Skip to main content
SpringerLink
Log in

Fractional-Order Model of Wine

  • Chapter
  • First Online:
Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Electrical impedance spectroscopy is used for characterizing several types of wine and the experimental results are compared with those of chemical analysis. The electrical impedance of wine is measured and modeled by means of fractional transfer functions. The model is compared with standard chemical analysis, showing strong correlation between the two distinct descriptions. Hierarchical clustering is adopted for analyzing and visualizing the relationships embedded in the data. The results demonstrate that fractional models describe wine adequately with a reduced number of parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.00
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Åberg, P., Birgersson, U., Elsner, P., Mohr, P., Ollmar, S.: Electrical impedance spectroscopy and the diagnostic accuracy for malignant melanoma. Exp. Dermatol. 20(8), 648–652 (2011)

    Article  Google Scholar 

  2. Adachi, M., Sakamoto, M., Jiu, J., Ogata, Y., Isoda, S.: Determination of parameters of electron transport in dye-sensitized solar cells using electrochemical impedance spectroscopy. J. Phys. Chem. B 110(28), 13872–13880 (2006)

    Article  Google Scholar 

  3. Ando, Y., Maeda, Y., Mizutani, K., Wakatsuki, N., Hagiwara, S., Nabetani, H.: Effect of air-dehydration pretreatment before freezing on the electrical impedance characteristics and texture of carrots. J. Food Eng. 169, 114–121 (2016)

    Article  Google Scholar 

  4. Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus: Models and Numerical Methods, vol. 3. World Scientific (2012)

    Google Scholar 

  5. Cole, K.S., Cole, R.H.: Dispersion and absorption in dielectrics I. Alternating current characteristics. J. Chem. Phys. 9(4), 341–351 (1941)

    Article  ADS  Google Scholar 

  6. Davidson, D., Cole, R.: Dielectric relaxation in glycerol, propylene glycol, and \(n\)-propanol. J. Chem. Phys. 19(12), 1484–1490 (1951)

    Article  ADS  Google Scholar 

  7. Debye, P.: Interferenz von Röntgenstrahlen und Wärmebewegung. Annalen der Physik 348(1), 49–92 (1913)

    Article  ADS  Google Scholar 

  8. Debye, P.J.W.: Polar Molecules. Chemical Catalog Company, Incorporated (1929)

    Google Scholar 

  9. Diethelm, K., Ford, N.J.: Analysis of fractional differential equations. J. Math. Anal. Appl. 265(2), 229–248 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. El Khaled, D., Castellano, N., Gazquez, J., Salvador, R.G., Manzano-Agugliaro, F.: Cleaner quality control system using bioimpedance methods: a review for fruits and vegetables. J. Cleaner Prod. (2015)

    Google Scholar 

  11. Emmert, S., Wolf, M., Gulich, R., Krohns, S., Kastner, S., Lunkenheimer, P., Loidl, A.: Electrode polarization effects in broadband dielectric spectroscopy. Eur. Phys. J. B 83(2), 157–165 (2011)

    Article  ADS  Google Scholar 

  12. Eremenko, Z., Skresanov, V., Shubnyi, A., Anikina, N., Gerzhikova, V., Zhilyakova, T.: Complex permittivity measurement of high loss liquids and its application to wine analysis. In: Electromagnetic Waves. InTech (2011)

    Google Scholar 

  13. Feldman, Y., Puzenko, A., Ryabov, Y.: Non-Debye dielectric relaxation in complex materials. Chem. Phys. 284(1), 139–168 (2002)

    Article  ADS  Google Scholar 

  14. Fraga, H., Malheiro, A., Moutinho-Pereira, J., Jones, G., Alves, F., Pinto, J.G., Santos, J.: Very high resolution bioclimatic zoning of Portuguese wine regions: present and future scenarios. Reg. Environ. Change 14(1), 295–306 (2014)

    Article  Google Scholar 

  15. Freeborn, T.J.: A survey of fractional-order circuit models for biology and biomedicine. IEEE J. Emerg. Sel. Top. Circ. Syst. 3(3), 416–424 (2013)

    Article  Google Scholar 

  16. Freeborn, T.J., Elwakil, A.S., Maundy, B.: Compact wide frequency range fractional-order models of human body impedance against contact currents. Math. Prob. Eng. 2016 (2016)

    Google Scholar 

  17. Fröhlich, H.: Theory of Dielectrics: Dielectric Constant and Dielectric Loss. Clarendon Press (1958)

    Google Scholar 

  18. Garra, R., Giusti, A., Mainardi, F., Pagnini, G.: Fractional relaxation with time-varying coefficient. Fract. Calc. Appl. Anal. 17(2), 424–439 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ghasemi, S., Darestani, M.T., Abdollahi, Z., Gomes, V.G.: Online monitoring of emulsion polymerization using electrical impedance spectroscopy. Polym. Int. 64(1), 66–75 (2015)

    Article  Google Scholar 

  20. Glatthaar, M., Riede, M., Keegan, N., Sylvester-Hvid, K., Zimmermann, B., Niggemann, M., Hinsch, A., Gombert, A.: Efficiency limiting factors of organic bulk heterojunction solar cells identified by electrical impedance spectroscopy. Solar Energy Mater. Solar Cells 91(5), 390–393 (2007)

    Article  Google Scholar 

  21. Groeber, F., Engelhardt, L., Egger, S., Werthmann, H., Monaghan, M., Walles, H., Hansmann, J.: Impedance spectroscopy for the non-destructive evaluation of in vitro epidermal models. Pharm. Res. 32(5), 1845–1854 (2015)

    Article  Google Scholar 

  22. Hartigan, J.A.: Clustering Algorithms. Wiley (1975)

    Google Scholar 

  23. Havriliak, S., Negami, S.: A complex plane analysis of \(\alpha \)-dispersions in some polymer systems. J. Polym. Sci. Part C: Polym. Symp. 14, 99–117 (1966). Wiley Online Library

    Google Scholar 

  24. Hilfer, R.: Analytical representations for relaxation functions of glasses. J. Non-Cryst. Solids 305(1), 122–126 (2002)

    Article  ADS  Google Scholar 

  25. International Organisation of Vine and Wine: Compendium of International Methods of Wines and Musts Analysis, vol. 1. International Organisation of Vine and Wine, Paris (2016)

    Google Scholar 

  26. Irvine, J.T., Sinclair, D.C., West, A.R.: Electroceramics: characterization by impedance spectroscopy. Adv. Mater. 2(3), 132–138 (1990)

    Article  Google Scholar 

  27. Jesus, I.S., Machado, J.T., Cunha, J.B.: Fractional electrical impedances in botanical elements. J. Vib. Control 14(9–10), 1389–1402 (2008)

    Article  MATH  Google Scholar 

  28. Jonscher, A.: Low-frequency dispersion in carrier-dominated dielectrics. Philos. Mag. B 38(6), 587–601 (1978)

    Article  ADS  Google Scholar 

  29. Jonscher, A.: Dielectric Relaxation in Solids. Chelsea Dielectrics Press, London (1983)

    Google Scholar 

  30. Jonscher, A.K.: The ‘universal’ dielectric response. Nature 267(5613), 673–679 (1977)

    Article  ADS  Google Scholar 

  31. Kern, R., Sastrawan, R., Ferber, J., Stangl, R., Luther, J.: Modeling and interpretation of electrical impedance spectra of dye solar cells operated under open-circuit conditions. Electrochim. Acta 47(26), 4213–4225 (2002)

    Article  Google Scholar 

  32. Kerner, T.E., Paulsen, K.D., Hartov, A., Soho, S.K., Poplack, S.P.: Electrical impedance spectroscopy of the breast: clinical imaging results in 26 subjects. IEEE Trans. Med. Imaging 21(6), 638–645 (2002)

    Article  Google Scholar 

  33. Kertész, Á., Hlaváčová, Z., Vozáry, E., Staroňová, L.: Relationship between moisture content and electrical impedance of carrot slices during drying. Int. Agrophys. 29(1), 61–66 (2015)

    Article  Google Scholar 

  34. Kiryakova, V.S.: Generalized Fractional Calculus and Applications. Longman Scientific & Technical, Harlow (1994)

    MATH  Google Scholar 

  35. Kuang, W., Nelson, S.: Dielectric relaxation characteristics of fresh fruits and vegetables from 3 to 20 GHz. J. Microw. Power Electromagn. Energy 32(2), 115–123 (1997)

    Article  Google Scholar 

  36. Laufer, S., Ivorra, A., Reuter, V.E., Rubinsky, B., Solomon, S.B.: Electrical impedance characterization of normal and cancerous human hepatic tissue. Physiol. Meas. 31(7), 995 (2010)

    Article  Google Scholar 

  37. Lopes, A.M., Machado, J.T.: Analysis of temperature time-series: embedding dynamics into the MDS method. Commun. Nonlinear Sci. Numer. Simul. 19(4), 851–871 (2014)

    Article  ADS  Google Scholar 

  38. Lopes, A.M., Machado, J.T.: Fractional order models of leaves. J. Vib. Control 20(7), 998–1008 (2014)

    Article  MathSciNet  Google Scholar 

  39. Lopes, A.M., Machado, J.T.: Modeling vegetable fractals by means of fractional-order equations. J. Vib. Control 22(8), 2100–2108 (2016)

    Article  Google Scholar 

  40. Lopes, A.M., Machado, J.T., Ramalho, E.: On the fractional-order modeling of wine. European Food Research and Technology, pp. 1–9 (2016)

    Google Scholar 

  41. Machado, J., Lopes, A., Duarte, F., Ortigueira, M., Rato, R.: Rhapsody in fractional. Fract. Calc. Appl. Anal. 17(4), 1188–1214 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  42. Machado, J., Mata, M.E., Lopes, A.M.: Fractional state space analysis of economic systems. Entropy 17(8), 5402–5421 (2015)

    Article  ADS  Google Scholar 

  43. Machado, J.A.T., Lopes, A.M.: Analysis and visualization of seismic data using mutual information. Entropy 15(9), 3892–3909 (2013)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  44. Machado, J.T.: Matrix fractional systems. Commun. Nonlinear Sci. Numer. Simul. 25(1), 10–18 (2015)

    Article  ADS  Google Scholar 

  45. Magin, R.L.: Fractional Calculus in Bioengineering. Begell House Redding (2006)

    Google Scholar 

  46. Maundy, B., Elwakil, A., Allagui, A.: Extracting the parameters of the single-dispersion Cole bioimpedance model using a magnitude-only method. Comput. Electron. Agric. 119, 153–157 (2015)

    Article  Google Scholar 

  47. Nigmatullin, R., Nelson, S.: Recognition of the “fractional” kinetics in complex systems: dielectric properties of fresh fruits and vegetables from 0.01 to 1.8 GHz. Signal Process. 86(10), 2744–2759 (2006)

    Article  MATH  Google Scholar 

  48. Nigmatullin, R., Ryabov, Y.E.: Cole-Davidson dielectric relaxation as a self-similar relaxation process. Phys. Solid State 39(1), 87–90 (1997)

    Article  ADS  Google Scholar 

  49. Novikov, V., Wojciechowski, K., Komkova, O., Thiel, T.: Anomalous relaxation in dielectrics. Equations with fractional derivatives. Mater. Sci.-Pol. 23(4), 977 (2005)

    Google Scholar 

  50. de Oliveira, E.C., Mainardi, F., Vaz Jr., J.: Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics. Eur. Phys. J. Spec. Top. 193(1), 161–171 (2011)

    Article  Google Scholar 

  51. Riul, A., de Sousa, H.C., Malmegrim, R.R., dos Santos, D.S., Carvalho, A.C., Fonseca, F.J., Oliveira, O.N., Mattoso, L.H.: Wine classification by taste sensors made from ultra-thin films and using neural networks. Sens. Actuators B: Chem. 98(1), 77–82 (2004)

    Article  Google Scholar 

  52. Rosa, E.C., de Oliveira, E.C.: Relaxation Equations: Fractional Models. arXiv:1510.01681 (2015)

  53. Sibatov, R.T., Uchaikin, D.V.: Fractional relaxation and wave equations for dielectrics characterized by the Havriliak-Negami response function. arXiv:1008.3972 (2010)

  54. Stanislavsky, A., Weron, K., Trzmiel, J.: Subordination model of anomalous diffusion leading to the two-power-law relaxation responses. EPL (Europhys. Lett.) 91(4), 40,003 (2010)

    Google Scholar 

  55. Tarasov, V.E.: Fractional equations of Curie–von Schweidler and Gauss laws. J. Phys. Condens. Matter 20(14), 145,212 (2008)

    Google Scholar 

  56. Tarasov, V.E.: Universal electromagnetic waves in dielectric. J. Phys. Condens. Matter 20(17), 175,223 (2008)

    Google Scholar 

  57. Tarasov, V.E.: Fractional integro-differential equations for electromagnetic waves in dielectric media. Theoret. Math. Phys. 158(3), 355–359 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  58. Tomkiewicz, D., Piskier, T.: A plant based sensing method for nutrition stress monitoring. Precis. Agric. 13(3), 370–383 (2012)

    Article  Google Scholar 

  59. Vosika, Z., Lazarević, M., Simic-Krstić, J., Koruga, D.: Modeling of bioimpedance for human skin based on fractional distributed-order modified Cole model. FME Trans. 42(1), 74–81 (2014)

    Article  Google Scholar 

  60. Watanabe, K., Taka, Y., Fujiwara, O.: Cole-Cole measurement of dispersion properties for quality evaluation of red wine. Meas. Sci. Rev. 9(5), 113–116 (2009)

    Article  Google Scholar 

  61. Watanabe, T., Orikasa, T., Shono, H., Koide, S., Ando, Y., Shiina, T., Tagawa, A.: The influence of inhibit avoid water defect responses by heat pretreatment on hot air drying rate of spinach. J. Food Eng. 168, 113–118 (2016)

    Article  Google Scholar 

  62. West, A.R., Sinclair, D.C., Hirose, N.: Characterization of electrical materials, especially ferroelectrics, by impedance spectroscopy. J. Electroceram. 1(1), 65–71 (1997)

    Article  Google Scholar 

  63. Zhang, L., Shen, H., Luo, Y.: A nondestructive method for estimating freshness of freshwater fish. Eur. Food Res. Technol. 232(6), 979–984 (2011)

    Article  Google Scholar 

  64. Zhang, M., Repo, T., Willison, J., Sutinen, S.: Electrical impedance analysis in plant tissues: on the biological meaning of Cole-Cole \(\alpha \) in Scots pine needles. Eur. Biophys. J. 24(2), 99–106 (1995)

    Article  Google Scholar 

  65. Zheng, S., Fang, Q., Cosic, I.: An investigation on dielectric properties of major constituents of grape must using electrochemical impedance spectroscopy. Eur. Food Res. Technol. 229(6), 887–897 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, UISPA–LAETA/INEGI, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    António M. Lopes

  2. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    J. A. Tenreiro Machado

  3. Chemical Engineering Department, CIETI/DEQ/ISEP, Centre of Innovation on Engineering and Industrial Technology, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    Elisa Ramalho

Authors
  1. António M. Lopes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. A. Tenreiro Machado
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elisa Ramalho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to António M. Lopes .

Editor information

Editors and Affiliations

  1. Stern College for Women, Yeshiva University, New York, New York, USA

    Mark Edelman

  2. INPE/LAC, Instituto Nacional de Pesquisas Espaciai, São José dos Campos, São Paulo, Brazil

    Elbert E. N. Macau

  3. Departamento de Fisica, Universidad Rey Juan Carlos, Móstoles, Madrid, Spain

    Miguel A. F. Sanjuan

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lopes, A.M., Machado, J.A.T., Ramalho, E. (2018). Fractional-Order Model of Wine. In: Edelman, M., Macau, E., Sanjuan, M. (eds) Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-68109-2_10

Download citation

Publish with us

Policies and ethics

Search

Navigation