Browsing by Subject "Stability"
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Item Open Access A mathematical interpretation for outbreaks of bacterial meningitis under the effect of time-dependent transmission parameters(Springer Science and Business Media B.V., 2023-06-02) Türkün, C.; Gölgeli, M.; Atay, Fatihcan MehmetWe consider a SIR-type compartmental model divided into two age classes to explain the seasonal exacerbations of bacterial meningitis, especially among children outside of the meningitis belt. We describe the seasonal forcing through time-dependent transmission parameters that may represent the outbreak of the meningitis cases after the annual pilgrimage period (Hajj) or uncontrolled inflows of irregular immigrants. We present and analyse a mathematical model with time-dependent transmission. We consider not only periodic functions in the analysis but also general non-periodic transmission processes. We show that the long-time average values of transmission functions can be used as a stability marker of the equilibrium. Furthermore, we interpret the basic reproduction number in case of time-dependent transmission functions. Numerical simulations support and help visualize the theoretical results. © 2023, The Author(s), under exclusive licence to Springer Nature B.V.Item 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, UluçThe 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.Item Open Access Better stability with measurement errors(Springer New York LLC, 2016-06) Argun, A.; Volpe, G.Often it is desirable to stabilize a system around an optimal state. This can be effectively accomplished using feedback control, where the system deviation from the desired state is measured in order to determine the magnitude of the restoring force to be applied. Contrary to conventional wisdom, i.e. that a more precise measurement is expected to improve the system stability, here we demonstrate that a certain degree of measurement error can improve the system stability. We exemplify the implications of this finding with numerical examples drawn from various fields, such as the operation of a temperature controller, the confinement of a microscopic particle, the localization of a target by a microswimmer, and the control of a population.Item Open Access Cesium–lead based inorganic perovskite quantum-dots as interfacial layer for highly stable perovskite solar cells with exceeding 21% efficiency(Elsevier, 2019) Akın, S.; Altıntaş, Y.; Mutlugün, Evren; Sonmezoglu, S.Despite the excellent photovoltaic performances of perovskite solar cells (PSCs), the instability of PSCs under severe environment (e.g. humidity, light-induced, etc.) limits further commercialization of such devices. Therefore, in recent years, research on the long-term stability improvement of PSCs has been actively carried out in perovskite field. To address these issues, we demonstrated the incorporation of ultra-thin interfacial layer of inorganic CsPbBr1.85I1.15 perovskite quantum-dots (PQDs) that can effectively passivate defects at or near to the perovskite/hole transport material (HTM) interface, significantly suppressing interfacial recombination. This passivation layer increased the open circuit voltage (Voc) of triple-cation perovskite cells by as much as 50 mV, with champion cells achieving Voc ∼ 1.14 V. As a result, we obtained hysteresis-free cells with the efficiency beyond 21%. More importantly, devices based on such architecture are capable of resisting humidity and lightinduced. Remarkably, the device employing CsPbBr1.85I1.15 demonstrated a superb shelf-stability aganist to humidity under ambient conditions (R.H.≥40%), retaining nearly 91% of initial efficiency after 30 days, while the efficiency of control device rapidly dropped to 45% from its initial value under the same conditions. Besides benefiting from the high moisture resistivity as well as supressed ion migration, PSCs based on PQDs showed better operational stability (retaining 94% of their initial performance) than that of the PQDs-free one under continuous light irradiation over 400 h. In addition, a faster PL decay time of 4.66 ns was attained for perovskite/PQDs structure (5.77 ns for only PQDs structure) due to the favorable energy transfer at the interface, indicating a Förster resonance energy transfer (FRET) mechanism. This work indicates that inorganic PQDs are important materials as interlayer in PSCs to supremely enhance the device stability and efficiency.Item Open Access A characterization of the optimal set of linear programs based on the augmented lagrangian(Taylor & Francis, 1999) Pınar, M. Ç.It is proved that in a certain neighborhood of the optimal set of multipliers, the set of minimizers of the augmented lagrangian nmction generates a new characterization of the optimal solution set of the linear program.Item Open Access The coauthors' problem revisited : from networks to covers(Bilkent University, 2010) Mermer, Ayşe GülIn this thesis, we reexamine the Coauthors’ Problem, introduced by Jackson and Wolinsky, 1996. We propose the Extended Coauthor Model using the cover notion, allowing for multilateral links among authors. We study the model under two utility functions, which are the extreme members of the class of utility functions induced by different synergy terms. We find the structure of the efficient and the link-wise stable covers formed under different utility functions, which depend on the synergy term under consideration. Moreover we introduce the core and core stability concepts for covers and investigate the properties possessed by core-stable covers. We find the relationship between the allocation induced by core-stable covers and the allocations in core, under player based flexible allocation rule. Finally we investigate the endogenous cover formation via a strategic form game, called the hyper-link formation game. We define Nash stability and Strong Nash stability for covers and study the characteristics of such covers.Item Open Access Coincidence of Myerson allocation rule with Shapley value(Bilkent University, 2003) Kapan, TümerThis thesis studies the coincidence of the Myerson allocation rule in the context of networks with the Shapley value in the context of transferable utility games. We start with a value function defined on networks and derive a transferable utility game from that. We show that without any restrictions on the value function, Myerson allocation rule may not lead to the same payoff vector as the Shapley value of the derived TU game for any network. Under the assumption of monotonicity of the value function, we show the existence of such coincidence and examine the relation of the set of networks satisfying this coincidence to the set of pairwise stable and strongly stable networks. Next, we propose a new stability notion and examine the coincidence of the two vectors under this stability notion. Finally an alternative allocation rule is introduced whose payoff vector coincide with the Shapley value of the derived transferable utility game on the set of efficient networks which coincides with the set of strongly stable networks under this allocation rule.Item Open Access Conditions of well-posedness for planar conewise linear systems(Sage Publications, 2023-04-24) Namdar, Daniyal; Özgüler, Arif BülentA planar (2D) conewise linear system (CLS) is considered. This is a piecewise linear system of two states and multiple modes, where each mode is linear with its state-space constrained into a polyhedral, finitely generated, convex cone. It is allowed to have a discontinuous vector field and sliding modes. Alternative conditions for well-posedness of Caratheodory solutions of this system that have intuitive interpretations with respect to eigenvectors and cone-boundary vectors are derived. It is also shown that a well-known condition for well-posedness of bimodal systems also applies to two adjacent modes of this system without any change.Item Open Access Conewise linear systems: a characterization of transitive cones in 3D-space(The European Control Association (EUCA), 2019-06) Özgüler, A. Bülent; Zakwan, MuhammadA spatial (3D) piecewise linear system with multiple modes having conewise state spaces is considered. A single mode in this system is called transitive from one (respectively, two) of its borders if every trajectory that starts in its interior or at a border travels in its interior, hits that border (respectively, one of the two borders), and goes out of the cone. This paper characterizes transitive cones in case the dynamics in the cone is dictated by real and distinct eigenvalues. An example of a 3D piecewise linear system composed of transitive cones illustrates how a nonlinear oscillator can be synthesized.Item Open Access Constructing convex directions for stable polynomials(IEEE, 2000) Özgüler, A. B.The constructions of convex directions based on phase-derivative interpretations were obtained for Hurwitz-stable polynomials. The phase-derivative conditions were based on the sensitivity of root-locus associated with the even and odd parts of a polynomial. The phase-growth condition directly established anti-Hurwitz polynomials, polynomials of degree one, even polynomials and odd polynomials for the entire set of Hurwitz polynomials.Item Open Access Control and stabilization of a rotating flexible structure(Elsevier, 1994) Morgül, Ö.We consider a flexible beam clamped to a rigid base at one end and free at the other end. We assume that the rigid base rotates with a constant angular velocity and that the motion of the flexible beam takes place on a plane. To suppress the beam vibrations, we propose dynamic control laws for boundary control force and torque, both applied to the free end of the beam. We show that, under some conditions, one of which is the strict positive realness of the actuator transfer functions which generate the boundary control force and torque, the beam vibrations asymptotically decay to zero if the rigid base angular frequency is sufficiently small. Moreover, if the transfer functions are proper but not strictly proper, we show that the decay is exponential. We also give a bound on the constant angular velocity above which the system becomes unstable.Item Open Access Controlled enzymatic stability and release characteristics of supramolecular chiral peptide amphiphile nanofiber gels(Elsevier B.V., 2017) Zengin, A.; Cinar, G.; Güler, Mustafa O.Supramolecular bioarchitectures formed by assembly of achiral or chiral building blocks play important roles in various biochemical processes. Stereochemistry of amino acids is important for structural organization of peptide and protein assemblies and structure-microenvironment interactions. In this study, oppositely charged peptide amphiphile (PA) molecules with L-, D- and mixture of L- and D-amino acid conformations are coassembled into supramolecular nanofibers and formed self-supporting gels at pH 7.4 in water. The enzymatic stability of the PA nanofiber gels was studied in the presence of proteinase K enzyme, which digest a broad spectrum of proteins and peptides. The structural changes on the chiral PA nanofibers were also analyzed at different time periods in the presence of enzymatic activity. Controlled release of a model cargo molecule through the chiral PA nanofiber gels was monitored. The diffusivity parameters were measured for all gel systems. Release characteristics and the enzymatic stability of the peptide nanofiber gels were modulated depending on organization of the chiral PA molecules within the supramolecular assemblies.Item Open Access Decentralized stabilization of interconnected systems: Structural conditions(1992) Yu, R.; Sezer, M. E.A unified framework is provided for the design of high-gain decentralized controllers for the stabilization of several classes of interconnected systems. These classes are characterized in terms of the structure of the interconnections among the subsystems, and include all those known in the literature to be decentrally stabilizable. The simple decentralized stabilizability tests, on which the results are based, can also be used to check the stabilizability of individual interconnected systems that do not belong to any one of the classes considered.Item Open Access Dipolar bose-einstein condensate in a cylindrically symmetric trap(Bilkent University, 2016-08) Gültekin, HabibBose-Einstein Condensate (BEC) and particularly its stability dynamics has been a subject to many investigations since the first realization of this new condensed state in alkali atoms interacting via short range potential. Short range or contact interactions account for a great number of physical properties ranging from formation of quantum vortices to the super uid character of cold gases. In this thesis, dipolar Bose-Einstein condensate, which inherently possess longrange and anisotropic potential for the interaction of the constituent particles, is studied and its stability depending on the geometry of the system is investigated. The dipolar Bose gas is confined to a cylindrically symmetric harmonic trap and the dipoles within the gas is initially oriented along the symmetry axis of the confining prolate trap. In the condensed state, the condensate is observed to be elongated along harmonic trap symmetry axis as long as the axis corresponds to weak confinement direction. This elongation is understood to be resulting from the energy minimization of the system by adding the dipoles head to tail along the center of the trap, thereby determining the nature of the long-range interaction to be attractive and the condensate is liable to collapse. Below a certain value for the ratio of the dipolar and contact interactions (Edd = Cdd=3g = 1), the condensate is stable, while above this value it undergoes collapse. In the opposite case where the trap axis is the strong confinement direction (oblate trap), the elongation occurs perpendicularly to the symmetry axis of the confining trap (with highly oblate geometry) with the energetically most favorable configuration being the alignment of the dipoles side by side implying mostly repulsive interactions in which case the condensate is always stable. To further understand the effect of the geometry on the stability, the dipoles are finally oriented at an angle from the trap axis by tuning the external field and elongation direction of the condensate is calculated; stable, metastable and unstable states of the condensate are observed in this new geometry.Item Open Access 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.Item Open Access A dynamic control law for the wave equation(Elsevier, 1994) Morgül, Ö.We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is restricted to be a positive real function which could be strictly proper. We then show that, if the transfer function of the controller is strictly proper, then the resulting closed-loop system is asymptotically stable, and if proper but not strictly proper, then the resulting closed-loop system is exponentially stable.Item Open Access Effect of time delays on the convergence speed of consensus dynamics(Bilkent University, 2020-01) Alhassan, Mohammed KamilWe discuss consensus problems under time delays. The presence of time delays results in an infinite-dimensional system rather than a system of ordinary differential equations. It has been shown that information transmission delays do not influence whether the system converges to a consensus value; however, further effects of delays are unknown. We show that time delays in most graphs decreases the convergence speed; while somewhat surprisingly, they can improve convergence in certain special graphs. We discuss the structure of graphs for which such improvement is possible.Item Open Access Effects of temperature, pH and counterions on the stability of peptide amphiphile nanofiber structures(Royal Society of Chemistry, 2016) Ozkan A.D.; Tekinay, A. B.; Güler, Mustafa O.; Tekin, E. D.Peptide amphiphiles are a class of self-assembling molecules that are widely used to form bioactive nanostructures for various applications in bionanomedicine. However, peptide molecules can exhibit distinct behaviors under different conditions, suggesting that environmental variables such as temperature, pH, electrolytes and the presence of biological factors may greatly affect the self-assembly process. In this work, we used united-atom molecular dynamics simulations to understand the effects of three counterions (Na+, Ca2+ at pH 7 and Cl- at pH 2) and temperature change on the stability of the lauryl-VVAGERGD peptide amphiphile self-assembly. This molecule contains a bioactive RGD peptide sequence and has been shown to support cellular adhesion and proliferation in vitro. A 19-layered peptide nanostructure, containing 12 peptide amphiphile molecules per layer, was previously shown to exhibit optimal stability and it was used as the model nanofiber system. Peptide backbone stability was studied under increasing temperatures (300-358 K) using the number of hydrogen bonds and root-mean-square deviations of nanofiber size. At higher temperatures, fiber disintegration was observed to be dependent on the type of counter-ion used for nanofiber formation. Interestingly, rapid heating to higher temperatures could sometimes reestablish the integrity of the nanofiber backbone, possibly by allowing the system to bypass an energy barrier and assuming a more thermodynamically stable configuration. As counterion identity was observed to exhibit remarkable effects on the thermal stability of peptide nanofibers, we suggest that these behaviors should be considered while developing new materials for potential applications.Item Open Access Efficiency and stability of probabilistic assignments in marriage problems(Academic Press, 2016) Doğan, B.; Yıldız, K.We study marriage problems where two groups of agents, men and women, match each other and probabilistic assignments are possible. When only ordinal preferences are observable, stochastic dominance efficiency (sd-efficiency) is commonly used. First, we provide a characterization of sd-efficient allocations in terms of a property of an order relation defined on the set of man-woman pairs. Then, using this characterization, we constructively prove that for each probabilistic assignment that is sd-efficient for some ordinal preferences, there is a von Neumann-Morgenstern utility profile consistent with the ordinal preferences for which the assignment is Pareto efficient. Second, we show that when the preferences are strict, for each ordinal preference profile and each ex-post stable probabilistic assignment, there is a von Neumann-Morgenstern utility profile, consistent with the ordinal preferences, for which the assignment belongs to the core of the associated transferable utility game. © 2015 Elsevier Inc.Item Open Access An exponential stability result for the wave equation(Elsevier, 2002) Morgül, Ö.We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize this system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function which consists of a strictly positive real function and some poles on the imaginary axis. We then show that under some conditions the closed-loop system is exponentially stable. © 2002 Published by Elsevier Ltd.