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

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

Interfering resonances in a quantum billiard

We present a method for numerically obtaining the positions, widths and wavefunctions of resonance states in a two dimensional billiard connected to a waveguide. For a rectangular billiard, we study the dynamics of three resonance poles lying separated from the other ones. As a function of increasing coupling strength between the waveguide and the billiard two of the states become trapped while the width of the third one continues to increase for all coupling strengths. This behavior of the resonance poles is reflected in the time delay function which can be studied experimentally.Comment: 2 pages, 3 figure

К ВОПРОСУ О РАЦИОНАЛЬНОМ ИСПОЛЬЗОВАНИИ КОРМОВОЙ БАЗЫ В РАЗВИТИИ ЖИВОТНОВОДСТВА РЕГИОНА СИБИРИ

The paper considers development of forage production in agribusiness to be the important socioeconomic task due to complicated and difficult geopolitical situation. The task assumes systematic studies on the industry from the point of view of development and efficient applying of forage by means of innovations and further development of business mechanism aimed at supply with high-energy cheep forages. The authors suggest it is necessary to found the main directions and methods aimed at productivity of natural forage grasslands; prepare scientific recommendations on development of forage grasslands, applying of cultivated grasslands, soil-conservation measures in meadows and pastures, applying mineral and organic fertilizers. The article mentions necessity to develop measures on forages quality increasing, reducing losses of nutrition forages when harvesting and storing. The authors suggest it is significant to specify recommendations on applying progressive ways of forages preparing and storing in respect to the regional conditions and efficient applying of hayfields, pastures and perennial plantings. It is necessary to build regional variants of technological schemes aimed at forage production and demand in the main industrial resources. The research analyzes areas which can be applied as natural forage grasslands and areas for specific sub-industries of livestock farming in the region. The authors declare there is no well-defined strategy of regional forage production development.В условиях геополитической нестабильности устойчивое развитие кормопроизводства в АПК представляет собой стратегически важную социально-экономическую задачу, предполагающую системные исследования организации отрасли как с точки зрения наращивания и  эффективного использования кормов на основе инновационных технологий, так и  дальнейшего совершенствования организационно-экономического механизма системы обеспечения высоко- энергетическими дешевыми кормами. В этих целях необходимо обосновать основные направления и методы повышения продуктивности естественных кормовых угодий, подготовить научно обоснованные предложения по их улучшению, созданию и использованию культурных пастбищ, проведению почвозащитных мероприятий на лугах и пастбищах, внесению минеральных и органических удобрений. Следует разработать систему мероприятий по улучшению качества всех видов кормов, уменьшению потерь их питательной ценности при уборке и хранении. Целесообразно конкретизировать рекомендации по использованию прогрессивных способов заготовки и хранения кормов для условий региона, эффективному использованию сенокосов и пастбищ и многолетних насаждений. Необходимо сформировать зональные варианты технологических схем производства кормов, потребность в основных видах производственных ресурсов. В результате исследования проведен анализ зон, благоприятных для использования в качестве естественных кормовых угодий и размещения определенных подотраслей животноводства в регионе. Также установлено, что в настоящее время отсутствует четко аргументированна

Investigation of shock waves in explosive blasts using fibre optic pressure sensors

The published version of this article may be accessed at the link below. Copyright @ IOP Publishing, 2006.We describe miniature all-optical pressure sensors, fabricated by wafer etching techniques, less than 1 mm(2) in overall cross-section with rise times in the mu s regime and pressure ranges typically 900 kPa (9 bar). Their performance is suitable for experimental studies of the pressure-time history for test models exposed to shocks initiated by an explosive charge. The small size and fast response of the sensors promises higher quality data than has been previously available from conventional electrical sensors, with potential improvements to numerical models of blast effects. Results from blast tests are presented in which up to six sensors were multiplexed, embedded within test models in a range of orientations relative to the shock front.Support from the UK Engineering&Physical Sciences Research Council and Dstl Fort Halstead through the MoD Joint Grants Scheme are acknowledged. WN MacPherson is supported by an EPSRC Advanced Research Fellowship