Condensed Matter Theory

Abstract:

In this correspondence, we consider a narrow-band point-to-point communication system with many (input) transmitters and a single (output) receiver (i.e., a multiple-input single output (MISO) system). We assume the receiver has perfect knowledge of the channel but the transmitter only knows the channel distribution. We focus on two canonical classes of Gaussian channel models: a) the channel has zero mean with a fixed covariance matrix and b) the channel has nonzero mean with covariance matrix proportional to the identity. In both cases, we are able to derive simple analytic expressions for the ergodic average and the cumulative distribution function (cdf) of the mutual information for arbitrary input (transmission) signal covariance. With minimal numerical effort, we then determine the ergodic and outage capacities and the corresponding capacity-achieving input signal covariances. Interestingly, we find that the optimal signal covariances for the ergodic and outage cases have very different behavior. In particular, under certain conditions, the outage capacity optimal covariance is a discontinuous function of the parameters describing the channel (such as strength of the correlations or the nonzero mean of the channel).

Abstract:

Simulations show that, when a phase-separated binary [Formula presented] fluid is driven to flow past chemically patterned substrates in a microchannel, the fluid exhibits unique morphological instabilities. For the pattern studied, these instabilities give rise to the simultaneous, periodic formation of monodisperse droplets of [Formula presented] in [Formula presented] and [Formula presented] in [Formula presented]. The system bifurcates between time-independent behavior and different types of regular, nondecaying oscillations in the structural characteristics. The surprisingly complex behavior is observed even in the absence of hydrodynamic interactions and arises from the interplay between the fluid flow and patterned substrate, which introduces nonlinearity into the dynamical system. © 2003 The American Physical Society.