Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.     

Symmetries and conservation laws of Kadomtsev-Pogutse equations

Kadomtsev-Pogutse equations are of great interest from the viewpoint of the theory of symmetries and conservation laws and, in particular, enable us to demonstrate their potentials in action. This paper presents, firstly, the results of computations of symmetries and conservation laws for these equations and the methods of obtaining these results. Apparently, all the local symmetries and conservation laws admitted by the considered equations are exhausted by those enumerated in this paper. Secondly, we point out some reductions of Kadomtsev-Pogutse equations to more simpler forms which have less independent variables and which, in some cases, allow us to construct exact solutions. Finally, the technique of solution deformation by symmetries and their physical interpretation are demonstrated.     

Effect of hydrodynamic interactions on the evolution of chemically reactive ternary mixtures

We investigate the structural evolution of an A/B/C ternary mixture in which the A and B components can undergo a reversible chemical reaction to form C. We developed a lattice Boltzmann model for this ternary mixture that allows us to capture both the reaction kinetics and the hydrodynamic interactions within the system. We use this model to study a specific reactive mixture in which C acts as a surfactant, i.e., the formation of C at the A/B interface decreases the interfacial tension between the A and B domains. We found that the dynamics of the system is different for fluids in the diffusive and viscous regimes. In the diffusive regime, the formation of a layer of C at the interface leads to a freezing of the structural evolution in the fluid; the values of the reaction rate constants determine the characteristic domain size in the system. In the viscous regime, where hydrodynamic interactions are important, interfacial reactions cause a slowing down of the domain growth, but do not arrest the evolution of the mixture. The results provide guidelines for controlling the morphology of this complex ternary fluid.     

Destruction Kinetics of 2,4 Dichlorophenol Aqueous Solutions in an Atmospheric Pressure Dielectric Barrier Discharge in Oxygen

The processes of degradation of 2,4-dichlorophenol (2,4-DCP) aqueous solutions under the action of atmospheric pressure of DBD in oxygen were studied. The degradation of 2,4-DCP proceeds efficiently, the degree of decomposition reaching 100%. The degradation kinetics of 2,4-DCP obeys a formal first-order kinetic law on concentration of 2,4-DCP. The effective rate constants depend weakly on the experimental conditions and are equal to ~ 2 s^?1. Based on experimental data, the energy efficiency of 2,4-DCP decomposition was determined to be in the range of 0.039–0.173 molecules per 100 eV depending on the experimental conditions. The composition of the products was studied by gas chromatography, chromatography-mass spectrometry, UV/visible spectroscopy, fluorescent methods and some chemical methods. The main decomposition products present in the solution were found to be carboxylic acids, aldehydes and chloride ions, whereas carbon dioxide and molecular chlorine appear in the gas. The results obtained are compared with similar data from other advanced oxidation processes (AOP’s) methods.     

Cohomological uniqueness of the Cauchy problem solutions for the Einstein equation

In this paper we analyze the Cauchy problem for the Einstein equation in the case of a non-characteristic initial hypersurface. To find the correct notions for the characteristic and Cauchy data we introduce a complex, which we call the Einstein complex. Then the Cauchy problem acquires correctness in terms of the associated spectral sequence. We define the Cauchy data in such way that they allow us to reconstruct a cohomologously unique formal solution.     

Directed Gas Phase Formation of Silene (H2SiCH2)

The silene molecule (H₂SiCH₂; X¹A₁) has been synthesized under single collision conditions via the bimolecular gas phase reaction of ground state methylidyne radicals (CH) with silane (SiH₄). Exploiting crossed molecular beams experiments augmented by high-level electronic structure calculations, the elementary reaction commenced on the doublet surface through a barrierless insertion of the methylidyne radical into a silicon-hydrogen bond forming the silylmethyl (CH₂SiH₃; X²A′) complex followed by hydrogen migration to the methylsilyl radical (SiH₂CH₃; X²A′). Both silylmethyl and methylsilyl intermediates undergo unimolecular hydrogen loss to silene (H₂SiCH₂; X¹A₁). The exploration of the elementary reaction of methylidyne with silane delivers a unique view at the widely uncharted reaction dynamics and isomerization processes of the carbon–silicon system in the gas phase, which are noticeably different from those of the isovalent carbon system thus contributing to our knowledge on carbon silicon bond couplings at the molecular level.     

Asymptotic multiphase Σ-solutions to the singularly perturbed Korteweg–de Vries equation with variable coefficients

The paper deals with constructing the asymptotic solution to the singularly perturbed Korteweg–de Vries equation with variable coefficients. The notion of an asymptotic multiphase Σ-solution is proposed, and an algorithm of its construction in a neighborhood of the point t = 0 is given. Some theorems concerning the exactness, with which such local asymptotic solution satisfies the equation under study are proved.     

Synthesis and Therapeutic Use of Dimephosphone

Abstract

The synthesis of dimephosphone (1) was carried out on Pudovik's reaction.     

Combined Crossed Molecular Beams and Ab Initio Study of the Bimolecular Reaction of Ground State Atomic Silicon (Si; 3P) with Germane (GeH4; X1A1)

The chemical dynamics of the elementary reaction of ground state atomic silicon (Si; ³P) with germane (GeH₄; X¹A₁) were unraveled in the gas phase under single collision condition at a collision energy of 11.8±0.3 kJ mol⁻¹ exploiting the crossed molecular beams technique contemplated with electronic structure calculations. The reaction follows indirect scattering dynamics and is initiated through an initial barrierless insertion of the silicon atom into one of the four chemically equivalent germanium-hydrogen bonds forming a triplet collision complex (HSiGeH₃; ³ i1 ). This intermediate underwent facile intersystem crossing (ISC) to the singlet surface (HSiGeH₃; ¹ i1 ). The latter isomerized via at least three hydrogen atom migrations involving exotic, hydrogen bridged reaction intermediates eventually leading to the H₃SiGeH isomer i5 . This intermediate could undergo unimolecular decomposition yielding the dibridged butterfly-structured isomer ¹ p1 (Si(μ-H₂)Ge) plus molecular hydrogen through a tight exit transition state. Alternatively, up to two subsequent hydrogen shifts to i6 and i7 , followed by fragmentation of each of these intermediates, could also form ¹ p1 (Si(μ-H₂)Ge) along with molecular hydrogen. The overall non-adiabatic reaction dynamics provide evidence on the existence of exotic dinuclear hydrides of main group XIV elements, whose carbon analog structures do not exist.