Clock States Research Articles

Fuzzy time point compatibility reasoning for microprocessor systems

Time range reasoning and fuzzy time point reasoning have been proposed and implemented for microprocessor systems diagnosis. These approaches provide effective temporal constraint reasoning based on two primitive mechanisms: the constraint satisfaction and the constraint propagation. Through the reasoning process, the occurrence time of a microprocessor system event is determined with respect to a previously occurred reference event. In the domain of microprocessor systems, however, the two primitive mechanisms are insufficient in some cases. In some situations, a timing parameter of a system component imposes a temporal constraint on an event with respect to a future event which has an unknown occurrence time at that instance. Thus, it is very difficult for an event to make reference to that future event. In particular, for the read cycle of the MC68000 microprocessor, the DTACK signal must be asserted at least t/sub ASI/ before the falling edge of the CPU clock state S/sub 5/. As the clock is a well defined periodical signal, the parameter t/sub ASI/ does not directly affect the occurrence time of S/sub 5/. In fact, t/sub ASI/ imposes a compatibility constraint on the event S/sub 5/. If the constraint is not satisfied, either an event or a sequence of events might be initiated to resolve the constraint violation, or the operation fails. In our case. Wait states are Hence, a supplemental reasoning mechanism is desired which ensures this kind of temporal constraint compatibility.

Predictions for laser-cooled Rb clocks

Using information from a recent ${}^{85}$Rb two-color photoassociation experiment, we evaluate the merits of fountain clocks based on ${}^{87}$Rb and ${}^{85}$Rb isotopes as alternatives to ${}^{133}$Cs and find that they offer significant advantages. In the case of ${}^{87}$Rb the collisionally induced fractional frequency shift is 15 times smaller than for ${}^{133}$Cs. This small shift is associated with a small difference in the triplet and singlet scattering lengths for ${}^{87}$Rb. For ${}^{85}$Rb, the shift produced by the two ${m}_{f}=0$ clock states may have opposite signs allowing the shift to be eliminated by controlling the relative populations of these states. We also present collision quantities relevant to atomic fountain clocks containing multiply launched groups of atoms, and for evaporative cooling of ${}^{85}$Rb atoms.

Low-power and low-voltage CMOS digital design

Low-voltage and low-power digital design has to be performed at several levels such as architecture, logic and basic cell levels, while considering activity, capacitance, frequency and supply voltage reduction. Examples of activity and capacitance reduction will be provided for a low-power digital cell library and for gated clock and asynchronous Finite State Machines. Reduction of supply voltage and operating frequency is considered for complex gate decomposition and parallelized logic circuits such as parallelized memories, synchronous counters and shift registers. Reduction of the number of basic operations to execute a given task is illustrated by the design of an efficient 8-bit pipelined microprocessor.

Lifetime of the metastable 6s′ [1/2]_0 clock state in xenon

To investigate the potential of a proposed optical frequency standard, we have measured the lifetime of the metastable 6s' [(1/2)](0) state in xenon. Magneto-optically trapped xenon atoms were prepared in the 6s' [(1/2)](0) state, and the time dependence of the vacuum-ultraviolet decay signature was analyzed. The total decay rate of 75(3) s(-1) is the sum of a 7.8(38)-s(-1) spontaneous emission rate (1-sigma uncertainties) and a much larger deexcitation rate that is due to a transition driven by room-temperature blackbody radiation.

On the parallel dynamics of the diluted clock neural network

We present explicit formulae for one-step evolution of the overlaps in a clock neural network for the parallel dynamics. These formulae constitute recursion relations for the exact dynamics in the case of extreme dilution. The fixed point equation for this exactly soluble model is investigated for varying temperature T, capacity parameter α and the number q of the clock states.

Incompletely ordered phases and phase transitions in the three-dimensional general clock model.

In our previous studies of the antiferromagnetic Potts and Q=6 clock models in three dimensions, we have argued the existence of an incompletely ordered phase (IOP) which is characterized by soft rigidity with a nonintegral stiffness exponent and an incomplete order (though long ranged) such that some of the spin states are exclusively dominant. To investigate the IOP's further, we study Q-state general clock models with one varying energy parameter which can include the ferromagnetic Potts models, by means of our Monte Carlo twist method and analytically in the pair approximation. The twist method gives the following results for Q=6. There are two kinds of IOP's (IOP1 and IOP2) on the opposite side of the ferromagnetic Potts model. Their stiffness exponents are about 1.2 less than 2 (for the highest rigidity) in good agreement with those previously obtained. A pair of adjacent clock states are dominantly well mixed in the IOP1, as are a set of three adjacent ones in the IOP2. Thermal fluctuations in the IOP's can be characterized by the spin configurations of the soft structures with buffers that prevent spins in different states by more than the least angle from getting close with other, which is consistent with the nonintegral stiffness exponent. Large entropy contributions to the IOP's are revealed in both approaches. The phase boundary, which extends from the ferromagnetic Potts point, is clearly of first order, while among those relevant to the IOP's one is discontinuous and the other is continuous but the last two are not evident. It is strongly suggested that there is a transition without symmetry breaking between the IOP2 and the rigid phase. In the pair approximation applied for Q=4\ensuremath{\sim}12, various properties for Q=6 are consistent with those obtained by the simulation, except some other properties. Peculiar Q dependence of the highest critical temperature of the IOP in the extreme case is also found.

Chaos in gauge glasses in the critical region

Chaos in the XY gauge glasses in the critical region is studied by using the discretized Migdal-Kadanoff renormalization group scheme. The thermal exponent y c is found to be independent of the number of clock states q. However, the Lyapunov exponent ζ c characterizing the chaotic behavior in the critical region varies with q providing non-universal behavior of the interfacial entropy in this region. The exponent ζ c is smaller than the Lyapunov exponent found away from the criticality. This is similar to what was proposed by Nifle and Hilhorst for 3D Ising spin glasses.

Compositional semantics of a real-time prototyping language

The formal semantics of a prototyping language for hard real-time systems, PSDL, is given. PSDL provides a data flow notation augmented by application-orientation timing and control constraints to describe a system as a hierarchy of networks of processing units communicating via data streams. The semantics of PSDL are defined in terms of algebraic high-level Petri nets. This formalism combines algebraic specifications of abstract data types with process and concurrency concepts of Petri nets. Its data abstraction facilities are used to define the meaning of PSDL data types, while high-level Petri nets serve to model the casual and timing behavior of a system. The net model exposes potential concurrency of computation and makes all synchronization needs implied by timing and control constraints explicit and precise. Time is treated as state of clocks, and clocks are modeled as ordinary system components. The net semantics provides the basis for applying analysis techniques and semantic tools available for high-level Petri nets.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Frustration, scaling, and local gauge invariance.

A variety of two- and three-dimensional random frustrated systems with continuous and discrete symmetries are studied within the Migdal-Kadanoff renormalization-group scheme. The continuous-symmetry {ital XY} models are approximated by discretized clock models with a large number of clock states. In agreement with earlier studies of the random gauge {ital XY} model using a {ital T}=0 scaling approach, a nonzero transition temperature is observed in three-dimensional {ital XY} models with O(2) local gauge invariance. Our analysis points to the possible importance of local gauge invariance in determining the lower critical dimensionality of frustrated systems.

Time in a quantum mechanical world

In quantum mechanics it is usual to represent physical reality as a vector in Hilbert space at a particular time, with evolution being governed by Schrodinger's equation which involves an externally imposed time parameter. This leads to difficulties if one wishes to regard the universe as a quantum mechanical system, because there should no time external to such a system. The approach in this paper is to represent the totality of reality as a vector in Hilbert space. The author shows how time evolution follows, where time now is defined in terms of the states of a quantum mechanical clock which is part of the system. Rather than the correlation between the clock states and the states of the rest of the system arising because both are governed by an imposed law involving an external time parameter, it is seen that this correlation is of the separation-independent Einstein-Podolsky-Rosen type. The total reality vector, which incorporates the whole history of the system, is shown to be a zero-energy eigenstate of the system Hamiltonian. He discusses systems of finite and infinite lifetime, and is able to answer the question: what was the state before the initial state? He concludes that the quantum mechanical system of this paper is a reasonable representation of the observed universe.

Geodetic point positioning with GPS carrier beat phase data from the CASA UNO Experiment

The Global Positioning System (GPS) carrier beat phase data collected by the TI4100 GPS receiver has been successfully utilized by the US Defense Mapping Agency in an algorithm which is designed to estimate individual absolute geodetic point positions from data collected over a few hours. The algorithm uses differenced data from one station and two to four GPS satellites at a series of epochs separated by 30 second intervals. The ‘precise’ GPS ephemerides and satellite clock states, held fixed in the estimation process, are those estimated by the Naval Surface Warfare Center (NSWC). Broadcast ephemerides and clock states are also utilized for comparative purposes.An outline of the data corrections applied, the mathematical model and the estimation algorithm are presented. Point positioning results and statistics are presented for a globally‐distributed set of stations which contributed to the CASA UNO experiment. Statistical assessment of 114 GPS point positions at 11 CASA UNO stations indicates that the overall standard deviation of a point position component, estimated from a few hours of data, is 73 centimeters. Solution of the long line geodetic inverse problem using repeated point positions such as these can potentially offer a new tool for those studying geodynamics on a global scale.