91 research outputs found
Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
A quantum version of transition state theory based on a quantum normal form
(QNF) expansion about a saddle-centre-...-centre equilibrium point is
presented. A general algorithm is provided which allows one to explictly
compute QNF to any desired order. This leads to an efficient procedure to
compute quantum reaction rates and the associated Gamov-Siegert resonances. In
the classical limit the QNF reduces to the classical normal form which leads to
the recently developed phase space realisation of Wigner's transition state
theory. It is shown that the phase space structures that govern the classical
reaction d ynamicsform a skeleton for the quantum scattering and resonance
wavefunctions which can also be computed from the QNF. Several examples are
worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008)
R1-R11
Nonlinear Evolution Problems
In this workshop three types of nonlinear evolution problems— geometric evolution equations (essentially of parabolic type), nonlinear hyperbolic equations, and dispersive equations— were the subject of 22 talks
Applications of Asymptotic Analysis
This workshop focused on asymptotic analysis and its fundamental role in the derivation and understanding of the nonlinear structure of mathematical models in various fields of applications, its impact on the development of new numerical methods and on other fields of applied mathematics such as shape optimization. This was complemented by a review as well as the presentation of some of the latest developments of singular perturbation methods
Homogenization and norm resolvent convergence for elliptic operators in a strip perforated along a curve
We consider an infinite planar straight strip perforated by small holes along
a curve. In such domain, we consider a general second order elliptic operator
subject to classical boundary conditions on the holes. Assuming that the
perforation is non-periodic and satisfies rather weak assumptions, we describe
all possible homogenized problems. Our main result is the norm resolvent
convergence of the perturbed operator to a homogenized one in various operator
norms and the estimates for the rate of convergence. On the basis of the norm
resolvent convergence, we prove the convergence of the spectrum
Challenges in Optimal Control of Nonlinear PDE-Systems
The workshop focussed on various aspects of optimal control problems for systems of nonlinear partial differential equations. In particular, discussions around keynote presentations in the areas of optimal control of nonlinear/non-smooth systems, optimal control of systems involving nonlocal operators, shape and topology optimization, feedback control and stabilization, sparse control, and associated numerical analysis as well as design and analysis of solution algorithms were promoted. Moreover, also aspects of control of fluid structure interaction problems as well as problems arising in the optimal control of quantum systems were considered
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