2,274 research outputs found
On a result of R. R. Hall
AbstractAn upper bound for the mean value of a non-negative submultiplicative function by R. R. Hall [3] is sharpened and generalised. Hall's inequality implies a certain rather accurate upper sieve estimate, and this aspect of Hall's result is exploited in deriving good lower bounds for π(x) via the sieve
Combinatorial sieves of dimension exceeding one
AbstractA general sieve for each dimension Îş > 1 is given which improves the sieve estimates of Ankeny and Onishi. The work depends on a combinatorial identity which is invariant under Buchstab iteration and on the solution of a pair of differential-difference equations with side conditions
Topologically disordered systems at the glass transition
The thermodynamic approach to the viscosity and fragility of amorphous oxides was used to determine the topological characteristics of the disordered network-forming systems. Instead of the disordered system of atoms we considered the congruent disordered system of interconnecting bonds. The Gibbs free energy of network-breaking defects (configurons) was found based on available viscosity data. Amorphous silica and germania were used as reference disordered systems for which we found an excellent agreement of calculated and measured glass transition temperatures. We reveal that the Hausdorff dimension of the system of bonds changes from Euclidian three-dimensional below to fractal 2.55 ± 0.05-dimensional geometry above the glass transition temperature
Renormalisation and fixed points in Hilbert Space
The energies of low-lying bound states of a microscopic quantum many-body
system of particles can be worked out in a reduced Hilbert space. We present
here and test a specific non-perturbative truncation procedure. We also show
that real exceptional points which may be present in the spectrum can be
identified as fixed points of coupling constants in the truncation procedure.Comment: 4 pages, 1 tabl
Finite size effects and the order of a phase transition in fragmenting nuclear systems
We discuss the implications of finite size effects on the determination of
the order of a phase transition which may occur in infinite systems. We
introduce a specific model to which we apply different tests. They are aimed to
characterise the smoothed transition observed in a finite system. We show that
the microcanonical ensemble may be a useful framework for the determination of
the nature of such transitions.Comment: LateX, 5 pages, 5 figures; Fig. 1 change
Corresponding States of Structural Glass Formers
The variation with respect to temperature T of transport properties of 58
fragile structural glass forming liquids (68 data sets in total) are analyzed
and shown to exhibit a remarkable degree of universality. In particular,
super-Arrhenius behaviors of all super-cooled liquids appear to collapse to one
parabola for which there is no singular behavior at any finite temperature.
This behavior is bounded by an onset temperature To above which liquid
transport has a much weaker temperature dependence. A similar collapse is also
demonstrated, over the smaller available range, for existing numerical
simulation data.Comment: 6 pages, 2 figures. Updated References, Table Values, Submitted for
Publicatio
Relationship between dynamical heterogeneities and stretched exponential relaxation
We identify the dynamical heterogeneities as an essential prerequisite for
stretched exponential relaxation in dynamically frustrated systems. This
heterogeneity takes the form of ordered domains of finite but diverging
lifetime for particles in atomic or molecular systems, or spin states in
magnetic materials. At the onset of the dynamical heterogeneity, the
distribution of time intervals spent in such domains or traps becomes stretched
exponential at long time. We rigorously show that once this is the case, the
autocorrelation function of the renewal process formed by these time intervals
is also stretched exponential at long time.Comment: 8 pages, 4 figures, submitted to PR
Statistical Mechanics of Glass Formation in Molecular Liquids with OTP as an Example
We extend our statistical mechanical theory of the glass transition from
examples consisting of point particles to molecular liquids with internal
degrees of freedom. As before, the fundamental assertion is that super-cooled
liquids are ergodic, although becoming very viscous at lower temperatures, and
are therefore describable in principle by statistical mechanics. The theory is
based on analyzing the local neighborhoods of each molecule, and a statistical
mechanical weight is assigned to every possible local organization. This
results in an approximate theory that is in very good agreement with
simulations regarding both thermodynamical and dynamical properties
Critical temperature for the nuclear liquid-gas phase transition (from multifragmentation and fission)
Critical temperature Tc for the nuclear liquid-gas phase transition is
stimated both from the multifragmentation and fission data. In the first
case,the critical temperature is obtained by analysis of the IMF yields in
p(8.1 GeV)+Au collisions within the statistical model of multifragmentation
(SMM). In the second case, the experimental fission probability for excited
188Os is compared with the calculated one with Tc as a free parameter. It is
concluded for both cases that the critical temperature is higher than 16 MeV.Comment: 15 pages, 8 figure
Heterogeneities in systems with quenched disorder
We study the strong role played by structural (quenched) heterogeneities on
static and dynamic properties of the Frustrated Ising Lattice Gas in two
dimensions, already in the liquid phase. Differently from the dynamical
heterogeneities observed in other glass models in this case they may have
infinite lifetime and be spatially pinned by the quenched disorder. We consider
a measure of local frustration, show how it induces the appearance of spatial
heterogeneities and how this reflects in the observed behavior of equilibrium
density distributions and dynamic correlation functions.Comment: 8 page
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