35,569 research outputs found
Cooperation between Top-Down and Bottom-Up Theorem Provers
Top-down and bottom-up theorem proving approaches each have specific
advantages and disadvantages. Bottom-up provers profit from strong redundancy
control but suffer from the lack of goal-orientation, whereas top-down provers
are goal-oriented but often have weak calculi when their proof lengths are
considered. In order to integrate both approaches, we try to achieve
cooperation between a top-down and a bottom-up prover in two different ways:
The first technique aims at supporting a bottom-up with a top-down prover. A
top-down prover generates subgoal clauses, they are then processed by a
bottom-up prover. The second technique deals with the use of bottom-up
generated lemmas in a top-down prover. We apply our concept to the areas of
model elimination and superposition. We discuss the ability of our techniques
to shorten proofs as well as to reorder the search space in an appropriate
manner. Furthermore, in order to identify subgoal clauses and lemmas which are
actually relevant for the proof task, we develop methods for a relevancy-based
filtering. Experiments with the provers SETHEO and SPASS performed in the
problem library TPTP reveal the high potential of our cooperation approaches
Non--Newtonian viscosity of interacting Brownian particles: comparison of theory and data
A recent first-principles approach to the non-linear rheology of dense
colloidal suspensions is evaluated and compared to simulation results of
sheared systems close to their glass transitions. The predicted scenario of a
universal transition of the structural dynamics between yielding of glasses and
non-Newtonian (shear-thinning) fluid flow appears well obeyed, and calculations
within simplified models rationalize the data over variations in shear rate and
viscosity of up to 3 decades.Comment: 6 pages, 2 figures; J. Phys. Condens. Matter to be published (Jan.
2003
Competition between glass transition and liquid-gas separation in attracting colloids
We present simulation results addressing the phenomena of colloidal gelation
induced by attractive interactions. The liquid-gas transition is prevented by
the glass arrest at high enough attraction strength, resulting in a colloidal
gel. The dynamics of the system is controlled by the glass, with little effect
of the liquid-gas transition. When the system separates in a liquid and vapor
phases, even if the denser phase enters the non-ergodic region, the vapor phase
enables the structural relaxation of the system as a whole.Comment: Proceedings of the glass conference in Pisa (September 06
Statistical mechanics derivation of hydrodynamic boundary conditions: the diffusion equation
Considering the example of interacting Brownian particles we present a linear
response derivation of the boundary condition for the corresponding
hydrodynamic description (the diffusion equation). This requires us to identify
a non-analytic structure in a microscopic relaxation kernel connected to the
frequency dependent penetration length familiar for diffusive processes, and
leads to a microscopic definition of the position where the hydrodynamic
boundary condition has to be applied. Corrections to the hydrodynamic limit are
obtained and we derive general amplitudes of spatially and temporally long
ranged states in the considered diffusive system.Comment: 15 pages; slightly revised and shortened version; J. Phys.: Condens.
Matter in prin
Flow curves of colloidal dispersions close to the glass transition: Asymptotic scaling laws in a schematic model of mode coupling theory
The flow curves, viz. the curves of stationary stress under steady shearing,
are obtained close to the glass transition in dense colloidal dispersions using
asymptotic expansions in a schematic model of mode coupling theory. The shear
thinning of the viscosity in fluid states and the yielding of glassy states is
discussed. At the transition between fluid and shear-molten glass, simple and
generalized Herschel-Bulkley laws are derived with power law exponents that can
be computed for different particle interactions from the equilibrium structure
factor.Comment: 14 pages, 14 figures, 4 tables, Eur. Phys. J. E (submitted
Tagged-particle dynamics in a hard-sphere system: mode-coupling theory analysis
The predictions of the mode-coupling theory of the glass transition (MCT) for
the tagged-particle density-correlation functions and the mean-squared
displacement curves are compared quantitatively and in detail to results from
Newtonian- and Brownian-dynamics simulations of a polydisperse
quasi-hard-sphere system close to the glass transition. After correcting for a
17% error in the dynamical length scale and for a smaller error in the
transition density, good agreement is found over a wide range of wave numbers
and up to five orders of magnitude in time. Deviations are found at the highest
densities studied, and for small wave vectors and the mean-squared
displacement. Possible error sources not related to MCT are discussed in
detail, thereby identifying more clearly the issues arising from the MCT
approximation itself. The range of applicability of MCT for the different types
of short-time dynamics is established through asymptotic analyses of the
relaxation curves, examining the wave-number and density-dependent
characteristic parameters. Approximations made in the description of the
equilibrium static structure are shown to have a remarkable effect on the
predicted numerical value for the glass-transition density. Effects of small
polydispersity are also investigated, and shown to be negligible.Comment: 20 pages, 23 figure
Equations of structural relaxation
In the mode coupling theory of the liquid to glass transition the long time
structural relaxation follows from equations solely determined by equilibrium
structural parameters. The present extension of these structural relaxation
equations to arbitrarily short times on the one hand allows calculations
unaffected by model assumptions about the microscopic dynamics and on the other
hand supplies new starting points for analytical studies. As a first
application, power-law like structural relaxation at a glass-transition
singularity is explicitly proven for a special schematic MCT model.Comment: 11 pages, 3 figures; talk given at the Seventh international Workshop
on disordered Systems, Molveno, Italy, March 199
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