Incorporating an Optical Clock Into a Time Scale.

This paper discusses the results of a simulation of a time scale based on continuously operating commercial hydrogen masers and an optical frequency standard that does not operate continuously as a clock. The simulation compares the performance of this time scale with one that is based on the same commercial devices but incorporates a continuously operating cesium fountain instead of the optical standard. The results are independent of the detailed characteristics of the optical frequency standard; the only requirement is that the optical device be much more stable than the masers in the ensemble. We discuss two methods for realizing the results of this simulation in an operational time scale.

Confidence Estimates in Simulation of Phase Noise or Spectral Density.

In this paper, we apply the method of discrete simulation of power-law noise, developed by Timmer and König, Ashby, and Ashby and Patla, to the problem of simulating phase noise for a combination of power-law noises. We derive analytic expressions for the probability of observing a value of phase noise L(f) or of any of the one-sided spectral densities Sϕ(f), Sy(f) , or Sx(f) , for arbitrary superpositions of power-law noise.

Simulations of the Hadamard Variance: Probability Distributions and Confidence Intervals.

Power-law noise in clocks and oscillators can be simulated by Fourier transforming a modified spectrum of white phase noise. This approach has been applied successfully to simulation of the Allan variance and the modified Allan variance in both overlapping and nonoverlapping forms. When significant frequency drift is present in an oscillator, at large sampling times the Allan variance overestimates the intrinsic noise, while the Hadamard variance is insensitive to frequency drift. The simulation method is extended in this paper to predict the Hadamard variance for the common types of power-law noise. Symmetric real matrices are introduced whose traces-the sums of their eigenvalues-are equal to the Hadamard variances, in overlapping or nonoverlapping forms, as well as for the corresponding forms of the modified Hadamard variance. We show that the standard relations between spectral densities and Hadamard variance are obtained with this method. The matrix eigenvalues determine probability distributions for observing a variance at an arbitrary value of the sampling interval τ, and hence for estimating confidence in the measurements.

Probability distributions and confidence intervals for simulated power law noise.

A method for simulating power law noise in clocks and oscillators is presented based on modification of the spectrum of white phase noise, then Fourier transforming to the time domain. Symmetric real matrices are introduced whose traces-the sums of their eigenvalues-are equal to the Allan variances, in overlapping or non-overlapping forms, as well as for the corresponding forms of the modified Allan variance. We show that the standard expressions for spectral densities, and their relations to Allan variance, are obtained with this method. The matrix eigenvalues determine probability distributions for observing a variance at an arbitrary value of the sampling interval τ, and hence for estimating confidence in the measurements. Examples are presented for the common power-law noises. Extension to other variances such as the Hadamard variance, and variances with dead time, are discussed.

Topographic-pattern-induced homeotropic alignment of liquid crystals.

Polymer films nanoimprinted with checkerboard patterns of square wells align calamitic (rodlike) liquid crystals vertically, horizontally, or tilted depending on the depth/width ratio of the wells. The liquid crystal prefers planar orientation on polymer films that are smooth but when the films are topographically patterned, the increasing elastic energy density as the wells become narrower eventually overcomes the surface anchoring of the polymer and the liquid crystal director field makes a transition from planar to homeotropic. Similar effects have been demonstrated in both nematics and smectics, and the behavior is confirmed by theory and computer simulation.

Relativistic effects in earth-orbiting Doppler lidar return signals.

Frequency shifts of side-ranging lidar signals are calculated to high order in the small quantities (v/c), where v is the velocity of a spacecraft carrying a lidar laser or of an aerosol particle that scatters the radiation back into a detector (c is the speed of light). Frequency shift measurements determine horizontal components of ground velocity of the scattering particle, but measured fractional frequency shifts are large because of the large velocities of the spacecraft and of the rotating earth. Subtractions of large terms cause a loss of significant digits and magnify the effect of relativistic corrections in determination of wind velocity. Spacecraft acceleration is also considered. Calculations are performed in an earth-centered inertial frame, and appropriate transformations are applied giving the velocities of scatterers relative to the ground.

Power dependence of distributed cavity phase-induced frequency biases in atomic fountain frequency standards.

We discuss the implications of using high-power microwave tests in a fountain frequency standard to measure the frequency bias resulting from distributed cavity-phase shifts. We develop a theory which shows that the frequency bias from distributed cavity phase depends on the amplitude of the microwave field within the cavity. The dependence leads to the conclusion that the frequency bias associated with the distributed cavity phase is typically both misestimated and counted twice within the error budget of fountain frequency standards.

Bridging interaction between a water drop stabilised by solid particles and a planar oil/water interface.

We demonstrate that the particle mediated interaction between a pendant water drop, covered by a latex particle monolayer, and a planar decane/water interface leads to bridging, analogous to flocculation in solid-stabilised emulsions. The results also provide information about the particle contact angle at the oil/water interface.

Relativity in the Global Positioning System.

The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work. This paper discusses the conceptual basis, founded on special and general relativity, for navigation using GPS. Relativistic principles and effects which must be considered include the constancy of the speed of light, the equivalence principle, the Sagnac effect, time dilation, gravitational frequency shifts, and relativity of synchronization. Experimental tests of relativity obtained with a GPS receiver aboard the TOPEX/POSEIDON satellite will be discussed. Recently frequency jumps arising from satellite orbit adjustments have been identified as relativistic effects. These will be explained and some interesting applications of GPS will be discussed.