Browsing by Subject "Dynamics"

Now showing 1 - 20 of 37

Open Access
The adiabatic and non-adiabatic behavior of a particle in optical lattices
(2018-06) Yılmaz, Fırat
The cold atom experiments provide a clean and controlled environment for realizing many body systems. Recent realizations of artificial gauge fields and adjustable optical lattices paved the way for the study of effectively charged particles with neutral atoms in various lattice and continuum systems. Moreover, it is possible to precisely control the external system parameters, i.e. the artificial gauge fields much faster or slower than the time scales associated with atomic motion in the lattice. It still needs further analysis to fully understand how the adiabatic and non-adiabatic changes affect the stationary and dynamical behavior of the system. We first investigate the effect of the adiabatic changes in the artificial gauge fields, and focus on the famous problem: A charged particle in a periodic potential under magnetic field. This simple system leads a complicated and involved selfsimilar energy spectrum, the Hofstadter butterfly. The whole structure of this energy spectrum is determined by the lattice geometry as well as the external field. In this regard, we consider all possible Bravais lattices in two dimensions and investigate the structure of the Hofstadter butterfly as the different point symmetry groups of the lattices are adiabatically deformed from one into another. We find that each 2D Bravais lattice is uniquely mapped to a fractal energy spectrum and it is possible to understand the interplay between the point symmetry groups and the energy spectrum. This beautiful spectrum, in addition, consists of infinitely many topologically distinct regions as a function of magnetic flux and gap number. The topological character of energy bands are determined through their Chern numbers. We calculate the Chern numbers of the major gaps and Chern number transfer between bands during the topological transitions. In the second part, we investigate the dramatic effect of the non-adiabatic changes in the artificial gauge fields. In a synthetic lattice, the precise control over the hopping matrix elements makes it possible to change this artificial magnetic field non-adiabatically even in the quench limit. We consider such a magneticflux quench scenario in synthetic dimensions. Sudden changes have not been considered for real magnetic fields as such changes in a conducting system would result in large induced currents. Hence we first study the difference between a time varying real magnetic field and an artificial magnetic field using a minimal six-site model which leads to gauge dependent results. This model proves the relation between the gauge dependant dynamics and the absence of scalar potential terms connecting different gauge potentials. In this context, we secondly search for clear indication of the gauge dependent dynamics through magnetic flux quenches of wave packets in two- and three-leg synthetic ladders. We show that the choice of gauge potentials have tremendous effect on the post-quench dynamics of wave packets. Even trivially distinct two vector potentials by an additive constant can produce observable effects, we investigate the effects on the Landau levels and the Laughlin wave function for a filling factor ν = 1/q. We also show that edge solutions in a wide synthetic ladder are protected under a flux quench only if there is another edge state solution in the quenched Hamiltonian.
Open Access
An analytical solution to the stance dynamics of passive spring-loaded inverted pendulum with damping
(World Scientific, 2009-09) Ankaralı, M. M.; Arslan, Ömür; Saranlı, Uluç
The Spring-Loaded Inverted Pendulum (SLIP) model has been established both as a very accurate descriptive tool as well as a good basis for the design and control of running robots. In particular, approximate analytic solutions to the otherwise non integrable dynamics of t his model provide principled ways in which gait controllers can be built, yielding invaluable insight into their stability properties. However, most existing work on the SLIP model completely disregards the effects of damping, which often cannot be neglected for physical robot platforms. In this paper, we introduce a new approximate analytical solution to the dynamics of this system that also takes into account viscous damping in the leg. We compare both the predictive performance of our approximation as well as the tracking performance of an associated deadbeat gait controller to similar existing methods in the literature and show t hat it significantly outperforms them in the presence of damping in the leg.
Open Access
Attractive versus repulsive excitonic interactions of colloidal quantum dots control blue-to red-shifting (and non-shifting) amplified spontaneous emission
(American Chemical Society, 2013-11-21) Cihan, A. F.; Kelestemur, Y.; Guzelturk, B.; Yerli, O.; Kurum, U.; Yaglioglu, H. G.; Elmali, A.; Demir, Hilmi Volkan
Tunable, high-performance, two-photon absorption (TPA)-based amplified spontaneous emission (ASE) from near-unity quantum efficiency colloidal quantum dots (CQDs) is reported. Besides the absolute spectral tuning of ASE, the relative spectral tuning of ASE peak with respect to spontaneous emission was shown through engineering excitonic interactions in quasi-type-II CdSe/CdS core/shell CQDs. With core shell size adjustments, it was revealed that Coulombic exciton-exciton interactions can be tuned to be attractive (type-I-like) or repulsive (type-II-like) leading to red- or blue-shifted ASE peak, respectively, and that nonshifting ASE can be achieved with the right core shell combinations. The possibility of obtaining ASE at a specific wavelength from both type-I-like and type-II-like CQDs was also demonstrated. The experimental observations were supported by parametric quantum-mechanical modeling, shedding light on the type-tunability. These excitonically engineered CQD-solids exhibited TPA-based ASE threshold as low as 6.5 mJ/cm(2) under 800 nm excitation, displaying one of the highest values of TPA cross-section of 44 660 GM.
Open Access
An automotive vehicle dynamics prototyping platform based on a remote control model car
(2013) Solmaz, S.; Coşkun, Türker
The use of a modified remote control (RC) model car as a vehicle dynamics testing and development platform is detailed. Vehicle dynamics testing is an important aspect of automotive engineering and it plays a key role during the design and tuning of active safety control systems. Considering the fact that such tests are conducted at great expense, scaled model cars can potentially be used to help with the process to reduce the costs. With this view, we instrument and develop a standard electric RC model car into a vehicle dynamics testing platform. We then implement 2 representative active safety control applications based on this platform, namely an antilock brake system using open-loop pulse brake control and a roll-over prevention system utilizing lateral acceleration feedback. Both applications are presented with sensor measurements and the effectiveness of the suggested control algorithms are demonstrated. © TÜBİTAK.
Open Access
Capital dependent population growth induces cycles
(Elsevier, 2011-09) Yuksel, M. K.
Cobb–Douglas type production functions and time-delay are not sufficient for the economy to behave cyclic. However, capital dependent population dynamics can enforce Hopf bifurcation. 2011 Elsevier Ltd. All rights reserved.
Open Access
Capital maintenance versus technology adoption under embodied technical progress
(B E Press, 2006) Boucekkine, R.; Martínez, B.; Saglam, C.
We study an optimal growth model with one-hoss-shay vintage capital, where labor resources can be allocated freely either to production, technology adoption or capital maintenance. Technological progress is partly embodied. Adoption labor increases the level of embodied technical progress. First, we are able to disentangle the amplification-propagation role of maintenance in business fluctuations: in the short run, the response of the model to transitory shocks on total factor productivity in the final good sector are definitely much sharper compared to the counterpart model without maintenance but with the same average depreciation rate. Moreover, the one-hoss shay technology is shown to reinforce this amplification-propagation mechanism. We also find that accelerations in embodied technical progress should be responded by a gradual adoption effort, and capital maintenance should be the preferred instrument in the short run. Copyright © 2006 The Berkeley Electronic Press. All rights reserved.
Open Access
Concurrent design of energy management and vehicle stability algorithms for a parallel hybrid vehicle using dynamic programming
(AACC, 2012-06) Dokuyucu H. İbrahim; Çakmakçı, Melih
In this paper, concurrent design of controllers for a vehicle equipped with a parallel hybrid powertrain is studied. Our work focuses on designing the two control algorithms, the energy management and the vehicle stability, concurrently which are traditionally considered separately. Dynamic Programming (DP) technique is used in order to obtain the optimal response trace for the controllers. In energy management strategy torque split ratio between engine and electric motor is used as a control signal. Additionally, in vehicle dynamics control strategy the torque split factor between front and rear axles is used as a control signal. Minimizing the fuel consumption and wheel slip is used as cost functions in energy management and vehicle dynamics control strategies respectively. Two dynamic problems are solved separately first and compared to the concurrent solution of the problems. Results show promising benefits can be obtained from the concurrent DP solution and rule extraction for designing better hybrid vehicle controllers. © 2012 AACC American Automatic Control Council).
Open Access
Development of a rapid-scan fiber-integrated terahertz spectrometer
(Springer New York LLC, 2014) Keskin, H.; Altan, H.; Yavas, S.; Ilday, F. O.; Eken, K.; Sahin, A. B.
Scientists in terahertz (THz) wave technologies have benefited from the recent developments in ultrafast laser technologies and RF technologies and applied these new gained techniques into characterizing a wide variety of phenomena. Undoubtedly, the most successful of these applications has been in the development of time-domain terahertz spectroscopic and imaging systems which has been utilized in the characterization of dielectrics and semiconductors. This pulsed technique has allowed users to characterize dynamical behavior inside materials under illumination with picosecond resolution. Typically pump/probe or similar dynamical measurements require the use of amplified pulses derived from free-space solid state lasers in the μJ-mJ range and since interferometric techniques are typically used in pulsed measurements the measurement time of a THz spectrum can last at least tens of minutes. Better systems can be realized based on fiber laser technologies. Here we discuss the advantages of a THz spectrometer driven by an ultrafast Ytterbium doped fiber laser whose repetition rate can be tuned rapidly allowing for rapid dynamical measurements. The efficient gain medium, robust operation and compact design of the system opens up the possibility of exploring rapid detection of various materials as well as studying dynamical behavior using the high brightness source.
Open Access
Dynamic Boundary Control of a Euler-Bernoulli Beam
(Institute of Electrical and Electronics Engineers, 1992) Morgül, Ö.
We consider a flexible beam clamped to a rigid base at one end and free at the other end. To stabilize the beam vibrations, we propose a dynamic boundary force control and a dynamic boundary torque control applied at the free end of the beam. We prove that with the proposed controls, the beam vibrations decay exponentially. The proof uses a Lyapunov functional based on the energy functional of the system. © 1992 IEEE
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Dynamic boundary control of the timoshenko beam
(Pergamon Press, 1992) Morgül, Ö.
We consider a clamped-free Timoshenko beam. To stabilize the beam vibrations, we propose a dynamic boundary control law applied at the free end of the beam. We prove that with the proposed control law, the beam vibrations uniformly and exponentially decay to zero. The proof uses a Lyapunov functional based on the energy of the system. © 1992.
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Dynamic modeling and gait analysis for miniature robots in the absence of foot placement control
(Institute of Electrical and Electronics Engineers Inc., 2019) Askari, Mohammad; Özcan, Onur
The study of animals and insects have led to realization that animals select their gaits, patterns of leg movement, according to speed. For proper gait planning, the legs must be controlled for proper foot placement with respect to the body motion and ground interactions. However, in small scale robotic platforms gait planning through foot placement control is neither cost effective nor easily attainable due to a lack of available sensors. Thus, even though a desired gait is envisioned at the design phase, it is not known whether the gait is optimum. In this work, we present the comprehensive dynamic model of the miniature foldable robot, MinIAQ-II, which has four independently actuated legs. Dynamic model is used to perform gait analysis, to investigate the difference between the intended gait and the achieved gait in the absence of foot placement control. The model is verified through slow speed walking experiments on flat terrain. The work presented can be modified for different miniature robots with passive legs to predict their locomotion under no foot placement control.
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Enforcing multilabel consistency for automatic spatio-temporal assessment of shoulder pain intensity
(Association for Computing Machinery, 2020) Erekat, Diyala; Hammal, Z.; Siddiqui, M.; Dibeklioğlu, Hamdi
The standard clinical assessment of pain is limited primarily to self-reported pain or clinician impression. While the self-reported measurement of pain is useful, in some circumstances it cannot be obtained. Automatic facial expression analysis has emerged as a potential solution for an objective, reliable, and valid measurement of pain. In this study, we propose a video based approach for the automatic measurement of self-reported pain and the observer pain intensity, respectively. To this end, we explore the added value of three self-reported pain scales, i.e., the Visual Analog Scale (VAS), the Sensory Scale (SEN), and the Affective Motivational Scale (AFF), as well as the Observer Pain Intensity (OPI) rating for a reliable assessment of pain intensity from facial expression. Using a spatio-temporal Convolutional Neural Network - Recurrent Neural Network (CNN-RNN) architecture, we propose to jointly minimize the mean absolute error of pain scores estimation for each of these scales while maximizing the consistency between them. The reliability of the proposed method is evaluated on the benchmark database for pain measurement from videos, namely, the UNBC-McMaster Pain Archive. Our results show that enforcing the consistency between different self-reported pain intensity scores collected using different pain scales enhances the quality of predictions and improve the state of the art in automatic self-reported pain estimation. The obtained results suggest that automatic assessment of selfreported pain intensity from videos is feasible, and could be used as a complementary instrument to unburden caregivers, specially for vulnerable populations that need constant monitoring.
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Essays on growth and macroeconomic dynamics
(2015-09) Özer, Mehmet
This dissertation is composed of four essays on economic growth and macro- economic dynamics. The first essay analyzes how the dynamic strategic in- teractions among agents a¤ect the long-run distribution of wealth in terms of catching up and the transitional dynamics. It is shown that incorporating the strategic behavior among agents leads to the wealth level of the initially poor and the rich households to be the same at the stationary state. Extending the model by incorporating relative wealth concern; the resulting equilibria depends the valuation of relative wealth concern by each individual and it is proved that under some plausible conditions the catching up occurs thanks to the strategic interaction in the form of open-loop. The stability of these two models are carried out for arbitrary number of people in the economy. In the second essay studies the e¤ects of above mentioned strategic interac- tion in Ramsey model with "Easterlin hypothesis". It is shown that strategic interaction among agents in the economy leads to a change not only in the distribution of wealth but also in the transitional dynamics substantially. The obtained complex dynamics is in the form of Hopf bifurcation which is one of the main tool to explain the economic fluctuations. Third essay of this thesis introduces Stone-Geary Preferences with an endoge- nous reference level of consumption in an Ak model in which reference level of consumption is an increasing function of the capital. It is shown that the result- ing equilibrium presents richer dynamics under such a Stone-Geary preferences. It is proved that endogenous reference level leads to global and local indetermi- nacy: economies starting with di¤erent initial conditions does not necessarily converge to the same steady state and also economies starting with the same initial conditions does not necessarily follow the same transition path. The aim of the fourth essay is to analyze the e¤ects of a pure public good that reduces the subsistence level of consumption on the long run equilibrium and the optimal tax rate. It is shown that although the steady state amount of public good is higher for the first best allocation, the subsistence level of consumption is the same with that of the second best equilibrium. On the other hand, the capital stock and the consumption of the private good are higher for the first best equilibria. Another important result of the essay is the "government revenue-tax rate" locus with a dynamic threshold which depends on the total factor productivity (TFP). The optimal amount of tax rate that maximizes the revenue of the government is an increasing function of the TFP and thus revenue maximizing tax rate varies across countries.
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Four essays on overlapping generations resource economies : optimality, sustainability and dynamics
(2012) Fazlıoğlu, Burcu
This dissertation is made up of four essays on overlapping generations resource economies. The Örst essay studies the e§ects of energy saving technological progress and substitution of renewable energy resources with non-renewable resources on natural resource depletion and long run growth. A growth model in two-period overlapping generations framework incorporating the presence of both resources and resource augmenting technological progress is developed. The e§ect of an increase in the intensity of the renewable resources in producing energy on long run growth is found to be positive. Although exhaustible resources are essential in production the economy can be sustained and the balanced growth path is optimal. In the second essay, the implications of assuming di§erent energy intensities for physical capital accumulation and the Önal good production is studied in an overlapping generations resource economy where energy is obtained from the extraction of the natural resources. Apart from the standard literature, physical capital accumulation is assumed to be relatively more energy-intensive than consumption. Multiple steady states, indeterminacy and bifurcations are obtained, without taking non-linearizing assumptions evident in the literature. For the non-renewable resources if the share of energy resources is low enough, local indeterminacy and hopf bifurcations may arise in the model. The aim of third essay is to analyze can costly resource extraction and di§erentiating energy intensities induce dynamics other than saddles in an overlapping generations resource economy. The capital accumulation sector is assumed to be more energy intensive. The energy input is extracted from the natural resources with some extraction costs. The main Önding of the essay is that both naturally evident assumptions contribute to the richness of the dynamics. Depending on the share of resources in capital accumulation dynamics other than saddle ñindeterminacy, áip and hopf bifurcationsñ can arise in the model for the non-zero steady state. In the fourth essay, a feedback mechanism between population and natural resource to a standard model of renewable resource based OLG economy is incorporated to check the stability of the dynamics. Multiple steady states and indeterminacy have been obtained even in the absence of logistic regeneration and independent of intertemporal elasticity of substitution. In particular, transcritical bifurcations may arise in the model varying the rate of constant regeneration with respect to population growth rate.
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Impurity coupled to an artificial magnetic field in a Fermi gas in a ring trap
(American Physical Society, 2015) Ünal, F. N.; Hetényi, B.; Oktel, M. Ö.
The dynamics of a single impurity interacting with a many-particle background is one of the central problems of condensed-matter physics. Recent progress in ultracold-atom experiments makes it possible to control this dynamics by coupling an artificial gauge field specifically to the impurity. In this paper, we consider a narrow toroidal trap in which a Fermi gas is interacting with a single atom. We show that an external magnetic field coupled to the impurity is a versatile tool to probe the impurity dynamics. Using a Bethe ansatz, we calculate the eigenstates and corresponding energies exactly as a function of the flux through the trap. Adiabatic change of flux connects the ground state to excited states due to flux quantization. For repulsive interactions, the impurity disturbs the Fermi sea by dragging the fermions whose momentum matches the flux. This drag transfers momentum from the impurity to the background and increases the effective mass. The effective mass saturates to the total mass of the system for infinitely repulsive interactions. For attractive interactions, the drag again increases the effective mass which quickly saturates to twice the mass of a single particle as a dimer of the impurity and one fermion is formed. For excited states with momentum comparable to number of particles, effective mass shows a resonant behavior. We argue that standard tools in cold-atom experiments can be used to test these predictions.
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Independent estimation of input and measurement delays for a hybrid vertical spring-mass-damper via harmonic transfer functions
(IFAC, 2015-06) Uyanık, İsmail; Ankaralı, M. M.; Cowan, N. J.; Saranlı, U.; Morgül, Ömer; Özbay, Hitay
System identification of rhythmic locomotor systems is challenging due to the time-varying nature of their dynamics. Even though important aspects of these systems can be captured via explicit mechanics-based models, it is unclear how accurate such models can be while still being analytically tractable. An alternative approach for rhythmic locomotor systems is the use of data-driven system identification in the frequency domain via harmonic transfer functions (HTFs). To this end, the input-output dynamics of a locomotor behavior can be linearized around a stable limit cycle, yielding a linear, time-periodic system. However, few if any model-based or data-driven identification methods for time-periodic systems address the problem of input and measurement delays in the system. In this paper, we focus on data-driven system identification for a simple mechanical system and analyze its dynamics in the presence of input and measurement delays using HTFs. By exploiting the way input delays are modulated by the periodic dynamics, our results enable the separate, independent estimation of input and measurement delays, which would be indistinguishable were the system linear and time invariant. © 2015, IFAG.
Open Access
Lattice dynamics and elastic properties of lanthanum monopnictides
(2008) Gökoǧlu G.; Erkişi, A.
In this study, first principles calculation results of the second order elastic constants and lattice dynamics of two lanthanum monopnictides, LaN and LaBi, which crystallize in rock-salt structure (B1 phase), are presented. Calculations were based on plane wave basis sets and pseudopotential methods in the framework of Density Functional Theory (DFT) with generalized gradient approximation. Elastic constants are calculated by tetragonal and orthorhombic distortions on cubic structure. Phonon dispersion spectra was constructed in the linear response approach of the Density Functional Perturbation Theory (DFPT). The complete phonon softening with negative frequencies and large elastic anisotropy were observed for LaN single crystal as a sign of the structural instability. The phonon dispersion curve for LaBi is typical for lanthanum monopnictides and does not show any anomalous physical property. The calculated structural quantities for both LaN and LaBi systems agree well with the available experimental and theoretical data. © 2008 Elsevier Ltd. All rights reserved.
Open Access
Local asymptotic stability conditions for the positive equilibrium of a system modeling cell dynamics in leukemia
(Springer, Berlin, Heidelberg, 2012) Özbay, Hitay; Bonnet, C.; Benjelloun H.; Clairambault J.
A distributed delay system with static nonlinearity has been considered in the literature to study the cell dynamics in leukemia. In this chapter local asymptotic stability conditions are derived for the positive equilibrium point of this nonlinear system. The stability conditions are expressed in terms of inequalities involving parameters of the system. These inequality conditions give guidelines for development of therapeutic actions. © 2012 Springer-Verlag GmbH Berlin Heidelberg.
Open Access
Low-order controller design for haptic systems under delayed feedback
(2012) Liacu, B.; Koru, A. T.; Özbay, Hitay; Niculescu, S. -I.; Andriot, C.
In this paper, we consider PD controller design for haptic systems under delayed feedback. More precisely, we present a complete stability analysis of a haptic system where local dynamics are described by some second-order mechanical dynamics. Next, using two optimization techniques (H ∞ and stability margin optimization) we propose an optimal choice for the controller gains. The derived results are tested on a three degree of freedom real-time experimental platform to illustrate the theoretical results. © 2012 IFAC.
Open Access
Modeling and animation of brittle fracture in three dimensions
(2007) Küçükyılmaz, Ayşe
This thesis describes a system for simulating fracture in brittle objects. The system combines rigid body simulation methods with a constraint-based model to animate fracturing of arbitrary polyhedral shaped objects under impact. The objects are represented as sets of masses, where pairs of adjacent masses are connected by a distance-preserving linear constraint. The movement of the objects is normally realized by unconstrained rigid body dynamics. The fracture calculations are only done at discrete collision events. In case of an impact, the forces acting on the constraints are calculated. These forces determine how and where the object will break. The problem with most of the existing fracture systems is that they only allow simulations to be done offline, either because the utilized techniques are computationally expensive or they require many small steps for accuracy. This work presents a near-real-time solution to the problem of brittle fracture and a graphical user interface to create realistic animations.