20 resultados para K most critical paths
em Chinese Academy of Sciences Institutional Repositories Grid Portal
Resumo:
A closed, trans-scale formulation of damage evolution based on the statistical microdamage mechanics is summarized in this paper. The dynamic function of damage bridges the mesoscopic and macroscopic evolution of damage. The spallation in an aluminium plate is studied with this formulation. It is found that the damage evolution is governed by several dimensionless parameters, i.e., imposed Deborah numbers De* and De, Mach number M and damage number S. In particular, the most critical mode of the macroscopic damage evolution, i.e., the damage localization, is deter-mined by Deborah number De+. Deborah number De* reflects the coupling and competition between the macroscopic loading and the microdamage growth. Therefore, our results reveal the multi-scale nature of spallation. In fact, the damage localization results from the nonlinearity of the microdamage growth. In addition, the dependence of the damage rate on imposed Deborah numbers De* and De, Mach number M and damage number S is discussed.
Resumo:
The effect of subgrid-scale (SGS) modeling on velocity (space-) time correlations is investigated in decaying isotropic turbulence. The performance of several SGS models is evaluated, which shows superiority of the dynamic Smagorinsky model used in conjunction with the multiscale large-eddy simulation (LES) procedure. Compared to the results of direct numerical simulation, LES is shown to underpredict the (un-normalized) correlation magnitude and slightly overpredict the decorrelation time scales. This can lead to inaccurate solutions in applications such as aeroacoustics. The underprediction of correlation functions is particularly severe for higher wavenumber modes which are swept by the most energetic modes. The classic sweeping hypothesis for stationary turbulence is generalized for decaying turbulence and used to analyze the observed discrepancies. Based on this analysis, the time correlations are determined by the wavenumber energy spectra and the sweeping velocity, which is the square root of the total energy. Hence, an accurate prediction of the instantaneous energy spectra is most critical to the accurate computation of time correlations. (C) 2004 American Institute of Physics.
Resumo:
The application of large-eddy simulation (LES) to particle-laden turbulence raises such a fundamental question as whether the LES with a subgrid scale (SGS) model can correctly predict Lagrangian time correlations (LTCs). Most of the currently existing SGS models are constructed based on the energy budget equations. Therefore, they are able to correctly predict energy spectra, but they may not ensure the correct prediction on the LTCs. Previous researches investigated the effect of the SGS modeling on the Eulerian time correlations. This paper is devoted to study the LTCs in LES. A direct numerical simulation (DNS) and the LES with a spectral eddy viscosity model are performed for isotropic turbulence and the LTCs are calculated using the passive vector method. Both a priori and a posteriori tests are carried out. It is observed that the subgrid-scale contributions to the LTCs cannot be simply ignored and the LES overpredicts the LTCs than the DNS. It is concluded from the straining hypothesis that an accurate prediction of enstrophy spectra is most critical to the prediction of the LTCs.
Resumo:
Unlike those of the wild-type strain, proheterocysts of the Anabaena sp. strain PCC 7120 hetC strain keep dividing. ftsZ, the most critical cell division gene, is up-regulated in hetC proheterocysts. Heterocyst differentiation genes hglD, hglE, patB, nijB, and xisA are no longer expressed in the hetC mutant. hetC also regulates the expression of patA, a pattern formation gene.
Resumo:
木质纤维素原料种类多、分布广、数量巨大,通过燃料乙醇生产技术、厌氧沼气发酵技术将其转化成乙醇、沼气等二次能源,一定程度上可以缓解化石能源的不断消耗所带来的能源危机,也解决了农林废弃物引起的环境污染问题。其中以木质纤维素原料生产燃料乙醇,还可以避免以淀粉类和糖类原料生产燃料乙醇时带来的“与人争粮”等一系列问题。因此具有重要的经济效益、环境效益和社会效益。 然而,木质纤维素原料结构致密,木质素包裹在纤维素、半纤维素外围,导致其很难被降解利用,必须进行适当的预处理,去除木质素,打破原有的致密结构,利于原料的后续利用。因此,预处理成为木质纤维素原料能源化利用的关键。而目前预处理环节的费用过于昂贵,于是寻找一种高效、低成本的预处理方法是当今研究的热点。 本论文采用组合白腐真菌对木质纤维素原料进行生物预处理研究,与其他物理化学法相比,该法有着专一性较强、反应温和、不造成环境污染、成本低等优势。白腐真菌主要通过分泌木质素降解酶对木质素进行降解,从而破坏原料的致密结构,提高后续利用效率。所以木质素降解酶酶活的高低是影响原料预处理效果的一个关键因素。于是本论文首先通过将白腐真菌进行组合的方式提高木质素降解酶(漆酶,Lac)酶活;接着对组合菌的菌株相互作用机理进行研究,阐明组合菌Lac 酶活提高的原因,为菌株组合提高Lac 酶活这种方法的应用提供理论依据,同时也为后续组合白腐真菌预处理木质纤维素原料提供指导;进一步采用固态发酵和木质素降解酶两种方式对木质纤维素原料进行预处理研究,最大化去除木质素成分,破坏原料的致密结构;最终对预处理后原料的酶解糖化进行初步研究,为原料后续的能源化应用奠定基础。具体研究结果如下: (1) 以实验室保存的三株主要分泌Lac 的白腐真菌为出发菌株,筛选得到一组Lac 酶活明显提高的组合菌55+m-6,其中菌株55 为Trametes trogii sp.,m-6 为Trametes versicolor sp.,组合后Lac 酶活较单菌株分别提高24.13倍和4.07 倍。组合菌的最适产酶条件为pH 6.5、C/N 16:1、Tween 80 添加量为0.01%,在该条件下组合菌的Lac 酶活峰值比未优化时提高4.11倍。 (2) 对组合菌55+m-6 菌株间相互作用机理进行研究,发现菌株之间不存在抑制作用;平板培养时,菌丝交界处Lac 酶活最高并分泌棕色色素;液体培养时,菌株m-6 对组合后Lac 酶活的提高起着更为重要的作用:菌株m-6的菌块、过滤灭菌胞外物以及高温灭菌胞外物均能明显刺激菌株55 的Lac产生;菌株55、m-6 进行组合后,同工酶种类未发生增减,但有三种Lac同工酶浓度有所提高;对菌株胞外物进行薄层层析和质谱分析,结果表明组合前后菌株胞外物中各物质在浓度上存在较大的变化。推测组合菌Lac酶活的明显提高,主要是由于菌株m-6 胞外物中的一些物质能刺激菌株55 分泌大量Lac 进行代谢,且这些刺激物质并非菌株m-6 特有,菌株55自身也可以代谢生成,但是适当的浓度才能刺激Lac 的大量分泌。 (3) 将组合菌55+m-6 用于固态发酵预处理木质纤维素原料,发现其对玉米秆的降解程度最大,在粉碎度40 目、含水率65%的最优处理条件下,处理至第15d,秸秆失重率为41.24%,其中木质素、纤维素、半纤维素均有降解,且Lac 和纤维素酶(CMC)酶活以及还原糖量均达到峰值。 (4) 对玉米秆进行木质素降解酶预处理,发现Lac/1-羟基苯并三唑(HBT)系统对玉米秆木质素的降解效果最好,在最优处理条件时,即HBT 用量0.2%、处理时间1d、Lac 用量50U/g,木质素降解率可达12.60%。预处理后玉米秆的致密结构被破坏,比表面积增大,利于后续酶与纤维素、半纤维素成分的结合。 (5) 对预处理后的玉米秆进行酶解糖化,其中组合菌固态发酵预处理后玉米秆的糖化率比对照高4.33 倍;Lac/HBT 系统预处理后玉米秆的糖化率比对照高2.99%,糖化液中主要含有木糖、葡萄糖两种单糖。 There are many kinds and large quantities of lignocellulosic biomass widely distributed on the earth. They can be converted into secondary energy such as fuel ethanol, biogas, et al., which can relieve the energy crisis caused by consumption of fossil energy resources and solve the problem of environmental pollution caused by agriculture and forestry waste. Meanwhile, the production of fuel ethanol from lignocellulosic biomass can ensure food supply to human kind instead of starch- and sugar-containing raw materials. So the energy conversion of lignocellulosic biomass contributes considerable economic, environment and social benefits. However, lignocellulosic biomass has the compact structure, in which lignin surrounds cellulose and hemicellulose, so it must be pretreated before energy usage and pretreatment is one of the most critical steps in the energy conversion of lignocellulosic biomass. At present, the cost of pretreatment is too expensive, so looking for an efficient and low-cost pre-treatment method is one of recent research hot spots. In this research, combined white rot fungi pretreatment method was used, which had some advantages in low cost, high specificity, mild reacting conditions and friendly environmental effects compared with the other physical and chemical methods. White rot fungi secrete lignin degrading enzymes to degrade the content of lignin and damage the contact structure of lignocellulosic biomass, so the activity of the lignin degrading enzymes is the key factor to the degradation effect of raw materials. Firstly, the combined fungi with high laccase activity were screened; secondly, the interaction mechanism between strains was studied, and the cause of higher laccase activity after strains combination was also preliminary clarified; under the guidance of the mechanism, lignocellulosic biomass was pretreated by the combined fungi; lastly, the enzymatic hydrolysis of pretreated lignocellulosic biomass was also preliminary studied; all of the researches could lay the foundation for the energy application of lignocellulosic biomass. The specific research results were as follows: (1) The combined fungi 55+m-6 with significant higher laccase activity were screened from the three white rot fungi stored in our lab which mainly secreted laccase. Strain 55 and strain m-6 were Trametes trogii sp. and Trametes versicolor sp., respectively. The laccase activity of combined fungi was 24.13 and 4.07-fold than strain 55 and strain m-6, respectively. The optimized condition for laccase production of the combined fungi in liquid medium was pH 6.5, C/N 16:1 and Tween 80 0.01%. In this optimized condition, the laccase activity of combined fungi was 4.11-fold higher comparing with which in non-optimized medium. (2) The interaction mechanism between strain 55 and strain m-6 was further studied, and no inhibition effect was observed. Brown pigment was secreted on the junction of the two strains on the plate, where the highest laccase activity was detected. Strain m-6 was much important to boost laccase activity of combined fungi in liquid medium, and strain 55 was stimulated by fungal plug, filter sterilized extracellular substances and high temperature sterilized extracellular substances of strain m-6 to produce laccase. The types of laccase isozymes did not change after combining strain 55 and strain m-6, but the concentrations of three types increased. Mass Spectrometry and TLC analysis of extracellular substances of each strain showed that concentration of some substances considerably changed after strains were combined. It was supposed that the cause of higher laccase activity of combined fungi was mainly due to some extracellular substances of strain m-6 with the appropriate concentration which stimulated laccase secretion of strain 55 and generated not only by strain m-6 but also by strain 55. (3) Combined fungi 55+m-6 were used to lignocellulosic biomass pretreatment with the type of solid-state fermentation. The highest degree of degradation of corn straw was obtained, including the rate of weight loss was 41.24% and the lignin, cellulose and hemicellulose were degraded partially under the optimized condition of 40 mesh, 65% water content on 15th day. Laccase, CMCase activities and content of reducing sugar reached the maximum value on that day. (4) Lignin degrading enzymes from combined fungi 55+m-6 were used for corn straw pretreatment. The most remarkable degradation of lignin in corn straw with Lac/1-hydroxybenzotriazole (HBT) system was observed, and the 12.60% lignin degradation was obtained under the optimized condition of 0.2% HBT, 50 U/g laccase for 1 d. After pretreated by Lac/HBT, the tight structure of corn straw was demolished and specific surface area increased, which had advantages for accessible of enzyme to cellulose and hemicellulose. (5) The corn straws pretreated by combined fungi 55+m-6 with the type of solid-state fermentation and Lac/HBT were used for enzymatic hydrolysis, and the saccharification rates of each pretreatment type were 4.33 times and 2.99% higher than CK, respectively. The enzymatic hydrolysis liquid of corn straw pretreated by Lac/HBT mainly contained xylose and glucose.
Resumo:
A number of functional neuroimaging studies with skilled readers consistently showed activation to visual words in the left mid-fusiform cortex in occipitotemporal sulcus (LMFC-OTS). Neuropsychological studies also showed that lesions at left ventral occipitotemporal areas result in impairment in visual word processing. Based on these empirical observations and some theoretical speculations, a few researchers postulated that the LMFC-OTS is responsible for instant parallel and holistic extraction of the abstract representation of letter strings, and labeled this piece of cortex as “visual word form area” (VWFA). Nonetheless, functional neuroimaging studies alone is basically a correlative rather than causal approach, and lesions in the previous studies were typically not constrained within LMFC-OTS but also involving other brain regions beyond this area. Given these limitations, it remains unanswered for three fundamental questions: is LMFC-OTS necessary for visual word processing? is this functionally selective for visual word processing while unnecessary for processing of non-visual word stimuli? what are its function properties in visual word processing? This thesis aimed to address these questions through a series of neuropsychological, anatomical and functional MRI experiments in four patients with different degrees of impairments in the left fusiform gyrus. Necessity: Detailed analysis of anatomical brain images revealed that the four patients had differential foci of brain infarction. Specifically, the LMFC-OTS was damaged in one patient, while it remained intact in the other three. Neuropsychological experiments showed that the patient with lesions in the LMFC-OTS had severe impairments in reading aloud and recognizing Chinese characters, i.e., pure alexia. The patient with intact LMFC-OTS but information from the left visual field (LVF) was blocked due to lesions in the splenium of corpus callosum, showed impairment in Chinese characters recognition when the stimuli were presented in the LVF but not in the RVF, i.e. left hemialexia. In contrast, the other two patients with intact LMFC-OTS had normal function in processing Chinese characters. The fMRI experiments demonstrated that there was no significant activation to Chinese characters in the LMFC-OTS of the pure alexic patient and of the patient with left hemialexia when the stimuli were presented in the LVF. On the other hand, this patient, when Chinese characters were presented in right visual field, and the other two with intact LMFC-OTS had activation in the LMFC-OTS. These results together point to the necessity of the LMFC-OTS for Chinese character processing. Selectivity: We tested selectivity of the LMFC-OTS for visual word processing through systematically examining the patients’ ability for processing visual vs. auditory words, and word vs. non-word visual stimuli, such as faces, objects and colors. Results showed that the pure alexic patients could normally process auditory words (expression, understanding and repetition of orally presented words) and non-word visual stimuli (faces, objects, colors and numbers). Although the patient showed some impairments in naming faces, objects and colors, his performance scores were only slightly lower or not significantly different relative to those of the patients with intact LMFC-OTS. These data provide compelling evidence that the LMFC-OTS is not requisite for processing non-visual word stimuli, thus has selectivity for visual word processing. Functional properties: With tasks involving multiple levels and aspects of word processing, including Chinese character reading, phonological judgment, semantic judgment, identity judgment of abstract visual word representation, lexical decision, perceptual judgment of visual word appearance, and dictation, copying, voluntary writing, etc., we attempted to reveal the most critical dysfunction caused by damage in the LMFC-OTS, thus to clarify the most essential function of this region. Results showed that in addition to dysfunctions in Chinese character reading, phonological and semantic judgment, the patient with lesions at LMFC-OTS failed to judge correctly whether two characters (including compound and simple characters) with different surface features (e.g., different fonts, printed vs. handwritten vs. calligraphy styles, simplified characters vs. traditional characters, different orientations of strokes or whole characters) had the same abstract representation. The patient initially showed severe impairments in processing both simple characters and compound characters. He could only copy a compound character in a stroke-by-stroke manner, but not by character-by-character or even by radical-by-radical manners. During the recovery process, namely five months later, the patient could complete the abstract representation tasks of simple characters, but showed no improvement for compound characters. However, he then could copy compound characters in a radical-by-radical manner. Furthermore, it seems that the recovery of copying paralleled to that of judgment of abstract representation. These observations indicate that lesions of the LMFC-OTS in the pure alexic patients caused several damage in the ability of extracting the abstract representation from lower level units to higher level units, and the patient had especial difficulty to extract the abstract representation of whole character from its secondary units (e.g., radicals or single characters) and this ability was resistant to recover from impairment. Therefore, the LMFC-OTS appears to be responsible for the multilevel (particularly higher levels) abstract representations of visual word form. Successful extraction seems independent on access to phonological and semantic information, given the alexic patient showed severe impairments in reading aloud and semantic processing on simple characters while maintenance of intact judgment on their abstract representation. However, it is also possible that the interaction between the abstract representation and its related information e.g. phonological and semantic information was damaged as well in this patient. Taken together, we conclude that: 1) the LMFC-OTS is necessary for Chinese character processing, 2) it is selective for Chinese character processing, and 3) its critical function is to extract multiple levels of abstract representation of visual word and possibly to transmit it to phonological and semantic systems.
Resumo:
Human being’s visual attentional system is the direct results of millions of years of evolutionary selection. As an adaptation to the environment, the most prominent function of attentional system is to facilitate the effective selection and subsequent processing of the most critical information and events from the environment with the aim of enhancing a given individual’s chance of passing his/her gene to the next generation. In the living environment of ancestral human beings, animals were undoubtedly one of those stimulus categories of great evolutionary significance. Since the process of animal-related information had life-or-death consequences for ancestral human beings, some researchers proposed a so-called animate monitoring hypothesis which states that there exists a category-specific module in the attentional system of human beings which specializes in the detection and frequent re-inspection of animal stimuli. Drawing on the available findings and theories regarding the inhibition-of-return effect, the present study utilized several variants of the spatial cueing paradigm to test the two main predictions of animate monitoring hypothesis:(1) animal stimuli in the environment are capable of summon attention in a reflexive way; (2) the inhibitory effect of attentional process on animal stimuli is less pronounced when compared to stimuli of other categories. The results of the present study provide supportive evidence to the existence of a category-specific module for animals in the attentional system. The present study contributes to the further understanding of the important role played by attentional mechanism in solving the critical adaptive problem faced by ancestral human beings during the course of evolution.
Resumo:
Among various mutation detection methods, constant denaturant capillary electrophoresis (CDCE) is one of the most common techniques for rapid identification of known or unknown mutations. In this report, a CDCE analysis method with homemade linear polyacrylamide (LPA) kit was developed on ABI 310 genetic analyzer, the effect and relationship of various denaturing factors in CDCE analysis were investigated and K-ras gene mutations of 31 coloerctal cancer patients were detected. Results indicate that, with the increase of chemical danaturant concentration, the optimum temperature was lowered, and when the concentration of urea (formamide) was higher than 7 M (40%), the homoduplex and heteroduplex of mutant samples were separated with difficulty. Detection results of K-ras gene in colorectal samples indicated that mutations were present in eight (26%) of 31 patients; most mutations were localized in codon 12, which is thought to be a critical step and plays an important role in human colorectal carcinogenesisas. Copyright (C) 2004 John Wiley Sons, Ltd.
Resumo:
Accurate and fast genotyping of single nucleotide polymorphisms (SNPs) is important in the human genome project. Here an automated fluorescent method that can rapidly and accurately genotype multiplex known SNPs was developed by using a homemade kit, which has lower cost but higher resolution than commercial kit. With this method, oncogene K-ras was investigated, four known SNPs of K-ras gene exon 1 in 31 coloerctal cancer patients were detected. Results indicate that mutations were present in 8(26%) of 31 patients, and most mutations were localized in codon 12. The presence of these mutations is thought to be a critical step and plays an important role in human colorectal carcinogenesisas. (C) 2003 Elsevier B.V. All rights reserved.
Resumo:
La57.6Al17.5(Cu,Ni)(24.9) and La64Al14(Cu,Ni)(22) bulk metallic glasses (BMGs) were prepared by copper-mould casting method. Plastic deformation behavior of the two BMGs at various loading rates was studied by nanoindentation. The results showed that the La57.6Al17.5(Cu,Ni)(24.9) BMG with a glass transition temperature of 423 K exhibited prominent serrated flow at low loading rates, whereas less pronounced serrated flow at high rates during nanoindentation. In contrast, the La64Al14(Cu,Ni)(22) BMG with a glass transition temperature of 401 K exhibited prominent serrated flow at high loading rates. The different rate dependency of serrated flow in the two La-based BMGs is related to the different glass transition temperature, and consequently the degree of viscous flow during indentation at room temperature. A smoother flow occurs in the alloy with relatively lower glass transition temperature, due to the relaxation of stress concentration.
Resumo:
Background Mitochondrial DNA (mtDNA) is being analyzed by an increasing number of laboratories in order to investigate its potential role as an active marker of tumorigenesis in various types of cancer. Here we question the conclusions drawn in most of these investigations, especially those published in high-rank cancer research journals, under the evidence that a significant number of these medical mtDNA studies are based on obviously flawed sequencing results. Methods and Findings In our analyses, we take a phylogenetic approach and employ thorough database searches, which together have proven successful for detecting erroneous sequences in the fields of human population genetics and forensics. Apart from conceptual problems concerning the interpretation of mtDNA variation in tumorigenesis, in most cases, blocks of seemingly somatic mutations clearly point to contamination or sample mix-up and, therefore, have nothing to do with tumorigenesis. Conclusion The role of mitochondria in tumorigenesis remains unclarified. Our findings of laboratory errors in many contributions would represent only the tip of the iceberg since most published studies do not provide the raw sequence data for inspection, thus hindering a posteriori evaluation of the results. There is no precedent for such a concatenation of errors and misconceptions affecting a whole subfield of medical research.
Resumo:
Ga1-xMnxAs films with exceptionally high saturation magnetizations of approximate to 100 emu/cm(3) corresponding to effective Mn concentrations of x(eff)approximate to 0.10 still have a Curie temperature T-C smaller than 195 K contradicting mean-field predictions. The analysis of the critical exponent beta of the remnant magnetization-beta = 0.407(5)-in the framework of the models for disordered/amorphous ferromagnets suggests that this limit on T-C is intrinsic and due to the short range of the ferromagnetic interactions resulting from the small mean-free path of the holes. This result questions the perspective of room-temperature ferromagnetism in highly doped GaMnAs.
Resumo:
We investigated the temperature dependence (10-250 K) of the photoluminescence (PL) emission spectrum of self-organized Ge/Si(001) islands in a multilayer structure. With elevated temperature, we find that the thermally activated holes and electrons are gathered by the Ge islands in different ways. The holes drift from the wetting layer into the islands, while the electrons, confined in Si due to type-II band alignment, leak into the Ge islands by the electrostatic interaction with the holes accumulated there. It results in an increase of the integrated intensity of island-related PL at a certain temperature range and a reduction of the phonon energy in the phonon-assisted PL of the islands by involving a type-I transition into a type-II transition. (C) 2001 American Institute of Physics.
Resumo:
The K-best detector is considered as a promising technique in the MIMO-OFDM detection because of its good performance and low complexity. In this paper, a new K-best VLSI architecture is presented. In the proposed architecture, the metric computation units (MCUs) expand each surviving path only to its partial branches, based on the novel expansion scheme, which can predetermine the branches' ascending order by their local distances. Then a distributed sorter sorts out the new K surviving paths from the expanded branches in pipelines. Compared to the conventional K-best scheme, the proposed architecture can approximately reduce fundamental operations by 50% and 75% for the 16-QAM and the 64-QAM cases, respectively, and, consequently, lower the demand on the hardware resource significantly. Simulation results prove that the proposed architecture can achieve a performance very similar to conventional K-best detectors. Hence, it is an efficient solution to the K-best detector's VLSI implementation for high-throughput MIMO-OFDM systems.
Resumo:
In conventional metals, there is plenty of space for dislocations-line defects whose motion results in permanent material deformation-to multiply, so that the metal strengths are controlled by dislocation interactions with grain boundaries(1,2) and other obstacles(3,4). For nano-structured materials, in contrast, dislocation multiplication is severely confined by the nanometre-scale geometries so that continued plasticity can be expected to be source-controlled. Nano-grained polycrystalline materials were found to be strong but brittle(5-9), because both nucleation and motion of dislocations are effectively suppressed by the nanoscale crystallites. Here we report a dislocation-nucleation-controlled mechanism in nano-twinned metals(10,11) in which there are plenty of dislocation nucleation sites but dislocation motion is not confined. We show that dislocation nucleation governs the strength of such materials, resulting in their softening below a critical twin thickness. Large-scale molecular dynamics simulations and a kinetic theory of dislocation nucleation in nano-twinned metals show that there exists a transition in deformation mechanism, occurring at a critical twin-boundary spacing for which strength is maximized. At this point, the classical Hall-Petch type of strengthening due to dislocation pile-up and cutting through twin planes switches to a dislocation-nucleation-controlled softening mechanism with twin-boundary migration resulting from nucleation and motion of partial dislocations parallel to the twin planes. Most previous studies(12,13) did not consider a sufficient range of twin thickness and therefore missed this strength-softening regime. The simulations indicate that the critical twin-boundary spacing for the onset of softening in nano-twinned copper and the maximum strength depend on the grain size: the smaller the grain size, the smaller the critical twin-boundary spacing, and the higher the maximum strength of the material.