates of the posterior realizations indicate a strong influence of the DFN structure, in that it induces large variations of equivalent transmissivities between realizations. The transmissivity estimates agree well with previous estimates at the site based on pumping, flowmeter and temperature data.

Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization

The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that the space subdivision process is in accordance with the premises of the Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the time dependency of nucleation and growth rates. We have also developed an approximate analytical cell size probability density function. Finally, we have applied our approach to the distributions resulting from solid phase crystallization under isochronal heating conditions

Passage times for the decay of an unstable state triggered by colored noise

We study the decay of an unstable state in the presence of colored noise by calculating the moment generating function of the passage-time distribution. The problems of the independence of the initial condition in this non-Markovian process and that of nonlinear effects are addressed. Our results are compared with recent analog simulations.

Heat fluctuations in Brownian transducers

The heat fluctuation probability distribution function in Brownian transducers operating between two heat reservoirs is studied. We find, both analytically and numerically, that the recently proposed fluctuation theorem for heat exchange [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)] has to be applied carefully when the coupling mechanism between both baths is considered. We also conjecture how to extend such a relation when an external work is present.

Canonical transformations theory for presymplectic systems

We develop a theory of canonical transformations for presymplectic systems, reducing this concept to that of canonical transformations for regular coisotropic canonical systems. In this way we can also link these with the usual canonical transformations for the symplectic reduced phase space. Furthermore, the concept of a generating function arises in a natural way as well as that of gauge group.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

Integrated random processes exhibiting long tails, finite moments, and power-law spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution¿which can be obtained from our model in certain limits¿which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This

Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.

Probabilistic electrical resistivity tomography of a CO2 sequestration analog

Electrical resistivity tomography (ERT) is a well-established method for geophysical characterization and has shown potential for monitoring geologic CO2 sequestration, due to its sensitivity to electrical resistivity contrasts generated by liquid/gas saturation variability. In contrast to deterministic inversion approaches, probabilistic inversion provides the full posterior probability density function of the saturation field and accounts for the uncertainties inherent in the petrophysical parameters relating the resistivity to saturation. In this study, the data are from benchtop ERT experiments conducted during gas injection into a quasi-2D brine-saturated sand chamber with a packing that mimics a simple anticlinal geological reservoir. The saturation fields are estimated by Markov chain Monte Carlo inversion of the measured data and compared to independent saturation measurements from light transmission through the chamber. Different model parameterizations are evaluated in terms of the recovered saturation and petrophysical parameter values. The saturation field is parameterized (1) in Cartesian coordinates, (2) by means of its discrete cosine transform coefficients, and (3) by fixed saturation values in structural elements whose shape and location is assumed known or represented by an arbitrary Gaussian Bell structure. Results show that the estimated saturation fields are in overall agreement with saturations measured by light transmission, but differ strongly in terms of parameter estimates, parameter uncertainties and computational intensity. Discretization in the frequency domain (as in the discrete cosine transform parameterization) provides more accurate models at a lower computational cost compared to spatially discretized (Cartesian) models. A priori knowledge about the expected geologic structures allows for non-discretized model descriptions with markedly reduced degrees of freedom. Constraining the solutions to the known injected gas volume improved estimates of saturation and parameter values of the petrophysical relationship. (C) 2014 Elsevier B.V. All rights reserved.