Let R denote a 2-fir. The notions of F -independence and algebraic subsets of R are defined. The decomposition of an algebraic subset into similarity classes gives a simple way of translating the F -independence in terms of dimension of some vector spaces. In particular to each element a ∈ R is attached a certain algebraic set of atoms and the above decomposition gives a lower bound of the leng...

A conceptually new approach is introduced for the decomposition of the molecular energy calculated at the density functional theory level of theory into sum of one- and two-atomic energy components, and is realized in the "fuzzy atoms" framework. (Fuzzy atoms mean that the three-dimensional physical space is divided into atomic regions having no sharp boundaries but exhibiting a continuous tran...

A Unified Flow Solver (UFS) has been developed for simulations of rarefied, transitional and continuum flows based on direct numerical solution of the Boltzmann equation coupled to kinetic schemes of gas dynamics. The UFS uses dynamically adaptive mesh and automatic domain decomposition into kinetic and continuum domains based on continuum breakdown criteria. This paper describes UFS extensions...

Photochemical processes in planetary atmospheres are strongly influenced by catalytic effects of minor constituents. Catalytic cycles in the atmospheres of Earth and Venus are closely related. For example, chlorine oxides (CIOx) act as catalysts in the two atmospheres. On Earth, they serve to convert odd oxygen (atomic oxygen and ozone) to molecular oxygen. On Venus they have a similar effect, ...

The complete evaporation of three dimensional submicron droplets under both subcrit ical and supercritical conditions has been modeled using parallel molecular dynamics In this initial study the two phase simulations consist entirely of argon atoms The inter atomic forces are based on a Lennard Jones potential and the resultant atomic displacements are determined using a modi ed velocity Verlet...

We study conditions on a Banach frame that ensures the validity of a reconstruction formula. In particular, we show that any Banach frames for (a subspace of) Lp or Lp,q (1 ≤ p <∞) with respect to a solid sequence space always satisfies an unconditional reconstruction formula. The existence of reconstruction formulae allows us to prove some James-type results for atomic decompositions: an uncon...

This paper introduces recent optical measurements of radicals in atmospheric pressure non-thermal plasma. Laser-induced fluorescence (LIF), laser absorption, and optical emission spectroscopy (OES) techniques have been applied for density and temperature measurements of OH radicals, NO molecules, ozone, atomic oxygen, atomic nitrogen, and N2( A3Σ u ) metastables in pulsed corona and pulsed diel...

For given matrix A ∈ Zd×n, the set Pb = { z : Az = b, z ∈ Z+ } describes the preimage or fiber of b ∈ Z under the Z-linear map fA : Z+ → Z, x 7→ Ax. The fiber Pb is called atomic if it has no nontrivial Minkowski decomposition, that is, Pb = Pb1 +Pb2 implies b = b1 or b = b2. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to subproblems, comput...

Thermal motions in a microscopic model for a strong glass ~B2O3) are studied by means of computer molecular dynamics simulations. A decomposition of the atomic dynamics in terms of normal modes allows the separation of the truly harmonic components of the generalized frequency distributions. This enables us to discuss a number of magnitudes relevant to current issues on glassy dynamics on quant...