On linear and nonlinear Rossby waves in an ocean

This paper deals with recent developments of linear and nonlinear Rossby waves in an ocean. Included are also linear Poincaré, Rossby, and Kelvin waves in an ocean. The dispersion diagrams for Poincaré, Kelvin and Rossby waves are presented. Special attention is given to the nonlinear Rossby waves on a β-plane ocean. Based on the perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies a modified nonlinear Schrödinger equation. The solution of this equation represents solitary waves in a dispersive medium. In other words, the envelope of the amplitude of the waves has a soliton structure and these envelope solitons propagate with the group velocity of the Rossby waves. Finally, a nonlinear analytical model is presented for long Rossby waves in a meridional channel with weak shear. A new nonlinear wave equation for the amplitude of large Rossby waves is derived in a region where fluid flows over the recirculation core. It is shown that the governing amplitude equations for the inner and outer zones are both KdV type, where weak nonlinearity is balanced by weak dispersion. In the inner zone, the nonlinear amplitude equation has a new term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude, and this term occurs to account for a nonlinearity due to the flow over the vortex core. The solution of the amplitude equations with the linear shear flow represents the solitary waves. The present study deals with the lowest mode (n=1) analysis. An extension of the higher modes (n?2) of this work will be made in a subsequent paper.     

Asymptotic behavior of solutions of forced nonlinear neutral delay differential equations with impulses

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7] are generalized and improved.     

Thiol-mediated radical cyclization: regioselective formation of indole-annulated sulfur heterocycles by tandem cyclization

Indole-2-yl-prop-2-ynyl sulfides, under thiophenol-mediated alkenyl radical cyclization conditions, afforded exclusively 4-thiophenyl-2,3,4,9-tetrahydrothiopyrano[2,3-b]indoles or 3-thiophenylmethyl-2,3,8-trihydrothieno[2,3-b]indoles depending on the substituent at the indole nitrogen.     

Kinetics and Mechanism of the Reactions of Picolinic Acid with Dichloro-{1-alkyl-2-(arylazo)imidazole}palladium(II) Complexes

The reaction between Pd(N,N′)Cl₂ [N,N′ ≡ 1-alkyl-2-(arylazo)imidazole (N,N′) and picolinic acid (picH) have been studied spectrophotometrically at λ = 463 nm in MeCN at 298 K. The product is [Pd(pic)₂] which has been verified by the synthesis of the pure compound from Na₂[PdCl₄] and picH. The kinetics of the nucleophilic substitution reaction have been studied under pseudo-first-order conditions. The reaction proceeds in a two-step-consecutive manner (A → B → C); each step follows first order kinetics with respect to each complex and picH where the rate equations are: Rate 1 = {k′₀ + k′₂[picH]₀} × [Pd(N,N′)Cl₂] and Rate 2 = {k′′₀ + k′′₂[picH]₀}[Pd(N,O)(monodentate N,N′)Cl₂] such that the first step second order rate constant (k′₂) is greater than the second step second order rate constant (k′′₂). External addition of Cl⁻ (as LiCl) suppresses the rate. Increase in π-acidity of the N,N′ ligand, increases the rate. The reaction has been studied at different temperatures and the activation parameters (Δ^‡H° and Δ^‡S°) were calculated from the Eyring plot.     

Kinetic and mechanistic studies of the interaction of 2-mercapto pyridine with dichloro[1-alkyl-2-(arylazo)imidazole]palladium(II) complexes

Nucleophilic substitution of Pd(RaaiR′)Cl₂ [(RaaiR′ = 1-alkyl-2-(arylazo)imidazole, p-R-C₆H₄-N=N-C₃H₂NN-1-R′; where R = H(a)/ Me(b)/ Cl(c) and R′ = Et(1)/Bz(2)] with 2-Mercaptopyridine (2-SH-Py) in acetonitrile (MeCN) at 298 K, to form [Pd₂(2-S-Py)₄], has been studied spectrophotometrically under pseudo-first-order conditions and the analyses support the nucleophilic association path. The reaction follows the rate law, Rate = {k ₀ + k [2-SH-Py] ₀ ² }[Pd(RaaiR′)Cl₂]: first order in Pd(RaaiR′)Cl₂ and second order in 2-SH-Py. The rate of the reaction follows the order: Pd(RaaiEt)Cl₂ (1) < Pd(RaaiBz)Cl₂ (2) and Pd(MeaaiR′)Cl₂ (b) < Pd(HaaiR′)Cl₂ (a) < Pd(ClaaiR′)Cl₂ (c). External addition of Cl⁻ (LiCl) and HCl suppresses the rate (Rate ∝ 1/[Cl⁻]₀ & ∝1/[HCl]₀). The reactions have been studied at different temperatures (293–308 K) and activation parameters (Δ^‡ H° and Δ ^‡ S°) of the reactions were calculated from the Eyring plot and support the proposed mechanism.     

Natures of Statefinder Parameters and Om Diagnostic for Cardassian Universe in Ho?ava-Lifshitz Gravity

In this work, we have considered Cardassian Universe in Ho?ava-Lifshitz gravity. Four types of Cardassian Universe models i.e., polytropic/power law, modified polytropic, exponential and modified exponential models have been considered for accelerating models. The natures of statefinder parameters, deceleration parameter, Om diagnostic and EoS parameters have been investigated for all types of Cardassian models in Ho?ava-Lifshitz gravity.     

Wilker-type inequalities for hyperbolic functions

Using classical analytic techniques, the Wilker–Anglesio inequality and parameterized Wilker inequality for hyperbolic functions are proved. The main result is then applied to deriving a hyperbolic analogue of the Sándor–Bencze inequality.     

One Way Traffic: Base-to-Backbone Hole Transfer in Nucleoside Phosphorodithioate

The directionality of the hole-transfer processes between DNA backbone and base was investigated by using phosphorodithioate [P(S⁻)=S] components. ESR spectroscopy in homogeneous frozen aqueous solutions and pulse radiolysis in aqueous solution at ambient temperature confirmed initial formation of G^.+-P(S⁻)=S. The ionization potential of G-P(S⁻)=S was calculated to be slightly lower than that of guanine in 5′-dGMP. Subsequent thermally activated hole transfer from G^.+ to P(S⁻)=S led to dithiyl radical (P-2S^.) formation on the μs timescale. In parallel, ESR spectroscopy, pulse radiolysis, and density functional theory (DFT) calculations confirmed P-2S^. formation in an abasic phosphorodithioate model compound. ESR investigations at low temperatures and higher G-P(S⁻)=S concentrations showed a bimolecular conversion of P-2S^. to the σ²-σ*¹-bonded dimer anion radical [-P-2S 2S-P-]⁻ [ΔG (150 K, DFT)=−7.2 kcal mol⁻¹]. However, [-P-2S 2S-P-]⁻ formation was not observed by pulse radiolysis [ΔG° (298 K, DFT)=−1.4 kcal mol⁻¹]. Neither P-2S^. nor [-P-2S 2S-P-]⁻ oxidized guanine base; only base-to-backbone hole transfer occurs in phosphorodithioate.     

H2-release from alcohols,diols, and compounds with amino functionality promoted by titanium(II) sandwich complex, [Cp2Ti]: a theoretical approach

Structural Chemistry - The role of Ti(II) sandwich complex, [Cp2Ti], generated by the combination of [Cp2TiCl2] and two equivalents of nBuLi, in situ, in toluene has been investigated theoretically...