Study of the q-Gaussian distribution with the scale index and calculating entropy by normalized inner scalogram

In this paper, we discuss a method based on wavelet analysis for the study of the q-index of the Gaussian distribution. We derive q-index from the scale index, $i_{\mathit{scale}}$, using the expression; $q\equiv 1+2i_{\mathit{scale}}$ where $i_{\mathit{scale}}$ is a wavelet based tool for measuring the degree of aperiodicity of a dynamical system in the range of $0\le i_{\mathit{scale}}\le 1$. We show that this expression gives consistent results with the numerical approach of q-Gaussian distribution which determines the degree of non-extensivity of a dynamical system in the range of $1<q<3$. We also suggest a new entropy calculation method based on the normalized inner scalogram for studying the chaotic characteristics of nonlinear dynamical systems.     

Ignition condition for degenerate plasma in magneto-inertial fusion

The present paper investigated the effect of radiation loss on the ignition temperature for the fuel pellet $(D/T_x{/}^{3}H{e}_y)$simulated in a degenerate plasma. The behavior of these plasmas was predicted by the energy equations that were different from the classical ones, and this was the main factor in decreasing the ignition temperature of the plasma. Therefore, the required ignition condition for fusion was described. For this condition, a hybrid of elements from the traditional Magnetic and Inertial Fusion concepts together with degenerated plasma were considered. Results suggested that a high-density low-temperature plasma can be obtained during the compression phase in an inertial confinement fusion system. Also, the plasma electrons can degenerate using the fast ignition approach when the plasma is of high density and low temperature.     

Effect of ultrasonic irradiation power on sonochemical synthesis of gold nanoparticles

In this work, optimized size distribution and optical properties in the colloidal synthesis of gold nanoparticles (GNPs) were obtained using a proposed ultrasonic irradiation assisted Turkevich-Frens method. The effect of three nominal ultrasound (20 kHz) irradiation powers: 60, 150, and 210 W have been analyzed as size and shape control parameters. The GNPs colloidal solutions were obtained from chloroauric acid (HAuCl₄) and trisodium citrate (C₆H₅Na₃O₇·2H₂O) under continuous irradiation for 1 h without any additional heat or stirring. The surface plasmon resonance (SPR) was monitored in the UV–Vis spectra every 10 min to found the optimal time for localized SPR wavelength (${\lambda }_{\mathrm{L}\mathrm{S}\mathrm{P}\mathrm{R}}$), and the 210 sample procedure has reduced the ${\lambda }_{\mathrm{L}\mathrm{S}\mathrm{P}\mathrm{R}}$ localization at 20 min, while 150 and 60 samples have showed ${\lambda }_{\mathrm{L}\mathrm{S}\mathrm{P}\mathrm{R}}$ at 60 min. The nucleation and growth of GNPs showed changes in shape and size distribution associated with physical (cavitation, temperature) and chemical (radical generation, pH) conditions in the aqueous solution. The results showed quasi-spherical GNPs as pentakis dodecahedron (${\lambda }_{\mathrm{L}\mathrm{S}\mathrm{P}\mathrm{R}}$ = 560 nm), triakis icosahedron (${\lambda }_{\mathrm{L}\mathrm{S}\mathrm{P}\mathrm{R}}$ = 535 nm), and tetrakis hexahedron (${\lambda }_{\mathrm{L}\mathrm{S}\mathrm{P}\mathrm{R}}$ = 525 nm) in a size range from 12 to 16 nm. Chemical effects of ultrasound irradiation were suggested in the disproportionation process, electrons of AuCl₂⁻ are rapidly exchanged through the gold surface. After AuCl₄⁻ and Cl⁻ were desorbed, a tetrachloroaurate complex was recycled for the two-electron reduction by citrate, aurophilic interaction between complexes AuCl₂⁻, electrons exchange, and gold seeds, the deposition of new gold atoms on the surface promoting the growth of GNPs. These mechanisms are enhanced by the effects of ultrasound, such as cavitation and transmitted energy into the solution. These results show that the plasmonic response from the reported GNPs can be tuned using a simple methodology with minimum infrastructure requirements. Moreover, the production method could be easily scalable to meet industrial manufacturing needs.