759 research outputs found
Liquid pair correlations in four spatial dimensions: Theory versus simulation
Using liquid integral equation theory, we calculate the pair correlations of
particles that interact via a smooth repulsive pair potential in d = 4 spatial
dimensions. We discuss the performance of different closures for the
Ornstein-Zernike equation, by comparing the results to computer simulation
data. Our results are of relevance to understand crystal and glass formation in
high-dimensional systems
Decidability Results for Saturation-based Model Building
Saturation-based calculi such as superposition can be successfully instantiated to decision procedures for many decidable fragments of first-order logic. In case of termination without generating an empty clause, a saturated clause set implicitly represents a minimal model for all clauses, based on the underlying term ordering of the superposition calculus. In general, it is not decidable whether a ground atom, a clause or even a formula holds in this minimal model of a satisfiable saturated clause set. Based on an extension of our superposition calculus for fixed domains with syntactic disequality constraints in a non-equational setting, we describe models given by ARM (Atomic Representations of term Models) or DIG (Disjunctions of Implicit Generalizations) representations as minimal models of finite saturated clause sets. This allows us to present several new decidability results for validity in such models. These results extend in particular the known decidability results for ARM and DIG representations
From Equilibrium to Steady State: The Transient Dynamics of Colloidal Liquids under Shear
We investigate stresses and particle motion during the start up of flow in a
colloidal dispersion close to arrest into a glassy state. A combination of
molecular dynamics simulation, mode coupling theory and confocal microscopy
experiment is used to investigate the origins of the widely observed stress
overshoot and (previously not reported) super-diffusive motion in the transient
dynamics. A link between the macro-rheological stress versus strain curves and
the microscopic particle motion is established. Negative correlations in the
transient auto-correlation function of the potential stresses are found
responsible for both phenomena, and arise even for homogeneous flows and almost
Gaussian particle displacements.Comment: 24 pages, 14 figures, J. Phys.: Condens. Matter, in pres
The Universal Fragment of Presburger Arithmetic with Unary Uninterpreted Predicates is Undecidable
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the known boundary between decidable and undecidable in that we show that the purely universal fragment of the extended theory is already undecidable. Our proof is based on a reduction of the halting problem for two-counter machines to unsatisfiability of sentences in the extended language of Presburger arithmetic that does not use existential quantification. On the other hand, we argue that a single quantifier alternation turns the set of satisfiable sentences of the extended language into a -complete set. Some of the mentioned results can be transfered to the realm of linear arithmetic over the ordered real numbers. This concerns the undecidability of the purely universal fragment and the -hardness for sentences with at least one quantifier alternation. Finally, we discuss the relevance of our results to verification. In particular, we derive undecidability results for quantified fragments of separation logic, the theory of arrays, and combinations of the theory of equality over uninterpreted functions with restricted forms of integer arithmetic. In certain cases our results even imply the absence of sound and complete deductive calculi
Band Crossing and Novel Low-Energy Behaviour in a Mean Field Theory of a Three-Band Model on a Cu--O lattice
We study correlation effects in a three-band extended Hubbard model of Cu --
O planes within the 1/N mean field approach, in the infinite U limit. We
investigate the emerging phase diagram and discuss the low energy scales
associated with each region. With increasing direct overlap between oxygen
orbitals, , the solution displays a band crossing which, for an
extended range of parameters, lies close to the Fermi level. In turn this leads
to the nearly nested character of the Fermi surface and the resulting linear
temperature dependence of the quasi-particle relaxation rate for sufficiently
large T. We also discuss the effect of band crossing on the optical
conductivity and comment on the possible experimental relevance of our
findings.Comment: 12 pages, Latex-Revtex, 6 PostScript figures. Submitted to Phys. Rev.
Tests of mode coupling theory in a simple model for two-component miscible polymer blends
We present molecular dynamics simulations on the structural relaxation of a
simple bead-spring model for polymer blends. The introduction of a different
monomer size induces a large time scale separation for the dynamics of the two
components. Simulation results for a large set of observables probing density
correlations, Rouse modes, and orientations of bond and chain end-to-end
vectors, are analyzed within the framework of the Mode Coupling Theory (MCT).
An unusually large value of the exponent parameter is obtained. This feature
suggests the possibility of an underlying higher-order MCT scenario for dynamic
arrest.Comment: Revised version. Additional figures and citation
Amorphous silica modeled with truncated and screened Coulomb interactions: A molecular dynamics simulation study
We show that finite-range alternatives to the standard long-range BKS pair
potential for silica might be used in molecular dynamics simulations. We study
two such models that can be efficiently simulated since no Ewald summation is
required. We first consider the Wolf method, where the Coulomb interactions are
truncated at a cutoff distance r_c such that the requirement of charge
neutrality holds. Various static and dynamic quantities are computed and
compared to results from simulations using Ewald summations. We find very good
agreement for r_c ~ 10 Angstroms. For lower values of r_c, the long--range
structure is affected which is accompanied by a slight acceleration of dynamic
properties. In a second approach, the Coulomb interaction is replaced by an
effective Yukawa interaction with two new parameters determined by a force
fitting procedure. The same trend as for the Wolf method is seen. However,
slightly larger cutoffs have to be used in order to obtain the same accuracy
with respect to static and dynamic quantities as for the Wolf method.Comment: 10 pages; 11 fig
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