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International Journal of Biomathematics 2018年第4期11卷 77-93页

作者： H. O. W. Peiris.s. s. N. Perera s. chakraverty s. M. W. Ranwala Department of Mathematics The Open University of Sri Lanka Nawala Nugegoda Sri Lanka Res.arch and Development Centre for Mathematical Modeling Faculty of s.ience University of Colombo 94 Cumaratunga Munidasa Mw Colombo 03 Sri Lanka Department of Mathematics.ational Ins.itute of Technology Rourkela Ronrkela India Department of Plant s.iences University of Colombo94 Cumaratunga Munidasa Mw Colombo 03 Sri Lanka

This.s.udy pres.nts.a novel approach to evaluate the rate of aggregate ris. of Invas.ve Alien Plant s.ecies. Us.ng ris. values.and grade of importance of weights.of ris. factors.which may reflect invas.venes. of plant s.ecies.are cons.dered. We us. Linguis.ic Ordered Weighted Averaging operator to evaluate the grade of important of weights. s.nce the ris. values.and important weights.are identified from two different linguis.ic term s.ts. fuzzy s.t theory techniques.were us.d to combine the two s.ts. The rates.obtained from the model were compared with NRA ris. levels.and the model was.validated with data from known and non-invas.ve s.ecies. The model is.improved by weighting the ris. values.of ris. factors. The improved model produced s.gnificant res.lts.and res.lted a better tracking s.s.em for identifying potential invaders.than the conventional ris. as.es.ment.

关键词： Invas.ve alien plant s.ecies invas.ve attributes fuzzy s.t theory operators linguis.ic ordered weighted averaging operator.

Buckling analys.s.of nanobeams.with exponentially varying s.iffnes. by differential quadrature method

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Chines. Phys.cs.B 2017年第7期26卷 218-227页

作者： s.chakraverty Laxmi Behera Department of Mathematics National Institute of Technology Rourkela

We pres.nt the application of differential quadrature（DQ） method for the buckling analys.s.of nanobeams.with exponentially varying s.iffnes. bas.d on four different beam theories.of Euler-Bernoulli, Timos.enko, Reddy, and *** formulation is.bas.d on the nonlocal elas.icity theory of Eringen. New res.lts.are pres.nted for the guided and s.mply s.pported guided boundary conditions. Numerical res.lts.are obtained to inves.igate the effects.of the nonlocal parameter,length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is.obs.rved that the critical buckling load decreas.s.with increas. in the nonlocal parameter while the critical buckling load parameter increas.s.with increas. in the length-to-height ratio.

关键词： differential quadrature method exponentially varying s.iffnes. different beam theories

Vibration and buckling analys.s.of nanobeams.embedded in an elas.ic medium

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Chines. Phys.cs.B 2015年第9期24卷 489-496页

作者： s.chakraverty Laxmi Behera Department of Mathematics National Institute of Technology Rourkela

Boundary characteris.ic orthogonal polynomials.are us.d as.s.ape functions.in the Rayleigh–Ritz method to inves.igate vibration and buckling of nanobeams.embedded in an elas.ic medium. The pres.nt formulation is.bas.d on the nonlocal Euler–Bernoulli beam theory. The eigen value equation is.developed for the buckling and vibration analys.s. The orthogonal property of thes. polynomials.makes.the computation eas.er with les. computational effort. It is.obs.rved that the frequency and critical buckling load parameters.are dependent on the temperature, elas.ic medium, s.all s.ale coefficient,and length-to-diameter ratio. Thes. obs.rvations.are us.ful in the mechanical des.gn of devices.that us. carbon nanotubes.

关键词： Rayleigh–Ritz method boundary characteris.ic orthogonal polynomials nonlocal elas.icity theory Euler–Bernoulli beam theory

Non-probabilis.ic s.lutions.of imprecis.ly defined fractional-order diffus.on equations

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Chines. Phys.cs.B 2014年第12期23卷 14-20页

作者： s.chakraverty s.ita Tapas.ini Department of Mathematics National Institute of Technology RourkelaOdisha–769 008 India

The fractional diffus.on equation is.one of the mos. important partial differential equations.PDEs. to model problems.in mathematical phys.cs. Thes. PDEs.are more practical when thos. are combined with uncertainties. Accordingly, this.paper inves.igates.the numerical s.lution of a non-probabilis.ic viz. fuzzy fractional-order diffus.on equation s.bjected to various.external forces. A fuzzy diffus.on equation having fractional order 0 〈 α≤ 1 with fuzzy initial condition is.taken into cons.deration. Fuzzines. appearing in the initial conditions.is.modelled through convex normalized triangular and Gaus.ian fuzzy numbers. A new computational technique is.propos.d bas.d on double parametric form of fuzzy numbers.to handle the fuzzy fractional diffus.on equation. Us.ng the s.ngle parametric form of fuzzy numbers. the original fuzzy diffus.on equation is.converted firs. into an interval-bas.d fuzzy differential equation. Next, this.equation is.trans.ormed into cris. form by us.ng the propos.d double parametric form of fuzzy numbers. Finally, the s.me is.s.lved by Adomian decompos.tion method（ADM） s.mbolically to obtain the uncertain bounds.of the s.lution. Computed res.lts.are depicted in terms.of plots. Res.lts.obtained by the propos.d method are compared with the exis.ing res.lts.in s.ecial cas.s.

关键词： double parametric form of fuzzy number fuzzy fractional diffus.on equation ADM

Dynamic Res.ons. and Os.illating Behaviour of Fractionally Damped Beam

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Computer Modeling in Engineering & s.iences 2015年第3期104卷 211-225页

作者： Diptiranjan Behera s.chakraverty Corres.onding Author.s.hool of Mechatronics.Engineering University of Electronic Science and Technology of ChinaNo.2006Xiyuan AvenueWest Hi-Tech ZoneChengduSichuan 611731P.R.China Department of Mathematics National Institute of Technology RourkelaOdisha-769008India

This.paper pres.nts.the numerical s.lution of a vis.oelas.ic continuous.beam whos. damping behaviours.are defined in term of fractional derivatives.of arbitrary *** Perturbation Method(HPM)is.us.d to obtain the dynamic res.ons. with res.ect to unit impuls. *** res.lts.are depicted in term of *** are made with the analytic s.lutions.obtained by Zu-feng and Xiao-yan(2007)to s.ow the effectivenes. and validation of the pres.nt method.

关键词： Vis.oelas.ic beam Fractional derivative Impuls. res.ons. function Homotopy Perturbation Method(HPM)

Numerical s.lution of the imprecis.ly defined invers. heat conduction problem

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Chines. Phys.cs.B 2015年第5期24卷 153-162页

作者： s.ita Tapas.ini s.chakraverty Diptiranjan Behera Department of Mathematics National Institute of Technology Rourkela

This.paper inves.igates.the numerical s.lution of the uncertain invers. heat conduction problem. Uncertainties.pres.nt in the s.s.em parameters.are modelled through triangular convex normalized fuzzy s.ts. In the s.lution proces., double parametric forms.of fuzzy numbers.are us.d with the variational iteration method （VIM）. This.problem firs. computes.the uncertain temperature dis.ribution in the domain. Next, when the uncertain temperature meas.rements.in the domain are known, the functions.des.ribing the uncertain temperature and heat flux on the boundary are recons.ructed. Related example problems.are s.lved us.ng the pres.nt procedure. We have als. compared the pres.nt res.lts.with thos. in [Inf. s.i. （2008） 178 1917] along with homotopy perturbation method （HPM） and [Int. Commun. Heat Mas. Trans.er （2012） 39 30] in the s.ecial cas.s.to demons.rate the validity and applicability.

关键词： triangular fuzzy number double parametric form of fuzzy numbers uncertain invers. heat con-duction variational iteration method (VIM)

s.lving Fully Fuzzy Nonlinear Eigenvalue Problems.of Damped s.ring-Mas. s.ructural s.s.ems.Us.ng Novel Fuzzy-Affine Approach

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Computer Modeling in Engineering & s.iences 2019年第12期121卷 947-980页

作者： s.Rout s.chakraverty Department of Mathematics National Institute of Technology RourkelaOdishaIndia

The dynamic analys.s.of damped s.ructural s.s.em by us.ng finite element method leads.to nonlinear eigenvalue problem(NEP)(particularly,quadratic eigenvalue problem).In general,the parameters.of NEP are cons.dered as.exact *** in actual practice becaus. of different errors.and incomplete information,the parameters.may have uncertain or vague values.and s.ch uncertain values.may be cons.dered in terms.of fuzzy *** article propos.s.an efficient fuzzy-affine approach to s.lve fully fuzzy nonlinear eigenvalue problems.FNEPs.where involved parameters.are fuzzy numbers.*** and *** on the parametric form,fuzzy numbers.have been trans.ormed into family of s.andard *** due to the pres.nce of interval overes.imation problem in s.andard interval arithmetic,affine arithmetic bas.d approach has.been *** the propos.d method,the FNEP has.been linearized into a generalized eigenvalue problem and further s.lved by us.ng the fuzzy-affine *** application problems.of s.ructures.and als. general NEPs.with fuzzy parameters.are inves.igated bas.d on the propos.d ***,fuzzy eigenvalue bounds.are illus.rated with fuzzy plots.with res.ect to its.members.ip *** comparis.ns.are als. demons.rated to s.ow the reliability and efficacy of the pres.nt approach.

关键词： Fuzzy nonlinear eigenvalue problem fuzzy s.t theory affine arithmetic interval overes.imation problem triangular fuzzy number trapezoidal fuzzy number fuzzy-affine approach

Effect of Coriolis.cons.ant on Geophys.cal Korteweg-de Vries.equation

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Journal of Ocean Engineering and s.ience 2019年第2期4卷 113-121页

作者： P.Karunakar s.chakraverty Department of Mathematics National Institute of Technology RourkelaRourkela 769008 OdishaIndia

The pres.nt article inves.igates.the effect of Coriolis.cons.ant on the s.lution of the Geophys.cal Korteweg-de Vries.gKdV)*** s.ch,the Homotopy Perturbation Method(HPM)has.been applied here for s.lving the nonlinear gKdV *** res.lts.are compared with exis.ing res.lts.that are available in the literature and they are found to be in good *** the Coriolis.term has.been cons.dered in terms.of the interval to form interval Geophys.cal Korteweg-de Vries.IgKdV)*** equation has.been s.lved by HPM to analys. the effect of *** this.analys.s.it has.been concluded that the cons.ant of Coriolis.is.directly proportional to wave height and invers.ly proportional to *** pres.nce of the Coriolis.term in gKdV equation has.a remarkable change in the s.ape of the s.lution.

关键词： Geophys.cal Korteweg-de Vries.Equation Coriolis.cons.ant HPM Interval gKdV.

AVAILABILITY MODEL FOR s.LF TEs. AND REPAIR IN FAULT TOLERANT FPGA-BAs.D s.s.EMs

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Journal of Electronics.China) 2014年第4期31卷 271-283页

作者： s.ampa chakraverty Anubhav Agarwal Broteen Kundu Anil Kumar Divis.on of Computer Engineering Netaji Subhas Institute of Technology

Dynamically reconfigurable Field Programmable Gate Array(dr-FPGA) bas.d electronic s.s.ems.on board mis.ion-critical s.s.ems.are highly s.s.eptible to radiation induced hazards.that may lead to faults.in the logic or in the configuration memory. The aim of our res.arch is.to characterize s.lf-tes. and repair proces.es.in Fault Tolerant(FT) dr-FPGA s.s.ems.in the pres.nce of environmental faults.and explore their interrelations.ips. We develop a Continuous.Time Markov Chain(CTMC) model that captures.the high level fail-repair proces.es.on a dr-FPGA with periodic online Built-In s.lf-Tes.(BIs.) and s.rubbing to detect and repair faults.with minimum latency. s.mulation res.lts.reveal that given an average fault interval of 36 s. an optimum s.lf-tes. interval of 48.3 s.drives.the s.s.em to s.end 13% of its.time in s.lf-tes.s. remain in s.fe working s.ates.for 76% of its.time and face ris.y fault-prone s.ates.for only 7% of its.time. Further, we demons.rate that a well-tuned repair s.rategy boos.s.overall s.s.em availability, minimizes.the occurrence of uns.fe s.ates. and accommodates.a larger range of fault rates.within which the s.s.em availability remains.s.able within 10% of its.maximum level.

关键词： Dynamically reconfigurable Field Programmable Gate Array (dr-FPGA) Built-In s.lf-Tes. (BIs.) Fault Tolerance (FT) s.ngle Event Effects.(s.Es. Continuous.Time Markov Chain (CTMC) s.rubbingCLC number:TN47