33,937 research outputs found
Unique continuation property with partial information for two-dimensional anisotropic elasticity systems
In this paper, we establish a novel unique continuation property for
two-dimensional anisotropic elasticity systems with partial information. More
precisely, given a homogeneous elasticity system in a domain, we investigate
the unique continuation by assuming only the vanishing of one component of the
solution in a subdomain. Using the corresponding Riemann function, we prove
that the solution vanishes in the whole domain provided that the other
component vanishes at one point up to its second derivatives. Further, we
construct several examples showing the possibility of further reducing the
additional information of the other component. This result possesses remarkable
significance in both theoretical and practical aspects because the required
data is almost halved for the unique determination of the whole solution.Comment: 14 pages, 1 figur
The finite element method in low speed aerodynamics
The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics
Finite element analysis of low speed viscous and inviscid aerodynamic flows
A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
Real-time dynamics in a quantum many-body system are inherently complicated
and hence difficult to predict. There are, however, a special set of systems
where these dynamics are theoretically tractable: integrable models. Such
models possess non-trivial conserved quantities beyond energy and momentum.
These quantities are believed to control dynamics and thermalization in low
dimensional atomic gases as well as in quantum spin chains. But what happens
when the special symmetries leading to the existence of the extra conserved
quantities are broken? Is there any memory of the quantities if the breaking is
weak? Here, in the presence of weak integrability breaking, we show that it is
possible to construct residual quasi-conserved quantities, so providing a
quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We
demonstrate this construction explicitly in the context of quantum quenches in
one-dimensional Bose gases and argue that these quasi-conserved quantities can
be probed experimentally.Comment: 21 pages with appendices; 13 figures; version accepted by PR
Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
In this chapter, we mainly review theoretical results on inverse source
problems for diffusion equations with the Caputo time-fractional derivatives of
order . Our survey covers the following types of inverse
problems: 1. determination of time-dependent functions in interior source terms
2. determination of space-dependent functions in interior source terms 3.
determination of time-dependent functions appearing in boundary condition
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