1,929 research outputs found
Analytical approximation to the multidimensional Fokker--Planck equation with steady state
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
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 () 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
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
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
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
Imperial Users onl
Koopman with inputs and control for constitutive law identification
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
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.
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