Identical Boundary Conditions Research Articles

The Casimir effect in the presence of infrared transparency

We revisit the Casimir effect perceived by two surfaces in the presence of infrared (IR) transparency. To address this problem, we study a model, where such a phenomenon naturally arises: the DGP model with two parallel 3-branes, each endowed with a localized curvature term. In that model, the ultraviolet modes of the 5-dimensional graviton are suppressed on the branes, while the IR modes can penetrate them freely. First, we find that the DGP branes act as “effective” (momentum-dependent) boundary conditions for the gravitational field, so that the (gravitational) Casimir force between them emerges. Second, we discover that the presence of an IR transparency region for the discrete modes modifies the standard Casimir force — as derived for ideal Dirichlet boundary conditions — in two competing ways: i) The exclusion of soft modes from the discrete spectrum leads to an increase of the Casimir force. ii) The non-ideal nature of the boundary conditions gives rise to a “leakage” of hard modes. As a result of i) and ii), the Casimir force becomes weaker. Since the derivation of this result involves only the localized kinetic terms of a quantum field on parallel surfaces (with codimension one), the derived Casimir force is expected to be present in a variety of setups in arbitrary dimensions.

An experimental and analytical study of rate-dependent shear behaviour of rough joints

Understanding the shear behaviour of rough joints is of great significance for dealing with rock engineering problems. In many cases, rock joints are often subjected to dynamic loadings, which are usually caused by explosions, impacts or earthquakes, etc. Until now, the dynamic shear characteristics of rock joints have not been well understood. In the present study, we investigate joint shear behaviour at different shear rates and develop a rate-dependent constitutive model of rough joints. Testing results shows that the shear/frictional strength of joints with meso-roughness (i.e., planar joints) is independent on the shear rate, while the strength of joints with macro-unevenness (i.e., saw-toothed joints) increases with the shear rate. Under identical boundary conditions, the residual strength of joints with macro-unevenness approximates to the kinetic frictional strength of planar joints. Based on the testing results, the shear stress-displacement curve of rough joints was divided into four phases, i.e., linear elastic phase, shear hardening phase, shear softening phase and residual strength phase. A viscous joint model was thus proposed and validated through comparison with laboratory measurements. This new model correlates the static joint shear stiffness with dynamic one, and has the ability to describe the shear stiffness evolution during the whole shearing process. Based on the proposed model, a hypothesis about shear rate effects of rough joints was introduced and then verified through numerical modelling. The findings in this paper could facilitate better understanding the dynamic behaviour of rough joints and be useful for analyzing rock engineering problems with discontinuous rock masses.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements.

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers (Re), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re, and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.

Influence of experimental boundary conditions on the calibration of a ductile fracture criterion

Hybrid experimental–numerical approach is the commonly used technique to identify the material parameters of ductile fracture criteria. In this work, attention is paid to the precise definition of the Finite Element (FE) model of fracture tests by applying real boundary conditions coming from the local displacement field. The aim is to investigate the effect of the way to reproduce experimental boundary conditions on the accuracy of the hybrid experimental–numerical approach. A stress triaxiality and Lode angle based ductile fracture criterion is used to predict the onset of ductile fracture for AA6061-T6 aluminum alloy sheets. To calibrate this criterion, a series of fracture tests is carried out up to fracture. Notched tensile specimens with different radius, tensile specimens with a central hole and shear specimens are used to cover a wide range of stress states. Strain distribution over the surface is measured with digital image correlation technique. Two numerical models are defined for each geometry type, a first one constrained with real experimental boundary conditions and a second one with ideal boundary conditions, to predict stress and strain distributions. By comparing results of both approaches with experiments, it is shown that the model constrained by local experimental boundary conditions provides a better agreement with the experiments than the simplified model does, which underlines the sensitivity of the hybrid method to the adopted boundary conditions. Furthermore, several fracture test combinations are used to calibrate the ductile criterion and the effect of the calibration tests is discussed.

Improving the Efficiency of I-Beams with a Thin Transverse Corrugated Web Plate

The article describes a way to increase the stability of the transversely corrugated thin web plate of an I-beam due to the use of a double corrugation profile (multi-corrugation). The results of a numerical experiment (performed at LIRA-CAD software) of a large-scale models of beams with transversely corrugated web plates of various profiles (including double corrugation profile), with identical spans, cross sections, boundary conditions, loads, and material characteristics are presented. Distribution diagram of normal and shear stresses in cross sections, deflections, and the forms of buckling of corrugated web plates with safety factors for various models are presented. Based on the calculation results, a comparative analysis of the stress-strain state of the beam models was completed.

Clouds and Radiation in a Mock‐Walker Circulation

AbstractThe Walker circulation connects the regions with deep atmospheric convection in the western tropical Pacific to the shallow‐convection, tropospheric subsidence, and stratocumulus cloud decks of the eastern Pacific. The purpose of this study is to better understand the multi‐scale interactions between the Walker circulation, cloud systems, and interactive radiation. To do this we simulate a mock‐Walker Circulation with a full‐physics general circulation model using idealized boundary conditions. Our experiments use a doubly‐periodic domain with grid‐spacing of 1, 2, 25, and 100 km. We thus span the range from General Circulation Models (GCMs) to Cloud‐system Resolving Models (CRMs). Our model is derived from the Geophysical Fluid Dynamics Laboratory atmospheric GCM (AM4.0). We find substantial differences in the mock‐Walker circulation simulated by our GCM‐like and CRM‐like experiments. The CRM‐like experiments have more upper level clouds, stronger overturning circulations, and less precipitation. The GCM‐like experiments have a low‐level cloud fraction that is up to 20% larger. These differences leads to opposite atmospheric responses to changes in the longwave cloud radiative effect (LWCRE). Active LWCRE leads to increased precipitation for our GCMs, but decreased precipitation for our CRMs. The LWCRE leads to a narrower rising branch of the circulation and substantially increases the fraction of precipitation from the large‐scale cloud parameterization. This work demonstrates that a mock‐Walker circulation is a useful generalization of radiative convective equilibrium that includes a large‐scale circulation.

Analytical continuation of two-dimensional wave fields.

Wave fields obeying the two-dimensional Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing ideal boundary conditions. This is for example the case for the classical canonical problems of diffraction by a half-line or a segment. In the present work, it is shown that such wave fields admit an analytical continuation into the domain of two complex coordinates. The branch sets of such continuation are given and studied in detail. For a generic scattering problem, it is shown that the set of all branches of the multi-valued analytical continuation of the field has a finite basis. Each basis function is expressed explicitly as a Green’s integral along so-called double-eight contours. The finite basis property is important in the context of coordinate equations, introduced and used by the authors previously, as illustrated in this article for the particular case of diffraction by a segment.

Numerical analysis of the effect of anisotropic gas diffusion layer permeability on polymer electrolyte membrane fuel cell performance with various channel types

In this study, polymer electrolyte membrane fuel cell (PEMFC) models with three types of channels (serpentine, parallel, and interdigitated) were employed to determine which directional permeability of the gas diffusion layer (GDL) predominantly affects PEMFC performance using computational fluid dynamics (CFD). Except for the cathode channel, all PEMFC models contained the same components and were analyzed at identical boundary conditions. The analysis was conducted on a GDL having an isotropic permeability of 10−11 m2 to compare the variations in performance based on changes in the directional permeability of the GDL. Subsequently, we studied permeabilities of 10−10 m2 and 10−12 m2 in each direction, which is the x (in-plane), y (in-plane), and z (through-plane) directions for the three types of channels. That is, seven permeability conditions were applied for each channel type. The CFD results demonstrated that permeability effects were observed at high current density conditions above 1 A/cm2. For the serpentine channel type, the x direction permeability has the most influence on PEMFC performance. The permeability of the specific direction hardly affected the performance of the other channel types. However, the pressure drop in the cathode flow field changed in the interdigitated channel but not the parallel channel.

Anisotropic plasticity model forms for extruded Al 7079: Part II, validation

This is the second part of a two-part contribution on modeling of the anisotropic elastic-plastic response of aluminum 7079 from an extruded tube. Part I focused on calibrating a suite of yield and hardening functions from tension test data; Part II concentrates on evaluating those calibrations. A rectangular validation specimen with a blind hole was designed to provide heterogeneous strain fields that exercise the material anisotropy, while at the same time avoiding strain concentrations near sample edges where Digital Image Correlation (DIC) measurements are difficult to make. Specimens were extracted from the tube in four different orientations and tested in tension with stereo-DIC measurements on both sides of the specimen. Corresponding Finite Element Analysis (FEA) with calibrated isotropic (von Mises) and anisotropic (Yld2004-18p) yield functions were also conducted, and both global force-extension curves as well as full-field strains were compared between the experiments and simulations. Specifically, quantitative full-field strain error maps were computed using the DIC-leveling approach proposed by Lava et al. The specimens experienced small deviations from ideal boundary conditions in the experiments, which had a first-order effect on the results. Therefore, the actual experimental boundary conditions had to be applied to the FEA in order to make valid comparisons. The predicted global force-extension curves agreed well with the measurements overall, but were sensitive to the boundary conditions in the nonlinear regime and could not differentiate between the two yield functions. Interrogation of the strain fields both qualitatively and quantitatively showed that the Yld2004-18p model was clearly able to better describe the strain fields on the surface of the specimen compared to the von Mises model. These results justify the increased complexity of the calibration process required for the Yld2004-18p model in applications where capturing the strain field evolution accurately is important, but not if only the global force-extension response of the elastic–plastic region is of interest.

Controllable vortex shedding from dissipative exchange flows in ferromagnetic channels

Ferromagnetic channels subject to spin injection at one extremum sustain long-range coherent textures that carry spin currents known as dissipative exchange flows (DEFs). In the weak injection regime, spin currents carried by DEFs decay algebraically and extend through the length of the channel, a regime known as spin superfluidity. Similar to fluids, these structures are prone to phase-slips that manifest as vortex-antivortex pairs. Here, we numerically study vortex shedding from DEFs excited in a magnetic nanowire with a physical obstacle. Using micromagnetic simulations, we find regimes of laminar flow and vortex shedding as a function of obstacle position tunable by the and spin injection sign and magnitude. Vortex-antivortex pairs translate forward (VF regime) or backward (VB regime) with respect to the detector's extremum, resulting in well-defined spectral features. Qualitatively similar results are obtained when temperature, anisotropy, and weak non-local dipole fields are included in the simulations. These results provide clear features associated with DEFs that may be detected experimentally in devices with nominally identical boundary conditions. Furthermore, our results suggest that obstacles can be considered as DEF control gates, opening an avenue to manipulate DEFs via physical defects.

Visible Light Refraction Effects on High-Speed Stereo Digital Image Correlation Measurement of a Thin Panel in Mach 2 Flow

This study utilized a Mach 2 wind tunnel, Research Cell 19 (RC-19), where the panel specimen became part of the test section top wall. Two stereo digital image correlation (3D-DIC) systems simultaneously acquired displacement measurements both with and without flow by filming the front and back sides of the panel. The two DIC results were then compared to note if any changes between the two measurements could be attributed to light refraction distortions. Various flow conditions were investigated including varying stagnation pressures and multiple shock angles to characterize and quantify potential distortions over a range of conditions. Previous work showed that the distortions were largely quasi-static in nature which had little or no bearing on vibration measurement however, static deflections caused by thermal gradients and less than ideal boundary conditions could be important for finite element model updating. Current results indicate that distortions at the shock wave foot were present in the DIC displacement results however, the level of distortion could be considered the same magnitude of typical sources of measurement noise and not significant.

Estimation of coastal aquifer properties: A review of the tidal method based on theoretical solutions

AbstractDetermination of the hydraulic properties of coastal aquifer systems has important implications that are related to the issues such as seawater intrusion, submarine groundwater discharge, migration of contaminants, assessment of water resources, and geotechnical engineering. Over recent decades, many analytical solutions that consider different types of coastal aquifer systems or models have been developed. These solutions can be used as a theoretical basis for the tidal method that characterizes the hydraulic properties of a coastal aquifer system using hydraulic response measurements in an observation well or wells induced by tidal waves in the ocean. The hydraulic properties of an aquifer can be estimated through fitting a series of time‐dependent changes of hydraulic head detected in an observation well to those calculated based on theoretical solutions. For simplicity, most theoretical solutions only consider one tidal component and idealized boundary conditions, although in reality multiple tidal components exist simultaneously and boundary conditions can be more complicated. For practical applications of the tidal method and to increase its reliability, multiple tidal components should be considered and models considering more complicated boundary conditions should be developed. In addition, methods that can determine both the hydraulic conductivity and storage coefficient, rather than only the hydraulic diffusivity, that is, the ratio of hydraulic conductivity to storage coefficient of coastal aquifer, should be developed. Cautions should be taken into account when using the tidal method because earth tides and changes in local atmospheric pressure may induce similar tidal fluctuations in the hydraulic head within inland observation wells.This article is categorized under: Science of Water > Hydrological Processes Science of Water > Methods

Experimental Reproducibility and Natural Variability of Hydraulic Transport Properties of Fractured Sandstone Samples

Flow and transport processes in fractured systems are not yet fully understood, and it is challenging to determine the respective parameters experimentally. Studies on 10 samples of 2 different sandstones were used to evaluate the reproducibility of tracer tests and the calculation of hydraulic transport properties under identical boundary conditions. The transport parameters were determined using the advection–dispersion equation (ADE) and the continuous time random walk (CTRW) method. In addition, the fracture surface morphology and the effective fracture aperture width was quantified. The hydraulic parameters and their variations were studied for samples within one rock type and between both rock types to quantify the natural variability of transport parameters as well as their experimental reproducibility. Transport processes dominated by the influence of fracture surface morphology experienced a larger spread in the determined transport parameters between repeated measurements. Grain size, effective hydraulic aperture and dispersivity were identified as the most important parameters to evaluate this effect, as with increasing fracture aperture the effect of surface roughness vanishes and the experimental reproducibility increases. Increasing roughness is often associated with the larger effective hydraulic aperture canceling out the expected increased influence of the fracture surface morphology.

Febio finite element models of the human cervical spine

Finite element (FE) analysis has proven to be useful when studying the biomechanics of the cervical spine. Although many FE studies of the cervical spine have been published, they typically develop their models using commercial software, making the sharing of models between researchers difficult. They also often model only one part of the cervical spine. The goal of this study was to develop and evaluate three FE models of the adult cervical spine using open-source software and to freely provide these models to the scientific community. The models were created from computed tomography scans of 26-, 59-, and 64-year old female subjects. These models were evaluated against previously published experimental and FE data. Despite the fact that all three models were assigned identical material properties and boundary conditions, there was notable variation in their biomechanical behavior. It was therefore apparent that these differences were the result of morphological differences between the models.

Finite element model updating using in-situ experimental data

Conventional model updating methods are based on frequency response function (FRF) and/or modal parameter estimates obtained from freely suspended, or sometimes rigidly constrained, sub-structures. These idealised boundary conditions are, however, often difficult to realise in a practical scenario. Furthermore, they are in conflict with the requirement that the sub-structure should also be measured whilst under a representative mounting condition. This paper addresses the question whether model updating can be achieved in the presence of an arbitrary or unknown boundary condition using in-situ measurements, i.e. without removing the sub-structure from its assembly. It is shown that some measurable properties, dynamic transfer stiffness and generalised transmissibility, are invariant to sub-structural boundary conditions and can therefore be obtained in-situ. It is further shown that, with minor adaption, existing transmissibility-based updating methods can be applied more widely than previously thought; to sub-structures whose boundary conditions are non-ideal. The theory is verified by a numerical beam example. Application to a resilient isolator is then demonstrated where a finite element model is successfully updated without removing the isolator from its assembly.

Influence of patellar implantation on the patellofemoral joint of an anatomic customised total knee replacement implant: A case study.

Few studies have been conducted to investigate kinematics and kinetics of the patellofemoral joint under physiological muscle forces and ankle joint loads. In this study, a preliminary design of a customised total knee implant was proposed and created. To compare the influences of different patella treatment scenarios, a dynamic knee simulation model was created with patient-specific muscle forces and ankle joint loads that are calculated from an OpenSim musculoskeletal model. The goal is to improve patellar implant-bone connection and restore patellofemoral joint mobility. Identical dynamic boundary conditions were applied on an unresurfaced patella and three different dome-shaped patellar implants. It was found that the unresurfaced patella and patellar implants resulted in different motions of patellar internal rotation and medial tilt. The size of the dome-shaped patellar implant affected the motion and loading of the patellofemoral joint. When the exposed patella bone was not fully covered by the patellar implant, the patella bone then contacted the femoral component during knee flexion. This would most likely lead to anterior knee pain and subsequent revision.

Prevention of multiple patterns of combined buoyancy- and pressure-driven flow in longitudinally ventilated sloping multi-branch traffic tunnel fires

Longitudinal ventilation is widely employed for smoke control in tunnels due to its relatively low installation cost and compactness. However, smoke control using a longitudinal ventilation system becomes complex when applied in a multi-branch sloping tunnel. In sloping tunnels, the stack effect and forced longitudinal ventilation may combine to produce multiple smoke flow patterns, even under identical or similar boundary conditions. Furthermore, such flow multiplicity behavior is considerably more complicated in a multi-branch sloping tunnel than in a single sloping tunnel. In this paper, an optimal longitudinal ventilation strategy was proposed to prevent smoke flow multiplicity induced by the combined buoyancy- and pressure-driven effects of a downhill sloping, longitudinally ventilated multi-branch tunnel fire. The ventilation network of the multi-branch tunnel was divided into three basic regions: the branches upstream of the intersection node, an on/off-ramp, and the other branches downstream of the intersection node. Based on this division and a hydraulic analysis, the multi-branch tunnel was characterized as a system consisting of several three-branch structures. The critical fan-induced pressure rise required to prevent smoke flow multiplicity was then derived by a potential analysis method according to the fire location in the tunnel. The optimal strategy was achieved by integrating the fan-induced pressure rises in each tunnel branch. The results reveal that the total pressure at the branch intersection node can be varied to regulate the integrated fan-induced pressure rise in each branch. The efficiency of this strategy in preventing flow multiplicity for all typical fire source locations in a three-branch structure was then demonstrated via numerical simulations. The proposed approach has implications for improving tunnel emergency ventilation design and fire protection.

Numerical and experimental investigation of different rib roughness in a solar air heater

A numerical study is aimed at comparing dissimilar types of repeated-rib roughness: arc-shape with gap and V-shape with gap on the absorber plate of the solar air heater having similar shape and size working under identical boundary conditions. Relative gap width (g/e) of 1, relative roughness height of 0.04, the relative roughness pitch of 10, p/P = 0.65, d/W = 0.69, No. of gaps = 1, attack angle α = 600 of the rib, heat flux 1000 W/m2, etc. are kept constant and variation in range of Reynolds number is 3000–15000. Numerical simulations are conducted with the help of ANSYS CFD tool, and results have been validated with the experimental studies. The V-shape ribs have maximum frictional loss penalty of 4.05 and Nusselt number enhancement of 3.4 at Re 3000. The arc-shape ribs have maximum frictional loss penalty of 3.94 and Nusselt number enhancement of 2.4 for Re 15000. The maximum THPP for the V-shape ribs and arc shape ribs are 2.21 and 1.5 respectively at Re 3000.

Improvements of the Adiabatic Film Cooling by Using Two-Row Holes of Different Geometries and Arrangements

Abstract Existing researches on two-row film cooling mainly focused on double-jet film cooling. However, researches on the effects by combining different kinds of hole shapes on film cooling performance are quite limited. In order to improve the film cooling effectiveness, the three-dimensional numerical method is utilized to investigate the effects of a novel structure composed of two-row holes with different shapes and arrangements on the adiabatic film cooling effectiveness with the blowing ratio of M = 1.5. To achieve this purpose, 30 different cases with two-row holes are designed and their film cooling effectiveness are compared with those of other seven cases with a single hole. Cases with two-row holes are designed by setting cylindrical, elliptical, or super-elliptical holes as the first-row, and arranging cylindrical holes with 30 deg, 45 deg, 60 deg, and 90 deg compound angles as the second row. The realizable k–ɛ turbulence model with enhanced wall function is utilized for all cases under identical boundary conditions. Similar film cooling performances are observed for cases with elliptical and super-elliptical holes being the first row, since the maximum deviation of film cooling effectiveness is less than 10%. It is found that the case integrates both a cylindrical hole and a cylindrical hole with 90 deg compound angle can greatly improve the film cooling performance with a higher discharge coefficient. However, the staggered case with an elliptical hole as both first- and second row gives the best film cooling effectiveness and the worst discharge coefficient due to the biggest resistance for the coolant flowing into the film hole.

Updating Geometrically Nonlinear Reduced-Order Models Using Nonlinear Modes and Harmonic Balance

Nonlinear reduced-order models are being investigated for use as digital twins for advanced aircraft and spacecraft. In concept, the digital twin would be tuned to accurately describe the behavior of the vehicle, and then it would be updated as the vehicle is modified or ages. Unfortunately, the linear model correlation and validation techniques that are commonly used in the aerospace industry are not valid for nonlinear models, so a new set of tools is needed. This work presents an algorithm to update geometrically nonlinear reduced-order models using nonlinear normal modes as a correlation metric. The nonlinear normal modes serve as a strong metric to correlate the numerical models because they can be extracted from experiments, and they describe the dynamics of the nonlinear system over a range of amplitudes and are independent of the loading applied to the system. This paper presents a novel method of computing analytical gradients of nonlinear normal mode solutions with respect to system parameters using the multiharmonic balance method. The procedure is first tested using numerical simulations and then applied to tune the reduced-order model of a curved beam based on nominal blueprints and idealized boundary conditions to match a nonlinear normal mode that has been measured experimentally from a three-dimensional printed test specimen.