Matrix Product Representation of Locality Preserving Unitaries

The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that are unitary provides a necessary and sufficient representation of 1D unitaries that preserve locality. That is, we show that matrix product operators that are unitary are guaranteed to preserve locality by mapping local operators to local operators while at the same time all locality preserving unitaries can be represented in a matrix product way. Moreover, we show that the matrix product representation gives a straight-forward way to extract the GNVW index defined in Ref.\cite{Gross2012} for classifying 1D locality preserving unitaries. The key to our discussion is a set of `fixed point' conditions which characterize the form of the matrix product unitary operators after blocking sites. Finally, we show that if the unitary condition is relaxed and only required for certain system sizes, the matrix product operator formalism allows more possibilities than locality preserving unitaries. In particular, we give an example of a simple matrix product operator which is unitary only for odd system sizes, does not preserve locality and carries a `fractional' index as compared to their locality preserving counterparts.Comment: 14 page

Boson condensation and instability in the tensor network representation of string-net states

The tensor network representation of many-body quantum states, given by local tensors, provides a promising numerical tool for the study of strongly correlated topological phases in two dimension. However, tensor network representations may be vulnerable to instabilities caused by small perturbations of the local tensor, especially when the local tensor is not injective. For example, the topological order in tensor network representations of the toric code ground state has been shown to be unstable under certain small variations of the local tensor, if these small variations do not obey a local $Z_2$ symmetry of the tensor. In this paper, we ask the questions of whether other types of topological orders suffer from similar kinds of instability and if so, what is the underlying physical mechanism and whether we can protect the order by enforcing certain symmetries on the tensor. We answer these questions by showing that the tensor network representation of all string-net models are indeed unstable, but the matrix product operator (MPO) symmetries of the local tensor can help to protect the order. We find that, `stand-alone' variations that break the MPO symmetries lead to instability because they induce the condensation of bosonic quasi-particles and destroy the topological order in the system. Therefore, such variations must be forbidden for the encoded topological order to be reliably extracted from the local tensor. On the other hand, if a tensor network based variational algorithm is used to simulate the phase transition due to boson condensation, then such variation directions must be allowed in order to access the continuous phase transition process correctly.Comment: 44 pages, 85 figures, comments welcom

Applying the fuzzy gain scheduling nonlinear PI controller to permanent magnet direct current motor - dynamo system

Bu makalede bulanık olarak kazancı ayarlanabilen PI kontrolör yapısı, RISC mimariye sahip bir mikrokontrolör ile gerçekleştirilmiştir. Bulanık kural yapısı ve bulanık işlemler, hata ve türevinin değişimini baz alarak, PI kontrolörün oran ve integral kazançlarını on-line olarak ayarlamaktadır. Bulanık-PI kontrol algoritması, kalıcı mıknatıslı doğru akım motorunun (KMDA) hızını kontrol etmek amacıyla RISC bir mikrokontrolör içerisinde on-line olarak çalıştırılmaktadır. Mikrokontrolör motorun hızını, endüvisine uygulanan gerilimi bir doğru akım kıyıcısı vasıtasıyla değiştirerek ayarlamaktadır. Uygulama sonuçları gözönüne alındığında, hazırlanan kontrolörün PI kontrolör ile karşılaştırılması sonucunda daha iyi bir kontrol performansı yakaladığı görülmüştür.This paper describes the realization of a fuzzy gain scheduling scheme of a PI controller using a RISC microcontroller. Fuzzy rules and reasoning are utilised on-line to determine the PI controller parameters based on the error signal and its first difference. The Fuzzy control algorithm is implemented in the RISC microcontroller to regulate the speed of a permanent magnet DC motor (PMDC) and works on-line. The microcontroller directly tunes the motor speed with a chopper converter which changes the motor terminal voltage. Application results demonstrate that better control performance can be achieved in comparison with traditional PI controllers

Boundary Value Problems For Integrable Equations Compatible With The Symmetry Algebra

Boundary value problems for integrable nonlinear partial differential equations are considered from the symmetry point of view. Families of boundary conditions compatible with the Harry-Dym, KdV and MKdV equations and the Volterra chain are discussed. We also discuss the uniqueness of some of these boundary conditions.Comment: 25 pages , Latex , no figure

Regulations and software evolution: An example from the military domain

AbstractIn this article, the impact of regulatory changes on software development is assessed in the context of military standards. A previously conducted experiment incorporating three standards is further investigated for this purpose, outlining the characteristics of the evolution in standards and its effects. In addition to this experiment that was designed with projects conducted as graduate class work, a real project from the industry is utilized, to demonstrate the similar effects of the evolution as discovered in the earlier experiment. Finally, the results of the assessment are generalized and a forecast is presented for the next potential regulation change, the IEEE Std 12207-2008

Harmonic Effects on Electromechanical Overcurrent Relays

Elektromekanik aşırı akım koruma röleleri sinüsoidal akım altında çalışmak üzere tasarlanmıştır. Bu rölelerin harmonikli akımda çalışmaları güvenilir değildir. Literatürde harmonikler ve rölelerle ilgili pek çok teorik çalışma bulunmaktadır. Bu makalede, harmoniklerin elektromekanik ters zamanlı aşırı akım rölesinin (TZAAR) çalışmasına etkileri incelenmiş ve TZAAR’nin bozulmuş dalga şekilleri için davranışı deneysel çalışma ile analiz edilmiştir. Deneyde, elektromekanik TZAAR olarak, indüksiyon disk yapısında bir röle kullanılmıştır. Değişik harmonik spektrumlara sahip, sinüsoidal olmayan yük akımları TZAAR’a uygulanmış ve bu yük akımları data toplama kartı ve harmonik analiz programı ile bilgisayar ortamında işlenmiştir. Deney sonuçları gözönüne alındığında, TZAAR’ın çalışma akımı ve çalışma zamanının, sinüsoidal olmayan akımın toplam harmonik distorsiyonu (THD) ile orantılı olarak arttığı görülmüştür. Bu yapıda olan bir rolenin, akımın harmonik içermesi durumunda sistemi güvenli bir şekilde koruyamayacağı sonucu elde edilmiştir.The electromechanical overcurrent protection relays are designed to operate with sinusoidal current. The operation of protective relay with harmonic currents is not reliable. The literature on harmonics and relays covers mostly the theoretical studies. In this paper, the harmonic effects on operation of electromechanical inverse time overcurrent relay (ITOCR) were examined. Not common in existing studies, the behaviour of ITOCR was analysed with laboratory experiments for distorted waveforms. A type of induction disc relay was used as an electromechanical ITOCR in the experiments. The non-sinusoidal load currents that consist of different harmonic spectra were applied to ITOCR and these nonlinear-load currents were processed by a data acquisition card and a harmonic analysis programme in the computer environment. According to the experiment results, the pick up current and the operating time of the ITOCR increase proportionally to the total harmonic distortion (THD) value of the non-sinusoidal current. It is concluded that, this type of relay cannot protect the system reliably due to the harmonic components of current

A New Paradigm: Correlation between Laboratory and Field Tests of Coordination

AbstractThe study aimed to compare the coordination tests in the study and those used in the laboratory and field. Thus coordination tests used in the field and in the lab were applied to individuals in pursuit of these aims and the relation between the results was investigated. It was thus aimed to demonstrate the utilitarian value of the measurement methods in the field in contrast to the high cost laboratory coordination tests. 69 Individuals (male:49: female 20) between the ages of 18-30 participated in the study on volunteer basis. In order to determine the coordination skills of the study participants, Throwing a Ball at the Target Test, Dart Test from the field tests and Double Hand Eye Coordination Test and the Flamingo Balance Test from amongst the laboratory protocols was applied. In conclusion there was a correlation between the double hand eye coordination test and the dart test (r=0,245; p=0,43). As a result it was decided that the dart test was adequate in measurement of the coordination skills and taking them into account its usability in the field, it was decided that it could be used in place of the expensive laboratory tests