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41.
Optimal explicit Runge–Kutta methods consider more stages in order to include a particular spectrum in their stability domain
and thus reduce time-step restrictions. This idea, so far used mostly for real-line spectra, is generalized to more general
spectra in the form of a thin region. In thin regions the eigenvalues may extend away from the real axis into the imaginary
plane. We give a direct characterization of optimal stability polynomials containing a maximal thin region and calculate these
polynomials for various cases. Semi-discretizations of hyperbolic–parabolic equations are a relevant application which exhibit
a thin region spectrum. As a model, linear, scalar advection–diffusion is investigated. The second-order-stabilized explicit
Runge–Kutta methods derived from the stability polynomials are applied to advection–diffusion and compressible, viscous fluid
dynamics in numerical experiments. Due to the stabilization the time step can be controlled solely from the hyperbolic CFL
condition even in the presence of viscous fluxes. 相似文献
42.
Marco Merkli 《Journal of Mathematical Analysis and Applications》2007,327(1):376-399
Level shift operators describe the second-order displacement of eigenvalues under perturbation. They play a central role in resonance theory and ergodic theory of open quantum systems at positive temperatures. We exhibit intrinsic properties of level shift operators, properties which stem from the structure of open quantum systems at positive temperatures and which are common to all such systems. They determine the geometry of resonances bifurcating from eigenvalues of positive temperature Hamiltonians and they relate the Gibbs state, the kernel of level shift operators, and zero energy resonances. We show that degeneracy of energy levels of the small part of the open quantum system causes the Fermi Golden Rule Condition to be violated and we analyze ergodic properties of such systems. 相似文献
43.
In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras. 相似文献
44.
We study the asymptotic behaviour of non-negative solutions of Yamabe type equations on a complete Riemannian manifold. Then we provide a comparison result, based on a form of the weak maximum principle at infinity, which together with the “a priori” estimates previously obtained, yields uniqueness under very general Ricci assumptions. The paper ends with an existence result and an application to the non-compact Yamabe problem. 相似文献
45.
Automatic detection and identification of shocks in Gaussian state‐space models: a Bayesian approach
An automatic monitoring and intervention algorithm that permits the supervision of very general aspects in an univariate linear Gaussian state–space model is proposed. The algorithm makes use of a model comparison and selection approach within a Bayesian framework. In addition, this algorithm incorporates the possibility of eliminating earlier interventions when subsequent evidence against them comes to light. Finally, the procedure is illustrated with two empirical examples taken from the literature. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
46.
We derive the Kramers equation, namely, the Fokker-Planck equation for an oscillator, from a completely deterministic picture. The oscillator is coupled to a “booster”, i.e., a deterministic system in a fully chaotic state, wherein diffusion is derived from the sensitive dependence of chaos on initial conditions and friction is a consequence of the linear response of the booster to the action exerted on it by the oscillator. To deal with the Hamiltonian nature of the system of interest and of its coupling to the booster, we extend the earlier theoretical derivation of macroscopic transport coefficients from deterministic dynamics. We show that the frequency of the oscillator can be tuned to the microscopic frequencies of the booster without affecting the canonical nature of the “macroscopic” statistics. The theoretical predictions are supported by numerical simulations. 相似文献
47.
48.
We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic
reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized
by two numbers, T
1 and T
2 (‘reservoir temperatures’). If T
1 ≠ T
2, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat
fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with
an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T
1 and T
2, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T
1,T
2) > g
2 + α, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions.
Submitted: March 20, 2006. Revised: March 19, 2007. Accepted: May 11, 2007.
Marco Merkli: Partly supported by an NSERC PDF, the Institute of Theoretical Physics of ETH Zürich, Switzerland, the Departments
of Mathematics of McGill University and the University of Toronto, Canada.
Matthias Mück: Supported by DAAD under grant HSP III.
Israel Michael Sigal: Supported by NSERC under grant NA7901. 相似文献
49.
Manuel Fernández-López Eduardo García-Río Demir N. Kupeli 《Annals of Global Analysis and Geometry》2002,21(1):1-13
A characterization of time functions on a spacetime is made by using theMöbius equation. It is shown that a time function characterized in this wayyields past timelike geodesic incompleteness and local Lorentzian warpedproduct decomposition of spacetime, provided that the stress-energy tensoris a fluid. Also, by imposing additional assumptions on the stress-energytensor and global analytic structure of the spacetime, more restrictivedecompositions closer to Robertson–Walker spacetimes are obtained. 相似文献
50.
Summary Differential scanning calorimetric measurements in the early stage of isothermal crystal growth of polyethylene oxide are
analysed in the light of irreversible thermodynamics. An accurate evaluation of the equilibrium melting temperature is done
by fitting the thermograms obtained at different undercoolings and referring to the activation energy values already known
from the literature.
Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994. 相似文献