Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model

This paper studies the asymptotic behavior of coexistence steady-states of the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. In the case when either one of two cross-diffusion coefficients tends to infinity, Lou and Ni [18] derived a couple of limiting systems, which characterize the asymptotic behavior of coexistence steady-states. Recently, a formal observation by Kan-on [10] implied the existence of a limiting system including the nonstationary problem as both cross-diffusion coefficients tend to infinity at the same rate. This paper gives a rigorous proof of his observation as far as the stationary problem. As a key ingredient of the proof, we establish a uniform $L^{\infty }$ estimate for all steady-states. Thanks to this a priori estimate, we show that the asymptotic profile of coexistence steady-states can be characterized by a solution of the limiting system.     

Applications of photocatalytic titanium dioxide-based nanomaterials in sustainable agriculture

Photocatalytic materials are attracting attention as emerging resources for agricultural applications. This timely review assesses the current developments in the use of biocompatible titanium dioxide (TiO₂)-based photocatalytic nanomaterials (TiO₂-PN) as models to unravel agricultural growth, harvest, and post-harvest problems. Such developments can lead to technological innovations aimed at addressing the pressing global environmental challenges faced by farming. TiO₂-PN have been used as antimicrobial, growth-regulating, and fertilizer-like agents. The promising agricultural research applications of TiO₂-PN are highlighted along with a discussion of the main challenges that will need to be overcome to fully understand the roles of TiO₂-PN in the sustainable and productive exploitation of land and water for agricultural applications under natural conditions. In particular, rhizosphere internalization, translocation, and plant bioaccumulation pathways of photocatalytic materials from environmental exposition are outlined to illustrate the effect of TiO₂ on the agricultural cycle. Nanotoxicology and regulations are also discussed to illustrate the importance of biocompatibility and green synthesis of nanomaterials for safe use in real applications. This overview is focused on motivating and intensifying our understanding of on-site agricultural studies. Complementary biological approaches and structural damage observed by biological transmission electron, scanning electron, and optical microscopies should accelerate the practical contribution of TiO₂-PN to sustainable agriculture in conjunction with plant factories and plasma nitrogen fixation technology. Loadings below 10 μg/L of TiO₂-PN with a size of 40 nm benefit seed germination and root elongation as well as partially suppressing metal root translocation. However, only approximately 5% of current studies were carried out in real agricultural settings.     

Synthesis,crystal structure,vibrational spectra,optical properties and theoretical investigation of a two-dimensional self-assembled organic-inorganic hybrid material

Organic–inorganic hybrid material of formula (C₄H₃SC₂H₄NH₃)₂[PbI₄] was synthesized and studied by X-ray diffraction, Infrared absorption, Raman scattering, UV–Visible absorption and photoluminescence measurements. The molecule crystallizes as an organic–inorganic two-dimensional (2D) structure built up from infinite PbI₆ octahedra surrounded by organic cations. Such a structure may be regarded as quantum wells system in which the inorganic layers act as semiconductor wells and the organic cations act as insulator barriers. Room temperature IR and Raman spectra were recorded in the 520–3500 and 10–3500 cm⁻¹ frequency range, respectively. Optical absorption measurements performed on thin films of (C₄H₃SC₂H₄NH₃)₂[PbI₄] revealed three distinct bands at 2.4, 2.66 and 3.25 eV. We also report DFT calculations of the electric dipole moments (μ), polarizability (α), the static first hyperpolarizability (β) and HOMO–LUMO analysis of the title compound investigated by GAUSSIAN 09 package. The calculated static first Hyperpolarizability is equal to 11.46 × 10⁻³¹ esu.     

Testing the energy diffusion approximation for the escape of a Brownian particle from a potential pocket

For the first time, the energy diffusion approximation is confronted at the percent level with the exact numerical modeling of thermal decay of a metastable state. This model is useful in many branches of natural sciences: e.g. in biology, nuclear physics, chemistry, etc. The exact (within the statistical errors about 2%) quasistationary decay rates result from the Langevin equations for the coordinate and conjugated momentum. For the energy (or action) diffusion approach, a Langevin-type equation for the action is constructed, validated, and solved numerically. The comparison of these two approaches is performed for four potentials (two of which are anharmonic) in a wide range of two dimensionless scaling parameters: i) the governing parameter G reflecting how high is the barrier with respect to the temperature and ii) the damping parameter φ expressing the friction strength. It turns out that the energy diffusion approach produces the rate which comes into 50%-agreement with the exact one only at φ < 0.02. Thus, we quantify, for the first time by our knowledge, the condition φ ≪ 1 known in the literature.     

Ultrathin CuF2-Rich Solid-Electrolyte Interphase Induced by Cation-Tailored Double Electrical Layer toward Durable Sodium Storage

Solid-electrolyte interphase (SEI) seriously affects battery's cycling life, especially for high-capacity anode due to excessive electrolyte decomposition from particle fracture. Herein, we report an ultrathin SEI (3–4 nm) induced by Cu⁺-tailored double electrical layer (EDL) to suppress electrolyte consumption and enhance cycling stability of CuS anode in sodium-ion batteries. Unique EDL with SO₃CF₃-Cu complex absorbing on CuS in NaSO₃CF₃/diglyme electrolyte is demonstrated by in situ surface-enhanced Raman, Cyro-TEM and theoretical calculation, in which SO₃CF₃-Cu could be reduced to CuF₂-rich SEI. Dispersed CuF₂ and F-containing compound can provide good interfacial contact for formation of ultrathin and stable SEI film to minimize electrolyte consumption and reduce activation energy of Na⁺ transport. As a result, the modified CuS delivers high capacity of 402.8 mAh g⁻¹ after 7000 cycles without capacity decay. The insights of SEI construction pave a way for high-stability electrode.     

Transition mechanisms of translational motions of bubbles in an ultrasonic field

The translation behaviors of oscillating bubbles are closely related to the polymerizations and dispersions between them, which are crucial for the ultrasonic cavitation effect. In this study, six types of translational motion of bubbles with a wide range of sizes (2–100 μm) in the R₀₁-R₀₂ plane are investigated. Our results demonstrate that in addition (to the 2nd order harmonic), the 1/2 order subharmonic can change the bubble pairs from the three states of the attraction, stable after attraction, and repulsion to that of the repulsion, coalescence, and attraction, respectively. Furthermore, within the range of the main resonance radius and the 1/2 order subharmonic resonance radius, the chaotic bubble pairs with alternating attractive and repulsive forces appear in the region between the coalescence pairs and stable pairs after attraction. Finally, the corresponding physical mechanisms of the chaotic translational motions are also revealed.     

Quick assessment methodology for reliability of solder joints in ball grid array (BGA) assembly—Part I: Creep constitutive relation and fatigue model

In this study, a new unified creep constitutive relation and a modified energy-based fatigue model have been established respectively to describe the creep flow and predict the fatigue life of Sn−Pb solders. It is found that the relation successfully elucidates the creep mechanism related to current constitutive relations. The model can be used to describe the temperature and frequency dependent low cycle fatigue behavior of the solder. The relation and the model are further employed in part II to develop the numerical simulation approach for the long-term reliability assessment of the plastic ball grid array (BGA) assembly. The project supported by the National Natural Science Foundation of China (59705008)     

Air transport in chute flows

The air bubble rise velocity in still water depends mainly on the bubble size and is basically influenced by buoyancy, viscosity and surface tension. In high-speed flows the number of forces acting on air bubbles increases with turbulence, non-hydrostatic pressure gradient, shear forces, bubble clouds and free-surface entrainment. Air bubbles in these flows are used for cavitation protection of hydraulic structures such as chutes, spillways and bottom outlets. Here, air is normally added by means of aerators upstream of regions where the cavitation number falls below a critical value mainly to reduce the sonic velocity of the fluid and cushion the cavitation bubble collapse process. The distance between successive aerators depends basically on the bubble rise velocity. Until today, the bubble rise velocity in high-speed flows was not thoroughly investigated because of limited laboratory instrumentation. The present project focused on the streamwise development of air concentrations in high-speed flows along a 14 m long model chute. The bubble rise velocity was indirectly derived from the air detrainment gradient of the air concentration contour lines downstream of an aeration device. It accounts for the main hydraulic parameters chute slope, Froude number and air concentration. It is demonstrated that the bubble rise velocity in high-speed flow and stagnant water differ significantly due to fracturing processes, turbulence, and the ambient air concentration.     

Numerical study of vortex reconnection for two anti-parallel vortex tubes

By direct numerical simulation of the Navier-Stokes equations we investigate the reconnection of two antiparallel vortex tubes. A new type of perturbation of the initial vorticity field is given which is different from that presented in Refs. [8] and [9]. The formation and the evolution of the “curved vortex belts”, their mutual action with the “bridges” are found. These are important phenomena not studied by others. The project supported by the LNM of Institute of Mechanics, Academia Sinica and The National Natural Science Foundation of China