A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation $$u_t+i{u}_{xx}+i|u{|}^{2}u+\gamma u=f,f\in {\mathrm{??}}^2(?).$$ “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?”     

Removal of Cd(II), Cu(II), and Pb(II) by adsorption onto natural clay: a kinetic and thermodynamic study

In this work, we study the elimination of three bivalent metal ions (Cd²⁺, Cu²⁺, and Pb²⁺) by adsorption onto natural illitic clay (AM) collected from Marrakech region in Morocco. The characterization of the adsorbent was carried out by X-ray fluorescence, Fourier transform infrared spectroscopy and X-ray diffraction. The influence of physicochemical parameters on the clay adsorption capacity for ions Cd²⁺, Cu²⁺, and Pb²⁺, namely the adsorbent dose, the contact time, the initial pH imposed on the aqueous solution, the initial concentration of the metal solution and the temperature, was studied. The adsorption process is evaluated by different kinetic models such as the pseudo-first-order, pseudo-second-order, and Elovich. The adsorption mechanism was determined by the use of adsorption isotherms such as Langmuir, Freundlich, and Temkin models. Experiments have shown that heavy metals adsorption kinetics onto clay follows the same order, the pseudo-second order. The isotherms of adsorption of metal cations by AM clay are satisfactorily described by the Langmuir model and the maximum adsorption capacities obtained from the natural clay, using the Langmuir isotherm model equation, are 5.25, 13.41, and 15.90 mg/g, respectively for Cd(II), Cu(II), and Pb(II) ions. Adsorption of heavy metals on clay is a spontaneous and endothermic process characterized by a disorder of the medium. The values of ΔH are greater than 40 kJ/mol, which means that the interactions between clay and heavy metals are chemical in nature.     

Diabatic investigation for the NaRb molecule

An extensive diabatic investigation of the NaRb species has been carried out for all excited states up to the ionic limit Na^‐Rb⁺. An ab initio calculation founded on the pseudopotential, core polarization potential operators and full configuration interaction has been used with an efficient diabatization method involving a combination of variational effective hamiltonian theory and an effective overlap matrix. Diabatic potential energy curves and electric dipole moments (permanent and transition) for all the symmetries Σ⁺, Π, and Δ have been studied for the first time. Thanks to a unitary rotation matrix, the examination of the diabatic permanent dipole moment (PDM) has shown the ionic feature clearly seen in the diabatic ¹Σ⁺ potential curves and confirming the high imprint of the Na^‐Rb⁺ ionic state in the adiabatic representation. Diabatic transition dipole moments have also been computed. Real crossings have been shown for the diabatic PDM, locating the avoided crossings between the corresponding adiabatic energy curves.     

Dissolution kinetics of fluorapatite in the hydrochloric acid solution

A thermochemical study of hydrochloric acid attack of synthetic fluorapatite was performed by a DRC. The calculated thermogenesis curves show one peak. The plot of the heat quantity as a function of the dissolved mass undergoes only one straight segment, and the thermogenesis curves present a single peak, suggesting the occurrence of a one-step dissolution process. The dissolution kinetics was examined according to the heterogeneous reaction models and showed that the dissolution is controlled by the product layer diffusion process with a reaction rate expressed by the following semiempirical equation; \(\left[ {1 + 2(1 - X) - 3(1 - X)^{{\frac{2}{3}}} } \right] = 3195 \times 10^{ - 2} C^{0.145} \left( {\frac{S}{L}} \right)^{ - 0.628} e^{{ - \frac{2600}{\text T}}} t\). The activation energy was determined as 21.6 ± 1.5 kJ mol^?1     

Phytochemical Investigation by Microwave‐Assisted Extraction of Essential Oil of the Leaves of Walnut Cultivated in Algeria

Walnut (Juglans regia L.) leaves are used traditionally as an herbal tea indicated for non‐insulin‐dependent diabetics. In recent years, the type‐II diabetes is occurring worldwide with increasing frequency. Thus, there is an urgent need to explore the new beneficial biomolecules on the human health. Our objective was to investigate, for the first time, the volatiles profile of Juglans regia L. leaves from Algiers region. The extraction of essential oil of fresh plant material was performed by microwave‐assisted hydrodistillation (MAHD), for the first time, a relatively recent method, then by the conventional hydrodistillation technique (HD) for comparison. The collected extracts were analyzed by GC‐FID and GC/MS using two capillary columns with different polarity. Extraction time of 1 h by MAHD provided higher yields (0.050±0.001% (w/w)) than by HD (0.030±0.006% (w/w)) after 3 h. A total of 38 compounds were identified using both techniques. Essential oils had similar qualitative but different quantitative composition in terms of chemical compounds. The MAHD method improved yield while reducing the extraction time. The sesquiterpenes were the dominant family in both MAHD and HD essential oils with β‐caryophyllene being the major constituent. Monoterpenes, including hydrocarbon and oxygenated, prevail in HD volatile fraction with β‐pinene and eucalyptol, respectively, as major components.     

Thermochemistry and kinetics of the aspect of diammonium hydrogen phosphate precipitation in phosphoric acid solution

Journal of Thermal Analysis and Calorimetry - The thermochemical and kinetic studies of diammonium hydrogen phosphate precipitation in phosphoric acid with ammonia were followed using a...     

Crystal Structure of a New Ammonium Potassium Selenomolybdate Compound K3.31(NH4)0.69[Se2Mo5O21]·2H2O

An inorganic compound formulated as K_3.31(NH₄)_0.69[Se₂Mo₅O₂₁]·2H₂O has been synthesized by conventional solution method and characterized by scanning electron microscopy, IR, UV-Vis spectroscopies behaviors. The structure of the title compound has been determined from a single-crystal X-ray diffraction. It crystallizes in the monoclinic space group P2₁/n, with a?=?9.9371(2) ?, b?=?23.3545(2) ?, c?=?10.5179(2) ?, β?=?114.12(3)°, V?=?2227.7(5) ?³ and Z?=?4. It was revealed that the Strandberg-type polyoxoselenomolybdate cluster can be considered as a ring formed by five distorted edge- and corner-sharing MoO₆ octahedra, capped on both poles by a selenate pyramids sharing three vertices with the ring molybdenum centers. The Strandberg clusters are connected with ammonium ions and water molecules through hydrogen-bonding interactions which ensure the cohesion of the structure into a three-dimensional network.     

Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity

A numerical study of the three-dimensional fluid flow has been carried out to determine the effects of the transverse aspect ratio, Ay, on the flow structure in two-sided non-facing lid-driven cavities. The flow is complex, unstable and can undergo bifurcation. The numerical method is based on the finite volume method and multigrid acceleration. Computations have been investigated for several Reynolds numbers and various aspect ratio values. At a fixed Reynolds number, Re=500, the three-dimensional flow characteristics are analyzed considering four transverse aspect ratios, Ay=1,0.75,0.5 and 0.25. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. An analysis of the flow evolution shows that, at Ay=0.75, the flow bifurcates to a periodic regime at (Re=600) with a frequency f=0.093 less than the predicted value in the cubical cavity. A correlation is established when Ay=0.5 and gives the critical Reynolds number value. At Ay=0.25, the periodic regime occurs at high Re value beyond 3500, after which the flow becomes chaotic. It is shown that, when increasing Ay over the unit, the flow in the cavity exhibits a complex behavior. The kinetic energy transmission from the driven walls to the cavity center is reduced at low Ay values.