Nonlinear electrohydrodynamic instability of a finitely conducting cylinder: Effect of interfacial surface charges

The nonlinear electrohydrodynamic stability of cylindrical interface, supporting surface charge, among two conducting fluids is investigated. The two fluids are subjected to a radial electric field. The analysis based on the multiple scale technique. It is shown that the evolution of the amplitude is governed by two partial differential equations. These equations are combined to yield two alternate Schrödinger equations with cubic nonlinearity. One of which calculates the nonlinear cutoff electric field, separating stable and unstable disturbances, while the other is used to analyze the stability of the system. The stability criteria are analytically discussed and numerically confirmed. Numerical calculations resulted in set of graphs to indicate the stability picture of the considered system.     

Ca(NO3)2•4H2O-catalysed Biginelli Reaction: One-pot Synthesis of 1,2,3,4-Tetrahydropyrimidin-2-ones/pyrimidine-2-thiones under Solvent-free Conditions

The synthesis of 1,2,3,4-dihydropyrimidinone/thione derivatives was achieved in good to excellent yields using calcium(II) nitrate as catalyst to promote the Biginelli three-component condensation reaction from a diversity of aromatic aldehydes, β-keto compounds and urea or thiourea. The reaction was carried out under solvent-free conditions.     

Nonlinear Rayleigh-Taylor instability in magnetic fluids with uniform horizontal and vertical magnetic fields

A weakly nonlinear evolution of two dimensional wave packets on the surface of a magnetic fluid in the presence of an uniform magnetic field is presented, taking into account the surface tension. The method used is that of multiple scales to derive two partial differential equations. These differential equations can be combined to yield two alternate nonlinear Schrödinger equations. The first equation is valid near the cutoff wavenumber while the second equation is used to show that stability of uniform wave trains depends on the wavenumber, the density, the surface tension and the magnetic field. At the critical point, a generalized formulation of the evolution equation governing the amplitude is developed which leads to the nonlinear Klein-Gordon equation. From the latter equation, the various stability crteria are obtained.     

Nonlinear instability of superposed magnetic fluids in the presence of an oblique magnetic field

The nonlinear evolution of interfacial waves separating two magnetic fluids subjected to an oblique magnetic field is studied in two dimensions, with the use of the method of multiple scales. It is shown that the evolution of the envelope is governed by two partial differential equations. These equations can be combined to yield two alternate Schrödinger equations with cubic nonlinearity; one of them leads to the determination of the cutoff wave number separating stable from unstable deformations while the other Schrödinger equation is used to analyze the stability of the system. The stability of the system is discussed both theoretically and computationally, and the stability diagrams are obtained. It is found in the linear theory that the oblique magnetic field has a stabilizing influence if 0 ₁ + ₂ < /2, or 3/2 < ₁ + ₂ 2 and a destabilizing influence if /2 < ₁ + ₂ < 3/2, where 0 _j , (j=1, 2) and , is the angle between the field and the horizontal axis.In the nonlinear theory, the stability analysis reveals that there exist different regions of stability and instability. It is reported that the oblique magnetic field plays a dual role in the stability criterion and the angles ₁ and ₂ play a distinctive role in this analysis besides the effect of the variation of the magnetic permeabilities.     

Solvent-free synthesis of polyhydroquinoline and 1,8-dioxodecahydroacridine derivatives through the Hantzsch reaction catalyzed by a natural organic acid: A green method

Solvent-free and high yielding one-pot synthesis of 1,8-dioxodecahydroacridine and polyhydroquinoline derivatives have been described through Hantzsch condensation of various aldehydes, ammonium acetate with cyclic 1,3-dicarbonyl compounds and ethyl acetoacetate in a very simple, efficient, and environmentally benign method using ascorbic acid as a nontoxic organocatalyst.     

Problems on polygons and Bonnesen-type inequalities

In this paper we are interested in some Bonnesen-type isoperimetric inequalities for plane n-gons in relation with the two conjectures proposed by P. Levy and X.M. Zhang.     

Nonlinear electrohydrodynamic Kelvin-Helmholtz and Marangoni instabilities near the marginal state

The effects of surface tension and adsorption on the electrohydrodynamic Kelvin-Helmholtz instability are studied. The system is stressed by a normal electric field such that it allows for the presence of surface charges at the interface. The method used is that of multiple scales. The nonlinear Schrödinger equation describing the behavior of the disturbed system is derived. The stability of the perturbed system is discussed both analytically and numerically and the stability diagrams are obtained. At the critical point, a generalized formulation of the evolution equation is developed, which leads to the nonlinear Klein-Gordon equation. The various stability criteria are derived from this equation.     

The Aldehyde Ketone Rearrangement. Rearrangement of Bis(4-methoxyphenyl)-acetaldehyde into 4,4′-Dimethoxydeoxybenzoin

The formyl carbonyl group in bis(4-methoxyphenyl)-acetaldehyde does not contribute to the formation of the carbonyl group in 4,4′-dimethoxydeoxybenzoin when the former rearranges to the latter by treatment with 50% (w/w) sulfuric acid.     

Recent advances in vibro-impact dynamics and collision of ocean vessels

The treatment of ship impacts and collisions takes different approaches depending on the emphasis of each discipline. For example, dynamicists, physicist, and mathematicians are dealing with developing analytical models and mappings of vibro-impact systems. On the other hand, naval architects and ship designers are interested in developing design codes and structural assessments due to slamming loads, liquid sloshing impact loads in liquefied natural gas tanks and ship grounding accidents. The purpose of this review is to highlight the main differences of the two disciplines. It begins with a brief account of the theory of vibro-impact dynamics based on modeling and mapping of systems experiencing discontinuous changes in their state of motion due to collision. The main techniques used in modeling include power-law phenomenological modeling, Hertzian modeling, and non-smooth coordinate transformations originally developed by Zhuravlev and Ivanov. In view of their effectiveness, both Zhuravlev and Ivanov non-smooth coordinate transformations will be described and assessed for the case of ship roll dynamics experiencing impact with rigid barriers. These transformations have the advantage of converting the vibro-impact oscillator into an oscillator without barriers such that the corresponding equation of motion does not contain any impact term. One of the recent results dealing with the coefficient of restitution is that its value monotonically decreases with the impact velocity and not unique but random in nature. Slamming loads and grounding events of ocean waves acting on the bottom of high speed vessels will be assessed with reference to the ship structural damage. It will be noticed that naval architects and marine engineers are treating these problems using different approaches from those used by dynamicists. The problem of sloshing impact in liquefied natural gas cargo and related problems will be assessed based on the numerical and experimental results. It is important for vessel designers to determine the capacity of ships to resist random slamming loads, sloshing loading impact, grounding accidents and ships collisions.