The quasi-adiabatic approximation for coupled thermoelasticity

The equations of coupled thermoelasticity are considered in the case of stationary vibrations. The dimensional and order-of-magnitude analysis of the parameters occurring within these equations prompts the introduction of the new non-dimensionalisation scheme, highlighting the nearly-adiabatic nature of the resulting motions. The departure from the purely adiabatic regime is characterised by a natural small parameter, proportional to the ratio of the mean free path of the thermal phonons to the vibration wavelength. When the governing equations are expanded in terms of the small parameter, one can formulate an equivalent “quasi-adiabatic” system of the equations of ordinary elasticity with frequency-dependent modulae, characterising the thermoelastic issipation. Unfortunately, this model lacks the degrees of freedom necessary to satisfy boundary condition(s) for the temperature. Thus, we also derive a complementary boundary layer solution and show that to the leading order it is described by thermoelastic equations in the quasi-static approximation. Further simplifications are possible for purely dilatational motions; we illustrate this point by solving a model thermoelastic problem in 1D

An asymptotic membrane-like theory for long-wave motion in a pre-stressed elastic plate

An asymptotically consistent two-dimensional theory is developed to help elucidate dynamic response in finitely deformed layers. The layers are composed of incompressible elastic material, with the theory appropriate for long-wave motion associated with the fundamental mode and derived in respect of the most general appropriate strain energy function. Leading-order and refined higher-order equations for the mid-surface deflection are derived. In the case of zero normal initial static stress and in-plane tension, the leading-order equation reduces to the classical membrane equation, with its refined counterpart also being obtained. The theory is applied to a one-dimensional edge loading problem for a semi-infinite plate. In doing so, the leading- and higher-order governing equations are used as inner and outer asymptotic expansions, the latter valid within the vicinity of the associated quasi-front. A solution is derived by using the method of matched asymptotic expansions

Eigenvalue of a semi-infinite elastic strip

A semi-infinite elastic strip, subjected to traction free boundary conditions, is studied in the context of in-plane stationary vibrations. By using normal (Rayleigh–Lamb) mode expansion the problem of existence of the strip eigenmode is reformulated in terms of the linear dependence within infinite system of normal modes. The concept of Gram's determinant is used to introduce a generalized criterion of linear dependence, which is valid for infinite systems of modes and complex frequencies. Using this criterion, it is demonstrated numerically that in addition to the edge resonance for the Poisson ratio ν=0, there exists another value of ν≈0.22475 associated with an undamped resonance. This resonance is best explained physically by the orthogonality between the edge mode and the first Lamé mode. A semi-analytical proof for the existence of the edge resonance is then presented for both described cases with the help of the augmented scattering matrix formalism

Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids

We present a set of explicit conditions, involving the components of the elastic stiffness tensor, which are necessary and sufficient to ensure the strong ellipticity of an orthorhombic incompressible medium. The derivation is based on the procedure developed by Zee & Sternberg (Arch. Rat. Mech. Anal., 83, 53-90 (1983)) and, consequently, is also applicable to the case of the homogeneously pre-stressed incompressible isotropic solids. This allows us to reformulate the results by Zee & Sternberg in terms of components of the incremental stiffness tensor. In addition, the resulting conditions are specialized to higher symmetry classes and compared with strong ellipticity conditions for plane strain, commonly used in the literature.The first author’s work and the second author’s visit to Brunel University were partly supported by Brunel University’s ‘BRIEF’ award scheme

Non-principal surface waves in deformed incompressible materials

The Stroh formalism is applied to the analysis of infinitesimal surface wave propagation in a statically, finitely and homogeneously deformed isotropic half-space. The free surface is assumed to coincide with one of the principal planes of the primary strain, but a propagating surface wave is not restricted to a principal direction. A variant of Taziev’s technique [R.M. Taziev, Dispersion relation for acoustic waves in an anisotropic elastic half-space, Sov. Phys. Acoust. 35 (1989) 535–538] is used to obtain an explicit expression of the secular equation for the surface wave speed, which possesses no restrictions on the form of the strain energy function. Albeit powerful, this method does not produce a unique solution and additional checks are necessary. However, a class of materials is presented for which an exact secular equation for the surface wave speed can be formulated. This class includes the well-known Mooney–Rivlin model. The main results are illustrated with several numerical examples

Eco-evolutionary dynamics of clonal multicellular life cycles

The evolution of multicellular life cycles is a central process in the course of the emer-gence of multicellularity. The simplest multicellular life cycle is comprised of the growth of the propagule into a colony and its fragmentation to give rise to new propagules. The majority of theo-retical models assume selection among life cycles to be driven by internal properties of multicellular groups, resulting in growth competition. At the same time, the influence of interactions between groups on the evolution of life cycles is rarely even considered. Here, we present a model of colo-nial life cycle evolution taking into account group interactions. Our work shows that the outcome of evolution could be coexistence between multiple life cycles or that the outcome may depend on the initial state of the population – scenarios impossible without group interactions. At the same time, we found that some results of these simpler models remain relevant: evolutionary stable strategies in our model are restricted to binary fragmentation – the same class of life cycles that contains all evolutionarily optimal life cycles in the model without interactions. Our results demonstrate that while models neglecting interactions can capture short- term dynamics, they fall short in predicting the population- scale picture of evolution

Comparative evaluation of e-waste flows in Kostanay region

The paper studies the state of treatment of electronic waste in the Kostanay region. The calculation of the e-waste flows and comparative qualitative assessment are made first timeВ статье изучено состояние обращения электронных отходов в Костанайской области. Впервые приведены данные расчета потоков и выполнена их сравнительная качественная оценк

История библиотеки духовной семинарии в Новгороде (XVIII в.)

The paper is related to the history of creation and development of the Novgorod Ecclesiastical Seminary and its library in the XVIII-th century оn the materials of the Russian State Archives of Ancient Documents (RSAAD) and other sources.Статья посвящена истории возникновения и развития Новгородской духовной семинарии и семинарской библиотеке в XVIII в. Использованы материалы Российского государственного архива древних актов (РГАДА), другие источники, позволяющие судить о роли семинарской библиотеки в истории отечественного просвещения XVIII века

История библиотеки Владимиро-Суздальской духовной семинарии (XVIII век)

The article is devoted to the history of creation and development of Vladimir-Suzdal Theological Seminary Library in the XVIII century. In the paper there are used the materials of the State Archive of the Vladimir Region (SAVR) and other sources, allowing to judge about the place of seminary library in the history of National Enlightenment of the XVIII century.Статья посвящена истории возникновения и развития Владимиро-Суздальской духовной семинарии и семинарской библиотеки в XVIII веке. В статье использованы материалы Государственного архива Владимирской области (ГАВО) и другие источники, позволяющие судить о месте семинарской библиотеки в истории отечественного просвещения XVIII века