81 research outputs found
Dynamical modelling of superstatistical complex systems
We show how to construct the optimum superstatistical dynamical model for a
given experimentally measured time series. For this purpose we generalise the
superstatistics concept and study a Langevin equation with a memory kernel
whose parameters fluctuate on a large time scale. It is shown how to construct
a synthetic dynamical model with the same invariant density and correlation
function as the experimental data. As a main example we apply our method to
velocity time series measured in high-Reynolds number turbulent Taylor-Couette
flow, but the method can be applied to many other complex systems in a similar
way.Comment: 11 pages, 4 figure
Transition records of stationary Markov chains
In any Markov chain with finite state space the distribution of transition
records always belongs to the exponential family. This observation is used to
prove a fluctuation theorem, and to show that the dynamical entropy of a
stationary Markov chain is linear in the number of steps. Three applications
are discussed. A known result about entropy production is reproduced. A
thermodynamic relation is derived for equilibrium systems with Metropolis
dynamics. Finally, a link is made with recent results concerning a
one-dimensional polymer model.Comment: corrected error in the definition of the entropy production variable
and in the proof of the fluctuation theore
Skewed superstatistical distributions from a Langevin and Fokker-Planck approach
The superstatistics concept is a useful statistical method to describe
inhomogeneous complex systems for which a system parameter fluctuates
on a large spatio-temporal scale. In this paper we analyze a measured time
series of wind speed fluctuations and extract the superstatistical distribution
function directly from the data. We construct suitable Langevin and
Fokker-Planck models with a position dependent -field and show that they
reduce to standard type of superstatistics in the overdamped limit.Comment: 7 pages, 6 figure
Maximum entropy estimation of transition probabilities of reversible Markov chains
In this paper, we develop a general theory for the estimation of the
transition probabilities of reversible Markov chains using the maximum entropy
principle. A broad range of physical models can be studied within this
approach. We use one-dimensional classical spin systems to illustrate the
theoretical ideas. The examples studied in this paper are: the Ising model, the
Potts model and the Blume-Emery-Griffiths model
The 3-dimensional random walk with applications to overstretched DNA and the protein titin
We study the three-dimensional persistent random walk with drift. Then we
develop a thermodynamic model that is based on this random walk without
assuming the Boltzmann-Gibbs form for the equilibrium distribution. The
simplicity of the model allows us to perform all calculations in closed form.
We show that, despite its simplicity, the model can be used to describe
different polymer stretching experiments. We study the reversible
overstretching transition of DNA and the static force-extension relation of the
protein titin.Comment: 9 pages, 10 figure
The quantum double well anharmonic oscillator in an external field
The aim of this paper is twofold. First of all, we study the behaviour of the
lowest eigenvalues of the quantum anharmonic oscillator under influence of an
external field. We try to understand this behaviour using perturbation theory
and compare the results with numerical calculations. This brings us to the
second aim of selecting the best method to carry out the numerical calculations
accurately.Comment: 9 pages, 6 figure
Praomys degraaffi, a new species of Muridae (Mammalia) from central Africa
A new Praomys species from Burundi, Rwanda and Uganda, Praomys degraaffi n. sp., is described in the P. jacksoni species-complex. It occurs at high elevations in montane forests of the Albertine Rift. The new species is compared with P. jacksoni from the same region and with the other species in the P. jacksoni species-complex
A one-dimensional model for theoretical analysis of single molecule experiments
In this paper we compare two polymer stretching experiments. The outcome of
both experiments is a force-extension relation. We use a one-dimensional model
to show that in general the two quantities are not equal. In certain limits,
however, both force-extension relations coincide.Comment: 11 pages, 5 figure
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