1,468 research outputs found
Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions
We establish the stability under the formations of infimum and of convex
combinations of subsolutions of convex Hamilton-Jacobi equations, some
comparison and existence results for convex and coercive Hamilton-Jacobi
equations with the Neumann type boundary condition as well as existence results
for the Skorokhod problem. We define the Aubry-Mather set associated with the
Neumann type boundary problem and establish some properties of the Aubry-Mather
set including the existence results for the ``calibrated'' extremals for the
corresponding action functional (or variational problem).Comment: 39 pages, 1 figur
Arnold diffusion in the dynamics of a 4-machine power system undergoing a large fault
We focus on the seemingly complicated dynamics of a four-machine power system which is undergoing a sudden fault. Adopting a Hamiltonian (energy) formulation, we consider the system as an interconnection of (one degree of freedom) subsystems. Under certain configuration (a star network) and parameter values we establish the presence of Arnold diffusion which entails periodic, almost periodic, and complicated nonperiodic dyanmics all simultaneously present; and erratic transfer of energies between the subsystems. In section 1 we introduce the transient stability problem in a mathematical setting and explain what our results mean in the power systems context. Section 2 provides insights into Arnold diffusion and summarizes its mathematical formulation as in [8], [1]. Section 3 gives conditions for which Arnold diffusion arises on certain energy levels of the swing equations. These conditions are verified analytically in the case when all but one subsystem (machine) undergo relatively small oscillations
A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems
In this paper we introduce a new kind of Lax-Oleinik type operator with
parameters associated with positive definite Lagrangian systems for both the
time-periodic case and the time-independent case. On one hand, the new family
of Lax-Oleinik type operators with an arbitrary as
initial condition converges to a backward weak KAM solution in the
time-periodic case, while it was shown by Fathi and Mather that there is no
such convergence of the Lax-Oleinik semigroup. On the other hand, the new
family of Lax-Oleinik type operators with an arbitrary
as initial condition converges to a backward weak KAM solution faster than the
Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some
reference
A Requirement Model Of UUM Alumni Online Job Application
A web-based online job application has become the most useful tool to access the information about the applicant, and the applicant information is accessible at the press of
a button immediately. Graduates need to work hard to get jobs that may require cost and time. Thus this study proposal to model requirement of UUM Alumni Online Jobs that provide a flexible way to access jobs. The requirement model for the alumni students would provides the alumni with the capability to input, search and receive information of jobs via the online services
Weak KAM for commuting Hamiltonians
For two commuting Tonelli Hamiltonians, we recover the commutation of the
Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct
geometrical method (Stoke's theorem). We also obtain a "generalization" of a
theorem of Maderna ([Mad02]). More precisely, we prove that if the phase space
is the cotangent of a compact manifold then the weak KAM solutions (or
viscosity solutions of the critical stationary Hamilton-Jacobi equation) for G
and for H are the same. As a corrolary we obtain the equality of the Aubry
sets, of the Peierls barrier and of flat parts of Mather's functions.
This is also related to works of Sorrentino ([Sor09]) and Bernard ([Ber07b]).Comment: 23 pages, accepted for publication in NonLinearity (january 29th
2010). Minor corrections, fifth part added on Mather's function (or
effective Hamiltonian
The ratio of pattern speeds in double-barred galaxies
We have obtained two-dimensional velocity fields in the ionized gas of a set
of 8 double-barred galaxies, at high spatial and spectral resolution, using
their H emission fields measured with a scanning Fabry-Perot
spectrometer. Using the technique by which phase reversals in the non-circular
motion indicate a radius of corotation, taking advantage of the high angular
and velocity resolution we have obtained the corotation radii and the pattern
speeds of both the major bar and the small central bar in each of the galaxies;
there are few such measurements in the literature. Our results show that the
inner bar rotates more rapidly than the outer bar by a factor between 3.3 and
3.6.Comment: 5 pages, 1 figure, 1 tabl
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