Elastic Modulus Of Matrix Research Articles

Calculation and application of elastic modulus of mineral components in tight sandstone based on adaptive method

Abstract For the petrophysics modelling of tight sandstones, the elastic modulus of their sandstone and mudstone components are often substituted with those of quartz and clay, which affects model accuracy. To solve this problem, we innovate an adaptive approach for modelling the rock physics characteristics of tight sandstone. First, based on the relationship between P- and S-wave velocities from well logs and the elastic modulus of the rocks, the equivalent elastic modulus of tight sandstone under saturated conditions is calculated. Next, The Lee model and the Gassmann equation were jointly used to determine the equivalent elasticity modulus of tight sandstone matrix. The upper and lower limits of the equivalent elasticity modulus for mudstone and sandstone are established using the mudstone content curve, the least squares method and the Voigt–Reuss–Hill (V-R-H) model. We used the random-walk algorithm to accurately calculate the equivalent elastic modulus of the sandstone and mudstone components. Finally, using the accurately obtained elastic modulus of sandstone and mudstone, the equivalent elastic modulus of the matrix is calculated. The Kuster–Toksöz (K-T) model is subsequently applied to compute the dry frame bulk modulus and shear modulus of the rock. Following this, the Brie model is used to calculate the elastic modulus of the mixed fluid, thereby completing the construction of the rock physics model for the study area. The results demonstrate that our improved petrophysics model can predict the S-wave velocity curve with ≤ 15% errors relative to the true curve. When sweet spot prediction was performed using reservoir-sensitive parameter (Vp/Vs) derived from the petrophysics template, the agreement between the predictions and well-log data was 80%. Thus, our petrophysics modelling method can be used to predict tight gas reservoirs effectively and will aid efforts to improve petroleum exploration works in the study area.

High-modulus engineered cementitious composites: Design mechanism and performance characterization

Engineered cementitious composites features with high tensile performance while relatively weak compressive stiffness. This study endeavors to address the inherent trade-off between tensile properties and elastic modulus in conventional Engineered Cementitious Composites (ECC). Utilizing the distinctive characteristics of iron ore aggregates, known for their relatively stiff nature, smooth surface and rounded shape, an Iron Sand-based ECC (IS-ECC) emphasizing both high elastic modulus and ductility is formulated. Guided by micromechanical design theory and multiscale homogenization model, this study systematically explores the impacts of aggregate types, water-to-binder (w/b) ratios, sand-to-binder (s/b) ratios, and sand particle sizes on ECC properties. Compared with Quartz Sand-based ECC (QS-ECC), IS-ECC exhibits notably enhanced matrix fluidity and elastic modulus, reduced matrix toughness, and more robust strain-hardening behavior. The proposed three-level multiscale homogenization model accurately predicts the elastic modulus of ECC and provides insights into the underlying mechanism contributing to the enhanced elastic modulus of IS-ECC. With a resulting high elastic modulus of 33.3–48.6 GPa and superior tensile properties, IS-ECC holds promise for widespread applications in structural engineering.

Viscoelastic stiffening of gelatin hydrogels for dynamic culture of pancreatic cancer spheroids

The tumor microenvironment (TME) in pancreatic adenocarcinoma (PDAC) is a complex milieu of cellular and non-cellular components. Pancreatic cancer cells (PCC) and cancer-associated fibroblasts (CAF) are two major cell types in PDAC TME, whereas the non-cellular components are enriched with extracellular matrices (ECM) that contribute to high stiffness and fast stress-relaxation. Previous studies have suggested that higher matrix rigidity promoted aggressive phenotypes of tumors, including PDAC. However, the effects of dynamic viscoelastic matrix properties on cancer cell fate remain largely unexplored. The focus of this work was to understand the effects of such dynamic matrix properties on PDAC cell behaviors, particularly in the context of PCC/CAF co-culture. To this end, we engineered gelatin-norbornene (GelNB) based hydrogels with a built-in mechanism for simultaneously increasing matrix elastic modulus and viscoelasticity. Two GelNB-based macromers, namely GelNB-hydroxyphenylacetic acid (GelNB-HPA) and GelNB-boronic acid (GelNB-BA), were modularly mixed and crosslinked with 4-arm poly(ethylene glycol)-thiol (PEG4SH) to form elastic hydrogels. Treating the hybrid hydrogels with tyrosinase not only increased the elastic moduli of the gels (due to HPA dimerization) but also concurrently produced 1,2-diols that formed reversible boronic acid-diol bonding with the BA groups on GelNB-BA. We employed patient-derived CAF and a PCC cell line COLO-357 to demonstrate the effect of increasing matrix stiffness and viscoelasticity on CAF and PCC cell fate. Our results indicated that in the stiffened environment, PCC underwent epithelial-mesenchymal transition. In the co-culture PCC and CAF spheroid, CAF enhanced PCC spreading and stimulated collagen 1 production. Through mRNA-sequencing, we further showed that stiffened matrices, regardless of the degree of stress-relaxation, heightened the malignant phenotype of PDAC cells. Statement of significanceThe pancreatic cancer microenvironment is a complex milieu composed of various cell types and extracellular matrices. It has been suggested that stiffer matrices could promote aggressive behavior in pancreatic cancer, but the effect of dynamic stiffening and matrix stress-relaxation on cancer cell fate remains largely undefined. This study aimed to explore the impact of dynamic changes in matrix viscoelasticity on pancreatic ductal adenocarcinoma (PDAC) cell behavior by developing a hydrogel system capable of simultaneously increasing stiffness and stress-relaxation on demand. This is achieved by crosslinking two gelatin-based macromers through orthogonal thiol-norbornene photochemistry and post-gelation stiffening with mushroom tyrosinase. The results revealed that higher matrix stiffness, regardless of the degree of stress relaxation, exacerbated the malignant characteristics of PDAC cells.

Spatial and Temporal Control of 3D Hydrogel Viscoelasticity through Phototuning.

The mechanical properties of the extracellular environment can regulate a variety of cellular functions, such as spreading, migration, proliferation, and even differentiation and phenotypic determination. Much effort has been directed at understanding the effects of the extracellular matrix (ECM) elastic modulus and, more recently, stress relaxation on cellular processes. In physiological contexts such as development, wound healing, and fibrotic disease progression, ECM mechanical properties change substantially over time or space. Dynamically tunable hydrogel platforms have been developed to spatiotemporally modulate a gel's elastic modulus. However, dynamically altering the stress relaxation rate of a hydrogel remains a challenge. Here, we present a strategy to tune hydrogel stress relaxation rates in time or space using a light-triggered tethering of poly(ethylene glycol) to alginate. We show that the stress relaxation rate can be tuned without altering the elastic modulus of the hydrogel. We found that cells are capable of sensing and responding to dynamic stress relaxation rate changes, both morphologically and through differences in proliferation rates. We also exploited the light-based technique to generate spatial patterns of stress relaxation rates in 3D hydrogels. We anticipate that user-directed control of the 3D hydrogel stress relaxation rate will be a powerful tool that enables studies that mimic dynamic ECM contexts or as a means to guide cell fate in space and time for tissue engineering applications.

Agglomeration and interphase-influenced effective elastic properties of Metal/Graphene nanocomposites: A developed mean-field model

The strength of metallic nanocomposites structures can be greatly improved by adding nanofillers to the matrix. However, there is a discrepancy between the conventional theories and the experimental evidence on the effect of nanofiller loading on the strength of the nanocomposite. The conventional theories predict that the strength increases with the nanofiller loading, but the experimental evidence shows that there is an optimal nanofiller loading beyond which the strength does not improve much. This discrepancy, especially at high filler loadings, is due to the neglect of the agglomeration and the interphase region formation in the composite structure modeling. In this paper, we propose a new micromechanical model based on mean-field theory to examine how the agglomeration and the interphase region influence the elastic modulus of metal/graphene nanocomposites (MGNs). We also explore how other factors, such as interphase region thickness and strength, graphene size, and metallic matrix elastic modulus, influence the elastic modulus of MGNs. We present a mathematical model that describes how the thickness and modulus of the interphase layer of graphene nanoplatelets change due to agglomeration. This model allows us to reproduce the parabolic behavior of the elastic modulus of the composite, which is more consistent with the experimental results.

Elastic modulus of hydrogel regulates osteogenic differentiation via liquid-liquid phase separation of YAP.

Craniofacial bone defects induced by congenital malformations, trauma, or diseases frequently challenge the orthodontic or restorative treatment. Stem cell-based bone regenerative approaches emerged as a promising method to resolve bone defects. Microenvironment physical cues, such as the matrix elastic modulus or matrix topography, regulate stem cell differentiation via multiple genes. We constructed gelatin methacryloyl (GelMA), a well-known scaffold, to investigate the impact of elastic modulus on osteogenic differentiation in a three-dimensional environment. Confocal microscope was used to observe and assess the condensates fission and fusion. New bone formation was evaluated by micro-computed tomography at 6 weeks in calvarial defect rat. We found that the light curing increased elastic modulus of GelMA, and the pore size of GelMA decreased. The expression of osteogenic markers was inhibited in hBMSCs cultured in the low-elastic-modulus GelMA. In contrast, the expression of YAP, TAZ and TEAD was increased in the hBMSCs in the low-elastic-modulus GelMA. Furthermore, YAP assembled via liquid-liquid phase separation (LLPS) into condensates that were sensitive to 1'6-hexanediol. YAP recruit TAZ and TEAD4, but not RUNX2 into the condensates. In vivo, we also found that hBMSCs in high-elastic-modulus GelMA was more apt to form new bone. This study provides new insight into the mechanism of osteogenic differentiation. Reagents that can regulate the elastic modulus of substrate or LLPS may be applied to promote bone regeneration.

Nanoindentation of embedded particles

We address the effect of elastic inhomogeneity on elastic modulus and hardness determinations made by depth-sensing indentations performed on individual particles embedded within a matrix of different elastic modulus. Finite element simulations and nanoindentation experiments are used to quantify the consequences of particle/matrix elastic inhomogeneity and we propose an adaptation of the Oliver–Pharr method that gives access to particle properties knowing those of the matrix. The method is suitable for any combination of matrix and particle elastic modulus and for any type of indenter, provided that the area of the tested particles along the surface of the sample is measured and that a large number of particles are probed. Further conditions for the implementation of the method are that testing conditions be such (i) that permanent deformation of the matrix is avoided, and (ii) that permanent deformation in each probed particle under the indenter is not affected by the matrix.Graphical abstract

Effect of Sintering Temperature on Mechanical Behaviors of an Oxide Fiber‐Reinforced Oxide Matrix Composite

Sintering temperature can significantly affect the mechanical behaviors of ceramic matrix composites. Herein, the effect of sintering temperature (900–1200 °C) on micro‐ and macromechanical properties of an oxide fiber‐reinforced oxide matrix (oxide/oxide) composite is investigated. The crack propagation path is predicted by the He–Hutchinson model. Results show that the elastic modulus of matrix and interfacial shear strength increase with sintering temperature. The propagating crack converts from deflection along the interface to direct penetration into the matrix at 1200 °C. With increase of the sintering temperature, the flexural strength and interlaminar shear strength monotonically increase, while the fracture toughness increases and then decreases at 1200 °C. A good balance between the fracture strength and fracture toughness is achieved on the 1100 °C sintered composite, which possesses a high flexural strength of ≈276.7 MPa, a high interlaminar shear strength of ≈17.2 MPa, and a high fracture toughness of ≈13.9 MPa m1/2. The study offers a new sight in deep understand of the preparation and applicability of oxide/oxide composite at high temperatures.

A positive mechanobiological feedback loop controls bistable switching of cardiac fibroblast phenotype

Cardiac fibrosis is associated with activation of cardiac fibroblasts (CFs), a pathological, phenotypic transition that is widely believed to be irreversible in the late stages of disease development. Sensing of a stiffened mechanical environment through regulation of integrin-based adhesion plaques and activation of the Piezo1 mechanosensitive ion channel is known to factor into this transition. Here, using integrated in vitro and in silico models, we discovered a mutually reinforcing, mechanical positive feedback loop between integrin β1 and Piezo1 activation that forms a bistable switch. The bistable switch is initiated by perturbations in matrix elastic modulus that amplify to trigger downstream signaling involving Ca2+ and YAP that, recursively, leads fibroblasts to further stiffen their environment. By simultaneously interfering with the newly identified mechanical positive feedback loop and modulating matrix elastic modulus, we reversed markers of phenotypical transition of CF, suggesting new therapeutic targets for fibrotic disease.

Stress Profile in Coating Layers of TRISO Fuel Particles in Contact with One Another

This work presents a discussion on a series of finite element analyses that assess stress evolution in the coating layers of tristructural isotropic (TRISO) particles in contact with each other while embedded in a matrix. The initial simulations were of applied uniaxial pressure versus matrix elastic modulus. These simulations predicted increasing stress in the silicon carbide coating layers of the TRISO particles with decreasing matrix elastic modulus. The second set of simulations focused on the effects of heating and cooling and the associated dimensional change on the state of stress in the coating layers. The general finding was that there was no significant difference below the coating layer’s deposition temperature. However, above the deposition temperature, the contacting particles had higher stress compared with those that were separated. The third set of simulations focused on the effects of irradiation, specifically, creep, dimensional change, and swelling. An interface debonding model was introduced since these potential effects have a significant bearing on predicted stresses.

Modeling of Modulus of elasticity of Nano-Composite Materials: Review and Evaluation

To improve the mechanical properties of polymer, the mineral particles are added to produce composite material. For example, the mineral particles are added to polymer to improve the stiffness of polymer because of the higher stiffness of mineral particles. When the micron-sized particles are used in composite usually cause a reduction in impact resistance. On the other hand, adding the nano scale minerals leads to improve the impact and wear properties of the composite materials (nanocomposites). Several factors effect on the mechanical properties of nanocomposites like adhesion between the polymer and nanoparticles. If the interfacial deboning of particles from the matrix decreases, the tensile strength of the composite could be reduced.In this article, the micromechanical models dealing with calculating modulus of elasticity of nanocomposite are reviewed and discussed using the comparison between the results of the micromechanical models with experimental data factors effect on the modulus of elasticity of nanocomposite are matrix and filler elastic modulus, volume fraction of filler, aspect ratio of filler, maximum volumetric packing and the thickness and elastic modulus of interphone surrounding the nanoparticles and these factors are studied in each mechanical models.

Enhancing the Strengthening Effect of Graphene-Nanoplates in Al Matrix Composites by Heterogeneous Matrix Design.

In the present work, the properties of graphene-nanoplates/aluminum (GNPs/Al) composites with a heterogeneous matrix design were investigated. The advantage of the heterogeneous matrix was investigated by the finite element method. Then, 0.6 wt.% (GNPs/6061Al)/2024Al (heterogeneous matrix) and 0.6 wt.% GNPs/6061Al composites were prepared by ball milling, pressure infiltration technology, and hot extrusion. The aggregation of GNPs was eliminated and the interlayer slide of GNPs was observed. Mechanical property test results show that the mechanical properties of the heterogeneous matrix composite are better than that of a homogeneous matrix composite, including strength, elastic modulus, and plasticity. It is assumed that the heterogeneous matrix design enhances the non-uniform stress field during the deformation treatment. This improves the dispersion of GNPs, grain refinement, and produces the few-layer graphene (FLG), thus enhancing the strengthening effect of GNPs. Meanwhile, heterogeneous matrix design is thought to introduce more hardening mechanisms to increase the plasticity of materials and improve the intrinsic trade-off of strength and toughness.

Elastic Modulus Prediction Model of Foamed Concrete Based on the Walsh Formula

Foamed concrete consists of cement matrix and air-foam and has more complicated structure characteristics than normal concrete. However, current research on the elastic modulus of foamed concrete is still limited to empirical equations. In this work, a new theoretical prediction model was proposed for calculating the elastic modulus of foamed concrete. The elastic modulus calculation model for the spherical shell element of foamed concrete is constructed based on the Walsh formula and the assumption of spherical pores. Moreover, the theoretical prediction model is established by introducing the two-layer embedded model for the elastic modulus of foamed concrete. Then, the compressive test is employed to verify the accuracy of the model. The results show that the elastic modulus of foamed concrete decreases with the increase in porosity and matrix Poisson’s ratio, and increases with the increase in the matrix elastic modulus. The research results can improve the mechanical theories of foamed concrete materials and have good engineering application values.

Effect of TiC content on the microstructure and mechanical properties of Ti-30Mo-xTiC composites

TiC reinforced titanium matrix composites are promising for advanced applications. In this study, the Ti-30Mo-xTiC composites with the TiC content of 0, 0.5, 2.5 and 5 wt% were prepared using a powder metallurgy method. The results showed that TiC in Ti-30Mo exhibited a stoichiometric ratio of Ti to C over 1:1, along with demonstrating a semi-coherent lattice relationship with the β-Ti matrix lattice. Further, the excess C element diffused from the TiC particles to the matrix at the interface with large solid solubility, thus, promoting the sintering densification. Compared with Ti-30Mo, the composites with TiC addition revealed much higher relative density. Increasing the TiC content could increase the matrix microhardness and elastic modulus, however, the ultimate tensile strength and elongation were decreased. The mechanical properties were improved owing to the cooperative effect of densification, TiC particle reinforcement, solid solution of Mo and C elements and semi-coherent interface. As a result, the Ti-30Mo-0.5TiC composite presented an excellent combination of properties: matrix microhardness of 294 HV0.3, ultimate tensile strength of 820 MPa, elongation of 6.5% and elastic modulus of 112 GPa.

Time-Lapse Integration at FWU: Fluids, Rock Physics, Numerical Model Integration, and Field Data Comparison

We present the current status of time-lapse seismic integration at the Farnsworth (FWU) CO2 WAG (water-alternating-gas) EOR (Enhanced Oil Recovery) project at Ochiltree County, northwest Texas. As a potential carbon sequestration mechanism, CO2 WAG projects will be subject to some degree of monitoring and verification, either as a regulatory requirement or to qualify for economic incentives. In order to evaluate the viability of time-lapse seismic as a monitoring method the Southwest Partnership (SWP) has conducted time-lapse seismic monitoring at FWU using the 3D Vertical Seismic Profiling (VSP) method. The efficacy of seismic time-lapse depends on a number of key factors, which vary widely from one application to another. Most important among these are the thermophysical properties of the original fluid in place and the displacing fluid, followed by the petrophysical properties of the rock matrix, which together determine the effective elastic properties of the rock fluid system. We present systematic analysis of fluid thermodynamics and resulting thermophysical properties, petrophysics and rock frame elastic properties, and elastic property modeling through fluid substitution using data collected at FWU. These analyses will be framed in realistic scenarios presented by the FWU CO2 WAG development. The resulting fluid/rock physics models will be applied to output from the calibrated FWU compositional reservoir simulation model to forward model the time-lapse seismic response. Modeled results are compared with field time-lapse seismic measurements and strategies for numerical model feedback/update are discussed. While mechanical effects are neglected in the work presented here, complementary parallel studies are underway in which laboratory measurements are introduced to introduce stress dependence of matrix elastic moduli.

Regulating Tissue-Mimetic Mechanical Properties of Bottlebrush Elastomers by Magnetic Field.

We report on a new class of magnetoactive elastomers (MAEs) based on bottlebrush polymer networks filled with carbonyl iron microparticles. By synergistically combining solvent-free, yet supersoft polymer matrices, with magnetic microparticles, we enable the design of composites that not only mimic the mechanical behavior of various biological tissues but also permit contactless regulation of this behavior by external magnetic fields. While the bottlebrush architecture allows to finely tune the matrix elastic modulus and strain-stiffening, the magnetically aligned microparticles generate a 3-order increase in shear modulus accompanied by a switch from a viscoelastic to elastic regime as evidenced by a ca. 10-fold drop of the damping factor. The developed method for MAE preparation through solvent-free coinjection of bottlebrush melts and magnetic particles provides additional advantages such as injection molding of various shapes and uniform particle distribution within MAE composites. The synergistic combination of bottlebrush network architecture and magnetically responsive microparticles empowers new opportunities in the design of actuators and active vibration insulation systems.

Recycling of industrial waste based on jute fiber-polypropylene: Manufacture of sustainable fiber-reinforced polymer composites and their characterization before and after accelerated aging

This paper addresses the recycling of an industrial waste of jute (Corchoruscapsularis) and polypropylene fibers from Tapetes São Carlos carpet manufacturer conducted through the manufacture of composite materials and use of polypropylene (PP), a compatibilizer (C), and nano-calcium carbonate (N). The components were mixed in a co-rotational twin-screw extruder and dumbbell-shaped specimens were produced by injection molding. A masterbatch was previously processed for improving N dispersion in the polymer matrix. The composites were exposed to accelerated aging and tested by tensile and contact angle measurements, and evaluated by visual appearance before and after accelerated aging. The morphological evaluation was conducted by scanning electron microscopy (SEM). The processing techniques used provided composites with 50 wt.% waste, good N dispersion, no thermal or mechanical degradation of fibers, and better mechanical properties than pure PP. The presence of industrial waste led to a 135 % improvement in the elastic modulus of PP matrix and decreased deformation at break from 435 % to 5 %.N acted as mechanical reinforcement and decreased wettability. 18 % and 16 % improvements were achieved in the elastic modulus of the matrix when N was incorporated through the masterbatch and by direct extrusion, respectively. The composite processed after the manufacture of the masterbatch and with no compatibilizer showed a 186 % improvement in the elastic modulus of the matrix, lowest wettability, and best average performance under accelerated aging. Accelerated aging promotes a small reduction in stiffness, but a drastic dropping in the elongation of the materials. The composites can potentially be used in several commercial applications due to their properties and processing flexibility, which are relevant from both sustainable and economic viewpoints.

Topology Optimization of Multi-Materials Compliant Mechanisms

In this article, a design method of multi-material compliant mechanism is studied. Material distribution with different elastic modulus is used to meet the rigid and flexible requirements of compliant mechanism at the same time. The solid isotropic material with penalization (SIMP) model is used to parameterize the design domain. The expressions for the stiffness matrix and equivalent elastic modulus under multi-material conditions are proposed. The least square error (LSE) between the deformed and target displacement of the control points is defined as the objective function, and the topology optimization design model of multi-material compliant mechanism is established. The oversaturation problem in the volume constraint is solved by pre-setting the priority of each material, and the globally convergent method of moving asymptotes (GCMMA) is used to solve the problem. Widely studied numerical examples are conducted, which demonstrate the effectiveness of the proposed method.

Influence of Elastic Modulus of Matrix on Conductivity of VGCF Dispersed in Plastic Matrix

Pressure-sensitive conductive material is used for various pressure sensors consists of a polymer nanocomposite with carbon nanotubes (VGCF). And the resistance in it were changed by adding applied load. Recently, carbon nanotubes (VGCF) has drawn attention as a function filler that imparts various functions to a resin, including electrical properties. In polycarbonate (PC) composite with VGCF, the resistance decreases with increase in applied load. And increase of the addition amount of VGCF was enhanced the mechanical properties and electronic properties. In addition, this conclusion suggested that strain of PC/VGCF caused reducing the resistance. Therefore, changing matrix is predictably effective on electrical properties in pressure-conductive materials. In the present study, we used various matrix had different elastic modulus. The addition amount of VGCF was 12.5% volume rate. We made silicone/VGCF and polyethylene (PE)/VGCF and polycarbonate (PC)/VGCF by twin screw extruder and injection moldings. To clarify the influence of elastic modulus of matrix on conductivity of VGCF dispersed plastic matrix composites. The experimental results showed that conductive property of pressure-sensitive conductive materials is related to elastic modulus of them.

Nanocellulose for ecological nanoengineered strain-hardening cementitious composites incorporating high-volume ground-glass pozzolans

Nanomodification of concrete has a promising potential to allow engineering concrete properties for specific applications. This study shows how nanoscale cellulose filaments (CF) can be used as a novel tool for tailoring the properties of strain-hardening cementitious composites (SHCC) incorporating high-volume ground-glass pozzolans (HVGP) towards improved strength and ductility. CF was introduced (at 0 − 0.10% by weight of cement) into SHCC incorporating ground-glass pozzolans (GP)−also known as postconsumption glass powder−in replacement of fly ash (FA) at 0, 40, and 100%. Micromechanical guidelines were adopted for tailoring SHCC formulations. The performance of resulting SHCC was then validated by uniaxial tensile and flexural tests. Results indicate that CF allows nanoengineering matrix and interface properties by increasing matrix elastic modulus and imparting a significant slip-hardening effect. Consequently, higher complementary energy and lower crack tip toughness were obtained, thereby leading to enhanced ductility. Therefore, whereas at high GP content (above 40%) matrix strength increases at the detriment of its ductility, the incorporation of CF imparted a characteristic slip-hardening effect enabling restoring the ductility loss at high GP content. This made possible to produce SHCC with up to 100% GP replacement of FA exhibiting higher strength and ductility than conventional FA-SHCC (with similar water to binder ratio), while contributing to promoting ecoefficiency.