1,243 research outputs found

### Scaling behavior in the dynamics of a supercooled Lennard-Jones mixture

We present the results of a large scale molecular dynamics computer
simulation of a binary, supercooled Lennard-Jones fluid. At low temperatures
and intermediate times the time dependence of the intermediate scattering
function is well described by a von Schweidler law. The von Schweidler exponent
is independent of temperature and depends only weakly on the type of
correlator. For long times the correlation functions show a Kohlrausch behavior
with an exponent $\beta$ that is independent of temperature. This dynamical
behavior is in accordance with the mode-coupling theory of supercooled liquids.Comment: 6 pages, RevTex, three postscript figures available on request,
MZ-Physics-10

### 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
${\bf F}_{ll'}^m(q)$ and the critical amplitudes of the $\beta$ - relaxation
${\bf H}_{ll'}^m(q)$ are solved up to a cut off $l_{co}$ = 2 without any
further approximations.
Here $l,m$ 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 $T_c$. 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 $l_{co}=4$. In addition we
also propose a new method for the calculation of the critical nonergodicity
parameterComment: 27 pages, 17 figure

### Microscopic theory for the glass transition in a system without static correlations

We study the orientational dynamics of infinitely thin hard rods of length L,
with the centers-of-mass fixed on a simple cubic lattice with lattice constant
a.We approximate the influence of the surrounding rods onto dynamics of a pair
of rods by introducing an effective rotational diffusion constant D(l),l=L/a.
We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a
time-dependent torque-torque correlator of an isolated pair of rods. A glass
transition occurs at l_c, if v(l_c)=1. We present a variational and a
numerically exact evaluation of v(l).Close to l_c the diffusion constant
decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a
glass transition in the absence of any static correlations, in contrast to
present form of mode coupling theory.Comment: 6 pages, 3 figure

### Synthesizing benchmarks for predictive modeling

Predictive modeling using machine learning is an effective method for building compiler heuristics, but there is a shortage of benchmarks. Typical machine learning experiments outside of the compilation field train over thousands or millions of examples. In machine learning for compilers, however, there are typically only a few dozen common benchmarks available. This limits the quality of learned models, as they have very sparse training data for what are often high-dimensional feature spaces. What is needed is a way to generate an unbounded number of training programs that finely cover the feature space. At the same time the generated programs must be similar to the types of programs that human developers actually write, otherwise the learning will target the wrong parts of the feature space.
We mine open source repositories for program fragments and apply deep learning techniques to automatically construct models for how humans write programs. We sample these models to generate an unbounded number of runnable training programs. The quality of the programs is such that even human developers struggle to distinguish our generated programs from hand-written code.
We use our generator for OpenCL programs, CLgen, to automatically synthesize thousands of programs and show that learning over these improves the performance of a state of the art predictive model by 1.27×. In addition, the fine covering of the feature space automatically exposes weaknesses in the feature design which are invisible with the sparse training examples from existing benchmark suites. Correcting these weaknesses further increases performance by 4.30×

### 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

### General criteria for the stability of uniaxially ordered states of Incommensurate-Commensurate Systems

Reconsidering the variational procedure for uniaxial systems modeled by
continuous free energy functionals, we derive new general conditions for
thermodynamic extrema. The utility of these conditions is briefly illustrated
on the models for the classes I and II of incommensurate-commensurate systems.Comment: 5 pages, to be published in Phys. Rev. Let

### Brillouin scattering studies in Fe$_3$O$_4$ across the Verwey transition

Brillouin scattering studies have been carried out on high quality single
crystals of Fe$_3$O$_4$ with [100] and [110] faces in the temperature range of
300 to 30 K. The room temperature spectrum shows a surface Rayleigh wave (SRW)
mode at 8 GHz and a longitudinal acoustic (LA) mode at 60 GHz. The SRW mode
frequency shows a minimum at the Verwey transition temperature $T_V$ of 123 K.
The softening of the SRW mode frequency from about 250 K to $T_V$ can be
quantitatively understood as a result of a decrease in the shear elastic
constant C$_{44}$, arising from the coupling of shear strain to charge
fluctuations. On the other hand, the LA mode frequency does not show any
significant change around $T_V$, but shows a large change in its intensity. The
latter shows a maximum at around 120 K in the cooling run and at 165 K in the
heating run, exhibiting a large hysteresis of 45 K. This significant change in
intensity may be related to the presence of stress-induced ordering of
Fe$^{3+}$ and Fe$^{2+}$ at the octahedral sites, as well as to stress-induced
domain wall motion.Comment: 14 pages, 3 figures, accepted in Physical Review B 200

### Coupling of the lattice and superlattice deformations and hysteresis in thermal expansion for the quasi one-dimensional conductor TaS$_3$

An original interferometer-based setup for measurements of length of
needle-like samples is developed, and thermal expansion of o-TaS$_3$ crystals
is studied. Below the Peierls transition the temperature hysteresis of length
$L$ is observed, the width of the hysteresis loop $\delta L/L$ being up to $5
\cdot 10^{-5}$. The behavior of the loop is anomalous: the length changes so
that it is in front of its equilibrium value. The hysteresis loop couples with
that of conductivity. The sign and the value of the length hysteresis are
consistent with the strain dependence of the charge-density waves (CDW) wave
vector. With lowering temperature down to 100 K the CDW elastic modulus grows
achieving a value comparable with the lattice Young modulus. Our results could
be helpful in consideration of different systems with intrinsic
superstructures.Comment: 4 pages, 3 figures. Phys. Rev. Lett., accepted for publicatio

### A Model for the Two-Phase Behavior of Fluids in Dilute Porous Media

Experiments show that the coexistence region of a vapor-liquid system or binary liquid mixture is dramatically narrowed when the fluid is confined in a dilute porous medium such as a silica aerogel. We propose a simple model of the gel as a periodic array of cylindrical strands, and study the phase behavior of an Ising system confined in this geometry. Our results suggest that the coexistence region should widen out at lower temperatures, and that the narrowness observed near the critical point may be a fluctuation-induced effect

### 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 $q$-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

- …