Methods of mathematical modeling of processes of relaxation and creep of polymer filaments on the basis of a spectral interpretation of the processes are described. It is shown that the analytic forms of the relaxation and delay (creep) spectra are completely determined by the mean-statistical values of the relaxation and delay times as well as by the structural coefficients of these processes, which basically characterize the intensity of relaxation and creep processes.
Similar content being viewed by others
Change history
29 March 2018
The following should be added to the acknowledgement on page 73:
The work was financed within the framework of the base part of the state task of the Ministry of Education and Science of the Russian Federation, Project No. 11.4696.2017/8.9.
References
A. G. Makarov, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 2, 12–16 (2000).
A. M. Stalevich and A. G. Makarov, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 3, 8–13 (2000).
A. G. Makarov and A. M. Stalevich, Khim. Volokna, No. 4, 67–69; No. 5, 58–61 (2001).
A. M. Stalevich and A. G. Makarov, Khim. Volokna, No. 6, 68–70 (2001).
A. G. Makarov and A. M. Stalevich, Khim. Volokna, No. 3, 52–55 (2002).
A. M. Stalevich, A. G. Makarov, and Ye. D. Saidov, Khim. Volokna, No. 3, 55–57 (2002).
A. G. Makarov and A. M. Stalevich, Khim. Volokna, No. 6, 62–64 (2002).
A. G. Makarov, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 2, 13–17 (2002).
A. G. Makarov and A. M. Stalevich, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 3, 10–13 (2002).
A. M. Stalevich, A. G. Makarov, and Ye. D. Saidov, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 4–5, 15–18; No. 1, 16–22 (2002).
A. M. Makarov and D. A. Ovsyannikov, Vest. S.-Petersburg. Gos. Un-ta. Tekhnol. i Dizayna, No. 11, 5–9 (2005).
A. V. Demidov, A. G. Makarov, and A. M. Stalevich, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 3, 13–17 (2006).
A. V. Demidov, A. G. Makarov and A. M. Stalevich, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 4, 9–13 (2006).
D. A. Ovsyannikov, A. G. Makarov, et al., Vest. S.-Petersburg. Un-ta. Ser. 10. Prikl. Mat., Inform. Protsessy Uprav., No. 3, 46–54 (2006).
A. V. Demidov, A. G. Makarov and A. M. Stalevich, Khim. Volokna, No. 3, 58–61; No. 5, 38–43; No. 6, 47–51 (2006).
A. V. Demidov, A. G. Makarov and A. M. Stalevich, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 5, 18–22; No. 6, 14–22 (2006).
A. V. Demidov, A. G. Makarov and A. M. Stalevich, Materialovedenie, No. 8, 5–10 (2006).
A. V. Demidov, A. G. Makarov and A. M. Stalevich, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 2, 14–18; No. 3, 20–24 (2007).
A. G. Makarov, A. V. Demidov, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 1, 15–19 (2007).
A. V. Demidov, A. G. Makarov, and A. M. Stalevich, Khim. Volokna, No. 1, 62–65; No. 6, 49–55, 52–55 (2007).
A. V. Demidov, A. G. Makarov, and A. M. Stalevich, Prikl. Mekh. i Tekh. Fiz., 48, No. 5, 147–157 (2007).
A. G. Makarov, A. V. Demidov, and A. M. Stalevich, Mekh. Tv. Tela, No. 1, 155–165 (2009).
N. V. Drobotun, G. Ya. Slutsker, and A. G. Makarov, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 3, 36–39 (2009).
A. V. Demidov, Ye. N. Artem’eva, and O. E. Kalanchuk, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 2, 39–43 (2010).
A. S. Gorshkov, A. G. Makarov, et al., Dizayn. Materialy. Tekhnologiya, No. 4 (15), 88– 92 (2010).
N. V. Drobotun, G. Ya. Slutsker, and A. G. Makarov, No. 3, 34–37 (2009).
A. G. Makarov, S. V. Kiselev, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 1 (11), 56–60 (2011).
A. G. Makarov, S. V. Kiselev, et al., Dizayn. Materialy. Tekhnologiya, No. 1 (16), 91–94 (2011).
A. G. Makarov, S. V. Kiselev, et al., Dizayn. Materialy. Tekhnologiya, No. 2 (17), 95–97 (2011).
V. S. Zurakhov, A. G. Makarov, and M. A. Makarova, Dizayn. Materialy. Tekhnologiya, No. 4 (19), 81–86 (2011).
A. G. Makarov, S. V. Kiselev, et al., Vest. S.-Petersburg. Gos. Un-ta. Tekhnol. i Dizayna, Ser. 1, Yestest. i Tekhnol. Nauki, No. 1, 69–72 (2011).
P. P. Rymkevich, A. A. Romanova, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 2 (16), 70–73 (2012).
A. G. Makarov, G. Ya. Slutzker, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 4 (18), 28–31 (2012).
A. G. Makarov, A. S. Gorshkov, et al., Dizayn. Materialy. Tekhnologiya, No. 1 (21), 23–28 (2012).
A. G. Makarov, G. Ya. Slutzker, et al., Dizayn. Materialy. Tekhnologiya, No. 3 (23), 41–44 (2012).
A. G. Makarov, M. A. Yegorova, et al., Dizayn. Materialy. Tekhnologiya, No. 3 (23), 48–50 (2012).
A. G. Makarov, G. Ya. Slutzker, et al., Khim. Volokna, No. 5, 28–32 (2012).
A. G. Makarov, P. P. Rymkevich, et al., J. Macromol. Sci. Part B: Phys., 52, No. 12, 1829–1847 (2013).
A. G. Makarovm N. V. Pereborova, et al., Khim. Volokna, No. 5, 44–47 (2013).
V. V. Golovina, P. P. Rymkevich, et al., Khim. Volokna, No. 5, 33–40 (2013).
A. A. Grebenkin, A. N. Grebenkin, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 1 (19), 13–15 (2013).
V. V. Golovina, A. G. Makarova, and P. P. Rymkevich, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 1 (19), 67–70 (2013).
A. G. Makarov, G. Ya. Slutzker, et al., Khim. Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 2 (20), 66–69 (2013).
A. G. Makarov, G. Ya. Slutzker, et al., Khim. Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 2 (20), 70–74 (2013).
A. G. Makarovm N. V. Pereborova, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 3 (21), 27–31; No. 4 (22), 32–34 (2013).
A. G. Makarov, N. V. Pereborova, et al., Dizayn. Materialy. Tekhnologiya, No. 2 (27), 79–83 (2013).
A. S. Gorshkov, A. G. Makarov, et al., Inzh.-Stroitel’. Zh., No. 9 (44), 75–83 (2013).
A. G. Makarov, N. V. Pereborova, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 1 (23), 24–29 (2014).
A. G. Makarov, N. V. Pereborova, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 1 (23), 19–23 (2014).
A. G. Makarov, G. Ya. Slutzker, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 3 (25), 47–50; No. 4 (26), 57–63 (2014).
A. G. Makarov, N. V. Pereborova, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 1 (27), 96–100 (2015).
A. G. Makarov, G. Ya. Slutzker, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 1 (27), 101–105; No. 2 (28), 104–109 (2015).
P. P. Rymkevich, V. V. Golovina, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 2 (28), 98–103 (2015).
A. G. Makarov, N. V. Pereborova, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 2 (28), 78–87 (2015).
A. G. Makarov, G. Ya. Slutzker, and N. V. Drobotun, Tekh. Fiz., 60, No. 2, 240–245 (2015).
A. G. Makarov, N. V. Pereborova, et al., Khim. Volokna, No. 6, 37–41; No. 1, 52–57 (2014).
A. G. Makarov, G. Ya. Slutzker, et al., Fiz. Tv. Tela, No. 4 (58), 814–820 (2015).
A. G. Makarov, N. V. Pereborova, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 5 (359), 48–58 (2015).
A. G. Makarov, N. V. Pereborova, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 4 (30), 7–16 (2015).
A. G. Makarov, A. V. Demidov, et al., Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 6 (360), 194–205 (2015).
A. G. Makarov, P. P. Rymkevich, and A. S. Gorshkov, Vest. S.-Petersburg. Gos. Un-ta. Tekhnol. i Dizayna, Ser. 1, Yestest. i Tekhnol. Nauki, No. 4, 3–7, 8–12 (2015).
N. V. Pereborova, ibid., 60–66 (2015).
N. V. Pereborova, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 3 (29), 11–19, 35–42 (2015).
N. V. Pereborova, Dizayn. Materialy. Tekhnologiya, No. 4 (39), 98–102 (2015).
A. G. Makarov, N. V. Pereborova, et al., Khim. Volokna, No. 1, 37–42 (2016).
A. G. Makarov and A. M. Shvankin, Izv. Vuzov. Tekhnolol. Tekst. Prom-sti, No. 1 (31), 22–27 (2016).
A. G. Makarov and A. M. Shvankin, Vest. S.-Petersburg. Gos. Un-ta. Tekhnol. i Dizayna, Ser. 1, Yestest. i Tekhnol. Nauki, No. 1, 10–14 (2016).
The present study was financially supported by a grant from the Russian Foundation for Basic Research No. 15-08-06325.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Khimicheskie Volokna, No. 1, pp. 69–73, January–February, 2017.
Rights and permissions
About this article
Cite this article
Makarov, A., Pereborova, N.V., Egorova, M.A. et al. Development of Methods of Mathematical Modeling of Processes of Relaxation and Creep of Polymer Filaments Based on a Spectral Interpretation. Fibre Chem 49, 70–75 (2017). https://doi.org/10.1007/s10692-017-9846-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10692-017-9846-2