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Erik Van der Straeten

Publications and source records attributed to Erik Van der Straeten.

15 recordsLinked to original sources
arXiv2011

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.

cond-mat.stat-mech↗
arXiv2010

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 $β$ 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 $f(β)$ directly from the data. We construct suitable Langevin and Fokker-Planck models with a position dependent $β$-field and show that they reduce to standard type of superstatistics in the overdamped limit.

cond-mat.stat-mech↗
arXiv2010

Brownian motion with dry friction: Fokker-Planck approach

We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain both the time-dependent propagator of this equation and the velocity correlation function by solving the associated time-dependent Fokker-Planck equation. Exact results are found for the case where only dry friction acts on the particle. For the case where both dry and viscous friction forces are present, series representations of the propagator and correlation function are obtained in terms of parabolic cylinder functions. Similar series representations are also obtained for the case where an external constant force is added to the Langevin equation.

cond-mat.stat-mech↗
arXiv2009

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.

cond-mat.stat-mech↗
arXiv2009

Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence

We report a general technique to study a given experimental time series with superstatistics. Crucial for the applicability of the superstatistics concept is the existence of a parameter $β$ that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration. The proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions. We test the method thoroughly with surrogate data sets. Then the applicability of the superstatistical approach is illustrated using real experimental data. We study two examples, velocity time series measured in turbulent Taylor-Couette flows and time series of log returns of the closing prices of some stock market indices.

physics.data-an↗
arXiv2008

Superstatistical distributions from a maximum entropy principle

We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter $β$ of a superstatistical system, given certain constraints on the complex system under consideration. We apply the theory to three examples: The superstatistical quantum mechanical harmonic oscillator, the superstatistical classical ideal gas, and velocity time series as measured in a turbulent Taylor-Couette flow.

cond-mat.stat-mech↗
arXiv2008

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.

quant-ph↗
arXiv2008

Grand canonical ensemble in generalized thermostatistics

We study the grand-canonical ensemble with a fluctuating number of degrees of freedom in the context of generalized thermostatistics. Several choices of grand-canonical entropy functional are considered. The ideal gas is taken as an example.

cond-mat.stat-mech↗
arXiv2008

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.

cond-mat.stat-mech↗
arXiv2008

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.

cond-mat.stat-mech↗
arXiv2008

Residual entropy in a model for the unfolding of single polymer chains

We study the unfolding of a single polymer chain due to an external force. We use a simplified model which allows to perform all calculations in closed form without assuming a Boltzmann-Gibbs form for the equilibrium distribution. Temperature is then defined by calculating the Legendre transform of the entropy under certain constraints. The application of the model is limited to flexible polymers. It exhibits a gradual transition from compact globule to rod. The boundary line between these two phases shows reentrant behavior. This behavior is explained by the presence of residual entropy.

cond-mat.stat-mech↗
arXiv2006

The globule-coil transition in a mean field approach

In this paper we study the unfolding transition observed in polymer stretching experiments. We use a known model and extend it with a mean-field-like interaction. Expressions for all necessary thermodynamic variables as a function of the model parameters are derived in closed form. To obtain the exact force-extension relation at constant temperature, we invert these relations numerically. Below a critical temperature the model exhibits a sharp first order phase transition.

cond-mat.stat-mech↗
arXiv2006

A generalized quantum microcanonical ensemble

We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum entropy argument to resolve the lack of knowledge about initial conditions. As a result, statistical averages of linear observables coincide with values obtained in the canonical ensemble. Non-canonical averages can be obtained by taking into account conserved quantities which are non-linear functions of the microstate.

quant-ph↗
arXiv2006

A two-parameter random walk with approximate exponential probability distribution

We study a non-Markovian random walk in dimension 1. It depends on two parameters eps_r and eps_l, the probabilities to go straight on when walking to the right, respectively to the left. The position x of the walk after n steps and the number of reversals of direction k are used to estimate eps_r and eps_l. We calculate the joint probability distribution p_n(x,k) in closed form and show that, approximately, it belongs to the exponential family.

math-ph↗