Non-variational Solutions for Anisotropic (p, q)-Laplacian Systems with Nonhomogeneous Growth

Engineered mycelium-based composite materials: Comprehensive study of various properties and applications

This article concerns with the global H\"older regularity of weak solutions to a class of problems involving the fractional $(p,q)$-Laplacian, denoted by $(-\Delta)^{s_1}_{p}+(-\Delta)^{s_2}_{q}$, for $1<p,q<\infty$ and $s_1,s_2\in (0,1)$. We use a suitable Caccioppoli inequality and local boundedness result in order to prove the weak Harnack type inequality. Consequently, by employing a suitable iteration process, we establish the interior H\"older regularity for local weak solutions, which need not be assumed bounded. The global H\"older regularity result we prove expands and improves the regularity results of Giacomoni, Kumar and Sreenadh (arXiv: 2102.06080) to the subquadratic case (that is, $q<2$) and more general right hand side, which requires a different and new approach. Moreover, we establish a nonlocal Harnack type inequality for weak solutions, which is of independent interest.

An effective strategy to tackle the twin crises of global deforestation and fossil fuel depletion is to recycle biomass materials for energy storage devices. This study reports a unique and innovative solution to capitalize on a currently overlooked resource to produce high-performance lithium-sulfur (Li-S) batteries from recycled paper. The recycled paper fibers are creatively composited with graphene oxide sheets via a capillary adsorption method. The recycled paper/graphene oxide hybrid is then converted to activated paper carbon/reduced graphene oxide (APC/graphene) scaffold for sulfur infiltration. The assembled Li-APC/graphene/S battery exhibits a superior lifespan of 620 cycles with an excellent capacity retention rate of 60.5%. An APC interlayer is sandwiched between the Li anode and the separator to suppress the degradation of Li anode by preventing the nonhomogeneous growth of mossy Li whiskers, stretching the battery lifespan up to 1000 cycles with a capacitance retention rate of 52.3%. The capillary adsorption method coupled with the porous carbonaceous anode interlayer configuration creates a new opportunity for the development of batteries derived from porous biomass materials.

Instability analysis of shear bands using the instantaneous growth-rate method

The dynamic linear state feedback control problem is addressed for a class of nonlinear systems subject to time-delay. First, using the dynamic change of coordinates, the problem of global state feedback stabilization is solved for a class of time-delay systems under a type of nonhomogeneous growth conditions. With the aid of an appropriate Lyapunov-Krasovskii functional and the adaptive strategy used in coordinates, the closed-loop system can be globally asymptotically stabilized by the dynamic linear state feedback controller. The growth condition in perturbations are more general than that in the existing results. The correctness of the theoretical results are illustrated with an academic simulation example.

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Adsorption distribution impact on preferential transport within horizontal flow constructed wetland (HFCW)

A cartilage growth mixture (CGM) model is linearized for infinitesimal elastic and growth strains. Parametric studies for equilibrium and nonequilibrium boundary-value problems representing the in vitro growth of cylindrical cartilage constructs are solved. The results show that the CGM model is capable of describing the main biomechanical features of cartilage growth. The solutions to the equilibrium problems reveal that tissue composition, constituent pre-stresses, and geometry depend on collagen remodeling activity, growth symmetry, and differential growth. Also, nonhomogeneous growth leads to nonhomogeneous tissue composition and constituent pre-stresses. The solution to the nonequilibrium problem reveals that the tissue is nearly in equilibrium at all time points. The results suggest that the CGM model may be used in the design of tissue engineered cartilage constructs for the repair of cartilage defects; for example, to predict how dynamic mechanical loading affects the development of nonuniform properties during in vitro growth. Furthermore, the results lay the foundation for future analyses with nonlinear models that are needed to develop realistic models of cartilage growth.

Electrical waveform mediated through-mask deposition of solder bumps was investigated with several types of plating baths for wafer level packaging applications. The influence of varying duty cycle in the presence of additives on deposit properties including shape evolution within the cavity, abnormal growth, surface morphology, alloy composition, and thickness distribution was evaluated at a fixed, moderate frequency. Waveform mediation with properly selected duty cycles (i) improved surface flatness and morphology of deposits when the shape ratio with dc deposition was less than 1, (ii) suppressed the probability of abnormal growth (nonhomogeneous growth such as large nodules), (iii) reduced grain sizes resulting in smoother surfaces, and modulated alloy composition at a given bath and process condition. With decreasing duty cycle, the thickness distribution within the feature, pattern, and workpiece also changed due to the increased influence of primary current distribution. The fraction of current flowing along the cavity edge, die edge (when the space between dice is much larger than the bump pitch), and wafer edge seems to increase with decreasing duty cycle. © 2004 The Electrochemical Society. All rights reserved.

ABSTRACTTargeting very thin equivalent oxides (&lt;1 nm) requires the deposition of (very) thin dielectrica onto silicon surfaces with minimal interfacial oxide. Typically, high-k dielectric layers are deposited using ALD or MOCVD with, at present, a prime emphasis on Hf-based high-k dielectrics, either as pure HfO2, as silicate or mixed with Al2O3. In some cases nitrogen is added to improve the high-temperature stability. Depending on the deposition conditions ALD as well as MOCVD show serious deficiencies in terms of film closure and material density for ultra thin (&lt;3 nm) films. Various surface preparation methods and deposition conditions are used to improve the film quality. Detailed studies on the film growth and its evolution requires the use of many analytical methods such as Rutherford Backscattering Spectrometry, Low Energy Ion Scattering, Time-of-flight SIMS, (spectroscopic) ellipsometry and X-ray photoelectron spectroscopy. When trying to correlate the results in terms of film thickness, apparent discrepancies can be observed which relate to non-homogeneous growth and reduced material density.

The spinning of polymeric fibers, the processing of numerous foodstuffs and the peel and tack characteristics of adhesives are all associated with the formation, stability and, ultimately, the longevity of thin fluid `strands'. This tendency to form strands is usually described in terms of the tackiness of the fluid or by heuristic concepts such as `stringiness' (Lakrout et al. J Adhesion 1999). The dynamics of such processes are complicated due to spatially and temporally non-homogeneous growth of extensional stresses, the action of capillary forces and the evaporation of volatile solvents. We describe the development and application of a simple instrument referred to as a microfilament rheometer (MFR) that can be used to readily differentiate between the dynamical response of different pressure-sensitive adhesive fluid formulations. The device relies on a quantitative observation of the rate of extensional thinning or `necking' of a thin viscous or viscoelastic fluid filament in which the solvent is free to evaporate across the free surface. This high-resolution measurement of the radial profile provides a direct indication of the ultimate time to break up of the fluid filament. This critical time is a sensitive function of the rheological properties of the fluid and the mass transfer characteristics of the solvent, and can be conveniently reported in terms of a new dimensionless quantity we refer to as a processability parameter P. We demonstrate the usefulness of this technique by presenting our results in the form of a case study in which we measure the visco-elasto-capillary thinning of slender liquid filaments for a number of different commercial polymer/solvent formulations and relate this to the reported processing performance of the materials. We also compare the MFR observations with the prediction of a simple 1D theory derived from the governing equations that model the capillary thinning of an adhesive filament.

We studied the morphology of ramps in REBa/sub 2/Cu/sub 3/O/sub 7/ (REBCO) epitaxial films on SrTiO/sub 3/ substrates, fabricated by RF magnetron sputter deposition and pulsed laser deposition (PLD), by Atomic Force Microscopy (AFM) and High Resolution Electron Microscopy (HREM). The ramps were fabricated by Ar ion beam etching using different masks of standard photoresist and TiN. AFM-studies on ramps in sputter deposited films show a strong dependence, i.e., formation of facets and ridges, on the angle of incidence of the ion beam with respect to the substrate surface as well as the rotation angle with respect to the crystal axes of the substrate. Ramps in pulsed laser deposited films did not show this dependence. Furthermore, we studied the effect of an anneal step prior to the deposition of barrier layers (i.e. PrBa/sub 2/Cu/sub 3-x/Ga/sub x/O/sub 7/) on the ramp. First results show a crystallization of the ramp surface, resulting in terraces and a non-homogeneous growth of the barrier material on top of it. The thickness variations, for thin layers of barrier material, can even become much larger than expected from the amount of deposited material and are dependent on the deposition and anneal conditions. HREM studies show a well-defined interface between barrier layer and electrodes. The angle of the ramp depends on the etch rate of the mask and REBCO and on the angle of incidence of the ion beam. Hard masks, like TIN, have a much lower etch rate compared to photoresist, resulting in an angle of the ramp comparable to the angle of incidence and, subsequently, in a low etching rate on the ramp.

Characterisation of multilayer ramp-type REBa 2Cu 3O 7 −δ structures by scanning probe microscopy and high-resolution electron microscopy

Cyclic degradation and fracture of a random short-fiber SMC composite subjected to shear fatigue was studied. Experiments were conducted on double V-notched Iosipescu SMC-R50 specimens under completely reverse cyclic shear loading. Owing to the random microstructure of the SMC-R50 composite, homogeneous fatigue damage was treated in a continuum sense. The cyclic shear stress-strain behavior was studied first. Macroscopic shear stiffness degradation and the rate of damage evolution during the shear fatigue were investigated also. Cyclic shear stiffness reduction up to 25 per cent of its initial value was common in most cases studied. A power-law relationship among the rate of damage, the cyclic shear stress amplitude, and the fatigue loading history was determined. The shear-fatigue fracture, resulted from nonhomogeneous growth of fatigue damage, was well-behaved, and a cyclic shear stress-life diagram was constructed for the SMC-R50 material.