22,118 research outputs found
Supersymmetric KdV equation: Darboux transformation and discrete systems
For the supersymmetric KdV equation, a proper Darboux transformation is
presented. This Darboux transformation leads to the B\"{a}cklund transformation
found early by Liu and Xie \cite{liu2}. The Darboux transformation and the
related B\"{a}cklund transformation are used to construct integrable super
differential-difference and difference-difference systems. The continuum limits
of these discrete systems and of their Lax pairs are also considered.Comment: 13pages, submitted to Journal of Physics
Interacting dark energy, holographic principle and coincidence problem
The interacting and holographic dark energy models involve two important
quantities. One is the characteristic size of the holographic bound and the
other is the coupling term of the interaction between dark energy and dark
matter. Rather than fixing either of them, we present a detailed study of
theoretical relationships among these quantities and cosmological parameters as
well as observational constraints in a very general formalism. In particular,
we argue that the ratio of dark matter to dark energy density depends on the
choice of these two quantities, thus providing a mechanism to change the
evolution history of the ratio from that in standard cosmology such that the
coincidence problem may be solved. We investigate this problem in detail and
construct explicit models to demonstrate that it may be alleviated provided
that the interacting term and the characteristic size of holographic bound are
appropriately specified. Furthermore, these models are well fitted with the
current observation at least in the low red-shift region.Comment: 20 pages, 3 figure
Parametric entry corridors for lunar/Mars aerocapture missions
Parametric atmospheric entry corridor data are presented for Earth and Mars aerocapture. Parameter ranges were dictated by the range of mission designs currently envisioned as possibilities for the Human Exploration Initiative (HEI). This data, while not providing a means for exhaustive evaluation of aerocapture performance, should prove to be a useful aid for preliminary mission design and evaluation. Entry corridors are expressed as ranges of allowable vacuum periapse altitude of the planetary approach hyperbolic orbit, with chart provided for conversion to an approximate flight path angle corridor at entry interface (125 km altitude). The corridor boundaries are defined by open-loop aerocapture trajectories which satisfy boundary constraints while utilizing the full aerodynamic control capability of the vehicle (i.e., full lift-up or full lift-down). Parameters examined were limited to those of greatest importance from an aerocapture performance standpoint, including the approach orbit hyperbolic excess velocity, the vehicle lift to drag ratio, maximum aerodynamic load factor limit, and the apoapse of the target orbit. The impact of the atmospheric density bias uncertainties are also included. The corridor data is presented in graphical format, and examples of the utilization of these graphs for mission design and evaluation are included
Representations of linear dual rate system via single SISO LTI filter, conventional sampler and block sampler
In this brief, it is proved that a linear dual-rate system can be represented via a series cascade of: 1) a conventional expander, a single-input single-output (SISO) linear time-invariant (LTI) filter and a block decimator, or 2) a block expander, an SISO LTI filter and a conventional decimator. Hence, incompatible nonuniform filter banks could achieve perfect reconstruction via LTI filters, conventional samplers and block samplers without expanding the input-output dimension of a subsystem of linear dual-rate systems or converting the nonuniform filter banks to uniform filter banks. The main advantage of the proposed representations is to avoid complicated design of the circuit layout caused by connecting subsystems with large input-output dimension or a lot of subsystems togethe
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