Search

In this paper, we focus our attention on the defocusing Kundu-Eckhaus equation, which depicts the propagation of the ultra-short optical pulses in an optical fiber. With respect to the complex envelope of an electromagnetic wave, an N-fold binary Darboux transformation (DT) in the determinant form is constructed, where N is a positive integer. Via the limit technique, determinant operations and obtained N-fold binary DT, we derive the single dark soliton and then perform the N-dark solitons asymptotic analysis. Asymptotic expressions of the dark soliton components at the neighbouring areas along the characteristic lines are obtained, from which we can learn their dynamic properties. When N = 2 , we take the 2-dark solitons as the example and graphically illustrate them, which are consistent with the above analytical results. This work may provide a physical mechanism for the generations and interactions of the optical dark solitons in the optical fibers. [ABSTRACT FROM AUTHOR]

The Riemann–Hilbert approach is applied to the mixed Chen–Lee–Liu equation. The corresponding Jost solutions are found, the analytic, asymptotic and symmetric properties of Jost solutions are studied, and a modified Riemann–Hilbert problem is constructed that satisfies the normalization condition. The formulas for multiple solitons related to the simple poles of the Riemann–Hilbert problem are given in determinant form. According to the Cauchy–Binet formula, the formulas for multiple solitons are given explicitly. Based on these explicit formulas, the first- and second-order solitons are obtained, and the multiple-soliton collisions are verified to be elastic. [ABSTRACT FROM AUTHOR]

We formulate a centrally planned portfolio selection problem with the investor and the manager having S-shaped utilities under a recently popular first-loss contract. We solve for the closed-form optimal portfolio, which shows that a first-loss contract can sometimes behave like an option contract. We propose an asymptotic approach to investigate the portfolio. This approach can be adopted to illustrate economic insights, including the fact that the portfolio under a convex contract becomes more conservative when the market state is better. Furthermore, we discover a means of Pareto improvement by simultaneously considering the investor's utility and increasing the manager's incentive rate. This is achieved by establishing the collection of Pareto points of a single contract, proving that it is a strictly decreasing and strictly concave frontier, and comparing the Pareto frontiers of different contracts. These results may be helpful for the illustration of risk choices and the design of Pareto-optimal contracts. [ABSTRACT FROM AUTHOR]

We calculate the mean throughput, number of collisions, successes, and idle slots for random tree algorithms with successive interference cancellation. Except for the case of the throughput for the binary tree, all the results are new. We furthermore disprove the claim that only the binary tree maximizes throughput. Our method works with many observables and can be used as a blueprint for further analysis. [ABSTRACT FROM AUTHOR]

Problem definition: We study customer service chat (CSC) systems, in which agents can serve multiple customers simultaneously, with generally distributed service and patience times. The multitasking capability of agents introduces idiosyncratic challenges when making routing and staffing decisions. Methodology/results: To determine the dynamic matching of arriving customers with available agents, we first formulate a routing linear program (LP) based on system primitives. Inspired by the optimal solution of the routing LP, we design a parsimonious dynamic routing policy that is independent of arrival rate and service capacity information. We also use the optimal solution to develop closed-form approximations for crucial performance metrics and show that a similar LP can be utilized to make staffing decisions. Through extensive simulation experiments, we showcase the efficacy of our approximations and staffing decisions. Furthermore, under our proposed policy, the CSC system exhibits a unique stationary fluid model in which the steady-state performance measures align with our approximations. Managerial implications: The extant literature primarily focuses on Markovian systems with exponential distributions. In this paper, customers' service and patience times are allowed to be generally distributed to agree with practical settings. Our findings indicate that the distributions have a significant impact on routing policies, staffing decisions, and system performance. Funding: Z. Long was supported by the National Natural Science Foundation of China [Grants 72101112, 72132005, and 72271119] and Jiangsu Province, China [Grant BK20210171]. J. Zhang was supported by the Hong Kong Research Grants Council, General Research Fund [Grants 16208120 and 16214121]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0114. [ABSTRACT FROM AUTHOR]

Symbiotic radio (SR) is one of the attractive communication technologies to facilitate large-scale Internet of Things (IoT) connections with enhanced energy and spectrum efficiency, where passive backscatter devices (BDs) modulate their information over the radio frequency (RF) signals emitted by the active primary transmitters (PTs). Meanwhile, the primary transmission can be strengthened with the additional multipaths created by BDs. To capitalize to a greater extent on the mutualism relationship between the two types of communication, this paper studies multiple-input multiple-output (MIMO) SR communication systems including multiple PTs and massive BDs. We derive the achievable rate expressions of each PT and BD, as well as the sum rate expressions of primary and secondary communication, respectively. Then asymptotic analysis is given to derive the active and passive communication rates with a large number of BDs. Furthermore, for the general case with a finite number of BDs, we study the precoding optimization problem to maximize the sum rate of primary communication, while ensuring that the sum rate of secondary communication and the individual rate for each PT and BD in the prescribed active and passive user sets satisfy the specified thresholds. Simulation results are presented to verify the analytical studies. [ABSTRACT FROM AUTHOR]

As the size of a layered structure scales down, the adhesive layer thickness correspondingly decreases from macro- to micro-scale. The influence of the material microstructure of the adhesive becomes more pronounced, and possible size effect phenomena can appear. This paper describes the mechanical behaviour of composites made of two solids, bonded together by a thin layer, in the framework of strain gradient and micropolar elasticity. The adhesive layer is assumed to have the same stiffness properties as the adherents. By means of the asymptotic methods, the contact laws are derived at order 0 and order 1. These conditions represent a formal generalization of the hard elastic interface conditions. A simple benchmark equilibrium problem (a three-layer composite micro-bar subjected to an axial load) is developed to numerically assess the asymptotic model. Size effects and non-local phenomena, owing to high strain concentrations at the edges, are highlighted. The example proves the efficiency of the proposed approach in designing micro-scale-layered devices. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]

The objective of this work is to study the asymptotic justification of the two-dimensional model of viscoelastic von Kármán membrane shells. More precisely, we consider a three-dimensional model for a nonlinearly viscoelastic membrane shell with a specific class of boundary conditions of von Kármán type. Using techniques 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 two-dimensional model of viscoelastic von Kármán membrane shells. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic properties of a particular class of state-dependent sweeping processes. While extensive research has been conducted on the existence and uniqueness of solutions for sweeping processes, there is a scarcity of studies addressing their behavior in the limit of large time. Additionally, we introduce novel algorithms designed for the resolution of quasi-variational inequalities. As a result, we introduce a new derivative-free algorithm to find zeros of nonsmooth Lipschitz continuous mappings with a linear convergence rate. This algorithm can be effectively used in nonsmooth and nonconvex optimization problems that do not possess necessarily second-order differentiability conditions of the data. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlocal model for a hyperbolic phase field system coupling the standard energy balance equation for temperature with a dynamic for the phase variable: the latter includes an inertial term and a nonlocal convolution-type operator where the family of kernels depends on a small parameter. We rigorously study the asymptotic convergence of the system as the approximating parameter tends to zero and we obtain at the limit the local system with the elliptic laplacian operator acting on the phase variable. Our analysis is based on some asymptotic properties on nonlocal-to-local convergence that have been recently and successfully applied to families of Cahn–Hilliard models. [ABSTRACT FROM AUTHOR]

We study a system of equations, involving a large parameter, arising from the study of stellar pulsation for which a combination of procedures is used to approximate a fun damental solution. We present a combination of singular and non-singular perturbation methods which, aided by symbolic computation, may be of multi-disciplinary interest for the analysis as well as a astrophysics application. Example software is presented in the Wolfram Language (Mathematica version 13.2). [ABSTRACT FROM AUTHOR]

A constant weight asset allocation is a popular investment strategy and is optimal under a suitable continuous model. We study the tracking error for the target continuous rebalancing strategy by a feasible discrete-in-time rebalancing under a general multi-dimensional Brownian semimartingale model of asset prices. In a high-frequency asymptotic framework, we derive an asymptotically efficient sequence of simple predictable strategies. [ABSTRACT FROM AUTHOR]

This paper reports the analytical results on the non-isothermal stationary fluid flow inside thin vertical annular region formed by two co-axial cylinders. The annulus is packed with the fluid-saturated sparsely packed porous medium which is cooled through the side wall. The flow is governed by the prescribed pressure drop between the top and bottom walls which are maintained at uniform, but different temperatures. The main objective of this work is to propose the approximate model describing the effective flow using rigorous asymptotic analysis with respect to the thickness of the annular region. Starting from the dimensionless Darcy-Brinkman-Boussinesq system endowed with the appropriate boundary conditions, we derive the explicit asymptotic approximation clearly showing the effects of the porous structure and thermal transfer. We also provide the theoretical error analysis in order to indicate the order of accuracy of the proposed model and justify its usage. [ABSTRACT FROM AUTHOR]

We review a model for a solid electrolyte derived under thermodynamics principles. We nondimensionalize and scale the model to identify small parameters where we identify a scaling that controls the width of the space charge layer in the electrolyte. We present asymptotic analyses and numerical solutions for the one-dimensional zero charge flux equilibrium problem. We introduce an auxiliary variable to remove singularities from the domain in order to facilitate robust numerical simulations. From the asymptotics, we identify three distinct regions: bulk, boundary, and intermediate layers. The boundary and intermediate layers form the space charge layer of the solid electrolyte, which we can further distinguish as strong and weak space charge layers, respectively. The weak space charge layer is characterized by a length, λ, which is equivalent to the Debye length of a standard liquid electrolyte. The strong space charge layer is characterized by a scaled Debye length, which is larger than λ. We find that both layers exhibit distinct behavior; we see quadratic behavior in the strong space charge layer and exponential behavior in the weak space charge layer. We find that matching between these two asymptotic regimes is not standard, and we implement a pseudomatching approach to facilitate the transition between the quadratic and exponential behaviors. We demonstrate excellent agreement between asymptotics and simulation. [ABSTRACT FROM AUTHOR]

We consider an elastic body surrounded by thin elastic layers along a part of its boundary. We study the asymptotic behavior of the structure as the maximum thickness of the layers tends to zero.We derive an effective boundary integral energy involving a matrix of Borel measures not charging polar sets and having the same support contained in the boundary. We characterize this matrix for three special cases: periodic layers, layers which are determined by a given nonnegative function h, and layers with abrupt changes along self similar fractals. We then consider an optimal control problem, which consists in determining the shape of the best material distribution around the elastic body, under the maximal work of external loads, and characterize the optimal zones on its boundary where possible elastic layers could take place. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a highly efficient computational model compared to the current cycle-by-cycle simulation strategy to compute the viscoelastic responses of asphalt concretes and pavement structures under large numbers of load cycles. An explicit constitutive relation for viscoelastic solids in multiple time scales was developed based on the temporal homogenization. The original initial-boundary value problem was divided into a global part in the slow time scale and a local part in the fast time scale. Two simulation studies were presented to validate the computational accuracy and efficiency of the proposed model: (1) a cylindrical asphalt concrete subject to a uniaxial cyclic compression load, and (2) a pavement structure subject to a locally cyclic loading. The laboratory test results and field measurements were compared with the modeled responses to validate the models before comparing with the reference solutions. Results indicate that the temporal homogenization-based viscoelastic model saves considerable computational cost and maintains a satisfactory accuracy. The absolute values of relative error of the modeled responses between the time homogenization and reference solutions are lower than 1% and 4% for the cylindrical asphalt concrete and pavement structure under locally cyclic loadings, respectively. Based on the proposed computational approach, only 4 min are needed to model the response of a cylindrical asphalt concrete subject to 104 repeated load cycles under a uniaxial compression load. The computational time is reduced from 7 h of the reference solution to 38 min of the temporal homogenization solution to model 103 load cycles of a viscoelastic pavement structure. Practical Applications: This study introduces a highly efficient computational model to compute the viscoelastic responses of asphalt concretes and pavement structures under large numbers of load cycles. Multiple time scales were applied to an explicit constitutive relation of asphalt concretes to obtain the formula of global and local initial-boundary value problems. Its computational accuracy and efficiency were verified by comparing the temporal homogenization-based solutions with the testing results and reference solutions for a cylindrical sample and a pavement structure. It is the basis for the long-term pavement performance prediction after including the fatigue damage analysis in the present temporal homogenization framework. By successfully implementing a mechanistic framework for the long-term pavement performance prediction, the pavement design can more rely on the material inherent properties instead of using redundant empirical transfer functions. It is promising that the local calibrations of the current empirical performance transfer functions can be minimized as the proposed pavement long-term performance predictions depend on the material inherent properties and constitutive models. [ABSTRACT FROM AUTHOR]

Webbing structures are critical load-bearing components in a wide array of applications from structural restraint layers in inflatable space habitats to safety harness belts used by construction workers. In the field, webbings are subjected to ultraviolet (UV) irradiation from sunlight, leading to material degradation and a loss of mechanical strength. To date, health monitoring of webbings has relied on empirically correlating UV-induced strength loss with variations in their inherent color, which often yields inconsistent and imprecise results. To fill this gap, we propose a novel class of photochromic webbing structures that afford noninvasive monitoring of UV-induced degradation of their mechanical strength. The webbings' sensing capabilities are achieved by integrating a class of photochromic yarns, fabricated through a pressurized coating process. Under continuous UV irradiation, the proposed photochromic webbings exhibit a substantial color change, demonstrating a sensing lifetime equivalent to several months in field conditions. We establish a strong correlation between the webbings' photochromic response and their strength loss, supporting the feasibility of the proposed webbings in monitoring their mechanical integrity. To elucidate the sensing mechanism, we propose a physics-based mathematical model that describes the underlying photochemical reactions. Through an asymptotic analysis, we demonstrate that the model accurately predicts the webbing's long-term photochromic responses under extended UV irradiation. The proposed photochromic webbing structures and the predictive mathematical model could enhance the safety and integrity of webbing-based engineering systems. [ABSTRACT FROM AUTHOR]

The subject of mathematical study and modelling in this paper is an inbound call center that receives calls initiated by customers. A closed exponential queueing network with customer retrials and impatient customers is used as a stochastic model of call processing. A brief review of published results on the application of queueing models in the mathematical modeling of customer service processes in call centers is discussed. The network model is described. The possible customer states, customer routing, parameters, and customer service features are given. The allocation of customers by network nodes at a fixed time fully describes the situation in the call center at that time. The state of the network model under study is represented by a continuous-time Markov chain on finite state space. The model is studied in the asymptotic case under the critical assumption of a large number of customers in the queueing network. The mathematical approach used makes it possible to use the passage to the limit from a Markov chain to a continuous-state Markov process. It is proved that the probability density function of the model state process satisfies the Fokker – Planck – Kolmogorov equation. Using the drift coefficients of the Fokker – Planck – Kolmogorov equation, a system of ordinary differential equations for calculating the expected number of customers in each network node over time can be written. The solution of this system allows for predicting the dynamics of the expected number of customers at the model nodes and regulating the parameters of the call center operation. The asymptotic technique used is applicable both in transient and steady states. The areas of implementation of research results are the design of call centers and the analysis of their workload.

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]

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]

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]

The influence of certain parameters on the stability conditions of the reaction front in a porous medium is studied in this article. The mathematical model includes the heat equation, the concentration equation and the equations of motion under the Boussinesq–Darcy approximation. An asymptotic analysis was carried out using the method of Zeldovich and Frank-Kamentskii to obtain the interface problem. A stability analysis was performed to determine a linearized problem that will be solved numerically using the finite difference method with an implicit scheme. This will allow to conclude the effect of each parameter on the stability of the front, in particular the amplitude and the frequency of the vibrations. [ABSTRACT FROM AUTHOR]

A model of oil inflow to a well in a fractured reservoir with a vast gas cap and an underlying water layer is presented in the conditions of gravity-induced segregation of fluids. Using an asymptotic analysis of the equations it was possible to simplify the description of the seepage process before and after the water and gas breakthrough into the well and at a distance from it, as well as to estimate the possibility of waterless and gasless extraction in the conditions of the stabilization of phase fractions in the total rate. It is shown that the hydrostatic equilibrium model can be used in the large-scale approximation fairly far from the well. It is noted that in most practical cases the finite-conductance effect of a fracture is negligible in the large-scale approximation, so that the model of an infinitely permeable fracture can be applied. The equations for determining gas and water fractions in the production after the breakthrough of the water and gas cones in the vicinity of the sink were derived on the flow scale. Finally, the coupling of the models presented makes it possible to describe adequately the inflow to the well before and after the breakthrough of the water and gas cones. The plausibility of the models presented is confirmed by the comparison of the calculated results with the actual data. [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]

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]

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]

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]

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 study the asymptotic behavior of a two dimensional linear PDE with a degenerate diffusion and a drift term. The structure of this equation typically arises in some mathematical mean-field models of neural network, and the investigation of the qualitative properties of this equation is still open, and a challenging question. We prove, via a Doeblin-Harris type method, that the solutions converge exponentially fast to the unique stationary state in a L1-weighted norm. [ABSTRACT FROM AUTHOR]

First hitting times (FHTs) describe the time it takes a random "searcher" to find a "target" and are used to study timescales in many applications. FHTs have been well-studied for diffusive search, especially for small targets, which is called the narrow capture or narrow escape problem. In this paper, we study the FHT to small targets for a one-dimensional superdiffusive search described by a Lévy flight. By applying the method of matched asymptotic expansions to a fractional differential equation we obtain an explicit asymptotic expansion for the mean FHT (MFHT). For fractional order s ε (0, 1) (describing a (2s)-stable Lévy flight whose squared displacement scales as t1/s in time t) and targets of radius \varepsilon \ll 1, we show that the MFHT is order one for s ε (1/2, 1) and diverges as log(1/\varepsilon) for s = 1/2 and \varepsilon 2s 1 for s ε (0, 1/2). We then use our asymptotic results to identify the value of s ε (0, 1] which minimizes the average MFHT and find that (a) this optimal value of s vanishes for sparse targets and (b) the value s = 1/2 (corresponding to an inverse square Lévy search) is optimal in only very specific circumstances. We confirm our results by comparison to both deterministic numerical solutions of the associated fractional differential equation and stochastic simulations. [ABSTRACT FROM AUTHOR]

Active Brownian particles (ABPs) are a model for nonequilibrium systems in which the constituent particles are self-propelled in addition to their Brownian motion. Compared to the well-studied mean first passage time (MFPT) of passive Brownian particles, the MFPT of ABPs is much less developed. In this paper, we study the MFPT for ABPs in a 1-D domain with absorbing boundary conditions at both ends of the domain. To reveal the effect of swimming on the MFPT, we consider an asymptotic analysis in the weak-swimming or small Péclet (Pe) number limit. In particular, analytical expressions for the survival probability and the MFPT are developed up to O (Pe²). We explore the effects of the starting positions and starting orientations on the MFPT. Our analysis shows that if the starting orientations are biased towards one side of the domain, the MFPT as a function of the starting position becomes asymmetric about the center of the domain. The analytical results were confirmed by the numerical solutions of the full PDE model. [ABSTRACT FROM AUTHOR]

We propose and analyze a new methodology based on linear-quadratic regulation (LQR) for stabilizing falling liquid films via blowing and suction at the base. LQR methods enable rapidly responding feedback control by precomputing a gain matrix, but they are only suitable for systems of linear ordinary differential equations (ODEs). By contrast, the Navier--Stokes equations that describe the dynamics of a thin liquid film flowing down an inclined plane are too complex to stabilize with standard control-theoretical techniques. To bridge this gap, we use reduced-order models--the Benney equation and a weighted-residual integral boundary layer model--obtained via asymptotic analysis to derive a multilevel control framework. This framework consists of an LQR feedback control designed for a linearized and discretized system of ODEs approximating the reducedorder system, which is then applied to the full Navier--Stokes system. The control scheme is tested via direct numerical simulation (DNS) and compared to analytical predictions of linear stability thresholds and minimum required actuator numbers. Comparing the strategy between the two reduced-order models, we show that in both cases we can successfully stabilize towards a uniform flat film across their respective ranges of valid parameters, with the more accurate weighted-residual model outperforming the Benney-derived controls. The weighted-residual controls are also found to work successfully far beyond their anticipated range of applicability. The proposed methodology increases the feasibility of transferring robust control techniques towards real-world systems and is also generalizable to other forms of actuation. [ABSTRACT FROM AUTHOR]

Evidence shows that resource quality can determine the costs and benefits of the fear effect on consumer dynamics. However, mechanistic modeling and analysis are lacking. This paper formulates a tritrophic level food chain model that integrates both stoichiometric food quality and fear effect. We establish the well-posedness of the model and examine the existence and stability of equilibria. Through extensive numerical simulations, we validate our findings and visually explore the interactive effects of fear and food quality. Our results reveal that the fear effect from predators stabilizes the system. Furthermore, we demonstrate that the fear effect amplifies the influence of food quality on consumers. When food quality is favorable, the fear effect enhances consumer production efficiency, whereas, in the case of poor food quality, the fear effect exacerbates the decline in production efficiency caused by low-nutrient food. [ABSTRACT FROM AUTHOR]

We consider an\varepsilon -periodic (ε → 0) tubular structure, modeled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on R which is fourth order at a discrete set of values of the magnetic potential (critical points) and second order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases. [ABSTRACT FROM AUTHOR]

For a locally finite set, A ⊆ Rd, the kth Brillouin zone of a ∈ A is the region of points x ∈Rd for which ||x -- a|| is the kth smallest among the Euclidean distances between x and the points in A. If A is a lattice, the kth Brillouin zones of the points in A are translates of each other, and together they tile space. Depending on the value of k, they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our results include the stability of a Brillouin zone under perturbations, a linear upper bound on the number of chambers in a zone for lattices in R², and the convergence of the maximum volume of a chamber to zero for the integer lattice. [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]

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]

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]

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]

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]

An energy functional for the obstacle problem in linear elasticity is obtained as a variational limit of nonlinear elastic energy functionals describing a material body subject to pure traction load under a unilateral constraint representing the rigid obstacle. There exist loads pushing the body against the obstacle, but unfit for the geometry of the whole system body-obstacle, so that the corresponding variational limit turns out to be different from the classical Signorini problem in linear elasticity. However, if the force field acting on the body fulfils an appropriate geometric admissibility condition, we can show coincidence of minima. The analysis developed here provides a rigorous variational justification of the Signorini problem in linear elasticity, together with an accurate analysis of the unilateral constraint.

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.