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We study a diffusion problem in a periodic fibered composite consisting of two materials with highly contrasting diffusion coefficients. An important feature of our problem is the existence of an imperfect interface between the two phases of the composite medium, characterized by the continuity of the solution and the presence of a jump flux. By applying suitable homogenization techniques, we get the limit problems corresponding to two different choices for the flux jump. [ABSTRACT FROM AUTHOR]

We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior a hom of a stationary random medium. The latter is described by a coefficient field a(x) generated from a given ensemble ⟨ · ⟩ and the corresponding linear elliptic operator - ∇ · a ∇ . In line with the theory of homogenization, the method proceeds by computing d = 3 correctors (d denoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realization a(x) from the whole-space ensemble ⟨ · ⟩ . We make this point by investigating the bias (or systematic error), i.e., the difference between a hom and the expected value of the RVE method, in terms of its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x), we heuristically argue that this error is generically O (L - 1) . In case of a suitable periodization of ⟨ · ⟩ , we rigorously show that it is O (L - d) . In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles ⟨ · ⟩ of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function. [ABSTRACT FROM AUTHOR]

We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the multiscale finite element method is similar to the performance of standard finite element methods for smooth problems and present corroborating numerical results. [ABSTRACT FROM AUTHOR]

In this paper we investigate the 2d-model for a thin plate Ω ε : = ω × ε I of R 3 having two components: a circular stiff layer F ε and its complement the soft matrix M ε with 1 ε 2 as a ratio between their respective elasticity coefficients. We prove that the limit model is associated to a nonlocal system involving Kirchoff-Love displacements in the layer and we exhibit a corrector for the displacements in the initial cylindrical structure of R 3 . [ABSTRACT FROM AUTHOR]

We study the effective properties of a linear elastic or perfectly viscoplastic composite consisting of a soft matrix reinforced by possibly very stiff fibers. The effective material is characterized by the emergence of a discrepancy between the displacement in the fibers and the overall averaged displacement, giving rise to a concentration strain in the matrix. The effective energy stored in the fibers is a combination of stretching, bending and torsional energies. This work completes and corrects results previously obtained by the author and coworkers, who failed to notice the torsional contribution. [ABSTRACT FROM AUTHOR]

We derive several properties of the heat equation with the Hodge operator associated with the Rumin’s complex on Heisenberg groups and prove several properties of the fundamental solution. As an application, we use the heat kernel for Rumin’s differential forms to construct a Calderón reproducing formula on Rumin’s forms.

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]

The present study deals with shear wave propagation in a fully coupled Magneto-Electro-Elastic (MEE) multi-laminated periodic structure having non-uniform and imperfect interfaces. As a solution methodology, we applied a more general low-frequency dynamic asymptotic homogenization technique where the solution will be single-frequency dependent and the obtained results generalize those published in Chaki and Bravo-Castillero (Compos Struct 322:117410, 2023b) where the perfect contact case was studied. Effective homogenized dispersive equations of motion in second- and fourth-order approximations, also known as "Good" Boussinesq equations in elastic case, are derived. Local problems, closed-form expression of dispersion equations in second and fourth-order approximations and closed-form solutions of first and second local problems in second-order approximation for tri-laminated MEE periodic structure have been obtained and also validated for elastic laminates with imperfect contact case and MEE laminates with perfect contact case. The effect of non-uniform and imperfect contact, angle of incidence, unit cell size, volume fraction and ME-coupling on the wave propagation is illustrated through dispersion graphs. The effect of non-uniform and imperfect contact on dispersion curve serves as the highlight of the present work. [ABSTRACT FROM AUTHOR]

In this paper we consider the homogenization of the evolution problem associated with a jump process that involves three different smooth kernels that govern the jumps to/from different parts of the domain. We assume that the spacial domain is divided into a sequence of two subdomains A n ∪ B n and we have three different smooth kernels, one that controls the jumps from A n to A n , a second one that controls the jumps from B n to B n and the third one that governs the interactions between A n and B n . Assuming that χ A n (x) → X (x) weakly in L ∞ (and then χ B n (x) → 1 - X (x) weakly in L ∞ ) as n → ∞ and that the initial condition is given by a density u 0 in L 2 we show that there is an homogenized limit system in which the three kernels and the limit function X appear. When the initial condition is a delta at one point, δ x ¯ (this corresponds to the process that starts at x ¯ ) we show that there is convergence along subsequences such that x ¯ ∈ A n j or x ¯ ∈ B n j for every n j large enough. We also provide a probabilistic interpretation of this evolution equation in terms of a stochastic process that describes the movement of a particle that jumps in Ω according to the three different kernels and show that the underlying process converges in distribution to a limit process associated with the limit equation. We focus our analysis in Neumann type boundary conditions and briefly describe at the end how to deal with Dirichlet boundary conditions. [ABSTRACT FROM AUTHOR]

Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a versatile multiscale approach to modelling a moving self-adhesive cell population that combines a careful microscopic description of a deterministic adhesion-driven motion component with an efficient mesoscopic representation of a stochastic velocity-jump process. This approach gives rise to mesoscopic models in the form of kinetic transport equations featuring multiple non-localities. Subsequent parabolic and hyperbolic scalings produce general classes of equations with non-local adhesion and myopic diffusion, a special case being the classical macroscopic model proposed in Armstrong et al. (J Theoret Biol 243(1): 98–113, 2006). Our simulations show how the combination of the two motion effects can unfold. Cell-cell adhesion relies on the subcellular cell adhesion molecule binding. Our approach lends itself conveniently to capturing this microscopic effect. On the macroscale, this results in an additional non-linear integral equation of a novel type that is coupled to the cell density equation. [ABSTRACT FROM AUTHOR]

An effective model is identified for thin perfectly plastic plates whose microstructure consists of the periodic assembling of two elastoplastic phases, as the periodicity parameter converges to zero. Assuming that the thickness of the plates and the periodicity of the microstructure are comparably small, a limiting description is obtained in the quasistatic regime via simultaneous homogenization and dimension reduction by means of evolutionary Γ -convergence, two-scale convergence, and periodic unfolding. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the rate O (ε 1 / 2) of convergence in periodic homogenization of forced graphical mean curvature flows in the laminated setting. We also discuss with an example that a faster rate cannot be obtained by utilizing Lipscthiz estimates. [ABSTRACT FROM AUTHOR]

Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of our proof is the justification of the uniform exponential stabilization of the corresponding Riccati equations, which is derived from the uniform null control properties of the model. Then, we focus on a heat equation with rapidly oscillating coefficients. In the one-dimensional setting, we obtain a uniform turnpike property with respect to the highly oscillatory heterogeneous medium. Afterward, we establish the homogenization of the turnpike property. Finally, our results are validated by numerical experiments. [ABSTRACT FROM AUTHOR]

The work is motivated by the Faraday cage effect. We consider the Helmholtz equation over a 3D domain containing a thin heterogeneous interface of thickness $ \delta \ll 1 $ δ ≪ 1. The layer has a δ-periodic structure in the in-plane directions and is cylindrical in the third direction. The periodic layer has one connected component and a collection of isolated regions. The isolated region in the thin layer represents air or liquid, and the connected component represents a solid metal grid with a δ thickness. The main issue is created by the contrast of the coefficients in the air and in the grid and that the zero-order term has a complex-valued coefficient in the connected faze while a real-valued in the complement. An asymptotic analysis with respect to $ \delta \to 0 $ δ → 0 is provided, and the limit Helmholtz problem is obtained with the Dirichlet condition on the interface. The periodic unfolding method is used to find the limit. [ABSTRACT FROM AUTHOR]

In this article, we consider the optimal control problem governed by the wave equation in a 2-dimensional domain Ω ϵ in which the state equation and the cost functional involves highly oscillating periodic coefficients A ϵ and B ϵ , respectively. This paper aims to examine the limiting behavior of optimal control and state and identify the limit optimal control problem, which involves the influences of the oscillating coefficients. [ABSTRACT FROM AUTHOR]

In this article, we study the homogenization of optimal control problems subject to second-order semi-linear elliptic PDEs with matrix coefficients in two different types of oscillating domains: a circular domain and a domain with general low-dimensional oscillations. The cost functionals considered are of general energy type with oscillating matrix coefficients, and the coefficient matrix in the cost functional is allowed to differ from the coefficient matrix in the constrained PDE. We prove well-defined limit problems for both domains and obtain explicit forms for the limiting coefficient matrices of the cost functionals and constrained PDEs. As expected, the coefficient matrix of the limit cost functional is a combination of the original cost functional’s and constrained PDE’s coefficient matrices. [ABSTRACT FROM AUTHOR]

This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is illustrated numerically and contrasted to the higher-dimensional case. For general unstructured high-contrast coefficients, we present the Localized Orthogonal Decomposition and show a priori error estimates in suitably weighted norms. Numerical experiments illustrate the convergence rates in various settings. [ABSTRACT FROM AUTHOR]

We consider a boundary value problem for a general second-order linear equation in a perforated domain. The perforation is made by small cavities, a minimal distance between the cavities is also small. We impose minimal natural geometric conditions on the shapes of the cavities and no conditions on their distribution in the domain. On the boundaries of the cavities, a nonlinear Robin condition is imposed. The sizes of the cavities and the minimal distance between them are supposed to satisfy a certain simple condition ensuring that under the homogenization the cavities disappear and we obtain a similar problem in a non-perforated domain. Our main results state the convergence of the solution of the perturbed problem to that of the homogenized one in $ W_2^1 $ W 2 1 - and $ L_2 $ L 2 -norms uniformly in $ L_2 $ L 2 -norm of the right-hand side in the equation and provide the estimates for the convergence rates. [ABSTRACT FROM AUTHOR]

In this article, we study stochastic homogenization of non-homogeneous Gaussian free fields Ξ g , a and bi-Laplacian fields Ξ b , a . They can be characterized as follows: for f = δ the solution u of ∇ · a ∇ u = f , a is a uniformly elliptic random environment, is the covariance of Ξ g , a . When f is the white noise, the field Ξ b , a can be viewed as the distributional solution of the same elliptic equation. Our results characterize the scaling limit of such fields on both, a sufficiently regular domain D ⊂ R d , or on the discrete torus. Based on stochastic homogenization techniques applied to the eigenfunction basis of the Laplace operator Δ , we will show that such families of fields converge to an appropriate multiple of the GFF resp. bi-Laplacian. The limiting fields are determined by their respective homogenized operator a ¯ Δ , with constant a ¯ depending on the law of the environment a . The proofs are based on the results found in Armstrong et al. (in: Grundlehren der mathematischen Wissenschaften, Springer International Publishing, Cham, 2019) and Gloria et al. (ESAIM Math Model Numer Anal 48(2):325-346, 2014). [ABSTRACT FROM AUTHOR]

Multiscale high-contrast media can cause astonishing wave propagation phenomena through resonance effects. For instance, waves could be exponentially damped independent of the incident angle or waves could be re-focused as through a lense. In this review article, we discuss the numerical treatment of wave propagation through multiscale high-contrast media at the example of the Helmholtz equation. First, we briefly summarize the findings of analytical homogenization theory, which inspire the design of numerical methods and indicate interesting regimes for simulation. In the main part, we discuss two different classes of numerical multiscale methods and focus on how to treat especially high-contrast media. Some elements of a priori error analysis are discussed as well. Various numerical simulations showcase the applicability of the numerical methods to explore unusual wave phenomena, for instance exponential damping and lensing with flat interfaces. [ABSTRACT FROM AUTHOR]

In $ L_2(\mathbb{R}) $ L 2 (R) , we consider an elliptic differential operator $ A_\varepsilon $ A ϵ , $ \varepsilon \gt 0 $ ϵ > 0 , of the form $ A_\varepsilon = - \frac {{\rm d}}{{\rm d}x} g(x/\varepsilon) \frac {{\rm d}}{{\rm d}x} + \varepsilon ^{-2} V (x/\varepsilon) $ A ϵ = − d d x g (x / ϵ) d d x + ϵ − 2 V (x / ϵ) with periodic coefficients. For the nonstationary Schrödinger equation with the Hamiltonian $ A_\varepsilon $ A ϵ and for the hyperbolic equation with the operator $ A_\varepsilon $ A ϵ , analogs of homogenization problems, related to the edges of the spectral bands of the operator $ A_\varepsilon $ A ϵ , are studied (the so-called high-frequency homogenization). For the solutions of the Cauchy problems for these equations with special initial data, approximations in $ L_2(\mathbb {R}) $ L 2 (R) -norm for small ε are obtained. [ABSTRACT FROM AUTHOR]

Pareto hull peeling is a discrete algorithm, generalizing convex hull peeling, for sorting points in Euclidean space. We prove that Pareto peeling of a random point set in two dimensions has a scaling limit described by a first-order Hamilton–Jacobi equation and give an explicit formula for the limiting Hamiltonian, which is both non-coercive and non-convex. This contrasts with convex peeling, which converges to curvature flow. The proof involves direct geometric manipulations in the same spirit as Calder (Nonlinear Anal 141:88–108, 2016). [ABSTRACT FROM AUTHOR]

We prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of the scale parameter ε. The main tools for the homogenization procedure are multiscale convergence and very weak multiscale convergence, both adapted to evolution problems. [ABSTRACT FROM AUTHOR]

In this article, based on probabilistic methods, we discuss periodic homogenization of a class of weakly coupled systems of linear elliptic and parabolic partial differential equations. Under the assumption that the systems have rapidly periodically oscillating coefficients, we first prove that the appropriately centered and scaled continuous component of the associated regime-switching diffusion process converges weakly to a Brownian motion with covariance matrix given in terms of the coefficients of the systems. The homogenization results then follow by employing probabilistic representation of the solutions to the systems and the continuous mapping theorem. The presented results generalize the well-known results related to periodic homogenization of the classical elliptic boundary-value problem and the classical parabolic initial-value problem for a single equation. [ABSTRACT FROM AUTHOR]

We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the plate converges to zero on a much faster scale than the periodicity parameter and the opposite scenario in which homogenization occurs on a much finer scale than dimension reduction. After performing a static analysis of the problem, we show convergence of the corresponding quasistatic evolutions. The methodology relies on two-scale convergence and periodic unfolding, combined with suitable measure-disintegration results and evolutionary Γ-convergence. [ABSTRACT FROM AUTHOR]

We study continuous dependence estimates for viscous Hamilton–Jacobi equations defined on a network Γ . Given two Hamilton–Jacobi equations, we prove an estimate of the C 2 -norm of the difference between the corresponding solutions in terms of the distance among the Hamiltonians. We also provide two applications of the previous estimate: the first one is an existence and uniqueness result for a quasi-stationary Mean Field Games defined on the network Γ ; the second one is an estimate of the rate of convergence for homogenization of Hamilton–Jacobi equations defined on a periodic network, when the size of the cells vanishes and the limit problem is defined in the whole Euclidean space. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of uniform W 1 , np n - p - and W 2 , p -estimates for periodic homogenization problems of fully nonlinear elliptic equations. We establish sharp, global, large-scale estimates under the Dirichlet boundary conditions. The main novelty of this paper can be found in the characterization of the size of the "effective" Hessian and gradient of viscosity solutions to homogenization problems. Moreover, the large-scale estimates work in a large class of non-convex problems. It should be stressed that our global estimates are new even for the standard problems without homogenization. [ABSTRACT FROM AUTHOR]

We consider a composite material made up of a hosting medium containing an ε-periodic array of perfect thermal conductors. Comparing with the previous contributions in the literature, in the present paper, the inclusions are completely disconnected and form two families with dissimilar physical behaviour. More specifically, the imperfect contact between the hosting medium and the inclusions obeys two different laws, according to the two different types of inclusions. The contact conditions involve the small parameter ε and two positive constants D 1 , D 2 . We investigate the homogenization limit ϵ → 0 and the limits for D 1 , D 2 going to 0 or + ∞ , taken in any order, with the aim to find out the cases in which the two limits commute. [ABSTRACT FROM AUTHOR]

We study the homogenization limit of the renewal equation with heterogeneous external constraints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical approximation of the homogenized equation via the two-scale limit gives an alternative way for the numerical study of the solution of the limiting problem. [ABSTRACT FROM AUTHOR]

We consider the homogenization for time-fractional diffusion equations in a periodic structure. First, we derive the homogenized time-fractional diffusion equations. Next, we prove the stability in determining a constant diffusion coefficient by minimum data. Moreover, we investigate the inverse problems of estimating the homogenized diffusion coefficient by the data for non-homogenized structure. [ABSTRACT FROM AUTHOR]

The model analyzed in this paper has its origins in the description of composites made by a hosting medium containing a periodic array of inclusions coated by a thin layer consisting of sublayers of two different materials. This two-phase coating material is such that the external part has a low diffusivity in the orthogonal direction, while the internal one has high diffusivity along the tangential direction. In a previous paper (Amar in IFB 21:41–59, 2019), by means of a concentration procedure, the internal layer was replaced by an imperfect interface. The present paper is concerned with the concentration of the external coating layer and the homogenization, via the periodic unfolding method, of the resulting model, which is far from being a standard one. Despite the fact that the limit problem looks like a classical Dirichlet problem for an elliptic equation, in the construction of the homogenized matrix and of the source term, a very delicate analysis is required. [ABSTRACT FROM AUTHOR]

We prove that quadratic pair interactions for functions defined on planar Poisson clouds and taking into account pairs of sites of distance up to a certain (large-enough) threshold can be almost surely approximated by the multiple of the Dirichlet energy by a deterministic constant. This is achieved by scaling the Poisson cloud and the corresponding energies and computing a compact discrete-to-continuum limit. In order to avoid the effect of exceptional regions of the Poisson cloud, with an accumulation of sites or with ‘disconnected’ sites, a suitable ‘coarse-grained’ notion of convergence of functions defined on scaled Poisson clouds must be given. [ABSTRACT FROM AUTHOR]

H-measures and semiclassical (Wigner) measures were introduced in early 1990 s and since then they have found numerous applications in problems involving L 2 weakly converging sequences. Although they are similar objects, neither of them is a generalisation of the other, the fundamental difference between them being the fact that semiclassical measures have a characteristic length, while H-measures have none. Recently introduced objects, the one-scale H-measures, generalise both of them, thus encompassing properties of both. The main aim of this paper is to fully develop this theory to the L p setting, p ∈ (1 , ∞) , by constructing one-scale H-distributions, a generalisation of one-scale H-measures and, at the same time, of H-distributions, a generalisation of H-measures to the L p setting. We also address an alternative approach to L p extension of semiclassical measures via the Wigner transform, introducing new type of objects (semiclassical distributions). Furthermore, we derive a localisation principle in a rather general form, suitable for problems with a characteristic length, as well as those not involving a specific characteristic length, providing some applications. [ABSTRACT FROM AUTHOR]

The cultural hedging and fusion of the new era embodied in literary works is of great significance to the communication, development, and prosperity of Chinese and Western cultures. This paper selects the English works compiled and published by Lin Yutang as the research object and analyzes the communication value generated in the process of its compilation and publication. After designing a questionnaire qualified by reliability and relevance analysis, the questionnaire is used to investigate the audience’s exposure to English works and the degree of understanding of the newage cultural hedging embodied in the works. The results of the survey show that multimedia has become the main channel for audiences to access Lin Yutang’s English works. The audience’s understanding of the new age cultural hedges embodied in the works is poor; the acceptance of the new age cultural hedges is at a medium level (3.514 points), and there is a significant correlation between the acceptance level and the understanding effect. It is also found that the multimedia communication method consisting of video and text in a compiled publication has the best comprehension effect (4.857 points) on the new age cultural hedging of the audience. This paper provides a reference path for the compilation and publication of Lin Yutang’s English works under multimedia and lays a foundation for deepening the audience’s understanding of the new age cultural hedge.

The revitalization of rural culture is an important part of the comprehensive revitalization of the countryside in the new era and is of great strategic significance to the realization of the development goal of agricultural modernization. Guided by the value orientation of rural cultural revitalization, the article analyzes the characteristics of multimedia communication and the application strategy in rural cultural communication. Using Oracle as the data storage module and combining the B/S structure, a rural culture digital resource library was established, rural culture images were digitally converted through deep features, end-to-end detection was introduced to extract rural music audio, and a three-dimensional model was also established for rural cultural landscape. The DEA model was also combined with the Malmquist index to explore the utilization efficiency of rural cultural resources. The data on rural cultural revitalization in Province S were used to analyze the efficiency and change trends of its rural cultural revitalization, and the application of the digital resource library of rural culture was studied. The overall efficiency index of rural cultural revitalization practice increased by 7.21% between 2013 and 2023, the average value of the change in the Malmquist index was 1.037, the audience’s satisfaction with the rural cultural services was 3.48 points, and the experience assessment of digital resource library is 83.35 points. The revitalization of rural culture needs to focus on accessing multimedia platforms and relying on digital resource libraries to achieve the deepening of the scope of rural cultural communication.

The traditional paradigms and methods of student management no longer suffice to meet the evolving needs of students in the era of new media. Hence, it is imperative for higher education institutions to continually seek innovative approaches to student work management. To this end, a structured questionnaire was developed to investigate the adoption and impact of new media on student work management in colleges and universities. This survey was designed to align with the distinctive attributes of contemporary students and to explore novel pathways for student work in the context of the new media landscape. To further understand the factors influencing the quality of student work management services, a subset of students was selected for a detailed questionnaire survey. The data collected was subjected to causality analysis and multiple linear regression to assess the satisfaction levels concerning the evolution of student work management in the new media milieu. The findings revealed that the most frequently accessed media platforms among the sampled institutions were WeChat official accounts, with a usage rate of 76.01%, and university official websites, at 40.09%. Additionally, more than 80% of the students exhibited a preference for new media platforms over traditional media. Statistical analysis at the 1% significance level confirmed the impactful roles of respect and care, campus environment, and school management in influencing student job satisfaction. Notably, school management emerged as the most influential factor, with a standardized coefficient of 0.329, underscoring its paramount importance in enhancing student job satisfaction. This study provides valuable insights and serves as a foundational reference for the enhancement of student work management strategies in the digital age.

In the contemporary integrated media environment, the innovation of enterprise short video operation and management, as well as the strategic utilization of modern network technologies, are pivotal in amplifying an enterprise’s influence among users on burgeoning integrated media platforms. This study delves into refining the existing recommendation algorithms, which are crucial for enhancing user engagement and retention rates in enterprise short video services. By integrating the Vulture Search Algorithm to optimize the Fuzzy C-Means user clustering technique and leveraging user profiles developed from questionnaire surveys, this research pioneers a novel approach for tailoring the short video recommendation processes. The enhanced algorithm effectively addresses research needs aligned with user pReferencesand enhances the Fuzzy C-Means method. The application of this refined recommendation algorithm demonstrated significant improvements in user stickiness, driven by the recommendations’ accuracy, engagement, enjoyment, and novelty. Factor analysis revealed that these attributes account for 89.553% of the total variance, which highlights their significant impact on user engagement. Consequently, enterprises seeking to innovate their short video operations within the integrated media landscape must prioritize optimizing video recommendation systems to foster user attachment and satisfaction.

Accompanied by the continuous development of Internet information technology and the promotion of technologies such as big data, artificial intelligence, and machine learning, AI-enabled services are gradually integrated into daily life, and remediation in the face of AI service interactions has also become an inevitable research issue. This study examines the impact of remediation in the event of service failures, particularly in the context of intelligent robot service failures that lead to negative customer experiences. Through the dissection of service failure remediation methods, combined with the customer satisfaction index model, a theoretical research model is constructed from the two aspects of willingness to use and satisfaction, and five hypotheses of remediation are proposed, and then experiments are designed to test them. The results of regression analysis indicated that the mean values of perception and willingness to use in the low anthropomorphism group were 4.875 and 5.052. The mean values of perception and willingness to use in the high anthropomorphism group were increased by 0.718 and 0.649 compared to those of the low anthropomorphism group. The customer’s satisfaction in terms of robot anthropomorphism in the high anthropomorphism was 4.055, and in the low anthropomorphism was 3.410, which indicated that there were positive correlations between the degree of anthropomorphism and both willingness to use and satisfaction have a positive effect, and all five hypotheses of this paper are proved. The purpose of this study is to provide an in-depth analysis of the use of AI anthropomorphization in service failure and service remediation and to offer guidance and references for AI services and related development and design decisions.