Regularity for the 3D evolution Navier-Stokes equations under Navier boundary conditions in some Lipschitz domains

<p style='text-indent:20px;'>For the evolution Navier-Stokes equations in bounded 3D domains, it is well-known that the uniqueness of a solution is related to the existence of a regular solution. They may be obtained under suitable assumptions on the data and smoothness assumptions on the domain (at least <inline-formula><tex-math id="M1">\begin{document}$ C^{2,1} $\end{document}</tex-math></inline-formula>). With a symmetrization technique, we prove these results in the case of Navier boundary conditions in a wide class of merely <i>Lipschitz domains</i> of physical interest, that we call <i>sectors</i>.</p>

Identifying quantum logics by numerical events

Let S be a set of states of a physical system and let p(s) be the probability of an occurrence of an event when the system is in the state s ∈ S. The function p from S to [0, 1] is called a numerical event, multidimensional probability or, alternatively, S-probability. Given a set of numerical events which has been obtained by measurements and not supposing any knowledge of the logical structure of the events that appear in the physical system, the question arises which kind of logic is inherent to the system under consideration. In particular, does one deal with a classical situation or a quantum one?In this survey several answers are presented. Starting by associating sets of numerical events to quantum logics we study structures that arise when S-probabilities are partially ordered by the order of functions and characterize those structures which indicate that one deals with a classical system. In particular, sequences of numerical events are considered that give rise to Bell-like inequalities. At the center of all studies there are so called algebras of S-probabilities, subsets of these and their generalizations. A crucial feature of these structures is that order theoretic properties can be expressed by the addition and subtraction of real functions entailing simplified algorithmic procedures.The study of numerical events and algebras of S-probabilities goes back to a cooperation of E. G. Beltrametti and M. J. Mączyński in 1991 and has since then resulted in a series of subsequent papers of physical interest the main results of which will be commented on and put in an appropriate context.

A Simplified Analytic Treatment of Shell-Effects in Metal Clusters

A simplified treatment of shell-effects in metal clusters, such as those of Na, is considered. This treatment is carried out by means of an approximate scheme based on the spherical harmonic oscillator jellium model and its advantage is that it suggests the possibility quantities of physical interest to be calculated analytically. As a result, the variation of these quantities with the number of the valence electrons of the atoms in the cluster could be given explicitly in certain cases.

A way of decoupling gravitational sources in pure Lovelock gravity

We provide an algorithm that shows how to decouple gravitational sources in pure Lovelock gravity. This method allows to obtain several new and known analytic solutions of physical interest in scenarios with extra dimensions and with presence of higher curvature terms. Furthermore, using our method, it is shown that applying the minimal geometric deformation to the Anti de Sitter space time it is possible to obtain regular black hole solutions.

Damping Acoustic Modes in Compressible Horizontally Explicit Vertically Implicit (HEVI) and Split-Explicit Time Integration Schemes

Although the equations of motion for a compressible atmosphere accommodate acoustic waves, these modes typically play an insignificant role in atmospheric processes of physical interest. In numerically integrating the compressible equations, it is often beneficial to filter these acoustic modes to control acoustic noise and prevent its artificial growth. Here, a new technique is proposed for filtering the 3D divergence that may damp acoustic modes more effectively than filters previously implemented in numerical modes using horizontally explicit vertically implicit (HEVI) and split-explicit time integration schemes. With this approach, a divergence damping term is added as a final adjustment to the horizontal velocity at the new time level after completing the vertically implicit portion of the time step. In this manner, the divergence used in the filter term has exactly the same numerical form as that used in the discrete pressure equation. Analysis of the dispersion equation for this form of the filter documents its stability characteristics and confirms that it effectively damps acoustic modes with little artificial influence on the amplitude or propagation of the gravity wave modes that are of physical interest. Some specific aspects of the implementation of the filter in the Model for Prediction Across Scales (MPAS) are discussed, and results are presented to illustrate some of the beneficial aspects of suppressing acoustic noise.

Explicit positive representation for complex weights on Rd

It is an old idea to replace averages of observables with respect to a complex weight by expectation values with respect to a genuine probability measure on complexified space. This is precisely what one would like to get from complex Langevin simulations. Unfortunately, these fail in many cases of physical interest. We will describe method of deriving positive representations by matching of moments and show simple examples of successful constructions. It will be seen that the problem is greatly underdetermined.

Generating solutions to the Einstein field equations

Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this space, the set of potentials associated to a known solution is transformed into a new set, either by continuous transformations or by discrete transformations. In view of this method, and upon consideration of continuous transformations, we arrive at some exact, stationary axisymmetric solutions to the Einstein field equations in vacuum, that may be of geometrical or/and physical interest.

Division algebra representations of SO(4, 2)

Representations of SO (4, 2) are constructed using 4×4 and 2×2 matrices with elements in ℍ' ⊗ ℂ and the known isomorphism between the conformal group and SO (4, 2) is written explicitly in terms of the 4×4 representation. The Clifford algebra structure of SO (4, 2) is briefly discussed in this language, as is its relationship to other groups of physical interest.

Three-body problem, the measure of oscillating types. A short review

The theoretical three body problem, with three given non infinitesimal point masses, has two types of oscillating motions. In the first type at least two mutual distances are unbounded, but their inferior limit is bounded: there are an infinite number of larger and larger ejections, but without escape. In the second type, it is the velocities that are unbounded: there are an infinite number of nearer and nearer quasi-collisions, without exact collisions.The first type has only a theoretical interest: its measure in phase space is zero. But the second type has a positive measure in phase space and a physical interest: it governs most of the collisions of stars.