3,371 research outputs found
Stability of Attached Transonic Shocks in Steady Potential Flow past Three-Dimensional Wedges
We develop a new approach and employ it to establish the global existence and
nonlinear structural stability of attached weak transonic shocks in steady
potential flow past three-dimensional wedges; in particular, the restriction
that the perturbation is away from the wedge edge in the previous results is
removed. One of the key ingredients is to identify a "good" direction of the
boundary operator of a boundary condition of the shock along the wedge edge,
based on the non-obliqueness of the boundary condition for the weak shock on
the edge. With the identification of this direction, an additional boundary
condition on the wedge edge can be assigned to make sure that the shock is
attached on the edge and linearly stable under small perturbation. Based on the
linear stability, we introduce an iteration scheme and prove that there exists
a unique fixed point of the iteration scheme, which leads to the global
existence and nonlinear structural stability of the attached weak transonic
shock. This approach is based on neither the hodograph transformation nor the
spectrum analysis, and should be useful for other problems with similar
difficulties.Comment: 28 Pages; 2 figure
Transonic Flows with Shocks Past Curved Wedges for the Full Euler Equations
We establish the existence, stability, and asymptotic behavior of transonic
flows with a transonic shock past a curved wedge for the steady full Euler
equations in an important physical regime, which form a nonlinear system of
mixed-composite hyperbolic-elliptic type. To achieve this, we first employ the
coordinate transformation of Euler-Lagrange type and then exploit one of the
new equations to identify a potential function in Lagrangian coordinates. By
capturing the conservation properties of the Euler system, we derive a single
second-order nonlinear elliptic equation for the potential function in the
subsonic region so that the transonic shock problem is reformulated as a
one-phase free boundary problem for a second-order nonlinear elliptic equation
with the shock-front as a free boundary. One of the advantages of this approach
is that, given the shock location or quivalently the entropy function along the
shock-front downstream, all the physical variables can expressed as functions
of the gradient of the potential function, and the downstream asymptotic
behavior of the potential function at the infinite exit can be uniquely
determined with uniform decay rate.
To solve the free boundary problem, we employ the hodograph transformation to
transfer the free boundary to a fixed boundary, while keeping the ellipticity
of the second-order equations, and then update the entropy function to prove
that it has a fixed point. Another advantage in our analysis here is in the
context of the real full Euler equations so that the solutions do not
necessarily obey Bernoulli's law with a uniform Bernoulli constant, that is,
the Bernoulli constant is allowed to change for different fluid trajectories.Comment: 35 pages, 2 figures in Discrete and Continuous Dynamical Systems, 36
(2016
Multimodal estimation of distribution algorithms
Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima
Multi-epoch, multi-frequency VLBI study of the parsec-scale jet in the blazar 3C 66A
We present the observational results of the Gamma-ray blazar, 3C 66A, at 2.3,
8.4, and 22 GHz at 4 epochs during 2004-05 with the VLBA. The resulting images
show an overall core-jet structure extending roughly to the south with two
intermediate breaks occurring in the region near the core. By model-fitting to
the visibility data, the northmost component, which is also the brightest, is
identified as the core according to its relatively flat spectrum and its
compactness. As combined with some previous results to investigate the proper
motions of the jet components, it is found the kinematics of 3C 66A is quite
complicated with components of inward and outward, subluminal and superluminal
motions all detected in the radio structure. The superluminal motions indicate
strong Doppler boosting exists in the jet. The apparent inward motions of the
innermost components last for at least 10 years and could not be caused by
new-born components. The possible reason could be non-stationarity of the core
due to opacity change.Comment: 24 pages, 4 figure
An hourglass model for the flare of HST-1 in M87
To explain the multi-wavelength light curves (from radio to X-ray) of HST-1
in the M87 jet, we propose an hourglass model that is a modified two-zone
system of Tavecchio & Ghisellini (hereafter TG08): a slow hourglass-shaped or
Laval nozzle-shaped layer connected by two revolving exponential surfaces
surrounding a fast spine, through which plasma blobs flow. Based on the
conservation of magnetic flux, the magnetic field changes along the axis of the
hourglass. We adopt the result of TG08---the high-energy emission from GeV to
TeV can be produced through inverse Compton by the two-zone system, and the
photons from radio to X-ray are mainly radiated by the fast inner zone system.
Here, we only discuss the light curves of the fast inner blob from radio to
X-ray. When a compressible blob travels down the axis of the first bulb in the
hourglass, because of magnetic flux conservation, its cross section experiences
an adiabatic compression process, which results in particle acceleration and
the brightening of HST-1. When the blob moves into the second bulb of the
hourglass, because of magnetic flux conservation, the dimming of the knot
occurs along with an adiabatic expansion of its cross section. A similar broken
exponential function could fit the TeV peaks in M87, which may imply a
correlation between the TeV flares of M87 and the light curves from radio to
X-ray in HST-1. The Very Large Array (VLA) 22 GHz radio light curve of HST-1
verifies our prediction based on the model fit to the main peak of the VLA 15
GHz radio light curve.Comment: 14 pages, 2 figures, accepted for publication in A
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