Vertical Boundary Research Articles

Dynamic anti-plane response of circular inclusion in bi-material structure with interfacial periodic cracks due to the SH wave

This paper investigates the dynamic anti-plane response of the circular inclusion in the bi-material structure with interfacial periodic cracks due to the SH wave. In our analysis, we use the ‘conjunction’ technology and Green’s function method. The bi-material structure consists of two isotropic elastic right-angle domains consisting of a circular elastic inclusion and a series of periodic cracks at the bi-material interface. The periodic cracks are created to satisfy the free conditions of the stresses by using the interface ‘conjunction’ technology. The Green’s functions are also solved to obtain the displacement solutions of the out-place point source loaded on the vertical boundaries of the right-angle plane. The first Fredholm integral equations with unknown force systems are then established based on the continuity conditions at the bi-material interface. As an example, the distributions of the dynamic stress concentration factor (DSCF) around the circular inclusion are obtained and shown graphically. The numerical results indicate that compared with a single crack having periodic cracks strengthens the situation of the dynamic stress concentration around the inclusion.

Transcending the senpai ‘senior’/kōhai ‘junior’ boundary through cross-speaker repetition in Japanese

Abstract This study explores the role of cross-speaker repetition in creating interpersonal connections between interactants in Japanese. The analysis focuses on Japanese non-reciprocal conversations between senpai ‘senior’ and kōhai ‘junior’ interactants, where the kōhai are normatively expected to speak using the honorific desu/masu markers. The analysis demonstrates that in such conversations, the kōhai sometimes drop the honorific markers while repeating the senpai’s utterances, thereby momentarily transcending the vertical boundary separating them from the senpai. Two types of plain form repetition are presented: (1) the kōhai repeat the senpai’s funny and/or questionable comments to savor the expressions, and (2) the kōhai repeat the senpai’s ideas, wishes or assessments to synchronize with the senpai. The analysis explicates how cross-speaker repetition allows the kōhai to drop the honorific markers in a way that is acceptable to the senpai. This study underscores the significance of the cross-speaker repetition device for creating harmonious relationships in Japanese.

An effective strategy for improving the performance of electrodeposited Fe-W alloy plating: Tailoring microstructure by graphene incorporation

Despite the excellent performance of hard Cr plating using hexavalent chromium (Cr6+), its use is being restricted owing to recent environmental regulations. Electrodeposited Fe-W alloy is considered a possible alternative, but its high coefficient of friction (COF), high wear rate owing to tribo-oxidation, and high corrosion rate hinder its practical application. In this study, we attempted to solve these problems by modifying the microstructure of Fe-W alloy by incorporating 2D-structured graphene. The effect of graphene incorporation on the structure of the Fe-W alloy and its properties, especially microhardness, wear, and corrosion resistance, were investigated. The results showed the graphene effectively modified the columnar structure of the Fe-W alloy by inhibiting the vertical growth of clusters during electrodeposition, leading to fragmentation of the vertical cluster boundaries. This improved the hardness by as much as 17 % up to 9.1 GPa, and the corrosion resistance by changing the corrosion mechanism from localized corrosion to uniform corrosion. In addition, the graphene reduced the COF and wear rate by reducing the Fe2O3 formed by tribo-oxidation to a lower oxidation state. The structural modification of the plating by graphene incorporation thus provides an effective solution to improving the performance of Fe-W alloys.

An appraisal using magnetic data of the continent-to-ocean transition structure west of Iberia

SUMMARYAbout half of the rifted margins purportedly formed by extension with minor magmatism. The conceptual models of those magma-poor systems are greatly influenced by the continent-to-ocean transition structure of the archetypal magma-poor West Iberia Margin. In the past, interpretation of magnetic data of West Iberia has been used to constrain conceptual rifting models, including the structure of the transition from the exhumed mantle domain to the oceanic crust formed at a spreading centre. However, uncertainties on geophysical data were generally not considered leading to overdetailed interpretations. We use synthetic magnetic modelling to show that magnetic data acquired at sea level cannot resolve subhorizontal lithological layering in deep-water continental margins. We then present new magnetic modelling guided by a refined velocity model of the wide-angle seismic IAM-9 profile that shows that the magnetic J-anomaly correlates with oceanic crust that abuts exhumed mantle across a vertical boundary. This well-constrained observation supports that seafloor spreading initiated abruptly, terminating mantle exhumation. Conventional wisdom dictates that the sudden efficient melt extraction relates to a mechanical threshold during lithospheric thinning and concomitant asthenospheric upwelling under which melt can migrate toward the surface. However, our results support that mantle melting creating oceanic crust was probably not driven by gradual lithospheric thinning and asthenospheric upwelling, but by seafloor spreading centre propagation that cut across the lithosphere, creating the abrupt structure.

Numerical Study of Tsunami Force on Superstructure of Offshore Rigid Frame Box Girder Bridge

Offshore bridges need to bear complex wave and current loads and face the threat of extreme loads such as tsunamis. Potential tsunamis will have disastrous effects on coastal areas. Compared with conventional beam bridges, there are few studies on rigid frame box girder bridges. In this paper, based on a continuous rigid frame box girder bridge in the offshore area, the parameters of tsunami impact force are analyzed. First, based on Stoke theory and water level in the storage area, the water level in the static water area and quasi stable area in the dam break wave working conditions are obtained, and 12 kinds of dam break wave working conditions are preliminarily proposed to be used for the background bridge. Then, according to the determined simulation working conditions, the box girder dam break impact numerical model is simulated. According to the calculated results, the stress characteristics of the box girder under the tsunami impact are described in the way of time history stage division, and on this basis, The stress mechanism is analyzed from the whole level and local level. The results show that on the whole level, the variation of horizontal force and vertical force with time can correspond to the variation of dam break flow around the box girder. At the local level, the horizontal wall boundary bears the vertical force, the vertical wall boundary bears the horizontal force, and the inclined wall boundary bears both the horizontal force and the vertical force. In addition, negative pressure is the cause of suction on the wall boundary. It provides a reference for the calculation and analysis of tsunami load of offshore rigid frame box girder bridges, the identification of bridge failure modes and the formulation of protective measures.

Engineering of Grain Boundaries in CeO2 Enabling Tailorable Resistive Switching Properties

AbstractDefect engineering in valence change memories aimed at tuning the concentration and transport of oxygen vacancies are studied extensively, however mostly focusing on contribution from individual extended defects such as single dislocations and grain boundaries. In this work, the impact of engineering large numbers of grain boundaries on resistive switching mechanisms and performances is investigated. Three different grain morphologies, that is, “random network,” “columnar scaffold,” and “island‐like,” are realized in CeO2 thin films. The devices with the three grain morphologies demonstrate vastly different resistive switching behaviors. The best overall resistive switching performance is shown in the devices with “columnar scaffold” morphology, where the vertical grain boundaries extending through the film facilitate the generation of oxygen vacancies as well as their migration under external bias. The observation of both interfacial and filamentary switching modes only in the devices with a “columnar scaffold” morphology further confirms the contribution from grain boundaries. In contrast, the “random network” or “island‐like” structures result in excessive or insufficient oxygen vacancy concentration migration paths. The research provides design guidelines for grain boundary engineering of oxide‐based resistive switching materials to tune the resistive switching performances for memory and neuromorphic computing applications.

EHD stability of a cylindrical boundary separating double Reiner–Rivlin fluids

The major aim of this work is to achieve a mathematical technique to scrutinize the nonlinear instability of a vertical cylindrical boundary separation of two streaming Reiner–Rivlin liquids. The system is portrayed by an unchanged longitudinal electric strength. Furthermore, the action of mass and heat transfer (MHT) and permeable media are also considered. The problem is not only of methodological interest but also of scientific and practical interest. To shorten the mathematical analysis, Hsieh’s modulation together with the viscous potential theory (VPT) is employed. The nonlinear diagram is contingent on tackling the governing linear mechanism along with the nonlinear applicable border restrictions. A non-dimensional process produces several non-dimensional physical numbers. A linear dispersion equation is attained and the stability standards are theoretically governed and numerically established. The nonlinear stability procedure reveals a Ginzburg–Landau formula. Consequently, nonlinear stability stipulations are accomplished. Furthermore, by way of the Homotopy perturbation approach, along with the expanded frequency concept, an accurate perturbed technique of surface deflection is attained theoretically and numerically. To validate the theoretical outcomes, the analytical expression is confirmed through the Rung–Kutta of the fourth order. The stable and unstable zones are signified graphically displaying the influences of several non-dimensional numbers.

Experimental and numerical study on seismic performance of concrete-infilled double steel corrugated-plate walls

The Concrete-infilled Double Steel Corrugated-plate Wall (CDSCW) consists of a corrugated part and vertical boundary elements. The corrugated part is composed of outer steel corrugated plates (SCPs), infilled concrete, and intermediate bolts connecting the outer plates. The vertical boundary elements may adopt the concrete-filled steel tubes (CFSTs). This paper presents experimental and numerical investigations into the seismic performance of CDSCWs. Firstly, two specimens with different axial compression ratios were tested under combined axial compression and cyclic lateral loads. The experimental results indicated that the CDSCWs had significant ductility and excellent seismic performance. It was observed that the sufficient strength and stiffness of boundary elements were vital in achieving high load-bearing capacity and ductility of CDSCWs. The failure of the experimental specimens was closely related to the axial compression ratio, involving local buckling and fracture of SCPs and steel tubes and crushing of the infilled concrete. Subsequently, an additional numerical investigation into the performance of CDSCWs was carried out using a finite element (FE) model validated through the test data. The effects of the shear span-to-depth ratio, the axial compression ratio, the strength and stiffness of the boundary elements, and the width-to-thickness ratio of the steel tubes on the load-bearing capacities of CDSCWs are involved in this investigation. It is found that the CDSCWs with small shear span-to-depth ratios are mainly subjected to bending-shear failure, while those with large shear span-to-depth ratios are subjected to compression-bending failure. The strength and ductility of CDSCWs could be improved by strengthening the strength and stiffness of the boundary elements and limiting the width-to-thickness ratio of steel tubes. The conclusions obtained can provide fundamentals for further improving the strength design of CDSCWs.

Perturbation methodology for electromagnetic radiative fluxing of chemical reactive Casson fluid flow under heat source (sink) effectiveness

In this paper, magnetohydrodynamics of a Casson fluid flow is inspected with the presence of thermal radiation and chemical reaction. Employing the perturbation procedure, the modeling equations are tenacious; the graphs are acquired to illustrate the results. The Casson fluid velocity increases as the perturbation parameter increases. Grashof values for heat and mass transport enhanced Casson fluid velocity. Increasing Casson, magnetic, heat source, and radiation parameters reduce the flow velocity. Prandtl number, heat source, and radiation parameter all reduced the temperature profiles. Chemical reaction parameters lowered the concentration profiles. The skin friction enhances with Casson parameter impact. However, the skin-friction coefficient, Sherwood and Nusselt numbers reduce with an increment in the perturbation parameter. In certain cases, this study’s answers agreed well with the previous literature. Casson liquid with a magnetic region using mixed convection by an exponential vertical boundary layer is the novelty of the work.

Easy-to-use formulas for predicting ultimate shear resistance and tension field distribution of semi-supported steel plate shear walls

Semi-supported steel plate shear wall (SPSW) is one type of highly effective lateral load-resisting member. However, the current researches on evaluation of ultimate resistance for semi-supported SPSWs are limited. In this paper, a general finite element (FE) model for the two-side connected, semi-supported and four-side connected SPSWs is developed and verified by existing experimental results. The FE results demonstrate that the mechanical behavior of the SPSW is controlled by the in-plane moments of inertia of the vertical boundary elements (VBEs). The hysteretic behavior of the semi-supported SPSW is between the two-side and the four-side connected SPSWs. The minimum initial lateral stiffness, shear resistance and energy dissipation ability of the semi-supported SPSW are 0.43, 0.24 and 0.29 times of the four-side connected SPSW, respectively. Meanwhile, the equations for determining the inclination angle and the span of the tension field in the two-side connected and semi-supported SPSWs are recommend. Furthermore, an easy-to-use formulas are developed for predicting ultimate shear resistance and tension field distribution of SPSWs with various wall-to-frame connections and validated by the experimental and numerical results. The formula analysis results show that the inclination angle and the span of the tension field in two-side connected SPSW vary from 13.3° to 35.8° and 0.53 to 0.76 times the span of the steel plate. The inclination angle and the span of the tension field in the semi-supported SPSW increase rapidly with the rise in in-plane moments of inertia of the VBEs and the height-to-thickness ratio of the steel plate, and then increase gradually to 45° and the span of the steel plate, respectively. Finally, a unified tension strip model for two-side connected, semi-supported, and four-side connected SPSWs is suggested.

Three-Dimensional Inversion of Multi-Component Semi-Airborne Electromagnetic Data in an Undulating Terrain for Mineral Exploration

For the mineral exploration in complex terrain areas, the semi-airborne transient electromagnetic (SATEM) technology is one of the most powerful methods due to its high efficiency and low cost. However, since the mainstream SATEM systems only observe the component dBz/dt and the data are usually processed by simple interpretation or one-dimensional (1D) inversion, their resolutions are too low to accurately decipher the fine underground structures. To overcome these problems, we proposed a novel 3D forward and inversion method for the multi-component SATEM system. We applied unstructured tetrahedron grids to finely discretize the model with complex terrain, subsequently we used the vector finite element method to calculate the SATEM responses and sensitivity information, and finally we used the quasi-Newton method to achieve high-resolution underground structures. Numerical experiments showed that the 3D inversion could accurately recover the location and resistivities of the underground anomalous bodies under the complex terrain. Compared to a single component data, the inversion of the multi-component data was more accurate in describing the vertical boundary of the electrical structures, and preferable for high-resolution imaging of underground minerals.

Experimental Study on Steel Plate Shear Walls with Partially Encased Composite Columns Composed of Thin Steel Plate

The steel plate shear wall structure has excellent seismic performance, mainly consists of embedded steel plate, horizontal boundary elements (HBEs) and vertical boundary elements (VBEs). Under the action of additional bending moment, the VBEs of SPSW often produce the failure mode of “hourglass specimen”. As a solution, the SPSWs proposed in this paper adopts PEC columns, which are composed of concrete filled between flanges of thin-wall channel steel, and transverse steel bars welded between flanges to prevent it from buckling. A slow cyclic test was conducted on two specimens of 1/3-scaled prefabricated SPSWs with thin steel plate composite section PEC column. According to the validated finite element method, the parameters including the height-thickness ratio of filled steel plate, concrete strength grade, bolt spacing and axial compression ratio were also studied. The results show that the new structure has high bearing capacity and good ductility. In addition, the PEC column has enough stiffness to form a good anchoring effect for the inner steel plate. The inner steel plate fully yields after buckling and provides bearing capacity and energy consumption through the action of tension field. The peak load of specimens with concrete has a higher level approximately 18% than the no-concrete specimen. The height-thickness ratio has a great impact on the post buckling performance of SPSWs. With the increase of height-thickness ratio, the ultimate bearing capacity of the structure will increase by 10% – 30%. Moreover, to give full play to the outstanding performance of prefabricated SPSW with PEC column, the value range of bolt spacing is suggested to be in the range of 120 mm – 60 mm.

Digital ethnicity affordances: from a liability to an asset in immigrant entrepreneurship

PurposeThis paper aims to understand how immigrant entrepreneurs use digital opportunities to overcome the liability of newness and foreignness and how an immigrant's ethnicity can be digitally performed as an asset in business.Design/methodology/approachThe study adopts an inductive multiple case study approach using social media content. The data consist of over 3,500 posts, images and screenshots from Facebook, Instagram and the webpages of seven successful Vietnamese restaurants in Sweden. Grounded content analysis was conducted using NVivo.FindingsThe findings suggest that digitalising ethnic artifacts can mediate and facilitate three digital performances that together can turn ethnicity from a liability to an asset: (i) preserving performance through digital ethnicising, (ii) embracing performance through digital generativitising and (iii) appropriating performance through digital fusionising. The results support the introduction of a conceptual framework depicting the interwoven duality of horizontal and vertical boundary blurring, in which the former takes place between the offline and online spaces of immigrant businesses, and the latter occurs between the home and host country attachment of the immigrant businesses.Originality/valueThis study responds to calls for understanding how immigrant entrepreneurs can overcome the liability of foreignness. It offers a fresh look at ethnicity, which has been seen in a negative light in the field of immigrant entrepreneurship. This study illuminates that ethnicity can be used as a resource in immigrant entrepreneurship, specifically through the use of digital artifacts and digital platforms.

MHD convective flow of Ag–TiO[formula omitted] hybrid nanofluid in an inclined porous annulus with internal heat generation

The current article deals with the computational study of buoyant convection and heat dissipation processes of hybrid nanoliquid saturated in an inclined porous annulus. The fluid flow movement in the porous annular region is modeled using Darcy–Brinkman–Forchheimer model. The vertical boundaries of the cylinder are subjected to uniform but different heating profiles and horizontal surfaces are maintained adiabatic. In the current investigation, for the conservation laws which govern the considered physical process, numerical simulations have been performed using the time-splitting ADI (Alternating Direction Implicit) and line over-relaxation methods. Computations have been performed for broad range of physical and geometric parameters, such as Hartmann number (0≤Ha≤50), geometric inclination angle (−60∘≤γ≤60∘), Darcy number (10−5≤Da≤10−1), aspect ratio (0.5≤Ar≤2) and internal heat generation (0≤Q≤20) to address their impacts on hybrid nanofluid movement and associated heat dissipation rate in the annulus. In addition, heat transfer rate has also been estimated by considering the impact of concentration of each nanoparticle present in the hybrid nanofluid pair. The outcome of numerical computations reveal that an increment in Darcy number enhances the average Nusselt number. Additionally, it has been noticed that the geometric tilt angle of 30° results in dissipating maximum amount of thermal energy in the system. Through this investigation, it is also noticed that shallow annular enclosure exhibits greater amount of heat transport compared to other aspect ratios. Also, significant impact of magnetic field on fluid flow and thermal transport rate has been noticed from the detailed numerical simulations. Further, an enhancement in internal heat generation deteriorates the heat transfer rate and this reduction becomes more steep as the internal heat generation increases.

Theoretical analysis on horizontal rectification of tunnel near deep foundation pit by grouting

In a city with crowded underground space, the excavation of deep foundation pit leads to excessive displacement of adjacent subways and tunnels, which poses serious threats to the safety of existing tunnel structures. At present, theoretical analysis of the horizontal displacement rectification of tunnel by compaction grouting near a deep foundation pit is rarely reported. In this study, the analytical solution is derived based on the source-source theory and cavity expansion theory for grouting in a quarter-infinite space with a vertical rigid boundary (i.e. a rigid retaining structure). The horizontal displacement of tunnel can be determined onthebasisof the Pasternak foundation beam theory. Then the calculated horizontal displacement of tunnel is validated against the measured results obtained from a tunnel rectification test based on grouting in Tianjin and a rectification engineering in Shenzhen. Based on the theoretical solution proposed in this study, the grouting parameters and modes are optimized to reach a high-efficient rectification. For the single-opening grouting, with the increase of horizontal distance from the grouting tube, the horizontal displacement of soil gets lower and becomes negligible (less than 0.5 mm) at 12 m away from the tube. For the multi-row grouting, the depth of the end of the grouting tube should be reduced for high-efficient rectification.

Experimental, numerical and theoretical study on heat transfer in paper honeycomb structure

The fabrication of most current thermal insulation materials from polymeric foams has created an unfavorable impact on the environment. With the aim of reducing the use of foam plastic, this paper focuses on honeycomb paperboard, an alternative thermal insulation material which is recyclable and cost-effective, and evaluates its heat transfer performance under different conditions. The experimental results show the effective thermal conductivity of honeycomb paperboard increases as the honeycomb height or the side length increases. This paper also establishes a novel theoretical model based on a newly developed convective heat transfer correlation to predict the effective thermal conductivity under different conditions. The model's results conform well to the experimental results, and the effect of convective heat transfer is investigated quantitatively using this model. As the vertical adiabatic boundary surfaces are replaced by honeycomb walls, the convection heat transfer strictly depends on the thermal boundary condition of the honeycomb walls and highly depends on honeycomb height and side length.

Синхронизация конвективных течений двухкомпонентной жидкости в смежных ячейках пористой среды

In this work, we study the Soret-driven convection of a two-component fluid in adjacent rectangu-lar cells of a porous medium heated from below in the presence of a gravitational field. In each cell, a long-wavelength oscillatory instability is possible; it can be described by means of phase reduction, which makes it possible to study the synchronization of currents. The horizontal bounda-ries of the cells are assumed to be impenetrable (including for impurities), the heat flux is assumed to be fixed. The vertical boundaries have low thermal conductivity. Fluid motions are described by the Darcy-Boussinesq approximation. Additionally, in this system there is a distributed heat source term describing the heat exchange between the cells. In this way, the equations become coupled via the temperature field. The equations within the long-wavelength approximation are derived using the standard method of multiple scales. An analytical description of the system within the frame-work of a weakly nonlinear analysis can only be constructed near the threshold of the convective instability of the system, and the issue of collective effects is relevant for oscillatory modes; there-fore, we restrict our study to the case of an oscillatory instability. On the basis of equations for the amplitudes of the coupled oscillatory modes, we derived equations for the oscillation phases, which are the key equations of the phase description. For these equations, we found the values of the pa-rameters at which the system has the regime of synchronization of currents; the solution for a stable synchronous regime is also reported.

Maximum density perspectives on the stability of Brinkman porous convection in a vertical channel

The stability of parallel buoyant flow is studied in a vertical layer of Brinkman porous medium possessing a density maximum in its interior with quadratic density law. The vertical boundaries are considered to be rigid and maintained at different uniform temperatures. The similarities and differences between the linear and quadratic density-temperature relationships on the base flow, stability features of fluid flow, and the mode of instability are underlined. If the flow is governed by classical Darcy's law, then it is proved analytically that the base flow remains unconditionally stable irrespective of how the density varies with temperature. On the contrary, the change in the density-temperature relationship affects the stability of base flow when the flow is governed by either unsteady Darcy's law or the Brinkman-extended Darcy law and for these cases, the eigenvalue problem is solved numerically. For the unsteady Darcy flow model, instability occurs through the traveling-wave mode in a certain range of Darcy–Prandtl number for the quadratic density law yet the base flow is always stable if the density law is linear. The nature of the density-temperature relationship and the magnitude of governing parameters combine together in influencing the instability of fluid flow in the Brinkman regime. The possibility of otherwise stabilization of the base flow becoming unstable with the change in the density-temperature relationship from linear to quadratic for the same values of governing parameters is identified. These intricacies are discussed in detail by computing the critical stability parameters for different values of the Darcy–Prandtl number and the Darcy number.

In-plane seismic performance of an innovative steel modular reinforcement system for URM walls

An experimental and numerical research, aimed at evaluating the in-plane seismic performance of an innovative steel modular system for the reinforcement of load-bearing masonry walls (named "Resisto 5.9", designed by Progetto Sisma s.r.l.), is currently underway at the EUCENTRE Foundation in Pavia. Two different masonry typologies, representing common solutions in Italian existing buildings, were considered in this campaign: one made up with solid clay bricks and lime mortar, with "header bond" pattern, and the other with a typical Italian hollow clay "doppio UNI" unit and cement-lime mortar, assembled in a "Flemish bond" pattern. The experimental tests included first the complete mechanical characterization of units, mortars, masonry typologies and of the strengthening system components (i.e. steel elements and anchors). In-plane quasi-static tests were performed on different batches of full--scale specimens to investigate the influence of the proposed reinforcement system on the lateral in-plane response of the walls, compared to their unreinforced conditions. The cyclic behaviour of the masonry piers was analysed in terms of elastic stiffness, lateral strength, displacement capacity and energy dissipation, depending on the achieved damage mechanism. The numerical study of the ongoing campaign consisted of a series of parametric analyses on advanced discontinuous models based on the Distinct Element Method (DEM), considering different wall dimensions, vertical load levels and boundary conditions, in addition to those tested experimentally. Moreover, the numerical campaign was extended also to other possible masonry typologies, varying the bond pattern and the mechanical properties with respect to the experimentally tested solutions. In this paper, the results of the experimental tests on solid brick masonry together with a preliminary overview of the findings of the numerical study, still ongoing, were reported.

The vertical boundary for cross-border e-tailers’ logistics operations considering transaction costs

ABSTRACT This paper examines the effect of transaction costs on the vertical boundary and performance of in-house overseas warehouse logistics operations and outsourcing. So far, the total-cost perspective for an e-commerce company (e-tailer) has only been sketched conceptually, leaving a gap to close with quantitative formulations. This paper finds following points: First, no transaction cost considered can exaggerate not only profit but also the scale of the logistics operation, with a right shift of the vertical boundary for a cross-border e-tailer. Second, with an increase in logistics capacity, the scale of an e-tailer’s in-house logistics operation shrinks. Third, an increase in the service differentiation coefficient is beneficial to a cross-border e-tailer that hires a logistics integrator rather than handling logistics operations in-house. Fourth, an increase in the markup rate of in-house logistics production costs, compared to an external operation, can lead to a decrease in the vertical boundary.