12 research outputs found
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment
A procedure is described for efficiently finding the ground state energy and
configuration for a Frenkel-Kontorova model in a periodic potential, consisting
of N parabolic segments of identical curvature in each period, through a
numerical solution of the convex minimization problem described in the
preceding paper. The key elements are the use of subdifferentials to describe
the structure of the minimization problem; an intuitive picture of how to solve
it, based on motion of quasiparticles; and a fast linear optimization method
with a reduced memory requirement. The procedure has been tested for N up to
200.Comment: 9 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 3 Postscript
figures, accepted by Phys.Rev.B to be published together with
cond-mat/970722
Test of the semischematic model for a liquid of linear molecules
We apply to a liquid of linear molecules the semischematic mode-coupling
model, previously introduced to describe the center of mass (COM) slow dynamics
of a network-forming molecular liquid. We compare the theoretical predictions
and numerical results from a molecular dynamics simulation, both for the time
and the wave-vector dependence of the COM density-density correlation function.
We discuss the relationship between the presented analysis and the results from
an approximate solution of the equations from molecular mode-coupling theory
[R. Schilling and T. Scheidsteger, Phys. Rev. E 56 2932 (1997)].Comment: Revtex, 10 pages, 4 figure
Molecular mode-coupling theory for supercooled liquids: Application to water
We present mode-coupling equations for the description of the slow dynamics
observed in supercooled molecular liquids close to the glass transition. The
mode-coupling theory (MCT) originally formulated to study the slow relaxation
in simple atomic liquids, and then extended to the analysis of liquids composed
by linear molecules, is here generalized to systems of arbitrarily shaped,
rigid molecules. We compare the predictions of the theory for the -vector
dependence of the molecular nonergodicity parameters, calculated by solving
numerically the molecular MCT equations in two different approximation schemes,
with ``exact'' results calculated from a molecular dynamics simulation of
supercooled water. The agreement between theory and simulation data supports
the view that MCT succeeds in describing the dynamics of supercooled molecular
liquids, even for network forming ones.Comment: 22 pages 4 figures Late
Test of mode coupling theory for a supercooled liquid of diatomic molecules. II. q-dependent orientational correlators
Using molecular dynamics computer simulations we study the dynamics of a
molecular liquid by means of a general class of time-dependent correlators
S_{ll'}^m(q,t) which explicitly involve translational (TDOF) and orientational
degrees of freedom (ODOF). The system is composed of rigid, linear molecules
with Lennard- Jones interactions. The q-dependence of the static correlators
S_{ll'}^m(q) strongly depend on l, l' and m. The time dependent correlators are
calculated for l=l'. A thorough test of the predictions of mode coupling theory
(MCT) is performed for S_{ll}^m(q,t) and its self part S_{ll}^{(s)m}(q,t), for
l=1,..,6. We find a clear signature for the existence of a single temperature
T_c, at which the dynamics changes significantly. The first scaling law of MCT,
which involves the critical correlator G(t), holds for l>=2, but no critical
law is observed. Since this is true for the same exponent parameter lambda as
obtained for the TDOF, we obtain a consistent description of both, the TDOF and
ODOF, with the exception of l=1. This different behavior for l \ne 1 and l=1
can also be seen from the corresponding susceptibilities
(chi'')_{ll}^m(q,omega) which exhibit a minimum at about the same frequency
omega_{min} for all q and all l \ne 1, in contrast to (chi'')_{11}^m(q,omega)
for which omega'_{min} approx 10 omega_{min} . The asymptotic regime, for which
the first scaling law holds, shrinks with increasing l. The second scaling law
of MCT (time-temperature superposition principle) is reasonably fulfilled for l
\ne 1 but not for l=1. Furthermore we show that the q- and (l,m)-dependence of
the self part approximately factorizes, i.e. S_{ll}^{(s)m}(q,t) \cong
C_l^{(s)}(t) F_s(q,t) for all m.Comment: 11 pages of RevTex, 16 figure
Test of mode coupling theory for a supercooled liquid of diatomic molecules.I. Translational degrees of freedom
A molecular dynamics simulation is performed for a supercooled liquid of
rigid diatomic molecules. The time-dependent self and collective density
correlators of the molecular centers of mass are determined and compared with
the predictions of the ideal mode coupling theory (MCT) for simple liquids.
This is done in real as well as in momentum space. One of the main results is
the existence of a unique transition temperature T_c, where the dynamics
crosses over from an ergodic to a quasi-nonergodic behavior. The value for T_c
agrees with that found earlier for the orientational dynamics within the error
bars. In the beta- regime of MCT the factorization of space- and time
dependence is satisfactorily fulfilled for both types of correlations. The
first scaling law of ideal MCT holds in the von Schweidler regime, only, since
the validity of the critical law can not be confirmed, due to a strong
interference with the microscopic dynamics. In this first scaling regime a
consistent description within ideal MCT emerges only, if the next order
correction to the asymptotic law is taken into account. This correction is
almost negligible for q=q_max, the position of the main peak in the static
structure factor S(q), but becomes important for q=q_min, the position of its
first minimum. The second scaling law, i.e. the time-temperature superposition
principle, holds reasonably well for the self and collective density
correlators and different values for q. The alpha-relaxation times tau_q^(s)
and tau_q follow a power law in T-T_c over 2 -- 3 decades. The corresponding
exponent gamma is weakly q-dependent and is around 2.55. This value is in
agreement with the one predicted by MCT from the value of the von Schweidler
exponent but at variance with the corresponding exponent gammaComment: 14 pages of RevTex, 19 figure
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
Molecular mode-coupling theory applied to a liquid of diatomic molecules
We study the molecular mode coupling theory for a liquid of diatomic
molecules. The equations for the critical tensorial nonergodicity parameters
and the critical amplitudes of the - relaxation
are solved up to a cut off = 2 without any
further approximations.
Here are indices of spherical harmonics. Contrary to previous studies,
where additional approximations were applied, we find in agreement with
simulations, that all molecular degrees of freedom vitrify at a single
temperature . The theoretical results for the non ergodicity parameters
and the critical amplitudes are compared with those from simulations. The
qualitative agreement is good for all molecular degrees of freedom. To study
the influence of the cut off on the non ergodicity parameter, we also calculate
the non ergodicity parameters for an upper cut off . In addition we
also propose a new method for the calculation of the critical nonergodicity
parameterComment: 27 pages, 17 figure
Dynamics in a supercooled molecular liquid: Theory and Simulations
We report extensive simulations of liquid supercooled states for a simple
three-sites molecular model, introduced by Lewis and Wahnstr"om [L. J. Lewis
and G. Wahnstr"om, Phys. Rev. E 50, 3865 (1994)] to mimic the behavior of
ortho-terphenyl. The large system size and the long simulation length allow to
calculate very precisely --- in a large q-vector range --- self and collective
correlation functions, providing a clean and simple reference model for
theoretical descriptions of molecular liquids in supercooled states. The time
and wavevector dependence of the site-site correlation functions are compared
with detailed predictions based on ideal mode-coupling theory, neglecting the
molecular constraints. Except for the wavevector region where the dynamics is
controlled by the center of mass (around 9 nm-1), the theoretical predictions
compare very well with the simulation data.
The concordance of field-normalized scores based on Web of Science and Microsoft Academic data: A case study in computer sciences
In order to assess Microsoft Academic as a useful data source for evaluative bibliometrics it is crucial to know, if citation counts from Microsoft Academic could be used in common normalization procedures and whether the normalized scores agree with the scores calculated on the basis of established databases. To this end, we calculate the field-normalized citation scores of the publications of a computer science institute based on Microsoft Academic and the Web of Science and estimate the statistical concordance of the scores. Our results suggest that field-normalized citation scores can be calculated with Microsoft Academic and that these scores are in good agreement with the corresponding scores from the Web of Science