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Bifurcations in the equilibrium shape of a thick elastic layer attached to a circular rigid cylinder rotating about its axis are investigated analytically and numerically. The centrifugal force breaks the symmetry of the system leading to deformations invariant along the axis as the result of an instability. The instability threshold depends at linear order on the relative thickness of the compliant layer, and on a dimensionless control parameter based on the elastic modulus, the angular velocity and the outer radius. A weakly non linear analysis, carried out for layers following the Mooney–Rivlin constitutive law, points out the discontinuous (sub-critical) features of the bifurcation, except for relative thickness laying in a very narrow range in which the bifurcation is super-critical. Numerical simulations in the fully post-buckled regime yield the absolute instability threshold, and the order in the rotational symmetry of the developed equilibrium shape. [ABSTRACT FROM AUTHOR]

A combination of cone heater experiments and asymptotic analysis was used to determine the moisture content of Nordic spruce with varying degree of drying. The fuel moisture content was measured by weighing the specimens before and after a drying procedure in an oven. A high-flux asymptotic solution from an integral model established that the ignition temperature from the experiments (directly linked to the intercept heat flux) was constant for both the dry and the moist wood. As a result, one simple equation was developed that can be used to determine the time to ignition for a piece of wet spruce from the time to ignition of dry wood. This simple correlation, combined with models giving the fuel moisture content of wood from humidity and temperature of air surrounding, can be used as an engineering equation for monitoring the ignition propensity of timber. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the second type of complete integrable complex Wadati–Konno–Ichikawa-II (cWKI-II) equation. We first study the conservation laws and construct the hodograph transformation for this equation. Based on the resulting transformation, we construct a new two-component associated cWKI-II equation, which is completely equivalent to the cWKI-II equation. Based on the corresponding Lax pair for this new associated equation, we construct its N -fold Darboux transformation and generalized (m , N − m) -fold Darboux transformation. Then, the associated Bäcklund transformation is used to give various exact solutions, such as smooth soliton, bursting soliton, singular-loop soliton, position controllable semi-rational soliton, breather and rogue wave solutions. The soliton structures along with dynamical evolution behaviors are discussed and shown graphically. Moreover, we investigate some important physical quantities of some soliton solutions such as amplitude, wave number, wave width, velocity, energy and phase by using the asymptotic analysis technique. Finally, we also summarize the formation reasons for some singular structures under some parameter constraints. • The second type of complex Wadati–Konno–Ichikawa (cWKI-II) equation is studied. • The hodograph transformation of cWKI-II equation is constructed. • The generalized (m, N -m)-fold Darboux transformation is established. • Formation reasons of smooth, singular and singular-loop solitons are analyzed. • Solitonic physical quantities are investigated via the asymptotic analysis technique. [ABSTRACT FROM AUTHOR]

An efficient asymptotic approach, referred to as the Effective Non-Local Asymptotic Model (ENLAM), is developed for the elastodynamic homogenization of periodic composites. In comparison with the relevant two-scale asymptotic method reported in the literature, the effective motion equation obtained by ENLAM has a very compact form which holds for any order of asymptotic approximation. This compact form makes direct use of the effective displacement vector and of its different gradients whose highest order depends on the accuracy degree required. For every wavenumber belonging to the first Brillouin zone, the Floquet-Bloch wave expansion is employed, and compact recursive formulae are derived for determining the effective material parameters of periodic composites. For simplicity, all the results are presented only for a shear wave propagating in a periodic composite. Numerical examples for discussing the effective material parameters, the dispersion relation and the asymptotic approximation error are provided when a periodic composite with inclusions is concerned. [ABSTRACT FROM AUTHOR]

We study the sensitivity of optimal consumption streams with respect to perturbations of the random endowment. At the leading order, the consumption adjustment does not matter: any choice that matches the budget constraint simply shifts the original utility by the marginal value of the perturbation. Nontrivial results can be obtained by considering the next-to-leading order. Here, one first solves the problem for a deterministic perturbation, which leads to a "prognosis measure". The desired consumption adjustment for a general endowment perturbation is in turn given by the conditional expectation of the latter, computed under this measure and appropriately weighted with the conditional expectations of the remaining risk-tolerance. [ABSTRACT FROM AUTHOR]

In this paper we introduce a model describing a layered structure composed by two thermoelastic adherents and a thin adhesive subject to a degradation process. By an asymptotic expansion method, we derive a model of imperfect interface coupling damage and temperature evolution. Moreover, assuming that the behaviour of the adhesive is ruled by two different regimes, one in traction and one in compression, we derive a second limit model where unilateral contact conditions on the interface are also included. [ABSTRACT FROM AUTHOR]

We consider a micropolar fluid flow in a two-dimensional domain. We assume that the velocity field satisfies a non-linear slip boundary condition of friction type on a part of the boundary while the micro-rotation field satisfies non-homogeneous Dirichlet boundary conditions. We prove the existence and uniqueness of a solution. Then motivated by lubrication problems we assume that the thickness and the roughness of the domain are of order 0 < ε < < 1 and we study the asymptotic behaviour of the flow as ε tends to zero. By using the two-scale convergence technique we derive the limit problem which is totally decoupled for the limit velocity and pressure (v 0 , p 0) on one hand and the limit micro-rotation Z 0 on the other hand. Moreover we prove that v 0 , p 0 and Z 0 are uniquely determined via auxiliary well-posed problems. [ABSTRACT FROM AUTHOR]

We consider a family of linearly viscoelastic shells of thickness 2 ε , all with the same middle surface and fixed on the lateral boundary. By using asymptotic analysis, we find that for external forces of a particular order of ε , a two-dimensional viscoelastic flexural shell model is an accurate approximation of the three-dimensional quasistatic problem. Most noticeable is that the limit problem includes a long-term memory that takes into account the previous history of deformations. We provide convergence results which justify our asymptotic approach. [ABSTRACT FROM AUTHOR]

Highlights • The physical mechanism of Henry's Law is analyzed. • Henry's Law is expressed as a simple scheme in LBM. • A unified lattice Boltzmann equation for conjugate mass transfer is proposed. • The asymptotic analysis proves that the interface conditions can be ensured. Abstract The most challenging problem for simulating conjugate mass transfer problem is the variable concentration jump described by the double film theory at the phase interface. In the present paper, the physical mechanism of Henry's law is analyzed, and it is found that Henry's law can be expressed as a relation between two constant weight coefficients in lattice Boltzmann method (LBM). As a consequence, a unified multi-relaxation-time (MRT) lattice Boltzmann equation (LBE) for conjugate mass transfer is proposed. The asymptotic analysis proves that the interface conditions, including the concentration jump determined by the double film theory and mass flux continuity, can be ensured with second-order accuracy. Five test cases containing both transient and steady conjugate mass transfer problems with straight or curved interfaces are calculated to validate the present method. The results show that the proposed MRT LBE has both simplicity and good accuracy. It is capable of simulating conjugate mass transfer at both steady and transient periods, with a stationary or moving interface. Especially, it has a good numerical stability at large distribution coefficient and diffusivity coefficient ratio. [ABSTRACT FROM AUTHOR]

The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K -field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip plasticity is suppressed when the material length scale ℓ of the gradient theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J -integral for strain gradient plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk plasticity and an outer J -field. • We investigate, numerically and analytically, the crack tip asymptotic behaviour of strain gradient plasticity solids. • Results reveal the existence of an elastic stress state near the crack tip, reminiscent of a dislocation-free zone. • The nature of the crack tip stress elevation is analytically assessed and full field asymptotic solutions obtained. • Strain gradient plasticity delays the onset of crack tip plasticity. • The elastic K-field persists in the case of short cracks and a regime of J-dominance. [ABSTRACT FROM AUTHOR]

Abstract Solute trapping is an important phenomenon in rapid solidification of alloys, for which the continuous growth model (CGM) of Aziz et al. [1] is a popular sharp interface theory. By modulating the so-called anti-trapping current and using asymptotic analysis, we show how to quantitatively map the thin interface behavior of an ideal dilute binary alloy phase field model onto the CGM kinetics. We present the parametrizations that allow our phase field model to map onto the sharp interface kinetics of the CGM, both in terms of partition coefficient k (V) and kinetic undercooling. We also show that the mapping is convergent for different interface widths, both in transient and steady state simulations. Finally we present the effect that solute trapping can have on cellular growth in directional solidification. The presented treatment for solute trapping can be easily implemented in different phase field models, and is expected to be an important feature in future studies of quantitative phase field modeling in quasi-rapid solidification regimes, such as those relevant to metal additive manufacturing. Graphical abstract Image 1 [ABSTRACT FROM AUTHOR]

Abstract We consider a problem of transport of a physical entity by an incompressible velocity in a domain composed of a fixed region and thin varying layers. We suppose that these layers display a cellular microstructure with random thin varying thickness. We suppose that, within the layers, the diffusion and velocity coefficients admit random large-scale structures. Under mixing properties of the diffusion and velocity processes we study the asymptotic behavior of the problem with respect to a vanishing parameter describing the thickness of the layers. We derive the effective boundary conditions on the boundary of the fixed region. These boundary conditions reveal the effects of the random time fluctuations of the diffusion coefficient and fluid velocity. Highlights • We introduced a transport problem in a domain with random turbulent layers near the boundary. • The layers display a cellular microstructure whose characteristics alternate in time and are rapidly oscillating stationary random processes. • We studied the asymptotic analysis of the problem. • We derived the effective boundary conditions on the boundary of the domain. [ABSTRACT FROM AUTHOR]

Abstract By using the Darboux transformation, we obtain two new types of exponential-and-rational mixed soliton solutions for the defocusing nonlocal nonlinear Schrödinger equation. We reveal that the first type of solution can display a large variety of interactions among two exponential solitons and two rational solitons, in which the standard elastic interaction properties are preserved and each soliton could be either the dark or antidark type. By developing the asymptotic analysis method, we also find that the second type of solution can exhibit the elastic interactions among four mixed asymptotic solitons. But in sharp contrast to the common solitons, the mixed asymptotic solitons have the t -dependent velocities and their phase shifts before and after interaction also grow with | t | in the logarithmical manner. In addition, we discuss the degenerate cases for such two types of mixed soliton solutions when the four-soliton interaction reduces to a three-soliton or two-soliton interaction. Highlights • We derive two new types of exponential-and-rational mixed soliton solutions. • The elastic interactions are discovered among exponential and rational solitons, or among mixed solitons. • The mixed asymptotic solitons have the t-dependent velocities and phase shift upon an interaction. • The asymptotic analysis method is developed by considering the balance between the algebraic and exponential terms. [ABSTRACT FROM AUTHOR]

Abstract A study of high-order soliton matrices for Sasa–Satsuma equation in the framework of the Riemann–Hilbert problem approach is presented. Through a standard dressing procedure, soliton matrices for simple zeros and elementary high-order zeros in the Riemann–Hilbert problem for Sasa–Satsuma equation are constructed, respectively. It is noted that pairs of zeros are simultaneously tackled in the situation of the high-order zeros, which is different from other NLS-type equation. Furthermore, the generalized Darboux transformation for Sasa–Satsuma equation is also presented. Moreover, collision dynamics along with the asymptotic behavior for the two-solitons are analyzed, and long time asymptotic estimations for the high-order one-soliton are concretely calculated. In this case, two double-humped solitons with nearly equal velocities and amplitudes can be observed. [ABSTRACT FROM AUTHOR]

Abstract Stochastic approximation (SA) is a general framework for analyzing the convergence of a large collection of stochastic root-finding algorithms. The Kiefer–Wolfowitz and stochastic gradient algorithms are two well-known (and widely used) examples of SA. Because of their applicability to a wide range of problems, many results have been obtained regarding the convergence properties of SA procedures. One important reference in the literature, Fabian (1968), derives general conditions for the asymptotic normality of the SA iterates. Since then, many results regarding asymptotic normality of SA procedures have relied heavily on Fabian's theorem. Unfortunately, some of the assumptions of Fabian's result are not applicable to some modern implementations of SA in control and learning. In this paper we explain the nature of this incompatibility and show how Fabian's theorem can be generalized to address the issue. [ABSTRACT FROM AUTHOR]

To consider the effect of cross diffusion more rigorously, the onset and the growth of the gravitational instabilities in a Hele-Shaw cell saturated with ternary solution are analyzed by considering all cross diffusion coefficients. Through the asymptotic analysis, we identify the double-diffusive (DD)-, diffusive-layer convection (DLC)- and extended double diffusive (EDD)-type instability regimes. To support the asymptotic stability analysis, new linear stability equations are derived in the global domain and then transformed into the similar domain. In the similar domain, we prove that initially the system is unconditionally stable. For transient stability analysis, the linear stability equations are solved by employing quasi-steady state approximations (QSSA’s). To avoid the limit of the conventional QSSAz, we obtain the critical time for the onset of instability motion using the QSSA in the similar domain (QSSAζ). [ABSTRACT FROM AUTHOR]

Abstract Capillary–gravity waves generated by a steadily translating disturbance are studied via a direct analysis based on the geometrical relationship between dispersion curves on the Fourier plane and the corresponding wave pattern on the free surface, through which wave crestlines, wavelength, cusp angles and phase & group velocities are explicitly obtained. [ABSTRACT FROM AUTHOR]

Abstract The lubrication theory is mostly concerned with the behaviour of a lubricant flowing through a narrow gap. Motivated by the experimental findings from the tribology literature, we take the lubricant to be a micropolar fluid and study its behaviour in a thin domain with rough boundary. Instead of considering (commonly used) simple zero boundary conditions, we impose physically relevant (nonzero) boundary conditions for the microrotation and perform the asymptotic analysis of the corresponding 3D boundary value problem. We formally derive a simplified mathematical model acknowledging the roughness-induced effects and the effects of the nonzero boundary conditions on the macroscopic flow. Using the obtained asymptotic model, we study numerically the influence of the roughness on the performance of a linear slider bearing. The numerical results clearly indicate that the use of the rough surfaces may contribute to enhance the mechanical performance of such device. [ABSTRACT FROM AUTHOR]

We present a one-dimensional model describing the blood flow through a moderately curved and elastic blood vessel. We use an existing two dimensional model of the vessel wall along with Navier−Stokes equations to model the flow through the channel while taking factors, namely, surrounding muscle tissue and presence of external forces other than gravity into account. Our model is obtained via a dimension reduction procedure based on the assumption of thinness of the vessel relative to its length. Results of numerical simulations are presented to highlight the influence of different factors on the blood flow. [ABSTRACT FROM AUTHOR]

In the continuous casting of steel, solidification begins at a triple point where solid steel, molten steel and molten flux meet; the motion of this point determines how surface defects known as oscillation marks (OSMs) are formed. Here, under a number of simplifying assumptions, we derive an asymptotic model in 15 dimensionless parameters that describes the relevant momentum and heat transfer for the process, and involves both surface tension at the meniscus between molten flux and molten steel and solidification; further development couples an earlier lubrication-theory model for the region below the triple point to a reduced model for the region above that is based around a regular perturbation treatment of the Navier Stokes equations in terms of the capillary number. The resulting problem is then broken up into a hierarchy of four sub-problems; the first one – for the velocity field in the molten flux – is considered in depth. A numerical algorithm is developed for an isothermal situation in which the triple point moves only perpendicular to the casting direction; this involves the solution of a novel “moving point” problem to determine motion of the triple point. Comparison of model and experimental results indicates that this reduced model could produce OSMs having the observed depth if the triple point were not too far below the top of the meniscus; otherwise, the computed marks would be too deep. The analysis also tentatively relates the location of the triple point to the fold- and overflow-type OSMs that generally form in practice. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study a time-dependent flow of an incompressible micropolar fluid through a pipe with arbitrary cross-section. The effective behavior of the flow is found by means of rigorous asymptotic analysis with respect to the small parameter representing the pipe's thickness. The complete asymptotic expansion (up to an arbitrary order) of the solution is constructed with detailed analysis of the boundary layers provided. The convergence of the expansion is proved justifying the usage of the formally derived asymptotic model. [ABSTRACT FROM AUTHOR]

Abstract We study the asymptotic dynamics of dark energy as a mixture of presssureless matter and an interacting vacuum component. We find that the only dynamics compatible with current observational data favours an asymptotically vanishing matter-vacuum energy interaction in a model where dark energy is simulated by a generalised Chaplygin gas cosmology. [ABSTRACT FROM AUTHOR]

Abstract Theoretical derivation of the perturbed transport due to a sudden weak impact in a presumed slab-like region filled with solid-gouge and vacancies was conducted. The induced transport which is of the second order is created by a small-amplitude surface elastic wave propagating along the flexible interface by considering the weakly nonlinear coupling between the interfaces and the slip effect. We simplify the original system of lower-order partial differential equations (related to the momentum and mass transport) to one single higher-order quasi-linear partial differential equation in terms of the unknown stream function. Via numerical searching we identify the possible critical threshold values for zero-flux states corresponding to certain Navier-slip parameter and wave number which could be relevant to the possible seismic reversal or disappearance of moving of solid-gouge. Our numerical results are useful to the seismic pattern recognition together with synthetic earthquake catalogs. Graphical abstract Highlights • We capture the critical behavior of entrained transport via wavy interfaces. • Wave number as well as velocity slip are crucial to the entrained transport. • Complicated evolutional pattern as well as crucial parameters are shown. [ABSTRACT FROM AUTHOR]

Nanoscale solidification is becoming increasingly relevant in applications involving ultra-fast freezing processes and nanotechnology. However, thermal transport on the nanoscale is driven by infrequent collisions between thermal energy carriers known as phonons and is not well described by Fourier’s law. In this paper, the role of non-Fourier heat conduction in nanoscale solidification is studied by coupling the Stefan condition to the Guyer–Krumhansl (GK) equation, which is an extension of Fourier’s law, valid on the nanoscale, that includes memory and non-local effects. A systematic asymptotic analysis reveals that the solidification process can be decomposed into multiple time regimes, each characterised by a non-classical mode of thermal transport and unique solidification kinetics. For sufficiently large times, Fourier’s law is recovered. The model is able to capture the change in the effective thermal conductivity of the solid during its growth, consistent with experimental observations. The results from this study provide key quantitative insights that can be used to control nanoscale solidification processes. [ABSTRACT FROM AUTHOR]

In this study, we employ the well-known method of a singularly perturbed vector field (SPVF) and its application to the thermal runaway of diesel spray combustion. Given a system of governing equations, consisting of hidden multi-scale variables, the SPVF method transfers and decomposes such a system into fast and slow singularly perturbed subsystems. The resulting subsystem enables us to better understand the complex system and simplify the calculations. Powerful analytical, numerical, and asymptotic methods (e.g., the method of slow invariant manifolds and the homotopy analysis method) can subsequently be applied to each subsystem. In this paper, we compare the results obtained by the methods of slow invariant manifolds and SPVF, as applied to the spray (polydisperse) droplets combustion model. [ABSTRACT FROM AUTHOR]

We consider a system of two coupled integro-differential equations modelling populations of healthy and cancer cells under chemotherapy. Both populations are structured by a phenotypic variable, representing their level of resistance to the treatment. We analyse the asymptotic behaviour of the model under constant infusion of drugs. By designing an appropriate Lyapunov function, we prove that both cell densities converge to Dirac masses. We then define an optimal control problem, by considering all possible infusion protocols and minimising the number of cancer cells over a prescribed time frame. We provide a quasi-optimal strategy and prove that it solves this problem for large final times. For this modelling framework, we illustrate our results with numerical simulations, and compare our optimal strategy with periodic treatment schedules. [ABSTRACT FROM AUTHOR]

The kernel-based regularization method has two core issues: kernel design and hyperparameter estimation. In this paper, we focus on the second issue and study the properties of several hyperparameter estimators including the empirical Bayes (EB) estimator, two Stein’s unbiased risk estimators (SURE) (one related to impulse response reconstruction and the other related to output prediction) and their corresponding Oracle counterparts, with an emphasis on the asymptotic properties of these hyperparameter estimators. To this goal, we first derive and then rewrite the first order optimality conditions of these hyperparameter estimators, leading to several insights on these hyperparameter estimators. Then we show that as the number of data goes to infinity, the two SUREs converge to the best hyperparameter minimizing the corresponding mean square error, respectively, while the more widely used EB estimator converges to another best hyperparameter minimizing the expectation of the EB estimation criterion. This indicates that the two SUREs are asymptotically optimal in the corresponding MSE senses but the EB estimator is not. Surprisingly, the convergence rate of two SUREs is slower than that of the EB estimator, and moreover, unlike the two SUREs, the EB estimator is independent of the convergence rate of Φ T Φ ∕ N to its limit, where Φ is the regression matrix and N is the number of data. A Monte Carlo simulation is provided to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

We present asymptotic and numerical solutions for the axisymmetric diverging radial flow of a viscoplastic Bingham fluid in narrow gaps of varying thickness. The asymptotic solution by Muravleva (2017) is used, which is compared with the finite element analysis result. The result clarifies the recent confusion discussed by Zou et al. (2021) and the articles referred to therein. The viscosity regularization error is also discussed briefly. The flow kinematics is investigated by using the non-persistence-of-straining tensor developed by Thompson and Souza Mendes (2005). It is noted that the local kinematics of the diverging radial flow can be significantly affected by the variable gap thickness, especially in the pseudo-plug region. • Compared asymptotic and numerical solutions of the diverging radial flow. • Presented flow kinematics by using the non-persistence-of-straining. • Investigated the effect of variable gap thickness on the flow structure. [ABSTRACT FROM AUTHOR]

The electro-elastic problem in a three-dimensional thin domain Ω ɛ is considered. In modeling the contact the Coulomb free boundary friction condition is used. First, we show the variational formulation of the problem and give the existence and the uniqueness of the solution. Then, we study the asymptotic analysis when then the small parameter ɛ tends to zero. A limit problem, the uniqueness result of the limit displacement and electric potential are obtained. [ABSTRACT FROM AUTHOR]

The SIR (Susceptible–Infected–Removed) is one of the simplest models for epidemic outbreaks. The present paper derives a novel, simple, analytical asymptotic solution for the I-variable, which is valid on the entire real line. Connections with the Gompertz and Gumbel distributions are also demonstrated. The approach is applied to the ongoing coronavirus disease 2019 (COVID-19) pandemic in four European countries — Belgium, Italy, Sweden, and Bulgaria. The reported raw incidence data from the outbreaks in 2020–2021 have been fitted using constrained least squares. It is demonstrated that the asymptotic solution can be used successfully for parametric estimation either in stand-alone mode or as a preliminary step in the parametric estimation using numerical inversion of the exact parametric solution. [ABSTRACT FROM AUTHOR]

We study a modified Kadomtsev–Petviashvili (mKP) equation with variable coefficients, which has important applications in fluid dynamics, ferromagnetics and plasma. The Lax pair, Hirota bilinear form and Darboux transformation (DT) are obtained through the two-singular manifold method. The N -soliton solution with Grammian type in a compact determinant representation is derived from the N -fold DT. A complete classification of the mKP-type solitons is given, namely, the bright and dark solitons, as well as resonant bright and dark solitons. Dynamics of the nonautonomous solitons with parabolic, periodic and kink shapes under different kinds of variable-coefficient oscillations are shown. Interactions between the nonautonomous two bright solitons and two resonant bright solitons are discussed through the asymptotic analysis method. [ABSTRACT FROM AUTHOR]

Learning curves of simple perceptron were derived here. The learning curve of the perceptron learning with noisy teacher was shown to be non-monotonic, which has never appeared even though the learning curves have been analyzed for half a century. In this paper, we showed how this phenomenon occurs by analyzing the asymptotic property of the perceptron learning using a method in systems science, that is, calculating the eigenvalues of the system matrix and the corresponding eigenvectors. We also analyzed the AdaTron learning and the Hebbian learning in the same way and found that the learning curve of the AdaTron learning is non-monotonic whereas that of the Hebbian learning is monotonic. [ABSTRACT FROM AUTHOR]

In this paper, we present an effective low-Mach number improvement for upwind schemes. The artificial viscosity of upwind schemes scales with 1 ∕ M a incurring a loss of accuracy for the Mach number approaching zero. The remedy is based on three steps: (i) the jump of the left and right states is split into the density diffusion part and velocity diffusion part; (ii) the velocity diffusion part is rescaled by multiplying a scaling function; (iii) the scaling function is only related to the local Mach number without the cut-off reference Mach number and meantime restricted by a shock senor. The resulting modification is very easily implemented and applied within Roe, HLL and Rusanov, etc. Then, asymptotic analysis and numerical experiments for a wide Mach number demonstrate that this novel approach is equipped with these attractive properties: (1) free from the cut-off global problem and damping checkerboard modes; (2) satisfying the correct M a 2 scaling of pressure fluctuations, the divergence constraint and a Poisson equation; (3) independent of Mach number in terms of accuracy; (4) better accurate and higher resolution in low Mach number regimes when compared with existing upwind schemes, and applicable for moderate or high Mach numbers. Thus, the proposed modification is expected to provide as an excellent and reliable candidate to simulate turbulent flows at all Mach numbers. [ABSTRACT FROM AUTHOR]

The expansion of a bacterial biofilm on an agar substrate is modeled as a system of Föppl–von Kármán equations modified to include growth and coupling to a viscoelastic substrate. Analysis shows that wrinkles appear on the biofilm as a result of growth incompatibility and their frequency increases due to interaction with the agar layer. Simple cases of homogeneous radial and azimuthal growth are approximated by cone and corona solutions of the Monge–Ampère equation that are corrected by corner and boundary layers. A weak formulation of the problem allows us to express in-plane elastic strains and Airy potential solely in terms of the vertical displacement. We have developed a numerical method based on finite elements and simulated biofilm deformation for wide spectra of different growths. For heterogeneous growth, we find wrinkled patterns that are combinations of cones and coronas. [ABSTRACT FROM AUTHOR]

In this study, we present a method of numerical homogenization, combining asymptotic analysis and finite element modelling, to establish constitutive laws of heterogeneous materials with periodic microstructures tacking into account high-order strain gradients. By performing asymptotic analysis, the problem of local homogenization was split up into differential equations of different orders, which were solved using finite element modelling. This approach allows researcher to accurately calculate high-order stiffness tensors from representative volume elements (RVEs) with complicated microstructures and geometrical forms. The efficiency and accuracy of this approach were verified by means of numerical examples. The mechanical implications, consistency, and strain energy convexity of the strain gradient constitutive laws, obtained using the proposed approach, are analyzed on the basis of the numerical results. [ABSTRACT FROM AUTHOR]

We are interested in a time harmonic acoustic problem in a waveguide with locally perturbed sound hard walls. We consider a setting where an observer generates incident plane waves at −∞ and probes the resulting scattered field at −∞ and +∞. Practically, this is equivalent to measure the reflection and transmission coefficients respectively denoted R and T . In [9] , a technique has been proposed to construct waveguides with smooth walls such that R = 0 and | T | = 1 (non-reflection). However the approach fails to ensure T = 1 (perfect transmission without phase shift). In this work, first we establish a result explaining this observation. More precisely, we prove that for wavenumbers smaller than a given bound k ⋆ depending on the geometry, we cannot have T = 1 so that the observer can detect the presence of the defect if he/she is able to measure the phase at +∞. In particular, if the perturbation is smooth and small (in amplitude and in width), k ⋆ is very close to the threshold wavenumber. Then, in a second step, we change the point of view and, for a given wavenumber, working with singular perturbations of the domain, we show how to obtain T = 1 . In this case, the scattered field is exponentially decaying both at −∞ and +∞. We implement numerically the method to provide examples of such undetectable defects. [ABSTRACT FROM AUTHOR]

The behavior analysis of complex structures like corrugated panels usually requires high-cost shell modeling which is an obstacle in subsequent studies such as parametric study and optimization. To overcome the difficulty, many homogenization models in which equivalent orthotropic plates replaces the original shells have been proposed. However, there is a lack of investigations for verifying their accuracy and reliability. In this paper, the cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) is integrated with typical homogenization models to give some homogenization methods for free vibration analyses of trapezoidally and sinusoidally corrugated panels. Using the results of ANSYS and ABAQUS shell simulations as references, the accuracy and reliability of the homogenization methods are illustrated through several numerical examples. The influences of geometric parameters such as the number of corrugation units, corrugation amplitude, trough angle, and panel thickness are studied and some important remarks about the performances of these methods are derived. [ABSTRACT FROM AUTHOR]

We analyze the dynamics of a class B laser with optoelectronic delayed feedback and periodic modulation of the delay time. For the delay-differential model, we describe asymptotically spike regimes with various properties, namely, with inter-spikes intervals greater than delay, less delay, and a mixed type. Sets of initial conditions in an infinite-dimensional phase space are determined for each type of pulsed solutions. The dynamics of each regime is described by the dynamics of a certain finite-dimensional mapping. By computing the maps we obtain the modulation parameters at which the chaotic spiking of desired structure is realized. We demonstrate bistability of chaotic spiking, their intermittence and merge. [ABSTRACT FROM AUTHOR]

We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a regular perturbation method from asymptotic analysis of partial differential equations, we derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2-hypergeometric stochastic volatility model. The asymptotic convergence of the method is proved under appropriate regularity conditions, and a multi-stage method for improving the quality of the approximation is discussed. Numerical examples are also provided. [ABSTRACT FROM AUTHOR]

This work proposes new transmission conditions at the interfaces between the layers of a three-dimensional composite structures. The proposed transmission conditions are obtained by applying the asymptotic expansion technique in the framework of Lagrange-Hamilton's principle. The proposed conditions take into account interfacial effects of higher order, thus representing an extension of the classical zero-thickness interface models. In particular, the (small) thickness of the interface together with its inertia, stiffness and anisotropy are accounted for. The effect of the transmission conditions on the band structure of Bloch–Floquet waves propagating in a one dimensional phononic crystal is discussed based on numerical results. [ABSTRACT FROM AUTHOR]

This work aims at designing a numerical strategy towards assessing the nocivity of a small defect in terms of its size and position in a structure, at low computational cost, using only a mesh of the defect-free reference structure. The modification of the fields induced by the presence of a small defect is taken into account by using asymptotic corrections of displacements or stresses. This approach helps determining the potential criticality of defects by considering trial micro-defects with varying positions, sizes and mechanical properties, taking advantage of the fact that parametric studies on defect characteristics become feasible at virtually no extra computational cost. The proposed treatment is validated and demonstrated on two numerical examples involving 2D elastic configurations. [ABSTRACT FROM AUTHOR]

Starting from isentropic compressible Navier–Stokes equations with growth term in the continuity equation, we rigorously justify that performing an incompressible limit one arrives to the two-phase free boundary fluid system. [ABSTRACT FROM AUTHOR]

Mode II creeping crack tip fields with three terms from an asymptotic analysis under plane strain conditions are presented in this paper. Comparisons among the three term asymptotic solutions, finite element (FE) results and HRR solutions are made for boundary layer model (BLM) and single edge notched (SEN) specimen. Two typical power-law materials having different creep exponents are adopted for the numerical analyses. Results show that the three term asymptotic solutions coincide with the FE results quite well for all cases at both transient creep and extensive creep stages. It indicates that the three term solution is sufficient to characterize the full mechanics field of a mode II creep crack under various conditions. Some typical fracture parameters under creep conditions are extended and discussed. The effect of creep time on the integration constant I n under mode II case is also studied and discussed. [ABSTRACT FROM AUTHOR]

Inhomogeneity and anisotropy play a crucial role in attributing articular cartilage its properties. The frictionless contact involves two thin biphasic transversely isotropic transversely homogeneous (TITH) cartilage layers firmly attached onto rigid substrates and shaped as elliptic paraboloids of different radii. Using asymptotic techniques, a solution to the deformation problem of such material has been recently obtained extending previous ones referred to homogeneous materials. The layer itself is thin in comparison with the size of the contact area and the observed time is shorter than the hydrogel characteristic time. The emerging three-dimensional contact problem is solved in closed-form and numerical benchmarks for constant and oscillating loads are given. The results are shown in terms of contact pressure and approach of the bones. The latter is derived to be directly proportional to the contact area. Existing experimental data are reinterpreted in view of the current model formulation. Comparisons are made with existing solutions for homogeneous biphasic materials in order to underline the functional importance of inhomogeneity in spreading the contact pressure distribution across the contact area. Particular attention is paid to the applicability of the retrieved formulas for interpreting measurements of in vivo experiments. Future directions are also prospected. [ABSTRACT FROM AUTHOR]

This paper proposes a mathematical model of a pressure-sensitive conductive fabric sensor, which adopts the technique of electrical impedance tomography (EIT) with a composite fabric being capable of changing its effective electrical property due to an applied pressure. We model the composite fabric from an electrically conductive yarn and a sponge-like non-conductive fabric with high pore density, and the conductive yarn is woven in a wavy pattern to possess a pressure-sensitive conductive property, in the sense of homogenization theory. We use a simplified version of EIT technique to image the pressure distribution associated with the conductivity perturbation. A mathematical ground for the effective conductivity in one-direction is provided. We conduct an experiment to test the feasibility of the proposed pressure sensor. [ABSTRACT FROM AUTHOR]

Conduction heat transfer through building construction elements is one of the main components of space heating and cooling loads, and, thus, one of the key aspects when planning sustainable energy designs in the building sector. The Response Factors (RF) method sets the base for related dynamic calculations implemented by most well-known Building Energy Simulation (BES) software, and it represents a research topic of present interest. In this regard, this work introduces a new method for calculating conduction Response Factors in building multilayer constructions, based on the definition of an approximated wall model through Frequency–Domain Spline Interpolation (FDSI) and asymptotic analysis. Its conceptual development as well as first validations comparing with existing methods from previous literature are presented. Finally, as a result of applying a table-lookup approach and the possibility of pre-calculating most of the involved operations, an accurate, fast and easy-to-code algorithm is obtained, which constitutes a promising alternative to improve the current state-of-art calculation procedures. [ABSTRACT FROM AUTHOR]

We study the static equilibria of a simplified Leslie–Ericksen model for a unidirectional uniaxial nematic flow in a prototype microfluidic channel, as a function of the pressure gradient G and inverse anchoring strength, B . We numerically find multiple static equilibria for admissible pairs ( G , B ) and classify them according to their winding numbers and stability. The case G = 0 is analytically tractable and we numerically study how the solution landscape is transformed as G increases. We study the one-dimensional dynamical model, the sensitivity of the dynamic solutions to initial conditions and the rate of change of G and B . We provide a physically interesting example of how the time delay between the applications of G and B can determine the selection of the final steady state. [ABSTRACT FROM AUTHOR]

For typical two-layer wetland flows where wind occurs frequently, indicators for flow and contaminant dispersion with wind effect are considered in this paper. Based on the general formulation for porous media flows, the velocity distribution of a fully developed flow through a wetland is illustrated, with that for a single-layer wetland flow under wind recovered as a special case. And the contrary wind of high speed might result in the appearance of an inverse-flow layer. For the more complex case of a two-layer wetland flow under wind, the more simplified method of asymptotic analysis is adopted instead of Aris's method of concentration moments to determine the dispersivity in terms of the longitudinal evolution of the depth-averaged concentration. And it is illustrated with the effect of dimensionless parameters. The velocity profile and environmental dispersivity for the two-layer wetland flow in the absence of wind can be included as a limiting case. Both the direction and the strength of the wind can affect the environmental dispersivity considerably under long-term evolution. Analytical solutions for the mean concentration and the region influenced by the contaminant cloud are derived. And for the instantaneous emission of typical contaminant constituents, the related indicators for water quality assessment, such as the critical length and duration of the influenced region are illustrated. The results show that the critical length and duration of the concentration cloud can change considerably because of the wind and vegetation heterogeneity. [ABSTRACT FROM AUTHOR]