1,929 research outputs found

    Analytical approximation to the multidimensional Fokker--Planck equation with steady state

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    The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein--Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are `far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered.Comment: Updated version as publishe

    Gravitational radiation from compact binary systems: gravitational waveforms and energy loss to second post-Newtonian order

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    We derive the gravitational waveform and gravitational-wave energy flux generated by a binary star system of compact objects (neutron stars or black holes), accurate through second post-Newtonian order (O[(v/c)4]O[(Gm/rc2)2]O[(v/c)^4] \sim O[(Gm/rc^2)^2]) beyond the lowest-order quadrupole approximation. We cast the Einstein equations into the form of a flat-spacetime wave equation together with a harmonic gauge condition, and solve it formally as a retarded integral over the past null cone of the chosen field point. The part of this integral that involves the matter sources and the near-zone gravitational field is evaluated in terms of multipole moments using standard techniques; the remainder of the retarded integral, extending over the radiation zone, is evaluated in a novel way. The result is a manifestly convergent and finite procedure for calculating gravitational radiation to arbitrary orders in a post-Newtonian expansion. Through second post-Newtonian order, the radiation is also shown to propagate toward the observer along true null rays of the asymptotically Schwarzschild spacetime, despite having been derived using flat spacetime wave equations. The method cures defects that plagued previous ``brute- force'' slow-motion approaches to the generation of gravitational radiation, and yields results that agree perfectly with those recently obtained by a mixed post-Minkowskian post-Newtonian method. We display explicit formulae for the gravitational waveform and the energy flux for two-body systems, both in arbitrary orbits and in circular orbits. In an appendix, we extend the formalism to bodies with finite spatial extent, and derive the spin corrections to the waveform and energy loss.Comment: 59 pages ReVTeX; Physical Review D, in press; figures available on request to [email protected]

    Metamaterials for radiactive cooling

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    The increasing pressure of society to decrease energy consumption and to enhance energetic efficiency has lead to search novel technologies to accomplish it. Notwithstanding the increasing electricity production of renewable energies, it is a fact that the energy expenses can be drastically reduced in most areas. Among these areas, cooling systems stand out for being energetically inefficient. Furthermore, both economical and energy cost of such systems are increasing due to the global warming, which is aggravated by the energy production for them, making a loop that is increasingly damaging the environment. A solution to this problem has emerged under the name of radiative cooling, which is a physical phenomenon by which any terrestrial object losses heat in form of radiation that is sent to outer space. This process can be explained by black body radiation theory and the atmospheric window. The former states that any object at some temperature above 0 K radiates energy at all wavelengths, with its radiation peak and spectral location modulated by its temperature. The latter is a frequency band in which the atmosphere is transparent to radiation, making possible for waves at certain frequencies to cross freely. These phenomena allows a direct heat transmission between earth and space, which is cold and almost infinite, making a great storage for excess warmth without wasting energy in the process. In this work, it has been studied one of the main technologies that can implement radiative cooling in practice, metamaterials, with the aim to understand how to improve its associated problems of manufacturing and design for radiative cooling applications. In Chapter 1, the fundamentals of radiative cooling are introduced along with the state of the art. Then, Chapter 2 presents the materials used in the literature and in this work to develop later analytical models for thin film multilayered metamaterials and a possible way to automatically design them. To better understand the analytical developments, two appendices introducing the underlying theory and equations are included. Also, the software used in this work is presented. Finally, the performance and analysis of three different radiative cooling devices is exposed in Chapter 3, one of them using the materials and methods of Chapter 2.Máster Universitario en Ingeniería de Telecomunicación por la Universidad Pública de NavarraNafarroako Unibertsitate Publikoko Unibertsitate Masterra Telekomunikazio Ingeniaritza

    Efficient computer-aided verification of parallel and distributed software systems

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    The society is becoming increasingly dependent on applications of distributed software systems, such as controller systems and wireless telecommunications. It is very difficult to guarantee the correct operation of this kind of systems with traditional software quality assurance methods, such as code reviews and testing. Formal methods, which are based on mathematical theories, have been suggested as a solution. Unfortunately, the vast complexity of the systems and the lack of competent personnel have prevented the adoption of sophisticated methods, such as theorem proving. Computerised tools for verifying finite state asynchronous systems exist, and they been successful on locating errors in relatively small software systems. However, a direct translation of software to low-level formal models may lead to unmanageably large models or complex behaviour. Abstract models and algorithms that operate on compact high-level designs are needed to analyse larger systems. This work introduces modelling formalisms and verification methods of distributed systems, presents efficient algorithms for verifying high-level models of large software systems, including an automated method for abstracting unneeded details from systems consisting of loosely connected components, and shows how the methods can be applied in the software development industry.reviewe

    Physico-chemical studies in flow analysis

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    The first part of this study was the characterisation of an impinging jet electrode in an amperometric detector; the device having found extensive application in flow injection analysis. A voltammetric study of the detector in the stopped flow mode was carried out and evidence is presented of restricted diffusion imposed by the shallow depth of the cell. In hydrodynamic voltammetry, the detector exhibited a gradual progression from thin-layer to wall jet behaviour as the flow rate increased. This gradation is discussed in terms of a model in which flow in the electrode chamber forms concentric rings, the streamlines being successively perpendicular, oblique and parallel to the electrode. The response of the detector and its associated equipment was studied by two experiments. Firstly, the fidelity of the electrochemical instrumentation and recording system was ascertained from its electronic response to a RC (resistance-capacitance) circuit functioning as a flow injection transport analogue. Secondly, the dynamic response of the electrochemical cell was established from an experiment using a concentration step input delivered through a short, straight manifold. The results indicated that laminar flow in the delivery tube was modified by mixing stages in the cell channel and its connections to produce a final dispersion which defines an effective detection volume of only 7µL. The electronic and cell responses indicate that the total detection system would impose little extra dispersion in a practical flow injection line. In the second part of this study, photometric titrations were carried out in a stirred tank reactor in which the volume changed linearly with time. The general relation for the concentration gradient when the tank is used as a mixing device was examined experimentally under various flow conditions. In particular, the precision of linear concentration gradients was ascertained when peristaltic pumping was employed. These gradients were utilised to titrate analyte within the tank by means of titrant delivered by pump flow with photometric detection in an exit stream. Self-indicating titrations, following changes in the absorbance of analyte, titrant or reaction product, were performed each conforming to theoretical prediction. Due to the external detection system employed, dispersion and transportation lag effects were observed and accounted for

    In-situ absorption and fluorescence studies of electrogenerated species

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    Koopman with inputs and control for constitutive law identification

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    Constitutive laws characterise the stress-strain relationship in a material. Determining a consti- tutive law experimentally typically involves subjecting the material to a prescribed deformation and measuring the force required to achieve it. There are numerous constitutive laws which have been developed to model the stress response of viscoelastic fluids, and the decision on which constitutive law should be fitted to data is largely based on the rheologist’s knowledge about the fluid in relation to the catalogue of standard models appearing in the literature. In this thesis, we present an alternative approach for determining a viscoelastic fluid’s constitutive law based on methods related to Koopman operator theory and Dynamic Mode Decomposition in the context of control. Our approach systematically extracts the material parameters that arise in stress-evolution equations of viscoelastic fluids directly from simulation or experimen- tal data. We will present results from various applications of the framework that highlight its accuracy and robustness in identifying material parameters and reconstructing the under- lying constitutive law. We will discuss how data should be supplied to the method, and also demonstrate how data from recently developed experimental protocols, as well as combined data from multiple experiments, can be used to improve resolution. Finally, we will show that our approach provides a natural way to utilise data from the nonlinear regime and extends to higher-dimensional data sets where spatial data within a sample is available.Open Acces

    The Buffered Block Forward Backward technique for solving electromagnetic wave scattering problems

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    This work focuses on efficient numerical techniques for solving electromagnetic wave scattering problems. The research is focused on three main areas: scattering from perfect electric conductors, 2D dielectric scatterers and 3D dielectric scattering objects. The problem of fields scattered from perfect electric conductors is formulated using the Electric Field Integral Equation. The Coupled Field Integral Equation is used when a 2D homogeneous dielectric object is considered. The Combined Field Integral Equation describes the problem of scattering from 3D homogeneous dielectric objects. Discretising the Integral Equation Formulation using the Method of Moments creates the matrix equation that is to be solved. Due to the large number of discretisations necessary the resulting matrices are of significant size and therefore the matrix equations cannot be solved by direct inversion and iterative methods are employed instead. Various iterative techniques for solving the matrix equation are presented including stationary methods such as the ”forwardbackward” technique, as well its matrix-block version. A novel iterative solver referred to as Buffered Block Forward Backward (BBFB) method is then described and investigated. It is shown that the incorporation of buffer regions dampens spurious diffraction effects and increases the computational efficiency of the algorithm. The BBFB is applied to both perfect electric conductors and homogeneous dielectric objects. The convergence of the BBFB method is compared to that of other techniques and it is shown that, depending on the grouping and buffering used, it can be more effective than classical methods based on Krylov subspaces for example. A possible application of the BBFB, namely the design of 2D dielectric photonic band-gap TeraHertz waveguides is investigated. i
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