505 research outputs found
Air parcel random walk and droplet spectra broadening in clouds
We study the effect of turbulent flow on the droplet growth in a cloud during
the condensational phase. Using the air parcel model, we describe analytically
how the distribution of droplets over sizes evolves at the different stages of
parcel movement. We show that turbulent random walk superimposed on an
accelerated ascent of the parcel make the relative width of droplet
distribution to grow initially as and then decay as .Comment: 4 pages,3 figure
Stability analysis of polarization attraction in optical fibers
The nonlinear cross-polarization interaction among two intense
counterpropagating beams in a span of lossless randomly birefringent telecom
optical fiber may lead to the attraction an initially polarization scrambled
signal towards wave with a well-defined state of polarization at the fiber
output. By exploiting exact analytical solutions of the nonlinear polarization
coupling process we carry out a linear stability study which reveals that
temporally stable stationary solutions are only obtained whenever the output
signal polarization is nearly orthogonal to the input pump polarization.
Moreover, we predict that polarization attraction is acting in full strength
whenever equally intense signal and pump waves are used
Fast Algorithm for N-2 Contingency Problem
We present a novel selection algorithm for N-2 contingency analysis problem.
The algorithm is based on the iterative bounding of line outage distribution
factors and successive pruning of the set of contingency pair candidates. The
selection procedure is non-heuristic, and is certified to identify all events
that lead to thermal constraints violations in DC approximation. The complexity
of the algorithm is O(N^2) comparable to the complexity of N-1 contingency
problem. We validate and test the algorithm on the Polish grid network with
around 3000 lines. For this test case two iterations of the pruning procedure
reduce the total number of candidate pairs by a factor of almost 1000 from 5
millions line pairs to only 6128.Comment: HICC
Recent Advances in Computational Methods for the Power Flow Equations
The power flow equations are at the core of most of the computations for
designing and operating electric power systems. The power flow equations are a
system of multivariate nonlinear equations which relate the power injections
and voltages in a power system. A plethora of methods have been devised to
solve these equations, starting from Newton-based methods to homotopy
continuation and other optimization-based methods. While many of these methods
often efficiently find a high-voltage, stable solution due to its large basin
of attraction, most of the methods struggle to find low-voltage solutions which
play significant role in certain stability-related computations. While we do
not claim to have exhausted the existing literature on all related methods,
this tutorial paper introduces some of the recent advances in methods for
solving power flow equations to the wider power systems community as well as
bringing attention from the computational mathematics and optimization
communities to the power systems problems. After briefly reviewing some of the
traditional computational methods used to solve the power flow equations, we
focus on three emerging methods: the numerical polynomial homotopy continuation
method, Groebner basis techniques, and moment/sum-of-squares relaxations using
semidefinite programming. In passing, we also emphasize the importance of an
upper bound on the number of solutions of the power flow equations and review
the current status of research in this direction.Comment: 13 pages, 2 figures. Submitted to the Tutorial Session at IEEE 2016
American Control Conferenc
Dynamics of wrinkles on a vesicle in external flow
Recent experiments by Kantsler et. al. (2007) have shown that the
relaxational dynamics of a vesicle in external elongation flow is accompanied
by the formation of wrinkles on a membrane. Motivated by these experiments we
present a theory describing the dynamics of a wrinkled membrane. Formation of
wrinkles is related to the dynamical instability induced by negative surface
tension of the membrane. For quasi-spherical vesicles we perform analytical
study of the wrinkle structure dynamics. We derive the expression for the
instability threshold and identify three stages of the dynamics. The scaling
laws for the temporal evolution of wrinkling wavelength and surface tension are
established and confirmed numerically.Comment: 4 pages, 2 figure
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