Method of reducing time base error in digital magnetic recorders

Apparatus reduces Time Base Error /TBE/ in the playback of digital data from magnetic recording equipment. The apparatus uses a magnet which employs a servo position control of the tape by which the playback data clock is phase locked with a fixed frequency reference signal

Extensional tectonics of the Saturnian Satellites

The saturnian satellites were imaged by the Voyager spacecraft at sufficient resolutions to reveal landforms that indicate histories of extensional tectonics for several of these bodies. The relationships among landforms on various satellites imply that extensional tectonism is a consequence of several different energy sources. Case histories of several satellites are discussed to illustrate the interaction of various phenomena associated with extensional tectonism

Absence of hyperuniformity in amorphous hard-sphere packings of nonvanishing complexity

We relate the structure factor $S(\mathbf{k} \to \mathbf{0})$ in a system of jammed hard spheres of number density $\rho$ to its complexity per particle $\Sigma(\rho)$ by the formula $S(\mathbf{k} \to \mathbf{0})=-1/ [\rho^2\Sigma''(\rho)+2\rho\Sigma'(\rho)]$. We have verified this formula for the case of jammed disks in a narrow channel, for which it is possible to find $\Sigma(\rho)$ and $S(\mathbf{k})$ analytically. Hyperuniformity, which is the vanishing of $S(\mathbf{k} \to \mathbf{0})$, will therefore not occur if the complexity is nonzero. An example is given of a jammed state of hard disks in a narrow channel which is hyperuniform when generated by dynamical rules that produce a non-extensive complexity.Comment: 5 pages, 3 figure

Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel

We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter $\sigma$ confined to a two-dimensional channel of width $1.95\,\sigma$ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction $\phi_K$ that is less than the maximum possible $\phi_{\rm max}$, the latter corresponding to a buckled crystal. In this quasi-one-dimensional problem there is no question of there being any \emph{real} divergence of the pressure at $\phi_K$. We give arguments that this avoided phase transition is a structural feature -- the remnant in our narrow channel system of the hexatic to crystal transition -- but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scale $\tilde{\xi}_3$ as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around $15\,\sigma$ at $\phi_K$, which is larger than the penetration lengths that have been reported for three dimensional systems. It is argued that the $\alpha$-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches $\phi_K$.Comment: 17 pages, 16 figure

Air-cushioning in impact problems

This paper concerns the displacement potential formulation to study the post-impact influence of an aircushioning layer on the two-dimensional impact of a liquid half-space by a rigid body. The liquid and air are both ideal and incompressible and attention is focussed on cases when the density ratio between the air and liquid is small. In particular, the correction to classical Wagner theory is analysed in detail for the impact of circular cylinders and wedges

Disappearance of the de Almeida-Thouless line in six dimensions

We show that the Almeida-Thouless line in Ising spin glasses vanishes when their dimension d -> 6 as h_{AT}^2/T_c^2 = C(d-6)^4(1- T/T_c)^{d/2 - 1}, where C is a constant of order unity. An equivalent result which could be checked by simulations is given for the one-dimensional Ising spin glass with long-range interactions. It is shown that replica symmetry breaking also stops as d -> 6.Comment: Additional text and one figure adde