Numerical solution of ordinary differential equations by Fluctuationlessness theorem

This paper presents a numerical method based on Fluctuationlessness Theorem for the solution of Ordinary Differential Equations over appropriately defined Hilbert Spaces. We focus on the linear differential equations in this work. The approximated solution is written in the form of an nth degree polynomial of the independent variable. The unknown coefficients are obtained by setting up a system of linear equations which satisfy the initial or boundary conditions and the differential equation at the grid points, which are constructed as the independent variable’s matrix representation restricted to an n dimensional subspace of the Hilbert Space. An error comparison of the numerical solution and the MacLaurin series with the analytical solution is performed. The results show that the numerical solution obtained here converges to the analytical solution without using too many mesh points.     

A Simplified Proof of a Liouville Theorem for Nonnegative Solution of a Subcritical Semilinear Heat Equations

We give a new proof of the Liouville theorem proved by Merle and Zaag for nonnegative solutions of the semilinear heat equation with power nonlinearity. Our proof has a pedagogical interest and is based on Kaplan’s blow-up criterion.      

Structural study,intermolecular interactions in view of X-ray and Hirshfeld surface analysis,DSC characterization,and electrical properties of <Emphasis Type="Italic">bis</Emphasis>-(4-benzylpyridinium) tetrabromozincate

The synthesis and crystal structure of the bis-(4-benzylpyridinium) tetrabromozincate(II) “(4-BP)₂[ZnBr₄]” salt are reported in the present paper. After an X-ray investigation, it has been shown that the title compound belongs to the centrosymmetric monoclinic system at 296 K, in the space group P2₁/n with the following lattice parameters a = 15.0764(8) Å, b = 22.5575(12) Å, c = 16.0739(9) Å, and β = 93.887(3)°. The FT-IR and Raman spectra confirm the presence of both cationic and anionic parts. The crystal packing is governed by an extensive network: N–H…Br, (N: pyridinium), C–H…Br hydrogen bonds, π…π, and C–H…π stacking between identical 4-BP (aromatic–aromatic), in which they may be effective in the stabilization of the crystal structure. Moreover, Hirshfeld surface analysis was used for visually analyzing intermolecular interactions in crystal structures. The phase transitions at T = 323 K have been confirmed by the differential scanning calorimetry. The electrical technique was measured in the 209 Hz–5-MHz frequency range and 298–393-K temperature intervals. The evolution of the dielectric constant as a function of frequency and temperature proved the presence of a first-order phase transition at 323 K.

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On asymptotic distributions of exceedance statistics

In this study, two independent samples X₁,X₂,…,X_n and Y₁,Y₂,…,Y_m with respective distribution functions F and Q are considered. The joint asymptotic distributions of exceedance statistics defined as the number of Y observations falling into a random interval of order statistics constructed from the X sample is investigated. The results can be used in the context of a two-sample problem.     

Effect of the coflow stream on a plane wall jet

We propose in this work to study an isothermal and a non-isothermal laminar plane wall jet emerging in a coflow steam. The numerical solution of the governing equations was performed by a finite difference method. In this work, we are interested in the study of the influence of Grashof numbers on the wall jet emerging in a medium at rest. Further, we will examine the effect of the coflow stream on the behavior of the dynamic and thermal properties of the wall jet subjected to a constant temperature. A comparison with a simple wall jet is carried out. The results show that for a buoyant wall jet, two parameters can influence the flow: the inertial and buoyancy forces. The velocity effect indicates that the potential core length increases with the velocity ratio. We are also showed that when using a momentum length scale, the normalized longitudinal maximum velocity can reach an asymptotic curve at different velocity ratios.     

Investigation of a turbulent wall jet in forced convection issuing into a directed coflow stream

In the present paper, we have studied numerically the directed coflow stream effects on mean and turbulent flow properties of a turbulent plane wall jet in forced convection emerging into a directed coflow stream. The system of equations governing the studied configuration is solved with a finite difference scheme using a staggered grid for numerical stability, not uniform in the two directions of the flow. The modified version of the first-order low Reynolds number k–? turbulence model is used and compared to existing experimental findings. It is found that predicted results are in satisfactory agreement with the experimental data and that the wall jet fluid decays faster in presence of a directed coflow stream. Results show also that the increase of coflow deviation angles causes an increase of the growth rates of the dynamic and thermal half-width of the jet and enhances the turbulent mixing. It is found that the longitudinal development of normalised forms of the jet characteristics parameters at different directed coflow velocity ratios can be reasonably well collapsed onto universal trends through the use of momentum length scale.