2,280 research outputs found
An independent axiomatisation for free short-circuit logic
Short-circuit evaluation denotes the semantics of propositional connectives
in which the second argument is evaluated only if the first argument does not
suffice to determine the value of the expression. Free short-circuit logic is
the equational logic in which compound statements are evaluated from left to
right, while atomic evaluations are not memorised throughout the evaluation,
i.e., evaluations of distinct occurrences of an atom in a compound statement
may yield different truth values. We provide a simple semantics for free SCL
and an independent axiomatisation. Finally, we discuss evaluation strategies,
some other SCLs, and side effects.Comment: 36 pages, 4 tables. Differences with v2: Section 2.1: theorem
Thm.2.1.5 and further are renumbered; corrections: p.23, line -7, p.24, lines
3 and 7. arXiv admin note: substantial text overlap with arXiv:1010.367
Application of the Optimized Baxter Model to the hard-core attractive Yukawa system
We perform Monte Carlo simulations on the hard-core attractive Yukawa system
to test the Optimized Baxter Model that was introduced in [P.Prinsen and T.
Odijk, J. Chem. Phys. 121, p.6525 (2004)] to study a fluid phase of spherical
particles interacting through a short-range pair potential. We compare the
chemical potentials and pressures from the simulations with analytical
predictions from the Optimized Baxter Model. We show that the model is accurate
to within 10 percent over a range of volume fractions from 0.1 to 0.4,
interaction strengths up to three times the thermal energy and interaction
ranges from 6 to 20 % of the particle diameter, and performs even better in
most cases. We furthermore establish the consistency of the model by showing
that the thermodynamic properties of the Yukawa fluid computed via simulations
may be understood on the basis of one similarity variable, the stickiness
parameter defined within the Optimized Baxter Model. Finally we show that the
Optimized Baxter Model works significantly better than an often used, naive
method determining the stickiness parameter by equating the respective second
virial coefficients based on the attractive Yukawa and Baxter potentials.Comment: 11 pages, 8 figure
Propositional logic with short-circuit evaluation: a non-commutative and a commutative variant
Short-circuit evaluation denotes the semantics of propositional connectives
in which the second argument is evaluated only if the first argument does not
suffice to determine the value of the expression. Short-circuit evaluation is
widely used in programming, with sequential conjunction and disjunction as
primitive connectives.
We study the question which logical laws axiomatize short-circuit evaluation
under the following assumptions: compound statements are evaluated from left to
right, each atom (propositional variable) evaluates to either true or false,
and atomic evaluations can cause a side effect. The answer to this question
depends on the kind of atomic side effects that can occur and leads to
different "short-circuit logics". The basic case is FSCL (free short-circuit
logic), which characterizes the setting in which each atomic evaluation can
cause a side effect. We recall some main results and then relate FSCL to MSCL
(memorizing short-circuit logic), where in the evaluation of a compound
statement, the first evaluation result of each atom is memorized. MSCL can be
seen as a sequential variant of propositional logic: atomic evaluations cannot
cause a side effect and the sequential connectives are not commutative. Then we
relate MSCL to SSCL (static short-circuit logic), the variant of propositional
logic that prescribes short-circuit evaluation with commutative sequential
connectives.
We present evaluation trees as an intuitive semantics for short-circuit
evaluation, and simple equational axiomatizations for the short-circuit logics
mentioned that use negation and the sequential connectives only.Comment: 34 pages, 6 tables. Considerable parts of the text below stem from
arXiv:1206.1936, arXiv:1010.3674, and arXiv:1707.05718. Together with
arXiv:1707.05718, this paper subsumes most of arXiv:1010.367
Using nonequilibrium fluctuation theorems to understand and correct errors in equilibrium and nonequilibrium discrete Langevin dynamics simulations
Common algorithms for computationally simulating Langevin dynamics must
discretize the stochastic differential equations of motion. These resulting
finite time step integrators necessarily have several practical issues in
common: Microscopic reversibility is violated, the sampled stationary
distribution differs from the desired equilibrium distribution, and the work
accumulated in nonequilibrium simulations is not directly usable in estimators
based on nonequilibrium work theorems. Here, we show that even with a
time-independent Hamiltonian, finite time step Langevin integrators can be
thought of as a driven, nonequilibrium physical process. Once an appropriate
work-like quantity is defined -- here called the shadow work -- recently
developed nonequilibrium fluctuation theorems can be used to measure or correct
for the errors introduced by the use of finite time steps. In particular, we
demonstrate that amending estimators based on nonequilibrium work theorems to
include this shadow work removes the time step dependent error from estimates
of free energies. We also quantify, for the first time, the magnitude of
deviations between the sampled stationary distribution and the desired
equilibrium distribution for equilibrium Langevin simulations of solvated
systems of varying size. While these deviations can be large, they can be
eliminated altogether by Metropolization or greatly diminished by small
reductions in the time step. Through this connection with driven processes,
further developments in nonequilibrium fluctuation theorems can provide
additional analytical tools for dealing with errors in finite time step
integrators.Comment: 11 pages, 4 figure
The steady-state of heterogeneous catalysis, studied by first-principles statistical mechanics
The turn-over frequency of the catalytic oxidation of CO at RuO2(110) was
calculated as function of temperature and partial pressures using ab initio
statistical mechanics. The underlying energetics of the gas-phase molecules,
dissociation, adsorption, surface diffusion, surface chemical reactions, and
desorption were obtained by all-electron density-functional theory. The
resulting CO2 formation rate [in the full (T, p_CO, p_O2)-space], the movies
displaying the atomic motion and reactions over times scales from picoseconds
to seconds, and the statistical analyses provide insights into the concerted
actions ruling heterogeneous catalysis and open thermodynamic systems in
general.Comment: 4 pages including 3 figures, Related publications can be found at
http://www.fhi-berlin.mpg.de/th/paper.htm
Crystal Nucleation of Colloidal Suspensions under Shear
We use Brownian Dynamics simulations in combination with the umbrella
sampling technique to study the effect of shear flow on homogeneous crystal
nucleation. We find that a homogeneous shear rate leads to a significant
suppression of the crystal nucleation rate and to an increase of the size of
the critical nucleus. A simple, phenomenological extension of classical
nucleation theory accounts for these observations. The orientation of the
crystal nucleus is tilted with respect to the shear direction.Comment: 4 pages, 3 figures, Submitted to Phys. Rev. Let
Phase diagram of Hertzian spheres
We report the phase diagram of interpenetrating Hertzian spheres. The Hertz
potential is purely repulsive, bounded at zero separation, and decreases
monotonically as a power law with exponent 5/2, vanishing at the overlapping
threshold. This simple functional describes the elastic interaction of weakly
deformable bodies and, therefore, it is a reliable physical model of soft
macromolecules, like star polymers and globular micelles. Using thermodynamic
integration and extensive Monte Carlo simulations, we computed accurate free
energies of the fluid phase and a large number of crystal structures. For this,
we defined a general primitive unit cell that allows for the simulation of any
lattice. We found multiple re-entrant melting and first-order transitions
between crystals with cubic, trigonal, tetragonal, and hexagonal symmetries.Comment: The inset in Fig. 4 in the previous version had incorrect ordinate
values. This has been corrected here. This mistake does not affect the
remaining content of the articl
FORGE enabling FIRE facilities for the eLearning community
International audienceMany engineering students at third-level institutions across the world will not have the advantage of using real-world experimentation equipment, as the infrastructure and resources required for this activity are too expensive. This paper explains how the FORGE (Forging Online Education through FIRE) FP7 project transforms Future Internet Research and Experimentation (FIRE) testbed facilities into educational resources for the eLearning community. This is achieved by providing a framework for remote experimentation that supports easy access and control to testbed infrastructure for students and educators. Moreover, we identify a list of recommendations to support development of eLearning courses that access these facilities and highlight some of the challenges encountered by FORGE
Melting of Polydisperse Hard Disks
The melting of a polydisperse hard disk system is investigated by Monte Carlo
simulations in the semigrand canonical ensemble. This is done in the context of
possible continuous melting by a dislocation unbinding mechanism, as an
extension of the 2D hard disk melting problem. We find that while there is
pronounced fractionation in polydispersity, the apparent density-polydispersity
gap does not increase in width, contrary to 3D polydisperse hard spheres. The
point where the Young's modulus is low enough for the dislocation unbinding to
occur moves with the apparent melting point, but stays within the density gap,
just like for the monodisperse hard disk system. Additionally, we find that
throughout the accessible polydispersity range, the bound dislocation-pair
concentration is high enough to affect the dislocation unbinding melting as
predicted by Kosterlitz, Thouless, Halperin, Nelson and Young.Comment: 6 pages, 6 figure
- …