87 research outputs found
Colored Noise in Oscillators. Phase-Amplitude Analysis and a Method to Avoid the Itô-Stratonovich Dilemma
We investigate the effect of time-correlated noise on the phase fluctuations of nonlinear oscillators. The analysis is based on a methodology that transforms a system subject to colored noise, modeled as an Ornstein-Uhlenbeck process, into an equivalent system subject to white Gaussian noise. A description in terms of phase and amplitude deviation is given for the transformed system. Using stochastic averaging technique, the equations are reduced to a phase model that can be analyzed to characterize phase noise. We find that phase noise is a drift-diffusion process, with a noise-induced frequency shift related to the variance and to the correlation time of colored noise. The proposed approach improves the accuracy of the previous phase reduced models
A Detailed Fluctuation Theorem for Heat Fluxes in Harmonic Networks out of Thermal Equilibrium
We continue the investigation, started in [J. Stat. Phys. 166, 926-1015
(2017)], of a network of harmonic oscillators driven out of thermal equilibrium
by heat reservoirs. We study the statistics of the fluctuations of the heat
fluxes flowing between the network and the reservoirs in the nonequilibrium
steady state and in the large time limit. We prove a large deviation principle
for these fluctuations and derive the fluctuation relation satisfied by the
associated rate function
A Circuit Theory Perspective on the Modeling and Analysis of Vibration Energy Harvesting Systems: A Review
This paper reviews advanced modeling and analysis techniques useful in the description, design, and optimization of mechanical energy harvesting systems based on the collection of energy from vibration sources. The added value of the present contribution is to demonstrate the benefits of the exploitation of advanced techniques, most often inherited from other fields of physics and engineering, to improve the performance of such systems. The review is focused on the modeling techniques that apply to the entire energy source/mechanical oscillator/transducer/electrical load chain, describing mechanical–electrical analogies to represent the collective behavior as the cascade of equivalent electrical two-ports, introducing matching networks enhancing the energy transfer to the load, and discussing the main numerical techniques in the frequency and time domains that can be used to analyze linear and nonlinear harvesters, both in the case of deterministic and stochastic excitations
Levitation and control of particles with internal degrees of freedom
Levitodynamics is a fast growing field that studies the levitation and manipulation of micro- and nanoobjects, fuelled by both fundamental physics questions and technological applications. Due to the isolated nature of trapped particles, levitated systems are highly decoupled from the environment, and offer experimental possibilities that are absent in clamped nanomechanical oscillators. In particular, a central question in quantum physics is how the transition between the classical and quantum world materializes, and levitated objects represent a promising avenue to study this intermediate regime.
In the last years, most levitation experiments have been restricted to optically trapped silica nanoparticles in vacuum, controlling the particle's position with intensity modulated laser beams. However, the use of optical traps severely constrains the experiments that can be performed, because few particle materials can withstand the optical absorption and resulting heating in vacuum. This completely prevents the use of objects with internal degrees of freedom, which---coupled to mechanical variables---offer a clear path towards the study of quantum phenomena at the macroscale.
In this thesis, we address these issues by considering other types of trap and feedback schemes, achieving excellent control on the dynamics of optically active nanoparticles. With stochastic calculus, simulations and experiments, we study the dynamics of trapped particles in different regimes, considering also a hybrid quadrupole-optical trapping scheme. Then, using a Paul trap of our own design, we demonstrate the trapping, interrogation and feedback cooling of a nanodiamond hosting a single NV center in vacuum, a clear candidate to perform quantum physics experiments at the single spin level. Finally, we discuss and implement an optimal controller to cool the center of mass motion of an optically levitated nanoparticle. The feedback is realized by exerting a Coulomb force on a charged particle with a pair of electrodes, and thus requires no optics.La levitodinà mica és un camp de la fÃsica en rà pida expansió que estudia la levitació i manipulació de micro- i nano-objectes, empesa per la possibilitat de solucionar trencaclosques de fÃsica fonamental i de desenvolupar noves aplicacions tecnològiques. Grà cies al gran aïllament de les partÃcules en levitació, l’evolució dels sistemes levitodinà mics està molt desacoplada del seu entorn. Per consegüent, permeten fer experiments que no serien possibles en nanooscil·ladors mecà nics sobre substrat. En particular, una qüestió central en fÃsica consisteix en entendre com es produeix la transició entre els mons clà ssic i quà ntic;
els objectes en levitació permeten estudiar aquest règim intermedi de manera innovadora.
En els últims anys, la majoria d’experiments de levitodinà mica s’han limitat a atrapar òpticament partÃcules de sÃlice en el buit, tot controlant la posició de la partÃcula amb feixos là ser modulats. Tot i aixÃ, l’ús de trampes òptiques suposa un obstacle a l’hora d’exportar
aquests experiments a règims més diversos perquè, a baixes pressions, pocs materials són capaços de suportar les altes temperatures resultants de l’absorció de llum là ser. Això impedeix l’ús d’objectes amb graus de llibertat interns, que –acoplats a variables mecà niques–
suposen un full de ruta clar per estudiar fenòmens quà ntics a escala macroscòpica
En aquesta tesi, adrecem aquestes qüestions tot considerant altres tipus de trampa i tècniques de feedback, i assolim un control excel·lent de la dinà mica de nanopartÃcules òpticament actives en levitació.
Mitjançant cà lcul estocà stic, simulacions i experiments, estudiem la dinà mica de les partÃcules en règims diversos, à dhuc considerant un esquema hÃbrid de trampa de Paul-òptica. A continuació, utilitzant una trampa de Paul, demostrem experimentalment l’atrapament, interrogació i feedback-cooling en el buit d’un nanodiamant que conté un únic NV− center, un clar candidat per a la realització d’experiments de fÃsica quà ntica amb un únic spin. Finalment, estudiem i implementem un controlador òptim per a refredar el centre de massa d’una partÃcula
òpticament levitada. El feedback es realitza exercint una força de Coulomb sobre una partÃcula carregada positivament mitjançant un parell d’elèctrodes, i per tant no requereix elements òptic
Quantum back-action evasion and filtering in optomechanical systems
The measurement precision of optomechanical sensors reached sensitivity levels such that they have to be described by quantum theory. In quantum mechanics, every measurement will introduce a back-action on the measured system itself. For optomechanical force sensors, a trade-off between back-action and measurement precision exists through the interplay of quantum shot noise and quantum radiation pressure noise. Finding the optimal power to balance these effects leads to the standard quantum limit (SQL), which bounds the sensitivity of force sensing. To overcome the SQL and reach the fundamental bound of parameter estimation, the quantum Cramér-Rao bound, techniques called quantum smoothing and quantum back-action evasion are required.
The first part of this thesis explores quantum smoothing in the context of optomechanical force sensing. Quantum smoothing combines the concepts of prediction and retrodiction to estimate the parameters of a system in the past. To illustrate the intricacies of these estimations in the quantum setting, two filters, the Kalman and Wiener filters, are introduced. Their prediction and retrodiction estimates are given for a simple optomechanical setup, and resulting differences are analyzed concerning the available quantum smoothing theories in the literature.
In the second part of this thesis, a back-action evasion technique called coherent quantum-noise cancellation (CQNC) is explored. In CQNC, an effective negative-mass oscillator is coupled to an optomechanical sensor to create destructive interference of quantum radiation pressure noise. An all-optical realization of such an effective negative-mass oscillator is introduced, and a comprehensive study of its performance in a cascaded CQNC scheme is given. We determine ideal CQNC conditions, analyze non-ideal noise cancellation and provide a case study.
Under feasible parameters, the case study shows a possible reduction of radiation pressure noise of 20% and that the effective negative-mass oscillator as the first subsystem in the cascade is the preferable order.Die Messgenauigkeit optomechanischer Sensoren hat eine Sensitvität erreicht,
sodass sie im Rahmen der Quantentheorie beschrieben werden müssen. Quantenmechanik
besagt, dass jede Messung eine Rückkopplung auf das vermessene
System induziert. Bei optomechanischen Kraftsensoren is ein Kompromiss zwischen
Rückkopplung und Messgenauigkeit durch die Verzahnung von Schrotrauschen
und Strahlungsdruckrauschen begründet. Die Verwendung der optimalen
Leistung, derart dass diese beiden Prozesse in Waage liegen, führt zum
Standardquantenlimit (SQL). Hierdurch wird die Messgenauigkeit begrenzt.
Um das SQL zu überwinden und die fundamentale Grenze der Parameterschätzung
zu erreichen, welche durch Quanten-Cramér-Rao-Ungleichung bestimmt
ist, werden die Methoden der Quantenglättung und Rückkopplungsumgehung
benötigt.
Im ersten Teil dieser Arbeit wird das Gebiet der Quantenglättung im Kontext
von optomechanischer Kraftmessung untersucht. Die Quantenglättung kombiniert
die Methoden der Vorhersage und Retrodiktion, um Abschätzungen
an die Parameter eines Quantensystems zu tätigen, welche in der Vergangenheit
liegen. Um die Feinheiten dieser Abschätzungen für Quantensysteme zu
demonstrieren, werden zwei Filter, der Kalman- und der Wiener-Filter eingeführt.
An einem einfachen optomechanischen System, werden deren Ergebnisse
für die Vorhersage und Retrodiktion berechnet. Mögliche Diskrepanzen werden
im Kontext der verfügbaren Theorien der Quantenglättung beleuchtet.
Im zweiten Teil dieser Dissertation wird eine Rückkopplungsumgehungsmethode,
die kohärente Quantenrauschunterdrückung (coherent quantum-noise
cancellation, CQNC) untersucht. Bei CQNC wird ein Oszillator mit effektiver
negativer Masse an einen optomechanischen Sensor gekoppelt, um destruktiv
mit dem Strahlungsdruckrauschen zu interferieren. Eine mögliche optische
Realisierung eines solchen negativen Masse Oszillators wird vorgestellt
und mit einem optomechanischem Kraftsensor kaskadiert. Dieser Aufbau wird
hinsichtlich seiner Rauschünterdrückungfähigkeit untersucht. Diesbezüglich ermitteln
wir die Bedingungen für eine vollständige Abwendung von Strahlungsdruckrauschen
und analysieren den Einfluss von möglichen Abweichungen
von diesen Bedingungen auf die Rauschünterdrückung. Zuletzt präsentieren
wir eine Fallstudie eines möglichen experimentellen Aufbaus.
Die Fallstudie zeigt eine mögliche Strahlungsdrückreduzierung von 20% und
dass der Oszillator mit effektiver negativer Masse als erstes System in der
Kaskade zu bervorzugen ist
Fractional Stochastic Dynamics in Structural Stability Analysis
The objective of this thesis is to develop a novel methodology of fractional
stochastic dynamics to study stochastic stability of viscoelastic
systems under stochastic loadings.
Numerous structures in civil engineering are driven by dynamic forces, such as
seismic and wind loads, which can be described satisfactorily only by using
probabilistic models, such as white noise processes, real noise processes, or
bounded noise processes. Viscoelastic materials exhibit time-dependent stress
relaxation and creep; it has been shown that fractional calculus provide a
unique and powerful mathematical tool to model such a hereditary property.
Investigation of stochastic stability of viscoelastic systems with fractional
calculus frequently leads to a parametrized family of fractional stochastic
differential equations of motion. Parametric excitation may cause parametric
resonance or instability, which is more dangerous than ordinary resonance as it
is characterized by exponential growth of the response amplitudes even in the
presence of damping.
The Lyapunov exponents and moment Lyapunov exponents provide not only the
information about stability or instability of stochastic systems, but also how
rapidly the response grows or diminishes with time. Lyapunov exponents
characterizes sample stability or instability. However, this sample stability
cannot assure the moment stability. Hence, to obtain a complete picture of the
dynamic stability, it is important to study both the top Lyapunov exponent and
the moment Lyapunov exponent. Unfortunately, it is very difficult to obtain the
accurate values of theses two exponents. One has to resort to numerical and
approximate approaches.
The main contributions of this thesis are: (1) A new numerical simulation
method is proposed to determine moment Lyapunov exponents of fractional
stochastic systems, in which three steps are involved: discretization of
fractional derivatives, numerical solution of the fractional equation, and an
algorithm for calculating Lyapunov exponents from small data sets. (2)
Higher-order stochastic averaging method is developed and applied to
investigate stochastic stability of fractional viscoelastic
single-degree-of-freedom structures under white noise, real noise, or bounded
noise excitation. (3) For two-degree-of-freedom coupled non-gyroscopic and
gyroscopic viscoelastic systems under random excitation, the Stratonovich
equations of motion are set up, and then decoupled into four-dimensional Ito
stochastic differential equations, by making use of the method of stochastic
averaging for the non-viscoelastic terms and the method of Larionov for
viscoelastic terms. An elegant scheme for formulating the eigenvalue problems
is presented by using Khasminskii and Wedig’s mathematical transformations from
the decoupled Ito equations. Moment Lyapunov exponents are approximately
determined by solving the eigenvalue problems through Fourier series expansion.
Stability boundaries, critical excitations, and stability index are obtained.
The effects of various parameters on the stochastic stability of the system are
discussed. Parametric resonances are studied in detail. Approximate analytical
results are confirmed by numerical simulations.1 yea
Stochastic P-bifurcation in a tri-stable Van der Pol system with fractional derivative under Gaussian white noise
In this paper, we study the tri-stable stochastic P-bifurcation problem of a generalized Van der Pol system with fractional derivative under Gaussian white noise excitation. Firstly, using the principle for minimal mean square error, we show that the fractional derivative term is equivalent to a linear combination of the damping force and restoring force, so that the original system can be transformed into an equivalent integer order system. Secondly, we obtain the stationary Probability Density Function (PDF) of the system’s amplitude by the stochastic averaging, and using the singularity theory, we find the critical parametric conditions for stochastic P-bifurcation of amplitude of the system, which can make the system switch among the three steady states. Finally, we analyze different types of the stationary PDF curves of the system amplitude qualitatively by choosing parameters corresponding to each region divided by the transition set curves, and the system response can be maintained at the small amplitude near the equilibrium by selecting the appropriate unfolding parameters. We verify the theoretical analysis and calculation of the transition set by showing the consistency of the numerical results obtained by Monte Carlo simulation with the analytical results. The method used in this paper directly guides the design of the fractional order controller to adjust the response of the system
A Detailed Fluctuation Theorem for Heat Fluxes in Harmonic Networks out of Thermal Equilibrium
International audienceWe continue the investigation, started in [J. Stat. Phys. 166, 926-1015 (2017)], of a network of harmonic oscillators driven out of thermal equilibrium by heat reservoirs. We study the statistics of the fluctuations of the heat fluxes flowing between the network and the reservoirs in the nonequilibrium steady state and in the large time limit. We prove a large deviation principle for these fluctuations and derive the fluctuation relation satisfied by the associated rate function
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