5,843 research outputs found
Vortex line representation for flows of ideal and viscous fluids
It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid
coincides with the equations of motion of a charged {\it compressible} fluid
moving due to a self-consistent electromagnetic field. Transition to the
Lagrangian description in a new hydrodynamics is equivalent for the original
Euler equations to the mixed Lagrangian-Eulerian description - the vortex line
representation (VLR). Due to compressibility of a "new" fluid the collapse of
vortex lines can happen as the result of breaking (or overturning) of vortex
lines. It is found that the Navier-Stokes equation in the vortex line
representation can be reduced to the equation of the diffusive type for the
Cauchy invariant with the diffusion tensor given by the metric of the VLR
Limitations of PLL simulation: hidden oscillations in MatLab and SPICE
Nonlinear analysis of the phase-locked loop (PLL) based circuits is a
challenging task, thus in modern engineering literature simplified mathematical
models and simulation are widely used for their study. In this work the
limitations of numerical approach is discussed and it is shown that, e.g.
hidden oscillations may not be found by simulation. Corresponding examples in
SPICE and MatLab, which may lead to wrong conclusions concerning the
operability of PLL-based circuits, are presented
Evolutionary origin of power-laws in Biochemical Reaction Network; embedding abundance distribution into topology
The evolutionary origin of universal statistics in biochemical reaction
network is studied, to explain the power-law distribution of reaction links and
the power-law distributions of chemical abundances. Using cell models with
catalytic reaction network, we find evidence that the power-law distribution in
abundances of chemicals emerges by the selection of cells with higher growth
speeds. Through the further evolution, this inhomogeneity in chemical
abundances is shown to be embedded in the distribution of links, leading to the
power-law distribution. These findings provide novel insights into the nature
of network evolution in living cells.Comment: 11 pages, 3 figure
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