131 research outputs found
Revisiting the slow dynamics of a silica melt using Monte Carlo simulations
We implement a standard Monte Carlo algorithm to study the slow, equilibrium
dynamics of a silica melt in a wide temperature regime, from 6100 K down to
2750 K. We find that the average dynamical behaviour of the system is in
quantitative agreement with results obtained from molecular dynamics
simulations, at least in the long-time regime corresponding to the
alpha-relaxation. By contrast, the strong thermal vibrations related to the
Boson peak present at short times in molecular dynamics are efficiently
suppressed by the Monte Carlo algorithm. This allows us to reconsider silica
dynamics in the context of mode-coupling theory, because several shortcomings
of the theory were previously attributed to thermal vibrations. A mode-coupling
theory analysis of our data is qualitatively correct, but quantitative tests of
the theory fail, raising doubts about the very existence of an avoided
singularity in this system. We discuss the emergence of dynamic heterogeneity
and report detailed measurements of a decoupling between translational
diffusion and structural relaxation, and of a growing four-point dynamic
susceptibility. Dynamic heterogeneity appears to be less pronounced than in
more fragile glass-forming models, but not of a qualitatively different nature.Comment: 13 pages, 10 figures; to be published in Phys. Rev.
Numerical simulation of inductive heating processes
For product optimization regarding weight reduction, material properties have
to be adapted efficiently. To achieve this, new compositions of materials can be created
or the manufacturing process can be changed in a way that heterogeneous distributions
of material properties are enabled. An example for such an improved process chain is
the production of thermo-mechanically graded structures like shafts. The manufacturing
method mainly consists of three stages. The first one is characterized by a local temperature
increase of the workpiece due to inductive heating. In the second phase the workpiece
is deformed and simultaneously cooled throughout the contact with the forming die. In
the last step, however, a high pressured air stream is applied, leading to a partial cooling
of the workpiece.
The inductive heating step is controlled by an alternating current inducing a high frequency
magnetic field, which causes a temperature increase due to the resulting eddy
currents. To analyse this process, the coupling between the electric and the magnetic
field is described by the fully coupled Maxwell equations. Moreover the heat conduction
equation is considered to describe thermal effects. To solve this multifield the
equations are in the first step decoupled using an additional time differentiation. In the
second step an axisymmetric case is considered, motivated by the fact that the inductive
heating process of a cylindrical shaft is analysed. Afterwards the resulting equations are
spatially discretized by the Galerkin finite element method. The temporal discretization
is carried out via the Newmark method so that afterwards the electrical source
distribution can be achieved. As a consequence the temperature evolution is determined
in a postprocessing step
Glassy dynamics in monodisperse hard ellipsoids
We present evidence from computer simulations for glassy dynamics in
suspensions of monodisperse hard ellipsoids. In equilibrium, almost spherical
ellipsoids show a first order transition from an isotropic phase to a rotator
phase. When overcompressing the isotropic phase into the rotator regime, we
observe super-Arrhenius slowing down of diffusion and relaxation, accompanied
by two-step relaxation in positional and orientational correlators. The effects
are strong enough for asymptotic laws of mode-coupling theory to apply. Glassy
dynamics are unusual in monodisperse systems. Typically, polydispersity in size
or a mixture of particle species is prerequisite to prevent crystallization.
Here, we show that a slight particle anisometry acts as a sufficient source of
disorder. This sheds new light on the question of which ingredients are
required for glass formation.Comment: included data of prolate system in all figures and text, extended
discussion of indicators of glassy dynamics, fixed symbol ambiguities,
preprint forma
Glassy behaviour in a simple topological model
In this article we study a simple, purely topological, cellular model which
is allowed to evolve through a Glauber-Kawasaki process. We find a
non-thermodynamic transition to a glassy phase in which the energy (defined as
the square of the local cell topological charge) fails to reach the equilibrium
value below a characteristic temperature which is dependent on the cooling
rate. We investigate a correlation function which exhibits aging behaviour, and
follows a master curve in the stationary regime when time is rescaled by a
factor of the relaxation time t_r. This master curve can be fitted by a von
Schweidler law in the late beta-relaxation regime. The relaxation times can be
well-fitted at all temperatures by an offset Arrhenius law. A power law can be
fitted to an intermediate temperature regime; the exponent of the power law and
the von Schweidler law roughly agree with the relationship predicted by
Mode-coupling Theory. By defining a suitable response function, we find that
the fluctuation-dissipation ratio is held until sometime later than the
appearance of the plateaux; non-monotonicity of the response is observed after
this ratio is broken, a feature which has been observed in other models with
dynamics involving activated processes.Comment: 11 pages LaTeX; minor textual corrcetions, minor corrections to figs
4 & 7
A mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid
Generalizing the mode-coupling theory for ideal liquid-glass transitions,
equations of motion are derived for the correlation functions describing the
glassy dynamics of a diatomic probe molecule immersed in a simple glass-forming
system. The molecule is described in the interaction-site representation and
the equations are solved for a dumbbell molecule consisting of two fused hard
spheres in a hard-sphere system. The results for the molecule's arrested
position in the glass state and the reorientational correlators for
angular-momentum index and near the glass transition are
compared with those obtained previously within a theory based on a
tensor-density description of the molecule in order to demonstrate that the two
approaches yield equivalent results. For strongly hindered reorientational
motion, the dipole-relaxation spectra for the -process can be mapped on
the dielectric-loss spectra of glycerol if a rescaling is performed according
to a suggestion by Dixon et al. [Phys. Rev. Lett. {\bf 65}, 1108 (1990)]. It is
demonstrated that the glassy dynamics is independent of the molecule's inertia
parameters.Comment: 19 pages, 10 figures, Phys. Rev. E, in prin
Reorientational relaxation of a linear probe molecule in a simple glassy liquid
Within the mode-coupling theory (MCT) for the evolution of structural
relaxation in glass-forming liquids, correlation functions and susceptibility
spectra are calculated characterizing the rotational dynamics of a top-down
symmetric dumbbell molecule, consisting of two fused hard spheres immersed in a
hard-sphere system. It is found that for sufficiently large dumbbell
elongations, the dynamics of the probe molecule follows the same universal
glass-transition scenario as known from the MCT results of simple liquids. The
-relaxation process of the angular-index-j=1 response is stronger,
slower and less stretched than the one for j=2, in qualitative agreement with
results found by dielectric-loss and depolarized-light-scattering spectroscopy
for some supercooled liquids. For sufficiently small elongations, the
reorientational relaxation occurs via large-angle flips, and the standard
scenario for the glass-transition dynamics is modified for odd-j responses due
to precursor phenomena of a nearby type-A MCT transition. In this case, a major
part of the relaxation outside the transient regime is described qualitatively
by the -relaxation scaling laws, while the -relaxation scaling
law is strongly disturbed.Comment: 40 pages. 10 figures as GIF-files, to be published in Phys. Rev.
The Debye-Waller factor of liquid silica: Theory and simulation
We show that the prediction of mode-coupling theory for a model of a
network-forming strong glass-former correctly describes the wave-vector
dependence of the Debye-Waller factor. To obtain a good description it is
important to take into account the triplet correlation function c_3, which we
evaluate from a computer simulation. Our results support the possibility that
this theory is able to accurately describe the non-ergodicity parameters of
simple as well as of network-forming liquids.Comment: 5 pages of Latex, 3 figure
The mean-squared displacement of a molecule moving in a glassy system
The mean-squared displacement (MSD) of a hard sphere and of a dumbbell
molecule consisting of two fused hard spheres immersed in a dense hard-sphere
system is calculated within the mode-coupling theory for ideal liquid-glass
transitions. It is proven that the velocity correlator, which is the second
time derivative of the MSD, is the negative of a completely monotone function
for times within the structural-relaxation regime. The MSD is found to exhibit
a large time interval for structural relaxation prior to the onset of the
-process which cannot be described by the asymptotic formulas for the
mode-coupling-theory-bifurcation dynamics. The -process for molecules
with a large elongation is shown to exhibit an anomalously wide cross-over
interval between the end of the von-Schweidler decay and the beginning of
normal diffusion. The diffusivity of the molecule is predicted to vary
non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin
Simulation study of Non-ergodicity Transitions: Gelation in Colloidal Systems with Short Range Attractions
Computer simulations were used to study the gel transition occurring in
colloidal systems with short range attractions. A colloid-polymer mixture was
modelled and the results were compared with mode coupling theory expectations
and with the results for other systems (hard spheres and Lennard Jones). The
self-intermediate scattering function and the mean squared displacement were
used as the main dynamical quantities. Two different colloid packing fractions
have been studied. For the lower packing fraction, -scaling holds and
the wave-vector analysis of the correlation function shows that gelation is a
regular non-ergodicity transition within MCT. The leading mechanism for this
novel non-ergodicity transition is identified as bond formation caused by the
short range attraction. The time scale and diffusion coefficient also show
qualitatively the expected behaviour, although different exponents are found
for the power-law divergences of these two quantities. The non-Gaussian
parameter was also studied and very large correction to Gaussian behaviour
found. The system with higher colloid packing fraction shows indications of a
nearby high-order singularity, causing -scaling to fail, but the
general expectations for non-ergodicity transitions still hold.Comment: 13 pages, 15 figure
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