Non-Differentiable Dynamics in Complex Systems

Name: Non-Differentiable Dynamics in Complex Systems
SKU: 11127
Availability: InStock

$0.00

Maricel Agcop
Gh. Asachi Technical University, Department of Physics, Iasi, Romania

Lacramioara Ochiuz
“Grigore.T. Popa” University of Medicine and Pharmacy from Iasi, Iasi, Romania

Dan Tesloianu
“Grigore.T. Popa” University of Medicine and Pharmacy from Iasi, Iasi, Romania

Călin Gheorghe Buzea
National Institute of Research and Development for Technical Physics, Iaşi, Romania

Ștefan Andrei Irimiciuc
Faculty of Physics, “Alexandru Ioan Cuza” University of Iasi, Iasi, Romania

Series: Systems Engineering Methods, Developments and Technology
BISAC: TEC009000

The models commonly used to study complex systems are based on the assumption – otherwise unjustified – of the differentiability of the physical quantities that describe it. The success of differentiable models must be understood sequentially, i.e., on domains large enough that differentiability and integrability are valid. But a differential method fails when faced with the physical reality.

In order to describe the physical dynamics of complex systems, but still remain tributary to a differential hypothesis, it is necessary to introduce, in an explicit manner, the resolution scale in the expressions of the physical variables that describe these dynamics and, implicitly, in the fundamental equations of “evolution”. This means that any classically dependent dynamic variable on both spatial coordinates and time becomes, in this new context, dependent also on the resolution scale. In other words, instead of working with a dynamic variable, described through a strictly non-differentiable mathematical function, this book will just work with different approximations of that function, derived through its averaging at different resolution scales. Consequently, any dynamic variable acts as the limit of a function’s family, the function being non-differentiable for a null resolution scale and differentiable for a non-zero resolution scale.

This approach, which is well adapted for applications in the field of complex systems where any real determination is conducted at a finite resolution scale, clearly implies the development both of a new geometric structure and of a physical theory for which the motion laws, invariant to spatial and temporal coordinate transformations, are integrated with scale laws that are invariant at scale transformations. Such a theory that includes the geometric structure based on the above presented assumptions was developed via scale relativity theory, and more recently with an arbitrary constant fractal dimension. Both theories define the “fractal physics models” class (non-differentiable physical models).

The aim of this book is to showcase the far reach of non-differentiable procedures for the analysis of dynamics for a wide range of physical phenomena, starting from the deformable continuous media, fluids dynamics, and cancer growth to drug release mechanisms, approached from a complex system viewpoint.

Binding

Clear

Add to Wishlist

ISBN: N/A Categories: Online Books, Systems Engineering, Systems Engineering Methods, Developments and Technology, Technology and Engineering Tags: 9781536131376, systems engineering

Table of Contents
Publish with Us

Table of Contents

Preface

Chapter 1. Dynamics in Complex Systems by Means of Fractal Information

Chapter 2. Non-differentiability in Complex Fluids Dynamics

Chapter 3. On a Holographic Type Model for the Evolution of Cancerous Diseases

Chapter 4. Phases in Temporal Multiscale Evolution of Drug Release Mechanism from IPN-Type Chitosan Based Hydrogels

References

References

Introduction

[1] H. H. Rotermund, H. H., W. Engel, M. Kordesch, and G. Ertl, Nature 343 355(1990).

[2] P. Foerster, S. C. Müller, and B. Hess, Science 241, 685, (1988).

[3] F. H. Fenton, S. Luther, E. M. Cherry, N. F. Otani, V. Krinsky, A. Pumir, E. Bodensch R. F., Circulation 120 467(2009).

Chapter 1

[1] Ballentine L. E., Quantum mechanics. A Modern Development, World Scientific, Singapore (1998).

[2] Phillips A. C., Introduction to Quantum Mechanics, John Wiley and Sons, New York (2003).

[3] Bohm D., Phys. Rev. 85, 166 (1952).

[4] Holland P. R., The quantum theory of motion, Cambridge Univ. Press (1993).

[5] Nottale L., Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity, World Scientific, Singapore (1993).

[6] Nottale L., Scale Relativity and Fractal Space-Time – A new Approach to Unifying Relativity and Quantum Mechanics, Imperial College Press, London (2011).

[7] Agop M., Nica P. E., Ioannou P. D., Antici A., and Paun V. P., Eur. Phys. J. D 49, 239–248 (2008).

[8] Casian-Botez I., Agop M., J. Comput. Theor. Nanos. 12(2), 263-269 (2015).

[9] Agop M., Nica P. E., Gurlui S., Focsa C., Paun V. P., Colotin M., Eur. Phys. J. D 56, 405-419 (2010).

[10] Agop M., Casian-Botez I., Birlescu V. S. and Popa R. F., J. Comput. Theor. Nanos. 12(4), 682-688 (2015).

[11] Mandelbrot B., The Fractal Geometry of Nature, Freeman, San Francisco (1982).

[12] Lifshitz E. M. and Landau L. D., Fluid mechanics, Pergamon Press, Oxford (1987).

[13] Vasilescu D. D., Corabieru P., Corabieru A., Boicu M., Mihaileanu D. and Agop M., J. Comput. Theor. Nanos. 13(1), 265-269 (2016).

[14] Livio M., The equation that couldn’t be solved: how mathematical genius discovered the language of symmetry, Simon & Schuster, New York (2005).

[15] Mazilu N., Internal Report (in Romanian), I. R. N. E., Pitesti (1982).

[16] Nonozhilov V. V., Foundations of the nonlinear theory of elasticity, Dover Publications, New York (1953).

[17] Keks W., Elasticity and viscoelasticity (in Romanian), Technical Publishing House, Bucharest (1986).

[18] Svoboda K. K., Fischman D. A. and Gordon M. K., Dev. Dynam. 237, 2667-2675 (2008).

[19] Giannoni E., Buricchi F., Grimaldi G., Parri M., Cialdai F., Taddei M. L., Raugei G., Ramponi G. and Chiarurgi P., Cell Death Differ. 15, 867-878 (2008).

[20] Chiarugi P. and E. Giannoni, Biochem. Pharmacol. 76, 1352-1364 (2008).

[21] Framson P. E. and Sage E. H., J. Cell. Biochem. 92, 679-690 (2004).

[22] Pupa S. M., Menard S., Forti S. and Tagliabue E., J. Cell. Physiol. 192, 259-267 (2002).

[23] Hofmann U. B., Houben R., Brocker E. B. and Becker J. C., Biochimie 87, 307-314 (2005).

[24] L. C. von Kempen, Ruiter D. J., G. N. van Muijen and Coussens L. M., Eur. J. Cell Biol. 82, 539-548 (2003).

[25] Lopez-Otin C., Palavalli L. H. and Samuels Y., Cell Cycle 8, 3657-3662 (2009).

[26] Wu Y. and Zhou B. P., Cell Cycle 8, 3267-3273 (2009).

[27] P. Weibel, Ord G. and Rosler O. E., Space Time Physics and Fractility, Springer, New York (2005).

[28] El Naschie M. S., Rossler O. E. and Prigogine I., Quantum Mechanics, Diffusion and Chaotic Fractals, Elsevier, Oxford (1995).

[29] Cristescu C. P., Non-linear dynamics and chaos. Theoretical fundaments and applications (in Romanian), Romanian Academy Publishing House, Bucharest (2008).

[30] Federer J. and Aharoner A., Fractals in physics, North Holland, Amsterdam (1990).

[31] Brantley W., Eliades T., Orthodontic Materials, Thieme Stuttgart, New York (2001).

[32] Schwierdrzik J. J., Wolfram U. and Zysset P. K., Biomech. Model. Mechanobiol. 12(6), 1155-1168 (2013).

[33] Lesser J. A. and Kody R. S., Polymer Physics 35, 10, 1473-1650 (1997).

[34] Gatto R., Stat. Comput. 18, 3, 321-331 (2008).

[35] Yang W. H., J. Appl. Mech. 6, 47(2), 297-300 (1980).

[36] Hosford W. F., Mechanical Behaviors of Materials, Cambridge University Press, Cambridge (2005).

[37] Novojilov V., Prikladnaya Matematik I Mehanica 15, Mir, Moscow (1952).

[38] Stoka M. I., Geometrie Integrale, Memorial des Sciences Mathematiques, Fasc. 165, Gauthier-Villars, Paris (1968).

[39] Bell J. F., The Physics of Large Deformation of Crystallique Solids, Springer Verlag, Viena (1987).

[40] Duistermaat J. J., Kolk J. A. C., Lie Groups, Springer-Verlag, Berlin (2000).

[41] Burnside W. S., The Theory of Equations, Constable, Dover (1960).

[42] Barbilian D., Mathematical Works, Didactics and Pedagogy, Publishing House, 286, Bucharest (1967).

[43] Kelly P. J., Am. Math. Mon. 61, 311–319 (1954).

[44] Hasan M., Hossain E., Balasubramaniam S. and Koucheryavy Y., IEEE Network 29(1), 26-34 (2014).

[45] Akyildiz I. F., Brunetti F. and Blazquez C., Comput. Netw. 52, 12, 2260–2279 (2008).

[46] Pierobon M. and Akyildiz I., IEEE J. Sel. Area. Comm. 28, 4, 602–611 (2010).

[47] Cobo L. C. and Akyildiz I. F., Nano. Comm. Netw. 1, 4, 244–256 (2010).

[48] Balasubramaniam S. and Lio P., IEEE T. Nano Biosci. 12, 1, 47–59 (2013).

[49] Bar-Yam Y., Dynamics of Complex Systems, The Advanced Book Program, Addison-Wesley, Reading, Massachusetts (1997).

[50] Mitchell M., Complexity: A Guided Tour, Oxford University Press, Oxford (2009).

[51] Flake G. W., The Computational Beauty of Nature, MIT Press, Cambridge, MA (1998).

[52] Bennett C. H., How to define complexity in physics and why, W. H. Zurek (editor) (1990).

[53] Badii R. and Politi A., Complexity: Hierarchical Structure and Scaling in Physics, Cambridge University Press, Cambridge (1997).

[54] Rice J. R., Continuum plasticity in relation to microscale deformation mechanisms in Metallurgical effects at high strain ratesi, ed. R. W. Rohde et al., Proc. AJME, Plenum (1973).

[55] Marcinkovski M. J., Phys. Stat. Sol. B 93, 703 (1979).

[56] Landau L. D., Lifshitz E. M., Theorie de l’elasticite [Theory of elasticity], Moscow (1967).

[57] Thurston R. N., Phys. Rev. B 2 (12), 1012 (1970).

[58] Zoos E., Modele discrete și continue ale solidelor, Ed. Științifică [Discrete and Continuous Models of Solids, Scientific Ed.], Bucharest (1974).

Chapter 2

[1] Mitchell M., Complexity: A Guided Tour, Oxford University Press, Oxford (2009).

[2] Thomas Y. H., Multi-scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations, World Scientific Publishing Company, Singapore (2009).

[3] Michel O. D. and Thomas B. G., Mathematical Modeling for Complex Fluids and Flows, Springer, New York (2012).

[4] Badii R. and Politi A., Complexity: Hierarchical Structure and Scaline in Physics, Cambridge University Press, Cambridge (1997).

[5] Mandelbrot B. B., The Fractal Geometry of Nature (Updated and augm. Ed.), W. H. Freeman, New York (1983).

[6] Winfree A. T., The Geometry of Biological Time, Springer 2nd edition, New Zork (2000).

[7] Weibel P., Ord G., Rosler O. E., Space Time Physics and Fractility, Springer, New York (2005).

[8] El Naschie M. S., Rossler O. E., Prigogine I., Quantum Mechanics, Diffusion and Chaotic Fractals, Elsevier, Oxford (1995).

[9] Cristescu C. P., Non-linear dinamics and chaos. Theoretical fundaments and applications (in Romanian), Romanian Academy Publishing House, Bucuresti (2008).

[10] Federer J., Aharoner A., Fractals in physics, North Holland, Amsterdam (1990).

[11] Nottale L., Scale Relativity and Fractal Space-Time. A New Approach to Unifying Relativity and Quantum Mechanics, Imperial College Press, London (2011).

[12] Nottale L., Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity, World Scientific, Singapore (1993).

[13] Merches I., Agop M., Differentiability and Fractality in Dynamics of Physical Systems, World Scientific, Singapore (2016).

[14] Nottale L., Fractals and the quantum theory of space-time, Int. J. Mod. Phys. A 4, 5047-5117 (1989).

[15] Cresson J., Int. J. Geom. Meth. Mod. Phys. 3, 1395 (2006).

[16] Stauffer D. and Stanley H. E., From Newton to Mandelbrot: A Primer in Theoretical Physics with Fractals for the Personal Computer, 2nd enlarged ed. Springer, New York (1995).

[17] Gouyet J. F., Physique et Structures Fractales [Physics and Fractal Structures], Masson, Paris (1992).

[18] Solovastru L. G., Ghizdovat V., Nedeff V., Lazar G., Eva L., Ochiuz L., Agop M. and Popa R. F., J. Comput. Theor. Nanosci. 13, 1-6 (2016).

[19] Batchelor G. K., An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge (2000).

[20] Landau L. D., Lifshitz E. M., Fluid Mechanics, 2 ed., Butterworth Heinemann, Oxford (1987).

[21] Miller J. C., Laser ablation: Principle and Applications, Springer (1994).

[22] Anisimov S. I., Bauerle D., and Luk’yanchuk B. S., Phys. Rev. B 48, 12076 (1993).

[23] Miotello A., Kelly R., Appl. Surf. Sci. 138–139, 44–51 (1999).

[24] Anisimov S. I., Luk’yanchuk B. S. and Luches A., Appl. Surf. Sci. 24, 96-98, (1996).

[25] Miloshevsky A., Harilal S. S., Miloshevsky G. and Hassanein A., Phys. Plasmas 21, 043111 (2014).

[26] Nica P., Agop M., Gurlui S. and Focsa C., Europhys. Lett. 89, 65001 (2010).

[27] Gurlui S., Agop M., Nica P., Ziskind M. and Focsa C., Phys. Rev. E 78, 026405 (2008).

[28] Tesloianu N. D., Ghizdovat V., Agop M., Flow Dynamics via non-differentiability and cardiovascular diseases, Scholar Press (2015).

[29] Singh R. B., Mengi S. A., Xu Y. J., Arneja A. S., Dhalla N. S., Exp. Clin. Cardiol. 7(1), 40-53 (2002).

[30] Tracy J. E., Currier D. P. and Threlkeld A. J., Phys. Theor. 68, 1526-1532 (1988).

[31] Webster M., Kinesitherapy, Retrieved 21 March (2012).

[32] Adelaide E. C., Aust. J. Physioth. 4, 19-22 (1958).

[33] S. Hassan, M. Mehani, Atherosclerosis, Bull. Fac. Ph. Th. Cairo Univ. 17 (1) 7-16 (2012).

[34] Armitage J. V., Eberlein W. F., Elliptic functions, Cambridge University Press (2006).

[35] Gurlui S., Agop M., Nica P., Ziskind M., Focsa C., Phys. Rev. E 78, 026405 (2008).

[36] Nica P., Agop M., Gurlui S., Bejinariu C., Focsa C., Jpn. J. Appl. Phys., 51, 106102 (2012).

[37] Pompilian O. G., Gurlui S., Nemec P., Nazabal V., Ziskind M., Focsa C., Appl. Surf. Sci., 278, 352-357 (2012).

[38] Focsa C., Nemec P., Ziskind M., Ursu C., Gurlui S., Nazabal V., Appl. Surf. Sci. 255, 10, 5307-5531 (2009).

[39] Ursu C., Gurlui S., Focsa C., Popa G., Nucl. Instrum. Meth. Phy. Res. B 267, 2, 446-450 (2009).

[40] Deift P., McLaughlin K. T. R., American Mathematical Soc. 624 (1998).

[41] Stan C., PBI Scientific Bulletin XLVIX(LIII), Fasc. 1-2, 17-25 (2003)

[42] Stan C., Cristescu C. P., Dimitriu D. G., Rom. J. Phys. 56 (SUPPL.), 79-82 (2011).

[43] Stan C., Cristescu C. P., Dimitriu D. G., Phys Plasmas 17, 4 (2010).

[44] Stan C., Cristescu C. P., Alexandroaei D., Czech. J. Phys. 54 (SUPPL. 3), 648-653 (2009).

[45] Stan C., Cristescu C. P., Chiriac S., Dimitriu D. G., Rom. J. Phys. 54, 7-8, 699-704 (2009).

[46] Stan C., Cristescu C. P., Alexandroaei D., UPB Sci. Bull. A 70, 4, 25-30 (2008).

[47] Alexandroaei D., Stan C., Cristescu C. P., J. Optoelectron. Adv. M. 10, 8, 1954-1957 (2008).

[48] Stan C., Cristescu C. P., Alexandroaei D., J. Optoelectron. Adv. M. 8, 1, 152-155 (2006).

[49] Stan C., Cristescu C. P., Alexandroaei D., J. Optoelectron. Adv. M. 7, 5, 2451-2454 (2005).

[50] Stan C., Cristescu C. P., Alexandroaei D., Contrib. Plasm. Phys. 42, 1, 81-89 (2002).

[51] Cristescu C. P., Stan C., Alexandroaei D., Phys. Rev. E 70, 12, 016613 (2004).

[52] Cristescu C. P., Stan C., Alexandroaei D., UPB Sci. Bull. A 63, 2, 60-61 (2001).

[53] Aronstein D. L., Stround Jr. C. R., Phys. Rev. A, 55, 6, 4526-4537 (1997).

[54] Pricop M., Raut M., Borsos Z., Baciu A., Agop M., J. Mod. Phys., 4, 8A, 165-171 (2013).

[55] Syrakos A., Goergian G. C., Alexandros A. N., J. Non- Newton. Fluid Mech. 195, 19, (2013).

[56] Murabito J.M., Evans J.C, Heart. J., 143, 961-966 (2002).

[57] Hiatt W. R., Baumgartner I., Bluemke D. A., Peripheral manifestations of atherothrombosis, Atlas of Atherothrombosis, Ed. By Topol J.E. Science Press Ltd., 109-110 (2004).

[58] Creager M. A, Libby P., Peripheral Arterial Disease, Braunwald’s Heart Disease, Textbook of Cardiovascular Medicine, 7th Edition, Elsevier Saunders, 1437-1461 (2005).

[59] Libby P., The vascular biology of atherosclerosis, Braunwald’s Heart Disease, Textbook of Cardiovascular Medicine, 7th Edition, Elsevier Saunders, 921-937 (2005).

[60] Sumner D. S., Essential hemodynamic principles, Rutherford RB, Vascular Surgery, vol.1, WB Saunders Ed (1989).

[61] D. M. Popescu, Hematologie clinică, Ed. Medicală [Clinical Hematology, Medical Ed.], București 19-23 (1996).

[62] Tesloianu D., Chronic Peripheral Arterial Disease and Chronic Obstructive Pulmonary Disease in smokers, PhD Thesis, Iasi (2014).

[63] Mandelbrot B., Les objectes fractals: forme, hazard et dimension [Fractal objects: form, hazard and dimension], Flamarion, Paris (1972).

[64] Vasincu D., Timofte D., Susanu S., Costin A., Barlescu V., Tesloianu D., Buletinul Institutului Politehnic din Iasi, Publicat de Universitatea Tehnica “Gheorghe Asachi” din Iaşi Tomul LX (LXIV), Fasc. 3, Secţia matematică, mecanică teoretică, fizică (2014) [Bulletin of the Polytechnic Institute of Iasi, published by “Gheorghe Asachi” Technical University of Iasi Tomul LX (LXIV), Fasc. 3, Mathematics, Theoretical, Physical Mechanics (2014)].

[65] Agop M., Gavriluţ A., Buzea C., Ochiuz L., Tesloianu D., Crumpei G., Popa C., Implications of quantum informational entropy in some fundamental physical and biophysical models, In Quantum Mechanics, Ed. Intech, 2015 (in press).

Chapter 3

[1] Anderson A. R. A., Chaplain M. A. J., Newman E. L., Steele R. J. C., Thompson A. M., J. Theoret. Med. 2, 129-154 (2000).

[2] Ivancevic T. T., Bottema M. J., Jain L. C., A Theoretical Model of Chaotic Attractor in Tumor Growth and Metastasis, 0807.4272 in Cornell University Library’s (2008).

[3] Liu C., Gao S., Zhang L., Med. Hypotheses 69 (3), 590-595 (2007).

[4] Brahimi-Horn M. C., Pouyssegur J., FEBS Lett. 581 (19), 3582-3591 (2007).

[5] Witz I. P., Levy-Nissenbaum O., Cancer Lett. 242 (1), 1-10 (2006).

[6] Cuvier C., Jang A, Hill R. P., Clin. Exp. Metastasis 15 (1), 19-25 (1997).

[7] Volpert V., Petrovskii S., Phys. Life Rev. 6, 267–310 (2009).

[8] Kozusko F., Bourdeau M., Cell Prolif. 40 (6), 824-834 (2007).

[9] Perumpanani A. J., Norbury J., Sherratt J. A., Byrne, H. M., Physica D 126, 145–159 (1999).

[10] Marchant B. P., Norbury J., Sherratt J. A., Nonlinearity 14

, 1653–1671 (2001).

[11] Tsuboi R., Rifkin D. B., Int. J. Cancer 46

, 56–60 (1990).

[12] Aznavoorian S., Strake M. L., Krutzsch H., Schiffman E., Liotta L. A., J. Cell. Biol., 110, 1427–1438 (1990).

[13] Pastor J., Bru A., Fernaud I., Berenguer I., Berenguer C., Fernaud, M. J., Melle S. An. Fis. (RSEF) 10, 1–2 (1998).

[14] Buzea C. Gh., Rusu I., Bulancea V., Bădărău Gh., Păun V. P., Agop M., Phys. Lett. A, 374, 2757–2765 (2010).

[15] Nottale L., Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity, World Scientific, Singapore (1993).

[16] Nottale L., Scale Relativity and Fractal Space-Time – A New Approach to Unifying Relativity and Quantum Mechanics, Imperial College Press, London (2011).

[17] Helfrich W., Z. Naturforsch. C 28, 693-703 (1973).

[18] Lipowsky R., Sackmann E., Structure and Dynamics of Membranes, Handbook of Biological Physics, Elsevier, North-Holland (1995).

[19] Kraus M., Wintz W., Seifert U., Lipowsky R., Phys. Rev. Lett. 77, 3685-3688 (1996).

[20] Kraus M., Wintz W., Seifert U., Lipowsky R., Phys. Rev. Lett. 77, 3685-3688 (1996).

[21] Prost J., Bruinsma R., Europhys. Lett. 33 (4), 321-326 (1996).

[22] Cantat I., Misbah C., Phys. Rev. Lett. 83, 235-238 (1999).

[23] Cantat I., Misbah C., Phys. Rev. Lett. 83, 880-883 (1999).

[24] Sukumaran S., Seifert U., Phys. Rev. E 64, 011916 (2001).

[25] Durand I., Jönson P., Misbah C., Valance A., Kassner K., Phys. Rev. E 56, 3776 (1997).

[26] Kern N., Fourcade B., Europhys. Lett. 46 (2), 262-267 (1999).

[27] Seifert U., Phys. Rev. Lett. 83, 876-879 (1999).

[28] Biben T., Misbah C., Euro. Phys. J. B 29, 311-316 (2002).

[29] Nardi J., Bruinsma R., Sackmann E., Phys. Rev. Lett. 82, 5168-5171 (1999).

[30] Abkarian M., Lartigue C., Viallat A., Phys. Rev. E 63, 041906 (2001).

[31] Abkarian M., Lartigue C., Viallat A., Phys. Rev. Lett. 88, 068103 (2002).

[32] Lortz B., Simon R., Nardi J., Sackmann E., Europhys. Lett. 51, 468 (2000).

[33] Cantat I., Kassner K., Misbah C., Eur. Phys. J. E 10, 175-189 (2003).

[34] Brochard F., Lennon J. F., J. Phys. France 36 (11), 1035-1047 (1975).

[35] Lorenz E. N., J. Atm. Sci. 20, 130-141 (1963).

[36] Lorenz E. N., J. Atm. Sci. 62, 5, 1574–1587 (2005).

[37] Fritz J., Partial Differential Equations (4th ed.), Springer, Berlin (1991).

[38] Manneville P., Structures dissipatives, chaos and turbulence, Collection Alea Saclay, Paris (1992).

[39] Johnson R. S., A modern introduction to the mathematical theory of water waves. Cambridge Texts in Applied Mathematics 19, Cambridge University Press, Cambridge (1997).

[40] Bousinessq J., Comptes Rendus de l’Academie des Sciences [Accounts of the Academy of Sciences] 72, 755–759 (1871).

Chapter 4

[1] Peppas N. A., Bures P., Leobandung W., Ichikawa H., Eur. J. Pharm. Biopharm. 50, 27 (2000).

[2] Tătaru G., Popa M., Desbrieres J., J. Bioact. Compat. Polym. 24, 525 (2000).

[3] Siepmann J., Siegel R., Rathbone, M., Fundamentals and Applications of Controlled Release Drug Delivery, Springer (2012).

[4] Bacaita E. S., Bejinariu C., Zoltan B., Peptu C., Andrei G., Popa M., Magop D., Agop M., J. Appl. Math., 653720 (2012).

[5] Vasile C., Zaikov G. E., Environmentally Degradable Materials Based on Multicomponent Polymeric Systems, Brill, Boston (2009).

[6] Peptu C. A., Buhuş G., Popa M., Perichaud A., Costin D., J. Bioact. Compat. Polym. 25, 98 (2010).

[7] Jătariu N., Popa M., Curteanu S., Peptu C. A., J. Biomed. Mater. Res. A, 98, 342 (2011).

[8] Ciobanu B. C., Cadinoiu A. N., Popa M., Desbrières J., Peptu C. A., Cell. Chem. Technol. 48, 485 (2014).

[9] Lao L. L., Peppas N. A. et al. Int. J. Pharm. 418, 28 (2011).

[10] Higuchi T., J. Pharm. Sci. 52, 1145 (1963).

[11] Korsmeyer R. W., Gurny R., Doelker E., Buri P., Peppas N. A. Int. J. Pharm.15, 25 (1983).

[12] Souto E. B., Eur. J. Med. Chem. 60, 249 (2013).

[13] Peppas N. A., Sahlin J. J., Int. J. Pharm. 57, 169 (1989).

[14] Papadopoulou V., Kosmidis K. et al., Int. J. Pharm. 309, 44 (2006).

[15] Kozlov G. V., Zaikov G. E. Fractals and Local Order in Polymeric Materials, Nova Science Publishers Inc., New York (2001).

[16] Novikov V. U., Kozlov G. V. Russ. Chem. Rev. 69, 323 (2000).

[17] Merches I., Agop M., Differentiability and Fractality in Dynamics of Physical Systems, World Scientific, Singapore (2016).

[18] Bacaita S., Uritu C., Popa M., Uliniuc A., Peptu C., Agop M. Smart Mater. Res. 26460948 (2012).

[19] Bowman F., Introduction to Elliptic Function with Applications, English University Press, London (1955).

[20] Peppas N. A., Sahlin J. J., Int. J. Pharm. 57, 169 (1989).

[21] Oliveira P. R., Bernardi L. S., Strusi O. L. et al. Int. J. Pharm. 405, 90–96 (2011).

Publish with Nova Science Publishers

We publish over 800 titles annually by leading researchers from around the world. Submit a Book Proposal Now!