35,035 research outputs found
Group analysis and renormgroup symmetries
An original regular approach to constructing special type symmetries for
boundary value problems, namely renormgroup symmetries, is presented. Different
methods of calculating these symmetries, based on modern group analysis are
described. Application of the approach to boundary value problems is
demonstrated with the help of a simple mathematical model.Comment: 17 pages, RevTeX LATeX file, to appear in Journal of Mathematical
Physic
On the use of finite fault solution for tsunami generation problems
The present study is devoted to the problem of tsunami wave generation. The
main goal of this work is two-fold. First of all, we propose a simple and
computationally inexpensive model for the description of the sea bed
displacement during an underwater earthquake, based on the finite fault
solution for the slip distribution under some assumptions on the dynamics of
the rupturing process. Once the bottom motion is reconstructed, we study waves
induced on the free surface of the ocean. For this purpose we consider three
different models approximating the Euler equations of the water wave theory.
Namely, we use the linearized Euler equations (we are in fact solving the
Cauchy-Poisson problem), a Boussinesq system and a novel weakly nonlinear
model. An intercomparison of these approaches is performed. The developments of
the present study are illustrated on the 17 July 2006 Java event, where an
underwater earthquake of magnitude 7.7 generated a tsunami that inundated the
southern coast of Java.Comment: 31 pages, 10 figures, 3 tables. Other author's papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
Synthesizing SystemC Code from Delay Hybrid CSP
Delay is omnipresent in modern control systems, which can prompt oscillations
and may cause deterioration of control performance, invalidate both stability
and safety properties. This implies that safety or stability certificates
obtained on idealized, delay-free models of systems prone to delayed coupling
may be erratic, and further the incorrectness of the executable code generated
from these models. However, automated methods for system verification and code
generation that ought to address models of system dynamics reflecting delays
have not been paid enough attention yet in the computer science community. In
our previous work, on one hand, we investigated the verification of delay
dynamical and hybrid systems; on the other hand, we also addressed how to
synthesize SystemC code from a verified hybrid system modelled by Hybrid CSP
(HCSP) without delay. In this paper, we give a first attempt to synthesize
SystemC code from a verified delay hybrid system modelled by Delay HCSP
(dHCSP), which is an extension of HCSP by replacing ordinary differential
equations (ODEs) with delay differential equations (DDEs). We implement a tool
to support the automatic translation from dHCSP to SystemC
- …