Search

In this paper, we consider the multi-dimensional distributed-order time-fractional diffusion equation with the unit density function. We introduce the new Volterra–Bessel function and give the integral representations of fundamental solutions of equations in terms of this function in the whole- and half-space. The fractional moments of fundamental solutions are also provided in the higher dimensions using the Mellin transforms. We further apply steepest descent method to find the asymptotic behaviors of solutions using the Schläfli integral of the Volterra–Bessel function. In this respect, we study the asymptotic analysis of the Volterra–Bessel function with the large parameters, and subsequently obtain the asymptotic behaviors of fundamental solutions with a discussion on the large space variable, large time variable, higher dimensions and small diffusivity constant. [ABSTRACT FROM AUTHOR]

We study the asymptotic behaviour of a linear optimal control problem posed on a locally periodic rapidly oscillating domain. We consider an $ L^2 $ L 2 -cost functional constrained by a Poisson problem having a mixed boundary condition: we assume a homogeneous Neumann condition on the oscillating part of the boundary and a homogeneous Dirichlet condition on the remaining part. [ABSTRACT FROM AUTHOR]

This work deals with the solution and asymptotic analysis for a porous-elastic system with internal damping of the fractional derivative type. We consider an augmented model. The energy function is presented and establishes the dissipativity property of the system. We use the semigroup theory. The existence and uniqueness of the solution are obtained by applying the well-known Lumer-Phillips Theorem. We present two results for the asymptotic behavior: Strong stability of the C 0 -semigroup associated with the system using Arendt-Batty and Lyubich-Vũ's general criterion and polynomial stability applying Borichev and Tomilov's Theorem. [ABSTRACT FROM AUTHOR]

We consider a general regularized variational model for simulating wetting/dewetting phenomena arising from solids or fluids. The regularized model leads to the appearance of a precursor layer which covers the bare substrate, with the precursor height depending on the regularization parameter ε . This model enjoys lots of advantages in analysis and simulations. With the help of the precursor layer, the spatial domain is naturally extended to a larger fixed one in the regularized model, which leads to both analytical and computational eases. There is no need to explicitly track the contact line motion, and difficulties arising from free boundary problems can be avoided. In addition, topological change events can be automatically captured. Under some mild and physically meaningful conditions, we show the positivity-preserving property of the minimizers of the regularized model. By using formal asymptotic analysis and Γ -limit analysis, we investigate the convergence relations between the regularized model and the classical sharp-interface model. Finally, numerical results are provided to validate our theoretical analysis, as well as the accuracy and efficiency of the regularized model. [ABSTRACT FROM AUTHOR]

In this paper, we present a new model as an alternative to the classical 3D Richards model for the description of water flow in shallow aquifers. The new model is designed to achieve three goals. First, it provides a good approximation to the Richards model over a wide range of time scales. More specifically we show that both models characterize a flow with the same dominant components when the ratio of the horizontal length to the depth of the aquifer is small. Second, the new model accurately describes the velocity field. In particular, it is not based on the Dupuit hypothesis, which is often used in the context of shallow aquifers. This allows the new model to be well accurate even in the presence of wells and in aquifers with variable bedrock. Third, the new model can be viewed as a coupling of numerous 1D vertical Richards problems with a 2D elliptic one. In practice, this coupling is treated numerically using a Picard fixed point scheme, avoiding the need to solve any three-dimensional problem. This results in a significant reduction in computational cost compared to solving the 3D Richards problem directly. [ABSTRACT FROM AUTHOR]

This paper concerns a diffusive predation model with nonlinear growth, cross-diffusion and protection zone terms. The main purpose is to investigate the effects of nonlinear growth and cross-diffusion on the coexistent solution when protection zone is present. Firstly, a priori estimate and the existence of positive solutions are discussed, including local and global existence. Then, some asymptotic properties of coexistent solutions induced by the mortality rate, nonlinear growth of predator and cross-diffusion are analyzed. It is revealed that there exist critical values related to certain principal eigenvalues such that the nonlinear growth, cross-diffusion and protection zone all have significant effects on the coexistent solutions; as far as the nonlinear growth concerned, we find that it has important influences on the coexistence region of two species undoubtedly. Biologically, this implies that these critical values greatly affect the survival of species. [ABSTRACT FROM AUTHOR]

We perform an asymptotic static analysis on a simple two degrees of freedom structure, made up of a highly stiff bar and two springs, which shows two different linear behaviours and different finite stiffness depending on the magnitude of an applied static force. Both regimes as well as the non-linear transition between them occur in the framework of small forces and displacements. The problem gives physical insight to the relations between linearity and small displacement hypothesis and it is suitable for a first course in asymptotic analysis to students with basic skills in structural or rational mechanics. [ABSTRACT FROM AUTHOR]

Asymptotic analysis for an elastic layer under light fluid loading was developed. The ratio of fluid and solid densities was chosen as the main small parameter determining a novel scaling. The leading- and next-order approximations were derived from the full dispersion relation corresponding to long-wave, low-frequency, antisymmetric motions. The asymptotic plate models, including the equations of motion and the impenetrability condition, motivated by the aforementioned shortened dispersion equations, were derived for a plane-strain setup. The key findings included, in particular, the necessity of taking into account transverse plate inertia at the leading order, which is not the case for heavy fluid loading. In addition, the transverse shear deformation, rotation inertia, and a number of other corrections appeared at the next order, contrary to the previous asymptotic developments for fluid-loaded plates not assuming a light fluid loading scenario. [ABSTRACT FROM AUTHOR]

In this work, we study the asymptotic characteristics of high‐order solitons for the focusing Kundu–Eckhaus (KE) equation. Based on the loop group theory, we construct the general Darboux transformation within the framework of Riemann–Hilbert problems to derive the general high‐order soliton solution. Using high‐order Bäcklund transformation, we derive the leading order term of the determinant solution to obtain the asymptotic representation for the high‐order soliton solution. Furthermore, this method is also extended to the construction of more general high‐order cases with multiple poles. We further find that if a soliton propagates along the logarithm characteristic curve, the high‐order soliton can be decomposed into n$$ n $$ individual solitons with the same amplitude and velocity. Finally, these solutions are theoretically and graphically analyzed in detail. [ABSTRACT FROM AUTHOR]

For the discrete PT-symmetric nonlinear Schrödinger (dPTNLS) equation, this paper gives a rigorous proof of the N-fold Darboux transformation (DT) and especially verifies the PT-symmetric relation between transformed potentials in the Lax pair. Meanwhile, some determinant identities are developed in completing the proof. When the tanh-function solution is directly selected as a seed for the focusing case, the onefold DT yields a three-soliton solution that exhibits the solitonic behavior with a wide range of parameter regimes. Moreover, it is shown that the solution contains three pairs of asymptotic solitons, and that each asymptotic soliton can display both the dark and antidark soliton profiles or vanish as t → ± ∞. It indicates that the focusing dPTNLS equation admits a rich variety of soliton interactions over the nonzero background, behaving like those in the continuous counterpart. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new integrable fractional Fokas--Lenells equation by using the completeness of the squared eigenfunctions, dispersion relation, and inverse scattering transform. To solve this equation, we employ the Riemann--Hilbert approach. Specifically, we focus on the case of the reflectionless potential with a simple pole for the zero boundary condition. And we provide the fractional N-soliton solution in determinant form. In addition, we prove the fractional one-soliton solution rigorously. Notably, we demonstrate that as |t| → ∞, the fractional N-soliton solution can be expressed as a linear combination of N fractional single-soliton solutions. [ABSTRACT FROM AUTHOR]

In this article, we introduce the notions of l-transfer lower continuous and q-level intersectionally closed for set-valued mappings with respect to the lower set less relation. Then, we obtain some existence results for strict weak l-efficient solutions of such set-valued mappings. Moreover, we prove some existence results for nonconvex set optimization problems via asymptotic analysis tools, in the setting of the Banach spaces equipped with a Hausdorff topology σ coarser than the norm topology. [ABSTRACT FROM AUTHOR]

How does the interplay between selection, mutation and horizontal gene transfer modify the phenotypic distribution of a bacterial or cell population? While horizontal gene transfer, which corresponds to the exchange of genetic material between individuals, has a major role in the adaptation of many organisms, its impact on the phenotypic density of populations is not yet fully understood. We study an elliptic integro-differential equation describing the evolutionary equilibrium of the phenotypic density of an asexual population. In a regime of small mutational variance, we characterize the solution which results from the balance between competition for a resource, mutation and horizontal gene transfer. We show that in a certain range of parameters polymorphic equilibria exist, which means that the phenotypic density may concentrate around several dominant traits. Such polymorphic equilibria result from an antagonist interplay between horizontal gene transfer and selection, while similar models which neglect the transfer lead only to monomorphic equilibria. [ABSTRACT FROM AUTHOR]

We present and analyze a new derivation of the meso-level behavior of a discrete microscopic model of heat transfer. This construction is based on the principle of dynamic consistency. Our work reproduces and corrects, when needed, all the major previous expressions which provide modifications to the standard heat PDE. However, unlike earlier efforts, we do not allow the microscopic level parameters to have zero limiting values. We also give insight into the difficulties of constructing physically valid heat equations within the framework of the general mathematically inequivalent of difference and differential equations. [ABSTRACT FROM AUTHOR]

Being able to characterise objects at low frequencies, but in situations where the modelling error in the eddy current approximation of the Maxwell system becomes large, is important for improving current metal detection technologies. Importantly, the modelling error becomes large as the frequency increases, but the accuracy of the eddy current model also depends on the object topology and on its materials, with the error being much larger for certain geometries compared to others of the same size and materials. Additionally, the eddy current model breaks down at much smaller frequencies for highly magnetic conducting materials compared to non-permeable objects (with similar conductivities, sizes and shapes) and, hence, characterising small magnetic objects made of permeable materials using the eddy current at typical frequencies of operation for a metal detector is not always possible. To address this, we derive a new asymptotic expansion for permeable highly conducting objects that is valid for small objects and holds not only for frequencies where the eddy current model is valid but also for situations where the eddy current modelling error becomes large and applying the eddy approximation would be invalid. The leading-order term we derive leads to new forms of object characterisations in terms of polarizability tensor object descriptions where the coefficients can be obtained from solving vectorial transmission problems. We expect these new characterisations to be important when considering objects at greater stand-off distance from the coils, which is important for safety critical applications, such as the identification of landmines, unexploded ordnance and concealed weapons. We also expect our results to be important when characterising artefacts of archaeological and forensic significance at greater depths than the eddy current model allows and to have further applications parking sensors and improving the detection of hidden, out-of-sight, metallic objects. [ABSTRACT FROM AUTHOR]

The problem of description of quasi-static behavior is studied for a planar thermoelastic body incorporating an inhomogeneity, which geometrically is a strip with a small cross-section. This problem contains a small positive parameter δ describing the thickness of the inhomogeneity, i.e., the size of the cross-section. Relying on the variational formulation of the problem, we investigate the behavior of solutions as δ tends to zero. As the result, by the version of the method of formal asymptotic expansions, we derive a closed limit model in which the inhomogeneity is thin (of zero width). After this, using the Galerkin method and the classical techniques of derivation of energy estimates, we prove existence, uniqueness, and stability of a weak solution to this model. [ABSTRACT FROM AUTHOR]

The heat exchange between a rigid body and a fluid is usually modelled by the Robin boundary condition saying that the heat flux through the interface is proportional to the difference between their temperatures. Such interface law describes only the unilateral heat exchange. The goal of this paper is to compare the Robin boundary condition starting with the transmission condition (the temperature and the flux continuity) using rigorous mathematical analysis. Our main results are the following. We first show that a generalized version of the Robin boundary condition can be justified. Second, we prove that replacing the generalized by the standard Robin condition can be justified for high convection velocity if the conductivity of the surrounding liquid is much lower than that of the body. On the other hand, if the fluid conducts much better than the body, then the effective boundary condition is shown not to be the Robin one, but it involves second-order derivatives. We strongly believe that those findings bring new insights to the physics of the heat exchange processes and, thus, could prove useful in engineering practice. [ABSTRACT FROM AUTHOR]

The main aim of this article is to study the Poisson type problem for anisotropic p-Laplace type equation on long cylindrical domains. The rate of convergence is shown to be exponential, thereby improving earlier known results for similar type of operators. The Poincaré inequality for a pseudo p-Laplace operator on an infinite strip-like domain is also studied and the best constant, like in many other situations in literature for other operators, is shown to be the same with the best Poincaré constant of an analogous problem set on a lower dimension. [ABSTRACT FROM AUTHOR]

The creation of hairpin or lambda vortices, typical for the early stages of the laminar-turbulent transition process in various boundary layer flows, in some sense may be associated with blow-up solutions of the Fisher--Kolmogorov--Petrovsky--Piskunov equation. In contrast to the usual applications of this nonlinear evolution equation of the reaction-diffusion type, the solution quantity in the present context needs to stay neither bounded nor positive. We focus on the solution behavior beyond a finite-time point blow-up event, which consists of two moving singularities (representing the cores of the vortex legs) propagating in opposite directions, and their initial motion is determined with the method of matched asymptotic expansions. After resolving subtleties concerning the transition between logarithmic and algebraic expansion terms regarding asymptotic layers, we find that the internal singularity structure resembles a combination of second- and first-order poles in the form of a singular traveling wave with a time-dependent speed imprinted through the characteristics of the preceding blow-up event. [ABSTRACT FROM AUTHOR]

High‐contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localization at low frequencies. We use an asymptotic framework to develop a landscape theory for high‐contrast systems that resonate in a subwavelength regime. Our from‐first‐principles asymptotic analysis yields a characterization in terms of the generalized capacitance matrix, giving a discrete approximation of the three‐dimensional scattering problem. We develop landscape theory for the generalized capacitance matrix and use it to predict the positions of three‐dimensional wave focusing and localization in random and non‐periodic systems of subwavelength resonators. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids have gained much attention due to their better stability, enhanced thermal conductivity, and physical strength. This manuscript investigates nanofluid flow, induced due to an infinite plate, which is moving (at a constant velocity) toward/receding from normal stagnation point flow. The surface of the plate is suspended and immersed with water as a base fluid and nanoparticles, namely Copper and Alumina. The flow is governed by Reynolds number (Re), which is proportional to the constant velocity of the moving plate and is an exact reduction of the Navier–Stokes equations. Moreover, Hiemenz's planar and Homann's axisymmetric flows normal to the stagnation point are considered. Heat transport analysis is carried out by using Cattaneo–Christov theory with Ohmic heating and heat source/sink effects. The governing equations are solved by bvp4c in MATLAB. The behavior of skin friction, flow, and energy distribution is perceived by variation of pertinent parameters. The numerical and asymptotic solutions are computed for the wall shear stress parameter. It is seen that the numerical solution matches its asymptotic behaviors over an intermediate range of small and large valued Reynolds number. The asymptotic values (small-Re) of wall stress reduces for plate advancing toward the stagnation-point flow and receding from the stagnation-point flow for Hiemenz and Homann flow. The increment in magnetic parameter reduced the fluid flow by generating a resistive force against it; however, the energy of the system is enhanced because of it. The augmentation of nanofluid volume fraction initiates the random motion among the nanoparticles which raises the temperature field. Thermal relaxation time parameter causes the particles to require supplementary time for the conduction of heat toward the adjacent particles, which declines the thermal transport. In general, the thermal transport is enhanced for the hybrid nanofluids rather than mono nanofluids. [ABSTRACT FROM AUTHOR]

We propose a general family of piecewise hyperbolic absolute risk aversion (PHARA) utilities, including many classic and non-standard utilities as examples. A typical application is the composition of a HARA preference and a piecewise linear payoff in asset allocation. We derive a unified closed-form formula of the optimal portfolio, which is a four-term division. The formula has clear economic meanings, reflecting the behavior of risk aversion, risk seeking, loss aversion and first-order risk aversion. We conduct a general asymptotic analysis to the optimal portfolio, which directly serves as an analytical tool for financial analysis. We compare this PHARA portfolio with those of other utility families both analytically and numerically. One main finding is that risk-taking behaviors are greatly increased by non-concavity and reduced by non-differentiability of the PHARA utility. Finally, we use financial data to test the performance of the PHARA portfolio in the market. [ABSTRACT FROM AUTHOR]

A simple HLLE-type scheme is proposed for all Mach number flows. In the proposed scheme, no extra wave structure is added in the HLLE scheme to resolve the shear wave while the contact wave is resolved by adding a wave structure similar to the HLLEM scheme. The resolution of the shear layers and the flow features at low Mach numbers is achieved by a velocity reconstruction method based on the face normal Mach number. Robustness against the numerical instabilities is achieved by scaling the velocity reconstruction function in the vicinity of shock with a multi-dimensional pressure sensor. The ability of the proposed scheme to resolve low Mach flow features is demonstrated through asymptotic analysis while the stability of the proposed scheme for strong shock is demonstrated through linear perturbation and matrix stability analyses. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems at high speeds and is capable of resolving the flow features at very low Mach numbers. • A new velocity reconstruction method for an all Mach number HLLE scheme. • Velocity reconstruction based on face normal Mach number and pressure function. • Velocity reconstruction resolves shear layers and low Mach flow features while presrving shock stability. • HLLEM type method for resolving contact wave while preserving shock stability. • Analytical and numerical demonstration of all Mach capability of the proposed scheme. [ABSTRACT FROM AUTHOR]

We derive asymptotic formulae in the limit when population size N tends to infinity for mean fixation times (conditional and unconditional) in a population with two types of individuals, A and B, governed by the Moran process. We consider only the case in which the fitness of the two types do not depend on the population frequencies. Our results start with the important cases in which the initial condition is a single individual of any type, but we also consider the initial condition of a fraction x ∈ (0 , 1) of A individuals, where x is kept fixed and the total population size tends to infinity. In the cases covered by Antal and Scheuring (Bull Math Biol 68(8):1923–1944, 2006), i.e. conditional fixation times for a single individual of any type, it will turn out that our formulae are much more accurate than the ones they found. As quoted, our results include other situations not treated by them. An interesting and counterintuitive consequence of our results on mean conditional fixation times is the following. Suppose that a population consists initially of fitter individuals at fraction x and less fit individuals at a fraction 1 - x . If population size N is large enough, then in the average the fixation of the less fit individuals is faster (provided it occurs) than fixation of the fitter individuals, even if x is close to 1, i.e. fitter individuals are the majority. [ABSTRACT FROM AUTHOR]

We study the Fredholm determinant of an integral operator associated to the hard edge Pearcey kernel. This determinant appears in a variety of random matrix and nonintersecting paths models. By relating the logarithmic derivatives of the Fredholm determinant to a 3 \times 3 Riemann-Hilbert problem, we obtain asymptotics of the determinant, which is also known as the large gap asymptotics for the corresponding point process. [ABSTRACT FROM AUTHOR]

Surface wave dispersion curves are widely used to constrain earth velocity structures and are important to compute theoretical synthetic seismograms with a mode-summation approach. While the computation of dispersion curves requires searching roots of nonlinear functions, some high-mode may be missed with improper choice of searching steps. The asymptotic distribution of eigenvalues of the elastic wave equation can be used as auxiliary information to design a sophisticated scheme to compute the surface wave dispersion curves. In this study, we show the Weyl's law, combined with the Liouville transformation, can be exploited to derive asymptotic eigenvalue counting functions of elastic surface waves in a horizontally stratified or radially heterogeneous medium. We also show the derived formulation according to the Weyl's law, in its simple case, agrees with previous studies. The derived asymptotic eigenvalue counting functions are validated by comparison with numerical results. This study demonstrates the Weyl's law can be used to derive eigenvalue counting functions of surface waves in elastic media, and it is also possible to be applied to more complex media. [ABSTRACT FROM AUTHOR]

We study kinetic models for swarming. The interaction between individuals is given by self-propelling and friction forces, alignment, and noise. We consider that each individual relaxes its velocity toward some average velocity, such that the total momentum does not change. We concentrate on fluid models obtained when the time and space scales become very large. We derive first and second order approximations. [ABSTRACT FROM AUTHOR]

We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a future null cone with a wider range of decaying profiles than previously considered. New estimates are then derived in order to prove that, for small data, the system has a unique global classical solution. We also show that the solution decays exponentially in (Bondi) time and that the radial decay is essentially polynomial, although containing logarithmic factors in some special cases. This improved asymptotic analysis allows us to show that, under appropriate and natural decaying conditions on the initial data, the future asymptotic solution is differentiable, up to and including spatial null-infinity, and approaches the de Sitter solution, uniformly, in a neighborhood of infinity. Moreover, we analyze the decay of derivatives of the solution up to second order showing the (uniform) C 2 -asymptotic stability of the de Sitter attractor in this setting. This corresponds to a surprisingly strong realization of the cosmic no-hair conjecture. [ABSTRACT FROM AUTHOR]

Summary: A refinement of a previous asymptotic analysis of the well‐known two‐capacitor circuit is presented. It rests on some mathematical results, which allow the originally conceived regularity constraint to be replaced with a new one, not only less restrictive but also and above all simpler and easier to check. On this basis, the main time domain diagrams of the circuit with the embedding switch are presented. In addition, the solution of the circuit in the transition interval is provided, and some calculations related to the distribution side of the analysis are also reconsidered and improved. [ABSTRACT FROM AUTHOR]

In this article, we study the influence of certain parameters on the stability conditions of the reaction front in a liquid medium. The mathematical model consists of the heat equation, the concentration equation and the Navier–Stockes equation under the Boussinesq approximation. An asymptotic analysis was performed using the approximation proposed by Zeldovich and Frank–Kamentskii to obtain the interface problem. A stability analysis was carried out to obtain a linearized problem which will be solved numerically using a multiquadric radial basis function method to find the convective threshold. This will allow us to conclude the effect of each parameter on the stability of the front, in particular the amplitude and the resonance frequency. [ABSTRACT FROM AUTHOR]

In our previous study (Part I), the anti-plane steady-state hyperbolic mode III fracture of a magneto-flexoelectric material was solved for the displacement, the polarization, and the magnetic fields. The solution, however, was based on the assumption of the development of strain discontinuities, and the propagation of the crack-tip was related to a critical shear strain. However, in the current study, the asymptotic details of the fields close to the crack-tip were investigated. The asymptotic analysis assumes strain continuity at the crack-tip (discontinuity in the strain gradients) and reveals the existence of a positive dynamic J-integral. The asymptotic analysis was performed not only for hyperbolic but also for elliptic conditions, and the energy release rate was calculated as a function of the crack-tip velocity in both regimes. These results are very different from those predicted by classical singular elastodynamics, where the dynamic J-integral is zero when super-shear is attained and there can be only an elliptic solution. Moreover, the results are very useful for couple-stress elastodynamics where equivalent length scales are present due to the analogy with flexoelectricity. [ABSTRACT FROM AUTHOR]

The influence of adding a seventh important elementary step to a six-step mechanism, previously employed for describing the asymptotic structure of normal-alkane droplet combustion supported by cool-flame chemistry in the negative-temperature-coefficient (NTC) range, is investigated by analytical methods. A development paralleling the classical activation-energy-asymptotic (AEA) analysis of the partial-burning regime, accompanied for the first time by an AEA analysis for a negative activation energy, to account properly for the removal of an important intermediate species, is pursued to make predictions of the combustion process, resulting in a revised asymptotic structure that agrees better with computational predictions based on detailed chemistry. [ABSTRACT FROM AUTHOR]

AbstractFlexibility design has been widely adopted in practice as a competitive strategy to respond effectively to uncertainties. In this article, we analyze the fulfillment flexibility for dual-channel retail networks, in which the firms should fulfill both online demands from retailing platforms and in-store offline demands. In particular, by setting the order of fulfillment, we find that a dual-channel retail network can be equivalently transformed to an online retail network with stochastic inventory and demand. By implementing copositive programming, we obtain an asymptotic robust lower bound for the ratio of expected sales to fully flexible expected sales under a K-chain design. This bound only depends on the partial moment information and support set of demands, rather than the complete demand distribution information. Interestingly, we derive the optimality of a K-chain in symmetric balanced networks and the performance of the K-chain under different distributions is robust. In addition, numerical experiments are conducted to further deliver some insights for practitioners. The uncertainties of in-store demand or inventory will reduce the expected sales while both fulfillment flexibility and safety inventory can be used to enhance the performance of a retail system. Finally, we find that the correlation coefficient between in-store demand and online demand will affect the decision-making significantly. [ABSTRACT FROM AUTHOR]

This paper reports the analytical results on the incompressible micropolar fluid flowing through a thin (or long) cylindrical pipe filled with porous medium. We start from the Brinkman-type system governing the filtration of the micropolar flow and perform the asymptotic analysis in the critical case characterized by the strong coupling between the velocity and microrotation. The error estimates are also derived providing the rigorous justification of the proposed effective model. [ABSTRACT FROM AUTHOR]

We consider the propagation of acoustic waves in a waveguide containing a penetrable dissipative inclusion. We prove that as soon as the dissipation, characterized by some coefficient η, is non zero, the scattering solutions are uniquely defined. Additionally, we give an asymptotic expansion of the corresponding scattering matrix when η → 0+ (small dissipation) and when η → +∞ (large dissipation). Surprisingly, at the limit η → +∞, we show that no energy is absorbed by the inclusion. This is due to the so-called skin-effect phenomenon and can be explained by the fact that the field no longer penetrates into the highly dissipative inclusion. These results guarantee that in monomode regime, the amplitude of the reflection coefficient has a global minimum with respect to η. The situation where this minimum is zero, that is when the device acts as a perfect absorber, is particularly interesting for certain applications. However it does not happen in general. In this work, we show how to perturb the geometry of the waveguide to create 2D perfect absorbers in monomode regime. Asymptotic expansions are justified by error estimates and theoretical results are supported by numerical illustrations. [ABSTRACT FROM AUTHOR]

The effects of spatial heterogeneity on the dynamics of reaction-diffusion models have been studied extensively. In particular, global dynamics of general spatially heterogeneous (but temporally static) Lotka–Volterra competition-diffusion systems were completely clarified by He and Ni in 2016. However, the evolutionary impacts of temporal periodicity combined with spatial heterogeneity in population ecology remain a challenging issue. In this work, we consider a population model of two competing species in a both spatially varying and temporally periodic environment, where the two species only differ in their random dispersal rates but are otherwise ecologically identical. In a pioneering 2001 work on this model by Hutson et al., by constructing various choices of resource functions and dispersal rates of the two species, the authors demonstrated that all the following three types of dynamics are possible: (i) stable coexistence of the two species; (ii) the slower diffuser invades the faster one but not vice versa; (iii) the faster diffuser invades the slower one but not vice versa. This is in drastic contrast with the spatially heterogeneous but temporally static case, where Dockery et al. showed in 1998 that the slower diffuser always wipes out the faster one. In this paper, we completely and explicitly characterize the asymptotic stability of both semitrivial periodic solutions in terms of the two dispersal rates and the resource function, when either dispersal rate is sufficiently small or large. In particular, the direction of selection on the dispersal rate during the evolution can be elucidated in these instances. Some novel analytical methods are developed to investigate asymptotic behaviors of the underlying time-periodic parabolic eigenvalue problem and its adjoint problem. We hope that these methods are of independent interest in the area of time-periodic parabolic equations. [ABSTRACT FROM AUTHOR]

In this paper, we corroborate the main theorems establishing the justification of Koiter's model, established by Ciarlet and his associates, for all the types of linearly elastic shells via a set of numerical experiments. [ABSTRACT FROM AUTHOR]

We present an effective model of "space-coiled metacrystals"" composed of a periodic array of sound rigid blocks into which long slots have been coiled up. The periodic cell of the block contains a coiled slot whose straight parts are at wavelength scale, which enables the appearance of Bragg resonances. These resonances, which prevent high transmission, compete with the Fabry--P\'erot resonances of the entire slot, which foster perfect transmission. This results in complex scattering properties driven by the characteristics of the turning regions that act as atoms in a onedimensional coiled crystal. Using appropriate scaling and combining two-scale homogenization with matched asymptotic techniques, the modeling of such metacrystals is proposed. The resulting model is validated through a comparison with full-wave numerics in both harmonic and transient regimes. [ABSTRACT FROM AUTHOR]

Rod and cone photoreceptors in the retina of vertebrates are the primary sensory neurons underlying vision. They convert light into an electrical current using a signal transduction pathway that depends on Ca 2 + feedback. It is known that manipulating the Ca 2 + kinetics affects the response shape and the photoreceptor sensitivity, but a precise quantification of these effects remains unclear. We have approached this task in mouse retina by combining numerical simulations with mathematical analysis. We consider a parsimonious phototransduction model that incorporates negative Ca 2 + feedback onto the synthesis of cyclic GMP, and fast buffering reactions to alter the Ca 2 + kinetics. We derive analytic results for the photoreceptor functioning in sufficiently dim light conditions depending on the photoreceptor type. We exploit these results to obtain conceptual and quantitative insight into how response waveform and amplitude depend on the underlying biophysical processes and the Ca 2 + feedback. With a low amount of buffering, the Ca 2 + concentration changes in proportion to the current, and responses to flashes of light are monophasic. With more buffering, the change in the Ca 2 + concentration becomes delayed with respect to the current, which gives rise to a damped oscillation and a biphasic waveform. This shows that biphasic responses are not necessarily a manifestation of slow buffering reactions. We obtain analytic approximations for the peak flash amplitude as a function of the light intensity, which shows how the photoreceptor sensitivity depends on the biophysical parameters. Finally, we study how changing the extracellular Ca 2 + concentration affects the response. [ABSTRACT FROM AUTHOR]

The dynamics of interfaces in slow diffusion equations with strong absorption are studied. Asymptotic methods are used to give descriptions of the behaviour local to a comprehensive range of possible singular events that can occur in any evolution. These events are: when an interface changes its direction of propagation (reversing and anti-reversing), when an interface detaches from an absorbing obstacle (detaching), when two interfaces are formed by film rupture (touchdown) and when the solution undergoes extinction. Our account of extinction and self-similar reversing and anti-reversing is built upon previous work; results on non-self-similar reversing and anti-reversing and on the various types of detachment and touchdown are developed from scratch. In all cases, verification of the asymptotic results against numerical solutions to the full PDE is provided. Self-similar solutions, both of the full equation and of its asymptotic limits, play a central role in the analysis. [ABSTRACT FROM AUTHOR]

The paper addresses the mathematical justification of a model describing steady vibrations for a planar thermoelastic body with an incorporated thin inclusion. The body is composed of three parts: two adherents and an adhesive layer between them, and we begin with a general mathematical formulation of a problem. By means of the modern methods of asymptotic analysis, we rigorously investigate the behavior of solutions as the thickness of the adhesive tends to zero. As a result, we construct the model that corresponds to the limit case. It turned out that the adhesive is reduced to the inclusion, which is thin (of zero thickness) and relatively hard (compared to the rigidity of the surrounding body). Furthermore, we supplement the obtained results with numerical experiments demonstrating the consistency of the theoretical conclusions. [ABSTRACT FROM AUTHOR]

The linear stability of a compressible flow in a pipe is examined using a modal analysis. A steady fully developed flow of a calorifically perfect gas, driven by a constant body acceleration, in a pipe of circular cross section is perturbed by small-amplitude normal modes and the temporal stability of the system is studied. In contrast to the incompressible pipe flow that is linearly stable for all modal perturbations, the compressible flow is unstable at finite Mach numbers due to modes that do not have a counterpart in the incompressible limit. We obtain these higher modes for a pipe flow through numerical solution of the stability equations. The higher modes are distinguished into an "odd" and an "even" family based on the variation of their wave-speeds with wave-number. The classical theorems of stability are extended to cylindrical coordinates and are used to obtain the critical Mach numbers below which the higher modes are always stable. The critical Reynolds number is calculated as a function of Mach number for the even family of modes, which are the least stable at finite Mach numbers. The numerical solution of the stability equations in the high Reynolds number limit demonstrates that viscosity is essential for destabilizing the even family of modes. An asymptotic analysis is carried out at high Reynolds numbers to obtain the scalings, and solutions for the eigenvalues in the high Reynolds number limit for the lower and upper branches of the stability curve. [ABSTRACT FROM AUTHOR]

Cocoa is an important crop that is predominantly grown in the western part of Africa. However, there have been fluctuations and declining trends in production and several factors have been identified to be responsible for this. A significant factor is the effect of climate variation, which could result in a low farm-level yield. Therefore, to understand the contribution of climate variability on the farm-level yield, we construct and analyse a time-delayed model to capture the effect of rainfall on cocoa production. This work uses a system of differential equations to model the crop transition from the flowering stage to pod formation, pod ripening and then to harvesting. We introduce a periodic forcing function into the model of flowering to account for the impact of seasonal rainfall variations. This leads to a novel nonlinear parametrically forced ODE for the flowering with periodically varying coefficients, which is coupled to a time-delayed model for the ripened pod formation and then harvesting. We perform an analysis of all parts of the system proving that it has a periodic solution when (parametrically) forced periodically, and we then conduct an asymptotic analysis on this periodic solution to show how its rich behaviour depends on the parameters of the climatic forcing in the model. [ABSTRACT FROM AUTHOR]

The objective of this work is to study the asymptotic justification of the two- dimensional equations for membrane shells with boundary conditions of von Kármán's type. More precisely, we consider a three-dimensional model for a nonlinearly elastic membrane shell of Saint Venant–Kirchhoff material, where only a portion of the lateral face is subjected to boundary conditions of von Kármán's type. Using technics from formal asymptotic analysis with the thickness of the shell as a small parameter, we show that the scaled three-dimensional solution still leads to the so-called two-dimensional equations of von Kármán membrane shell. [ABSTRACT FROM AUTHOR]

We study the time-domain acoustic wave propagation in the presence of a microbubble. This microbubble is characterized by a mass density and bulk modulus which are both very small compared to the ones of the background vacuum. The goal is to estimate the amount of pressure that is created very near (at a distance proportional to the radius of the bubble) to the bubble. We show that, at that small distance, the dominating field is reminiscent of the wave created by a point-like obstacle modeled formally by a Dirac-like heterogeneity with support at the location of the bubble and the contrast between the bubble and background material as the scattering coefficient. As a conclusion, we can tune the bubble's material properties so that the pressure near it reaches a desired amount. Such a design might be useful for the purpose of acoustic cavitation, where one needs enough, but not too much, pressure to eliminate unwanted anomalies. The mathematical analysis is done using time-domain integral equations and asymptotic analysis techniques. A well known feature here is that the contrasting scales between the bubble and the background generate resonances (mainly the Minnaert one) in the time-harmonic regime. Such critical scales, and the generated resonances, are also reflected in the time-domain estimation of the acoustic wave. In particular, reaching the desired amount of pressure x'prime near the location of the bubble is possible only with such resonating bubbles. [ABSTRACT FROM AUTHOR]

We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit disk in R 2 with one-speed velocity. The model consists of a kinetic equation satisfied by the specific intensity of radiation coupled a nonhomogeneous heat equation satisfied by the material temperature. For the well-prepared data, we prove the existence and the nonequilibrium diffusion limit of solutions to the initial boundary problem for the coupled model. [ABSTRACT FROM AUTHOR]

In the framework of 2D-elasticity, an equilibrium problem for an inhomogeneous body with a curvilinear inclusion located strictly inside the body is considered. The elastic properties of the inclusion are assumed to depend on a small positive parameter δ characterizing its width and are assumed to be proportional to δ − 1 . Moreover, it is supposed that the inclusion has a curvilinear rough boundary. Relying on the variational formulation of the equilibrium problem, we perform the asymptotic analysis, as δ tends to zero. As a result, a variational model of an elastic body containing a thin curvilinear rod is constructed. Numerical calculations give a relative error between the initial and limit problems depending on δ. [ABSTRACT FROM AUTHOR]

In this paper, we revisit large variable asymptotic expansions of tronquée solutions of the Painlevé I equation, obtained via the Riemann–Hilbert approach and the method of steepest descent. The explicit construction of an extra local parametrix around the recessive stationary point of the phase function, in terms of complementary error functions, makes it possible to give detailed information about exponential-type contributions beyond the standard Poincaré expansions for tronquée and tritronquée solutions. [ABSTRACT FROM AUTHOR]

The Brinkman–Bénard convection problem is chosen for investigation, along with very general boundary conditions. Using the Maclaurin series, in this paper, we show that it is possible to perform a relatively exact linear stability analysis, as well as a weakly nonlinear stability analysis, as normally performed in the case of a classical free isothermal/free isothermal boundary combination. Starting from a classical linear stability analysis, we ultimately study the chaos in such systems, all conducted with great accuracy. The principle of exchange of stabilities is proven, and the critical Rayleigh number,  R a c , and the wave number,  a c , are obtained in closed form. An asymptotic analysis is performed, to obtain  R a c  for the case of adiabatic boundaries, for which  a c ≃ 0 . A seemingly minimal representation yields a generalized Lorenz model for the general boundary condition used. The symmetry in the three Lorenz equations, their dissipative nature, energy-conserving nature, and bounded solution are observed for the considered general boundary condition. Thus, one may infer that, to obtain the results of various related problems, they can be handled in an integrated manner, and results can be obtained with great accuracy. The effect of increasing the values of the Biot numbers and/or slip Darcy numbers is to increase, not only the value of the critical Rayleigh number, but also the critical wave number. Extreme values of zero and infinity, when assigned to the Biot number, yield the results of an adiabatic and an isothermal boundary, respectively. Likewise, these extreme values assigned to the slip Darcy number yield the effects of free and rigid boundary conditions, respectively. Intermediate values of the Biot and slip Darcy numbers bridge the gap between the extreme cases. The effects of the Biot and slip Darcy numbers on the Hopf–Rayleigh number are, however, opposite to each other. In view of the known analogy between Bénard convection and Taylor–Couette flow in the linear regime, it is imperative that the results of the latter problem, viz., Brinkman–Taylor–Couette flow, become as well known. [ABSTRACT FROM AUTHOR]