3,609 research outputs found
From coupled elementary units to the complexity of the glass transition
Supercooled liquids display fascinating properties upon cooling such as the
emergence of dynamic length scales. Different models strongly vary with respect
to the choice of the elementary subsystems (CRR) as well as their mutual
coupling. Here we show via computer simulations of a glass former that both
ingredients can be identified via analysis of finite-size effects within the
continuous-time random walk framework. The CRR already contain complete
information about thermodynamics and diffusivity whereas the coupling
determines structural relaxation and the emergence of dynamic length scales
A Simple Non-Markovian Computational Model of the Statistics of Soccer Leagues: Emergence and Scaling effects
We propose a novel algorithm that outputs the final standings of a soccer
league, based on a simple dynamics that mimics a soccer tournament. In our
model, a team is created with a defined potential(ability) which is updated
during the tournament according to the results of previous games. The updated
potential modifies a teams' future winning/losing probabilities. We show that
this evolutionary game is able to reproduce the statistical properties of final
standings of actual editions of the Brazilian tournament (Brasileir\~{a}o).
However, other leagues such as the Italian and the Spanish tournaments have
notoriously non-Gaussian traces and cannot be straightforwardly reproduced by
this evolutionary non-Markovian model. A complete understanding of these
phenomena deserves much more attention, but we suggest a simple explanation
based on data collected in Brazil: Here several teams were crowned champion in
previous editions corroborating that the champion typically emerges from random
fluctuations that partly preserves the gaussian traces during the tournament.
On the other hand, in the Italian and Spanish leagues only a few teams in
recent history have won their league tournaments. These leagues are based on
more robust and hierarchical structures established even before the beginning
of the tournament. For the sake of completeness, we also elaborate a totally
Gaussian model (which equalizes the winning, drawing, and losing probabilities)
and we show that the scores of the "Brasileir\~{a}o" cannot be reproduced. Such
aspects stress that evolutionary aspects are not superfluous in our modeling.
Finally, we analyse the distortions of our model in situations where a large
number of teams is considered, showing the existence of a transition from a
single to a double peaked histogram of the final classification scores. An
interesting scaling is presented for different sized tournaments.Comment: 18 pages, 9 figure
Local Properties of the Potential Energy Landscape of a Model Glass: Understanding the Low Temperature Anomalies
Though the existence of two-level systems (TLS) is widely accepted to explain
low temperature anomalies in the sound absorption, heat capacity, thermal
conductivity and other quantities, an exact description of their microscopic
nature is still lacking. We performed computer simulations for a binary
Lennard-Jones system, using a newly developed algorithm to locate double-well
potentials (DWP) and thus two-level systems on a systematic basis. We show that
the intrinsic limitations of computer simulations like finite time and finite
size problems do not hamper this analysis. We discuss how the DWP are embedded
in the total potential energy landscape. It turns out that most DWP are
connected to the dynamics of the smaller particles and that these DWP are
rather localized. However, DWP related to the larger particles are more
collective
Particle rearrangements during transitions between local minima of the potential energy landscape of a supercooled Lennard-Jones liquid
The potential energy landscape (PEL) of supercooled binary Lennard-Jones
(BLJ) mixtures exhibits local minima, or inherent structures (IS), which are
organized into meta-basins (MB). We study the particle rearrangements related
to transitions between both successive IS and successive MB for a small 80:20
BLJ system near the mode-coupling temperature T_MCT. The analysis includes the
displacements of individual particles, the localization of the rearrangements
and the relevance of string-like motion. We find that the particle
rearrangements during IS and MB transitions do not change significantly at
T_MCT. Further, it is demonstrated that IS and MB dynamics are spatially
heterogeneous and facilitated by string-like motion. To investigate the
mechanism of string-like motion, we follow the particle rearrangements during
suitable sequences of IS transitions. We find that most strings observed after
a series of transitions do not move coherently during a single transition, but
subunits of different sizes are active at different times. Several findings
suggest that the occurrence of a successful string enables the system to exit a
MB. Moreover, we show that the particle rearrangements during two consecutive
MB transitions are basically uncorrelated. Specifically, different groups of
particles are highly mobile during subsequent MB transitions. Finally, the
relation between the features of the PEL and the relaxation processes in
supercooled liquids is discussed.Comment: 13 pages, 10 figure
Compressing nearly hard sphere fluids increases glass fragility
We use molecular dynamics to investigate the glass transition occurring at
large volume fraction, phi, and low temperature, T, in assemblies of soft
repulsive particles. We find that equilibrium dynamics in the (phi, T) plane
obey a form of dynamic scaling in the proximity of a critical point at T=0 and
phi=phi_0, which should correspond to the ideal glass transition of hard
spheres. This glass point, `point G', is distinct from athermal jamming
thresholds. A remarkable consequence of scaling behaviour is that the dynamics
at fixed phi passes smoothly from that of a strong glass to that of a very
fragile glass as phi increases beyond phi_0. Correlations between fragility and
various physical properties are explored.Comment: 5 pages, 3 figures; Version accepted at Europhys. Let
Tunneling dynamics of side chains and defects in proteins, polymer glasses, and OH-doped network glasses
Simulations on a Lennard-Jones computer glass are performed to study effects
arising from defects in glasses at low temperatures. The numerical analysis
reveals that already a low concentration of defects may dramatically change the
low temperature properties by giving rise to extrinsic double-well potentials
(DWP's). The main characteristics of these extrinsic DWP's are (i) high barrier
heights, (ii) high probability that a defect is indeed connected with an
extrinsic DWP, (iii) highly localized dynamics around this defect, and (iv)
smaller deformation potential coupling to phonons. Designing an extension of
the Standard Tunneling Model (STM) which parametrizes this picture and
comparing with ultrasound experiments on the wet network glass -BO
shows that effects of OH-impurities are accurately accounted for. This model is
then applied to organic polymer glasses and proteins. It is suggested that side
groups may act similarly like doped impurities inasmuch as extrinsic DWP's are
induced, which possess a distribution of barriers peaked around a high barrier
height. This compares with the structurlessly distributed barrier heights of
the intrinsic DWP's, which are associated with the backbone dynamics. It is
shown that this picture is consistent with elastic measurements on polymers,
and can explain anomalous nonlogarithmic line broadening recently observed in
hole burning experiments in PMMA.Comment: 34 pages, Revtex, 9 eps-figures, accepted for publication in J. Chem.
Phy
Energy landscape, two-level systems and entropy barriers in Lennard-Jones clusters
We develop an efficient numerical algorithm for the identification of a large
number of saddle points of the potential energy function of Lennard- Jones
clusters. Knowledge of the saddle points allows us to find many thousand
adjacent minima of clusters containing up to 80 argon atoms and to locate many
pairs of minima with the right characteristics to form two-level systems (TLS).
The true TLS are singled out by calculating the ground-state tunneling
splitting. The entropic contribution to all barriers is evaluated and
discussed.Comment: 4 pages, RevTex, 2 PostScript figure
Origin of non-exponential relaxation in a crystalline ionic conductor: a multi-dimensional 109Ag NMR study
The origin of the non-exponential relaxation of silver ions in the
crystalline ion conductor Ag7P3S11 is analyzed by comparing appropriate
two-time and three-time 109Ag NMR correlation functions. The non-exponentiality
is due to a rate distribution, i.e., dynamic heterogeneities, rather than to an
intrinsic non-exponentiality. Thus, the data give no evidence for the relevance
of correlated back-and-forth jumps on the timescale of the silver relaxation.Comment: 4 pages, 3 figure
Backward correlations and dynamic heterogeneities: a computer study of ion dynamics
We analyse the correlated back and forth dynamics and dynamic
heterogeneities, i.e. the presence of fast and slow ions, for a lithium
metasilicate system via computer simulations. For this purpose we define, in
analogy to previous work in the field of glass transition, appropriate
three-time correlation functions. They contain information about the dynamics
during two successive time intervals. First we apply them to simple model
systems in order to clarify their information content. Afterwards we use this
formalism to analyse the lithium trajectories. A strong back-dragging effect is
observed, which also fulfills the time-temperature superposition principle.
Furthermore, it turns out that the back-dragging effect is long-ranged and
exceeds the nearest neighbor position. In contrast, the strength of the dynamic
heterogeneities does not fulfill the time-temperature superposition principle.
The lower the temperature, the stronger the mobility difference between fast
and slow ions. The results are then compared with the simple model systems
considered here as well as with some lattice models of ion dynamics.Comment: 12 pages, 10 figure
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