15,203 research outputs found
Variational formulation of hybrid problems for fully 3-D transonic flow with shocks in rotor
Based on previous research, the unified variable domain variational theory of hybrid problems for rotor flow is extended to fully 3-D transonic rotor flow with shocks, unifying and generalizing the direct and inverse problems. Three variational principles (VP) families were established. All unknown boundaries and flow discontinuities (such as shocks, free trailing vortex sheets) are successfully handled via functional variations with variable domain, converting almost all boundary and interface conditions, including the Rankine Hugoniot shock relations, into natural ones. This theory provides a series of novel ways for blade design or modification and a rigorous theoretical basis for finite element applications and also constitutes an important part of the optimal design theory of rotor bladings. Numerical solutions to subsonic flow by finite elements with self-adapting nodes given in Refs., show good agreement with experimental results
Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances
Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears
The mean curvature flow for isoparametric submanifolds
A submanifold in space forms is isoparametric if the normal bundle is flat
and principal curvatures along any parallel normal fields are constant. We
study the mean curvature flow with initial data an isoparametric submanifold in
Euclidean space and sphere. We show that the mean curvature flow preserves the
isoparametric condition, develops singularities in finite time, and converges
in finite time to a smooth submanifold of lower dimension. We also give a
precise description of the collapsing.Comment: 24 pages, PDF fil
SRB Measures for A Class of Partially Hyperbolic Attractors in Hilbert spaces
In this paper, we study the existence of SRB measures and their properties
for infinite dimensional dynamical systems in a Hilbert space. We show several
results including (i) if the system has a partially hyperbolic attractor with
nontrivial finite dimensional unstable directions, then it has at least one SRB
measure; (ii) if the attractor is uniformly hyperbolic and the system is
topological mixing and the splitting is H\"older continuous, then there exists
a unique SRB measure which is mixing; (iii) if the attractor is uniformly
hyperbolic and the system is non-wondering and and the splitting is H\"older
continuous, then there exists at most finitely many SRB measures; (iv) for a
given hyperbolic measure, there exist at most countably many ergodic components
whose basin contains an observable set
Existence of SRB Measures for A Class of Partially Hyperbolic Attractors in Banach spaces
In this paper, we study the existence of SRB measures for infinite
dimensional dynamical systems in a Banach space. We show that if the system has
a partially hyperbolic attractor with nontrivial finite dimensional unstable
directions, then it has an SRB measure.Comment: arXiv admin note: text overlap with arXiv:1508.0330
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