1660
2008
deu
preprint
1
20080430


Complete monotone coupling for Markov processes
We formalize and analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuoustime, taking values in a finite partially ordered set. Similarly to what happens in discretetime, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuoustime but not in discretetime.
urn:nbn:de:kobv:517opus18286
1828
SI 990

Keine Nutzungslizenz vergeben  es gilt das deutsche Urheberrecht
Paolo Dai Pra
PierreYves Louis
Ida G. Minelli
Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint
2008, 01
eng
uncontrolled
Markov processes
eng
uncontrolled
coupling
eng
uncontrolled
partial ordering
eng
uncontrolled
monotonicity conditions
eng
uncontrolled
monotone random
eng
uncontrolled
dynamical system representation
Mathematik
open_access
Institut für Mathematik
Extern
Universität Potsdam
https://publishup.unipotsdam.de/files/1660/Preprint_2008_01.pdf
612
2006
eng
preprint
1
20060407


Infinite system of Brownian balls : equilibrium measures are canonical Gibbs
We consider a system of infinitely many hard balls in R<sup>d undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinitedimensional stochastic differential equation with a local time term. We prove that the set of all equilibrium measures, solution of a detailed balance equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.
urn:nbn:de:kobv:517opus6720
672
Stochastics and Dynamics.  6 (2006), 1, S. 97  122
<hr>AMS Classifications: 60H10 , 60J60 , 60K35<br><br>published at Stochastics and Dynamics.  6 (2006), 1, S. 97  122<br><a href="http://dx.doi.org/10.1142/S0219493706001669" target=_blanc>doi: 10.1142/S0219493706001669</a>
Sylvie Roelly
Myriam Fradon
eng
uncontrolled
Stochastic Differential Equation
eng
uncontrolled
hard core potential
eng
uncontrolled
Canonical Gibbs measure
eng
uncontrolled
detailed balance equation
eng
uncontrolled
reversible measure
Mathematik
open_access
Institut für Mathematik
Extern
Universität Potsdam
https://publishup.unipotsdam.de/files/612/roelly_fradon.pdf
1370
1999
eng
preprint
1
20070815


Heteroclinic behavior in rotating RayleighBénard convection
We investigate numerically the appearance of heteroclinic behavior in a threedimensional, buoyancydriven fluid layer with stressfree top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewedvaricose instability leads from stationary rolls to a stationary mixedmode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewedvaricose or mixedmode type and in some parameter regions skewedvaricose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle.
urn:nbn:de:kobv:517opus14914
1491

Ayhan Demircan
Stefan Scheel
Norbert Seehafer
NLD Preprints
paper 055
Physik
Buoyancydriven instabilities (e.g., RayleighBenard)
Nonlinearity, bifurcation, and symmetry breaking
Vortex dynamics; rotating fluids (for vortices in superfluid helium, see 67.25.dk and 67.30.he)
open_access
Institut für Physik und Astronomie
Interdisziplinäres Zentrum für Dynamik komplexer Systeme
Extern
Universität Potsdam
https://publishup.unipotsdam.de/files/1370/nld_preprint_55_demircan_etal.pdf
1371
1999
eng
preprint
1
20070815


Bifurcation analysis of the plane sheet pinch
A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the twodimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a timeasymptotic steady state, which proves to be sensitive to threedimensional perturbations even close to the point where the primary instability sets in. A comprehensive threedimensional stability analysis of the twodimensional steady tearingmode state is performed by varying parameters of the sheet pinch. The instability with respect to threedimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a threedimensional steady state.
urn:nbn:de:kobv:517opus14926
1492

Jörg Schumacher
Norbert Seehafer
NLD Preprints
paper 056
Physik
open_access
Institut für Physik und Astronomie
Interdisziplinäres Zentrum für Dynamik komplexer Systeme
Extern
Universität Potsdam
https://publishup.unipotsdam.de/files/1371/nld_preprint_56_schumacher_seehafer.pdf
1238
1995
eng
preprint
1
20070601


Detection of hidden resonances in Saturn's Bring
The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The Bring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the Fring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.
urn:nbn:de:kobv:517opus13618
1361

KaiUwe Thiessenhusen
Larry W. Esposito
Jürgen Kurths
Frank Spahn
NLD Preprints
paper 013
eng
uncontrolled
Planetary Rings
Physik
open_access
Institut für Physik und Astronomie
Interdisziplinäres Zentrum für Dynamik komplexer Systeme
Extern
Universität Potsdam
https://publishup.unipotsdam.de/files/1238/preprint_thiessenhusen_etal.pdf
1226
1994
eng
preprint
1
20070518


On the validity of a model for the reversals of the Earth‘s magnetic field
We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of wellknown characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.
urn:nbn:de:kobv:517opus13460
1346

Annette Witt
Jürgen Kurths
F. Krause
K. Fischer
NLD Preprints
paper 004
Physik
open_access
Institut für Physik und Astronomie
Interdisziplinäres Zentrum für Dynamik komplexer Systeme
Extern
Universität Potsdam
https://publishup.unipotsdam.de/files/1226/preprint_witt_etal.pdf
1227
1994
eng
preprint
1
20070518


Quantitative analysis of heart rate variability
In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, noninvasive diagnostic tools like Holtermonitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.
urn:nbn:de:kobv:517opus13470
1347

Jürgen Kurths
A. Voss
Annette Witt
P. Saparin
H. J. Kleiner
N. Wessel
NLD Preprints
paper 005
Physik
open_access
Institut für Physik und Astronomie
Interdisziplinäres Zentrum für Dynamik komplexer Systeme
Extern
Universität Potsdam
https://publishup.unipotsdam.de/files/1227/preprint_kurths_etal.pdf