329 research outputs found
Thermodynamics of condensed matter with strong pressure-energy correlations
We show that for any liquid or solid with strong correlation between its
virial and potential-energy equilibrium fluctuations, the temperature is
a product of a function of excess entropy per particle and a function of
density, . This implies that 1) the system's isomorphs (curves
in the phase diagram of invariant structure and dynamics) are described by
, 2) the density-scaling exponent is a function of
density only, 3) a Gr{\"u}neisen-type equation of state applies for the
configurational degrees of freedom. For strongly correlating atomic systems one
has in which the only non-zero terms are those
appearing in the pair potential expanded as . Molecular
dynamics simulations of Lennard-Jones type systems confirm the theory
NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
An algorithm is derived for computer simulation of geodesics on the constant
potential-energy hypersurface of a system of N classical particles. First, a
basic time-reversible geodesic algorithm is derived by discretizing the
geodesic stationarity condition and implementing the constant potential energy
constraint via standard Lagrangian multipliers. The basic NVU algorithm is
tested by single-precision computer simulations of the Lennard-Jones liquid.
Excellent numerical stability is obtained if the force cutoff is smoothed and
the two initial configurations have identical potential energy within machine
precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for
very long runs in order to compensate for the accumulation of numerical errors
that eventually lead to "entropic drift" of the potential energy towards higher
values. A modification of the basic NVU algorithm is introduced that ensures
potential-energy and step-length conservation; center-of-mass drift is also
eliminated. Analytical arguments confirmed by simulations demonstrate that the
modified NVU algorithm is absolutely stable. Finally, simulations show that the
NVU algorithm and the standard leap-frog NVE algorithm have identical radial
distribution functions for the Lennard-Jones liquid
Formidlende fortĂŚllinger - M.A. Goldschmidts forfatterskab
Tales that convey - the writings of M.A. GoldschmidtThe Jewish tales that author and journalist MeĂŻr Aron Goldschmidt wrote during the second half of the nineteenth century describe the religious development and emancipation of the Jews of Western Europe throughout the century. This article shows how Goldschmidtâs travels in Europe provided him with a cosmopolitan view on the religious development of the Jews and stresses the importance of his Jewish stories, not only in national but also in international means.When Goldschmidt first travelled abroad in 1846, he visited Germany, Italy and Switzerland and during his visits he gained a broader religious and political view on the Jewish emancipation. He brought home with him a new understanding of his religion and a political vision, which he communicated in his Jewish stories.Many of Goldschmidtâs viewpoints were similar to those of the Jewish philosopher Moses Mendelssohn, who expressed his viewpoints after his religion was challenged by philosopher and writer Gotthold Ephraim Lessing in the eighteenth century. Mendelssohn emphasised the Jewish laws and traditions and did not believe that integrating with the Christian people necessarily equalled a decrease of the Jewish faith. Goldschmidt shared Mendelssohnâs thoughts on the development of the Jewish religion, and he feared that the Jewish emancipation would lead to assimilation of the Jews.In his first novel, The Jew of Denmark, Goldschmidt expresses a criticism of the ambiguous politics behind the emancipation that he felt announced religious tolerance when really wishing for the Jews to convert to Christianity. He also criticises the Jewish reformers for wanting education and integration at the expense of their religion. Goldschmidt was a strong advocate of enlightenment and education like the Jewish reformers, but he did not want to compromise his religious beliefs.In his novel, The Raven, he conveys his political vision â a vision that unites his view on religion with the nation. To Goldschmidt, religion was a personal matter that no government should interfere with. In The Raven he implicitly shows how people can put their differences in religion, class and profession aside and agree on a common idea. Goldschmidt ended his literary career with a series of Jewish ghetto-stories that praise the Jewish religion but at the same time show that the meaning of the religion has changed and that the orthodox Jew is a diminishing kind.Goldschmidtâs Jewish stories are international literature that provides a personal insight into the Jewish emancipation of the Western European Jews in the nineteenth century
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
Isomorphs in model molecular liquids
Isomorphs are curves in the phase diagram along which a number of static and
dynamic quantities are invariant in reduced units. A liquid has good isomorphs
if and only if it is strongly correlating, i.e., the equilibrium
virial/potential energy fluctuations are more than 90% correlated in the NVT
ensemble. This paper generalizes isomorphs to liquids composed of rigid
molecules and study the isomorphs of two systems of small rigid molecules, the
asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for
both systems we find that the isochoric heat capacity, the excess entropy, the
reduced molecular center-of-mass self part of the intermediate scattering
function, the reduced molecular center-of-mass radial distribution function to
a good approximation are invariant along an isomorph. In agreement with theory,
we also find that an instantaneous change of temperature and density from an
equilibrated state point to another isomorphic state point leads to no
relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be
more approximative than those of the asymmetric dumbbell model, which is
consistent with the OTP model being less strongly correlating. For both models
we find "master isomorphs", i.e., isomorphs have identical shape in the
virial/potential energy phase diagram.Comment: 20 page
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
Growing Correlation Length on Cooling Below the Onset of Caging in a Simulated Glass-Forming Liquid
We present a calculation of a fourth-order, time-dependent density
correlation function that measures higher-order spatiotemporall correlations of
the density of a liquid. From molecular dynamics simulations of a glass-forming
Lennard-Jones liquid, we find that the characteristic length scale of this
function has a maximum as a function of time which increases steadily beyond
the characteristic length of the static pair correlation function in the
temperature range approaching the mode coupling temperature from above
Ac hopping conduction at extreme disorder takes place on the percolating cluster
Simulations of the random barrier model show that ac currents at extreme
disorder are carried almost entirely by the percolating cluster slightly above
threshold; thus contradicting traditional theories contributions from isolated
low-activation-energy clusters are negligible. The effective medium
approximation in conjunction with the Alexander-Orbach conjecture leads to an
excellent analytical fit to the universal ac conductivity with no nontrivial
fitting parameters
Communication: The Rosenfeld-Tarazona expression for liquidsâ specific heat:A numerical investigation of eighteen systems
We investigate the accuracy of the expression of Rosenfeld and Tarazona (RT)
for the excess isochoric heat capacity, C_V^{ex} \propto T^{-2/5}, for eighteen
model liquids. Previous investigations have reported no unifying features of
breakdown for the RT expression. Here liquids with different stoichiometric
composition, molecular topology, chemical interactions, degree of undercooling,
and environment are investigated. We find that the RT expression is a better
approximation for liquids with strong correlations between equilibrium
fluctuations of virial and potential energy, i.e., Roskilde simple liquids
[Ingebrigtsen et al., Phys. Rev. X 2, 011011 (2012)]. This observation holds
even for molecular liquids under severe nanoscale confinement, the physics of
which is completely different from the original RT bulk hard-sphere fluid
arguments. The density dependence of the specific heat is predicted from the
isomorph theory for Roskilde simple liquids, which in combination with the RT
expression provides a complete description of the specific heat's density and
temperature dependence.Comment: 6 page
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