Characterization of well-posedness of piecewise linear systems

One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carath\'eodory. The concepts of jump solutions or a sliding mode are not considered here. In this sense, the problem to be discussed is one of the most basic problems in the study of well-posedness for discontinuous dynamical systems. First, we derive necessary and sufficient conditions for bimodal systems to be well-posed, in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Next, its extensions to the multi-modal case are discussed. As an application to switching control, in the case that two state feedback gains are switched according to a criterion depending on the state, we give a characterization of all admissible state feedback gains for which the closed loop system remains well-posed. \u

Robust moving horizon H∞ control of discrete time-delayed systems with interval time-varying delays

In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC) is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI) based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method

ゴヤク エイゴ メディア ニ オケル ニホン ジョセイ ノ イメージ ノ コウシン

西洋の文化は、昔から日本人女性の"謎"に興味を掻き立てられてきた。外国のジャーナリスト・学者・研究者達にとって、伝統的な日本の家庭における女性の役割とこれとは相反する現代のビジネス界におけるキャリア・ウーマンの立場にみられる矛盾は、特に魅力的なテーマである。本論文では、日本語の出典と英語メディアの評論の対比を通して、時に時代遅れで、固定観念に囚われた日本のキャリア・ウーマン像への反論を試みる。具体的には、職場における日本女性の役割定義や女性総合職に関する誤った描写についてである。このような視点は、家庭における日本の男性像や男女の役割分担についても示唆する。こうしたイメージの脱構築後、英語メディアにおける"誤訳"の陰に潜む原因について論文の最後で考察する。これら全体を通して、日本女性が直面している変遷していく社会や家庭や職場における現実といかに西洋のメディアで頻繁に報道されている構図とは異なるかということに光をあてることができればと考える

Discontinuous Transition from a Real Bound State to Virtual Bound State in a Mixed-Valence State of SmS

Golden SmS is a paramagnetic, mixed-valence system with a pseudogap. With increasing pressure across a critical pressure Pc, the system undergoes a discontinuous transition into a metallic, anti-ferromagnetically ordered state. By using a combination of thermodynamic, transport, and magnetic measurements, we show that the pseudogap results from the formation of a local bound state with spin singlet. We further argue that the transition Pc is regarded as a transition from an insulating electron-hole gas to a Kondo metal, i.e., from a spatially bound state to a Kondo virtually bound state between 4f and conduction electrons.Comment: 5 pages, 5 figure

Anomalous tunneling conductances of a spin singlet \nu=2/3 edge states: Interplay of Zeeman splitting and Long Range Coulomb Interaction

The point contact tunneling conductance between edges of the spin singlet $\nu=2/3,\hat{K}=(3/3/0)$ quantum Hall states is studied both in the quasiparticle tunneling picture and in the electron tunneling picture. Due to the interplay of Zeeman splitting and the long range Coulomb interaction between edges of opposite chirality novel spin excitations emerge, and their effect is characterized by anomalous exponents of the charge and spin tunneling conductances in various temperature ranges. Depending on the kinds of scatterings at the point contact and the tunneling mechanism the anomalous interaction in spin sector may enhance or suppress the tunneling conductances. The effects of novel spin excitation are also relevant to the recent NMR experiments on quantum Hall edges.Comment: Revtex File, 7 pages: To be published in Physical Reviews

Strong quasi-particle tunneling study in the paired quantum Hall states

The quasi-particle tunneling phenomena in the paired fractional quantum Hall states are studied. A single point-contact system is first considered. Because of relevancy of the quasi-particle tunneling term, the strong tunneling regime should be investigated. Using the instanton method it is shown that the strong quasi-particle tunneling regime is described as the weak electron tunneling regime effectively. Expanding to the network model the paired quantum Hall liquid to insulator transition is discussed

Disorder-Induced Multiple Transition involving Z2 Topological Insulator

Effects of disorder on two-dimensional Z2 topological insulator are studied numerically by the transfer matrix method. Based on the scaling analysis, the phase diagram is derived for a model of HgTe quantum well as a function of disorder strength and magnitude of the energy gap. In the presence of sz non-conserving spin-orbit coupling, a finite metallic region is found that partitions the two topologically distinct insulating phases. As disorder increases, a narrow-gap topologically trivial insulator undergoes a series of transitions; first to metal, second to topological insulator, third to metal, and finally back to trivial insulator. We show that this multiple transition is a consequence of two disorder effects; renormalization of the band gap, and Anderson localization. The metallic region found in the scaling analysis corresponds roughly to the region of finite density of states at the Fermi level evaluated in the self-consistent Born approximation.Comment: 5 pages, 5 figure

Theory of non-equilibrium noise in general multi-terminal superconducting hydrid devices: application to multiple Cooper pair resonances

We consider the out-of-equilibrium behavior of a general class of mesoscopic devices composed of several superconducting or/and normal metal leads separated by quantum dots. Starting from a microscopic Hamiltonian description, we provide a non-perturbative approach to quantum electronic transport in the tunneling amplitudes between dots and leads: using the equivalent of a path integral formulation, the lead degrees of freedom are integrated out in order to compute both the current and the current correlations (noise) in this class of systems, in terms of the dressed Green's function matrix of the quantum dots. In order to illustrate the efficiency of this formalism, we apply our results to the "all superconducting Cooper pair beam splitter", a device composed of three superconducting leads connected via two quantum dots, where crossed Andreev reflection operates Cooper pair splitting. Commensurate voltage differences between the three leads allow to obtain expressions for the current and noise as a function of the Keldysh Nambu Floquet dressed Green's function of the dot system. This voltage configuration allows the occurrence of non-local processes involving multiple Cooper pairs which ultimately lead to the presence of non-zero DC currents in an out-of-equilibrium situation. We investigate in details the results for the noise obtained numerically in the specific case of opposite voltages, where the transport properties are dominated by the so called "quartet processes", involving the coherent exchange of two Cooper pairs among all three superconducting terminals. We show that these processes are noiseless in the non-resonant case, and that this property is also observed for other voltage configurations. When the dots are in a resonant regime, the noise characteristics change qualitatively, with the appearance of giant Fano factors.Comment: 18 pages, 12 figure

Edge Dynamics in Quantum Hall Bilayers II: Exact Results with Disorder and Parallel Fields

We study edge dynamics in the presence of interlayer tunneling, parallel magnetic field, and various types of disorder for two infinite sequences of quantum Hall states in symmetric bilayers. These sequences begin with the 110 and 331 Halperin states and include their fractional descendants at lower filling factors; the former is easily realized experimentally while the latter is a candidate for the experimentally observed quantum Hall state at a total filling factor of 1/2 in bilayers. We discuss the experimentally interesting observables that involve just one chiral edge of the sample and the correlation functions needed for computing them. We present several methods for obtaining exact results in the presence of interactions and disorder which rely on the chiral character of the system. Of particular interest are our results on the 331 state which suggest that a time-resolved measurement at the edge can be used to discriminate between the 331 and Pfaffian scenarios for the observed quantum Hall state at filling factor 1/2 in realistic double-layer systems.Comment: revtex+epsf; two-up postscript at http://www.sns.ias.edu/~leonid/ntwoup.p