BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Towards the problem of the Nesterenko’s soliton waves propagatio
n in nonlinear inhomogeneous Hertzian chains
DTSTART;VALUE=DATE-TIME:20181204T090500Z
DTEND;VALUE=DATE-TIME:20181204T092500Z
DTSTAMP;VALUE=DATE-TIME:20230330T002443Z
UID:indico-contribution-22@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Andrii Spivak (Odesa State Environmental University)
\nWe consider theoretically the problem of the pulse transmission along 1D
vertical chain of hard spheres\, which interact with each other by pair-w
ise nonlinear Hertz law [1-3]. System is subject into gravity and therefor
e became inhomogeneous [2\,3]. We show\, that being excited form the bound
ary (from the top)\, system is able to exhibit complex multimode dynamics
of pulse propagation. After long-wave approximation has been used to study
the dynamics of week perturbation\, in the lowest approximation\, resulte
d governing equation is satisfy by either singular solutions\, or combinat
ions of cylindrical waves [2]. In the higher approximation we obtaine nonl
inear equation of motion (generalized in form of Bussinesq equation) which
bring us to solution of Nesterenko-type soliton [1] with a negligible dif
ferences in the amplitudes\, and dispersions.\nWe conclude that initially
weekly nonlinear and inhomogeneous chain\, already in the linear approxima
tion\, is able to transmit either normal or singular modes\, whenever\, th
e accounting\, of the nonlinearity leads to familiar Nesterenko-type solit
on’s [1].\nTherefore under the appropriate values of the parameters (non
linearity\, inhomogeneity\, signal amplitudes) linearized Hertzian chain s
upport both discontinuous as well as quasinormal mode scenarios of pulse t
ransmission.\n\n[1] Nesterenko\, V.F. Propagation of nonlinear compression
pulses in granular media. J. Appl. Mech. Tech. Phys. 24 (1) (1984) 733-74
3\; Translated from : Zh. Prikl. Mekh. Tekh. Fiz. (5) (1983) 136-148. [Rus
sian] \n[2] Sen\, S.\, Hong\, J.\, Bang\, J.\, Avalos\, E.\, and Doney\, R
. Solitary waves in the granular chain. Physics Reports 462 (2) (2008) 21-
66.\n[3] Gerasymov\, O.I. and Vandewalle\, N. On the exact solutions of th
e problem of impulsive propagation in an inhomogeneous granular chain. Dop
ov. Nac. acad. nauk Ukr. (8) (2012) 67-72. [Ukrainian]\n\nhttps://indico.b
itp.kiev.ua/event/2/contributions/22/
LOCATION:
URL:https://indico.bitp.kiev.ua/event/2/contributions/22/
END:VEVENT
END:VCALENDAR