Asymptotic convergence of solutions for Laplace reaction–diffusion equations

We study the initial–boundary value problem for a Laplace reaction–diffusion equation. After constructing local solutions by using the theory of abstract degenerate evolution equations of parabolic type, we show asymptotic convergence of bounded global solutions if they exist under the assumption that the reaction function is analytic in neighborhoods of their $\omega$-limit sets. Reduction of degenerate evolution equation to multivalued evolution equation enables us to use the theory of the infinite-dimensional Łojasiewicz–Simon gradient inequality.     

Porphyrin-like porous nanomaterials as drug delivery systems for ibuprofen drug

In recent years, nanomaterial-based drug delivery carriers have become some of the most attractive to be studied. The purpose of this study is to investigate the interaction of C60 fullerene, carbon nanotube and graphene having porphyrin-like FeN4 clusters with a non-steroidal anti-inflammatory drug (ibuprofen) by means of the density functional theory. Results showed that the graphene with FeN4 clusters could remarkably increase the tendency of graphene for adsorption of ibuprofen drug. Also, our ultraviolet–visible results show that the electronic spectra of the complexes exhibit a blue shift toward lower wavelengths (higher energies). It was found that Ibp/FeN4-graphene had high chemical reactivity, which was important for binding of the drug onto the target site. In order to go further and gain insight into the binding features of considered systems with ibuprofen drug, the Atoms in Molecules analysis was performed. Our results determine the electrostatic features of the Ibp/FeN4-graphene bonding. Consequently, the results demonstrated that the FeN4-graphene could be used as potential carriers for the delivery of ibuprofen drug.     

Toward efficient interactions of bubbles and coal particles induced by stable cavitation bubbles under 600 kHz ultrasonic standing waves

The interactions of bubbles and coal particles in 600 kHz ultrasonic standing waves (USW) field has been investigated. A high-speed camera was employed to record the phenomena occurred under the USW treatment. The formation and behaviors of cavitation bubbles were analyzed. Under the driving of these cavitation bubbles, whose size is from several microns to dozens of microns, coal particles were aggregated and then attracted by large bubbles due to the acoustic radiation forces. The results of USW-assisted flotation show a significant improvement in recoveries at 600 kHz, which indicates that the interactions of bubbles and particles in the USW field are more efficient than that in the conventional gravitational field. Furthermore, the sound pressure distribution of the USW was measured and predicted by a hydrophone. The analysis of gravity and buoyancy, primary and secondary Bjerknes forces shows that bubble-laden particles can be attracted by the rising bubbles under large acoustic forces. This study highlights the potential for USW technology to achieve efficient bubble-particle interactions in flotation.     

One-dimensional displacement of active matter on curved substrates

We analytically find the diffusion of overdamped active Brownian particles (ABPs) constrained to move along curved one-dimensional channels. The autonomous motion of these particles is achieved by a projection of their internal propulsion force along the channels' long section. In particular, the diffusion of ABPs moving on one-dimensional channels with a form of a circle, an ellipse, and a limacon of second order is analysed. To characterise the effect of substrate's geometry and self-propulsion on their diffusion, analytical expressions for the ABPs short- and long-time variances, as well as their steady angular probability density functions are offered. Curvature effects are found to reduce the time an ABP reaches its steady state. Our theoretical results are validated using Brownian dynamics simulations. This model may be relevant for experiments dealing with catalytic driven systems, bacteria, and tumour cell dispersion in one-dimensional channels.     

A study on the spectral,microstructural, and magnetic properties of Eu–Nd double-substituted Ba0.5Sr0.5Fe12O19 hexaferrites synthesized by an ultrasonic-assisted approach

In this study, an examination on the spectral, microstructural, and magnetic characteristics of Eu–Nd double-substituted Ba_0.5Sr_0.5Fe₁₂O₁₉ hexaferrites (Ba_0.5Sr_0.5Nd_xEu_xFe_12−2xO₁₉ (x = 0.00–0.05) HFs) fabricated by an ultrasonic-assisted approach has been presented. An UZ SONOPULS HD 2070 ultrasonic homogenizer with frequency of 20 kHz and power of 70 W was used. The chemical bonding, structure and the morphology of the products were evaluated by Fourier-Transform Infrared (FT-IR) Spectroscopy, XRD (X-ray diffraction), scanning and transmission electron microscopy and techniques. The textural properties of the prepared nanomaterials were examined by using the Brunauer-Emmett-Teller (BET) method. The magnetic properties were studied using a vibrating sample magnetometer (VSM) at room temperature (RT) and low temperature 10 K. The magnitudes of various magnetic parameters including M_s (saturation magnetization), M_r (remanence) and H_c (coercivity) were estimated and evaluated. The M-H loops revealed the hard ferrimagnetic nature for all products at both temperatures. The M_s and M_r values showed a decreasing tendency with increasing degree of Eu³⁺ and Nd³⁺ substitutions whereas H_c values displayed an increasing trend. At RT, M_s, M_r and H_c values lie in the ranges of 63.0–68.8 emu·g⁻¹, 24.6–39.2 emu·g⁻¹ and 2252.4–2782.1 Oe, respectively. At 10 K, the values of M_s, M_r and H_c lie between 87.5–97.1 emu·g⁻¹, 33.5–40.1 emu·g⁻¹ and 2060.6–2417.2 Oe, respectively. The observed magnetic properties make the prepared products promising candidates to be applied in the recording media.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

Study on the changes of ultrasonic parameters over supercritical Ni-Co electroplating process

This work discusses the influence of changes to ultrasound (US) parameters over the nickel cobalt (Ni-Co) metal thin film properties produced by supercritical CO₂ (SC-CO₂) electroplating. Additionally, Ni-Co films were produced by conventional electroplating and silent SC-CO₂ and compared against each other.The discussion on metal thin film properties revolves around variations to the bath type ultrasonic power (15 W and 20 W) and frequency (42 k Hz and 72 kHz) during experiments. The properties provided by the three electroplating processes and analyzed include: grain sizes, film elemental content analyses, surface microstructures, film hardness, corrosion resistance, surface roughness, crystalline structure and preferential growth, etc. From the results it was clear that quality of films produced by US-SC-CO₂ was improved compared to that of films produced by silent SC-CO₂, which itself was better than those produced by conventional electroplating. However, when US power was varied we observed a decline in the mechanical properties of the produced films.The combination of ultrasonic agitation with SC-CO₂ allows for improved mechanical properties such as: lower surface roughness, finer grain size and surface morphologies, increased corrosion resistance and film hardness. The ultrasound agitation applied to SC-CO₂ electroplating enhanced the formation of alloyed metal as ultrasonic agitation increased the electrolyte flowability during electroplating process resulting in increased mass transfer while at the same time achieving a surface cleaning effect which removed metal ions with poor adhesion and other unwanted particles. Moreover, application of ultrasonic agitation avoids the use of surfactants so only changes to the physical phenomena and no changes to the chemical composition of the deposited thin films were observed, meaning less pollution to the electrolyte and higher purity of the deposited films.The US-SC-CO₂ electroplating method described in this work effectively enhanced the mechanical properties of the deposited thin films compared to those produced by both silent SC-CO₂ and conventional electroplating processes.