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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]

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]

We study linear equations describing the dynamics of acoustic waves and vortices in a uniform shear flow. Using the methods of asymptotic analysis, we derive Liouville–Green’s asymptotic solutions. We show that in the flow with moderate and high shear rate there exist, besides the standard adiabatic dynamics, two additional phenomena: acoustic wave over-reflection and wave generation by vortices. Original asymptotic method is developed for derivation of generated acoustic wave intensity. Detailed analytical study of the problem is performed and the main quantitative and qualitative characteristics of the processes are obtained and analyzed. [ABSTRACT FROM AUTHOR]

We study the response of the optimal investment problem to small changes of the stock price dynamics. Starting with a multidimensional semimartingale setting of an incomplete market, we suppose that the perturbation process is also a general semimartingale. We obtain second-order expansions of the value functions, first-order corrections to the optimisers, and provide the adjustments to the optimal control that match the objective function up to the second order. We also give a characterisation in terms of the risk-tolerance wealth process, if it exists, by reducing the problem to the Kunita–Watanabe decomposition under a change of measure and numéraire. Finally, we illustrate the results by examples of base models that allow closed-form solutions, but where this structure is lost under perturbations of the model where our results allow an approximate solution. [ABSTRACT FROM AUTHOR]

This work deals with wave propagation into a coaxial cable, which can be modelled by the 3D Maxwell equations or 1D simplified models. The usual model, called the telegrapher's model, is a 1D wave equation of the electrical voltage and current. We derived a more accurate model from the Maxwell equations that takes into account dispersive effects. These two models aim to be a good approximation of the 3D electromagnetic fields in the case where the thickness of the cable is small. We perform some numerical simulations of the 3D Maxwell equations and of the 1D simplified models in order to validate the usual model and the new one. Moreover, we show that, while the usual telegrapher model is of order one with respect to the thickness of the cable, the dispersive 1D model is of order two. [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]

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→±∞$t \rightarrow \pm \infty$. 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]

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]

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]

We consider the Riemann–Hilbert method for the Chen–Lee–Liu equation with a vanishing boundary condition. By analyzing the asymptotic, analytic, and symmetric properties of the Jost solutions, we display the expression of scattering coefficients, theta condition, and the residue conditions. A revised Riemann–Hilbert problem (RHP) is constructed from the Jost solutions, which satisfies the normalization condition. By assuming that the RHP has simple poles, we solve the RHP and display the raw formulae for N-th order solitons of the CLL equation. By applying the Cauchy–Binent formula, we present the explicit formulae for N-th order solitons and consider the exciting collisions of the multiple solitons. [ABSTRACT FROM AUTHOR]

Problem definition: Designing effective operational strategies requires a good understanding of customer behavior. The classic economic theory of customer choice has long been the paradigm in the operations literature. However, the rise of online marketplaces such as e-commerce has triggered considerable efforts in academia and industry to develop alternative models that not only provide a good approximation of customer behavior but also are easily scalable for large-scale implementations. In this paper, we consider a multiproduct dynamic pricing problem with limited inventories under the so-called cascade click model, which is one of the most popular click models used in practice and has been intensively studied in the computer science literature. Methodology/results: We present some fundamental results. First, we derive a sufficiently general characterization of the optimal pricing policy and show that it has a different structure than the optimal policy under the standard pricing model. Second, we show that the optimal expected total revenue under the cascade click model can be upper bounded by the objective value of an approximate deterministic pricing problem. Third, we show that two policies that are known to have strong performance guarantees in the standard revenue management setting can be properly adapted (in a nontrivial way) to the setting with cascade click model while retaining their strong performance. Finally, we also briefly discuss the joint ranking and pricing problem and provide an iterative heuristic to calculate an approximate ranking. Managerial implications: Taking into account customers' click-and-search behavior leads to different structures of the optimal pricing policy, and some common insights under the standard pricing models may no longer hold. Moreover, our simulation studies show that pricing under a (misspecified) classic choice model that is oblivious to customers click-and-search behavior can severely impact profitability. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0504. [ABSTRACT FROM AUTHOR]

This work deals with wave propagation into a coaxial cable, which can be modelled by the 3D Maxwell equations or 1D simplified models. The usual model, called the telegrapher's model, is a 1D wave equation of the electrical voltage and current. We derived a more accurate model from the Maxwell equations that takes into account dispersive effects. These two models aim to be a good approximation of the 3D electromagnetic fields in the case where the thickness of the cable is small. We perform some numerical simulations of the 3D Maxwell equations and of the 1D simplified models in order to validate the usual model and the new one. Moreover, we show that, while the usual telegrapher model is of order one with respect to the thickness of the cable, the dispersive 1D model is of order two.

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]

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]

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]

Timer options, which were first introduced by Société Générale Corporate and Investment Banking in 2007, are financial securities whose payoffs and exercise are determined by a random time associated with the accumulated realized variance of the underlying asset, unlike vanilla options exercised at the prescribed maturity date. In this paper, taking account of the correlation between the underlying asset price and volatility, we investigate the pricing of timer options under the constant elasticity of variance (CEV) model, proposed by Cox and Ross [10], taking advantage of the approach of asymptotic analysis. Additionally, we validate the pricing precision of the approximate formula for timer options using the Monte Carlo method. We conduct numerical experiments based on our corrected prices and analyze price sensitivities concerning various model parameters, with a focus on the value of elasticity.

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.

Customer satisfaction is a prevalent issue amongst manufacturing enterprises. Multi-agent scheduling models aim to optimise the given criteria for improving customer satisfaction by fulfilling the customisation requirements. An investigation is executed on a bi-agent flowshop scheduling model, where a mass of tasks maintained by two competitive agents share a group of successive processors over time. The objective is to determine a feasible schedule that minimises the weighted combination of makespans belonging to two different agents. Asymptotic and worst-case analyses are conducted on a class of dominant-agent-based heuristics proposed to find approximate solutions for large-scale instances. An effective branch and bound algorithm is presented to achieve optimal solutions for small-scale instances, where the release-date-based branching rules and the preemption-based lower bounds significantly speed up the convergence of the proposed algorithm. A discrete artificial bee colony algorithm is introduced to find high-quality solutions for medium-scale instances. Extensive computational experiments are conducted to reveal the effectiveness of the proposed algorithms. [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]

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]

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]

In this paper, we show a mathematical justification of the data assimilation of nudging type in L p - L q maximal regularity settings. We prove that the approximate solution of the primitive equations constructed by the data assimilation converges to the true solution with exponential order in the Besov space B q , p 2 / q (Ω) for 1 / p + 1 / q ≤ 1 on the periodic layer domain Ω = T 2 × (- h , 0) . [ABSTRACT FROM AUTHOR]

This paper explores the asymptotic collision properties of multiple pairs of antidark and dark solitons in the partially space-shifted (P-SS) and fully space-shifted (F-SS) P T -symmetric nonlocal Davey–Stewartson I (NDSI) equations. In the P-SS P T -symmetric NDSI equation, the two solitons of each single soliton pair intersect head-on in (x, y) plane, whereas they exhibit parallel intersections in the F-SS P T -symmetric NDSI equation. To investigate the asymptotic collision properties of multiple soliton pairs, we conduct asymptotic analysis as y → ± ∞ for the soliton pair solutions of the P-SS P T -symmetric NDSI equation, and as t → ± ∞ for the soliton pair solutions of the F-SS P T -symmetric NDSI equation. Based on the asymptotic analysis, the states of N soliton pairs in these two NDSI equations are categorized. The N soliton pairs possess a total of 2 N + 1 different non-degenerate states and N (2 N + 1) distinct degenerate states in the P-SS P T -symmetric NDSI equation, while they have 2 N + 1 different non-degenerate states and (3 N + 1) N 2 distinct degenerate states in the F-SS P T -symmetric NDSI equation. A highly unique state of the N soliton pairs is identified only in the P-SS P T -symmetric NDSI equation, wherein all the 2N solitons vanish into the background. Our asymptotic results also indicate that the SS factor x 0 in the P-SS P T -symmetric DSI equation, as well as the SS factor pair (x 0 , y 0) in the F-SS P T -symmetric DSI equation, selectively influence individual solitons within their respective soliton pairs, while leaving the other soliton in each pair unaffected. [ABSTRACT FROM AUTHOR]

The classical two-scale asymptotic paradigm provides macroscopic and microscopic analyses for the elastodynamic homogenization of periodic composites based on the spatial or/and temporal variable, which offers an approximate framework for the asymptotic homogenization analysis of the motion equation. However, in this framework, the growing complexity of the homogenization formulation gradually becomes an obstacle as the asymptotic order increases. In such a context, a compact, fast, and accurate asymptotic paradigm is developed. This work reviews the high-order spatial two-scale asymptotic paradigm with the effective displacement field representation and optimizes the implementation by symmetrizing the tensor to be determined. Remarkably, the modified implementation gets rid of the excessive memory consumption required for computing the high-order tensor, which is demonstrated by representative one- and two-dimensional cases. The numerical results show that (1) the contrast of the material parameters between media in composites directly affects the convergence rate of the asymptotic results for the homogenization of periodic composites, (2) the convergence error of the asymptotic results mainly comes from the truncation error of the modified asymptotic homogenized motion equation, and (3) the excessive norm of the normalized wavenumber vector in the two-dimensional inclusion case may lead to a non-convergence of the asymptotic results. [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|→∞$|t|\rightarrow \infty$, the fractional N‐soliton solution can be expressed as a linear combination of N fractional single‐soliton solutions. [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 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 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]

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]

This paper focuses on a class of (2 + 1) -dimensional Heisenberg ferromagnet equation, which is an important model for describing the magnetic dynamics of ferromagnetic materials in statistical physics. Firstly, the iterative N-fold Darboux transformation is constructed and established for this (2 + 1) -dimensional equation from its known Lax pair. Secondly, starting from the trigonometric function periodic seed solutions, we not only give multi-soliton and breather solutions on three types of constant backgrounds, but also give two types of breather solutions with different parameters on the trigonometric function periodic backgrounds by using the obtained Darboux transformation. Meanwhile, the elastic interaction of the two-soliton solutions is analyzed via the asymptotic analysis technique, and the abundant structures and propagation characteristics of such soliton solutions are presented graphically. Especially, some novel soliton and breather solutions with pulse like perturbation structures propagating along the peaks and valleys on constant and periodic backgrounds are derived, under the influence of pulse perturbation propagation, some structures undergo inversion relative to the background, some structures degenerate into localized lump soliton structures, which are different from the usual soliton and breather structures on constant backgrounds. Finally, some soliton surface structures are constructed and discussed graphically. These results might have potential applications in describing magnetization motion and explaining the magnetic dynamics of ferromagnetic materials. [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]

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]

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]

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]

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]

This paper concerns an inverse problem for fluorescence diffuse optical tomography (FDOT) identifying multiple point targets. The targets are the fluorescent agents. The FDOT process is modeled by two diffusion equations coupled with the source term. Our measured data are the time-domain data, measured at some detection points as the temporal response of the fluorescence intensity to an instantaneous injection of the excitation light from a source point. The peak time, clearly observed in the space-time data, has been used as an index to detect the targets. We introduce an approximate peak time based on an asymptotic analysis, which agrees very well with the peak time obtained by the numerical calculation using typical optical parameters. Then, using approximate peak time and combining it with the bisection method, we propose a mathematically rigorous inversion method for the FDOT. The proposed method is efficient, robust and accurate for identifying locations of the deeply embedded targets. [ABSTRACT FROM AUTHOR]

Continuous semigroup theory is applied to proof the existence and uniqueness of a solution to a fluid-structure interaction (FSI) problem of non-stationary Stokes flow in two bulk domains, separated by a 2D elastic, permeable plate. The plate's curvature is proportional to the jump of fluid stresses across the plate and the flow resistance is modeled by Darcy's law. In the weak formulation of the considered physical problem, a linear operator in space is associated with a sum of two bilinear forms on the fluid and the interface domains, respectively. One attains a system of equations in operator form, corresponding to the weak problem formulation. Utilizing the sufficient conditions in the Lumer-Phillips theorem, we show that the linear operator is a generator of a contraction semigroup, and give the existence proof to the FSI problem. [ABSTRACT FROM AUTHOR]

Microstructured optical fibres (MOFs) are a new type of optical fibres that possess a wide range of optical properties and many advantages over common optical fibres. Those are provided by unique structures defined by a pattern of periodic or quasi-periodic arrangement of air holes that run through the fibre length. In recent years, MOFs have opened up new possibilities in the field of optics and photonics, enabling the development of advanced devices and novel optical systems for different applications. The key application areas of MOFs vary from telecommunications and high-power energy transmission to quantum optics and sensing. The stack-and-draw method is a standard manufacturing technique for MOFs, where a preform is first manually created and then drawn in a sophisticated furnace into a fibre with the required final dimensions and position of the air holes. During the manufacturing process, experimenters can control only a few parameters, and mathematical models and numerical simulations of the drawing process are highly requested. They not only allow to deepen the understanding of physical phenomena occurring during the drawing process, but they also accurately predict the final cross-section shape and size of the fibre. In this manuscript, we assume thermal equilibrium between the furnace and the fibre and propose a functional form of the fibre temperature distribution. We utilise it with asymptotic mass, momentum, and evolution equations for free surfaces already available in the literature to describe the process of fibre drawing. By doing so, the complex heat exchange problem between the fibre and the furnace need not be solved. The numerical results of the whole asymptotic model overall agree well with experimental data available in the literature, both for the case of annular capillaries and for the case of holey fibres. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a new asynchronous rumor spreading protocol to deliver a rumor to all the nodes of a large-scale distributed network. This protocol relies on successive pull operations involving k different nodes, with k ≥ 2 , and called k-pull operations. Specifically during a k-pull operation, an uninformed node a contacts k - 1 other nodes at random in the network, and if at least one of them knows the rumor, then node a learns it. We perform a detailed study in continuous-time of the total time Θ k , n needed for all the n nodes to learn the rumor. These results extend those obtained in a previous paper which dealt with the discrete-time case. We obtain the mean value, the variance and the distribution of Θ k , n together with their asymptotic behavior when the number of nodes n tends to infinity. [ABSTRACT FROM AUTHOR]

Linear dynamics of acoustic waves in a uniform shear flow is studied. It is shown that in the case of very low shear rate the dynamics of perturbations is adiabatic and can be fully described by the Liouville-Green asymptotic solutions. In contrast, in the flow with a moderate and high shear rate the dynamics of perturbations consists of additional phenomenon, acoustic wave overreflection. Asymptotic analysis is performed and analytical expressions for the transmission and reflection coefficients are derived and analyzed. [ABSTRACT FROM AUTHOR]

Continuous semigroup theory is applied to proof the existence and uniqueness of a solution to a fluid-structure interaction (FSI) problem of non-stationary Stokes flow in two bulk domains, separated by a 2D elastic, permeable plate. The plate's curvature is proportional to the jump of fluid stresses across the plate and the flow resistance is modeled by Darcy's law. In the weak formulation of the considered physical problem, a linear operator in space is associated with a sum of two bilinear forms on the fluid and the interface domains, respectively. One attains a system of equations in operator form, corresponding to the weak problem formulation. Utilizing the sufficient conditions in the Lumer-Phillips theorem, we show that the linear operator is a generator of a contraction semigroup, and give the existence proof to the FSI problem.