474 research outputs found
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
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
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
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
Spin-orbit effects in a graphene bipolar pn junction
A graphene junction is studied theoretically in the presence of both
intrinsic and Rashba spin-orbit couplings. We show that a crossover from
perfect reflection to perfect transmission is achieved at normal incidence by
tuning the perpendicular electric field. By further studying angular dependent
transmission, we demonstrate that perfect reflection at normal incidence can be
clearly distinguished from trivial band gap effects. We also investigate how
spin-orbit effects modify the conductance and the Fano factor associated with a
potential step in both and cases.Comment: 6 pages, 5 figures, conductance and Fano factor plots adde
The edge state network model and the global phase diagram
The effects of randomness are investigated in the fractional quantum Hall
systems. Based on the Chern-Simons Ginzburg-Landou theory and considering
relevant quasi-particle tunneling, the edge state network model for the
hierarchical state is introduced and the plateau-plateau transition and
liquid-insulator transition are discussed. This model has duality which
corresponds to the relation of the quantum Hall liquid phase and the Hall
insulating phase and reveals a mechanism in the weak coupling regime.Comment: 5 page RevTe
Maternal embryonic leucine zipper kinase (MELK) regulates multipotent neural progenitor proliferation.
Maternal embryonic leucine zipper kinase (MELK) was previously identified in a screen for genes enriched in neural progenitors. Here, we demonstrate expression of MELK by progenitors in developing and adult brain and that MELK serves as a marker for self-renewing multipotent neural progenitors (MNPs) in cultures derived from the developing forebrain and in transgenic mice. Overexpression of MELK enhances (whereas knockdown diminishes) the ability to generate neurospheres from MNPs, indicating a function in self-renewal. MELK down-regulation disrupts the production of neurogenic MNP from glial fibrillary acidic protein (GFAP)-positive progenitors in vitro. MELK expression in MNP is cell cycle regulated and inhibition of MELK expression down-regulates the expression of B-myb, which is shown to also mediate MNP proliferation. These findings indicate that MELK is necessary for proliferation of embryonic and postnatal MNP and suggest that it regulates the transition from GFAP-expressing progenitors to rapid amplifying progenitors in the postnatal brain
Valley Spin Sum Rule for Dirac Fermions: Topological Argument
We consider a two-dimensional bipartite lattice system. In such a system, the
Bloch band spectrum can have some valley points, around which Dirac fermions
appear as the low-energy excitations. Each valley point has a valley spin +1 or
-1. In such a system, there are two topological numbers counting vortices and
merons in the Brillouin zone, respectively. These numbers are equivalent, and
this fact leads to a sum rule which states that the total sum of the valley
spins is absent even in a system without time-reversal and parity symmetries.
We can see some similarity between the valley spin and chirality in the
Nielsen-Ninomiya no-go theorem in odd-spatial dimensions.Comment: 5 pages, 1 figure, some comments are added/revised, accepted for
publication in J. Phys. Soc. Jp
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