Probabilistic and statistical problems related to long-range dependence

The thesis is made up of a number of studies involving long-range dependence (LRD), that is, a slow power-law decay in the temporal correlation of stochastic models. Such a phenomenon has been frequently observed in practice. The models with LRD often yield non-standard probabilistic and statistical results. The thesis includes in particular the following topics: Multivariate limit theorems. We consider a vector made of stationary sequences, some components of which have LRD, while the others do not. We show that the joint scaling limits of the vector exhibit an asymptotic independence property. Non-central limit theorems. We introduce new classes of stationary models with LRD through Volterra-type nonlinear filters of white noise. The scaling limits of the sum lead to a rich class of non-Gaussian stochastic processes defined by multiple stochastic integrals. Limit theorems for quadratic forms. We consider continuous-time quadratic forms involving continuous-time linear processes with LRD. We show that the scaling limit of such quadratic forms depends on both the strength of LRD and the decaying rate of the quadratic coefficient. Behavior of the generalized Rosenblatt process. The generalized Rosenblatt process arises from scaling limits under LRD. We study the behavior of this process as its two critical parameters approach the boundaries of the defining region. Inference using self-normalization and resampling. We introduce a procedure called "self-normalized block sampling" for the inference of the mean of stationary time series. It provides a unified approach to time series with or without LRD, as well as with or without heavy tails. The asymptotic validity of the procedure is established

Fracture mechanics studies of non-yielding materials like concrete : modelling of tensile fracture and applied strength analyses

Fracture mechanics studies of non-yielding materials are presented. The studies are based on theoretical models for the macroscopical mechanical behaviour of materials during tensile stress induced fracture. A number of applied numercal analysis are indicated. Fracture models and strength relations are discussed also from a few more general and fundamental points of view. A number of comparisons are made to test results from literature. The applications concern materials such as concrete, reinforced concrete, mortar and wood. Most numerical calculations are carried out by means of finite element methods. The fracture mechanics model called the fictìtious crack model is emphasized. This model gives a.description of gradual and localized fracture-softening in a single discrete tensile fracture process region. 0ther models dealt with: linear elastic fracture mechanics, Weibull-model, un-limited plasticity, conventional maximum stress theory and a few more special models. Specimens dealt with during numerical calculations: beams in bending, fracture mechanics tests specimens, tensile test specimens, pipes in bending and crushing, specimens with a re-entrant corner and longitudinally reinforced concrete beams in shear. According to the results obtained, it seems to be theoretically consistent and often of great practical importance to take into account the gradual and localized fracture-softening during strength analysis of specimens and structural elements

Modeling and Design of Multi-Stable Composite Structures

L'abstract è presente nell'allegato / the abstract is in the attachmen

Characterization of Ultra and nanofiltration commercial Filters by Liquid-Liquid Displacement Porosimetry

Membrane Technology applied, among others, in processes such as Ultrafiltration (UF) and Nanofiltration (NF), has become an important part of biotechnological separation processes in recent decades. Its main feature, the morphology of the porous filters, leading to a ¿sieving mechanism¿ allows effective separation with high selectivity features and made in energy and environmental conditions very interesting. Given the enormous development of membrane filters, it becomes necessary the growth in parallel of characterization techniques applied to such filters, as essential tools for both manufacturers and end-users or researchers. In this sense we need to know most exactly possible, both functional and structural parameters of the membrane, all necessary for a proper choice of that with a view to a particular application. The question we must face is: Is there a characterization method, by itself, giving us a clear and easily interpretable picture of the true structure and functionality of the filter?.The answer to this question is obviously no. There are so many structural and functional parameters that contribute to the exact knowledge of the membrane, that there is no technique that can bring us all this wealth of information.From the industrial and commercial standpoints, the parameter most used and required, in view of possible applications of the filters, it is the molecular weight cut-off (MWCO), although it is clear that by itself is not a definitive tool for choosing a membrane filter.SMAP® group long experience in membrane characterization allows us to conclude that porosimetric techniques give interesting information related to the size and size distribution of the pores present in a membrane, information that can be conveniently checked against functional aspects of it.In this sense, we can consider that Liquid-liquid displacement porosimetry (LLDP) is the most promising porosimetric technique in the range of Ultrafiltration, thus giving us important information about these filters.However, several problems arise regarding the best application of the LLDP technique:Departamento de Física Aplicad

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy

Partial Differential Equations in Ecology

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity