Ocean swell within the kinetic equation for water waves

Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions.Comment: Submitted to Journal of Geophysical Research 18 July 201

Universality of Sea Wave Growth and Its Physical Roots

Modern day studies of wind-driven sea waves are usually focused on wind forcing rather than on the effect of resonant nonlinear wave interactions. The authors assume that these effects are dominating and propose a simple relationship between instant wave steepness and time or fetch of wave development expressed in wave periods or lengths. This law does not contain wind speed explicitly and relies upon this asymptotic theory. The validity of this law is illustrated by results of numerical simulations, in situ measurements of growing wind seas and wind wave tank experiments. The impact of the new vision of sea wave physics is discussed in the context of conventional approaches to wave modeling and forecasting.Comment: submitted to Journal of Fluid Mechanics 24-Sep-2014, 34 pages, 10 figure

Symmetries and Interaction coefficients of Kelvin waves

We considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic is not forbidden, as one can expect by naive reasoning.Comment: 4 pages, submitted to J. of Low Temp. Phy

Boundary values as Hamiltonian variables. I. New Poisson brackets

The ordinary Poisson brackets in field theory do not fulfil the Jacobi identity if boundary values are not reasonably fixed by special boundary conditions. We show that these brackets can be modified by adding some surface terms to lift this restriction. The new brackets generalize a canonical bracket considered by Lewis, Marsden, Montgomery and Ratiu for the free boundary problem in hydrodynamics. Our definition of Poisson brackets permits to treat boundary values of a field on equal footing with its internal values and directly estimate the brackets between both surface and volume integrals. This construction is applied to any local form of Poisson brackets. A prescription for delta-function on closed domains and a definition of the {\it full} variational derivative are proposed.Comment: 26 pages, LaTex, IHEP 93-4

Cognitive impairments in patients with brain injury

The paper gives the data of Russian and foreign authors and the results of this paper authors’ investigation of higher cerebral functions in patients who have sustained brain injury (BI). It shows their high prevalence, the predominance of cognitive impairments (CI) over neurological disorders in patients with mild and moderate injury, presents their quantitative and qualitative features (a preponderance of focal symptoms in severe injury and neurodynamic disorders in mild injury), describes the predictors of their course and prognosis (the degree of injury is one of the most important predictors), and discusses current trends in the medical correction of detected abnormalities

Selective ethylene trimerization by titanium complexes bearing phenoxy-imine ligands: NMR and EPR Spectroscopic studies of the reaction intermediates

The catalyst systems (FI)TiCl₃/MAO (FI = phenoxyimine ligand with an additional aryl–O–CH₃ donor) display exceptionally high activity in selective ethylene trimerization. By means of NMR and EPR spectroscopy, the nature of the Ti species formed in the catalyst systems (FI)TiCl₃/MAO, (FI)TiCl₃/MMAO, and (FI)TiCl₃/AlR₃/[Ph₃C]⁺[B(C₆F₅)₄]⁻ (R = Me, Et, ⁱBu) has been studied. It was shown that outer-sphere ion pairs of the type [(FI)TiIVMe₂]⁺[A]⁻ ([A]− = [MeMAO]⁻, [MeMMAO]⁻, [B(C₆F₅)₄]⁻) are formed at the initial stage of the reaction of (FI)TiCl₃ with MAO, MMAO, and AlMe₃/[Ph₃C]⁺[B(C₆F₅)₄]⁻. These ion pairs further partially convert into TiIII and TiII species. In the systems (FI)TiCl₃/MAO and (FI)TiCl₃/AlMe₃/[Ph₃C]⁺[B(C₆F5)₄]⁻, complexes with the proposed structures (FI)TiIIIMe₂, (FI)TiIICl, and [(FI)TiII(S)]⁺[A]⁻ ([A]− = [MeMAO]⁻, [B(C₆F₅)4)]⁻, S = solvent, vacancy) were observed (concentrations of TiIII species was lower than those of the TiII congeners). In contrast, in the system (FI)TiCl₃/MMAO, the concentrations of TiIII species (ion pairs of the type [(FI)TiIII(μ-H)(μ-Cl)AlⁱBu₂]⁺[MeMMAO]⁻) were higher than those of the TiII counterparts (ion pairs [(FI)TiII(S)]⁺[MeMMAO]⁻). The system (FI)TiCl₃/MMAO displays lower activity and selectivity in 1-hexene formation, in comparison to (FI)TiCl₃/MAO, due to undesirable PE generation. Probably, TiII and TiIV ion pairs are those participating in ethylene trimerization