Optimization free neural network approach for solving ordinary and partial differential equations

Current work introduces a fast converging neural network-based approach for solution of ordinary and partial differential equations. Proposed technique eliminates the need of time-consuming optimization procedure for training of neural network. Rather, it uses the extreme learning machine algorithm for calculating the neural network parameters so as to make it satisfy the differential equation and associated boundary conditions. Various ordinary and partial differential equations are treated using this technique, and accuracy and convergence aspects of the procedure are discussed.

     

Soft and Hard Adhesion

The force needed to pull a cylindrical stud from a soft elastomeric film depends on their elastic and geometric properties. For a rigid stud and a thick elastomeric film, the pull-off stress (σ) depends on the elastic modulus (E) of the film and the radius (a) of the stud as σ ∼ (E/a)^1/2 (soft adhesion). However, when the film is very thin, the pull-off stress is significantly higher than the case with thick films, and its value depends on the elastic modulus and the thickness (h) of the film as σ ∼ (E/h)^1/2 (hard adhesion). Here, we study the pull-off behavior of a soft cylindrical stud, one flat end of which is coated with a high modulus thin baseplate. As the flexural rigidity of this baseplate is varied, we observe the transition between the two types of adhesion. We present a simple physical interpretation of the problem, which could be of value in understanding various biofouling and adhesive situations.     

A composite numerical scheme for the numerical simulation of coupled Burgers’ equation

In this work, a composite numerical scheme based on finite difference and Haar wavelets is proposed to solve time dependent coupled Burgers’ equation with appropriate initial and boundary conditions. Time derivative is discretized by forward difference and then quasilinearization technique is used to linearize the coupled Burgers’ equation. Space derivatives discretization with Haar wavelets leads to a system of linear equations and is solved using Matlab7.0. Convergence analysis of proposed scheme exhibits that the error bound is inversely proportional to the resolution level of the Haar wavelet. Finally, the adaptability of proposed scheme is demonstrated by numerical experiments and shows that the present composite scheme offers better accuracy in comparison with other existing numerical methods.     

Sustainable conducting polymer composites: study of mechanical and tribological properties of natural fiber reinforced PVA composites with carbon nanofillers

ABSTRACT

Ball milled jute fiber (JF) was added to Polyvinyl Alcohol (PVA)/20 wt.% multi-layer graphene (MLG) composites in various proportions (0, 5, 10, 15 and 20 wt.%) to prepare sustainable and biodegradable conducting polymer composites. Also, PVA/17.5wt.%MLG/2.5wt.%MWCNT/20wt.% JF composite was prepared for comparison purpose. A dynamic mechanical analysis of the composites was conducted to analyze their viscoelastic nature. The electrical conductivity of the composites was measured to study their suitability for various applications. Jute reinforcement increased the electrical conductivity of PVA/MLG nanocomposites. The PVA/20wt.%JF/17.5wt.%MLG/2.5wt.%MWCNT hybrid composite had the highest electrical conductivity of 3.64 × 10^?4 S/cm among all the composites prepared. Multilayered structures of the hybrid composite films were made by hot-pressing, and their effectiveness in electromagnetic interference shielding was tested. The shielding effectiveness of the composites decreased with jute addition. The wear resistance of PVA/MLG/JF composites increased with an increase in the jute content up to an optimum value of 10 wt.%, and then it started deteriorating.     

Miscibility and fracture toughness of thermoplastic polyurethane/poly(vinyl chloride)/nitrile rubber ternary blends with special reference to the blend composition

Ternary blends of thermoplastic polyurethane and a poly(vinyl chloride)/nitrile rubber blend were investigated in this work. The blends, with weight ratios of 100/0, 80/20, 40/60, 60/40, 80/20, and 0/100, were prepared via melt blending. Dynamic mechanical analysis showed that the blends with ratios of 20/80 and 80/20 were miscible, whereas the 40/60 and 60/40 blends were partially miscible. IR spectroscopy studies showed shifts in the peaks due to specific interactions in the blends. The blends showed degradation behavior between the blend components. The fracture toughness was investigated with the J‐integral by the locus method; the components and the miscible blends had good fracture toughness, whereas the other blends had lower toughness. Similar behavior was observed for the tensile properties. Scanning electron microscopy studies showed the morphological variations in the blends. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1763–1770, 2005     

Peel Adhesion of Poly(Vinyl Chloride) to Nitrile Rubbers

In addition to molecular interaction and physical entanglement of the molecular chains across the interface in poly (vinyl chloride)-nitrile rubber joints, at high temperatures and long contact times interfacial chemical bonds may be formed which seem to couple the two adherends thereby resulting in cohesive failure of the rubber matrix on peeling. This is verified by performing the peel tests at high temperatures, low peel rates and under swollen conditions. Infrared spectroscopic studies of the PVC/NBR blend reveal the formation of chemical bonds at the contact temperatures studied. The peel fracture energy is found to depend on the acrylonitrile content and presence of carboxylic content in the NBR, and the presence of stabilizer and plasticizer in the PVC phase, in addition to the molding and testing conditions.     

Cure characteristics,morphology, and mechanical properties of ethylene–propylene–diene–monomer rubber/acrylonitrile butadiene rubber blends

Blends based on ethylene–propylene–diene monomer rubber (EPDM) and acrylonitrile butadiene rubber (NBR) was prepared. Sulfur was used as the vulcanizing agent. The effects of blend ratio on the cure characteristics and mechanical properties, such as stress–strain behavior, tensile strength, elongation at break, hardness, rebound resilience, and abrasion resistance have been investigated. Tensile and tear strength showed synergism for the blend containing 30% of NBR, which has been explained in terms of morphology of the blends attested by scanning electron micrographs. A relatively cocontinuous morphology was observed for 70 : 30, EPDM/NBR blend system. The experimental results have been compared with the relevant theoretical models. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Aspects of the Softness and Hardness Concepts of Density-Functional Theory

In the density-functional theory of the ground state of an electronic system there arise the concepts of softness, hardness, local softness, and local hardness. Definitions of these quantities are reviewed, and then local softness and local hardness are discussed in some detail. The local softness of a species, the derivative , is a measure of the chemical reactivity of a site in the molecule. From it can be obtained the total global absolute softness in the sense of Pearson and a normalized chemical reactivity index of frontier type. Several formulas for s( r ) are obtained, including new fluctuation formulas, and its determinative role in chemisorption, catalysis, and frontier-controlled charge-transfer processes is briefly discussed. Local hardness is a corresponding appropriately defined functional derivative η(r) = [δμ/δp(r)]_v(r). Difficulties associated with ambiguities in this definition are discussed and resolved. It is concluded that for most purposes the best working formula for local hardness is , where η(r, r′) is the hardness kernel; , where F[p] is the usual Hohenberg-Kohn functional and f(r) is the Fukui function. With this definition, η(r) = η, a constant which is the global hardness. Just as the chemical potential equalizes in the ground state, so does the hardness. It is demonstrated that hardness can be taken to be an average of orbital contributions.     

Enhancing diamond drilling performance by the addition of non-ionic polymer to the flushing media

Drilling is a most important and crucial operation in the excavation industries.With the objective of looking into the enhancement of diamond drilling performance detailed laboratory investigations were carried out on phosphate rock.The effect of Poly (Ethylene Oxide) (PEO) added to the drilling water was studied by varying machine parameters and PEO concentration.The responses were rate of penetration and torque at the bit rock interface.Slake durability tests were also performed to understand the slaking behavior of phosphate rock in PEO solutions.