The homogenized model of small oscillations of complex fluids

Berezhnyi, Maksym; Berlyand, Leonid; Khruslov, E. Ya.

doi:10.3934/nhm.2008.3.831

Cited by 8 publications

(8 citation statements)

References 23 publications

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“…Among them, there are 11 multiperiodic δ Scuti variables (Khruslov 2010a) and 4 RRC stars with a nonradial pulsation co-existing with the first-overtone mode (Khruslov 2010d(Khruslov , 2012. Also found (Khruslov 2008(Khruslov , 2011(Khruslov , 2013 were biperiodic non-pulsating stars: a Double Periodic Variable (DPV type, Mennickent & Kolaczkowski 2010), a Cepheid of the spherical component of our Galaxy in an eclipsing binary, and a high-amplitude δ Scuti star with an eclipsing component. I also investigated one possible double-mode short-period semiregular star (Khruslov 2010b) and one double-periodic T Tauri star (Khruslov 2010c).…”

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confidence: 99%

A search for double‐mode pulsating variables

Khruslov

2013

Astron Nachr

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confidence: 99%

A search for double‐mode pulsating variables

Khruslov

2013

Astron Nachr

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“…One of the fundamental postulates of the elastic medium mechanics is the statement that under small deformations the stress tensor σ[u] = {σ ij [u]} 3 i,j=1 in the medium linearly depends on the strain tensor e[u] = {e ij [u] = 1 2 ( ∂ui ∂xj + ∂uj ∂xi )} 3 i,j=1 of the medium. Such a dependence is represented with the aid of the elasticity tensor A = {a npqr (x, t)} 3 n,p,q,r=1 . Namely, the following Hooke law holds:…”

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“…(1.1) where u = u(x, t) is the displacement of the medium, and the fourth rank tensor A = {a npqr (x, t)} 3 n,p,q,r=1 is symmetrical with respect to permutation of pairs of subscripts and of subscripts in pairs themselves. This law is experimentally corroborated for the wide class of the homogeneous elastic materials.…”

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Non-standard dynamics of elastic composites

Berezhnyi¹,

Khruslov²

2011

Networks &Amp; Heterogeneous Media

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An elastic medium with a large number of small axially symmetric solid particles is considered. It is assumed that the particles are identically oriented and under the influence of elastic medium they move translationally or rotate around symmetry axis but the direction of their symmetry axes does not change. The asymptotic behavior of small oscillations of the system is studied, when the diameters of particles and distances between the nearest particles are decreased. The equations, describing the homogenized model of the system, are derived. It is shown that the homogenized equations correspond to a nonstandard dynamics of elastic medium. Namely, the homogenized stress tensor linearly depends not only on the strain tensor but also on the rotation tensor.

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“…Because of the low orbital inclination, no eclipses have been detected in these binaries. Recently, Antipin, Sokolovski & Ignatieva (2007) and Khruslov (2008) have discovered two Cepheid variables in eclipsing binaries: TYC 1031 1262 1 and NSV 10993. The pulsation periods are nearly identical (i.e.…”

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TYC 1031 1262 1: an anomalous Cepheid in a double-lined eclipsing binary★

Sipahi

İbanoǧlu

Çakırlı

et al. 2012

Monthly Notices of the Royal Astronomical Society

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The multicolour light curves and radial velocities for TYC 1031 1262 1 have been obtained and analysed. TYC 1031 1262 1 includes a Cepheid with a period of 4.15270 ± 0.00061 d. The orbital period of the system is about 51.2857 ± 0.0174 d. The pulsation period indicates that the secular period is increasing at a rate of of 2.46 ± 0.54 min yr −1 . The observed B, V and R magnitudes have been cleaned of the intrinsic variations of the primary star. The remaining light curves that have been obtained consist of eclipses and proximity effects, and these have been analysed to obtain the orbital parameters. The system consists of two evolved stars, F8 II + G6 II, with masses of M 1 = 1.640 ± 0.151 M and M 2 = 0.934 ± 0.109 M and radii of R 1 = 26.9 ± 0.9 R and R 2 = 15.0 ± 0.7 R , respectively. The pulsating star almost fills its corresponding Roche lobe, which indicates the possibility that mass loss or transfer has taken place. We find an average distance of d = 5070 ± 250 pc, using the BVR and JHK magnitudes, and also the V-band extinction. The kinematic properties and the distance to the Galactic plane (i.e. 970 pc) indicate that it belongs to the thick-disc population. Most of the observed and calculated parameters of TYC 1031 1262 1 lead to its classification as an anomalous Cepheid.Key words: binaries: eclipsing -binaries: spectroscopic -stars: fundamental parametersstars: variables: Cepheids. I N T RO D U C T I O NPulsatingx variables are located in a restricted region, the so-called Cepheid instability strip (IS) in the Hertzsprung-Russell (HR) diagram. This region includes δ Scuti, RR Lyrae and Population I and II Cepheids. These can be used as an important basis for testing theories on stellar structure and evolution, as well as pulsation mechanisms. These variables have very different masses, effective temperatures and chemical abundances. The stars in the IS are found not only in a wide range of masses but also among very young Population I type stars to very old Population II type stars. These stars in the IS reveal many properties of the stellar interiors.At the beginning of the 20th century, Miss Leavitt made the great discovery that there is a relation between the period and the absolute magnitude of Cepheid variables in the Small Magellanic Cloud. Three decades later, Baade (1953) called attention to the difference in the period-luminosity (hereafter P-L) relations of the Cepheids in globular clusters and the classical Cepheids. Thus, the Cepheids are divided into two groups: Population I (usually called Type I) Cepheids and Population II (or Type II) Cepheids.Based on data obtained at the TÜBİTAK National Observatory. † E-mail: esin.sipahi@mail.ege.edu.tr Population I Cepheids are about 1.5 mag brighter than Population II Cepheids for the same pulsation periods. Taking into account this difference, Blaauw & Morgan (1954) made a revision of the P-L relation for the classical Cepheids. These variables are still used as distance indicators not only for our galaxy but also for nearby spiral and ir...

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The homogenized model of small oscillations of complex fluids

Cited by 8 publications

References 23 publications

A search for double‐mode pulsating variables

A search for double‐mode pulsating variables

Non-standard dynamics of elastic composites

TYC 1031 1262 1: an anomalous Cepheid in a double-lined eclipsing binary★

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