@article{ZNSL_2017_461_a9,
author = {V. A. Kozlov and S. A. Nazarov},
title = {Model of saccular aneurysm of the bifurcation node of the artery},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {174--194},
year = {2017},
volume = {461},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a9/}
}
V. A. Kozlov; S. A. Nazarov. Model of saccular aneurysm of the bifurcation node of the artery. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 174-194. http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a9/
[1] G. R. Kirchhoff, “Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisformige”, Annalen der Physik und Chemie, 64:4 (1845), 497–514 | DOI
[2] L. Pauling, “The diamagnetic anisotropy of aromatic molecules”, J. Chem. Phys., 4 (1936), 672–678
[3] Zh.-L. Lions, E. Madzhenes, Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | MR
[4] A. Bressan, S. Canic, M. Garavello, M. Herty, Piccoli B., “Flows on networks: recent results and perspectives”, European Mathematical Society (EMS Surveys in Mathematical Sciences), 1:1 (2014), 47–111 | DOI | MR | Zbl
[5] V. A. Kozlov, S. A. Nazarov, “Poverkhnostnaya entalpiya i uprugie svoistva krovenosnykh sosudov”, Doklady RAN, 441:1 (2011), 38–43 | MR
[6] V. A. Kozlov, S. A. Nazarov, “Asimptoticheskie modeli techeniya krovi v arteriyakh i venakh”, Zap. nauchn. semin. POMI, 409, 2012, 80–106 | MR
[7] V. A. Kozlov, S. A. Nazarov, “Prosteishaya odnomernaya model lozhnoi anevrizmy v bolshoi bedrennoi arterii”, Zap. nauchn. semin. POMI, 426, 2014, 64–86 | MR
[8] V. A. Kozlov, S. A. Nazarov, “Usloviya sopryazheniya v odnomernoi modeli razvetvlyayuscheisya arterii s uprugimi stenkami”, Zap. nauchn. semin. POMI, 438, 2015, 138–177 | MR
[9] V. A. Kozlov, S. A. Nazarov, “Asimptoticheskie modeli anizotropnykh neodnorodnykh uprugikh stenok krovenosnykh sosudov”, Problemy matem. analiza., 83, Novosibirsk, 2016, 93–110
[10] V. A. Kozlov, S. A. Nazarov, “Effektivnye odnomernye obrazy arterialnykh derevev iz krovenosnoi sistemy”, Doklady RAN, 473:2 (2017), 295–301 | DOI
[11] V. A. Kozlov, S. A. Nazarov, “Odnomernaya model techeniya v sochlenenii tonkikh kanalov v tom chisle arterialnykh derevev”, Matem. sbornik., 208:8 (2017), 56–105 | DOI | MR | Zbl
[12] H. Le Dret, “Modeling of the junction between two rods”, J. Math. Pures Appl., 68 (1989), 365–397 | MR | Zbl
[13] S. A. Nazarov, A. S. Slutskii, “Asimptoticheskii analiz proizvolnoi prostranstvennoi sistemy tonkikh sterzhnei”, Trudy Sankt-Peterburg. matem. o-va, 10, 2004, 63–115
[14] P. Kuchment (Ed.), Quantum graphs and their applications, Waves in Random media, 14, no. 1, Special issue, 2004 | MR
[15] P. Exner, H. Kovařík, Quantum Waveguides, Springer, Hidelberg, 2015 | MR | Zbl
[16] P. Kuchment, “Graph models for waves in thin structures”, Waves in Random Media, 12:12 (2002), R1–R24 | DOI | MR | Zbl
[17] P. Kuchment, O. Post, “On the spectrum of carbon nano-structures”, Communications in Mathematical Physics, 275:3 (2007), 805–826 | DOI | MR | Zbl
[18] E. Korotyaev, I. Lobanov, “Schrödinger operators on zigzag nanotubes”, Annales Henri Poincaré, 8:6 (2007), 1151–1176 | DOI | MR | Zbl
[19] A. V. Badanin, E. L. Korotyaev, “Ob odnom magnitnom operatore Shrëdingera na periodicheskom grafe”, Matem. sbornik, 201:10 (2010), 3–46 | DOI | MR | Zbl
[20] I. Y. Popov, A. N. Skorynina, I. V. Blinova, “On the existence of point spectrum for branching strips quantum graph”, J. Math. Phys., 55:3 (2014), 033504, 19 pp. | DOI | MR | Zbl
[21] V. A. Kozlov, S. A. Nazarov, A. Orlof, “Trapped modes supported by localized potentials in the zigzag graphene ribbon”, C. R. Acad. Sci. Paris. Sér. 1, 354:1 (2016), 63–67 | DOI | MR | Zbl
[22] S. Molchanov, B. Vainberg, “Scattering solutions in networks of thin fibers: small diameter asymptotics”, Comm. Math. Phys., 273:2 (2007), 533–559 | DOI | MR | Zbl
[23] D. Grieser, “Spectra of graph neighborhoods and scattering”, Proc. London Math. Soc., 97:3 (2008), 718–752 | DOI | MR | Zbl
[24] S. A. Nazarov, K. Ruotsalainen, P. Uusitalo, “Asymptotics of the spectrum of the Dirichlet Laplacian on a thin carbon nano-structure”, C. R. Mecanique, 343 (2015), 360–364 | DOI
[25] S. A. Nazarov, “Spektr pryamougolnykh reshetok kvantovykh volnovodov”, Izvestiya RAN. Seriya matem., 81:1 (2017), 31–92 | DOI | MR | Zbl
[26] F. L. Bakharev, S. G. Matveenko, S. A. Nazarov, “Diskretnyi spektr krestoobraznykh volnovodov”, Algebra i analiz, 28:2 (2016), 58–71 | MR
[27] F. S. Rofe-Beketov, “Samosopryazhennye rasshireniya differentsialnykh operatorov v prostranstve vektor-funktsii”, Doklady AN SSSR, 184 (1969), 1034–1037 | MR | Zbl
[28] B. S. Pavlov, “Teoriya rasshirenii i yavno reshaemye modeli”, Uspekhi matem. nauk, 42:6 (1987), 99–131 | MR | Zbl
[29] K. Pankrashkin, “Eigenvalue inequalities and absence of threshold resonances for waveguide junctions”, J. Math. Anal. Appl., 449 (2017), 907–925 | DOI | MR | Zbl
[30] S. A. Nazarov, K. I. Piletskas, “Reinoldsovo techenie zhidkosti v tonkom trekhmernom kanale”, Litovskii matem. sbornik, 30:4 (1990), 772–783 | MR | Zbl
[31] S. A. Nazarov, K. Pileckas, “Asymptotic conditions at infinity for the Stokes and Navier–Stokes problems in domains with cylindrical outlets to infinity”, Quaderni di matematica, 4 (1999), 141–243 | MR | Zbl
[32] G. Panasenko, K. Pileckas, “Asymptotic analysis of the nonsteady viscous flow with a given flow rate in a thin pipe”, Applicable Analysis, 91:3 (2012), 559–574 | DOI | MR | Zbl
[33] G. Panasenko, K. Pileckas, “Flows in a tube structure: equation on the graph”, J. Math. Phys., 55 (2014), 081505 | DOI | MR | Zbl
[34] S. A. Nazarov, “The Navier–Stokes problem in thin or long tubes with periodically varying cross-section”, ZAMM, 80:9 (2000), 591–612 | 3.0.CO;2-Q class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl
[35] V. A. Kozlov, S. A. Nazarov, “Odnomernaya model vyazkouprugogo techeniya krovi v tonkom uprugom sosude”, Problemy matem. analiza., 78, Novosibirsk, 2015, 123–140 | Zbl
[36] Y. C. Fung, Biomechanics. Mechanical Properties of Living Tissues, Springer, New York–Berlin, 1993
[37] Y. C. Fung, Biomechanics. Circulation, Second edition, Springer, New York–Berlin, 2011
[38] F. Berntsson, M. Karlsson, V. Kozlov, S. A. Nazarov, “A one-dimensional model of viscous blood flow in an elastic vessel”, Appl. Math. Comput., 274 (2016), 125–132 | MR
[39] F. Berntsson, M. Karlsson, V. Kozlov, S. A. Nazarov, “A one-dimensional model of a false aneurysm”, Int. J. Research in Engineering and Sci., 6:5 (2017), 61–73 | MR
[40] J. PHornak, The Basics of MRI, Interactive Learning Software, 2008
[41] V. A. Kozlov, S. A. Nazarov, G. Zavorokhin, “A fractal graph model of capillary type systems”, Complex Variables and Elliptic Equations (to appear)