1,648 research outputs found
Entropy and Long range correlations in literary English
Recently long range correlations were detected in nucleotide sequences and in
human writings by several authors. We undertake here a systematic investigation
of two books, Moby Dick by H. Melville and Grimm's tales, with respect to the
existence of long range correlations. The analysis is based on the calculation
of entropy like quantities as the mutual information for pairs of letters and
the entropy, the mean uncertainty, per letter. We further estimate the number
of different subwords of a given length . Filtering out the contributions
due to the effects of the finite length of the texts, we find correlations
ranging to a few hundred letters. Scaling laws for the mutual information
(decay with a power law), for the entropy per letter (decay with the inverse
square root of ) and for the word numbers (stretched exponential growth with
and with a power law of the text length) were found.Comment: 8 page
Thermodynamics of hot dense H-plasmas: Path integral Monte Carlo simulations and analytical approximations
This work is devoted to the thermodynamics of high-temperature dense hydrogen
plasmas in the pressure region between and Mbar. In particular
we present for this region results of extensive calculations based on a
recently developed path integral Monte Carlo scheme (direct PIMC). This method
allows for a correct treatment of the thermodynamic properties of hot dense
Coulomb systems. Calculations were performed in a broad region of the
nonideality parameter and degeneracy parameter . We give a comparison with a few available results from
other path integral calculations (restricted PIMC) and with analytical
calculations based on Pade approximations for strongly ionized plasmas. Good
agreement between the results obtained from the three independent methods is
found.Comment: RevTex file, 21 pages, 5 ps-figures include
Canonical active Brownian motion
Active Brownian motion is the complex motion of active Brownian particles.
They are active in the sense that they can transform their internal energy into
energy of motion and thus create complex motion patterns. Theories of active
Brownian motion so far imposed couplings between the internal energy and the
kinetic energy of the system. We investigate how this idea can be naturally
taken further to include also couplings to the potential energy, which finally
leads to a general theory of canonical dissipative systems. Explicit analytical
and numerical studies are done for the motion of one particle in harmonic
external potentials. Apart from stationary solutions, we study non-equilibrium
dynamics and show the existence of various bifurcation phenomena.Comment: 11 pages, 6 figures, a few remarks and references adde
Guessing probability distributions from small samples
We propose a new method for the calculation of the statistical properties, as
e.g. the entropy, of unknown generators of symbolic sequences. The probability
distribution of the elements of a population can be approximated by
the frequencies of a sample provided the sample is long enough so that
each element occurs many times. Our method yields an approximation if this
precondition does not hold. For a given we recalculate the Zipf--ordered
probability distribution by optimization of the parameters of a guessed
distribution. We demonstrate that our method yields reliable results.Comment: 10 pages, uuencoded compressed PostScrip
Excitation of solitons in hexagonal lattices and ways of controlling electron transport
This is a post-peer-review, pre-copyedit version of an article published in Philosophical Transactions A: Mathematical, Physical and Engineering Sciences. The final authenticated version is available online at: http://dx.doi.org/10.1007/s40435-017-0383-x.We construct metastable long-living hexagonal lattices with appropriately modified Morse interactions and show that highly-energetic solitons may be excited moving along crystallographic axes. Studying the propagation, their dynamic changes and the relaxation processes it appears that lump solitons create in the lattice running local compressions. Based on the tight-binding model we investigate the possibility that electrons are trapped and guided by the electric polarization field of the compression field of one soliton or two solitons with crossing pathways. We show that electrons may jump from a bound state with the first soliton to a bound state with a second soliton and changing accordingly the direction of their path. We discuss the possibility to control by this method the path of an excess electron from a source at a boundary to a selected drain at another chosen boundary by following straight pathways on crystallographic axes.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics
We develop the theory of canonical-dissipative systems, based on the
assumption that both the conservative and the dissipative elements of the
dynamics are determined by invariants of motion. In this case, known solutions
for conservative systems can be used for an extension of the dynamics, which
also includes elements such as the take-up/dissipation of energy. This way, a
rather complex dynamics can be mapped to an analytically tractable model, while
still covering important features of non-equilibrium systems. In our paper,
this approach is used to derive a rather general swarm model that considers (a)
the energetic conditions of swarming, i.e. for active motion, (b) interactions
between the particles based on global couplings. We derive analytical
expressions for the non-equilibrium velocity distribution and the mean squared
displacement of the swarm. Further, we investigate the influence of different
global couplings on the overall behavior of the swarm by means of
particle-based computer simulations and compare them with the analytical
estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref.
updated. For related work see also:
http://summa.physik.hu-berlin.de/~frank/active.htm
Directional motion of forced polymer chains with hydrodynamic interaction
We study the propulsion of a one-dimensional (1D) polymer chain under
sinusoidal external forces in the overdamped (low Reynolds number) regime. We
show that, when hydrodynamical interactions are included, the polymer presents
directional motion which depends on the phase differences of the external force
applied along the chain. Moreover, the velocity shows a maximum as a function
of the frequency. We discuss the relevance of all these results in light of
recent nanotechnology experiments.Comment: 5 pages, 6 figure
On anomalous diffusion in a plasma in velocity space
The problem of anomalous diffusion in momentum space is considered for
plasma-like systems on the basis of a new collision integral, which is
appropriate for consideration of the probability transition function (PTF) with
long tails in momentum space. The generalized Fokker-Planck equation for
description of diffusion (in momentum space) of particles (ions, grains etc.)
in a stochastic system of light particles (electrons, or electrons and ions,
respectively) is applied to the evolution of the momentum particle distribution
in a plasma. In a plasma the developed approach is also applicable to the
diffusion of particles with an arbitrary mass relation, due to the small
characteristic momentum transfer. The cases of an exponentially decreasing in
momentum space (including the Boltzmann-like) kernel in the PT-function, as
well as the more general kernels, which create the anomalous diffusion in
velocity space due to the long tail in the PT-function, are considered.
Effective friction and diffusion coefficients for plasma-like systems are
found.Comment: 18 pages, no figure
Reconstruction of a first-order phase transition from computer simulations of individual phases and subphases
We present a new method for investigating first-order phase transitions using
Monte Carlo simulations. It relies on the multiple-histogram method and uses
solely histograms of individual phases. In addition, we extend the method to
include histograms of subphases. The free energy difference between phases,
necessary for attributing the correct statistical weights to the histograms, is
determined by a detour in control parameter space via auxiliary systems with
short relaxation times. We apply this method to a recently introduced model for
structure formation in polypeptides for which other methods fail.Comment: 13 pages in preprint mode, REVTeX, 2 Figures available from the
authors ([email protected], [email protected]
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