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Highlights: [•] A two-scale homogenization method is elaborated to determine the effective properties of laminates. [•] The interface between any two neighboring layers quickly and periodically along two directions. [•] The results obtained are shown to agree well with the numerical ones provided by FEM. [ABSTRACT FROM AUTHOR]

Abstract: The present work aims to determine the effective elastic moduli of a composite having a columnar microstructure and made of two cylindrically anisotropic phases perfectly bonded at their interface oscillating quickly and periodically along the circular circumferential direction. To achieve this objective, a two-scale homogenization method is elaborated. First, the micro-to-meso upscaling is carried out by applying an asymptotic analysis, and the zone in which the interface oscillates is correspondingly homogenized as an equivalent interphase whose elastic properties are analytically and exactly determined. Second, the meso-to-macro upscaling is accomplished by using the composite cylinder assemblage model, and closed-form solutions are derived for the effective elastic moduli of the composite. Two important cases in which rough interfaces exhibit comb and saw-tooth profiles are studied in detail. The analytical results given by the two-scale homogenization procedure are shown to agree well with the numerical ones provided by the finite element method and to verify the universal relations existing between the effective elastic moduli of a two-phase columnar composite. [Copyright &y& Elsevier]

Highlights: [•] Asymptotic analysis of phase field model for void formation under irradiation. [•] Sensitivity of phase field model to parameter uncertainties. [•] Matching sharp interface theory to phase field model for parameter estimation. [•] Uncertainty of defect formation and migration energies strongly influence porosity. [ABSTRACT FROM AUTHOR]

Abstract: In this study, a universal model is developed to examine the behavior of combustion wave observed in porous solid matters (e.g., smoldering, self-propagating high-temperature synthesis (SHS), diesel particulate filter (DPF) regeneration process). Analytical expressions of the combustion characters of solid combustible (e.g., diesel particulate matters trapped in a DPF) deposited over an inert porous medium are obtained employing large activation energy asymptotic taking into account the sensible transport processes; namely, heat transfer between the porous medium and gas phases, radiation heat transfer from the porous medium, heat loss from the porous medium to the environment, mass transfer of oxygen from the gas stream to the surface of solid fuel and the effective diffusion in modeling the species diffusion. Then it has been validated that the present model is applicable and adaptable for predicting the characteristics of smoldering combustion and thus SHS process. As a result, the features of combustion wave of the present phenomena would be useful to other processes. From practical point of view and for deep understanding of the behavior of combustion wave of these processes, we investigate the effects of various physical parameters over a wide range of conditions. We observe that the moving speed of the reaction front increases with the increase of porosity of the porous medium, mass transfer coefficient and initial fuel mass fraction; while it decreases owing to the increase of heat transfer rate from the porous medium to the gas, heat loss to the environment and radiative heat transfer. Furthermore, the results reveal that extinction tends to occur due to lower porosity of the porous medium, higher radiative heat transfer from the porous medium, higher heat transfer rate from the porous medium to the gas and higher heat losses from the porous medium to the environment. Even the observed near-extinction behavior in reaction front speed versus heat loss diagram is found to be similar what we got in gaseous premixed flame propagating through the porous medium. An extinction limit diagram has been presented as a function of radiation-conduction parameter and the gas flow velocity. In addition to, the impact of radiation and the combined effect of the inclusion of Knudsen diffusion and tortuosity are demonstrated in terms of the spatial temperature and species profiles to examine how these two parameters modify the reaction front structure. Furthermore, the governing equations have been solved numerically and it is observed that asymptotic analysis gives a good agreement with the numerical solution. [Copyright &y& Elsevier]

Abstract: The dynamic characteristics of composite thin cylindrical shells are examined through a systematic order-of-magnitude analysis. The analysis is used to eliminate terms of secondary importance, while retaining the dominant terms in the dispersion relation and boundary conditions. This results in analytical expressions that can describe the vibration of composite cylindrical shells with high accuracy for a wide range of frequencies. Furthermore, the asymptotic analysis is carried out in such a way that the dynamic edge effect is accounted for when determining the vibration mode shapes and the associated internal stresses. Numerical examples are also presented. It is shown that the proposed methodology gives closed-form and analytical results that are in close agreement with numerical solutions of the equations of motion. [Copyright &y& Elsevier]

Abstract: In this paper, the asymptotic first order analysis, both mathematical and numerical, of two structures bonded together is presented. Two cases are considered, the gluing of an elastic structure with a rigid body and the gluing of two elastic structures. The glue is supposed to be elastic and to have its stiffness of the same order than those of the elastic structures. An original numerical method is developed to solve the mechanical problem of stiff interface at order 1, based on the Nitsche's method. Several numerical examples are provided to show the efficiency of both the analytical approximation and the numerical method. [Copyright &y& Elsevier]

Abstract: An experimental study on heat transfer enhancement in mini scale coiled tubing for constant wall temperature conditions is conducted. Copper coils with three different radii of curvature (1cm, 2cm, and 4cm), and in four lengths (1, 2, 3 and 4 coil turns) were used. The tube length is long enough to consider the flow to be hydro-dynamically fully developed. Hence, the effects of varying curvatures and lengths on heat transfer are studied. The pitch of the coil is restricted to diameter of the tube to minimize the effect of coiling. Dean number is used instead of Coiled number (modified Dean number), and hence, the results can be expanded to spiral and curved tubing. Water and two different silicone oils (0.65cSt,1cSt) were used in the experiments to examine the effect of Prandtl number on coiled tubing heat transfer augmentation. Prandtl number from 5 to 15 is covered in this paper. A new asymptotic correlation is proposed to calculate Nusselt number in fully developed coiled tubing based on the current results. In addition, dimensionless mean wall flux and dimensionless thermal length are also considered besides Nusselt, Reynolds, and Dean numbers. [Copyright &y& Elsevier]

Abstract: In this work, we focus on the time-domain simulation of the propagation of electromagnetic waves in non-homogeneous lossy coaxial cables. The full 3D Maxwell equations, that described the propagation of current and electric potential in such cables, are classically not tackled directly, but instead a 1D scalar model known as the telegraphist's model is used. We aim at justifying, by means of asymptotic analysis, a time-domain “homogenized” telegraphist's model. This model, which includes a nonlocal in time operator, is obtained via asymptotic analysis, for a lossy coaxial cable whose cross section is not homogeneous. [Copyright &y& Elsevier]

Abstract: We introduce a new thermodynamically consistent diffuse interface model of Allen–Cahn/Navier–Stokes type for multi-component flows with phase transitions and chemical reactions. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. We consider two scaling regimes, i.e. a non-dissipative and a dissipative regime, where we recover in the sharp interface limit a generalized Allen–Cahn/Euler system for mixtures with chemical reactions in the bulk phases equipped with admissible interfacial conditions. The interfacial conditions satisfy, for instance, a Young–Laplace and a Stefan type law. [Copyright &y& Elsevier]

Highlights: [•] Mode I deformation fields in gradient enhanced materials are derived in closed form. [•] The theory resembles experimental results in fracture experiments on a fiber material. [•] A structural effect results in crack tip blunting in heterogeneous materials such as fiber networks. [•] The average segment length gives the internal length scale parameter, hence allow for bridging between scales. [Copyright &y& Elsevier]

Abstract: Using the estimates of the principal eigenvalue of the -biharmonic operator on the ball from below and from above, we provide its asymptotic analysis as . [Copyright &y& Elsevier]

Abstract: Kadomtsev–Petviashvili (KP)-type equations are seen in fluid mechanics, plasma physics, and gas dynamics. Hereby we consider an integrable KP-based system. With the Hirota method, symbolic computation and truncated Painlevé expansion, we obtain bright one- and two-soliton solutions. Figures are plotted to help us understand the dynamics of regular and resonant interactions, and we find that the regular interaction of solitons is completely elastic. Based on the asymptotic and graphical behavior of the two-soliton solutions, we analyze two kinds of resonance between the solitons, both of which are non-completely elastic. A triple structure, a periodic resonant structure in the procedure of interactions and a high wave hump in the vicinity of the crossing point, can be observed. Through the linear stability analysis, instability condition for the soliton solutions can be given, which might be useful, e.g., for the ship traffic on the surface of water. [Copyright &y& Elsevier]

Abstract: In this work we analyze a diffusion flame established in a low-permeability medium. A low-strained impinging jet of oxidant against a pool of low-volatility liquid fuel is the considered geometry. Owing to the differences on the transport properties of gas, liquid and solid, the problem presents physical processes occurring in different length scales. Hence, we perform an asymptotic analysis in order to obtain the profiles of temperature and species concentration in each length scale. As a result of the low-permeability feature of the medium, the velocity field is determined mainly by the gradient pressure (Darcy equation). The viscous effects become confined into small regions near the stagnation-point and the liquid–fuel interface. The effects of porosity, fuel Lewis number, strain-rate and liquid–fuel volatility on the flame temperature, flame position and vaporization rate are discussed. It is shown that the low-permeability medium is necessary in order to sustain the vaporization process of the low-volatility liquid fuel, as it enhances the heat transfer to the fuel reservoir. This model is valid for high rates of interphase heat exchange and low rates of strain. [Copyright &y& Elsevier]

Abstract: Using the estimates of the principal eigenvalue of the -Laplacian on the ball from below and from above, we provide its asymptotic analysis as . [Copyright &y& Elsevier]

Abstract: We give an overview of basic methods that can be used for obtaining asymptotic expansions of integrals: Watson’s lemma, Laplace’s method, the saddle point method, and the method of stationary phase. Certain developments in the field of asymptotic analysis will be compared with De Bruijn’s book Asymptotic Methods in Analysis. The classical methods can be modified for obtaining expansions that hold uniformly with respect to additional parameters. We give an overview of examples in which special functions, such as the complementary error function, Airy functions, and Bessel functions, are used as approximations in uniform asymptotic expansions. [Copyright &y& Elsevier]

Fiber-reinforced materials are widely observed in biological tissue such as human arteries and tendons. Characterizing the influence of fibers on crack-tip fields in such nonlinear materials undergoing large deformation is an important precursor to understanding damage evolution and fracture or tearing. In this paper, we present asymptotic crack tip fields in a fiber-reinforced hyperelastic sheet and explore the competing roles of fiber and matrix stiffening. A generalized neo-Hookean model and a power-law model are employed to characterize the behavior of the matrix and fibers, respectively. We show that the asymptotic crack-tip fields are mainly determined by the phase with largest degree of stiffening. For example, when the stiffening effect of fibers is much larger than that of the matrix, the crack tip fields are determined by the constitutive behavior of fibers, and the wire model and the fabric model reasonably characterize the deformation and stress near the crack tip. On the contrary, if the matrix stiffening is larger than that of the fibers, we show that the crack tip fields approach those of a pure matrix material. The asymptotic results are complemented by finite element simulations which show good agreement. These findings may shed light on material damage at a crack tip in fiber reinforced materials. [ABSTRACT FROM AUTHOR]

We compute the Morse index m (u p) of any radial solution u p of the semilinear problem: (P) − Δ u = | x | α | u | p − 1 u in B u = 0 on ∂ B where B is the unit ball of R 2 centered at the origin, α ≥ 0 is fixed and p > 1 is sufficiently large. In the case α = 0 , i.e. for the Lane–Emden problem , this leads to the following Morse index formula m (u p) = 4 m 2 − m − 2 , for p large enough, where m is the number of nodal domains of u. [ABSTRACT FROM AUTHOR]

Understanding the three-dimensional (3D) effect on the notch tip field is important for the fracture mechanics analysis of engineering materials and structures. This paper presents an asymptotic solution for 3D sharp V-notched structures subjected to mode Ⅰ creep loading condition. The asymptotic solution, including the singularities and stress field distribution functions, is obtained by introducing the out-of-plane constraint factor. It is found that the singular behavior is related to the notch angle, material creeping exponents, and the out-of-plane constraint factor. Specifically, singularity changes sharply near the free surface. K N t - T z solution is presented to describe the mode Ⅰ stress field around the tip of 3D V-notch under creep condition. Its accuracy and advantages compared with plane strain or plane stress solutions are validated by finite element analysis. The difference between effective ranges of K N t - T z solution and that of plane strain solution is clarified. Moreover, the effect of the creep time on the stress field is also shown. The solutions given in this paper could be beneficial for understanding the 3D effect on notch considering creep loading conditions. [ABSTRACT FROM AUTHOR]

• A lumped-parameter model is used to reveal energy localization mechanisms of a PnC. • The asymptotic approach is applied into defect-band analysis for the first time. • Evanescent waves in a band gap result in a fixed-like boundary condition. • Mechanical resonance by the fixed-like boundary condition leads to defect modes. Phononic crystals (PnCs) have received growing attention in recent years, due to their ability to manipulate elastic waves, such as in the case of defect-mode-enabled energy localization. Although previous studies have explored defect modes of PnCs – from phenomenon observations to their potential applications – little effort has been made to date to reveal fundamental mechanisms of defect-mode-enabled energy localization. Thus, this study proposes a lumped-parameter analytical model to reveal the underlying principles of the formation of defect bands of a one-dimensional PnC when a single defect is introduced, or the splitting of defect bands when double defects are introduced. Through the investigation of 1) evanescent wave characteristics in the defect-mode shapes, and 2) the asymptotically equivalent behaviors of defect bands and defect-mode shapes with limiting behavior approaches, this study demonstrates a new aspect of why a band gap should be the prerequisite for achieving defect-mode-enabled energy localization. It is confirmed that defect-mode shapes are normal modes, rather than propagating wave modes. The key findings of this study are as follows: 1) the exponentially attenuating characteristics of evanescent waves in a band gap generate a fixed-like boundary condition, which surrounds single or double defects, and 2) mechanical resonance, attributed to the fixed-like boundary condition, leads to the formation and splitting of defect bands. [Display omitted] [ABSTRACT FROM AUTHOR]

The present study analyses the flame extinction of timber under different levels of external heating and oxygen contents in the surrounding atmosphere. An existing theoretical framework conceived initially for the analysis of a counter-flow diffusion flame established above the surface of a condensed fuel is extended for charring materials to deliver a fundamental understanding of the self-extinction of timber. This study shows that the energy balance at the burning surface is influenced primarily by the magnitude of external heating conditions, which directly influences the evolution of bulk properties such as flame temperature, location, and stagnation plane position. Variations in the oxygen content had a lesser influence over these bulk properties. For all investigated conditions, the limits of the strain rate range where a flame can be sustained were shown to vary substantially, and critical Damköhler number (Da) analyses were conducted. Blow-off at high strain rates (low Da) occurs for all investigated conditions. The value of this critical Da decreases when increasing either the magnitude of the external heating or the oxygen content as flame temperature increases. Quenching at low strain rates (high Da) is only found for sufficiently low magnitudes of external heating. There, the associated critical Da increases when increasing either the external heating or the oxygen content. Above a certain degree of external heating, the flame can be theoretically sustained even at infinitely-low strain rates. By comparing these results to experimental data, the experimental critical Da at quenching was found to behave like the theoretical results but with a lower sensitivity to variations in the parameters studied. To account for this discrepancy, a fuel dilution parameter is introduced to incorporate the complex dependencies of timber decomposition and surface reactions not captured by the theoretical framework. [ABSTRACT FROM AUTHOR]

The paper describes the mechanical behavior of composites made of piezoelectric spheres in perfect or imperfect contact. The imperfect contact is achieved by interposing piezoelectric thin adhesive layers between the spheres. First, using asymptotic analysis, transmission conditions of imperfect interface equivalent to the behavior of piezoelectric adhesive layers are obtained at order 0 and 1. These transmission conditions are calculated for "hard" adhesives, i.e. adhesive materials whose electromechanical constants do not rescale with their thickness. Next, under the assumption of spherical symmetry, the transmission conditions are condensed to a general law of imperfect contact, able to simultaneously describe different contact regimes: piezoelectric hard (order 0 and 1) and soft (or spring-type, order 0 and 1) interface conditions, the perfect continuity conditions, and the piezoelectric rigid (Gurtin–Murdoch or membrane-type) conditions. Lastly, following Bufler's approach, the homogenization problem of a spherical hollow piezoelectric assembly is solved, extending the classical transfer matrix method to take into account the presence of thin adhesive layers described using the proposed transmission conditions of imperfect contact. A simple numerical example is provided, illustrating the correctness and effectiveness of the homogenization approach in describing the electromechanical behavior of spherical piezoelectric assemblies. [ABSTRACT FROM AUTHOR]

Highlights: [•] Slip localization occurs frequently during plastic deformation of metallic polycrystals. [•] It is known to trigger grain boundary (GB) brittle fracture. [•] Based on FEs computations, analytical formulae are proposed for decribing GB stress fields. [•] The predicted remote stress to GB microcracking is lower than predicted by pile-up theories. [•] It is closer to experimental data due to the finite thickness of slip bands. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we developed a new numerical approach for the establishment of strain gradient constitutive equations in heterogeneous materials with periodic microstructure through homogenization over a unit cell. To this end, we considered a periodic unit cell of finite size, including different homogenous phases and subjected to gradient remote loading. The local elasticity problem was solved by combining the theoretical asymptotic analysis with the Fast Fourier Transform (FFT) method. The asymptotic analysis allows the establishment of differential equations of different orders. These equations were resolved by using the FFT method. By using the homogenization procedure proposed in Li (2011a,b), intrinsic strain gradient constitutive relations can be constructed. This approach fulfils the severe exigency on accuracy of the high-order homogenization. Numerical simulations on examples with 1D and 2D microstructures showed that this approach is highly accurate and efficient. Discussions were completed on the mechanical implications of the strain gradient constitutive laws through the obtained numerical results. [Copyright &y& Elsevier]

Abstract: In this paper, the asymptotic expansions of stress tensor for linearly elastic shell have been proposed by new asymptotic analysis method, which is different from the classical asymptotic analysis. The new asymptotic analysis method has two distinguishing features: one is that the displacement is expanded with respect to the thickness variable of the middle surface not to the thickness; another is that the first order term and the second order term of the displacement variable can be algebraically expressed by the leading term. To decompose stress tensor totally into 2-D variable and thickness variable, we have three steps: operator splitting, variables separation and dimension splitting. In the end, a numerical experiment of special hemispherical shell by FEM (finite element method) is provided. We derive the distribution of displacements and stress fields in the middle surface. [Copyright &y& Elsevier]

Abstract: Singular perturbation problems with turning points arise as mathematical models for various physical phenomena. The problem with interior turning point represent one-dimensional version of stationary convection–diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin. Boundary turning point problems, on the other hand, arise in geophysics and in modeling thermal boundary layers in laminar flow. In this paper, we review some existing literature on asymptotic and numerical analysis of singularly perturbed turning point and interior layer problems. The purpose is to find out what problems are treated and what numerical/asymptotic methods are employed, with an eye towards the goal of developing general methods to solve such problems. Since major work in this area started after 1970 so this paper limits its coverage to the work done by numerous researchers between 1970 and 2011. [Copyright &y& Elsevier]

Abstract: We study a stationary motion of incompressible viscous fluid with a pressure-dependent viscosity in a thin (or long) straight pipe with variable cross-section. We assume that the flow is governed by the prescribed pressure drop between pipe’s ends. Under very general assumption on the viscosity law satisfied by the Barus formula and other empiric laws, the effective behavior of the flow is found via rigorous asymptotic analysis with respect to the pipe’s thickness. [Copyright &y& Elsevier]

Highlights: [•] Calculation of the topological derivative of a modified energy shape functional associated to the steady-state heat conduction problem. [•] Extention of the topological-shape sensitivity method to deal with the modified adjoint method. [•] Alternative approach to calculate the topological derivative based on shape sensitivity analysis together with a modified Lagrangian method. [•] The new approach is general and simplifies the most delicate step of the topological derivative calculation, namely, the asymptotic analysis of the adjoint state. [ABSTRACT FROM AUTHOR]

Abstract: In the paper we considered a model of immune reaction against malignant glioma. The model proposed by Kronik et al. (Cancer Immunol. Immunother., 2008) describes simplified interactions between tumour cells and five components of the immune system. We studied the effects of uncertainties of the parameters values to the system behaviour. We showed that the tumour growth rate is one of the most important parameters only in case of fast growing tumours, that is for GBM in our case. On the basis of the performed sensitivity analysis we proposed a reduced model in which the role of time delays in loops appearing in the described interactions is considered. The proposed model includes only two main components of the reaction, that is tumour cells and cytotoxic T-lymphocytes. It occurs that although the reduced system is described by several non-linear terms with three time delays, its dynamics is simple and time delays have hardly any influence on it. Both considered models confirmed that the non-linearities present in interactions between tumour cells and CTLs play a major role in the system dynamics, while other components or delays can be taken into account as supplementary elements only. [Copyright &y& Elsevier]

Abstract: The results of a detailed, step-by-step, asymptotic analysis of the signaling system are reported, in the case where the system exhibits limit cycle behavior. The analysis is based on the dimensional form of the model and exploits the various fast/slow time scale gaps that develop as the solution evolves along the limit cycle. It is shown that under the action of fast time scales of dissipative character, the limit cycle is confined on a low-dimensional surface in the phase space. The cycle can be divided in three parts, each one related to a different characteristic time scale. The first part refers to the slow rate of release in the cytoplasm. The second part refers to the even slower rate by which the free enters into the nucleus. The last part refers to the fast rate by which the nuclear is first produced and then depleted. It is demonstrated that these and many other findings (regarding the fast variables, the equilibrated fast processes, the rate limiting and/or driving steps, etc.) can be acquired by simple algorithmic tools. [Copyright &y& Elsevier]

Abstract: The topological derivative measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation. According to the literature, the topological derivative has been fully developed for a wide range of one single physical phenomenon modeled by partial differential equations. In addition, the topological asymptotic analysis associated to multi-physics problems has been reported in the literature only on the level of mathematical analysis of singularly perturbed geometrical domains. In this work, we present the topological derivative in its closed form for the total potential mechanical energy associated to a thermo-mechanical semi-coupled system, when a small circular inclusion is introduced at an arbitrary point of the domain. In particular, we consider the linear elasticity system (modeled by the Navier equation) coupled with the steady-state heat conduction problem (modeled by the Laplace equation). The mechanical coupling term comes out from the thermal stress induced by the temperature field. Since this term is non-local, we introduce a non-standard adjoint state, which allows to obtain a closed form for the topological derivative. Finally, we provide a full mathematical justification for the derived formulas and develop precise estimates for the remainders of the topological asymptotic expansion. [Copyright &y& Elsevier]

Summary: Understanding the fate of contaminant in wetland flows is essential in applications such as ecological risk assessment and environmental hydraulic design. Presented in this paper is an analytical study on the dispersion of contaminant in a two-zone wetland, with the effect of ecological degradation taken into consideration. Environmental dispersion is discussed separately via an exponential transformation for the general formulation of contaminant transport. Taylor’s classical analysis for solute dispersion in a long and thin tube flow is rigorously generalized for the dispersion of the lateral mean contaminant concentration in the longitudinal direction. A method of asymptotic analysis is adopted instead of the concentration moment method in order to simplify the process of deduction and the expression of the analytical solution. Gill’s method of mean concentration expansion is applied to model the concentration deviation terms produced in an averaging operation. With the velocity profile obtained previously, the enhancement of the environmental dispersivity under long time evolution is determined and shown to be consistent with that obtained by the method of concentration moment. Analytical solutions for the evolution of the contaminant concentration and the influenced region of the contaminant cloud are obtained by combining both the hydraulic and the ecological effects. For typical pollutant as the heavy metal Hg, the evolution of contaminant cloud is illustrated by critical length and duration in an application with concentration beyond some given environmental standard level. Results show that for wetland flows with a two-zone structure, the influenced region is reduced evidently while the duration of the contaminant cloud remains nearly unchanged, compared with that for the single-zone wetland flow. [Copyright &y& Elsevier]

Abstract: Radix-rational sequences are solutions of systems of recurrence equations based on the radix representation of the index. For each radix-rational sequence with complex values we provide an asymptotic expansion, essentially in the scale . The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence of first-order differences. The coefficients are Hölderian functions obtained through some dilation equations, which are usual in the domains of wavelets and refinement schemes. The proofs are ultimately based on elementary linear algebra. [Copyright &y& Elsevier]

Abstract: When a crack or sharp notch is subjected to anti-plane shear loading the boundary conditions negate the transverse shear stress components at the free surfaces and generate a coupled in-plane shear stress field, which can be singular. For sharp V-notches with zero notch opening angle (or cracks) this 3D phenomenon was known for a long period of time. However this mode was largely ignored in stress analysis of notched components. Till now it is still unclear how significant this mode is and whether it has to be taken into consideration in integrity and failure analysis of engineering structures. The present paper is aimed to investigate this singular mode by means of the 3D Finite Element method, which is applied to notched plates with different notch opening angles and plate thicknesses. The stress state associated with the coupled mode is localised and quickly decays with the distance from the notch tip. Therefore, the obtained theoretical results can be applied to a wide range of notched components provided that the boundaries are sufficiently far from the notch tip. Among these results is the effect of the plate thickness on the intensity of the coupled mode; the latter increases with the decrease of the plate thickness. Significance of these new results to failure and integrity assessments of plate and shell components with sharp notches, including through-the-thickness cracks, is discussed in the final section of the paper. [Copyright &y& Elsevier]

Abstract: With the increasing pressure on natural resources, the sustainability study of socio-ecological systems has become a crucial scientific issue. In this paper we emphasize that transient behaviors have to be taken into account in sustainability analysis. We illustrate their impact with a model of tourism development from the literature, where the sustainability study is based on asymptotic properties. In order to evaluate relevant space and time characteristics of transient dynamics, we propose to use the concepts and tools of the mathematical viability theory. We also extend this analysis to controlled dynamical systems, which are particularly appropriate to model socio-ecological systems when management issues are at stake. [Copyright &y& Elsevier]