Time-invariant States Research Articles

Denial-of-Service Power Dispatch Against Linear Quadratic Control via a Fading Channel

This paper addresses the secure control problem of cyber-physical systems (CPSs) under Denial-of-Service (DoS) attack with power constraint. The purpose of the attacker is to degenerate the control performance of CPSs at the reduced cost of attack power. Unlike the existing works developed under the assumption of time-invariant channel states, the sensor-to-estimator communication channel under consideration is a standard block fading communication channel. By taking the angle of the DoS attacker, an optimization problem is formulated to deal with both the linear quadratic control cost of the CPS and the expenditure of attack power. Then, the formulated problem is transformed into a Markov decision problem. As it is difficult to provide an analytical expression of optimal attack power, the objective function is approximated to derive an analytical expression of the suboptimal attack power. Next the attack strategies for two specific communication schemes, namely, the capacity achieving coding scheme and the forward error correction scheme, are studied. Finally, the validity of the proposed attack strategy is demonstrated by an illustrative example.

Quantum spin chain dissipative mean-field dynamics

We study the emergent dynamics resulting from the infinite volume limit of the mean-field dissipative dynamics of quantum spin chains with clustering, but not time-invariant states. We focus upon three algebras of spin operators: the commutative algebra of mean-field operators, the quasi-local algebra of microscopic, local operators and the collective algebra of fluctuation operators. In the infinite volume limit, mean-field operators behave as time-dependent, commuting scalar macroscopic averages while quasi-local operators, despite the dissipative underlying dynamics, evolve unitarily in a typical non-Markovian fashion. Instead, the algebra of collective fluctuations, which is of bosonic type with time-dependent canonical commutation relations, undergoes a time-evolution that retains the dissipative character of the underlying microscopic dynamics and exhibits non-linear features. These latter disappear by extending the time-evolution to a larger algebra where it is represented by a continuous one-parameter semigroup of completely positive maps. The corresponding generator is not of Lindblad form and displays mixed quantum-classical features, thus indicating that peculiar hybrid systems may naturally emerge at the level of quantum fluctuations in many-body quantum systems endowed with non time-invariant states.

Comparison of production risks in the state-contingent framework: application to balanced panel data

In a balanced panel data setting, this article proposes an empirical application of the state-contingent (SC) framework for production uncertainty. The SC approach (e.g., Chambers and Quiggin 2000) casts production decisions under uncertainty as the decision to select a portfolio of Arrow-Debreu SC outputs, scheduled to be delivered in the contingent states of nature. Under some stationarity assumptions on the SC decisions (i.e., no technical change, time-invariant states of nature, time-invariant SC portfolio decisions) and regularity assumptions on the data generating process (i.e., cross-sectionally homogeneous state realizations), SC technology can be estimated from balanced panel data that are framed as cross-sectional data of partially-revealed SC portfolio decisions. This allows one to simulate an optimal SC portfolio, determined by the interaction between the estimated SC technology and given risk preferences. In the application to Maryland dairy production data, the stochastic technologies of confinement and intensive-grazing dairy systems are compared. Of the two time intervals (years 2000–2004 and ye0ars 2006–2009) separately analyzed, the optimal production decision has generally become riskier for the confinement system and less risky for the grazing system. These contrasting trends appear directly related to the volatile milk prices, feed cost hikes, and increasing organic milk production during 2006–2009. The risk associated with the optimal portfolio is substantially lower under the SC analysis compared to a typical residual-as-uncertainty approach, suggesting that the typical approach may overstate the risk due to uncertainty.

MJO and Tropical Cyclogenesis in the Gulf of Mexico and Eastern Pacific: Case Study and Idealized Numerical Modeling

Abstract The role of the Madden–Julian oscillation (MJO) in modulating the frequency and location of tropical cyclogenesis over the eastern Pacific and the Gulf of Mexico during August–September 1998 is examined. During the nonconvective phase of the MJO, convection and low-level cyclonic vorticity occurred primarily in conjunction with the intertropical convergence zone (ITCZ). During the convective phase, convection, low-level cyclonic vorticity, and convergence expanded into the northeastern Pacific and the Gulf of Mexico. This was accompanied by enhanced eddy kinetic energy and barotropic energy conversions as compared to the nonconvective phase, consistent with previous research. During the nonconvective phase of the MJO, vertical shear was relatively weaker but tropical cyclones tended to form mainly within the ITCZ. On the contrary, during the convective phase, vertical wind shear exceeded 10 m s−1 over much of this region and tropical cyclone development occurred north of the ITCZ, near the Mexican Pacific coast and the Gulf of Mexico. Idealized numerical experiments are conducted using a barotropic model with time-invariant basic states representative of the nonconvective and convective phases of the MJO. The simulations indicate that the propagation paths as well as the amplification of the eddies differ substantially between the two phases. During the nonconvective phase, the waves tend to propagate westward into the eastern Pacific. During the convective phase, stronger southerlies steer the waves into the Gulf of Mexico. The MJO-related modulation of tropical cyclogenesis in the eastern Pacific and Gulf of Mexico thus appears to involve anomalous convergence, cyclonic vorticity, vertical wind shear, and differing tracks of easterly waves.

Weak asymptotic abelianess for Galilei invariant time evolution

We extend the result of weak asymptotic abelianess for Galilei invariant time evolution from the tracial state to a set of time-invariant states which are uniformly clustering with respect to space translation.

Stable and unstable behavior of inductively coupled electronegative discharges

Plasma instabilities have been observed in low-pressure inductive discharges, in the transition between low density capacitively driven and high density inductively driven discharges when attaching gases such as SF6 and Ar/SF6 mixtures are used. Oscillations of charged particles, plasma potential, and light, with frequencies from a few hertz to tens of kilohertz, are seen for gas pressures between 1 and 100 mTorr and discharge powers in the range of 75–1200 W. The region of instability increases as the plasma becomes more electronegative and the frequency of plasma oscillations increases as the power, pressure, and gas flow rate increase. Time-resolved measurements of electron temperature, and time averaged ion energy distribution at the wall have been made. A volume-averaged (global) model of the instability has been developed, for a discharge containing time varying densities of electrons, positive ions, and negative ions, and time invariant excited states and neutral densities. The particle and energy balance equations are integrated to produce the dynamical behavior. The model agrees well with experimental observations, and also shows a significant influence of the matching network. Values of plasma parameters and of chemical composition are measured to set the values used in the model, as required to obtain the good agreement with experiment. Capacitive coupling plays a crucial role in the instability process. A variable electrostatic (Faraday) shield has been used to control the capacitive coupling from the excitation coil to the plasma. The plasma instability disappears when the shielded area exceeds 65% of the total area of the coil. The model gives a slightly higher value of 85% for instability suppression with the same discharge conditions (Ar/SF6 1:1, 5 mTorr).

Effects of Shear on the Lamellar Phase of a Dialkyl Cationic Surfactant

The effect of shear on the lamellar phase of the dialkyl cationic surfactant dihardened tallow dimethylammonium chloride has been determined using small-angle neutron scattering rheological measurements, and conductivity. We demonstrate that the formation of multilamelllar vesicles from rigid electrostatically charged membranes shows many of the features seen in the more flexible membrane systems previously studied. A shear-induced transition from an aligned lamellar phase to multilamellar vesicles has been observed, and the kinetics of the conductivity change associated with this shear induced transition has been characterized. The time invariant states that were characterized were also compared with the earlier results of Diat et al. on the mixture of sodium dodecyl sulfate, pentanol, and dodecane. For the latter system a second transition was observed at a higher shear rate, separating the vesicular state from a well-oriented lamellae state. This third time invariant state has not been observed for the system reported here. This difference in the phase behavior is discussed in terms of the coupling between the shear-induced deformation of the multilamellar vesicle and the interaction between membranes, which is different for the two systems.

Instabilities in low-pressure electronegative inductivedischarges

Plasma instabilities have been studied in low-pressure inductiveprocessing discharges with SF6 and Ar/SF6 mixtures, i.e. attachinggases. Oscillations are seen in charged particle density, electrontemperature and plasma potential using electrostatic probe and opticalemission measurements. For SF6, instability onset in pressure anddriving power has been explored for gas pressures between 2.5 and 100 mTorrand absorbed powers between 150 and 900 W. For pressures above 20 mTorr,increasing power is required to obtain the instability with increasingpressure, with the frequency of the instability increasing with pressure,mainly lying between 1 and 100 kHz. For Ar/SF6 mixtures, we observe asimilar low power transition, with an upper transition to a stableinductive mode. The instability windows become smaller as the argon partialpressure increases. For Ar/SF6 mixtures, we observe a significant effectof the matching network. We improve a previously developed volume-averaged(global) model to describe the instability. We consider a cylindricaldischarge containing time varying electrons, positive ions, negative ions,and time invariant excited states. The driving power is applied to thedischarge through a conventional L-type capacitive matching network, and weuse realistic models for the inductive and capacitive energy deposition.The particle and energy balance equations are integrated, consideringquasi-neutrality in the plasma volume and charge balance at the walls, toproduce the dynamical behaviour. As pressure or power is varied to cross athreshold, the instability is born at a Hopf bifurcation, with relaxationoscillations between higher and lower density states. The modelqualitatively agrees with experimental observations, and also shows asignificant influence of the matching network.

Comparing the time invariant and time-variant dielectric relaxation data simulated for a macromolecule's growth

The reliability of information obtained from dielectric data on the time-variant relaxation behaviour of a material has been examined. To do this, we first simulated the dielectric permittivity and loss data as a function of ac frequency for a series of time-invariant systems, which contained contributions from interfacial impedance, dc conductivity and dipolar relaxation, assuming that the static and high-frequency permittivities, the dc conductivity and the characteristic relaxation time change with time in a way that qualitatively agreed with those determined from experiments. These data were then transformed into sets of fixed frequency dielectric data as a function of time, and then analyzed pretending that the original parameters were unknown to us. The analysis gave parameters in reasonable agreement with those used for the simulation of the data. Thus, fixed frequency dielectric measurements on a time-variant system may be relied upon to yield information on the time-invariant states of the system, although, ideally speaking, measurement of time-invariant states would be desirable if errors arising from the interpolation needed to obtain the data for a time-invariant state could be eliminated.

Molecular kinetics during the growth of the macromolecule poly(di-2-hydroxypropyl ether of bisphenol-A–n-hexylamine) studied by dielectric spectroscopy

The growth of a polymer by step-polymerization reactions between n-hexylamine and the diglycidyl ether of bisphenol-A has been studied by measuring the dielectric properties over a wide range of frequency. Additionally, the dielectric properties of the monomeric and polymerized states have been studied and the effect of non-stoichiometry on localized motions in their glassy states investigated. This has led to an examination of the dielectric behaviour of the time-invariant states and time-variant states of a chemically reacting substance ultimately producing a macromolecule. Both states could be described by analogous equations in which the relaxation had a broad distribution of times expressed as the non-exponential decay of polarization. For the α-relaxation process in the polymerized states, this distribution was narrower than for the molecular state. Part of this effect was due to the temperature. In the polymerized state, the shape of the spectrum remained constant with changing temperature but it narrowed with increasing temperature for the molecular state. The study showed how the relaxation time evolved with the reaction time and that the relaxations observed in the glassy state are appropriately interpreted in terms of difference in the local packing density of the structure.

The limiting dynamics of an imperfect Bose gas

For an imperfect Bose gas consisting of massive particles and interacting through a long-range pair potential in a mean-field approximation, both in equilibrium and far from equilibrium, the dynamics are derived in the thermodynamic limit. This is done in the framework of the operator algebraic quantum theory. The limiting dynamics is formulated in the Schrödinger picture as a group of affine transformations of certain folia of physical states. Similar to the mean-field models for spin lattices, the algebra of quasilocal observables is not invariant under the Heisenberg dynamics in the GNS representation of general time invariant states. It is known that above critical density the infinite system exhibits condensation, and the condensate is characterized by the classical parameters density and phase. For these parameters a classical nonlinear equation of motion is derived.