A parametric study for thick plates resting on elastic foundation with variable soil depth

The soil depth is generally considered to be constant for the analysis of plates resting on elastic foundation in the literature. However, it is most reasonable to have a variable subsoil depth as the plate dimensions get larger. In present study, linearly varying subsoil depth is considered as well as constant, linear and quadratic variation of modulus of elasticity with subsoil depth. Also, a parametric study is performed to demonstrate the behavior of thick plates on elastic foundations with variable soil depth. Modified Vlasov Model is used for the analysis of the plate foundation system, and 8-noded Mindlin plate element incorporating shear strain throughout plate thickness is used for the finite element model. Numerical examples are obtained from the literature to compare results and to show the influence of variable soil stratum depth on the behavior of plates. Displacements, bending moments, and shear forces are presented in tabular and graphical formats. As far as results are compared, it can be concluded that variable soil depth significantly affects the variation of the displacements and therefore the internal forces of the plate while keeping it constant ends up with unrealistic results.     

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.     

Taylor collocation method for the numerical solution of the nonlinear Schrödinger equation using quintic B-spline basis

In this study, we construct a Taylor collocation method for the numerical solution of the nonlinear Schrödinger (NLS) equation. We use suitable initial and boundary conditions. Taylor series expansion is used for time discretization. The cubic B-spline collocation method is applied to spatial discretization. Test problems concerning the single soliton motion, interaction of two colliding solitons, and the formation and bound states of solitons of the NLS equation are studied to evaluate the method. The L ₂ and L _∞ error norms are calculated to improve the accuracy of the numerical results.     

Symmetries of boundary layer equations of power-law fluids of second grade

A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.     

Modeling Ergodic, Measure Preserving Actionson Shifts of Finite Type

 In this paper we show that shifts of finite type satisfying a strong topological mixing property are universal models for ergodic measure preserving dynamical systems.     

Synthesis and characterization of fully aromatic thermotropic liquid‐crystalline copolyesters containing m‐hydroxybenzoic acid units

A series of fully aromatic copolyesters based on p‐acetoxybenzoic acid (p‐ABA), hydroquinone diacetate (HQDA), terephthalic acid (TPA), and m‐acetoxybenzoic acid (m‐ABA) were prepared by a modified melt‐polycondensation reaction. The copolyesters were characterized by DSC, thermogravimetric analysis, ¹H NMR, polarized optical microscopy, X‐ray diffraction, and intrinsic viscosity measurements. The copolyesters exhibited nematic liquid‐crystalline phases in a broad temperature range of about 150 °C, when the content of linear (p‐ABA, HQDA, and TPA) units was over 67 mol %. DSC analysis of the anisotropic copolyesters revealed broad endotherms associated with the nematic phases, and the melting or flow temperatures were found to be in the processable region. The flow temperatures and crystal‐to‐nematic and nematic‐to‐isotropic transitions depend on the type of linear monomer units, and these transitions increased as the content of the p‐ABA units increased, as compared to the HQDA/TPA units. When the content of the p‐ABA units increased, as compared to other linear units (HQDA and TPA), the intrinsic viscosity and degree of crystallinity of the copolyesters also increased, implying a higher reactivity for p‐ABA in the p‐ABA/HQDA/TPA/m‐ABA polymer system. The aromatic region in the ¹H NMR spectra of the copolyesters containing equal molar compositions of p‐ABA, HQDA, and TPA units were sensitive to the sequence distribution of aromatic rings. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3263–3277, 2001     

Entropy analysis for third grade fluid flow with Vogel model viscosity in annular pipe

The steady-state flow of a third grade fluid between concentric circular cylinders is considered and entropy generation due to fluid friction and heat transfer in the annular pipe is examined. Depending upon the fluid viscosity, entropy generation in the flow system varies. The third grade fluid is employed to account for the non-Newtonian effect while Vogel model is accommodated for temperature-dependent viscosity. The analysis is based on perturbation technique. The closed form solutions for velocity, temperature and entropy fields are presented. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that entropy generation number reduces with increasing viscosity parameter A, which is more pronounced in the region close to the annular pipe inner wall and opposite is true for increasing viscosity parameter B.     

Assessment of different hazard indices around coal-fired power plants in Turkey

Journal of Radioanalytical and Nuclear Chemistry - This paper presents the radiological and heavy metal risk assessment to evaluate the impact of coal-fired power plants on humans and the...