On mesh restrictions to satisfy comparison principles,maximum principles,and the non-negative constraint: Recent developments and new results

This article concerns mesh restrictions that are needed to satisfy several important mathematical properties—maximum principles, comparison principles, and the nonnegative constraint—for a general linear second-order elliptic partial differential equation. We critically review some recent developments in the field of discrete maximum principles, derive new results, and discuss some possible future research directions in this area. In particular, we derive restrictions for a three-node triangular (T3) element and a four-node quadrilateral (Q4) element to satisfy comparison principles, maximum principles, and the nonnegative constraint under the standard single-field Galerkin formulation. Analysis is restricted to uniformly elliptic linear differential operators in divergence form with Dirichlet boundary conditions specified on the entire boundary of the domain. Various versions of maximum principles and comparison principles are discussed in both continuous and discrete settings. In the literature, it is well-known that an acute-angled triangle is sufficient to satisfy the discrete weak maximum principle for pure isotropic diffusion. Herein, we show that this condition can be either too restrictive or not sufficient to satisfy various discrete principles when one considers anisotropic diffusivity, advection velocity field, or linear reaction coefficient. Subsequently, we derive appropriate restrictions on the mesh for simplicial (e.g., T3 element) and nonsimplicial (e.g., Q4 element) elements. Based on these conditions, an iterative algorithm is developed to construct simplicial meshes that preserve discrete maximum principles using existing open source mesh generators. Various numerical examples based on different types of triangulations are presented to show the pros and cons of placing restrictions on a computational mesh. We also quantify local and global mass conservation errors using representative numerical examples and illustrate the performance of metric.     

Tunable,Grating-Gated,Graphene-On-Polyimide Terahertz Modulators

An electrically switchable graphene terahertz (THz) modulator with a tunable-by-design optical bandwidth is presented and it is exploited to compensate the cavity dispersion of a quantum cascade laser (QCL). Electrostatic gating is achieved by a metal grating used as a gate electrode, with an HfO₂/AlO_x gate dielectric on top. This is patterned on a polyimide layer, which acts as a quarter wave resonance cavity, coupled with an Au reflector underneath. The authors achieve 90% modulation depth of the intensity, combined with a 20 kHz electrical bandwidth in the 1.9–2.7 THz range. The modulator is then integrated with a multimode THz QCL. By adjusting the modulator operational bandwidth, the authors demonstrate that the graphene modulator can partially compensate the QCL cavity dispersion, resulting in an integrated laser behaving as a stable frequency comb over 35% of the operational range, with 98 equidistant optical modes and a spectral coverage ~1.2 THz. This paves the way for applications in the terahertz, such as tunable transformation-optics devices, active photonic components, adaptive and quantum optics, and metrological tools for spectroscopy at THz frequencies.     

Estimation of Hardness During Heat Treatment of Steels

Metal Science and Heat Treatment - A hardness model employing the end quench Jominy method is developed for steels C25, EN8, EN19, EN31 and EN24. The time-temperature data are obtained from four...     

Multi-Objective Optimization of Spur Gearbox with Inclusion of Tribological Aspects

In this paper, a novel multi-objective optimization of a two-stage spur gearbox is carried out with a comprehensive range of constraints. The first objective function aims to reduce the weight/volume and second aims to minimize the power losses in the gearbox. Various design constraints and tribological constraints such as scuffing and wear are included. By using a specially formulated discrete version of NSGA-II optimization code, these objective functions are minimized for three different gear profiles (unmodified profile, smooth meshing, and high load) and for different SAE oil grades. Optimization is first carried out based on standard single objective minimization using regular constraints based on existing literature and then based on multi-objective optimization with comprehensive constraints which include tribological aspects. Finally, these two cases are compared for different gear profiles and oils. The results indicate that there is a high probability of wear failure, for solutions obtained from single objective minimization. The total power loss is reduced by half when using multi-objective compared to single objective optimization.     

The EphB6 Receptor: Kinase-Dead but Very Much Alive

The Eph receptor tyrosine kinase member EphB6 is a pseudokinase, and similar to other pseudoenzymes has not attracted an equivalent amount of interest as its enzymatically-active counterparts. However, a greater appreciation for the role pseudoenzymes perform in expanding the repertoire of signals generated by signal transduction systems has fostered more interest in the field. EphB6 acts as a molecular switch that is capable of modulating the signal transduction output of Eph receptor clusters. Although the biological effects of EphB6 activity are well defined, the molecular mechanisms of EphB6 function remain enigmatic. In this review, we use a comparative approach to postulate how EphB6 acts as a scaffold to recruit adaptor proteins to an Eph receptor cluster and how this function is regulated. We suggest that the evolutionary repurposing of EphB6 into a kinase-independent molecular switch in mammals has involved repurposing the kinase activation loop into an SH3 domain-binding site. In addition, we suggest that EphB6 employs the same SAM domain linker and juxtamembrane domain allosteric regulatory mechanisms that are used in kinase-positive Eph receptors to regulate its scaffold function. As a result, although kinase-dead, EphB6 remains a strategically active component of Eph receptor signaling.     

Measurement of effective permeability of reinforcement mats using sensitivity analysis

A methodology using sensitivity analysis is proposed to measure the effective permeability which includes the interaction of the resin and the reinforcement. Initially, mold‐filling experiments were performed at isothermal conditions on the test specimen and the positions of the flow front were tracked with time using a flow visualization method. Following this, mold‐filling experiments were simulated using a commercial software to obtain the positions of the flow front with time at the process conditions used for experiments. Several iterations were performed using different trial values of the permeability until the experimentally tracked and simulated positions of the flow front with time were matched. Finally, the value of the permeability thus obtained was validated by comparing the positions obtained by performing the experiments at different process conditions with the positions obtained by simulating the experiments. In this study, woven roving and chopped strand mats of E‐class glass fiber and unsaturated polyester resin were used for the experiments. From the results, it was found that the measured permeabilities were consistent with varying process conditions. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Effect of External Lubricant on Mechanical Properties of Dry-Pressed Green Bodies

Tensile strength and fracture toughness of uniaxially compacted spray-dried ferrite powders, with and without external lubricant were measured. The addition of external lubricant significantly increased the fracture strength and decreased the strength variability. The external lubricant also led to an increase in fracture toughness and a decrease in the critical flaw size. Scanning electron microscopy examination of fracture surfaces showed an increase in the amount of transgranular fracture for the pellets compacted from the externally lubricated powder. It was concluded that the external lubricant strengthened the bonds between the spray-dried granules, thereby increasing the fracture toughness and reducing the critical flaw size. X-ray tomography of pellets showed that there was no appreciable difference in density gradients between the samples.     

Effect of Relative Humidity on the Viscoelastic and Mechanical Properties of Spray-Dried Powder Compacts

Spray-dried powder compacts exhibit viscoelastic properties such as stress relaxation, creep, and delayed elastic strain. This behavior is attributed to the organic binder, which forms bridges between the particles in spray-dried granules, thereby affecting their deformation characteristics. The viscosity and distribution of the binder within the powder compact can affect its mechanical and viscoelastic properties. In this study, the powder was conditioned at different ambient relative humidity (RH) levels, to vary the binder viscosity. Load deformation, stress relaxation, fracture strength, and fracture toughness behavior of ferrite powder compacts were studied as a function of ambient RH both before and after compaction. The loading rate was found to significantly affect the time-dependent response, and the relaxation times decreased at high humidity levels during compaction. It is proposed that increasing the humidity level during compaction increases the number of particle–particle contacts. This simple mechanism of binder redistribution led to slower relaxation times, increases in fracture strength, and elastic modulus of the green bodies, without significantly altering the fracture toughness when powders were compacted at high humidity to a given density.     

SWCNT induced crystallization in amorphous and semi-crystalline poly(etherimide)s: Morphology and thermo-mechanical properties

In this study we contrast the behavior of an amorphous polyetherimide (ODPA-P3) with that of a semi-crystalline one (BPDA-P3) on introducing single-wall carbon nanotubes (SWCNTs; 0.1–4.4 vol.%). The SWCNTs act as a nucleating agent and induce crystallinity (up to 45%) in amorphous ODPA-P3; in BPDA-P3, the SWCNTs lower the onset of crystallization during thermal imidization, but decrease the overall degree of crystallinity. Tensile tests show that the yield strength is the same for both polyimides up to 0.3% SWCNT loadings. Above this concentration the yield strength for the BPDA-P3 nanocomposites remains constant whereas in the ODPA-P3 nanocomposites it increases from 80 to 126 MPa (1.2 vol.%). In the amorphous PEI, SWCNTs enhance the thermo-mechanical properties (Tg, storage- and elastic modulus, and yield strength), but in the semi-crystalline PEI there are little or no effects on the mechanical performance.