NUMERICAL QUENCHING FOR A NONLINEAR DIFFUSION EQUATION WITH SINGULAR BOUNDARY FLUX

In this paper, we study the semidiscrete approximation of the solution of a nonlinear diffusion equation with nonlinear source and singular boundary flux. We find some conditions under which the solution of the semidiscrete form quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time to the theoretical one when the mesh size tends to zero. Finally, we give some numerical experiments for a best illustration of our analysis.

Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation

The 3D quenching problem reflecting solid-burn scene based on convection–reaction–diffusion equation is creatively concerned in this work. The spatial derivatives of original equation are discretized by Taylor series and the temporal derivatives are approximated by the Crank–Nicolson (CN) method. After the discrete schemes are arranged, an alternating direction implicit (ADI) scheme on adaptive grid is constructed to interpret quenching phenomena of the three-dimension (3D) equation with singularity source. Quenching time, quenching domain, and characteristics relative to temperature as well as variation of temperature over time are achieved via scientific experiment and analysis. Comparing with the 1D or 2D problem, it is harder for the 3D problem to produce quenching phenomena. Regardless of different convection functions, it can form quenching behaviors through experiments when only the elements which include degeneracy parameter, convection parameters, and domain sizes are configured properly. We hope all this can offer references for the 3D engineering problem. At the same time, it will offer support to research the relationship between quenching phenomena and degeneracy parameter, convection parameters, and domain sizes in the future, respectively.

Defeating antibiotic-resistant bacteria with protein-resistant polyGGE film

Biofouling on medical device surfaces, which is initiated by protein adsorption and adhesion of microbes especially the antibiotic-resistant bacteria, attracts global attention for centuries due to its enduring challenges in healthcare. Here, the antifouling effect of hydrophilic poly(glycerol glycidyl ether) (polyGGE) film is explored in comparison to hemocompatible and protein-resistant control polymers. The chemical and thermomechanical stability of polyGGE in hydrated conditions at body temperature was achieved via adjusting UV curing and KOH quenching time. The polyGGE surface is inert to the plasma protein adsorption and interfered the metabolism conditions, biofilm formation and growth of both Gram negative (Gram–) and antibiotic-resistant Gram positive (Gram+) bacteria. These results indicate the potential application of polyGGE for combating the risk of hospital-acquired infections and preventing drug-resistant superbug spreading.

Quenching for Porous Medium Equations

This paper studies the following two porous medium equations with singular boundary conditions. First, we obtain that finite time quenching on the boundary, as well as kt blows up at the same finite time and lower bound estimates of the quenching time of the equation kt = (kn)xx + (1 − k)−α, (x,t) ∈ (0,L) × (0,T) with (kn)x (0,t) = 0, (kn)x (L,t) = (1 − k(L,t))−β, t ∈ (0,T) and initial function k(x,0) = k0 (x), x ∈ [0, L] where n > 1, α and β and positive constants. Second, we obtain that finite time queching on the boundary, as well as kt blows up at the same finite time and a local existence resultbythehelpofsteadystateoftheequationkt =(kn)xx,(x,t)∈(0,L)×(0,T)with (kn)x (0,t) = (1 − k(0,t))−α, (kn)x (L,t) = (1 − k(L,t))−β, t ∈ (0,T) and initial function k (x, 0) = k0 (x), x ∈ [0, L] where n > 1, α and β and positive constants.

Asymptotic properties of quenching for the quasilinear electrostatic micro-electro-mechanical system

This study focuses on the asymptotic properties of quenching solutions for the quasilinear parabolic electrostatic micro-electro-mechanical system with singular logarithm boundary flux. Under some assumptions on initial data, quenching in finite time, blowup phenomenon of a time derivative, lower and upper bounds of quenching rate are studied theoretically, and the asymptotic behaviors near quenching time are verified numerically.

Microstructure and Mechanical Properties of V-Alloyed Rebars Subjected to Tempcore Process

Two B400B-R and B500B grade rebars were industrially produced through a Tempcore process. The standard chemical composition of B500B grade was additionally alloyed with 0.067 wt.% V to enhance its mechanical properties. A set of optimized processing parameters were applied to manufacture two different diameters D20 (Ø 20 mm) and D32 (Ø 32 mm). The microstructure -mechanical properties relationships were evaluated using optical and scanning electron microscopes, hardness, and tensile testing. In addition, a thermal model was developed to define the thermal cycle evolution during cooling in the quenching & tempering box (QTB) to simulate the kinetics of V(C,N) precipitation. The microstructure observations showed a typical graded microstructure consisting of ferrite-pearlite core and outer tempered martensite ring for both grades of both diameters. The optimized processing parameters for B400B-R of D32 (compared with D20) resulted in softening of the core (from 160 to 135 HV10) and tempered martensite surface (from 220 to 200 HV10) as well as in decreasing the yield strength (from 455 to 413 MPa) and tensile strength (from 580 to 559 MPa). On the contrary, an increase in hardness of the core (from 165 to 175 HV10) and the outer tempered martensite (from 240 to 270 HV10), in addition to an increase in yield strength (from 510 to 537 MPa) at almost the same level of tensile strength of 624–626 MPa are observed for B500B grade D32 compared with D20. The modeling and simulation calculations suggest that the manufacturing D32 rebars of B500B grade involves longer quenching time in the QTB which allow deeper tempered martensite surface along with a relatively higher core temperature that renders faster kinetics and larger volume fraction of V(C,N) precipitates. The current study demonstrates that the full potential of V-alloying can be exploited when a sufficient quenching time at the equalization temperature is achieved, which is valid for D32 rebars.

The Phenomenon of Quenching for a Reaction-Diffusion System with Non-Linear Boundary Conditions

We study the quenching behavior of the solution of a semi- linear reaction-diffusion system with nonlinear boundary conditions. We prove that the solution quenches in finite time and its quenching time goes to the one of the solution of the differential system. We also obtain lower and upper bounds for quenching time of the solution.

General Research on the Process of the Indirect Hot Stamping Ultra-High-Strength Steel

Aiming at the need for lightweight requirements of the components in the bus, combined with the advantages of the hot stamping ultra-high-strength steel, a new television (TV) bracket was proposed. The finite element (FE) simulation of the beam part in the TV bracket during the indirect hot stamping process was discussed. After two-stages of pre-forming, the blank was in good formability and without visible cracks. According to the FE simulation results, the punch speed, quenching force, and quenching time significantly affected the temperature, microstructure, hardness, and mechanical properties of the beam part during hot stamping. With the increase of the quenching force and quenching time, the martensite fraction of the beam part was increased. For the beam part, the punch speed should be at least 80 mm/s during the forming stage. For complete quenching, the quenching force should be above 1000 kN and quenching time should be up to 10 s. Based on the parameters from the FE simulation, the forming experiment of the beam part was discussed. Microstructure analyses and microhardness tests as well as tensile tests of the hot stamping beam part were performed. The results confirmed that the FE simulation of the beam part was reliable.

SDSS-IV MaNGA: Global and local stellar population properties of elliptical galaxies

Context. We study the spatially resolved properties of 343 elliptical galaxies with the Mapping Nearby Galaxies at the Apache Point Observatory (MaNGA) survey. Aims. Our goal is to understand the fundamental processes of formation and quenching of elliptical galaxies. Methods. We used the DESI Legacy Imaging Surveys for accurate morphological classification. Based on integrated spectroscopic properties and colors, we classified seven classes of elliptical galaxies. We inferred the stellar age and metallicity gradients out to a 1.5 effective radius (Reff) of classical “red and dead”, recently quenched, and blue star-forming ellipticals (CLEs, RQEs, and BSFs), corresponding to 73%, 10%, and 4% of the sample, respectively. Additionally, we reconstructed their global and radial histories of star formation and mass growth. Results. The mass- and luminosity-weighted age gradients of CLEs are nearly flat or mildly negative, with small differences between both ages. The respective metallicity gradients are negative (∇log[Zmw] = −0.11−0.08+0.07 dex/Reff and ∇log[Zlw] = −0.11−0.07+0.06 dex/Reff, respectively), being flatter as the mass is smaller. The more massive CLEs formed stars earlier and quenched faster than the less massive ones. The CLEs show a weak inside-out growth and a clear inside-out quenching. They finished their quenching globally 3.8 ± 1.2 Gyr ago on average, with quenching time-scales of 3.4 ± 0.8 Gyr. At M⋆ < 1011 M⊙, the age and Z gradients of the RQEs and BSFs are flatter than those of the CLEs, but with larger scatters. They show very weak inside-out growth and quenching, which is slow and not even completed at z ∼ 0 for the BSFs. Instead, the massive RQEs show an outside-in quenching and positive gradients in the luminosity-weighted age and stellar metallicities. The RQEs of all masses quenched 1.2 ± 0.9 Gyr ago on average. Conclusions. Our results for the CLEs are consistent with a two-phase scenario where their inner parts formed by an early and coeval dissipative collapse with a consequent burst of star formation and further quenching, whereas the outer parts continued their assembly, likely by dry mergers. We also discuss some evolutionary scenarios for the RQE and BSF galaxies that would agree with the generic results.