1,050 research outputs found
Nonlocal spectral properties of disordered alloys
A general method is proposed for calculating a fully k-dependent, continuous,
and causal spectral function A(k,E) within the recently introduced nonlocal
version of the coherent-potential approximation (NLCPA). The method involves
the combination of both periodic and anti-periodic solutions to the associated
cluster problem and also leads to correct bulk quantities for small cluster
sizes. We illustrate the method by investigating the Fermi surface of a
two-dimensional alloy. Dramatically, we find a smeared electronic topological
transition not predicted by the conventional CPA.Comment: 17 pages, 5 figures, Submitted to: J. Phys.: Condens. Matter
Editorial receipt 25 May 200
Existence of axially symmetric static solutions of the Einstein-Vlasov system
We prove the existence of static, asymptotically flat non-vacuum spacetimes
with axial symmetry where the matter is modeled as a collisionless gas. The
axially symmetric solutions of the resulting Einstein-Vlasov system are
obtained via the implicit function theorem by perturbing off a suitable
spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page
Spherically symmetric steady states of galactic dynamics in scalar gravity
The kinetic motion of the stars of a galaxy is considered within the
framework of a relativistic scalar theory of gravitation. This model, even
though unphysical, may represent a good laboratory where to study in a
rigorous, mathematical way those problems, like the influence of the
gravitational radiation on the dynamics, which are still beyond our present
understanding of the physical model represented by the Einstein--Vlasov system.
The present paper is devoted to derive the equations of the model and to prove
the existence of spherically symmetric equilibria with finite radius.Comment: 13 pages, mistypos correcte
On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system
In a previous work \cite{An1} matter models such that the energy density
and the radial- and tangential pressures and
satisfy were considered in the context of
Buchdahl's inequality. It was proved that static shell solutions of the
spherically symmetric Einstein equations obey a Buchdahl type inequality
whenever the support of the shell, satisfies
Moreover, given a sequence of solutions such that then the
limit supremum of was shown to be bounded by
In this paper we show that the hypothesis
that can be realized for Vlasov matter, by constructing a
sequence of static shells of the spherically symmetric Einstein-Vlasov system
with this property. We also prove that for this sequence not only the limit
supremum of is bounded, but that the limit is
since for Vlasov matter.
Thus, static shells of Vlasov matter can have arbitrary close to
which is interesting in view of \cite{AR2}, where numerical evidence is
presented that 8/9 is an upper bound of of any static solution of the
spherically symmetric Einstein-Vlasov system.Comment: 20 pages, Late
Regularity results for the spherically symmetric Einstein-Vlasov system
The spherically symmetric Einstein-Vlasov system is considered in
Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem
is the issue of global existence for initial data without size restrictions.
The main purpose of the present work is to propose a method of approach for
general initial data, which improves the regularity of the terms that need to
be estimated compared to previous methods. We prove that global existence holds
outside the centre in both these coordinate systems. In the Schwarzschild case
we improve the bound on the momentum support obtained in \cite{RRS} for compact
initial data. The improvement implies that we can admit non-compact data with
both ingoing and outgoing matter. This extends one of the results in
\cite{AR1}. In particular our method avoids the difficult task of treating the
pointwise matter terms. Furthermore, we show that singularities never form in
Schwarzschild time for ingoing matter as long as This removes an
additional assumption made in \cite{A1}. Our result in maximal-isotropic
coordinates is analogous to the result in \cite{R1}, but our method is
different and it improves the regularity of the terms that need to be estimated
for proving global existence in general.Comment: 25 pages. To appear in Ann. Henri Poincar\'
Thin-film flow in helically wound rectangular channels with small torsion
Laminar gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section with small torsion in which the fluid depth is small is considered. Neglecting the entrance and exit regions we obtain the steady-state solution that is independent of position along the axis of the channel, so that the flow, which comprises a primary flow in the direction of the axis of the channel and a secondary flow in the cross-sectional plane, depends only on position in the two-dimensional cross-section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity and pressure in terms of the free-surface shape, the latter satisfying a non-linear ordinary differential equation that has a simple exact solution in the special case of a channel of rectangular cross-section. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier–Stokes equations. The present work has particular relevance to spiral particle separators used in the mineral-processing industry. The validity of an assumption commonly used in modelling flow in spiral separators, namely that the flow in the outer region of the separator cross-section is described by a free vortex, is shown to depend on the problem parameters
Hybrid modeling of biological networks: mixing temporal and qualitative biological properties
<p>Abstract</p> <p>Background</p> <p>Modeling a dynamical biological system is often a difficult task since the a <it>priori </it>unknown parameters of such models are not always directly given by the experiments. Despite the lack of experimental quantitative knowledge, one can see a dynamical biological system as (i) the combined evolution tendencies (increase or decrease) of the biological compound concentrations, and: (ii) the temporal features, such as delays between two concentration peaks (i.e. the times when one of the components completes an increase (resp. decrease) phase and starts a decrease (resp. increase) phase).</p> <p>Results</p> <p>We propose herein a new hybrid modeling framework that follows such biological assumptions. This hybrid approach deals with both a qualitative structure of the system and a quantitative structure. From a theoretical viewpoint, temporal specifications are expressed as equality or inequality constraints between delay parameters, while the qualitative specifications are expressed as an ordered pattern of the concentrations peaks of the components. Using this new hybrid framework, the temporal specifications of a biological system can be obtained from incomplete experimental data. The model may be processed by a hybrid model-checker (e.g. Phaver) which is able to give some new constraints on the delay parameters (e.g. the delay for a given transition is exactly 5 hours after the later peak of a gene product concentration). Furthermore, by using a constraint solver on the previous results, it becomes possible to get the set of parameters settings which are consistent with given specifications. Such a modeling approach is particularly accurate for modeling oscillatory biological behaviors like those observed in the Drosophila circadian cycles. The achieved results concerning the parameters of this oscillatory system formally confirm the several previous studies made by numerical simulations. Moreover, our analysis makes it possible to propose an automatic investigation of the respective impact of per and tim on the circadian cycle.</p> <p>Conclusions</p> <p>A new hybrid technique for an automatic formal analysis of biological systems is developed with a special emphasis on their oscillatory behaviors. It allows the use of incomplete and empirical biological data.</p
BioDiVinE: A Framework for Parallel Analysis of Biological Models
In this paper a novel tool BioDiVinEfor parallel analysis of biological
models is presented. The tool allows analysis of biological models specified in
terms of a set of chemical reactions. Chemical reactions are transformed into a
system of multi-affine differential equations. BioDiVinE employs techniques for
finite discrete abstraction of the continuous state space. At that level,
parallel analysis algorithms based on model checking are provided. In the
paper, the key tool features are described and their application is
demonstrated by means of a case study
Доработка электронного исполнительного пункта
Тез. докл. VI Междунар. науч.-техн. конф. (науч. чтения, посвящ. П. О. Сухому), Гомель, 19–20 окт. 2006 г
Reachability in Biochemical Dynamical Systems by Quantitative Discrete Approximation (extended abstract)
In this paper, a novel computational technique for finite discrete
approximation of continuous dynamical systems suitable for a significant class
of biochemical dynamical systems is introduced. The method is parameterized in
order to affect the imposed level of approximation provided that with
increasing parameter value the approximation converges to the original
continuous system. By employing this approximation technique, we present
algorithms solving the reachability problem for biochemical dynamical systems.
The presented method and algorithms are evaluated on several exemplary
biological models and on a real case study.Comment: In Proceedings CompMod 2011, arXiv:1109.104
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