Evolution on a smooth landscape

We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population is governed by correlation functions that although being formally down by powers ofN (the population size), nonetheless control the evolution process after a very short transient. The long-time behavior can be found analytically since only one of these higher order correlators (the two-point function) is relevant. We compare and contrast the exact findings derived herein with a previously proposed phenomenological treatment employing mean-field theory supplemented with a cutoff at small population density. Finally, we relate our results to the recently studied case of mutation on a totally flat landscape.     

On the simultaneous measurement of position and momentum: Naimark embeddings and projections

Single and double meter simultaneous measurements of a harmonic oscillator are reviewed and compared. Naimark extensions are constructed and relevant projection properties are exhibited for both cases. The theory is extended to the simultaneous measurement of squeezed position and momentum measurements.     

Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity

Lower bounds for the eigenvalues of some elliptic equations and elliptic systems over bounded regions are obtained. The bounds are universal in that they depend only upon the volume of the region. Specific applications include the clamped plate, the buckling problem for the clamped plate and the equations of linear elasticity. Our results are consequences of extensions of the methods of Li and Yau (Comm. Mat. Phys. 88 (1983) 309–318) who obtained such results for the eigenvalues of the fixed membrane problem.     

Information content analysis for reaction of oreinted molecules

Experimental data on the orientation dependence of the reactivity in NO + O₃ and Rb + CH₃I collisions is analyzed. Error limits of the measurements are used to conclude that one low-order, or “Legendre moment” accounts for much of the observed dependence on the orientation. The same procedure applies also to data on the polarization of the products.     

Theory of the quantized Hall effect (III)

In the previous paper, we have demonstrated the need for a phase transition as a function of θ in the non-linear σ-model describing the quantized Hall effect. In this work, we present arguments for the occurrence of exactly such a transition. We make use of a dilute gas instanton approximation as well as present a more rigorous duality argument to show that the usual scaling of the conductivity to zero at large distances is altered whenever $\text{σ}{}_{\mathrm{xy}}{}^{\mathrm{(0)}}\text{≈}\text{1}\text{2}\text{ne}{}^2\text{/h}$, n integer. This then completes our theory of the quantized Hall effect.     

Techniques for high power microwave sources at high average power

Experiments on CLIA (compact linear induction accelerator), capable of generating 750 kV and 10 kA into a matched load using magnetic switching to produce 60 ns long pulses, are described. As a first application, the authors used CLIA to drive a water-cooled L-band magnetron at repetition rates as high as 250 Hz with no breakdown or pulse shortening. This gives an average power of 6.3 kW. A short burst at 1 kHz demonstrates operation that would translate to an average power of approximately 25 kW. In this regime operation is not limited by gas build-up, electrode erosion or microwhisker depletion. Currently, the authors are operating on CLIA with a high current relativistic klystron. Beams with modulated current powers of approximately 1 GW have been generated at 100 Hz for bursts as long as 5000 pulses. It is concluded that there are no apparent obstacles to much higher average powers at higher peak powers     

States of total pure radiation in general relativity

Summary In this paper we investigate and exhibit space-times which admit states of pure radiation in the sense of Lichnerowicz. In § 1 the notion of special total pure radiation is introduced, and in § 2 we derive the canonical line element for this type of radiation. An additional type of spacetime admitting radiation is considered in § 3. A class of singular integrable electromagnetic fields for the space-times of § 2 are constructed in § 4. The final section is concerned with the radiation condition proposed by Zakharov. Work supported by National Science Foundation Grants GP 6876 and GP 7401.