On the numerical solution of nonplanar dust-acoustic super rogue waves in a strongly coupled dusty plasma

The occurrence of cylindrical and spherical low-frequency dust-acoustic freak waves (DAFWs) in a strongly coupled dusty plasma is numerically investigated in the framework of the phenomenological generalized hydrodynamic model. The basic equations are reduced to a modified/nonplanar nonlinear Schrödinger equation (mNLSE) using a reductive perturbation method. The existing regions of instability structures have been carefully identified. For studying the propagation of rogue waves in case of nonplanar (cylindrical and spherical coordinates), the mNLSE has been solved numerically. The effects of nonplanar geometries on the basic features of the DAFWs for the first- and second-orders rogue waves are discussed. Finally, our results are of relevance in ultradense situations where nonplaner geometrical effects are significant. In particular, we expect for our findings to be important to understand the DA breathers experimentally in a strongly coupled dusty plasma.     

Redundant exact solutions of nonlinear differential equations

We analyze the paper by Wazwaz and Mehanna [Wazwaz AM, Mehanna MS. A variety of exact travelling wave solutions for the (2 + 1)-dimensional Boiti–Leon–Pempinelli equation. Appl Math Comput 2010;217:1484–90]. The authors claim that they have found exact solutions of the (2 + 1)-dimensional Boiti–Leon–Pempinelli equation using the tanh–coth method and the Exp-function method. We demonstrate that two of their solutions are incorrect. All the others can be simplified and they are the partial cases of the well-known solution. Wazwaz and Mehanna made a number of typical mistakes in finding exact solutions of nonlinear differential equations. Taking the results of this paper we introduce the definition of redundant exact solutions for the nonlinear ordinary differential equations.     

New solutions of the C.S.Y. equation reveal increases in freak wave occurrence

In this article we study the time evolution of broad banded, random inhomogeneous fields of deep water waves. Our study is based on solutions of the equation derived by Crawford, Saffman and Yuen in 1980, (Crawford et al., 1980). Our main result is that there is a significant increase in the probability of freak wave occurrence than that predicted from the Rayleigh distribution. This result follows from the investigation of three related aspects. First, we study the instability of JONSWAP spectra to inhomogeneous disturbances whereby establishing a wider instability region than that predicted by Alber’s equation. Second, we study the long time evolution of such instabilities. We observe that, during the evolution, the variance of the free surface elevation and thus, the energy in the wave field, localizes in regions of space and time. Last, we compute the probabilities of encountering freak waves and compare it with predictions obtained from Alber’s equation and the Rayleigh distribution.     

Obliquely propagating ion-acoustic solitary and shock waves in magnetized quantum degenerate multi-ions plasma in the presence of trapped electrons

The properties of obliquely propagating ion-acoustic waves have been investigated in multi-ions magnetized plasma comprising of inertial, positively and negatively charged ion fluids, trapped electrons, and negatively charged stationary heavy ions. The propagation of the waves is oblique to the ambient magnetic field which is along the z-direction. Only fast type of modes exists in the linear regime. The reductive perturbation method was adopted to derive the Korteweg– de Vries (KdV) and Burger equations, as well as the solitary and shock wave solutions of the evolved equations, have been used to analyze the properties of the small but finite amplitude waves. The effects of the constituent plasma parameters, namely, the trapping effect of electrons, the electron degenerate temperature and the viscosity coefficient on the dynamics of the small amplitude solitary and shock waves have been examined. The influence of the magnetic field and the obliquity parameter on the propagation characteristics of ion-acoustic waves are discussed.     

Shock waves in magnetized plasmas with superthermal trapped electrons.

Formation of ion-acoustic shock waves (IAShWs) and their propagation nature in a magnetized plasma in the presence of superthermal trapped electrons are investigated for the first time via the fluid dynamical approach. A magnetized plasma system, comprising of inertial ions and non-inertial electrons following $\kappa$-superthermal trapped distribution, is considered to examine the basic features (amplitude, width, phase speed, etc.) of IAShWs in such a plasma. A diffusion effect (due to the ion kinematic viscosity) is taken into account. The reductive perturbation technique is adopted to derive the modified Korteweg de-Vries Burgers’ (mKdVB) equation and the solution of mKdVB equation (derived by adopting the tangent hyperbolic method) is used to investigate the dynamical and structural characteristics (speed, amplitude, width, etc.) of IAShWs. The influence of relevant plasma (configuration) parameters (e.g., the superthermality index $\kappa ,$ concentration of trapped electrons, external magnetic field, and obliquity angle, etc.) on the nature of IAShWs is examined. The applications of the results in space and laboratory plasma environments, where nonthermal trapped electrons are available, are briefly discussed.     

Modelling of reaction–diffusion processes: the theory of catalytic electrode processes at hemispheroidal ultramicroelectrodes

The transient chronoamperometric current for a catalytic electrode reaction (EC′ reaction) at a hemispheroidal Ultramicroelectrode is reported. This simple new approximate multidimensional analytical expression is valid for all values of time and all values of the rate constant. It is more accurate for all times and large K than for short times and small K. The analytical results are compared with recently presented digital simulation results (Galceran and co-workers, J. Electroanal. Chem 466 (1999) 15) for a disc electrode and are found to be in good agreement.     

Synthesis,anticancer evaluation,and molecular modeling study of new 2-(phenylamino)pyrazolo[1,5-a]pyrimidine analogues

The reaction of 3-amino-5-phenylaminopyrazoles 2 with 3-(dimethylamino) acrylonitrile derivatives resulted in a series of substituted pyrazolopyrimidine analogues 4 and 6. The DFT studies of the isolated compounds showed that the frontier molecular orbitals energy gap was close and in the 2.65–2.81 eV range where the derivative 6b has the lowest and both of 4a and 4c have the highest values. Meanwhile, the anticancer activity of the newly synthesized pyrazolopyrimidine analogues have been tested against several different cell lines (MCF-7, PC3, Hep-2 and WI38). The investigated pyrazolopyrimidines showed remarkable cytotoxicity activity against the MCF-7 and Hep-2 cell lines. In comparison to the effects of 5-fluorouracil, IC₅₀ = 10.19 ± 0.42 and 7.19 ± 0.47, compounds 6a-c demonstrated potential anticancer activity with IC₅₀ values for MCF-7 (10.80 ± 0.36–19.84 ± 0.49 μM) and Hep-2 (8.85 ± 0.24–12.76 ± 0.16 μM). Important details regarding the protein's binding sites were disclosed when the produced analogues docked with the crystal structure of the KDM5A protein, which was located in the protein data library.     

Eulerian codes for the numerical solution of the Vlasov equation

A historical overview of Eulerian codes for the numerical solution of the Vlasov equation is presented, with special attention to characteristic methods. An evaluation of the performance of the cubic spline used for interpolation in the characteristic methods, with respect to other methods of interpolation, will be presented by comparing the solutions obtained by solving numerically different Vlasov–Poisson and Vlasov–Maxwell systems on a fixed Eulerian grid. Some recent developments of characteristic methods in two dimensions will be presented.     

Catalysis of cyclohexane oxidation with air using various chitosan-supported metallotetraphenylporphyrin complexes

Three types of chitosan-supported metallotetraphenylporphyrins were prepared at room temperature by loading iron, cobalt and manganese tetraphenylporphyrins (TPP) onto chitosan. These were employed as catalysts for the aerobic oxidation of cyclohexane in the absence of additives and solvents. Three chitosan-supported and three simple metallotetraphenylporphyrins (MTPPs) showed different catalytic activity for the oxidation of cyclohexane. Under optimum reaction conditions of 418 K and 0.8 MPa, both the cobalt TPP and the corresponding chitosan-supported complex showed the highest catalytic activity, but lower ketone and alcohol selectivity. The reverse situation was observed for the iron TPP and the corresponding chitosan-supported complex. For cyclohexane oxidation, there was a difference in catalytic activity and ketone and alcohol selectivity between the simple MTTPs or the corresponding chitosan-supported complexes. These differences in catalysis probably result from two factors: the potential for O₂ activation of the different bivalent metal ions, which affects the activity of the corresponding chitosan-supported MTPPs and chitosan assistance of the MTPP catalysis.