DSpace Angular ::Πλοήγηση Σχολή Μηχανικών Ορυκτών Πόρων ανά Ημερομηνία έκδοσης

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Stochastic diagrammatic analysis of groundwater flow in heterogeneous porous media

(1995) G. Christakos; D.T. Hristopulos; C.T. Miller

The diagrammatic approach is an alternative to standard analytical methods for solving stochastic differential equations governing groundwater flow with spatially variable hydraulic conductivity. This approach uses diagrams instead of abstract symbols to visualize complex multifold integrals that appear in the perturbative expansion of the stochastic flow solution and reduces the original flow problem to a closed set of equations for the mean and the covariance functions. Diagrammatic analysis provides an improved formulation of the flow problem over conventional first-order series approximations, which are based on assumptions such as constant mean hydraulic gradient, infinite flow domain, and neglect of cross correlation terms. This formulation includes simple schemes, like finite-order diagrammatic perturbations that account for mean gradient trends and boundary condition effects, as well as more advanced schemes, like diagrammatic porous media description operators which contain infinite-order correlations. In other words, diagrammatic analysis covers not only the cases where low-order diagrams lead to good approximations of flow, but also those situations where low-order perturbation is insufficient and a more sophisticated analysis is needed. Diagrams lead to a nonlocal equation for the mean hydraulic gradient in terms of which necessary conditions are formulated for the existence of an effective hydraulic conductivity. Three-dimensional flow in an isotropic bounded domain with Dirichlet boundary conditions is considered, and an integral equation for the mean hydraulic head is derived by means of diagrams. This formulation provides an explicit expression for the boundary effects within the three-dimensional flow domain. In addition to these theoretical results, the numerical performance of the diagrammatic approach is tested, and useful insight is obtained by means of one-dimensional flow examples where the exact stochastic solutions are available.

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Practical calculation of non-gaussian multivariate moments in spatiotemporal BME analysis

(Kluwer Academic Publishers-Plenum Publishers, 2001) George Christakos; D.T. Hristopulos

During the past decade, the Bayesian maximum entropy (BME) approach has been used with considerable success in a variety of geostatistical applications, including the spatiotemporal analysis and estimation of multivariate distributions. In this work, we investigate methods for calculating the space/time moments of such distributions that occur in BME mapping applications, and we propose general expressions for non-Gaussian model densities based on Gaussian averages. Two explicit approximations for the covariance are derived, one based on leading-order perturbation analysis and the other on the diagrammatic method. The leading-order estimator is accurate only for weakly non-Gaussian densities. The diagrammatic estimator includes higher-order terms and is accurate for larger non-Gaussian deviations. We also formulate general expressions for Monte Carlo moment calculations including precision estimates. A numerical algorithm based on importance sampling is developed, which is computationally efficient for multivariate probability densities with a large number of points in space/time. We also investigate the BME moment problem, which consists in determining the general knowledge-based BME density from experimental measurements. In the case of multivariate densities, this problem requires solving a system of nonlinear integral equations. We refomulate the system of equations as an optimization problem, which we then solve numerically for a symmetric univariate pdf. Finally, we discuss theoretical and numerical issues related to multivariate BME solutions.

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New anisotropic covariance models and estimation of anisotropic parameters based on the covariance tensor identity

(Springer-Verlag, 2002) D.T. Hristopulos

Many heterogeneous media and environmental processes are statistically anisotropic, that is, their moments have directional dependence. The term range anisotropy denotes processes that have variograms characterized by direction-dependent correlation lengths and directionally independent sill. We distinguish between two classes of anisotropic covariance models: Class (A) models are reducible to isotropic after rotation and rescaling operations. Class (B) models are separable and reduce to a product of one- dimensional functions along the principal axes. We present a Class (A) model for multiscale processes and suggest applications in subsurface hydrology. This model is based on a truncated power law with short and long-range cutoffs. We also present a family of Class (B) models generated by superellipsoidal functions that are based on non- Euclidean distance metrics. We propose a new method for determining the orientation of the principal axes and the degree of anisotropy (i.e., the ratios of the correlation lengths). This information reduces the degrees of freedom of anisotropic variograms and thus simplifies the estimation procedure. In particular, Class (A) models are reduced to isotropic, and Class (B) models to one-dimensional functions. Our method is based on an explicit relation between the second-rank slope tensor (SRST), which can be estimated from the data, and the second-rank covariance tensor. The method is conceptually simple and numerically efficient. It is more accurate for regular (on-grid) data distributions, but it can also be used for irregular (off-grid) spatial distributions. We illustrate its implementation with numerical simulations.

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A model of machine-direction tension variations in paper webs with runnability applications

(2002) T. Uesaka; D.T. Hristopulos

We developed a model of web dynamics to investigate tension (strain) variations, which play a major role in runnability and paper breaks.We focus on a simplified version of the model, which is valid for low-frequency tension variations (<100 Hz). The model predicts abrupt changes in the web speed and tension at contact points where external forces are applied, high strain rates at nip contacts, and tension surges during start-up, as observed in many pressrooms. We prove that the mechanical draw is an accurate estimate of the strain increment for time-independent, but not fluctuating, web speeds. We also investigate the impact of out-of-round rolls on runnability by coupling the web dynamics model to a weak-link model of web failure. We find that, for moderate roll deformations (<5 mm), the out-of-roundness contributes statistically to the increase in break frequency. The risk of web breaks is significant for extreme deformations (>6 mm), especially when a new roll begins unwinding.

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Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields

(Springer-Verlag, 2003) D.T. Hristopulos

The fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) random field models have many applications in the environmental sciences. An issue of practical interest is the permissible range and the relations between different fractal exponents used to characterize these processes. Here we derive the bounds of the covariance exponent for fGn and the Hurst exponent for fBm based on the permissibility theorem by Bochner. We exploit the theoretical constraints on the spectral density to construct explicit two-point (covariance and structure) functions that are band-limited fractals with smooth cutoffs. Such functions are useful for modeling a gradual cutoff of power-law correlations. We also point out certain peculiarities of the relations between fractal exponents imposed by the mathematical bounds. Reliable estimation of the correlation and Hurst exponents typically requires measurements over a large range of scales (more than 3 orders of magnitude). For isotropic fractals and partially isotropic self-affine processes the dimensionality curse is partially lifted by estimating the exponent from measurements along fixed directions. We derive relations between the fractal exponents and the one-dimensional spectral density exponents, and we illustrate the relations using measurements of paper roughness.

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Μοντελοποίηση της υπόγειας ροής και μεταφοράς μάζας στους πλακώδεις ασβεστόλιθους του δυτικού τμήματος του ορεινού όγκου της Δίκτης με τη χρήση γεωγραφικών συστημάτων πληροφοριών

(Technical University of Crete, 2003) Αβραμάκη Χρυσούλα; Karatzas Giorgos; Καρατζας Γιωργος; Kelesidis Vasilis; Κελεσιδης Βασιλειος

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Spartan gibbs random field models for geostatistical applications

(SIAM, 2003) D.T. Hristopulos

The inverse problem of determining the spatial dependence of random fields from an experimental sample is a central issue in Geostatistics. We propose a computationally efficient approach based on Spartan Gibbs random fields. Their probability density function is determined by a small set of parameters, which can be estimated by enforcing sample-based constraints on the stochastic moments. The computational complexity of calculating the constraints increases linearly with the sample size. We investigate a specific Gibbs probability density with spatial dependence derived from generalized gradient and Laplacian operators, and we derive permissibility conditions for the model parameters.

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Renormalization group methods in subsurface hydrology: Overview and applications in hydraulic conductivity upscaling

(2003) D.T. Hristopulos

The renormalization group (RG) approach is a powerful theoretical framework, more suitable for upscaling strong heterogeneity than low-order perturbation expansions. Applications of RG methods in subsurface hydrology include the calculation of (1) macroscopic transport parameters such as effective and equivalent hydraulic conductivity and dispersion coefficients, and (2) anomalous exponents characterizing the dispersion of contaminants due to long-range conductivity correlations or broad (heavy-tailed) distributions of the groundwater velocity. First, we review the main ideas of RG methods and their hydrological applications. Then, we focus on the hydraulic conductivity in saturated porous media with isotropic lognormal heterogeneity, and we present an RG calculation based on the replica method. The RG analysis gives rigorous support to the exponential conjecture for the effective hydraulic conductivity [38]. Using numerical simulations in two dimensions with a bimodal conductivity distribution, we demonstrate that the exponential expression is not suitable for all types of heterogeneity. We also introduce an RG coarse-grained conductivity and investigate its applications in estimating the conductivity of blocks or flow domains with finite size. Finally, we define the fractional effective dimension, and we show that it justifies fractal exponents in the range 1−2 d ≤α <1 (where d is the actual medium dimension) in the geostatistical power average.

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Environmental time series interpolation based on spartan random processes

(2008) D.T. Hristopulos; M. Zukovic

In many environmental applications, time series are either incomplete or irregularly spaced. We investigate the application of the Spartan random process to missing data prediction. We employ a novel modified method of moments (MMoM) for parameter inference. The CPU time of MMoM is shown to be much faster than that of maximum likelihood estimation and almost independent of the data size. We formulate an explicit Spartan interpolator for estimating missing data. The model validation is performed on both synthetic data and real time series of atmospheric aerosol concentrations. The prediction performance is shown to be comparable with that attained by the best linear unbiased (Kolmogorov-Wiener) predictor at reduced computational cost.

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TXRF cation analysis by anionic membrane collection

(John Wiley and Sons, 2009) Kallithrakas-Kontos Nikolaos; Καλλιθρακας-Κοντος Νικολαος; Hatzistavros Vasilios; Χατζησταύρος Βασίλειος

A new method for the determination of trace levels of cationic ions by anion selective membrane collection is presented. Anion selective membranes containing a few micrograms of different complexing reagents in polyvinyl chloride (PVC) matrix were produced in quartz reflectors. The membranes were immersed in water solutions with low concentrations of cationic metals, Cu, Co, Ni, Zn, and of anionic ligands (CN−, etc.). After the equilibration time the reflectors were left to dry and they were analyzed by Total X-Ray Fluorescence (TXRF). Many experimental parameters (pH effect, size of the membrane, volume sample) were examined. The minimum detection limits were estimated to be 1 ng/ml for all metallic cations even in seawater. The method needs less working labor than other enrichment procedures, the cations are collected directly on the TXRF reflector surface and very small chemical reagent consumption is needed.

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Μελέτη συμπεριφοράς κονιαμάτων από συνθετικό λαρνίτη και πορτλανδίτη με διαβαθμισμένη χαλαζιακή άμμο

(Πολυτεχνείο Κρήτης, 2011) Diakrousis Stylianos-Gerasimos; Διακρουσης Στυλιανος-Γερασιμος; Markopoulos Theodoros; Μαρκοπουλος Θεοδωρος; Alevizos Georgios; Αλεβιζος Γεωργιος; Repouskou Eftychia; Ρεπουσκου Ευτυχια

Η παρούσα διπλωματική εργασία εκπονήθηκε στο εργαστήριο Πετρολογίας και Οικονομικής Γεωλογίας, του τμήματος Μηχανικών Ορυκτών Πόρων του Πολυτεχνείου Κρήτης. Σκοπός της διπλωματικής εργασίας ήταν η κατασκευή υδραυλικών κονιαμάτων με μίγματα συνθετικού λαρνίτη, υδράσβεστου, και χαλαζιακής άμμου ως αδρανές για την μελέτη τους ως προς την αντοχή τους και τις ορυκτολογικές αλλαγές τους. Η εργασία πραγματοποιήθηκε σε τέσσερα βασικά στάδια. Στο πρώτο στάδιο πραγματοποιήθηκε η σύνθεση του λαρνίτη, η οποία προέκυψε ύστερα από ανάμειξη πορτλανδίτη με χαλαζία, με βάση τη στοιχειομετρία του λαρνίτη, σε συγκεκριμένες συνθήκες θερμοκρασίας και χρόνου έψησης. Στο δεύτερο στάδιο δημιουργήθηκαν τρία διαφορετικά μείγματα υδραυλικών κονιών με βάση την περιεκτικότητά της σε λαρνίτη και πορτλανδίτη. Στο τρίτο στάδιο κατασκευάστηκαν δοκίμια από τα παραπάνω τρία είδη κονιών, τα οποία χαρακτηρίζονται από συγκεκριμένες αναλογίες κονίας, αδρανών υλικών (χαλαζιακή διαβαθμισμένη άμμο) και νερού. Έπειτα τα δοκίμια αυτά υποβλήθηκαν σε δοκιμές μονοαξονικής θλίψης και εφελκυσμού τύπου Brazil, σε 7, 28, 60 και 90 ημέρες. Στο τέταρτο στάδιο πραγματοποιήθηκε ορυκτολογική ανάλυση των δειγμάτων τα οποία είχαν ληφθεί αμέσως μετά τις δοκιμές. Η ορυκτολογική ανάλυση έγινε με τη μέθοδο της περιθλασιμετρίας ακτίνων -Χ. Συνδυάζοντας τις μηχανικές αντοχές με τις αντίστοιχες ορυκτολογικές αναλύσεις των δοκιμίων, αποδεικνύεται ότι η θλιπτική αντοχή εξαρτάται από το ποσοστό του λαρνίτη στο δοκίμιο. Επιπλέον, διαπιστώθηκε γραμμική σχέση, και για τα τρία κονιάματα, μεταξύ του ποσοστού του λαρνίτη και του χρόνου ωρίμανσης

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Συμβολομετρία RADAR στην παρακολούθηση υψομετρικών παραμορφώσεων του εδάφους

(Technical University of Crete, 2011) Bikouvaraki Maria; Μπικουβαρακη Μαρια; Mertikas Stelios; Μερτικας Στελιος; Partsinevelos Panagiotis; Παρτσινεβελος Παναγιωτης; Mouslopoulou Vasiliki; Μουσλοπουλου Βασιλικη

Συχνά παρατηρούνται υψομετρικές παραμορφώσεις στο έδαφος, οι οποίες έχουν προκληθεί από φυσικά αίτια (π.χ. σεισμοί, κατολισθήσεις, καθιζήσεις κλπ) ή από την ανθρώπινη δραστηριότητα (π.χ. υπόγειες εκμεταλλεύσεις, υπεράντληση νερού κλπ). Η διαφορική συμβολομετρία RADAR συνθετικού ανοίγματος (DInSAR) είναι μία νέα τεχνική η οποία δύναται να μετρήσει αυτού του είδους τις παραμορφώσεις με ακρίβεια μερικών εκατοστών και συχνά χιλιοστών. Σκοπός της εργασίας αυτής είναι η εφαρμογή της διαφορικής συμβολομετρίας RADAR συνθετικού ανοίγματος στην περιοχή της Χρυσοσκαλίτισσας, στο νοτιοδυτικό άκρο της νήσου Κρήτης. Η επιλογή της θέσης αυτής έγινε βάσει του γεγονότος ότι εμφανίζεται στην περιοχή μία τάση για ανύψωση της τάξεως των πέντε χιλιοστών ανά έτος. Το λογισμικό που χρησιμοποιήθηκε για την επεξεργασία των εικόνων είναι το Repeat Orbit Interferometry PACkage (ROI_PAC) το οποίο δημιουργήθηκε από το Jet Propulsion Laboratory της NASA, και το Caltech.

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Crushing of clay bearing limestone and serpentine using a novel centrifugal crusher

(Πολυτεχνείο Κρήτης, 2012) Emejulu Chukwudubem Antony

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Rheological properties of Palygorskite-Smectite and Sepiolite-Smectite Mixed Clay Suspensions

(Πολυτεχνείο Κρήτης, 2012) Chemeda Yadeta Chemdesa

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Elliptical anisotropy statistics on spatial data and geostatistical applications

(Technical University of Crete, 2012) Petrakis Emmanouil; Πετρακης Εμμανουηλ; Christopoulos Dionysios; Χριστοπουλος Διονυσιος; Agioutantis Zacharias; Αγιουταντης Ζαχαριας; Galetakis Michalis; Γαλετακης Μιχαλης

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Διερεύνηση του τασικού και παραμορφωσιακού πεδίου κατά τη σύνδεση φυσικών δομικών λίθων για την αναστήλωση αρχαίων μνημείων

(Πολυτεχνείο Κρήτης, 2013) Agalaniotou Smaro; Αγαλανιωτου Σμαρω; Agioutantis Zacharias; Αγιουταντης Ζαχαριας; Exadaktylos Georgios; Εξαδακτυλος Γεωργιος; Steiakakis Manolis; Στειακακης Μανωλης; Maravelaki Pagona; Μαραβελακη Παγωνα; Providakis Konstantinos; Προβιδακης Κωνσταντινος; Stavroulaki Maria; Σταυρουλακη Μαρια

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Ανίχνευση πιθανών ρηγμάτων με χρήση τρισδιάστατης γεωλογικής μοντελοποίησης

(Πολυτεχνείο Κρήτης, 2013) Kissas Vasileios; Κισσας Βασιλειος; Manoutsoglou Emmanouil; Μανουτσογλου Εμμανουηλ; Vafeidis Antonios; Βαφειδης Αντωνιος; Steiakakis Manolis; Στειακακης Μανωλης

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Γεωλογικοί και ανθρωπογενείς παράγοντες στη διαμόρφωση ακτών: η περίπτωση της Βάρκιζας - Ν. Αττικής

(Πολυτεχνείο Κρήτης, 2013) Skanavis Vasileios; Σκαναβης Βασιλειος; Manoutsoglou Emmanouil; Μανουτσογλου Εμμανουηλ; Synolakis Kostas; Συνολακης Κωστας

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Διερεύνηση της χρήσης ζεόλιθου για τον έλεγχο της εκχύλισης του καλίου από εδάφη τροποποιημένα με κομπόστ

(Πολυτεχνείο Κρήτης, 2013) Papagiannidou Sotiria; Παπαγιαννιδου Σωτηρια; Pentari Despoina; Πενταρη Δεσποινα; Komnitsas Konstantinos; Κομνιτσας Κωνσταντινος; Moraitis Daniil; Μωραϊτης Δανιηλ

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Χαρακτηρισμός τεφρών από καύση υπολειμμάτων εσπεριδοειδών σε ρευστοποιημένη κλίνη

(Πολυτεχνείο Κρήτης, 2013) Trikouvertis Georgios; Τρικουβερτης Γεωργιος-Μαριος; Vamvouka Despoina; Βαμβουκα Δεσποινα; Galetakis Michalis; Γαλετακης Μιχαλης; Pentari Despoina; Πενταρη Δεσποινα

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