arXiv subjects

Werner Ebeling

Publications and source records attributed to Werner Ebeling.

At least 19 recordsLinked to original sources

arXiv2026

The virial expansion of the Hydrogen equation of state in comparison to PIMC simulations: the quasiparticle concept, IPD, and ionization degree

The properties of plasmas in the low-density limit are described by virial expansions. Analytical expressions are known for the lowest virial coefficients from Green's function approaches.Recently, accurate path-integral Monte Carlo simulations were performed for the hydrogen plasma at low densities by Filinov and Bonitz [Phys. Rev. E 108 (2023)055212], which made a comparison of the virial expansions and the derivation of interpolation formulas possible. The exact expression for the second virial coefficient is used to test the accuracy of the PIMC simulations and the range of application of the virial expansions.To describe plasmas in a wider range of density and temperature, the concept of quasiparticles is considered. Medium modifications of free and bound states are obtained from the spectral function. Mean-field effects are presented, such as exchange terms, Pauli blocking and screening. The density expansions of the quasiparticle shifts is considered. The combination of PIMC simulations with benchmarks from exact virial expansion results allows us to obtain precise results for the EoS in the low-density range. At low densities, the results are compared with the Saha equation to introduce the medium-dependent ionization potential. The relation to the Beth-Uhlenbeck formula and concepts such as the Mott effect, ionization potential depression (IPD), and ionization degree are discussed. The limits of current PIMC results for hydrogen plasmas are shown. Further improvements of the PIMC simulations are required to compare with analytical benchmarks.

physics.plasm-ph↗

arXiv2014

Modellierungskonzepte der Synergetik und der Theorie der Selbstorganisation

Mnay models situated in the current research landscape of modelling and simulating social processes have roots in physics. This is visible in the name of specialties as Econophysics or Sociophysics. This chapter describes the history of knowledge transfer from physics, in particular physics of self-organization and evolution, to the social sciences. We discuss why physicists felt called to describe social processes. Across models and simulations the question how to explain the emergence of something new is the most intriguing one. We present one model approach to this problem and introduce a game -- Evolino -- inviting a larger audience to get acquainted with abstract evolution-theory approaches to describe the quest for new ideas.

physics.hist-ph↗

arXiv2012

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.

cond-mat.other↗

arXiv2011

Two-Dimensional Anharmonic Crystal Lattices: Solitons, Solectrons, and Electric Conduction

Reported here are salient features of soliton-mediated electron transport in anharmonic crystal lattices.After recalling how an electron-soliton bound state (solectron) can be formed we comment on consequences like electron surfing on a sound wave and balistic transport, possible percolation in 2d lattices, and a novel form of electron pairing with strongly correlated electrons both in real space and momentum space.

cond-mat.supr-con↗

arXiv2008

Active Brownian Motion Models and Applications to Ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircase-like and Mateos ratchet potentials, also with the additional loads modeled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This \textit{stochastically driven directionality} effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed

physics.data-an↗

arXiv2005

Evolutionary search agents in complex landscapes - a new model for the role of competence and meta-competence (EVOLINO and other simulation tools)

The acquisition of competence is a key element in the ability to assert oneself in the complex and rapidly changing modern worlds of work. This paper examines the evolution of competence, i.e. the role of competences in an evolutionary problem-solving process, and the role of flexibility as a meta-competence from the perspective of the general concept of Geometrically-Oriented Evolution THEory (G_O_E_THE). We use evolutionary search agents as abstract models of real individuals and groups. In a first approach the agents search for better competence profiles. In a second approach they use competences to solve problems. A search agent operates in an abstract value landscape, a fitness landscape. The crucial difference between the evolutionary search agents and other agent models is the fact that interaction patterns of the new agents incorporate evolutionary search strategies. A special simulation tool called EVOLINO allows to simulate the hill-climbing process of search agents in complex landscapes.

physics.soc-ph↗

arXiv2005

On the attractors of two-dimensional Rayleigh oscillators including noise

We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise and nonlinearity of the conservative forces. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. For this case we provide results for the attractors and the bifurcations of the system. We show that for rational relations of the frequencies the system develops several rotational excitations with right/left symmetry, corresponding to limit cycles in the four-dimensional phase space. The corresponding noisy distributions have the form of hoops or tires in the four-dimensional space. For irrational frequency relations, as well as for increasing strength of driving or noise the periodic excitations are replaced by chaotic oscillations.

nlin.AO↗

arXiv2004

Noise-Induced Transition from Translational to Rotational Motion of Swarms

We consider a model of active Brownian agents interacting via a harmonic attractive potential in a two-dimensional system in the presence of noise. By numerical simulations, we show that this model possesses a noise-induced transition characterized by the breakdown of translational motion and the onset of swarm rotation as the noise intensity is increased. Statistical properties of swarm dynamics in the weak noise limit are further analytically investigated.

physics.bio-ph↗

arXiv2004

Modelling Selforganization and Innovation Processes in Networks

In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a non-linear system. We refer to the theory of complex networks and introduce the notion of sensitive networks. Sensitive networks are networks in which the introduction or the removal of a node/vertex dramatically changes the dynamic structure of the system. As an application we consider interaction networks of firms and technologies and describe technological innovation as a specific dynamic process. Random graph theory, percolation, master equation formalism and the theory of birth and death processes are the mathematical instruments used in this paper.

cond-mat.stat-mech↗

arXiv2004

Active Brownian Particle and Random Walk Theories of the Motions of Zooplankton: Application to Experiments with Swarms of Daphnia

Active Brownian Particles are self-propelled particles that move in a dissipative medium subject to random forces, or noise . Additionally, they can be confined by an external field and/or they can interact with one another. The external field may actually be an attractive marker, for example a light field (as in the experiment) or an energy potential or a chemical gradient (as in the theory). The potential energy can also be the result of interparticle attractive and/or repulsive forces summed over all particles (a mean field potential). Four, qualitatively different motions of the particles are possible: at small particle density their motions are approximately independent of one another subject only to the external field and the noise, which results in moving randomly through or performing rotational motions about a central point in space. At increasing densities interactions play an important role and individuals form a swarm performing several types of self-organized collective motion. We apply this model for the description of zooplankton Daphnia swarms. In the case of the zooplankton Daphnia (and probably many other aquatic animals that form similar motions as well) this vortex is hydrodynamical but motivated by the self-propelled motion of the individuals. Similar vortex-type motions have been observed for other creatures ranging in size from bacteria to flocks of birds and schools of fish. However, our experiment with Daphnia is unique in that all four motions can be observed in controlled laboratory conditions with the same animal. Moreover, the theory, presented in both continuous differential equation and random walk forms, offers a quantitative, physically based explanation of the four motions.

q-bio.PE↗

arXiv2004

Correction algorithm for finite sample statistics

Assume in a sample of size M one finds M_i representatives of species i with i=1...N^*. The normalized frequency p^*_i=M_i/M, based on the finite sample, may deviate considerably from the true probabilities p_i. We propose a method to infer rank-ordered true probabilities r_i from measured frequencies M_i. We show that the rank-ordered probabilities provide important informations on the system, e.g., the true number of species, the Shannon- and the Renyi-entropies.

q-bio.OT↗

arXiv2004

Self-Organization, Active Brownian Dynamics, and Biological Applications

After summarizing basic features of self-organization such as entropy export, feedbacks and nonlinear dynamics, we discuss several examples in biology. The main part of the paper is devoted to a model of active Brownian motion that allows a stochastic description of the active motion of biological entities based on energy consumption and conversion. This model is applied to the dynamics of swarms with external and interaction potentials. By means of analytical results, we can distiguish between translational, rotational and amoebic modes of swarm motion. We further investigate swarms of active Brownian particles interacting via chemical fields and demonstrate the application of this model to phenomena such as biological aggregation and trail formation in insects.

cond-mat.stat-mech↗

arXiv2003

Nonequilibrium statistical mechanics of swarms of driven particles

As a rough model for the collective motions of cells and organisms we develop here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion and the theory of canonical-dissipative systems. Free motion and motion of a swarms confined in an external field is studied. Briefly the case of particles confined on a ring and interacting by repulsive forces is studied. In more detail we investigate self-confinement by Morse-type attracting forces. We begin with pairs N = 2; the attractors and distribution functions are discussed, then the case N > 2 is discussed. Simulations for several dynamical modes of swarms of active Brownian particles interacting by Morse forces are presented. In particular we study rotations, drift, fluctuations of shape and cluster formation.

cond-mat.stat-mech↗

arXiv2002

Thermodynamics of ionization and dissociation in hydrogen plasmas including fluctuations and magnetic fields

Applying Gibb's geometrical methods to the thermodynamics of H-plasmas we explore the landscape of the free energy as a function of the degrees of ionization and dissociation. Several approximations for the free energy are discussed. We show that in the region of partial ionization/dissociation the quantum Debye-Hueckel approximation (QDHA) yields a rather good but still simple representation which allows to include magnetic field and fluctuation effects. By using relations of Onsager-Landau-type the probability of fluctuations and ionization/dissociation processes are described. We show that the degrees of ionization/dissociation are probabilistic quantities which are subject to a relatively large dispersion. Magnetic field effects are studied.

astro-ph↗

arXiv2002

Coulombic Phase Transitions in Dense Plasmas

We give a survey on the predictions of Coulombic phase transitions in dense plasmas (PPT) and derive several new results on the properties of these transitions. In particular we discuss several types of the critical point and the spinodal curves of quantum Coulombic systems. We construct a simple theoretical model which shows (in dependence on the parameter values) either one alkali-type transition (Coulombic and van der Waals forces determine the critical point) or one Coulombic transition and another van der Waals transition. We investigate the conditions to find separate Van der Waals and Coulomb transitions in one system (typical for hydrogen and noble gas-type plasmas). The separated Coulombic transitions which are strongly influenced by quantum effects are the hypothetical PPT, they are in full analogy to the known Coulombic transitions in classical ionic systems. Finally we give a discussion of several numerical and experimental results referring to the PPT in high pressure plasmas.

cond-mat.stat-mech↗

arXiv2002

Nonlinear Dynamics of Active Brownian Particles

We consider finite systems of interacting Brownian particles including active friction in the framework of nonlinear dynamics and statistical/stochastic theory. First we study the statistical properties for $1-d$ systems of masses connected by Toda springs which are imbedded into a heat bath. Including negative friction we find $N+1$ attractors of motion including an attractor describing dissipative solitons. Noise leads to transition between the deterministic attractors. In the case of two-dynamical motion of interacting particles angular momenta are generated and left/right rotations of pairs and swarms are found.

cond-mat.stat-mech↗

arXiv2002

SYNTAX: A computer program to compress a sequence and to estimate its information content

The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages, computer programs, neural spike trains, and biosequences. In this paper a new algorithm to construct a short context-free grammar (also called program or description) that generates a given sequence is introduced. It follows the general lines of a former algorithm, employed to compress biosequences (1,2) and to estimate the complexity of neural spike trains (4), which uses as valuation function the, so called, grammar complexity (2). The new algorithm employs the (observed) block-entropies instead. A variant, which employs a corrected "observed entropy", as discussed in (7) is also described. To illustrate its usefulness, applications of the program to the syntactic analysis of a sample biological sequences (DNA and RNA) is presented.

cond-mat.dis-nn↗

arXiv2002

Dynamic entropies, long-range correlations, and fluctuations in complex linear structures

We investigate symbolic sequences and in particular information carriers as e.g. books and DNA-strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is estimated by using Lempel-Ziv compression algorithms. In the third section the correlation function for distant letters, the low frequency Fourier spectrum and the characteristic scaling exponents are calculated. We show that all these measures are able to detect long-range correlations. However, as demonstrated by shuffling experiments, different measures operate on different length scales. The longest correlations found in our analysis comprise a few hundreds or thousands of letters and may be understood as long-wave fluctuations of the composition.

cond-mat.dis-nn↗