Learning nonlinear dynamics with behavior ordinary/partial/system of the differential equations: looking through the lens of orthogonal neural networks

In this paper, size-dependent dynamic stability of axially loaded functionally graded (FG) composite truncated conical microshells with magnetostrictive facesheets surrounded by nonlinear viscoelastic foundations including a two-parameter Winkler–Pasternak medium augmented via a Kelvin–Voigt viscoelastic approach is analyzed considering nonlinear cubic stiffness. To this purpose, von Karman-type kinematic nonlinearity along with modified couple stress theory of elasticity was applied to third-order shear deformation conical shell theory in the presence of magnetic permeability tensor and magnetic fluxes. The numerical technique of generalized differential quadrature (GDQ) was used for the solution of microstructural-dependent dynamic stability responses of FG composite truncated conical microshells. It was seen that moving from prebuckling to postbuckling domain somehow increased the significance of couple stress type of size dependency on frequency. In addition, within both prebuckling and postbuckling regimes, an increase of material gradient index decreased the importance of couple stress type of size dependency on the frequency of an axially loaded FG composite truncated conical microshell. Furthermore, it was revealed that by applying a positive magnetic field to an axially loaded truncated conical microshell with magnetostrictive facesheets, its frequency at a specific axial load value was increased in prebuckling domain and decreased in postbuckling domain. However, this pattern was reversed by applying a negative magnetic field.

     

An automated composite table algorithm considering zero liquid discharge possibility in water regeneration–recycle network

In this study, a novel Automated Composite Table Algorithm (ACTA) is developed for targeting the water regeneration–recycle network of single contaminant problem. The ACTA is based on Pinch Analysis, but is automated by taking into consideration the possibility of zero liquid discharge (ZLD) for the water network. In the existing literature, the targeting procedure for ZLD network is based on the graphical tool of Limiting Composite Curve (LCC). However, identification of key parameters (i.e. freshwater, wastewater, regenerated water flowrates, along with pre-regeneration concentrations) is very tedious for highly integrated water network system. The magnification around the turning point of LCC is required to identify the correct pinch points and targeting procedure is done iteratively until the reliable network targets can be determined. These limitations are now overcome by the ACTA, which is an improved version of Composite Table Algorithm that is capable of identifying key parameters algebraically for a given post-regeneration concentration. The newly developed ACTA is capable of handling a wide range of problems including ZLD and non-ZLD network, for both fixed load and fixed flowrate problems.     

Effect of oxygen and fluorine plasma surface treatment of silicon-incorporated diamond-like carbon coatings on cellular responses of mouse fibroblasts

The surface chemistry of silicon-incorporated diamond-like carbon (Si-DLC) was tailored utilizing oxygen and fluorine plasma treatments. Successful anchoring of oxygen and fluorine functional groups to the surface of Si-DLC was verified using X-ray photoelectron spectroscopy. The impact of surface modification of Si-DLC on hydrophobicity was correlated with the viability of L929 mouse fibroblasts. The confocal microscopy and viability results indicated that oxygen-treated Si-DLC showed increased cell viability compared to untreated Si-DLC and fluorine-treated Si-DLC samples 5 days after seeding. The increased cell viability was correlated with the conversion of the hydrophobic surface of Si-DLC into a hydrophilic surface by oxygen plasma treatment.     

A new numerical learning approach to solve general Falkner–Skan model

A new numerical learning approach namely Rational Gegenbauer Least Squares Support Vector Machines (RG_LS_SVM), is introduced in this paper. RG_LS_SVM method is a combination of collocation method based on rational Gegenbauer functions and LS_SVM method. This method converts a nonlinear high order model on a semi-infinite domain to a set of linear/nonlinear equations with equality constraints which decreases computational costs. Blasius, Falkner–Skan and MHD Falkner–Skan models and the effects of various parameters over them are investigated to satisfy accuracy, validity and efficiency of the proposed method. Both Primal and Dual forms of the problems are considered and the nonlinear models are converted to linear models by applying quasilinearization method to get the better results. Comparing the results of RG_LS_SVM method with available analytical and numerical solutions show that the present methods are efficient and have fast convergence rate and high accuracy.

     

Antifungal behavior of silicon-incorporated diamond-like carbon by tuning surface hydrophobicity with plasma treatment

Silicon-incorporated diamond-like carbon (Si-DLC), an amorphous material containing Si atoms with sp³- and sp²-hybridized carbon, is a promising biomaterial for versatile biomedical applications due to its excellent mechanical properties, chemical inertness, biocompatibility, and antimicrobial capability. However, the antifungal properties of plasma-treated Si-DLC have not been systematically evaluated. In this study, Si-DLC coatings were deposited by chemical vapor deposition and further treated with either oxygen or fluorine plasma to render the surface anchored with different functional groups and hydrophobicity. Surface roughness was probed with atomic force microscopy, whereas bonding character and surface composition were assessed using Raman and X-ray photoelectron spectroscopy. Wettability and surface charge were investigated via water contact angle and zeta potential measurements. Antifungal assessment was performed using a Candida albicans multi-well plate screening technique and crystal violet biomass quantification. The results demonstrate that oxygen plasma–treated Si-DLC exhibited hydrophilic properties, lower negative zeta potential, and significant antifungal behavior. This material can potentially be applied on surfaces for the prevention of reduced nosocomial infections.     

Least squares support vector regression for solving Volterra integral equations

In this paper, a numerical approach is proposed based on least squares support vector regression for solving Volterra integral equations of the first and second kind. The proposed method is based on using a hybrid of support vector regression with an orthogonal kernel and Galerkin and collocation spectral methods. An optimization problem is derived and transformed to solving a system of algebraic equations. The resulting system is discussed in terms of the structure of the involving matrices and the error propagation. Numerical results are presented to show the sparsity of resulting system as well as the efficiency of the method.

     

Application of ozone treatment and pinch technology in cooling water systems design for water and energy conservation

Re‐circulating cooling water systems offer the means to remove heat from a wide variety of industrial processes that generate excess heat. Such systems consist of a cooling tower and a heat‐exchanger network that conventionally has a parallel configuration. However, reuse of water between different cooling duties allows cooling water networks to be designed in a series arrangement. This results in performance improvement and increased cooling tower capacity. In addition, by the integration of ozone treatment into the cooling tower, the cycle of concentration can be increased. The ozone treatment also dramatically reduces the blow‐down that, in turn, is environmentally constructive. In this study, a new environmental‐friendly and cost‐effective design methodology for cooling water systems was introduced. Using this design methodology, Integrated Ozone Treatment Cooling System (IOTCS), achievement of minimum environmental impacts and total cost were afforded through a simultaneous integration of the cooling system components using an ozone treatment cooling tower and optimum heat‐exchanger network configuration. Moreover, in the proposed method, the cooling tower optimum design was achieved through a mathematical model. The IOTCS design method is based upon a complex design approach using a combined pinch analysis and mathematical programming that provides an optimum heat‐exchanger configuration while maximizing water and energy conservation and minimizing total cost. Related coding in MATLAB version 7.3 was used for the illustrative example to obtain optimal values in the IOTCS design method computations. The results of the recently introduced design methodology were compared with the conventional method. Copyright © 2009 John Wiley & Sons, Ltd.     

Collocation method to solve inequality-constrained optimal control problems of arbitrary order

In this paper, the generalized fractional order of the Chebyshev functions (GFCFs) based on the classical Chebyshev polynomials of the first kind is used to obtain the solution of optimal control problems governed by inequality constraints. For this purpose positive slack functions are added to inequality conditions and then the operational matrix for the fractional derivative in the Caputo sense, reduces the problems to those of solving a system of algebraic equations. It is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach one. The applicability and validity of the method are shown by numerical results of some examples, moreover a comparison with the existing results shows the preference of this method.

     

An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation (HFC) method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.     

Targeting water utilities for the threshold problem without waste discharge

Increasing water scarcity and stringent environmental regulation have necessitated effective water conservation policies. Pinch analysis has been proved as one of the powerful tools to locate targets of waste water minimization. Two earlier water pinch targeting methods known as Water Cascade Analysis and Material Recovery Pinch Diagram have focused on the “threshold problems”. However, these methodologies have not systematically analyzed the introduction of external utility. In this work, three scenarios are proposed for this reason. The “Infeasible Threshold Problem” is addressed prior to employing external utility through the proposed scenarios. By systematically analyzing this specific problem, it is revealed that existing Water Cascade Analysis method cannot locate correct infeasible targets. Some adjustments are proposed to deal with this drawback. Moreover, to illustrate the applicability of proposed scenarios, Water Cascade Analysis and Material Recovery Pinch Diagram approaches are utilized for addressing a literature problem as a case study. It is shown that harvesting the impure fresh water source with a higher quality, in the “threshold problem with zero discharge”, leads to more pure fresh water saving.