6,381 research outputs found
Integrated Optical Fiber Sensor for Simultaneous Monitoring of Temperature, Vibration, and Strain in High Temperature Environment
Important high-temperature parts of an aero-engine, especially the power-related fuel system and rotor system, are directly related to the reliability and service life of the engine. The working environment of these parts is extremely harsh, usually overloaded with high temperature, vibration and strain which are the main factors leading to their failure. Therefore, the simultaneous measurement of high temperature, vibration, and strain is essential to monitor and ensure the safe operation of an aero-engine.
In my thesis work, I have focused on the research and development of two new sensors for fuel and rotor systems of an aero-engine that need to withstand the same high temperature condition, typically at 900 °C or above, but with different requirements for vibration and strain measurement.
Firstly, to meet the demand for high temperature operation, high vibration sensitivity, and high strain resolution in fuel systems, an integrated sensor based on two fiber Bragg gratings in series (Bi-FBG sensor) to simultaneously measure temperature, strain, and vibration is proposed and demonstrated. In this sensor, an L-shaped cantilever is introduced to improve the vibration sensitivity. By converting its free end displacement into a stress effect on the FBG, the sensitivity of the L-shaped cantilever is improved by about 400% compared with that of straight cantilevers. To compensate for the strain sensitivity of FBGs, a spring-beam strain sensitization structure is designed and the sensitivity is increased to 5.44 pm/ΌΔ by concentrating strain deformation. A novel decoupling method âSteps Decoupling and Temperature Compensation (SDTC)â is proposed to address the interference between temperature, vibration, and strain. A model of sensing characteristics and interference of different parameters is established to achieve accurate signal decoupling. Experimental tests have been performed and demonstrated the good performance of the sensor.
Secondly, a sensor based on cascaded three fiber Fabry-PĂ©rot interferometers in series (Tri-FFPI sensor) for multiparameter measurement is designed and demonstrated for engine rotor systems that require higher vibration frequencies and greater strain measurement requirements. In this sensor, the cascaded-FFPI structure is introduced to ensure high temperature and large strain simultaneous measurement. An FFPI with a cantilever for high vibration frequency measurement is designed with a miniaturized size and its geometric parameters optimization model is established to investigate the influencing factors of sensing characteristics. A cascaded-FFPI preparation method with chemical etching and offset fusion is proposed to maintain the flatness and high reflectivity of FFPIsâ surface, which contributes to the improvement of measurement accuracy. A new high-precision cavity length demodulation method is developed based on vector matching and clustering-competition particle swarm optimization (CCPSO) to improve the demodulation accuracy of cascaded-FFPI cavity lengths. By investigating the correlation relationship between the cascaded-FFPI spectral and multidimensional space, the cavity length demodulation is transformed into a search for the highest correlation value in space, solving the problem that the cavity length demodulation accuracy is limited by the resolution of spectral wavelengths. Different clustering and competition characteristics are designed in CCPSO to reduce the demodulation error by 87.2% compared with the commonly used particle swarm optimization method. Good performance and multiparameter decoupling have been successfully demonstrated in experimental tests
Beam scanning by liquid-crystal biasing in a modified SIW structure
A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
Collective variables between large-scale states in turbulent convection
The dynamics in a confined turbulent convection flow is dominated by multiple
long-lived macroscopic circulation states, which are visited subsequently by
the system in a Markov-type hopping process. In the present work, we analyze
the short transition paths between these subsequent macroscopic system states
by a data-driven learning algorithm that extracts the low-dimensional
transition manifold and the related new coordinates, which we term collective
variables, in the state space of the complex turbulent flow. We therefore
transfer and extend concepts for conformation transitions in stochastic
microscopic systems, such as in the dynamics of macromolecules, to a
deterministic macroscopic flow. Our analysis is based on long-term direct
numerical simulation trajectories of turbulent convection in a closed cubic
cell at a Prandtl number and Rayleigh numbers and
for a time lag of convective free-fall time units. The simulations
resolve vortices and plumes of all physically relevant scales resulting in a
state space spanned by more than 3.5 million degrees of freedom. The transition
dynamics between the large-scale circulation states can be captured by the
transition manifold analysis with only two collective variables which implies a
reduction of the data dimension by a factor of more than a million. Our method
demonstrates that cessations and subsequent reversals of the large-scale flow
are unlikely in the present setup and thus paves the way to the development of
efficient reduced-order models of the macroscopic complex nonlinear dynamical
system.Comment: 24 pages, 12 Figures, 1 tabl
Unstable Periodic Orbits: a language to interpret the complexity of chaotic systems
Unstable periodic orbits (UPOs), exact periodic solutions of the evolution equation, offer a very
powerful framework for studying chaotic dynamical systems, as they allow one to dissect their
dynamical structure. UPOs can be considered the skeleton of chaotic dynamics, its essential
building blocks. In fact, it is possible to prove that in a chaotic system, UPOs are dense in
the attractor, meaning that it is always possible to find a UPO arbitrarily near any chaotic
trajectory. We can thus think of the chaotic trajectory as being approximated by different
UPOs as it evolves in time, jumping from one UPO to another as a result of their instability.
In this thesis we provide a contribution towards the use of UPOs as a tool to understand and
distill the dynamical structure of chaotic dynamical systems. We will focus on two models,
characterised by different properties, the Lorenz-63 and Lorenz-96 model.
The process of approximation of a chaotic trajectory in terms of UPOs will play a central role
in our investigation. In fact, we will use this tool to explore the properties of the attractor of
the system under the lens of its UPOs.
In the first part of the thesis we consider the Lorenz-63 model with the classic parametersâ value.
We investigate how a chaotic trajectory can be approximated using a complete set of UPOs
up to symbolic dynamicsâ period 14. At each instant in time, we rank the UPOs according to
their proximity to the position of the orbit in the phase space. We study this process from
two different perspectives. First, we find that longer period UPOs overwhelmingly provide the
best local approximation to the trajectory. Second, we construct a finite-state Markov chain
by studying the scattering of the trajectory between the neighbourhood of the various UPOs.
Each UPO and its neighbourhood are taken as a possible state of the system. Through the
analysis of the subdominant eigenvectors of the corresponding stochastic matrix we provide a
different interpretation of the mixing processes occurring in the system by taking advantage of
the concept of quasi-invariant sets.
In the second part of the thesis we provide an extensive numerical investigation of the variability
of the dynamical properties across the attractor of the much studied Lorenz â96 dynamical
system. By combining the Lyapunov analysis of the tangent space with the study of the
shadowing of the chaotic trajectory performed by a very large set of unstable periodic orbits,
we show that the observed variability in the number of unstable dimensions, which shows a
serious breakdown of hyperbolicity, is associated with the presence of a substantial number of
finite-time Lyapunov exponents that fluctuate about zero also when very long averaging times
are considered
Mathematical Modelling of Spread of Vector Borne Disease In Germany
Ziel dieser Doktorarbeit ist ein mathematisches Modell zu entwickeln, um
eine mögliche Ausbreitung des West-Nil-Virus (WNV) in Deutschland zu simulieren
und zu bewerten. Das entwickelte Werkzeug soll auch auf eine weitere,
durch Zecken ĂŒbertragene Krankheit, dem Krim-Kongo-HĂ€morrhagischen
Fieber (CCHFV) angewendet werden.
Die durch den Klimawandel verursachte globalen ErwĂ€rmung unterstĂŒtzt
auch die Verbreitung und Entwicklung verschiedener Vektorpopulationen.
Dabei hat eine Temperaturerhöhung einen positiven Einfluss auf den Lebenszyklus
des Vektors und die Zunahme der VektoraktivitÀt. In dieser Arbeit
haben wir ein Differentialgleichungsmodell (ODE) entwickelt, um den Einfluss
eines regelmĂ€Ăigen Eintrags von Infektionserregern auf die empfĂ€ngliche
Population unter BerĂŒcksichtigung des Temperatureinflusses zu verstehen.
Als Ergebnis haben wir einen analytischen Ausdruck der Basisreproduktionszahl
und deren Wechselwirkung mit der Temperatur gefunden. Eine
SensitivitĂ€tsanalyse zeigt, wie wichtig das VerhĂ€ltnis der anfĂ€lligen MĂŒcken
zur lokalen Wirtspopulation ist. Als ein zentrales Ergebnis haben wir den
zukĂŒnftigen Temperaturverlauf auf Basis der Modellergebnisse des IPCC in
unser Modell integriert und Bedingungen gefunden, unter denen es zu einer
dauerhaften Etablierung des West-Nil-Virus in Deutschland kommt. DarĂŒber hinaus haben wir die
entwickelten mathematischen Modelle verwendet, um verschiedene Szenarien
zu untersuchen, unter denen sich CCHFV möglicherweise in einer naiven
Population etablieren kann, und wir haben verschiedene Kontrollszenarien mathematisch abgeleitet, um die Belastung von einer Infektion durch Zecken
zu bewÀltigen.The objective of this thesis is to develop the necessary mathematical model
to assess the potential spread of West Nile Virus (WNV) in Germany and
employ the developed tool to analyse another tick-borne disease Crimean-
Congo Hemorrhagic Fever (CCHFV).
Given the backdrop of global warming and the climate change, increasing
temperature has benefitted the vector population. The increase in the
temperature has a positive influence in the life cycle of the vector and the
increase in its activities. In this thesis, we have developed an Ordinary Differential
Equation (ODE) model system to understand the influence of the
periodic introduction of infectious agents into the local susceptible population
while taking account of influence of temperature. As results, we have
found an analytic expression of the basic reproduction number and its
interplay with the temperature. The sensitivity analysis shows us the importance
of the ratio between the susceptible mosquitoes to the local host
population. As a central result we have extrapolated the temperature trend
under different IPCC conditions and found the condition under which the
circulation of West Nile Virus will be permanent in Germany.
Furthermore, we have utilised the developed mathematical models to
examine different scenarios under which CCHFV can potentially establish
in a naive population along with we mathematically derived different control
scenarios to manage the burden of tick infection
GNN-Assisted Phase Space Integration with Application to Atomistics
Overcoming the time scale limitations of atomistics can be achieved by
switching from the state-space representation of Molecular Dynamics (MD) to a
statistical-mechanics-based representation in phase space, where approximations
such as maximum-entropy or Gaussian phase packets (GPP) evolve the atomistic
ensemble in a time-coarsened fashion. In practice, this requires the
computation of expensive high-dimensional integrals over all of phase space of
an atomistic ensemble. This, in turn, is commonly accomplished efficiently by
low-order numerical quadrature. We show that numerical quadrature in this
context, unfortunately, comes with a set of inherent problems, which corrupt
the accuracy of simulations -- especially when dealing with crystal lattices
with imperfections. As a remedy, we demonstrate that Graph Neural Networks,
trained on Monte-Carlo data, can serve as a replacement for commonly used
numerical quadrature rules, overcoming their deficiencies and significantly
improving the accuracy. This is showcased by three benchmarks: the thermal
expansion of copper, the martensitic phase transition of iron, and the energy
of grain boundaries. We illustrate the benefits of the proposed technique over
classically used third- and fifth-order Gaussian quadrature, we highlight the
impact on time-coarsened atomistic predictions, and we discuss the
computational efficiency. The latter is of general importance when performing
frequent evaluation of phase space or other high-dimensional integrals, which
is why the proposed framework promises applications beyond the scope of
atomistics
Theoretical and computational tools to model multistable gene regulatory networks
The last decade has witnessed a surge of theoretical and computational models
to describe the dynamics of complex gene regulatory networks, and how these
interactions can give rise to multistable and heterogeneous cell populations.
As the use of theoretical modeling to describe genetic and biochemical circuits
becomes more widespread, theoreticians with mathematics and physics backgrounds
routinely apply concepts from statistical physics, non-linear dynamics, and
network theory to biological systems. This review aims at providing a clear
overview of the most important methodologies applied in the field while
highlighting current and future challenges, and includes hands-on tutorials to
solve and simulate some of the archetypical biological system models used in
the field. Furthermore, we provide concrete examples from the existing
literature for theoreticians that wish to explore this fast-developing field.
Whenever possible, we highlight the similarities and differences between
biochemical and regulatory networks and classical systems typically studied in
non-equilibrium statistical and quantum mechanics.Comment: 73 pages, 12 figure
Circulation Statistics in Homogeneous and Isotropic Turbulence
This is the committee version of a Thesis presented to the PostGrad Program
in Physics of the Physics Institute of the Federal University of Rio de Janeiro
(UFRJ), as a necessary requirement for the title of Ph.D. in Science (Physics).
The development of the Vortex Gas Model (VGM) introduces a novel statistical
framework for describing the characteristics of velocity circulation. In this
model, the underlying foundations rely on the statistical attributes of two
fundamental constituents. The first is a GMC field that governs intermittent
behavior and the second constituent is a Gaussian Free field responsible for
the partial polarization of the vortices in the gas. The model is revisited in
a more sophisticated language, where volume exclusion among vortices is
addressed. These additions were subsequently validated through numerical
simulations of turbulent Navier-Stokes equations. This revised approach
harmonizes with the multifractal characteristics exhibited by circulation
statistics, offering a compelling elucidation for the phenomenon of
linearization of the statistical circulation moments, observed in recent
numerical simulation.
In the end, a field theoretical approach, known as
Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) functional method is carried
out in the context of circulation probability density function. This approach
delves into the realm of extreme circulation events, often referred to as
Instantons, through two distinct methodologies: The First investigates the
linear solutions and, by a renormalization group argument a time-rescaling
symmetry is discussed. Secondly, a numerical strategy is implemented to tackle
the nonlinear instanton equations in the axisymmetric approximation. This
approach addresses the typical topology exhibited by the velocity field
associated with extreme circulation events.Comment: Ph.D. Thesis - preliminary versio
Statistical models of complex brain networks: a maximum entropy approach
The brain is a highly complex system. Most of such complexity stems from the
intermingled connections between its parts, which give rise to rich dynamics
and to the emergence of high-level cognitive functions. Disentangling the
underlying network structure is crucial to understand the brain functioning
under both healthy and pathological conditions. Yet, analyzing brain networks
is challenging, in part because their structure represents only one possible
realization of a generative stochastic process which is in general unknown.
Having a formal way to cope with such intrinsic variability is therefore
central for the characterization of brain network properties. Addressing this
issue entails the development of appropriate tools mostly adapted from network
science and statistics. Here, we focus on a particular class of maximum entropy
models for networks, i.e. exponential random graph models (ERGMs), as a
parsimonious approach to identify the local connection mechanisms behind
observed global network structure. Efforts are reviewed on the quest for basic
organizational properties of human brain networks, as well as on the
identification of predictive biomarkers of neurological diseases such as
stroke. We conclude with a discussion on how emerging results and tools from
statistical graph modeling, associated with forthcoming improvements in
experimental data acquisition, could lead to a finer probabilistic description
of complex systems in network neuroscience.Comment: 34 pages, 8 figure
Neural signature kernels as infinite-width-depth-limits of controlled ResNets
Motivated by the paradigm of reservoir computing, we consider randomly
initialized controlled ResNets defined as Euler-discretizations of neural
controlled differential equations (Neural CDEs). We show that in the
infinite-width-then-depth limit and under proper scaling, these architectures
converge weakly to Gaussian processes indexed on some spaces of continuous
paths and with kernels satisfying certain partial differential equations (PDEs)
varying according to the choice of activation function. In the special case
where the activation is the identity, we show that the equation reduces to a
linear PDE and the limiting kernel agrees with the signature kernel of Salvi et
al. (2021). In this setting, we also show that the width-depth limits commute.
We name this new family of limiting kernels neural signature kernels. Finally,
we show that in the infinite-depth regime, finite-width controlled ResNets
converge in distribution to Neural CDEs with random vector fields which,
depending on whether the weights are shared across layers, are either
time-independent and Gaussian or behave like a matrix-valued Brownian motion
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