11,836 research outputs found
Stiff polymer in monomer ensemble
We make use of the previously developed formalism for a monomer ensemble and
include angular dependence of the segments of the polymer chains thus
described. In particular we show how to deal with stiffness when the polymer
chain is confined to certain regions. We investigate the stiffness from the
perspectives of a differential equation, integral equations, or recursive
relations for both continuum and lattice models. Exact analytical solutions are
presented for two cases, whereas numerical results are shown for a third case.Comment: 10 pages, including 6 figure
Multifractality of the Feigenbaum attractor and fractional derivatives
It is shown that fractional derivatives of the (integrated) invariant measure
of the Feigenbaum map at the onset of chaos have power-law tails in their
cumulative distributions, whose exponents can be related to the spectrum of
singularities . This is a new way of characterizing multifractality
in dynamical systems, so far applied only to multifractal random functions
(Frisch and Matsumoto (J. Stat. Phys. 108:1181, 2002)). The relation between
the thermodynamic approach (Vul, Sinai and Khanin (Russian Math. Surveys 39:1,
1984)) and that based on singularities of the invariant measures is also
examined. The theory for fractional derivatives is developed from a heuristic
point view and tested by very accurate simulations.Comment: 20 pages, 5 figures, J.Stat.Phys. in pres
A practical guide to density matrix embedding theory in quantum chemistry
Density matrix embedding theory (DMET) provides a theoretical framework to
treat finite fragments in the presence of a surrounding molecular or bulk
environment, even when there is significant correlation or entanglement between
the two. In this work, we give a practically oriented and explicit description
of the numerical and theoretical formulation of DMET. We also describe in
detail how to perform self-consistent DMET optimizations. We explore different
embedding strategies with and without a self-consistency condition in hydrogen
rings, beryllium rings, and a sample S2 reaction. The source code
for the calculations in this work can be obtained from
\url{https://github.com/sebwouters/qc-dmet}.Comment: 41 pages, 10 figure
Dispersive stabilization of the inverse cascade for the Kolmogorov flow
It is shown by perturbation techniques and numerical simulations that the
inverse cascade of kink-antikink annihilations, characteristic of the
Kolmogorov flow in the slightly supercritical Reynolds number regime, is halted
by the dispersive action of Rossby waves in the beta-plane approximation. For
beta tending to zero, the largest excited scale is proportional to the
logarithm of one over beta and differs strongly from what is predicted by
standard dimensional phenomenology which ignores depletion of nonlinearity.Comment: 4 pages, LATEX, 3 figures. v3: revised version with minor correction
Proportion Regulation in Globally Coupled Nonlinear Systems
As a model of proportion regulation in differentiation process of biological
system, globally coupled activator-inhibitor systems are studied. Formation and
destabilization of one and two cluster state are predicted analytically.
Numerical simulations show that the proportion of units of clusters is chosen
within a finite range and it is selected depend on the initial condition.Comment: 11 pages (revtex format) and 5 figures (PostScript)
Analysis of Velocity Fluctuation in Turbulence based on Generalized Statistics
The numerical experiments of turbulence conducted by Gotoh et al. are
analyzed precisely with the help of the formulae for the scaling exponents of
velocity structure function and for the probability density function (PDF) of
velocity fluctuations. These formulae are derived by the present authors with
the multifractal aspect based on the statistics that are constructed on the
generalized measures of entropy, i.e., the extensive R\'{e}nyi's or the
non-extensive Tsallis' entropy. It is revealed that there exist two scaling
regions separated by a crossover length, i.e., a definite length approximately
of the order of the Taylor microscale. It indicates that the multifractal
distribution of singularities in velocity gradient in turbulent flow is robust
enough to produce scaling behaviors even for the phenomena out side the
inertial range.Comment: 10 Pages, 5 figure
Metastable anions of dinitrobenzene: resonances for electron attachment and kinetic energy release
Attachment of free, low-energy electrons to dinitrobenzene (DNB) in the gas phase leads to DNB as well as several fragment anions. DNB, (DNB-H), (DNB-NO), (DNB-2NO), and (DNB-NO(2)) are found to undergo metastable (unimolecular) dissociation. A rich pattern of resonances in the yield of these metastable reactions versus electron energy is observed; some resonances are highly isomer-specific. Most metastable reactions are accompanied by large average kinetic energy releases (KER) that range from 0.5 to 1.32 eV, typical of complex rearrangement reactions, but (1,3-DNB-H)(-) features a resonance with a KER of only 0.06 eV for loss of NO. (1,3-DNB-NO)(-) offers a rare example of a sequential metastable reaction, namely, loss of NO followed by loss of CO to yield C(5)H(4)O(-) with a large KER of 1.32 eV. The G4(MP2) method is applied to compute adiabatic electron affinities and reaction energies for several of the observed metastable channels. (C) 2010 American Institute of Physics. [doi:10.1063/1.3514931
Anomalous diffusion as a signature of collapsing phase in two dimensional self-gravitating systems
A two dimensional self-gravitating Hamiltonian model made by
fully-coupled classical particles exhibits a transition from a collapsing phase
(CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical
point of view, the two phases are characterized by two distinct single-particle
motions : namely, superdiffusive in the CP and ballistic in the HP. Anomalous
diffusion is observed up to a time that increases linearly with .
Therefore, the finite particle number acts like a white noise source for the
system, inhibiting anomalous transport at longer times.Comment: 10 pages, Revtex - 3 Figs - Submitted to Physical Review
Logarithmic scaling in the near-dissipation range of turbulence
A logarithmic scaling for structure functions, in the form , where is the Kolmogorov dissipation scale and
are the scaling exponents, is suggested for the statistical
description of the near-dissipation range for which classical power-law scaling
does not apply. From experimental data at moderate Reynolds numbers, it is
shown that the logarithmic scaling, deduced from general considerations for the
near-dissipation range, covers almost the entire range of scales (about two
decades) of structure functions, for both velocity and passive scalar fields.
This new scaling requires two empirical constants, just as the classical
scaling does, and can be considered the basis for extended self-similarity
Exclusion of Tiny Interstellar Dust Grains from the Heliosphere
The distribution of interstellar dust grains (ISDG) observed in the Solar
System depends on the nature of the interstellar medium-solar wind interaction.
The charge of the grains couples them to the interstellar magnetic field (ISMF)
resulting in some fraction of grains being excluded from the heliosphere while
grains on the larger end of the size distribution, with gyroradii comparable to
the size of the heliosphere, penetrate the termination shock. This results in a
skewing the size distribution detected in the Solar System.
We present new calculations of grain trajectories and the resultant grain
density distribution for small ISDGs propagating through the heliosphere. We
make use of detailed heliosphere model results, using three-dimensional (3-D)
magnetohydrodynamic/kinetic models designed to match data on the shape of the
termination shock and the relative deflection of interstellar neutral H and He
flowing into the heliosphere. We find that the necessary inclination of the
ISMF relative to the inflow direction results in an asymmetry in the
distribution of the larger grains (0.1 micron) that penetrate the heliopause.
Smaller grains (0.01 micron) are completely excluded from the Solar System at
the heliopause.Comment: 5 pages, 5 figures, accepted for publication in the Solar Wind 12
conference proceeding
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