Simple quasi-exponential slope generator

Circuitry for digitally generating an exponentially decaying wave function permits discrete values to be sampled from the exponential waveform for comparison with a binary number of specified accuracy. This exponential-decay generator employs a simple binary counter to count in the sequence of exponential decay

On Contact Anosov Flows

Exponential decay of correlations for \Co^{(4)} Contact Anosov flows is established. This implies, in particular, exponential decay of correlations for all smooth geodesic flows in strictly negative curvature

Statistical analysis of time-resolved emission from ensembles of semiconductor quantum dots: Interpretation of exponential decay models

We present a statistical analysis of time-resolved spontaneous emission decay curves from ensembles of emitters, such as semiconductor quantum dots, with the aim of interpreting ubiquitous non-single-exponential decay. Contrary to what is widely assumed, the density of excited emitters and the intensity in an emission decay curve are not proportional, but the density is a time integral of the intensity. The integral relation is crucial to correctly interpret non-single-exponential decay. We derive the proper normalization for both a discrete and a continuous distribution of rates, where every decay component is multiplied by its radiative decay rate. A central result of our paper is the derivation of the emission decay curve when both radiative and nonradiative decays are independently distributed. In this case, the well-known emission quantum efficiency can no longer be expressed by a single number, but is also distributed. We derive a practical description of non-single-exponential emission decay curves in terms of a single distribution of decay rates; the resulting distribution is identified as the distribution of total decay rates weighted with the radiative rates. We apply our analysis to recent examples of colloidal quantum dot emission in suspensions and in photonic crystals, and we find that this important class of emitters is well described by a log-normal distribution of decay rates with a narrow and a broad distribution, respectively. Finally, we briefly discuss the Kohlrausch stretched-exponential model, and find that its normalization is ill defined for emitters with a realistic quantum efficiency of less than 100%.\ud \u

Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la

Frequency decay for Navier-Stokes stationary solutions

We consider stationary Navier-Stokes equations in R 3 with a regular external force and we prove exponential frequency decay of the solutions. Moreover, if the external force is small enough, we give a pointwise exponential frequency decay for such solutions according to the K41 theory. If a damping term is added to the equation, a pointwise decay is obtained without the smallness condition over the force