editorial mathematical problems in packaging...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013, Article ID 691201, 2 pageshttp://dx.doi.org/10.1155/2013/691201

EditorialMathematical Problems in Packaging Engineering

Jun Wang,1 Changfeng Ge,2 Dong Sun Lee,3 Michael A. Sek,4 and Vanee Chonhenchob5

1 Jiangsu Province Key Laboratory of Advanced Food Manufacturing Equipment and Technology (Jiangnan University),Department of Packaging Engineering of Jiangnan University, Wuxi 214122, China

2Manufacturing & Mechanical Engineering Technology/Packaging Science of Rochester Institute of Technology,Rochester, NY 14623-5603, USA

3Department of Food Science and Biotechnology, Kyungnam University, Changwon 631-701, Republic of Korea4 School of Engineering and Science, Victoria University (VU), Melbourne, VIC 8001, Australia5 Department of Packaging and Materials Technology, Faculty of Agro-Industry, Kasetsart University, Bangkok 10900, Thailand

Correspondence should be addressed to Jun Wang; wangj [email protected]

Received 19 November 2013; Accepted 19 November 2013

Copyright © 2013 Jun Wang et al.This is an open access article distributed under theCreativeCommonsAttribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Modern packaging plays an important role in modern indus-try. There are more than 60,000 scientists conductingresearch related to packaging engineering. In the last fewdecades, the packaging materials and packaging logisticshave been rapidly developed that brought new challengesto mathematic modeling and simulation. This special issueaims at gathering the research and development of math-ematical modeling and computation methods which havebeen applied into packaging engineering. Papers submittedto this special issue represent the most recent application ofmathematical methods and models in the field of packagingresearch. Potential topics in this issue include, but are notlimited to (1) novel mathematical modeling of packagingsystem, (2) asymptotic methods for coupled nonlinear dif-ferential equations/partial differential equations arising inpackaging system, (3) fractional differential equations withapplications in packaging system, (4) mathematical mod-eling of the mass, heat transfer phenomenon for prod-uct/packaging/human/environment interaction, (5) differ-ential geometry with applications in packaging machineryand atomization, and (6) mathematical problems in smartpackaging, active packaging, and newly developed foodpackaging technology.

We have solicited submissions to this special issue frompackaging engineers, food engineers, mathematicians, andcomputer scientists. After a rigorous peer review process, 20papers have been selected that provide the audience with

overviews, solutions, and new concept for the complex pack-aging systems through mathematic methods. These papershave covered both the theoretical and practical aspects ofcomplex packaging systems in the broad areas of dynamicalsystems, mathematics, and engineering.

Seven papers are from the research community of pack-aging dynamics including “Application of experimental modalanalysis to determine damping properties for stacked corru-gated boxes,” “Drop impact analysis of cushioning system withan elastic critical component of cantilever beam type,” “Applica-tion of homotopy perturbation method with an auxiliary termfor nonlinear dropping equations arisen in polymer packagingsystem,” “Study of the nonlinear dropping shock response ofexpanded foam packaging system,” “Inner-Resonance condi-tions for honeycomb paperboard cushioning packaging sys-tem with critical component,” “Resonance analysis for tiltedsupport spring coupled nonlinear packaging system applyingvariational iteration method,” and “A mathematical modelingof resonances of the nonlinear tilted support spring systemunder harmonic excitation.” In C. Ge and S. Sutherland’swork “Application of experimental modal analysis to deter-mine damping properties for stacked corrugated boxes,” thedamping properties for stacked corrugated containers, whichare crucial for protective packaging design, are predictedaccurately by the ExperimentalModal Analysismethod. InD.Gao et al.’s work “Drop Impact analysis of cushioning Systemwith an elastic critical component of cantilever beam type,” the

2 Mathematical Problems in Engineering

packaged product is modeled by a cushioning system withan elastic critical component of cantilever beam type; thenthe dropping shock response of the system is studied. Themain influencing parameters on the system’s response areanalyzed in details. The results obtained in this paper matchwell with the actual packaging systemwhile other researchersfocus more on the so-called inner-resonance conditions fordifferent kinds of packaging system, as discussed thoroughlyin “Application of homotopy perturbation method with anauxiliary term for nonlinear dropping equations arisen inpolymer packaging system,” “Study of the nonlinear droppingshock response of expanded foam packaging system,” “Inner-Resonance conditions for honeycomb paperboard cushioningpackaging system with critical component,” “Resonance analy-sis for tilted support spring coupled nonlinear packaging systemapplying variational iteration method,” and “A mathematicalmodeling of resonances of the nonlinear tilted support springsystem under harmonic excitation.”

Food packaging plays a key role in food preservation andsafety, and over 45,000 researchers are engaged in some ofthe newer high-tech issues such as the modified atmospherepackaging, intelligent food packaging, and active packagingas well as more established novel packaging technologies.In this special issue, 7 papers from food packaging researchcommunity have been selected after a rigorous peer reviewprocess. The topics include simulation models for modifiedatmosphere packaging: “Applicability of simplified simulationmodels for perforation-mediated modified atmosphere packag-ing of fresh produce,” “A kinetic model for predicting the relativehumidity inmodified atmosphere packaging and its applicationin Lentinula edodes packages,” and “On respiratory rate ofcherry tomatoes under subcritical heights”; time temperatureintegrator (TTI) for intelligent food packaging: “Mathemati-cal evaluation of prediction accuracy for food quality by timetemperature integrator of intelligent food packaging throughvirtual experiments”; and models for mass/heat transferphenomena in food packaging system: “Study the migrationprocess of chemical substances through the packaging/foodinterface during microwave treatment,” “Release mathematicalmodel of active agent from packaging material into food,” and“Insulating packaging solution based on cylinder model.”

Three papers from the research community of packagingmaterials provide us with a new insight into the recentprogress in packaging materials research. In Z. Z. Sun etal.’s work “The viscoelasticity model of corn straw under thedifferent moisture contents,” the viscoelasticity model of cornstraw under the different moisture contents is suggested andcompared with the experiment, showing perfect agreement.In J.-W. Zhou et al.’s work “Application of digital imagecorrelation to measurement of packaging material mechanicalproperties,” a novel method, namely, the Digital Image Cor-relation method, is proposed to measure the mechanicalproperties of packaging material. While in J. Yu’s research“Analysis on Nonlinear stress-growth data for shear flow ofstarch material with shear process,” the shear flow of starchmaterial under shear process is modeled.

S. Liu et al. reported their recent research results inpackaging machinery. In Liu’s work “A Decoupling control

algorithm for unwinding tension system based on active dis-turbance rejection control,” a new control methodology basedon active disturbance rejection control (ADRC) for designingthe tension decoupling controller of the unwinding systemin a gravure printing machine is proposed. The dynamiccoupling can be actively estimated and compensated in realtime, which makes feedback control an ideal approach todesigning the decoupling controller of the unwinding system.While in “Knowledge-based approach to assembly sequenceplanning for wind-driven generator,” M. Wu et al. proposethe assembly connection graph (ACG) including engineeringassembly semantics, which provides an appropriate wayto express both geometric information and nongeometricknowledge.

In “Utilizing an adaptive grey model for short-term timeseries forecasting: a case study of wafer-level packaging,” C.-J.Chang et al. present a new adaptive model based on grey sys-tem theory to solve the small dataset forecasting problem forwafer-level packaging process.The experimental results showthat the AGM (1,1) model can obtain satisfactory outcomes.

Acknowledgments

We would like to thank our colleagues in the packagingcommunity for the support and overwhelming response tothe call of the paper. Finally, wewould like to acknowledge thefinancial support of the National Natural Science Foundationof China (Grant no. 51205167), Research Fund of YoungScholars for the Doctoral Program of Higher Educationof China (Grant no. 20120093120014), and FundamentalResearch Funds for the Central Universities (Grant no.JUSRP51302A) for their support for some invited submis-sions.

Jun WangChangfeng GeDong Sun LeeMichael A. Sek

Vanee Chonhenchob

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