Density of excess modes below the first phonon mode in four-dimensional glasses

Glasses are known to possess low-frequency excess modes beyond the Debye prediction.For decades,it has been assumed that evolution of low-frequency density of excess modes D(ω) with frequency ω follows a power-law scaling:D(ω)~ω~γ.However,it remains debated on the value of γ at low frequencies below the first phonon-like mode in finitesize glasses.Early simulation studies reported γ=4 at low frequencies in two-(2D),three-(3D),and four-dimensional(4D)glasses,whereas recent observations in 2D and 3D glasses suggested γ=3.5 in a lower-frequency regime.It is uncertain whether the low-frequency scaling of D(ω)~ω^(3.5) could be generalized to 4D glasses.Here,we conduct numerical simulation studies of excess modes at frequencies below the first phonon-like mode in 4D model glasses.It is found that the system size dependence of D(ω) below the first phonon-like mode varies with spatial dimensions:D(ω) increases in2D glasses but decreases in 3D and 4D glasses as the system size increases.Furthermore,we demonstrate that the ω^(3.5)scaling,rather than the ω~4 scaling,works in the lowest-frequency regime accessed in 4D glasses,regardless of interaction potentials and system sizes examined.Therefore,our findings in 4D glasses,combined with previous results in 2D and 3D glasses,suggest a common low-frequency scaling of D(ω)~ ω^3.5) below the first phonon-like mode across different spatial dimensions,which would inspire further theoretical studies.

Evaluation of mitral chordae tendineae length using four-dimensional computed

BACKGROUND Mitral valvuloplasty using artificial chordae tendineae represents an effective surgical approach for treating mitral regurgitation.Achieving precise measurements of artificial chordae tendineae length(CL)is an important factor in the procedure;however,no objective index currently exists to facilitate this measurement.Therefore,preoperative assessment of CL is critical for surgical planning and support.Four-dimensional x-ray micro-computed tomography(4D-CT)may be useful for accurate CL measurement considering that it allows for dynamic three-dimensional(3D)evaluation compared to that with transthoracic echocardiography,a conventional inspection method.AIM To investigate the behavior and length of mitral chordae tendineae during systole using 4D-CT.METHODS Eleven adults aged>70 years without mitral valve disease were evaluated.A 64-slice CT scanner was used to capture 20 phases in the cardiac cycle in electrocardiographic synchronization.The length of the primary chordae tendineae was measured from early systole to early diastole using the 3D image.The primary chordae tendineae originating from the anterior papillary muscle and attached to the A1-2 region and those from the posterior papillary muscle and attached to the A2-3 region were designated as cA and cP,respectively.The behavior and maximum lengths[cA(ma),cP(max)]were compared,and the correlation with body surface area(BSA)was evaluated.RESULTS In all cases,the mitral anterior leaflet chordae tendineae could be measured.In most cases,the cA and cP chordae tendineae could be measured visually.The mean cA(max)and cP(max)were 20.2 mm±1.95 mm and 23.5 mm±4.06 mm,respectively.cP(max)was significantly longer.The correlation coefficients(r)with BSA were 0.60 and 0.78 for cA(max)and cP(max),respectively.Both cA and cP exhibited constant variation in CL during systole,with a maximum 1.16-fold increase in cA and a 1.23-fold increase in cP from early to mid-systole.For cP,CL reached a plateau at 15%and remained elongated until end-systole,whereas for cA,after peaking at 15%,CL shortened slightly and then moved toward its peak again as end-systole approached.CONCLUSION The study suggests that 4D-CT is a valuable tool for accurate measurement of both the length and behavior of chordae tendineae within the anterior leaflet of the mitral valve.

Theory and practice for assessing structural integrity and dynamical integrity of high-speed trains

Purpose–The safety and reliability of high-speed trains rely on the structural integrity of their components and the dynamic performance of the entire vehicle system.This paper aims to define and substantiate the assessment of the structural integrity and dynamical integrity of high-speed trains in both theory and practice.The key principles and approacheswill be proposed,and their applications to high-speed trains in Chinawill be presented.Design/methodology/approach–First,the structural integrity and dynamical integrity of high-speed trains are defined,and their relationship is introduced.Then,the principles for assessing the structural integrity of structural and dynamical components are presented and practical examples of gearboxes and dampers are provided.Finally,the principles and approaches for assessing the dynamical integrity of highspeed trains are presented and a novel operational assessment method is further presented.Findings–Vehicle system dynamics is the core of the proposed framework that provides the loads and vibrations on train components and the dynamic performance of the entire vehicle system.For assessing the structural integrity of structural components,an open-loop analysis considering both normal and abnormal vehicle conditions is needed.For assessing the structural integrity of dynamical components,a closed-loop analysis involving the influence of wear and degradation on vehicle system dynamics is needed.The analysis of vehicle system dynamics should follow the principles of complete objects,conditions and indices.Numerical,experimental and operational approaches should be combined to achieve effective assessments.Originality/value–The practical applications demonstrate that assessing the structural integrity and dynamical integrity of high-speed trains can support better control of critical defects,better lifespan management of train components and better maintenance decision-making for high-speed trains.

Aging impairs the osteocytic regulation of collagen integrity and bone quality

Poor bone quality is a major factor in skeletal fragility in elderly individuals.The molecular mechanisms that establish and maintain bone quality,independent of bone mass,are unknown but are thought to be primarily determined by osteocytes.We hypothesize that the age-related decline in bone quality results from the suppression of osteocyte perilacunar/canalicular remodeling(PLR),which maintains bone material properties.We examined bones from young and aged mice with osteocyte-intrinsic repression of TGFβsignaling(TβRII^(ocy−/−))that suppresses PLR.The control aged bone displayed decreased TGFβsignaling and PLR,but aging did not worsen the existing PLR suppression in male TβRII^(ocy−/−)bone.This relationship impacted the behavior of collagen material at the nanoscale and tissue scale in macromechanical tests.The effects of age on bone mass,density,and mineral material behavior were independent of osteocytic TGFβ.We determined that the decline in bone quality with age arises from the loss of osteocyte function and the loss of TGFβ-dependent maintenance of collagen integrity.

Chromatin condensation but not DNA integrity of pig sperm is greater in the sperm-rich fraction

Background Protamination and condensation of sperm chromatin as well as DNA integrity play an essential role during fertilization and embryo development.In some mammals,like pigs,ejaculates are emitted in three separate fractions:pre-sperm,sperm-rich(SRF)and post sperm-rich(PSRF).These fractions are known to vary in volume,sperm concentration and quality,as well as in the origin and composition of seminal plasma(SP),with differences being also observed within the SRF one.Yet,whether disparities in the DNA integrity and chromatin condensation and pro-tamination of their sperm exist has not been interrogated.Results This study determined chromatin protamination(Chromomycin A3 test,CMA_(3)),condensation(Dibromobi-mane test,DBB),and DNA integrity(Comet assay)in the pig sperm contained in the first 10 m L of the SRF(SRF-P1),the remaining portion of the sperm-rich fraction(SRF-P2),and the post sperm-rich fraction(PSRF).While chromatin protamination was found to be similar between the different ejaculate fractions(P>0.05),chromatin condensation was seen to be greater in SRF-P1 and SRF-P2 than in the PSRF(P=0.018 and P=0.004,respectively).Regarding DNA integrity,no differences between fractions were observed(P>0.05).As the SRF-P1 has the highest sperm concentra-tion and ejaculate fractions are known to differ in antioxidant composition,the oxidative stress index(OSi)in SP,calcu-lated as total oxidant activity divided by total antioxidant capacity,was tested and confirmed to be higher in the SRF-P1 than in SRF-P2 and PSRF(0.42±0.06 vs.0.23±0.09 and 0.08±0.00,respectively;P<0.01);this index,in addition,was observed to be correlated to the sperm concentration of each fraction(Rs=0.973;P<0.001).Conclusion While sperm DNA integrity was not found to differ between ejaculate fractions,SRF-P1 and SRF-P2 were observed to exhibit greater chromatin condensation than the PSRF.This could be related to the OSi of each fraction.

Improving fatigue properties of normal direction ultrasonic vibration assisted face grinding Inconel 718 by regulating machined surface integrity

Fatigue properties are crucial for critical aero-engine components in extreme serviceenvironments,which are significantly affected by surface integrity(SI)indexes(especially surface topography,residual stressσ_(res),and microhardness)after machining processes.Normal-direction ultrasonic vibration-assisted face grinding(ND-UVAFG)has advantages in improving the machinability of Inconel 718,but there is a competitive relationship between higher compressiveσ_(res)and higher surface roughness R_(a)in affecting fatigue strength.The lack of a quantitative relationship between multiple SI indexes and fatigue strength makes theindeterminacy of a regulatory strategy for improving fatigue properties.In this work,a model of fatigue strength(σ_f)_(sur)considering multiple SI indexes was developed.Then,high-cycle fatigue tests were carried out on Inconel 718 samples with different SI characteristics,and the influence of ND-UVAFG process parameters on SI was analyzed.Based on SI indexes data,the(σ_f)_(sur)distribution in the grinding surface layer for ND-UVAFG Inconel 718 samples was determined using the developed model,and then the fatigue crack initiation(FCI)sites were furtherpredicted.The predicted FCI sites corresponded well with the experimental results,therebyverifying this model.A strategy for improving the fatigue life was proposed in this work,which was to transfer the fatigue source from the machined surface to the bulk material by controlling the SI indexes.Finally,a critical condition of SI indexes that FCI sites appeared on the surface or in bulk material was given by fitting the predicted results.According to the critical condition,an SI field where FCI sites appeared in the bulk material could be obtained.In this field,thefatigue life of Inconel 718 samples could be improved by approximately 140%.

Preserving Data Secrecy and Integrity for Cloud Storage Using Smart Contracts and Cryptographic Primitives

Cloud computing has emerged as a viable alternative to traditional computing infrastructures,offering various benefits.However,the adoption of cloud storage poses significant risks to data secrecy and integrity.This article presents an effective mechanism to preserve the secrecy and integrity of data stored on the public cloud by leveraging blockchain technology,smart contracts,and cryptographic primitives.The proposed approach utilizes a Solidity-based smart contract as an auditor for maintaining and verifying the integrity of outsourced data.To preserve data secrecy,symmetric encryption systems are employed to encrypt user data before outsourcing it.An extensive performance analysis is conducted to illustrate the efficiency of the proposed mechanism.Additionally,a rigorous assessment is conducted to ensure that the developed smart contract is free from vulnerabilities and to measure its associated running costs.The security analysis of the proposed system confirms that our approach can securely maintain the confidentiality and integrity of cloud storage,even in the presence of malicious entities.The proposed mechanism contributes to enhancing data security in cloud computing environments and can be used as a foundation for developing more secure cloud storage systems.

Sec-Auditor:A Blockchain-Based Data Auditing Solution for Ensuring Integrity and Semantic Correctness

Currently,there is a growing trend among users to store their data in the cloud.However,the cloud is vulnerable to persistent data corruption risks arising from equipment failures and hacker attacks.Additionally,when users perform file operations,the semantic integrity of the data can be compromised.Ensuring both data integrity and semantic correctness has become a critical issue that requires attention.We introduce a pioneering solution called Sec-Auditor,the first of its kind with the ability to verify data integrity and semantic correctness simultaneously,while maintaining a constant communication cost independent of the audited data volume.Sec-Auditor also supports public auditing,enabling anyone with access to public information to conduct data audits.This feature makes Sec-Auditor highly adaptable to open data environments,such as the cloud.In Sec-Auditor,users are assigned specific rules that are utilized to verify the accuracy of data semantic.Furthermore,users are given the flexibility to update their own rules as needed.We conduct in-depth analyses of the correctness and security of Sec-Auditor.We also compare several important security attributes with existing schemes,demonstrating the superior properties of Sec-Auditor.Evaluation results demonstrate that even for time-consuming file upload operations,our solution is more efficient than the comparison one.

Perspectives from a publishing ethics and research integrity team for required improvements

It is imperative that all stakeholders within the research ecosystem take responsibility to improve research integrity and reliability of published research.Based on the unique experiences of a specialist publishing ethics and research integrity team within a major publisher,this article provides insights into the observed trends of misconduct and how those have evolved over time,and addresses key actions needed to improve the interface between researchers,funders,institutions and publishers to collectively improve research integrity on a global scale.

Passive Attack Detection for a Class of Stealthy Intermittent Integrity Attacks

This paper proposes a passive methodology for detecting a class of stealthy intermittent integrity attacks in cyberphysical systems subject to process disturbances and measurement noise.A stealthy intermittent integrity attack strategy is first proposed by modifying a zero-dynamics attack model.The stealthiness of the generated attacks is rigorously investigated under the condition that the adversary does not know precisely the system state values.In order to help detect such attacks,a backward-in-time detection residual is proposed based on an equivalent quantity of the system state change,due to the attack,at a time prior to the attack occurrence time.A key characteristic of this residual is that its magnitude increases every time a new attack occurs.To estimate this unknown residual,an optimal fixed-point smoother is proposed by minimizing a piece-wise linear quadratic cost function with a set of specifically designed weighting matrices.The smoother design guarantees robustness with respect to process disturbances and measurement noise,and is also able to maintain sensitivity as time progresses to intermittent integrity attack by resetting the covariance matrix based on the weighting matrices.The adaptive threshold is designed based on the estimated backward-in-time residual,and the attack detectability analysis is rigorously investigated to characterize quantitatively the class of attacks that can be detected by the proposed methodology.Finally,a simulation example is used to demonstrate the effectiveness of the developed methodology.

An unequal fracturing stage spacing optimization model for hydraulic fracturing that considers cementing interface integrity

Determining reasonable fracturing stage spacing is the key to horizontal well fracturing.Different from traditional stage spacing optimization methods based on the principle of maximum stimulated reservoir volume,in this paper,by considering the integrity of the wellbore interface,a fracture propagation model was established based on displacement discontinuity method and the competition mechanism of multifracture joint expansion,leading to the proposal of an unequal stage spacing optimization model.The results show that in the first stage,the interfacial fractures spread symmetrically along the axis of the central point during that stage,while in the second and subsequent stages,the interfacial fractures of each cluster extend asymmetrically along the left and right sides.There are two kinds of interface connectivity behaviour:in one,the existing fractures first extend and connect within the stage,and in the other,the fractures first extend in the direction close to the previous stage,with the specific behaviour depending on the combined effect of stress shadow and flow competition during hydraulic fracture expansion.The stage spacing is positively correlated with the number of fractures and Young’s modulus of the cement and formation and is negatively correlated with the cluster spacing and horizontal principal stress difference.The sensitivity is the strongest when the Young’s modulus of the cement sheath is 10-20 GPa,and the sensitivity of the horizontal principal stress difference is the weakest.

Phytogenic feed additives alleviate pathogenic Escherichia coli-induced intestinal damage through improving barrier integrity and inhibiting inflammation in weaned pigs

Background:This study was conducted to investigate the effects of each phytogenic feed additive(PFA;PFA1,bitter citrus extract;PFA2,a microencapsulated blend of thymol and carvacrol;PFA3,a mixture of bitter citrus extract,thymol,and carvacrol;PFA4,a premixture of grape seed,grape marc extract,green tea,and hops;PFA5,fenugreek seed powder)on the growth performance,nutrient digestibility,intestinal morphology,and immune response in weaned pigs infected with Escherichia coli(E.coli).Results:A total of 634-week-old weaned pigs were placed in individual metabolic cages and assigned to seven treatment groups.The seven treatments were as follows:1)NC;basal diet without E.coli challenge,2)PC;basal diet with E.coli challenge,3)T1;PC+0.04%PFA1,4)T2;PC+0.01%PFA2,5)T3;PC+0.10%PFA3,6)T4;PC+0.04%PFA4,7)T5;PC+0.10%PFA5.The experiments lasted in 21 d,including 7 d before and 14 d after the first E.coli challenge.In the E.coli challenge treatments,all pigs were orally inoculated by dividing a total of 10 mL of E.coli F18 for 3 consecutive days.The PFA-added groups significantly increased(P<0.05)average daily gain and feed efficiency and decreased(P<0.05)the fecal score at d 0 to 14 post-inoculation(PI).Tumor necrosis factorαwas significantly lower(P<0.05)in the PFA-added groups except for T1 in d 14 PI compared to the PC treatment.The T3 had a higher(P<0.05)immunoglobulin G and immunoglobulin A concentration compared to the PC treatment at d 7 PI.Also,T3 showed significantly higher(P<0.05)villus height:crypt depth and claudin 1 expression in ileal mucosa,and significantly downregulated(P<0.05)the expression of calprotectin compared to the PC treatment.Conclusions:Supplementation of PFA in weaned pigs challenged with E.coli alleviated the negative effects of E.coli and improved growth performance.Among them,the mixed additive of bitter citrus extract,thymol,and carvacrol showed the most effective results,improving immune response,intestinal morphology,and expression of tight junctions.

Failure mechanism and influencing factors of cement sheath integrity under alternating pressure

The failure of cement sheath integrity can be easily caused by alternating pressure during large-scale multistage hydraulic fracturing in shale-gas well.An elastic-plastic mechanical model of casing-cement sheath-formation(CSF)system under alternating pressure is established based on the Mohr-Coulomb criterion and thick-walled cylinder theory,and it has been solved by MATLAB programming combining global optimization algorithm with Global Search.The failure mechanism of cement sheath integrity is investigated,by which it can be seen that the formation of interface debonding is mainly related to the plastic strain accumulation,and there is a risk of interface debonding under alternating pressure,once the cement sheath enters plasticity whether in shallow or deep well sections.The matching relationship between the mechanical parameters(elastic modulus and Poisson's ratio)of cement sheath and its integrity failure under alternating pressure in whole well sections is studied,by which it has been found there is a“critical range”in the Poisson's ratio of cement sheath.When the Poisson's ratio is below the“critical range”,there is a positive correlation between the yield internal pressure of cement sheath(SYP)and its elastic modulus.However,when the Poisson's ratio is above the“critical range”,there is a negative correlation.The elastic modulus of cement sheath is closely related to its Poisson's ratio,and restricts each other.Scientific and reasonable matching between mechanical parameters of cement sheath and CSF system under different working conditions can not only reduce the cost,but also protect the cement sheath integrity.

Insights into the relations between cell wall integrity and in vitro digestion properties of granular starches in pulse cotyledon cells after dry heat treatment

Natural foods,such as whole pulses,are recommended in the dietary guidelines of the US and China.The plant cell wall structure in whole pulses has important implications for the nutritional functionalities of starch.In this study,garbanzo bean cells with varying degrees of cell wall integrity were subjected to dry heat treatment(DHT)and used to elucidate the food structure-starch digestion properties of pulse food.The morphological features suggested that all cell samples do not exhibit remarkable changes after being subjected to DHT.Molecular rearrangement and the crystallite disruption of starch granules entrapped in cells occurred during DHT as assessed by the crystal structure and thermal properties.DHT decreased the inhibitory effects of enzymes of both the soluble and insoluble components,but the digestion rate and extent of slightly and highly damaged cell samples did not exhibit significant differences compared with their native counterparts.We concluded that the starch digestion of pulse cotyledon cells is primarily determined by the intactness of the cellular structure.This study reveals the role of food structure on the ability to retain the desirable nutritional properties of starch after subjection to physical modification.

Determination of rock mass integrity coefficient using a non-invasive geophysical approach

Determination of rock mechanical parameters is the most important step in rock mass quality evaluation and has significant impacts on geotechnical engineering practice.Rock mass integrity coefficient(KV)is one of the most efficient parameters,which is conventionally determined from boreholes.Such approaches,however,are time-consuming and expensive,offer low data coverage of point measurements,require heavy equipment,and are hardly conducted in steep topographic sites.Hence,borehole approaches cannot assess the subsurface thoroughly for rock mass quality evaluation.Alternatively,use of geophysical methods is non-invasive,rapid and economical.The proposed geophysical approach makes useful empirical correlation between geophysical and geotechnical parameters.We evaluated the rock mass quality via integration between KV measured from the limited boreholes and inverted resistivity obtained from electrical resistivity tomography(ERT).The borehole-ERT correlation provided KV along various geophysical profiles for more detailed 2D/3D(two-/three-dimensional)mapping of rock mass quality.The subsurface was thoroughly evaluated for rock masses with different engineering qualities,including highly weathered rock,semi-weathered rock,and fresh rock.Furthermore,ERT was integrated with induced polarization(IP)to resolve the uncertainty caused by water/clay content.Our results show that the proposed method,compared with the conventional approaches,can reduce the ambiguities caused by inadequate data,and give more accurate insights into the subsurface for rock mass quality evaluation.

Intelligent Small Sample Defect Detection of Concrete Surface Using Novel Deep Learning Integrating Improved YOLOv5

Dear Editor,This letter presents an intelligent small sample defect detection of concrete surface using novel deep learning integrating the improved YOLOv5 based on the Wasserstein GAN(WGAN)enhancement algorithm.The proposed method is capable of producing top-notch data sets to address the issues of insufficient samples and substandard quality.

基于Cadence Integrity 3D-IC的异构集成封装系统级LVS检查

随着硅工艺尺寸发展到单纳米水平,摩尔定律的延续越来越困难。2D Flip-Chip、2.5D、3D等异构集成的先进封装解决方案将继续满足小型化、高性能、低成本的市场需求,成为延续摩尔定律的主要方向。但它也提出了新的挑战,特别是对于系统级的LVS检查。采用Cadence Integrity 3D-IC平台工具,针对不同类型的先进封装,进行了系统级LVS检查验证,充分验证了该工具的有效性和实用性,保证了异构集成封装系统解决方案的可靠性。

Optimal synthesis of heat-integrated distillation configurations using the two-column superstructure

In the realm of the synthesis of heat-integrated distillation configurations,the conventional approach for exploring more heat integration possibilities typically entails the splitting of a single column into a twocolumn configuration.However,this approach frequently necessitates tedious enumeration procedures,resulting in a considerable computational burden.To surmount this formidable challenge,the present study introduces an innovative remedy:The proposition of a superstructure that encompasses both single-column and multiple two-column configurations.Additionally,a simultaneous optimization algorithm is applied to optimize both the process parameters and heat integration structures of the twocolumn configurations.The effectiveness of this approach is demonstrated through a case study focusing on industrial organosilicon separation.The results underscore that the superstructure methodology not only substantially mitigates computational time compared to exhaustive enumeration but also furnishes solutions that exhibit comparable performance.

PIMS:An Efficient Process Integrity Monitoring System Based on Blockchain and Trusted Computing in Cloud-Native Context

With the advantages of lightweight and high resource utilization,cloud-native technology with containers as the core is gradually becoming themainstreamtechnical architecture for information infrastructure.However,malware attacks such as Doki and Symbiote threaten the container runtime’s security.Malware initiates various types of runtime anomalies based on process form(e.g.,modifying the process of a container,and opening the external ports).Fortunately,dynamic monitoring mechanisms have proven to be a feasible solution for verifying the trusted state of containers at runtime.Nevertheless,the current routine dynamic monitoring mechanisms for baseline data protection are still based on strong security assumptions.As a result,the existing dynamicmonitoringmechanismis still not practical enough.To ensure the trustworthiness of the baseline value data and,simultaneously,to achieve the integrity verification of the monitored process,we combine blockchain and trusted computing to propose a process integrity monitoring system named IPMS.Firstly,the hardware TPM 2.0 module is applied to construct a trusted security foundation for the integrity of the process code segment due to its tamper-proof feature.Then,design a new format for storing measurement logs,easily distinguishing files with the same name in different containers from log information.Meanwhile,the baseline value data is stored on the blockchain to avoidmalicious damage.Finally,trusted computing technology is used to perform fine-grained integrity measurement and remote attestation of processes in a container,detect abnormal containers in time and control them.We have implemented a prototype system and performed extensive simulation experiments to test and analyze the functionality and performance of the PIMS.Experimental results show that PIMS can accurately and efficiently detect tampered processes with only 3.57% performance loss to the container.

An Investigation into the Effects of Oil-Well Cement Expansion Agent on the Integrity of Cement Sheath

Generally,the so-called expansion agent is very effective in eliminating all the micro-annuli that exist between the casing and the cement sheath or between the cement sheath and the formation.However,this approach can detrimentally affect the sealing ability of cement sheath if the expansion agent is used in an unreasonable way.For these reasons,in the present work,numerical simulations have been conducted to analyze the effect of elasticity modulus of cement sheath,the elasticity modulus of formation,the expansion rate of cement,the geo-stress on the micro-annulus caused by cement expansion,and the cement sheath expansion on the integrity of cement sheath and formation.The micro-annulus between the casing and the cement sheath has been found to decrease according to the ratio between the elasticity modulus of formation and the elasticity modulus of cement sheath.A positive correlation has been observed between the micro-annulus and the cement expansion ratio.The microannulus decreases as the geo-stress increases,but the effect of the geo-stress on the micro-annulus is much smaller.In conclusion,the expansion agent is suitable for the formation in which the elasticity modulus is higher than the cement sheath.