Band 79, Heft 1

A mesoporous cobalt ferrite nanostructure was prepared by a green chemistry approach using Pimpinella anisum extract for Cd (II) ions elimination from an aqueous medium. The metal ions adsorption was explored under varying operating conditions, comprising of the pH, initial adsorbate concentration, and contact time. The synthesized sorbent was characterized by various techniques where the XRD data verified a ferrite structure of ≈25 nm crystallite size and the EDX elemental analysis affirmed the presence of the corresponding elements. The CoFe 2 O 4 established porosity characteristic of 10.8 m 2  g −1 BET-specific surface area and 0.023 cm 3  g −1 pore volume values. Batch mode experiments ascertained that the Cd (II) ions uptake was pH-dependent, with peak removal of 170 mg/g accomplished at pH = 5. The adsorption process of the metal ions onto the mesoporous nanomaterial surface fitted well with the Langmuir isotherm and pseudo-second-order kinetics models. The mechanistic aspects indicated the role of intra-particle and film diffusion in the adsorption process. The adsorbent could efficiently remove the pollutant up 74.3 % to four cycles of successful regeneration. This investigation endorsed that CoFe 2 O 4 might be potent candidate for heavy metals from aqueous systems.

This study investigates the nonlinear vibration motions of the Euler–Bernoulli microbeam on a nonlinear elastic foundation in a uniform magnetic field based on Modified Couple Stress Theory (MCST). The effect of size, foundation, and magnetic field on the nonlinear vibration motion of microbeam has been examined. The governing equations related to the nonlinear vibration motions of the microbeam are obtained by using Hamilton’s Principle, and the Multiple Time Scale Method was used to obtain the solutions for the governing equations. The linear natural frequencies of microbeam are presented in the table according to nonlinear parameters and boundary conditions. The linear and nonlinear natural frequency ratio graphs are shown. The present study results are also compared with previous work for validation. It is observed that length scale parameters and magnetic force have a more significant effect on the natural frequency of microbeams. It is seen that when the linear elastic foundation coefficient, the Pasternak foundation and the magnetic force effects increase, the ratio of nonlinear and linear natural frequency decreases.

This article discusses the Riemann problem for the Chaplygin gas Euler equations that include the presence of two source terms. By means of variable substitution, two kinds of non-self-similar Riemann solutions involving delta-shock are constructed explicitly. For the delta-shock, the generalized Rankine–Hugoniot relations and the over-compressive entropy condition are clarified. Moreover, the position, propagation speed and strength of the delta-shock are given explicitly. It is discovered that the position of the delta-shock is a combination of an exponential function and a linear function, and the weight of the delta-shock is an exponential function of the time. Interestingly, even when the delta-shock is a straight line, the weight of the delta-shock is no longer a linear function of the time t . In addition, it is proved that the Riemann solutions converge to the corresponding ones of Chaplygin gas Euler equations with friction as k drops to zero, and the Riemann solutions converge to the corresponding ones of Chaplygin gas Euler equations as k and β tend to zero simultaneously. Furthermore, it is also shown that the limits of Riemann solutions are just the Riemann solutions to the transport equations with same source terms as the Chaplygin gas pressure falls to zero.

In the work reported in this paper, we have analyzed generalized Chaplygin gas (GCG) and modified generalized Chaplygin gas (MGCG) in an interacting scenario. The equation of state parameter has been analyzed in both the cases and the stability of the models has been discerned through squared speed of sound. Stability against gravitational perturbations has been observed for both GCG and MGCG interacting with pressureless dark matter. Also, the generalized second law (GSL) of thermodynamics has been tested for different enveloping horizons and validity of GSL has been observed throughout. Furthermore, f ( T ) gravity has been reconstructed with GCG and MGCG and phantom behaviour has been observed through reconstructed EoS parameters. The squared speed of sound has been derived for f ( T ) gravity and stability of the model has been established through its positivity.

We construct a new class of nonlinear coherent states for the isotonic oscillator by replacing the factorial of the coefficients z n / n ! ${z}^{n}/\sqrt{n!}$ of the canonical coherent states by the factorial x n γ ! = x 1 γ . x 2 γ … x n γ ${x}_{n}^{\gamma }!={x}_{1}^{\gamma }.{x}_{2}^{\gamma }\dots {x}_{n}^{\gamma }$ with x 0 γ = 0 ${x}_{0}^{\gamma }=0$ , where x n γ ${x}_{n}^{\gamma }$ is a sequence of positive numbers and γ is a positive real parameter. This also leads to the construction of a Bargmann-type integral transform which will allow us to find some integral transforms for orthogonal polynomials. The statistics of our coherent states will also be considered by the calculus of one called Mandel parameter. The squeezing phenomenon was also discussed.

Low-temperature elementary conductivity formula in Fermi metals is reviewed starting from Ohm’s law. This provides the background needed to understand why and how the equations exploited are complicated due to effective mass effect and complex scattering rate even in the presence of small-angle electron-electron scattering at low temperatures. Using the mathematical conditions and physical arguments exploited to derive the Drude conductivity formula, we arrive at our main result—the analytic scattering rate formula at low temperatures that gives rise to the famous T 2 dependence without any ad hoc constants. Our derivation formally proves that the formula, 1 / τ = ( A / ℏ ) ( k B T ) 2 / E F $1/\tau =\left(A/\hslash \right){\left({k}_{\text{B}}T\right)}^{2}/{E}_{\text{F}}$ first guessed by Ashcroft and Mermin to be correct where A = N impurity /4 π 2 and N impurity is the number of impurities (or scattering centers) present in a given sample. We also highlight the discovery of a new fundamental physical constant, λ Arulsamy = 3 ℏ 2 ( 4 π ϵ 0 ) 2 / m el e 4 ${\lambda }_{\text{Arulsamy}}=\left[3{\hslash }^{2}{\left(4\pi {{\epsilon}}_{0}\right)}^{2}\right]/\left[{m}_{\text{el}}{e}^{4}\right]$ that associates quantum mechanical energy with that of thermal energy, and is also related to Rydberg constant.