2,956 research outputs found
Tensor Products, Positive Linear Operators, and Delay-Differential Equations
We develop the theory of compound functional differential equations, which
are tensor and exterior products of linear functional differential equations.
Of particular interest is the equation with a single delay, where the delay
coefficient is of one sign, say with .
Positivity properties are studied, with the result that if then
the -fold exterior product of the above system generates a linear process
which is positive with respect to a certain cone in the phase space.
Additionally, if the coefficients and are periodic of
the same period, and satisfies a uniform sign condition, then there
is an infinite set of Floquet multipliers which are complete with respect to an
associated lap number. Finally, the concept of -positivity of the exterior
product is investigated when satisfies a uniform sign condition.Comment: 84 page
A compact design for the Josephson mixer: the lumped element circuit
We present a compact and efficient design in terms of gain, bandwidth and
dynamical range for the Josephson mixer, the superconducting circuit performing
three-wave mixing at microwave frequencies. In an all lumped-element based
circuit with galvanically coupled ports, we demonstrate non degenerate
amplification for microwave signals over a bandwidth up to 50 MHz for a power
gain of 20 dB. The quantum efficiency of the mixer is shown to be about 70
and its saturation power reaches dBm.Comment: 5 pages, 4 figure
In Silico Experimental Modeling of Cancer Treatment
In silico experimental modeling of cancer involves combining findings from biological literature with computer-based models of biological systems in order to conduct investigations of hypotheses entirely in the computer laboratory. In this paper, we discuss the use of in silico modeling as a precursor to traditional clinical and laboratory research, allowing researchers to refine their experimental programs with an aim to reducing costs and increasing research efficiency. We explain the methodology of in silico experimental trials before providing an example of in silico modeling from the biomathematical literature with a view to promoting more widespread use and understanding of this research strategy
A Modified Version of Taylor's Hypothesis for Solar Probe Plus Observations
The Solar Probe Plus (SPP) spacecraft will explore the near-Sun environment,
reaching heliocentric distances less than . Near Earth,
spacecraft measurements of fluctuating velocities and magnetic fields taken in
the time domain are translated into information about the spatial structure of
the solar wind via Taylor's "frozen turbulence" hypothesis. Near the perihelion
of SPP, however, the solar-wind speed is comparable to the Alfv\'en speed, and
Taylor's hypothesis in its usual form does not apply. In this paper, we show
that, under certain assumptions, a modified version of Taylor's hypothesis can
be recovered in the near-Sun region. We consider only the transverse,
non-compressive component of the fluctuations at length scales exceeding the
proton gyroradius, and we describe these fluctuations using an approximate
theoretical framework developed by Heinemann and Olbert. We show that
fluctuations propagating away from the Sun in the plasma frame obey a relation
analogous to Taylor's hypothesis when and , where is the component of the spacecraft velocity
perpendicular to the mean magnetic field and () is the
Elsasser variable corresponding to transverse, non-compressive fluctuations
propagating away from (towards) the Sun in the plasma frame. Observations and
simulations suggest that, in the near-Sun solar wind, the above inequalities
are satisfied and fluctuations account for most of the fluctuation
energy. The modified form of Taylor's hypothesis that we derive may thus make
it possible to characterize the spatial structure of the energetically dominant
component of the turbulence encountered by SPP.Comment: 5 pages, 1 figure, accepted in ApJ Lette
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