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We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence., 10 pages, 12 figures, additional references added

We study the finite temperature nature of a quantum phase transition between an Abelian and a non-Abelian topological phase in an exactly solvable model of a chiral spin liquid. By virtue of the exact solvability, this model can serve as a testbed for developing better measures for describing topological quantum phase transitions. We characterize this phase transition in terms of the global flux and entanglement entropy, and discuss to what extent the existence of a topologically ordered ground state with non-Abelian excitations is revealed at finite temperature., 5 pages, 5 figures

In an externally applied magnetic field, ultrapure crystals of the bilayer compound Sr₃Ru₂O₇ undergo a metamagnetic transition below a critical temperature, T*, which varies as a function of the angle between the magnetic field H and the Ru-O planes. Moreover, T* approaches zero when H is perpendicular to the planes. This putative "metamagnetic quantum critical point," however, is pre-empted by a nematic fluid phase with order one resistive anisotropy in the ab plane. In a "realistic" bilayer model with moderate strength local Coulomb interactions, the existence of a sharp divergence of the electronic density of states near a van Hove singularity of the quasi-one-dimensional bands, and the presence of spin-orbit coupling results in a mean-field phase diagram which accounts for many of these experimentally observed phenomena. Although the spin-orbit coupling is not overly strong, it destroys the otherwise near-perfect Fermi-surface nesting and hence suppresses spin-density-wave ordering., Facultad de Ciencias Exactas, Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Instituto de Física La Plata, Instituto de Física de Líquidos y Sistemas Biológicos

We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that, under quite general conditions, the entanglement entropy of a large and simply connected sub-system of an infinite system with a smooth boundary has a universal finite contribution, as well as scale-invariant terms for special geometries. The universal finite contribution to the entanglement entropy is computable in terms of the properties of the conformal structure of the wave function of these quantum critical systems. The calculation of the universal term reduces to a problem in boundary conformal field theory., 14 pages, 3 figures, v2 references updated, minor changes

We consider the stability conditions for half-quantum vortices in quasi two dimensional $p_x+ip_y$ superconductor (such as ${\rm Sr_2 RuO_4}$ is believed to be) through energetics calculations. Although the predicted exotic nature of these excitations have recently attracted much attention but they have not been observed yet. We pay particular attention to the fact that an isolated half quantum vortex has a divergent energy cost in the bulk due to the associated {\it unscreened} spin current, which requires two half-quantum vortices with opposite spin winding to pair. We show that the stability of such a pair in bulk is enhanced when the ratio of spin superfluid density to superfluid density $\rho_{{\rm sp}}/\rho_{\rm s}$ is small. As a step towards stabilizing and observing these exotic excitations, we propose using various mesoscopic geometries. We find that certain mesoscopic geometries can selectively allow only single half-quantum vortices to enter the sample for small $\rho_{{\rm sp}}/\rho_{\rm s}$., Comment: 4 pages, 2 figures. The version accepted for publication in Phys. Rev. Lett. Compared to version 1, the revised version is shorter and one reference was added

oz ANKARA ATTKSU ARITMA TESİSİNDE NİTROJEN ARrnMININ MODELLENMESİ Kim,Eun-ah Yüksek Lisans, Çevre Mühendisliği Bölümü Tez Danışmanı: Prof. Dr. Celal F. Gökçay Haziran 2002, 1 13 sayfa Günümüzde birçok ülkedeki çevre kanunları, arıtma tesisi atıksularında karbon, nitrojen ve fosfor için oldukça sıkı kalite standartları gerektirmektedir. Bu ise biyolojik arıtma sistemlerinde karmaşık dizayn, işletme ve kontrol yaklaşımları gerektirmektedir. Sonuç olarak, böylesi karmaşık sistemlerin simülasyonu için kompleks matematiksel modellere dayalı bilgisayar programlan geliştirilmiştir. Giriş suyu karakteristiklerinin KOİ ve Nitrojen dağılımına bağlı olarak belirlenmesi, biyolojik nütriyent arıtımı sistemlerinin dizayn ve işletmesinde önem kazanmıştır. Literatürde KOİ, N dağılımı ve biyokinetik parametrelerin belirlenmesi amacıyla birçok metod önerilmektedir. Buna rağmen, metodların hiçbiri henüz standartlaşmamıştır. Evsel atıksuların KOİ ve N dağılımları ülkeden ülkeye ve iklimden iklime değişim göstermektedir.Çalışma süresince, Ankara Merkezi Atıksu Arıtma Tesisi'nden (AMAAT), atıksu numuneleri düzenli olarak alınmış ve fiziksel-kimyasal metodlarla analiz edilmiştir. Laboratuvar ölçekli reaktör, nitrifikasyon için bir aerobik tank ve denitrifikasyon için bir anoksik tanktan oluşmaktaydı. Tanklardan alınan atıksuda TKN, N03-N, NH3-N analiz edilmiştir. Bu donelere bakılarak kurulan nitrifikasyon-denitrifikasyon sistemi Aktif Çamur Model 1 (ASMl)'e göre SSSP programı kullanılarak kalibre edilmiştir. Simülasyon sonucunda laboratuvar ölçeğindeki ünitede nitrojen arıtımı kabul edilebilir doğrulukta tahmin edilmiştir. Anahtar Kelimeler: ASM1, ototrofîk büyüme, kinetik parametreler, nitrojen dağılımı, SSSP, simülasyon. vı ABSTRACT MODELLING OF NITROGEN REMOVAL IN ANKARA WASTEWATER TREATMENT PLANT Kim,Eun-ah M.Sc, Environmental Engineering Department Supervisor: Pro£ Dr. Celal F. GÖkçay June 2002, 108 pages Nowadays environmental legislations in many countries have all imposed strict effluent quality standards for carbon, nitrogen and phosphorous for wastewater treatment plants. This in turn caused complicated design, operation and control of biological treatment systems. As a result, computer programs based on complex mathematical models are now developed for the simulation of such complicated systems. The influent wastewater characterization based on COD and Nitrogen fractionation became very important in design and operation of biological nutrient systems. Several methods for the determination of COD, N fractions and biokinetic parameters have already been proposed in the literature. However, none of these methods have yet been standardized. The COD and N fractions of domestic wastewaters alter appreciably from country to country and with the climate. In this 111work, a case study for Ankara is being presented. During the study, wastewater samples were taken periodically from Ankara Central Wastewater Treatment Plant (ACWTP), and were analysed and fractionated by the physical-chemical method. The biokmetic parameters required for the simulation studies were also determined in a lab-scale reactor, which was composed of one aerobic and one anoxic tank for nitrification and denitrification, respectively. Effluent TKN, NO3-N, NH3-N from each the reactor were analysed and the nitrification - denitrification system was calibrated for Activated Sludge Model Number 1 (ASM1) by using the SSSP software. The calibrated model simulations predicted performance of the lab-scale model with reasonable accuracy. As the next step the calibrated SSSP program was used for the verification of the retrofit design undertaken for the ACWTP, for additional N- removaL Keywords: ASM1, autotrophic growth, kinetic parameters, nitrogen fractionation, SSSP, simulation. IV 108