337 research outputs found
Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems
This series of papers is devoted to identifying and explaining the properties
of strongly correlating liquids, i.e., liquids with more than 90% correlation
between their virial W and potential energy U fluctuations in the NVT ensemble.
Paper IV [N. Gnan et al., J. Chem. Phys. v131, 234504 (2009)] showed that
strongly correlating liquids have "isomorphs", which are curves in the phase
diagram along which structure, dynamics, and some thermodynamic properties are
invariant in reduced units. In the present paper, using the fact that
reduced-unit radial distribution functions are isomorph invariant, we derive an
expression for the shapes of isomorphs in the WU phase diagram of generalized
Lennard-Jones systems of one or more types of particles. The isomorph shape
depends only on the Lennard-Jones exponents; thus all isomorphs of standard
Lennard-Jones systems (with exponents 12 and 6) can be scaled onto to a single
curve. Two applications are given. One is testing the prediction that the
solid-liquid coexistence curve follows an isomorph by comparing to recent
simulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellent
agreement is found on the liquid side of the coexistence, whereas the agreement
is worse on the solid side. A second application is the derivation of an
approximate equation of state for generalized Lennard-Jones systems by
combining the isomorph theory with the Rosenfeld-Tarazona expression for the
temperature dependence of potential energy on isochores. It is shown that the
new equation of state agrees well with simulations.Comment: 12 pages, 14 figures, Section on solid-liquid coexistence expande
Strong pressure-energy correlations in van der Waals liquids
Strong correlations between equilibrium fluctuations of the configurational
parts of pressure and energy are found in the Lennard-Jones liquid and other
simple liquids, but not in hydrogen-bonding liquids like methanol and water.
The correlations, that are present also in the crystal and glass phases,
reflect an effective inverse power-law repulsive potential dominating
fluctuations, even at zero and slightly negative pressure. In experimental data
for supercritical Argon, the correlations are found to be approximately 96%.
Consequences for viscous liquid dynamics are discussed.Comment: Phys. Rev. Lett., in pres
Excess specific heat and evidence of zero point entropy in magnetic glassy state of half-doped manganites
We show that specific heat C has non-Debye behavior for glassy states in
half-doped manganites. Irrespective of the magnetic order or electronic states,
these magnetic glasses have higher C compared to their equilibrium
counterparts. The excess C contributed by the glassy state varies linearly
with temperature similar to conventional glasses indicating tunneling in the
two-level systems. These glassy states show signature of zero point entropy.
Magnetic glasses can be produced simply by different field cooling protocols
and may be considered ideal magnetic counterpart of the conventional glass
A model for the generic alpha relaxation of viscous liquids
Dielectric measurements on molecular liquids just above the glass transition
indicate that alpha relaxation is characterized by a generic high-frequency
loss varying as , whereas deviations from this come from one or
more low-lying beta processes [Olsen et al, Phys. Rev. Lett. {\bf 86} (2001)
1271]. Assuming that long-wavelength fluctuations dominate the dynamics, a
model for the dielectric alpha relaxation based on the simplest coupling
between the density and dipole density fields is proposed here. The model,
which is solved in second order perturbation theory in the Gaussian
approximation, reproduces the generic features of alpha relaxation
Feasibility of single-order parameter description of equilibrium viscous liquid dynamics
Molecular dynamics results for the dynamic Prigogine-Defay ratio are
presented for two glass-forming liquids, thus evaluating the experimentally
relevant quantity for testing whether metastable-equilibrium liquid dynamics to
a good approximation are described by a single parameter. For the Kob-Andersen
binary Lennard-Jones mixture as well as for an asymmetric dumbbell model liquid
a single-parameter description works quite well. This is confirmed by
time-domain results where it is found that energy and pressure fluctuations are
strongly correlated on the alpha-time scale in the NVT ensemble; in the NpT
ensemble energy and volume fluctuations similarly correlate strongly.Comment: Phys. Rev. E, in pres
Solidity of viscous liquids. V. Long-wavelength dominance of the dynamics
This paper is the fifth in a series exploring the physical consequences of
the solidity of glass-forming liquids. Paper IV proposed a model where the
density field is described by a time-dependent Ginzburg-Landau equation of the
nonconserved type with rates in space of the form . The
model assumes that where is the average intermolecular
distance; this inequality expresses a long-wavelength dominance of the dynamics
which implies that the Hamiltonian (free energy) to a good approximation may be
taken to be ultralocal. In the present paper we argue that this is the simplest
model consistent with the following three experimental facts: 1) Viscous
liquids approaching the glass transition do not develop long-range order; 2)
The glass has lower compressibility than the liquid; 3) The alpha process
involves several decades of relaxation times shorter than the mean relaxation
time. The paper proceeds to list six further experimental facts characterizing
equilibrium viscous liquid dynamics and shows that these are readily understood
in terms of the model; some are direct consequences, others are quite natural
when viewed in light of the model
Solidity of Viscous Liquids
Recent NMR experiments on supercooled toluene and glycerol by Hinze and
Bohmer show that small rotation angles dominate with only few large molecular
rotations. These results are here interpreted by assuming that viscous liquids
are solid-like on short length scales. A characteristic length, the "solidity
length", separates solid-like behavior from liquid-like behavior.Comment: Plain RevTex file, no figure
Programmable models of growth and mutation of cancer-cell populations
In this paper we propose a systematic approach to construct mathematical
models describing populations of cancer-cells at different stages of disease
development. The methodology we propose is based on stochastic Concurrent
Constraint Programming, a flexible stochastic modelling language. The
methodology is tested on (and partially motivated by) the study of prostate
cancer. In particular, we prove how our method is suitable to systematically
reconstruct different mathematical models of prostate cancer growth - together
with interactions with different kinds of hormone therapy - at different levels
of refinement.Comment: In Proceedings CompMod 2011, arXiv:1109.104
Single-order-parameter description of glass-forming liquids:A one-frequency test
Thermo-viscoelastic linear-response functions are calculated from the master
equation describing viscous liquid inherent dynamics. From the imaginary parts
of the frequency-dependent isobaric specific heat, isothermal compressibility,
and isobaric thermal expansion coefficient, we define a "linear dynamic
Prigogine-Defay ratio" with the property that if this quantity is unity atone
frequency, then it is unity at all frequencies. This happens if and only if
there is a single-order-parameter description of the thermo-viscoelastic linear
responses via an order parameter (which may be non-exponential in time).
Generalizations to other cases of thermodynamic control parameters than
temperature and pressure are treated in an Appendix.Comment: Replaces arXiv:cond-mat/040570
Time-temperature superposition in viscous liquids
Dielectric relaxation measurements on supercooled triphenyl phosphite show
that at low temperatures time-temperature superposition (TTS) is accurately
obeyed for the primary (alpha) relaxation process. Measurements on 6 other
molecular liquids close to the calorimetric glass transition indicate that TTS
is linked to an high-frequency decay of the alpha loss, while
the loss peak width is nonuniversal.Comment: 4 page
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