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Publication Metadata only ‘Anti-commutable’ local pre-Leibniz algebroids and admissible connections(Elsevier, 2023) Department of Physics; N/A; Dereli, Tekin; Doğan, Keremcan; Faculty Member; PhD Student; Department of Physics; College of Sciences; Graduate School of Sciences and Engineering; 201358; N/AThe concept of algebroid is convenient as a basis for constructions of geometrical frameworks. For example, metric-affine and generalized geometries can be written on Lie and Courant algebroids, respectively. Furthermore, string theories might make use of many other algebroids such as metric algebroids, higher Courant algebroids, or conformal Courant algebroids. Working on the possibly most general algebroid structure, which generalizes many of the algebroids used in the literature, is fruitful as it creates a chance to study all of them at once. Local pre-Leibniz algebroids are such general ones in which metric-connection geometries are possible to construct. On the other hand, the existence of the 'locality operator', which is present for the left-Leibniz rule for the bracket, necessitates the modification of torsion and curvature operators in order to achieve tensorial quantities. In this paper, this modification of torsion and curvature is explained from the point of view that the modification is applied to the bracket instead. This leads one to consider 'anti-commutable' local pre-Leibniz algebroids which satisfy an anti-commutativity-like property defined with respect to a choice of an equivalence class of connections. These 'admissible' connections are claimed to be the necessary ones while working on a geometry of algebroids. This claim is due to the fact that one can prove many desirable properties and relations if one uses only admissible connections. For instance, for admissible connections, we prove the first and second Bianchi identities, Cartan structure equations, Cartan magic formula, the construction of Levi-Civita connections, the decomposition of connection in terms of torsion and non-metricity. These all are possible because the modified bracket becomes anti-symmetric for an admissible connection so that one can apply the machinery of almost-or pre-Lie algebroids. We investigate various algebroid structures from the literature and show that they admit admissible connections which are metric-compatible in some generalized sense. Moreover, we prove that local pre-Leibniz algebroids that are not anti-commutable cannot be equipped with a torsion-free, and in particular Levi-Civita, connection.Publication Metadata only A deep etching mechanism for trench-bridging silicon nanowires(Iop Publishing Ltd, 2016) Wollschlaeger, Nicole; Österle, Werner; Leblebici, Yusuf; N/A; Department of Mechanical Engineering; Taşdemir, Zuhal; Alaca, Burhanettin Erdem; PhD Student; Faculty Member; Department of Mechanical Engineering; Koç University Surface Science and Technology Center (KUYTAM) / Koç Üniversitesi Yüzey Teknolojileri Araştırmaları Merkezi (KUYTAM); Graduate School of Sciences and Engineering; College of Engineering; N/A; 115108Introducing a single silicon nanowire with a known orientation and dimensions to a specific layout location constitutes a major challenge. The challenge becomes even more formidable, if one chooses to realize the task in a monolithic fashion with an extreme topography, a characteristic of microsystems. The need for such a monolithic integration is fueled by the recent surge in the use of silicon nanowires as functional building blocks in various electromechanical and optoelectronic applications. This challenge is addressed in this work by introducing a topdown, silicon-on-insulator technology. The technology provides a pathway for obtaining wellcontrolled silicon nanowires along with the surrounding microscale features up to a three-orderof-magnitude scale difference. A two-step etching process is developed, where the first shallow etch defines a nanoscale protrusion on the wafer surface. After applying a conformal protection on the protrusion, a deep etch step is carried out forming the surrounding microscale features. A minimum nanowire cross-section of 35 nm by 168 nm is demonstrated in the presence of an etch depth of 10 mu m. Nanowire cross-sectional features are characterized via transmission electron microscopy and linked to specific process steps. The technology allows control on all dimensional aspects along with the exact location and orientation of the silicon nanowire. The adoption of the technology in the fabrication of micro and nanosystems can potentially lead to a significant reduction in process complexity by facilitating direct access to the nanowire during surface processes such as contact formation and doping.Publication Open Access A diversity combination model incorporating an inward bias for interaural time-level difference cue integration in sound lateralization(Multidisciplinary Digital Publishing Institute (MDPI), 2020) N/A; Department of Computer Engineering; Mojtahedi, Sina; Erzin, Engin; Ungan, Pekcan; Faculty Member; Faculty Member; Department of Computer Engineering; Graduate School of Sciences and Engineering; College of Engineering; School of Medicine; N/A; 34503; N/AA sound source with non-zero azimuth leads to interaural time level differences (ITD and ILD). Studies on hearing system imply that these cues are encoded in different parts of the brain, but combined to produce a single lateralization percept as evidenced by experiments indicating trading between them. According to the duplex theory of sound lateralization, ITD and ILD play a more significant role in low-frequency and high-frequency stimulations, respectively. In this study, ITD and ILD, which were extracted from a generic head-related transfer functions, were imposed on a complex sound consisting of two low- and seven high-frequency tones. Two-alternative forced-choice behavioral tests were employed to assess the accuracy in identifying a change in lateralization. Based on a diversity combination model and using the error rate data obtained from the tests, the weights of the ITD and ILD cues in their integration were determined by incorporating a bias observed for inward shifts. The weights of the two cues were found to change with the azimuth of the sound source. While the ILD appears to be the optimal cue for the azimuths near the midline, the ITD and ILD weights turn to be balanced for the azimuths far from the midline.Publication Metadata only A dynamical formulation of one-dimensional scattering theory and its applications in optics(Academic Press Inc Elsevier Science, 2014) NA; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical equations. By decoupling and partially integrating these equations, we reduce the scattering problem to a second order linear differential equation with universal initial conditions that is equivalent to an initial-value time-independent Schrodinger equation. We give explicit formulas for the reflection and transmission amplitudes in terms of the solution of either of these equations and employ them to outline an inverse-scattering method for constructing finite-range potentials with desirable scattering properties at any prescribed wavelength. In particular, we construct optical potentials displaying threshold lasing, antilasing, and unidirectional invisibility.Publication Metadata only A Hamiltonian formulation of the Pais-Uhlenbeck oscillator that yields a stable and unitary quantum system(Elsevier Science Bv, 2010) NA; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 105131We offer a new Hamiltonian formulation of the classical Pais-Uhlenbeck oscillator and consider its canonical quantization. We show that for the non-degenerate case where the frequencies differ, the quantum Hamiltonian operator is a Hermitian operator with a positive spectrum, i.e., the quantum system is both stable and unitary. Furthermore it yields the classical Pais-Uhlenbeck oscillator in the classical limit. A consistent description of the degenerate case based on a Hamiltonian that is quadratic in momenta requires its analytic continuation into a complex Hamiltonian system possessing a generalized PT-symmetry (an involutive antilinear symmetry). We devise a real description of this complex system, derive an integral of motion for it, and explore its quantization.Publication Open Access A hybrid broadband metalens operating at ultraviolet frequencies(Nature Publishing Group (NPG), 2021) Department of Physics; Ali, Farhan; Ramazanoğlu, Serap Aksu; Faculty Member; Department of Physics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 243745The investigation on metalenses have been rapidly developing, aiming to bring compact optical devices with superior properties to the market. Realizing miniature optics at the UV frequency range in particular has been challenging as the available transparent materials have limited range of dielectric constants. In this work we introduce a low absorption loss and low refractive index dielectric material magnesium oxide, MgO, as an ideal candidate for metalenses operating at UV frequencies. We theoretically investigate metalens designs capable of efficient focusing over a broad UV frequency range (200–400 nm). The presented metalenses are composed of sub-wavelength MgO nanoblocks, and characterized according to the geometric Pancharatnam–Berry phase method using FDTD method. The presented broadband metalenses can focus the incident UV light on tight focal spots (182 nm) with high numerical aperture (NA ≈ 0.8). The polarization conversion efficiency of the metalens unit cell and focusing efficiency of the total metalens are calculated to be as high as 94%, the best value reported in UV range so far. In addition, the metalens unit cell can be hybridized to enable lensing at multiple polarization states. The presented highly efficient MgO metalenses can play a vital role in the development of UV nanophotonic systems and could pave the way towards the world of miniaturization.Publication Metadata only A new class of adiabatic cyclic states and geometric phases for non-Hermitian Hamiltonians(Elsevier Science Bv, 1999) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231For a T-periodic non-Hermitian Hamiltonian H(t), we construct a class of adiabatic cyclic states of period T which are not eigenstates of the initial Hamiltonian H(O). We show that the corresponding adiabatic geometric phase angles are real and discuss their relationship with the conventional complex adiabatic geometric phase angles. We present a detailed calculation of the new adiabatic cyclic states and their geometric phases for a non-Hermitian analog of the spin 1/2 particle in a precessing magnetic field.Publication Metadata only A post-HF study on the halogen bonding interaction of pyrene with diatomic halogen molecules(Wiley, 2016) Sütay, Berkay; Yurtsever, Mine; Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; Department of Chemistry; College of Sciences; 7129We present a detailed SCS-MP2 study on the potential energy curves (PEC) for interactions between diatomic halogen molecules and pyrene. BSSE corrected CCSD[T] energies at equilibrium distances are computed and compared to CCSD(T) energies. The most stable conformation of these weakly bound van der Waals complexes is almost linear in the perpendicular direction to the pyrene plane. The complexes of highly polarizable bromine and iodine molecules with pyrene are very stable and they carry rather large number of vibrational states. Despite its small size, F-2 also forms strong halogen bonding similar to Br-2 and I-2. The interaction between Cl-2 and pyrene is the weakest and it is attributed to the highest polarizability/molar mass ratio of chlorine among the others. I-2-pyrene is found to be the most stable complex due to the strongest mutual polarization effects and is carrying more than 60 vibrational states. Due to the rather large number of electrons in some complexes, the relativistic corrections are also considered.Publication Metadata only A quantum mechanical study of the electrochemical polymerization of pyrrole(Elsevier Science Sa, 2001) Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; Department of Chemistry; College of Sciences; 7129Mechanism for the electrochemical polymerization of pyrrole is studied using accurate density functional theory; (DFT) calculations. The primary emphasis is on the structures and stability of intermediates generated during various mechanisms. Structures of the radical cations, which play role in reactions, an optimized to elucidate radical-radical and radical-neutral pathways. The competing probabilities of reactions between various size oligomers are discussed in terms of their thermodynamical stability.Publication Metadata only A theoretical study of structural defects in conjugated polymers(Elsevier Science Sa, 1999) Yurtsever, Mine; Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; Department of Chemistry; College of Sciences; 7129Accurate ab-initio calculations are performed for pyrrole and thiophene oligomers bonded through alpha and beta carbons. The thermodynamical stabilitiy of all possible binding types including the branched forms of tetramers and pentamers are compared. Employing the probabilities obtained from these calculations, a Monte Carlo type growth scheme is applied to predict branching as functions of the chain length and temperature. A high degree of branching for polypyrrole is reported whereas the linear chains dominate the structure of polythiophene.