110 research outputs found
Entropy, Dynamics and Instantaneous Normal Modes in a Random Energy Model
It is shown that the fraction f of imaginary frequency instantaneous normal
modes (INM) may be defined and calculated in a random energy model(REM) of
liquids. The configurational entropy S and the averaged hopping rate among the
states R are also obtained and related to f, with the results R~f and
S=a+b*ln(f). The proportionality between R and f is the basis of existing INM
theories of diffusion, so the REM further confirms their validity. A link to S
opens new avenues for introducing INM into dynamical theories. Liquid 'states'
are usually defined by assigning a configuration to the minimum to which it
will drain, but the REM naturally treats saddle-barriers on the same footing as
minima, which may be a better mapping of the continuum of configurations to
discrete states. Requirements of a detailed REM description of liquids are
discussed
Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids
We analytically compute the spectrum of the Hessian of the Hamiltonian for a
system of N particles interacting via a purely repulsive potential in one
dimension. Our approach is valid in the low density regime, where we compute
the exact spectrum also in the localized sector. We finally perform a numerical
analysis of the localization properties of the eigenfunctions.Comment: 4 RevTeX pages, 4 EPS figures. Revised version to appear on Phys.
Rev. Let
Instantaneous Normal Mode Analysis of Supercooled Water
We use the instantaneous normal mode approach to provide a description of the
local curvature of the potential energy surface of a model for water. We focus
on the region of the phase diagram in which the dynamics may be described by
the mode-coupling theory. We find, surprisingly, that the diffusion constant
depends mainly on the fraction of directions in configuration space connecting
different local minima, supporting the conjecture that the dynamics are
controlled by the geometric properties of configuration space. Furthermore, we
find an unexpected relation between the number of basins accessed in
equilibrium and the connectivity between them.Comment: 5 pages, 4 figure
String-like Clusters and Cooperative Motion in a Model Glass-Forming Liquid
A large-scale molecular dynamics simulation is performed on a glass-forming
Lennard-Jones mixture to determine the nature of dynamical heterogeneities
which arise in this model fragile liquid. We observe that the most mobile
particles exhibit a cooperative motion in the form of string-like paths
(``strings'') whose mean length and radius of gyration increase as the liquid
is cooled. The length distribution of the strings is found to be similar to
that expected for the equilibrium polymerization of linear polymer chains.Comment: 6 pages of RevTex, 6 postscript figures, uses epsf.st
Energy landscape of a Lennard-Jones liquid: Statistics of stationary points
Molecular dynamics simulations are used to generate an ensemble of saddles of
the potential energy of a Lennard-Jones liquid. Classifying all extrema by
their potential energy u and number of unstable directions k, a well defined
relation k(u) is revealed. The degree of instability of typical stationary
points vanishes at a threshold potential energy, which lies above the energy of
the lowest glassy minima of the system. The energies of the inherent states, as
obtained by the Stillinger-Weber method, approach the threshold energy at a
temperature close to the mode-coupling transition temperature Tc.Comment: 4 RevTeX pages, 6 eps figures. Revised versio
Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
We consider a system of coupled classical harmonic oscillators with spatially
fluctuating nearest-neighbor force constants on a simple cubic lattice. The
model is solved both by numerically diagonalizing the Hamiltonian and by
applying the single-bond coherent potential approximation. The results for the
density of states are in excellent agreement with each other. As
the degree of disorder is increased the system becomes unstable due to the
presence of negative force constants. If the system is near the borderline of
stability a low-frequency peak appears in the reduced density of states
as a precursor of the instability. We argue that this peak
is the analogon of the "boson peak", observed in structural glasses. By means
of the level distance statistics we show that the peak is not associated with
localized states
BUB-1 targets PP2A:B56 to regulate chromosome congression during meiosis I in C. elegans oocytes
Protein Phosphatase 2A (PP2A) is a heterotrimer composed of scaffolding (A), catalytic (C), and regulatory (B) subunits. PP2A complexes with B56 subunits are targeted by Shugoshin and BUBR1 to protect centromeric cohesion and stabilise kinetochore-microtubule attachments in yeast and mouse meiosis. In Caenorhabditis elegans, the closest BUBR1 orthologue lacks the B56-interaction domain and Shugoshin is not required for meiotic segregation. Therefore, the role of PP2A in C. elegans female meiosis is unknown. We report that PP2A is essential for meiotic spindle assembly and chromosome dynamics during C. elegans female meiosis. BUB-1 is the main chromosome-targeting factor for B56 subunits during prometaphase I. BUB-1 recruits PP2A:B56 to the chromosomes via a newly identified LxxIxE motif in a phosphorylation-dependent manner, and this recruitment is important for proper chromosome congression. Our results highlight a novel mechanism for B56 recruitment, essential for recruiting a pool of PP2A involved in chromosome congression during meiosis I
Molecular structural order and anomalies in liquid silica
The present investigation examines the relationship between structural order,
diffusivity anomalies, and density anomalies in liquid silica by means of
molecular dynamics simulations. We use previously defined orientational and
translational order parameters to quantify local structural order in atomic
configurations. Extensive simulations are performed at different state points
to measure structural order, diffusivity, and thermodynamic properties. It is
found that silica shares many trends recently reported for water [J. R.
Errington and P. G. Debenedetti, Nature 409, 318 (2001)]. At intermediate
densities, the distribution of local orientational order is bimodal. At fixed
temperature, order parameter extrema occur upon compression: a maximum in
orientational order followed by a minimum in translational order. Unlike water,
however, silica's translational order parameter minimum is broad, and there is
no range of thermodynamic conditions where both parameters are strictly
coupled. Furthermore, the temperature-density regime where both structural
order parameters decrease upon isothermal compression (the structurally
anomalous regime) does not encompass the region of diffusivity anomalies, as
was the case for water.Comment: 30 pages, 8 figure
Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids
We present a model for the motion of an average atom in a liquid or
supercooled liquid state and apply it to calculations of the velocity
autocorrelation function and diffusion coefficient . The model
trajectory consists of oscillations at a distribution of frequencies
characteristic of the normal modes of a single potential valley, interspersed
with position- and velocity-conserving transits to similar adjacent valleys.
The resulting predictions for and agree remarkably well with MD
simulations of Na at up to almost three times its melting temperature. Two
independent processes in the model relax velocity autocorrelations: (a)
dephasing due to the presence of many frequency components, which operates at
all temperatures but which produces no diffusion, and (b) the transit process,
which increases with increasing temperature and which produces diffusion.
Because the model provides a single-atom trajectory in real space and time,
including transits, it may be used to calculate all single-atom correlation
functions.Comment: LaTeX, 8 figs. This is an updated version of cond-mat/0002057 and
cond-mat/0002058 combined Minor changes made to coincide with published
versio
A single saddle model for the beta-relaxation in supercooled liquids
We study the Langevin equation for a single harmonic saddle as an elementary
model for the beta-relaxation in supercooled liquids close to Tc. The input of
the theory is the spectrum of the eigenvalues of the dominant stationary points
at a given temperature. We prove in general the existence of a time-scale
t_eps, which is uniquely determined by the spectrum, but is not simply related
to the fraction of negative eigenvalues. The mean square displacement develops
a plateau of length t_eps, such that a two-step relaxation is obtained if t_eps
diverges at Tc. We analyze the specific case of a spectrum with bounded left
tail, and show that in this case the mean square displacement has a scaling
dependence on time identical to the beta-relaxation regime of Mode Coupling
Theory, with power law approach to the plateau and power law divergence of
t_eps at Tc.Comment: Revised versio
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