Accurate modeling of many dynamic systems leads to a set of Fractional Differential Equations (FDEs). This paper presents a general formulation and a solution scheme for a class of Fractional Optimal ...Control Problems (FOCPs) for those systems. The fractional derivative is described in the Riemann–Liouville sense. The performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of FDEs. The Calculus of Variations, the Lagrange multiplier, and the formula for fractional integration by parts are used to obtain Euler–Lagrange equations for the FOCP. The formulation presented and the resulting equations are very similar to those that appear in the classical optimal control theory. Thus, the present formulation essentially extends the classical control theory to fractional dynamic system. The formulation is used to derive the control equations for a quadratic linear fractional control problem. An approach similar to a variational virtual work coupled with the Lagrange multiplier technique is presented to find the approximate numerical solution of the resulting equations. Numerical solutions for two fractional systems, a time-invariant and a time-varying, are presented to demonstrate the feasibility of the method. It is shown that (1) the solutions converge as the number of approximating terms increase, and (2) the solutions approach to classical solutions as the order of the fractional derivatives approach to 1. The formulation presented is simple and can be extended to other FOCPs. It is hoped that the simplicity of this formulation will initiate a new interest in the area of optimal control of fractional systems.
In the present study, SiC-Al ball milled powder reinforcement composite for AA6061 parent metal was synthesized by the gravity die casting process. Investigation for the impact of reinforcement ...addition was conducted according to the metallurgical and microstructural properties. In the process, refined SiC + Al powder mixture was added in AA-6061 slurry by stirring action and mixed liquid slurry was poured inside the cavity of the gravity die casting mold. Solidification of the melt was allowed under room temperature and conventional cooling took place inside the mold cavity. Solidified cast composites were investigated according to the impact, hardness and density with microstructural characteristics for 2% and 4% by wt. of SiC with respect to a combination of Al powder and AA6061 alloy. Investigation reveals that properties of cast composite are improved according to the reinforcement addition for SiC. Cast microstructure, EDX and XRD of the composite shows the formation of interfaces of Al + SiC near the cavities and spaces available at various location which is a key candidate for improvement in properties.
Additive manufacturing technology and its benefits have a significant impact on different industrial applications. The 3D printing technologies help manufacture lightweight intricate geometrical ...designs with enhanced strengths. The present study investigates the blended effects of previously recommended parameters of different infill patterns (line, triangle, and concentric) and infill densities (75, 80, and 85%) with varying thicknesses of layers (100, 200, and 300 μm). The test samples were created through Fused Filament Fabrication (FFF) technology using Acrylonitrile Butadiene Styrene (ABS) 3D printing. Mechanical properties were evaluated through tensile and impact strength tests conducted in accordance with ASTM standards. The experimental investigation reveals that the infill pattern greatly affected both tensile and impact strength. The best results were obtained with a concentric infill pattern, along with 80% infill density and 100 μm layer thickness. These conditions resulted in 123% and 115% higher tensile strength and 168% and 80% higher impact strength compared to line and triangle patterns, respectively.
There are 4 general approaches for imparting or improving thermal stability of explosives ‘Salt Formation’, ‘Introduction of Amino Group/s’, ‘Introduction of Conjugation’ & ‘Condensation with ...Triazole Ring/s’ as proposed by Agrawal which were supported by some typical examples. We have recently reported a large number of explosives which validate ‘Salt Formation’ & ‘Introduction of Amino Group/s’ approaches. In this review paper, we report additional examples of explosives scattered over in the literature to validate the ‘Introduction of Conjugation’ & ‘Condensation with Triazole Ring/s’ approaches for imparting/improving thermal stability of explosives. Wherever, data on thermal stability is not available in the literature, the same has been calculated using Energetic Materials Designing Bench (EMDB), Version 1.0. The data generated on a large number of explosives clearly brings out validation of ‘Introduction of Conjugation’ & ‘Condensation with Triazole Ring/s’ approaches for imparting/improving thermal stability of explosives. Further, as the number of triazole ring/s increases, thermal stability also increases. In addition, density, impact sensitivity & velocity of detonation data of promising explosives which are also essential from their application point of view, have been reported. This study also reveals that explosives (i) DAHNS (Explosive 3), PATO (Explosive 15), BTATNB (Explosive 17), TTTATNB (Explosive 19), DANTNP (Explosive 31) and TTATNB (Explosive 35) appear to be better substitutes of HNS and (ii) BDATTz (Explosive 36) and BTDAONAB (Explosive 39) appear to be better substitutes of TATB, a benchmark thermally stable explosive at present.
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Purpose
Digital supply chain (DSC) is an agile, customer-driven and productive way to develop different forms of returns for companies and to leverage efficient approaches with emerging techniques ...and data analytics. Though the advantages of digital supply chain management (DSCM) are many, its implementation is quite slow for several reasons. The purpose of this paper is to identify the major barriers which hinder the adoption of DSC and to analyse the interrelationship among them. The barriers of DSC are explored on the basis of existing literature and experts’ opinion.
Design/methodology/approach
This paper uses the interpretive structural modelling (ISM) approach to develop a hierarchical structural model which shows the mutual dependence among the barriers of DSC. Cross-impact matrix multiplication applied to classification analysis was performed to represent these barriers graphically on the basis of their driving power and dependence.
Findings
The research demonstrates that the barriers “no sense of urgency”, “lack of industry specific guidelines”, “lack of digital skills and talent” and “high implementation and running cost” are the most significant barriers to digital transformation of supply chain. This paper also suggests some managerial implications to overcome the barriers which hinder the implementation of digital transformation of supply chain.
Practical implications
This paper assists managers and policymakers to understand the order in which these barriers must be tackled and adopts a roadmap for successful implementation of DSCM and reap its benefits.
Originality/value
This is one of the initial research studies which has analysed the barriers of DSC using ISM approach.
This paper builds upon our recent paper on generalized fractional variational calculus (FVC). Here, we briefly review some of the fractional derivatives (FDs) that we considered in the past to ...develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs) which depend on two functions, and show that many of the one-parameter FDs considered in the past are special cases of the proposed GFDs. We develop several parts of FVC in terms of one parameter GFDs. We point out how many other parts could be developed using the properties of the one-parameter GFDs. Subsequently, we introduce two new two- and three-parameter GFDs. We introduce some of their properties, and discuss how they can be used to develop FVC. In addition, we indicate how these formulations could be used in various fields, and how the generalizations presented here can be further extended.
PurposeOver the years, technology development has rationalized supply chain processes. The demand economy is disrupting every sector causing the supply chain to be more innovative than ever before. ...The digitalization of the supply chain fulfils this demand. Several technologies such as blockchain, big data analytics, 3D printing, Internet of things (IoT), artificial intelligence (AI), augmented reality (AR), etc. have been innovated in recent years, which expedite the digitalization of the supply chain. The paper aims to analyse the applicability of these technological enablers in the digital transformation of the supply chain and to present an interpretive structural modelling (ISM) model, which presents a sequence in which enablers can be implemented in a sequential manner.Design/methodology/approachThis paper employed the ISM approach to propose a various levelled model for the enablers of the digital supply chain. The enablers are also classified graphically based on their driving and dependence powers using matrix multiplication cross-impact applied to classification (MICMAC) analysis.FindingsThe study indicates that the enablers “big data analytics”, “IoT”, “blockchain” and “AI” are the most powerful enablers for the digitalization of the supply chain and actualizing these enablers should be a topmost concern for organizations, which want to exploit new opportunities created by these technologies.Practical implicationsThis study presents a systematic approach to adopt new technologies for performing various supply chain activities and assists the policymakers better organize their assets and execution endeavours towards digitalization of the supply chain.Originality/valueThis is one of the initial research studies, which has analysed the enablers for the digitalization supply chain using the ISM approach.
Purpose: Respiratory-induced tumor motion is a major challenge in lung cancer (LC) radiotherapy. Four-dimensional computed tomography (4D-CT) using a maximum intensity projection (MIP) dataset is a ...commonly used and time-efficient method to generate internal target volume (ITV). This study compared ITV delineation using MIP or tumor delineation on all phases of the respiratory cycle. Materials and Methods: Thirty consecutive patients of LC who underwent 4D-CT from January 2014 to March 2017 were included. ITV delineation was done using MIP (ITVMIP) and all ten phases of the respiratory cycle (ITV10Phases). Both volumes were analyzed using matching index (MI). It is the ratio of the intersection of two volumes to the union of two volumes. A paired sample t-test was used for statistical analysis, and P < 0.05 was considered statistically significant. Results: The mean ± standard deviation volume of ITV10Phases was significantly larger compared to ITVMIP (134 cc ± 39.1 vs. 113 cc ± 124.2, P = 0.000). The mean MI was 0.75 (range 0.57-0.88). The mean volume of ITV10Phases not covered by ITVMIP was 26.33 cc (23.5%) and vice versa was 5.51 cc (6.1%). The mean MI was 0.73 for tumors close to the mediastinum, chest wall, and diaphragm. MI was not different between tumors ≤5 cm and >5 cm. The average time required for delineation was 9 and 96 min, respectively. The center of mass of two ITVs differed by 0.01 cm. Conclusion: ITV using MIP is significantly smaller and may miss a tumor compared to ITV delineation in 10 phases of 4D-CT. However, the time required is significantly less with MIP. Caution should be exercised in tumors proximity to the mediastinum, chest wall, and diaphragm.
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