137 research outputs found
Growing length and time scales in glass forming liquids
We study the growing time scales and length scales associated with dynamical
slow down for a realistic glass former, using computer simulations. We perform
finite size scaling to evaluate a length scale associated with dynamical
heterogeneity which grows as temperature decreases. However, relaxation times
which also grow with decreasing temperature, do not show the same kind of
scaling behavior with system size as the dynamical heterogeneity, indicating
that relaxation times are not solely determined by the length scale of
dynamical heterogeneity. We show that relaxation times are instead determined,
for all studied system sizes and temperatures, by configurational entropy, in
accordance with the Adam-Gibbs relation, but in disagreement with theoretical
expectations based on spin-glass models that configurational entropy is not
relevant at temperatures substantially above the critical temperature of mode
coupling theory. The temperature dependence of the heterogeneity length scale
shows significant deviations from theoretical expectations, and the length
scale one may extract from the system size dependence of the configurational
entropy has much weaker temperature dependence compared to the heterogeneity
length scale at all studied temperatures. Our results provide new insights into
the dynamics of glass-forming liquids and pose serious challenges to existing
theoretical descriptions
Short-time -relaxation in glass-forming liquids is cooperative in nature
Temporal relaxation of density fluctuations in supercooled liquids near the
glass transition occurs in multiple steps. The short-time -relaxation is
generally attributed to spatially local processes involving the rattling motion
of a particle in the transient cage formed by its neighbors. Using molecular
dynamics simulations for three model glass-forming liquids, we show that the
-relaxation is actually cooperative in nature. Using finite-size scaling
analysis, we extract a growing length-scale associated with -relaxation
from the observed dependence of the -relaxation time on the system size.
Remarkably, the temperature dependence of this length scale is found to be the
same as that of the length scale that describes the spatial heterogeneity of
local dynamics in the long-time -relaxation regime. These results show
that the conventional interpretation of -relaxation as a local process
is too simplified and provide a clear connection between short-time dynamics
and long-time structural relaxation in glass-forming liquids
Breakdown of the Stokes-Einstein relation in two, three and four dimensions
The breakdown of the Stokes-Einstein (SE) relation between diffusivity and
viscosity at low temperatures is considered to be one of the hallmarks of
glassy dynamics in liquids. Theoretical analyses relate this breakdown with the
presence of heterogeneous dynamics, and by extension, with the fragility of
glass formers. We perform an investigation of the breakdown of the SE relation
in 2, 3 and 4 dimensions, in order to understand these interrelations. Results
from simulations of model glass formers show that the degree of the breakdown
of the SE relation decreases with increasing spatial dimensionality. The
breakdown itself can be rationalized via the difference between the activation
free energies for diffusivity and viscosity (or relaxation times) in the
Adam-Gibbs relation in three and four dimensions. The behavior in two
dimensions also can be understood in terms of a generalized Adam-Gibbs relation
that is observed in previous work. We calculate various measures of
heterogeneity of dynamics and find that the degree of the SE breakdown and
measures of heterogeneity of dynamics are generally well correlated but with
some exceptions. The two dimensional systems we study show deviations from the
pattern of behavior of the three and four dimensional systems both at high and
low temperatures. The fragility of the studied liquids is found to increase
with spatial dimensionality, contrary to the expectation based on the
association of fragility with heterogeneous dynamics
Block Analysis for the Calculation of Dynamic and Static Length Scales in Glass-Forming Liquids
We present {\it block analysis}, an efficient method to perform finite-size
scaling for obtaining the length scale of dynamic heterogeneity and the
point-to-set length scale for generic glass-forming liquids. This method
involves considering blocks of varying sizes embedded in a system of a fixed
(large) size. The length scale associated with dynamic heterogeneity is
obtained from a finite-size scaling analysis of the dependence of the
four-point dynamic susceptibility on the block size. The block size dependence
of the variance of the -relaxation time yields the static point-to-set
length scale. The values of the obtained length scales agree quantitatively
with those obtained from other conventional methods. This method provides an
efficient experimental tool for studying the growth of length scales in systems
such as colloidal glasses for which performing finite-size scaling by carrying
out experiments for varying system sizes may not be feasible.Comment: 5 pages, 3 figure
Glass Transition in Supercooled Liquids with Medium Range Crystalline Order
The origins of rapid dynamical slow down in glass forming liquids in the
growth of static length scales, possibly associated with identifiable
structural ordering, is a much debated issue. Growth of medium range
crystalline order (MRCO) has been observed in various model systems to be
associated with glassy behaviour. Such observations raise the question about
the eventual state reached by a glass former, if allowed to relax for
sufficiently long times. Is a slowly growing crystalline order responsible for
slow dynamics? Are the molecular mechanisms for glass transition in liquids
with and without MRCO the same? If yes, glass formers with MRCO provide a
paradigm for understanding glassy behaviour generically. If not, systems with
MRCO form a new class of glass forming materials whose molecular mechanism for
slow dynamics may be easier to understand in terms of growing crystalline
order, and should be approached in that manner, even while they will not
provide generic insights. In this study we perform extensive molecular dynamics
simulations of a number of glass forming liquids in two dimensions and show
that the static and dynamic properties of glasses with MRCO are different from
other glass forming liquids with no predominant local order. We also resolve an
important issue regarding the so-called Point-to-set method for determining
static length scales, and demonstrate it to be a robust, order agnostic, method
for determining static correlation lengths in glass formers
Equilibrium glassy phase in a polydisperse hard sphere system
The phase diagram of a polydisperse hard sphere system is examined by
numerical minimization of a discretized form of the Ramakrishnan-Yussouff free
energy functional. Crystalline and glassy local minima of the free energy are
located and the phase diagram in the density-polydispersity plane is mapped out
by comparing the free energies of different local minima. The crystalline phase
disappears and the glass becomes the equilibrium phase beyond a "terminal"
value of the polydispersity. A crystal to glass transition is also observed as
the density is increased at high polydispersity. The phase diagram obtained in
our study is qualitatively similar to that of hard spheres in a quenched random
potential.Comment: 4 pages, 4 figure
Complex Correlation Measure: a novel descriptor for Poincaré plot
<p>Abstract</p> <p>Background</p> <p>Poincaré plot is one of the important techniques used for visually representing the heart rate variability. It is valuable due to its ability to display nonlinear aspects of the data sequence. However, the problem lies in capturing temporal information of the plot quantitatively. The standard descriptors used in quantifying the Poincaré plot (<it>SD</it>1, <it>SD</it>2) measure the gross variability of the time series data. Determination of advanced methods for capturing temporal properties pose a significant challenge. In this paper, we propose a novel descriptor "Complex Correlation Measure (<it>CCM</it>)" to quantify the temporal aspect of the Poincaré plot. In contrast to <it>SD</it>1 and <it>SD</it>2, the <it>CCM </it>incorporates point-to-point variation of the signal.</p> <p>Methods</p> <p>First, we have derived expressions for <it>CCM</it>. Then the sensitivity of descriptors has been shown by measuring all descriptors before and after surrogation of the signal. For each case study, <it>lag-1 </it>Poincaré plots were constructed for three groups of subjects (Arrhythmia, Congestive Heart Failure (CHF) and those with Normal Sinus Rhythm (NSR)), and the new measure <it>CCM </it>was computed along with <it>SD</it>1 and <it>SD</it>2. ANOVA analysis distribution was used to define the level of significance of mean and variance of <it>SD</it>1, <it>SD</it>2 and <it>CCM </it>for different groups of subjects.</p> <p>Results</p> <p><it>CCM </it>is defined based on the autocorrelation at different lags of the time series, hence giving an in depth measurement of the correlation structure of the Poincaré plot. A surrogate analysis was performed, and the sensitivity of the proposed descriptor was found to be higher as compared to the standard descriptors. Two case studies were conducted for recognizing arrhythmia and congestive heart failure (CHF) subjects from those with NSR, using the Physionet database and demonstrated the usefulness of the proposed descriptors in biomedical applications. <it>CCM </it>was found to be a more significant (<it>p </it>= 6.28E-18) parameter than <it>SD</it>1 and <it>SD</it>2 in discriminating arrhythmia from NSR subjects. In case of assessing CHF subjects also against NSR, <it>CCM </it>was again found to be the most significant (<it>p </it>= 9.07E-14).</p> <p>Conclusion</p> <p>Hence, <it>CCM </it>can be used as an additional Poincaré plot descriptor to detect pathology.</p
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