A new method for exact solutions of variant types of time‐fractional Korteweg‐de Vries equations in shallow water waves

The current article devoted on the new method for finding the exact solutions of some time‐fractional Korteweg–de Vries (KdV) type equations appearing in shallow water waves. We employ the new method here for time‐fractional equations viz. time‐fractional KdV‐Burgers and KdV‐mKdV equations for finding the exact solutions. We use here the fractional complex transform accompanied by properties of local fractional calculus for reduction of fractional partial differential equations to ordinary differential equations. The obtained results are demonstrated by graphs for the new solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

The transport dynamics in complex systems governing by anomalous diffusion modelled with Riesz fractional partial differential equations

In this paper, numerical solutions of fractional Fokker–Planck equations with Riesz space fractional derivatives have been developed. Here, the fractional Fokker–Planck equations have been considered in a finite domain. In order to deal with the Riesz fractional derivative operator, shifted Grünwald approximation and fractional centred difference approaches have been used. The explicit finite difference method and Crank–Nicolson implicit method have been applied to obtain the numerical solutions of fractional diffusion equation and fractional Fokker–Planck equations, respectively. Numerical results are presented to demonstrate the accuracy and effectiveness of the proposed numerical solution techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Pressure-dependent viscosity of powder injection moulding compounds

A single piston capillary rheometer was modified by the addition of a second chamber with a restricting valve (developed at the Polymer Centre, Zlín, Czech Republic), which provides backpressure and increasing the pressure in the melted material during the flow through the die. The Carreau–Yasuda model was employed to fit the measured viscosity data and determine the temperature and pressure coefficients for polyolefin based binder and its compounds with carbide powder. Both temperature and pressure sensitivity coefficients are largely dependent on the structure of a polymer, which should be taken into account for binder-formation’s development. Increasing the loading level of the powder in the compound diminishes the pressure sensitivity of their flow properties.     

Anelastic deformation as an internal parameter

Summary We consider continua for which a local configuration exists, whence the instantaneous elastic strain must be measured. Relations involving stress, strain and strain rate are indicated, which are compatible with objectivity and with the Clausius-Duhem inequality. Definitions and a theorem of Coleman and Gurtin regarding continua with internal parameters are adapted to advantage.

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Sommario Si studiano continui per i quali esiste una configurazione locale (variabile nel tempo) e a partire dalla quale va misurata istante per istante la deformazione elastica. Si specificano le relazioni permesse dalla disguaglianza di Clausius Duhem e dal principio di obbiettività e si adattano al caso alcune definizioni ed un teorema di Coleman e Gurtin sui continui con parametri interni.

     

Direct analysis of anabolic steroids in urine using Leidenfrost phenomenon assisted thermal desorption-dielectric barrier discharge ionization mass spectrometry

Rapid detection of trace level anabolic steroids in urine is highly desirable to monitor the consumption of performance enhancing anabolic steroids by athletes. The present article describes a novel strategy for identifying the trace anabolic steroids in urine using Leidenfrost phenomenon assisted thermal desorption (LPTD) coupled to dielectric barrier discharge (DBD) ionization mass spectrometry. Using this method the steroid molecules are enriched within a liquid droplet during the thermal desorption process and desorbed all-together at the last moment of droplet evaporation in a short time domain. The desorbed molecules were ionized using a dielectric barrier discharge ion-source in front of the mass spectrometer inlet at open atmosphere. This process facilitates the sensitivity enhancement with several orders of magnitude compared to the thermal desorption at a lower temperature. The limits of detection (LODs) of various steroid molecules were found to be in the range of 0.05–0.1 ng mL⁻¹ for standard solutions and around two orders of magnitude higher for synthetic urine samples. The detection limits of urinary anabolic steroids could be lowered by using a simple and rapid dichloromethane extraction technique. The analytical figures of merit of this technique were evaluated at open atmosphere using suitable internal standards. The technique is simple and rapid for high sensitivity and high throughput screening of anabolic steroids in urine.     

Multilayer Hierarchical Model for Mobility Management in IPv6: A Mathematical Exploration

The mobility solution provided by Mobile IPv6 (MIPv6) imposes too much signaling load to the network and enforces large handoff latency to end user. Hierarchical MIPv6 (HMIPv6) on the other hand, is designed by organizing MIPv6 in layered architecture and performs better than MIPv6 in terms of handoff latency and signaling load. Observation shows that, there is still possibility to shrink the handoff latency and the signaling load by further extending HMIPv6 into multiple layers. To explore this possibility of enhanced performance through layered architecture, this paper aimed at mathematical exploration of an N-layered MIPv6 network architecture in order to figure out the optimal levels of hierarchy for mobility management. A widespread analysis is carried out on various parameters such as location update frequency and cost, handoff latency and packet delivery cost. Influence of queuing delay on handoff latency is examined by modeling M/M/1/K queue in the architecture and user mobility is modeled using Markov chain. Analytical investigation reveals that three levels of hierarchy in MIPv6 architecture provide an optimal solution for mobility management.     

Magnetic property of a triply bridged linear trinuclear nickel complex

A new linear trinuclear nickel(II) complex, [Ni₃L₂(OCn)₄] (HL = 2-[(3-dimethylamino-propylimino)-methyl]-phenol, OCn = cinnamate), with phenoxo bridge and a novel tridentate bridging mode (in a 2.21 fashion according to Harris notation), of the cinnamate ligand has been synthesized and characterized by IR spectroscopy, UV-Vis spectroscopy, X-ray crystallography and static magnetic measurements. The molecular structure shows that each nickel ion occupies octahedral coordinating geometry. Apart from the phenoxo bridges, the carboxylic group of cinnamic anion shows two types of bridging modes viz. 2.11 and 2.21. The magnetic data indicate that a moderate intramolecular ferromagnetic and a weak intermolecular antiferromagnetic interaction are present in the complex under study. Broken symmetry density functional theory has been used to estimate the sign and magnitude of the coupling constants to understand the magnetic exchange mechanisms of the present system. The relative abilities of different bridging groups to mediate magnetic exchange interactions between paramagnetic nickel centers have been investigated by DFT calculation with variable angles. The results show that a small change in phenoxo-bridging angle has a very strong impact on the magnetic properties.     

Highly strained 2,3-bridged 2H-azirines at the borderline of closed-shell molecules

Substituted 1-azidocyclopentenes and 1-azidocyclohexenes were photolyzed to generate 2,3-bridged 2H-azirines. In the case of bridgehead azirines with a six-membered carbocycle, detection by NMR spectroscopic analysis was possible, whereas even kinetically stabilized bridgehead azirines with a five-membered ring could not be characterized by low-temperature NMR spectroscopic analysis. Thus, a recent report on the latter heterocycles was corrected. Depending on the substitution pattern, irradiation of 1-azidocyclopentenes either led to products that can be explained on the basis of short-lived 2,3-bridged 2H-azirines, or gave secondary products generated from triplet nitrenes. The diverse photoreactivity of 2,3-bridged 2H-azirines was also studied by quantum chemical methods (DFT, CCSD(T), CASSCF(6,6)) with respect to the singlet and triplet energy surfaces. The ring-opening processes leading to the corresponding vinyl nitrenes were identified as key steps for the observed reactivity.