Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.     

Emesis and space motion sickness in amphibians.

Amphibians possess the ability to vomit in response to a variety of stimuli that provoke emesis in mammals. Pharmacological studies have establish that the ejection of gastric contents and the basic mechanism for vomiting have been phylogenetically conserved among these tetrapods. As part of on-going comparative studies on emesis in vertebrates, we previously documented that some postmetamorphic anurans and salamander larvae experience motion-induced emesis when exposed to the provocative stimulus of parabolic aircraft flight. However, more recent experiments suggest that there are strict conditions for inducing emesis in amphibians exposed to parabolic flight and that amphibians are not as sensitive to this stimulus as mammals. Further studies on emesis in lower vertebrates may help us understand the processes that cause emesis in abnormal gravitational regimes.     

Energy conversion of the flare due to direct electric fields from the sheared reconnection

In this paper we present a new mechanism of the main energy conversion of the solar flare. Since a flare inducing prominence (flux tube) rises V_z ? 300 km s⁻¹, the plasmas below it cannot continuously eject with Alfvén speeds of V_A = 3000 km s⁻¹ but probably with V_z ≈ ±100 km s⁻¹. Plasma up and downflows with V_A will within a short duration be blocked between the chromosphere where reconnected flux tubes are piling up, and the slowly rising flux rope. Hence the Petschek slow shock mechanism is difficult to be realized as a major energy converting mechanism.     

Design and analysis of new p(n,k) polyphase pulse compression codes

P(n,k) codes as a new class of polyphase pulse compression codes are introduced and analyzed in detail. The P(n,k) codes are conceptually derived by step approximation of the phase function of a nonlinear-frequency modulated (NLFM) Chirp signal with a favorable energy density spectrum. The significant advantages of P(n,k) codes over conventional polyphase codes are lower autocorrelation sidelobes and an improved tolerance of low Doppler shifts and precompression bandwidth limitations. The primary disadvantage of the P(n,k) codes over conventional codes is a loss in range resolution. The uniform P(n,k) codes are especially attractive for radars employing digital signal professing because their favorable correlation properties also remain when quantization effects are taken into account     

The Juno Waves Investigation

Jupiter is the source of the strongest planetary radio emissions in the solar system. Variations in these emissions are symptomatic of the dynamics of Jupiter’s magnetosphere and some have been directly associated with Jupiter’s auroras. The strongest radio emissions are associated with Io’s interaction with Jupiter’s magnetic field. In addition, plasma waves are thought to play important roles in the acceleration of energetic particles in the magnetosphere, some of which impact Jupiter’s upper atmosphere generating the auroras. Since the exploration of Jupiter’s polar magnetosphere is a major objective of the Juno mission, it is appropriate that a radio and plasma wave investigation is included in Juno’s payload. This paper describes the Waves instrument and the science it is to pursue as part of the Juno mission.     

Do we understand the inner magnetotail dynamics during substorms?

Substorm evolution of the near-Earth (|X|<15 R_E) plasma sheet has been emphasized recently because the inner tail is thought to link closely to the substorm auroral activity in the ionosphere during the early stage of substorms. In this paper, we discuss how the inner tail substorm phenomena during the late substorm growth phase and early expansion phase are accounted for by the two prevailing substorm models, namely, the near-Earth neutral line model and the current disruption model. We find that the late growth phase features are more satisfactorily accounted for by the current disruption model than by the near-Earth neutral line model. In addition, detailed observations on current disruption show evidence inconsistent with the proposed idea of dipolarization being due to plasma flow braking from reconnection in the mid-tail region, which poses a difficulty to the near-Earth neutral line model as well.     

Evolution of the orbital elements for objects with high area-to-mass ratios in geostationary transfer orbits

A new population of uncatalogued objects in geosynchronous Earth orbits (GEO), with a mean motion of about 1 rev/day and eccentricities up to 0.6, has been identified recently. The first observations of this new type of objects were acquired in the framework of the European Space Agency’s (ESA) search for space debris in GEO and the geostationary transfer orbit (GTO) using the ESA 1-m telescope on Tenerife. Earlier studies have postulated that the perturbations due to the solar radiation pressure can lead to such large eccentricities for GEO objects with a high area-to-mass ratio (A/M). The simulations showed that the eccentricities of GEO objects with large A/M exhibit periodic variations with periods of about one year and amplitudes depending on the value of A/M. The findings of these studies could be confirmed by observations from the ESA 1-m telescope on Tenerife.