A (2+1)-dimensional KdV equation and mKdV equation: Symmetries,group invariant solutions and conservation laws

In this paper, we analyse the (2+1)-dimensional KdV and mKdV equations. Firtly, on the basis of the extended Lax pair, we derive these equations. Thereafter, the symmetry generators are determined followed by the application of the mCK method. Finally, conservation laws (including higher order) are studied.     

Invariance Analysis and Variational Conservation Laws for the Wave Equation on Some Manifolds

In this paper we discuss symmetries of a nonlinear wave equation that arises as a consequence of some Riemannian metrics of signature −2. The objective of this study is to show how geometry can be responsible in giving rise to a nonlinear inhomogeneous wave equation rather than assuming nonlinearities in the wave equation from physical considerations. We find Lie point symmetries of the corresponding wave equations and give their solutions in two cases. Some interesting physical conclusions relating to conservation laws such as energy, linear and angular momenta are also determined.     

Travelling wave solutions to Stokes’ problem for a fourth grade fluid

A non-linear partial differential equation modelling the flow of a fourth-grade fluid is derived. Both analytical and numerical travelling wave solutions admitted by the model equation are obtained.     

A hub covering network design problem for cargo applications in Turkey

Hub location problems involve locating hub facilities and allocating demand nodes to hubs in order to provide service between origin–destination pairs. In this study, we focus on cargo applications of the hub location problem. Through observations from the Turkish cargo sector, we propose a new mathematical model for the hub location problem that relaxes the complete hub network assumption. Our model minimizes the cost of establishing hubs and hub links, while designing a network that services each origin–destination pair within a time bound. We formulate a single-allocation hub covering model that permits visiting at most three hubs on a route. The model is then applied to the realistic instances of the Turkish network and to the Civil Aeronautics Board data set.     

Constrained regulation of continuous Petri nets

This paper deals with constrained regulation of continuous Petri nets under the so-called infinite servers semantics. Our aim is to design feedback gains that permit us to reach both desired stationary marking vector and desired asymptotic firing rate vector. The proposed approach takes into account constraints on the control, the marking of the Petri net, and the stability of the closed-loop system. The existence of a solution is first expressed geometrically, in terms of the inclusion of two polyhedral sets. They are reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem. Finally, an application to an assembly production system is given.     

Vapor-induced film formation from low-Tg particles for different solvent compositions

The photon transmission method was used to study latex film formation from poly(vinyl acetate) (PVAc) particles induced by two different solvents. Films with the same latex content were prepared from PVAc particles and exposed to vapor of ethanol-water and acetone-water mixtures in various compositions. Transmitted photon intensities, Itr, from these films increased with increasing vapor exposure time. The increase in Itr is attributed to the increase in crossing density at the polymer-polymer junction. The Prager-Tirrell model was employed to obtain the back-and-forth frequency, nu, of the reptating polymer chain during film formation induced by solvent vapor. It was observed that the produced nu values increase as the solvent content is increased for both solvents. Abilities of both solvents to form films were interpreted with the solubility parameters of the solvents and the PVAc.     

Adsorption of polyvinylimidazole onto kaolinite

The adsorption of polyvinylimidazole (PVI) onto kaolinite from aqueous solutions has been investigated systematically as a function of parameters such as calcination temperature of kaolinite, pH, ionic strength, and temperature. According to the experimental results, the adsorption of PVI increases with pH from 8.50 to 11.50, temperature from 25 to 55 degrees C, and ionic strength from 0 to 0.1 mol L(-1). The kaolinite sample calcined at 600 degrees C has a maximum adsorption capacity. Adsorption isotherms of PVI onto kaolinite have been determined and correlated with common isotherm equations such as Langmuir and Freundlich isotherm models. The Langmuir isotherm model appeared to fit the isotherm data better than the Freundlich isotherm model. The physical properties of this adsorbent are consistent with the parameters obtained from the isotherm equations. Furthermore, the zeta potentials of kaolinite suspensions have been measured in aqueous solutions of different PVI concentrations and pH. From the experimental results, (i) pH strongly alters the zeta potential of kaolinite; (ii) kaolinite has an isoelectric point at about pH 2.35 in water and about pH 8.75 in 249.9 ppm PVI concentration; (iii) PVI changes the interface charge from negative to positive for kaolinite. The study of temperature effect has been quantified by calculating various thermodynamic parameters such as Gibbs free energy, enthalpy, and entropy changes. The dimensionless separation factor (RL) has shown that kaolinite can be used for adsorption of PVI from aqueous solutions.     

Mathematical Characterization of Thermo-reversible Phase Transitions of Agarose Gels

The thermal phase transition temperatures of high (HMP) and low melting point (LMP) agarose gels were investigated by using UV–vis spectroscopy techniques. Transmitted light intensities from the gel samples with different agarose concentrations were monitored during the heating (gel-sol) and cooling (sol–gel) processes. It was observed that the transition temperatures, T_m, defined as the location of the maximum of the first derivative of the sigmoidal transition paths obtained from the UV–vis technique, slightly increased by increasing the agarose concentration in both the HMP and LMP samples. Here, we express the phase transitions of the agar-water system, as a representative of reversible physical gels, in terms of a modified Susceptible-Infected-Susceptible epidemic model whose solutions are the well-known 5-point sigmoidal curves. The gel point is hard to determine experimentally and various computational techniques are used for its characterization. Based on previous work, we locate the gel point, T₀, of sol-gel and gel-sol transitions in terms of the horizontal shift in the sigmoidal transition curve. For the gel-sol transition (heating), T₀ is greater than T_m, i.e. later in time, and the difference between T₀ and T_m is reduced as the agarose content increases. For the sol-gel transition (cooling), T₀ is again greater than T_m, but it is earlier in time for all agarose contents and moves forward in time and gets closer to T_m as the agarose content increases.     

Multiple exp-function method for soliton solutions of nonlinear evolution equations

We applied the multiple exp-function scheme to the(2+1)-dimensional Sawada-Kotera(SK) equation and(3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model.     

Full-trapped three-level ion in the lamb–dicke limit: analyzing and comparing quantum entanglement measures of two qudits

Our aim is to investigate the entanglement dynamics and quantum correlations of a full-trapped ion interacting with two time-independent laser beams in view of the Lamb–Dicke parameter. For this purpose, the three probability amplitudes in the trapped ion is taken as ?{1