Average Link Length Research Articles

Measuring Entanglement in Physical Networks.

The links of a physical network cannot cross, which often forces the network layout into nonoptimal entangled states. Here we define a network fabric as a two-dimensional projection of a network and propose the average crossing number as a measure of network entanglement. We analytically derive the dependence of the average crossing number on network density, average link length, degree heterogeneity, and community structure and show that the predictions accurately estimate the entanglement of both network models and of real physical networks.

Genetic analysis of grapevine root system architecture and loci associated gene networks.

Own-rooted grapevines and grapevine rootstocks are vegetatively propagated from cuttings and have an adventitious root system. Unraveling the genetic underpinnings of the adventitious root system architecture (RSA) is important for improving own-rooted and grafted grapevine sustainability for a changing climate. Grapevine RSA genetic analysis was conducted in an Vitis sp. 'VRS-F2' population. Nine root morphology, three total root system morphology, and two biomass traits that contribute to root anchorage and water and nutrient uptake were phenotyped. Quantitative trait loci (QTL) analysis was performed using a high density integrated GBS and rhAmpSeq genetic map. Thirty-one QTL were detected for eleven of the RSA traits (surface area, root volume, total root length, fresh weight, number of tips, forks or links, longest root and average root diameter, link length, and link surface area) revealing many small effects. Several QTL were colocated on chromosomes 1, 9, 13, 18, and 19. QTL with identical peak positions on chromosomes 1 or 13 were enriched for AP2-EREBP, AS2, C2C2-CO, HMG, and MYB transcription factors, and QTL on chromosomes 9 or 13 were enriched for the ALFIN-LIKE transcription factor and regulation of autophagy pathways. QTL modeling for individual root traits identified eight models explaining 13.2 to 31.8% of the phenotypic variation. 'Seyval blanc' was the grandparent contributing to the allele models that included a greater surface area, total root length, and branching (number of forks and links) traits promoting a greater root density. In contrast, V. riparia 'Manitoba 37' contributed the allele for greater average branch length (link length) and diameter, promoting a less dense elongated root system with thicker roots. LATERAL ORGAN BOUNDARY DOMAIN (LBD or AS2/LOB) and the PROTODERMAL FACTOR (PFD2 and ANL2) were identified as important candidate genes in the enriched pathways underlying the hotspots for grapevine adventitious RSA. The combined QTL hotspot and trait modeling identified transcription factors, cell cycle and circadian rhythm genes with a known role in root cell and epidermal layer differentiation, lateral root development and cortex thickness. These genes are candidates for tailoring grapevine root system texture, density and length in breeding programs.

干旱胁迫对不同根型苜蓿根系构型的影响

PDF HTML阅读 XML下载 导出引用 引用提醒 干旱胁迫对不同根型苜蓿根系构型的影响 DOI: 10.5846/stxb202109042504 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金（32160327）；甘肃省重点研发计划项目（20YF3FA011） Effects of drought stress on root architecture of different root- type alfalfa Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:采用盆栽试验，比较播种当年及生长第2年对照、中度、重度干旱胁迫下根茎型、直根型、根蘖型苜蓿根系平面、立体几何构型和分形特征差异，以探究不同根型苜蓿对干旱的适应策略。结果表明：随干旱胁迫增加，各根型苜蓿根系总长度、总表面积、总体积和平均直径均减小；各根型苜蓿的根系拓扑指数较小，根系分支模式为叉状分支结构；各根型苜蓿的根系具有较好的分形特征，其分形维数较小，而分形丰度和平均连接长度均较大，表明其根系分支相对简单，但空间拓展能力强，有利于对营养空间的占有；各根型苜蓿的总分支较小、逐级分支率较大，有助于资源的快速获取和促进主根的向下生长。对根系构型参数进行主成分分析，根系总表面积、分形丰度、根长、根体积、分形维数和比根长6个根系构型参数能较好反映不同根型苜蓿根系构型特征。重度胁迫下，根茎型、根蘖型苜蓿的根系总长度、总表面积、总体积、比根长、比表面积、平均连接长度均大于直根型苜蓿，表明根茎型、根蘖型苜蓿适应干旱环境的能力强于直根型苜蓿。 Abstract:To investigate the ecological adaptation strategies of drought stress on root plane and stereo geometry architecture and fractal characteristics, pot experiment using three root types of alfalfa (rhizomatous rooted Medicago sativa ‘Qingshui’, tap rooted M. sativa ‘Longdong’, creeping rooted M. varia Martin. ‘Gongnong’ No.4) as the experimental materials was conducted to set up the drought treatment experiments. The results showed that the total root length, total surface area, total root volume and root average diameter of different root-type alfalfa decreased with increasing of drought concentration. The root topological indices of different root-type alfalfa were small, and the root branching patterns were herring-bone-like. The roots of different root-type alfalfa had obviously fractal characteristics, and the fractal dimension was small, while the fractal abundance and the average link length were large, which indicated that they had simple root architecture and high ability to expand living space. Smaller branching ratio and larger stepwise branching rate of different root-type alfalfa were helpful to speed resource acquisition and promote taproot growth downward. Root architecture parameters were analyzed by the principal component analysis. The parameters of total surface area, fractal abundance, total root length, total root volume, fractal dimension, and specific root length could well present the root architecture characteristics of different root-type alfalfa. Under severe stress, the total root length, total surface area, total root volume, specific root length, and specific surface area of rhizomatous rooted and creeping rooted alfalfa were higher than tap rooted alfalfa, which showed that the adaptation to drought environment of rhizomatous rooted and creeping rooted alfalfa were stronger than that of tap rooted alfalfa. 参考文献 相似文献 引证文献

How local street networks contribute to the traffic accident occurrence: Mersin city case

In this study, the issue of the accident frequency/occurrence in local residential streets where vehicle counts are not obtained is discussed. The accident reports received from the Ministry of Interior include fatal and injury accidents. But since the number of deadly accidents is minor, a binomial regression was not employed in the statistical analysis. This study investigates the role of morphological characteristics of the street network where main arterials are excluded in the safety of residential neighborhoods of Mersin, Turkey. Results showed that commercial and industrial uses generate more traffic than residential neighborhoods, therefore, responsible for higher rates of accidents. The number of vehicles, employment, and population increase the accident rate. Empirical model results showed that population density, street length per capita (meters), and number of intersections significantly affect accident occurrence. Number of intersections increases accident frequencies while street length per capita reduces. In contrast, the number of links, street density, link to node ratio, and average link length have no significant effect on accident occurrence. Traffic safety cannot be achieved if the street length is not proportional to the number of vehicles. In addition, street design is also a matter of efficient use of urban space.

Plastic response of Medicago sativa L. root system traits and cold resistance to simulated rainfall events.

Climate change (rainfall events and global warming) affects the survival of alfalfa (Medicago sativa L.) in winter. Appropriate water management can quickly reduce the mortality of alfalfa during winter. To determine how changes in water affect the cold resistance of alfalfa, we explored the root system traits under different rainfall events and the effects on cold resistance in three alfalfa cultivars. These were exposed to three simulated rainfall events (SRE) × two phases in a randomized complete block design with six replications. The three cultivars were WL168, WL353 and WL440, and the three SRE were irrigation once every second day (D2), every four days (D4) and every eight days (D8). There were two phases: before cold acclimation and after cold acclimation. Our results demonstrated that a period of exposure to low temperature was required for alfalfa to achieve maximum cold resistance. The root system tended toward herringbone branching under D8, compared with D2 and D4, and demonstrated greater root biomass, crown diameter, root volume, average link length and topological index. Nevertheless, D8 had less lateral root length, root surface area, specific root length, root forks and fractal dimensions. Greater root biomass and topological index were beneficial to cold resistance in alfalfa, while more lateral roots and root forks inhibited its ability to survive winter. Alfalfa roots had higher proline, soluble sugar and starch content in D8 than in D2 and D4. In contrast, there was lower malondialdehyde in D8, indicating that alfalfa had better cold resistance following a longer irrigation interval before winter. After examining root biomass, root system traits and physiological indexes we concluded that WL168 exhibited stronger cold resistance. Our results contribute to greater understanding of root and cold stress, consequently providing references for selection of cultivars and field water management to improve cold resistance of alfalfa in the context of changes in rainfall patterns.

Emergence of Stable Laws for First Passage Times in Three-Dimensional Random Fracture Networks.

We study first passage behaviors in the flow through three-dimensional random fracture networks. Network and flow heterogeneity lead to the emergence of heavy-tailed first passage time distributions that evolve with increasing distance between the start and target planes, and transition toward stable laws. Analysis of the spatial memory of the first passage process shows that particle motion can be quantified stochastically by a time domain random walk conditioned on the initial velocity data. This approach identifies advective tortuosity, the velocity point distribution and the average fracture link length as key quantities for the prediction of first passage times. Using this approach, we develop a theory for the evolution of first passage times with increasing distance between the start and target planes and the convergence towards stable laws.

Capacity Analysis of UAV Communications: Cases of Random Trajectories

This paper analyzes the link capacity between autonomous unmanned aerial vehicles (UAVs) with random three-dimensional (3-D) trajectories. This is distinctively different from existing works typically under the assumption of either two-dimensional (2-D) or deterministic trajectories, and particularly interesting to applications such as surveillance and air combat. The key idea is that we geometrically derive the probability distributions of the UAV-to-UAV (U2U) distances which, by exploiting the Jensen's inequality, can be translated to the closed-form bounds for the capacity between UAVs, and between UAVs and ground stations. Another important aspect is that we extrapolate the idea to dense UAV networks, and analyze the impact of network densification, imperfect channel state information, and interference from ground transmitters on the capacity. Corroborated by simulations, our analysis shows that a U2U link with random 2-D trajectories is superior in terms of capacity due to its short average link distance. It is also revealed that a UAV-to-ground link can incur substantially lower capacity than a U2U link even in the case the 3-D coverage of the UAVs is the same, as the result of its longer average link length.

Potential-Game Based Optimally Rigid Topology Control in Wireless Sensor Networks

In this paper, the optimally rigid topology control problem in wireless sensor networks is considered to improve the algebraic rigidity properties. This problem is first formulated as a constrained optimization problem which can be solved by two stages. A minimally rigid network is constructed in the first stage, then the optimally rigid topology in the second stage. A potential game approach is proposed for solving the optimization problem by choosing a different performance metric as the potential function. It can be seen that the proposed algorithm can significantly improve the network performance, such as reducing communication complexity and transmit power, prolonging network lifetime, and so on. Finally, some simulations demonstrate the effectiveness of the proposed algorithms from multiple perspectives: topology complexity, average degree, consensus convergence speed, average radius, average link length, and network lifetime.

Merit of hybrid EDFA/Raman amplification in fixed‐grid all‐optical network exploiting multirate transponders

SummaryThe constant need to improve network capacity and reduce power consumption in current fixed‐grid WDM networks motivates researchers to find alternative solutions other than replacing the deployed equipment. One of the possible solutions is the use of hybrid EDFA/Raman amplifier, which improves signal‐to‐noise‐ratio in a point‐to‐point link. This work aims at quantifying, by means of a detailed power model, the effect of these novel ideas on the power consumption of the network, which is key to build a future green Internet. In particular, we consider the use of a randomly generated topology of 20 nodes to study the effect of hybrid amplification, fiber type, fiber span length, and sensitivity to average link length and average traffic per node. Results show that hybrid amplification in moderate pumping regime minimizes total network power consumption for networks made up of all 3 fiber types in particular for nonzero dispersion‐shifted fiber.

A power consumption sensitivity analysis of circuit-switched versus packet-switched backbone networks

While telecommunication networks have historically been dominated by a circuit-switched paradigm, the last decades have seen a clear trend towards packet-switched networks. In this paper we evaluate how both paradigms (which have also been referred to as optical bypass and non-bypass, respectively) perform in optical backbone networks from a power consumption point of view, and whether the general agreement of circuit switching being more power-efficient holds. We consider artificially generated topologies of various sizes, mesh degrees and – not yet previously explored in this context – transport linerates. We cross-validate our findings with a number of realistic topologies.Our results show that circuit switching is preferable when the average node-to-node demands are higher than half the transport linerates. However, packet switching can become preferable when the traffic demands are lower than half the transport linerate. We find that an increase in the network node count does not consistently increase the energy savings of circuit switching over packet switching, but the savings are heavily influenced by the mesh degree and (to a minor extent) by the average link length. Our results are consistent for uniform traffic demands and realistic traffic demands.A key take-away message for other research on power saving solutions in backbone networks is that the ratio between the average demand and the demand bitrate has considerable effect on the overall efficiency, and should be taken into account.

From the time series to the complex networks: The parametric natural visibility graph

We present the modification of natural visibility graph (NVG) algorithm used for the mapping of the time series to the complex networks (graphs). We propose the parametric natural visibility graph (PNVG) algorithm. The PNVG consists of NVG links, which satisfy an additional constraint determined by a newly introduced continuous parameter—the view angle. The alteration of view angle modifies the PNVG and its properties such as the average node degree, average link length of the graph as well as cluster quantity of built graph, etc. We calculated and analyzed different PNVG properties depending on the view angle for different types of the time series such as the random (uncorrelated, correlated and fractal) and cardiac rhythm time series for healthy and ill patients. Investigation of different PNVG properties shows that the view angle gives a new approach to characterize the structure of the time series that are invisible in the conventional version of the algorithm. It is also shown that the PNVG approach allows us to distinguish, identify and describe in detail various time series.

Architectural characteristics of roots in typical coastal psammophytes of South China

Aims Roots are an important part of plants; they not only facilitate the utilization of soil water and nutrients, but also successively anchor the plants against wind and water wave erosion. This study was conducted to determine the adaptive strategy of root architectural characteristics in different plant life forms, in order to assist the selec- tion of most suitable plant species for the coastal dune restoration. Methods After a detailed field investigation of sand dunes in South China, four species were sampled on a damaged coastal sand dune, including Casuarina equisetifolia, Ipomoea pes-caprae, Spinifex littoreus and Cyno- don dactylon, and roots were excavated for analyzing their architectural characteristics such as root bifurcation ratio, root link length, root topological index and root-shoot ratio. Important findings There were great differences as well as similarities in the root architectural characteristics among the four plant species. The total root bifurcation ratios in Spinifex littoreus and Cynodon dactylon were apparently higher than in other two species, and was lowest in Ipomoea pes-caprae, indicating that herbaceous plants are more competitive for soil resources by having a higher root bifurcation ratio. With except of Casuarina equisetifolia, all other three species were easily sand buried due to their flatten and extended shoots, which might further improve the transportation efficiency of soil resources. The average root link lengths of the four species were smaller in coastal sandy dunes than which in inland areas; Casuarina equisetifolia had the greatest average root link length of 19.25 cm among the four species studied, and greater proportion of transportation roots than other three species. This demonstrated that an increase in average root link length and proportion of transportation roots would favor the reduction of root competition for soil resources and high efficiency of resources transporta- tion. Ipomoea pes-caprae had a smaller proportion of the assimilation roots, but the adventitious roots on the shoot compensated for the low assimilation efficiency of resources. All the four species showed a dichotomous structure, of which the herbaceous species had more similar root architectures, indicating that herbaceous species are less affected by limitation of environmental resources and better to colonize the coastal dunes if being used in restoration. Compared with species in inland areas, there are greater differences for the species in coastal sandy areas in the acquisition of soil resources and spatial expansion, indicating different adaptive strategies among the

Statistical Model for Link Lengths in Optical Transport Networks

From the analysis of statistical properties of real networks, it is found that general extreme value (GEV) distribution provides an accurate model for link length statistics of optical transport networks (OTNs). The parameters of GEV distribution can be estimated from the average link length of the OTNs. Expressions for average link lengths, based only on the knowledge of network coverage area and number of nodes, are improved for better accuracy. It is shown that the optimized GEV distribution estimates the link statistics of OTNs with good accuracy (Kolmogorov–Smirnov statistic less than 0.18).

The 2012 Smart Growth Report: Progress Towards Smart Growth in Canada

Over the last decade and a half, the Smart Growth movement has matured in Canada. Early efforts to raise awareness on the need to better manage urban growth gave way to smart growth plans and policies adopted by municipal, regional and provincial governments. More recently, attention has shifted to measuring the impact and benefits of smart growth. As a reflection of this emerging interest, a report entitled Smart Growth in Canada: A Progress Report was published in 2005. The report reviewed the existing policy framework related to urban growth in six metropolitan regions – including Vancouver, Calgary, Saskatoon, Toronto, Montreal and Halifax – and assessed progress towards Smart Growth goals on the ground.The report was the first systematic attempt in Canada to assess progress on Smart Growth, but suffered from several weaknesses. Most importantly, data problems hampered the analysis; for many of the Smart Growth indicators, no pan-Canadian data was available. The present report attempts to address these deficiencies by bringing new data sources to bear and exploring in more detail the trends observed. In order to make this task manageable, we have chosen to focus on a specific dimension of Smart Growth, i.e., the link between land use and transportation. Although the concept of Smart Growth touches on many aspects of urbanization (e.g., housing affordability, social justice, citizen participation, preservation of agricultural and ecological lands, economic development, rationalization of infrastructure investment, etc.) the core concept is that significant benefits can be derived from integrating land use planning and development on the one hand and transportation goals on the other.The analyses presented in this report show that for the period studied, the six Canadian cities taken together were not moving in the right direction in terms achieving a pattern of development in line with Smart Growth goals. Of the trends on 16 key measures, only employment density, the number of jobs per dwelling, average street link length, and walk/bike mode share appear to be heading in the right direction. Residential intensification and employment growth patterns are essentially opposite to what is desired under Smart Growth. In terms of the former, the population of older urban areas is declining, new residential development falls short of Smart Growth goals, whereas the population and number of dwellings in rural areas is exploding. In terms of the latter, employment is growing fastest in areas that measure poorly on key parameters associated with the use of alternative modes of transportation.In terms of meeting thresholds for change in transportation behaviour, recently built areas in the six CMAs taken together fail to meet the thresholds for decreasing VKT, increasing transit use, and shifting mode choice from SOV to other modes. The only somewhat bright spot appears to be providing urban form that encourages walking and cycling – on average, the six CMAs met two out of three theoretical thresholds, namely for block length and the ratio of nodes to links in the street network, and were very close to meeting the third threshold, for intersection density.

Length adaptation of airway smooth muscle: a stochastic model of cytoskeletal dynamics

To account for cytoskeleton remodeling as well as smooth muscle length adaptation, here we represent the cytoskeleton as a two-dimensional network of links (contractile filaments or stress fibers) that connect nodes (dense plaques or focal adhesions). The network evolves in continuous turnover with probabilities of link formation and dissolution. The probability of link formation increases with the available fraction of contractile units, increases with the degree of network activation, and decreases with increasing distance between nodes, d, as 1/d(s), where s controls the distribution of link lengths. The probability of link dissolution decays with time to mimic progressive cytoskeleton stabilization. We computed network force (F) as the vector summation of link forces exerted at all nodes, unloaded shortening velocity (V) as being proportional to the average link length, and network compliance (C) as the change in network length per change in elastic force. Imposed deformation caused F to decrease transiently and then recover dynamically; recovery ability decreased with increasing time after activation, mimicking observed biological behavior. Isometric contractions showed small sensitivity of F to network length, thus maintaining high force over a wide range of lengths; V and C increased with increasing length. In these behaviors, link length regulation, as described by the parameter s, was found to be crucial. Concerning length adaptation, all phenomena reported thus far in the literature were captured by this extremely simple network model.

On Dislocation Link Length Statistics for Plastic Deformation of Crystals

The statistical distribution function for dislocation link lengths in a unit volume of plastically deformed crystalline materials as proposed by Wang et al. is used to derive the relationship between the average dislocation link length, 〈γ〉, and the dislocation density, Q. It is shown that 〈γ〉 = βϱ−½: β = (2/πc)½ where c is the dislocation network geometrical factor. Also, the mobile dislocation density, Qm, is shown to be directly proportional to the total dislocation density, Q, and the proportionality constant is determined by such factors as mobile dislocation fraction factor, fp, the geometrical factor, c, the Taylor factor, M, and a constant, α. The applicability of the distribution function, φ(λ), is also demonstrated with respect to the statistical constraints for the normalized distribution function, Φ (u), where u = λ/〈λ〉 is the normalized dislocation link length. The analysis is then applied to the strain-hardening and recovery processes during plastic deformation. It is shown that the strain-hardening coefficient, H, is related to the geometry of the three-dimensional dislocation network and is of the order of Young's modulus, E, which is in good agreement with other strain-hardening models and experimental measurements made by the stress change test. A creep rate equation is also obtained for high temperature recovery creep deformation.

Dynamic effects in the mesh length theory of workhardening

According to the mesh length theory of workhardening, low-temperature strain rate effects in materials exhibiting a dislocation cell structure are due to the simultaneous operation of a number X of super-critically bowing links in the average, typically roughly equiaxed, cell of diameter L. The corresponding length of mobile dislocations per cell is then LX. Defining g = L l ̄ , with l ̄ the average link length in the cell walls, dislocation cell breakdown is expected for X max ≈ 0.3 g 2, on the criterion that at the most 50% of all cell wall dislocations may be simultaneously destabilized and therefore at most 10% of all possible dislocation sources may be activated simultaneously since each destabilizes four adjoining links besides itself. When X = X max , the mobile dislocation density within the cells is about 30% of that in the walls, but significant interactions and thus extra hardening is expected only if the dislocation density in the cell interiors is about sixteen times the cell wall dislocation density. Therefore the mobile dislocations can add little, if anything, to the permanent strain hardening. However, on account of the decrease of average source length with increasing X a transient increase of flow stress and workhardening coefficient arises which typically amounts to a few percent per ten-fold increase of strain rate. Mobile dislocations remaining in the cell interiors decrease the elastic modulus and can give rise to anelastic creep as well as to recovery effects. Numerical estimates are in good agreement with observations.

Scaling characteristics of dislocation link length distributions generated during the creep of crystals

The distribution of dislocation link lengths comprising the dislocation network generated during the elevated temperature deformation of NaCl and Al monocrystals has been evaluated at several values of the applied stress, σ, and temperature, T, and at various stages of primary creep up to the steady state condition. The properties of the normalized function, Φ( u) = β 2 ρ −2 φ( L, t), where φ( L, t) dL is the number of dislocation links per unit volume of length between L and L + dL at time t, ρ is the dislocation density, u = L 〈L〉 , 〈 L〉 is the average link length and β is a constant defined by the relationship 〈L〉 = βρ − 1 2 , are analyzed. Within experimental error Φ( u) is independent of t during the primary creep of NaCl. The same appears to be true for Al, although the greater scatter render this conclusion less convincing. For these two materials Φ( u) has the attributes of a dynamic scaling function. It is tentatively concluded that Φ( u) is at most weakly dependent on σ and T and depends primarily on crystal structure. Specifically, Φ( u) ∝ u m as u → 0, with m ~ 1.5 for NaCl and MgO and m ~ 1.33 for Al. Since the data on Al were taken at stresses spanning the Harper-Dorn and power-law creep regimes the results suggest that m is independent of the mode of creep, although it may increase with increasing σ for NaCl. Evidence is presented that β is dependent on the mode of creep. It is smaller (0.75–0.8) for Al deformed in the H-D regime than for materials, including Al, deformed in the power-law regime, where the value of β typically exceeds 0.85 and may also increase with increasing σ. The limiting behavior of Φ( u) is related to the nature of the equation governing the rate of growth g = dL dt , of individual links. In particular, g( L, t) must approach L − m as L → 0. The implications of these observations are discussed.

Steady state creep of 20% Cr-25% Ni stainless steel with and without a dispersion of tin particles

The steady state creep behaviour of both single phase and TiN dispersion strengthened 20% Cr-25% Ni stainless steel is examined with the object of determining the role of the second phase particles on dislocation network creep. A correlation between the stress/strain rate variation in the two materials can be made by writing. ε ss = A( σ − σ 0) p , where σ is ∼0 and ~80 MPa for single-phase and dispersion hardened steels respectively, and p is ∼5. An expression of this form leads to the prediction of threshold behaviour at σ 0, but the creep rate data indicate that steady state creep also occurs below this stress. Microstructural observations are described which suggest that σ 0 in the TiN bearing alloy can be identified with σ p , the Orowan stress. The Orowan mechanism cannot operate below σ p , but an alternative mode of dislocation bypass around particles is available, which leads to a mechanistic transition at a stress σ gt where the rates of the two processes are the same. The stress/dislocation density relationship is investigated, and it is found that the density p in the dispersion hardened alloy becomes constant below the Orowan stress at a density ( p 0) such that the average network link length is equal to the interparticle spacing. Further, the strain rate/dislocation density variation in single phase material at high stress appears to be such that ε α σ − σ s pα p p 2 while at low stresses there is an excess of dislocations. It is argued that writing ε α ρ − ρ 0 p 2 with ρp 0 the annealed-in density, allows the strain rate to be self-consistent function of the active dislocation content over the entire stress range. Moreover, treating the data from the two-phase steel in the same manner reduces the ε/( ρ − ρ 0) points from both alloys to a single curve. The density ρ 0 is suggested to arise as a result of stress relaxation where dislocations are held up at hard parts of the microstrucure. The stress relaxation produces an increase in the total dislocation line length, but a reduction in the stored energy, so that the driving force for recovery is reduced at a given total density. The relaxation structures themselves must recover, and this is likely to happen over the microstructural wavelength of the plastic inhomogeneity which is not only responsible for the presence of the geometrically necessary dislocations, but which also determines the content of annealed material. The spatial inhomogeneity of the dislocation density can be described in terms of a steady-state internal stress distribution which acts so as to compensate for variations in local flow stress. The threshold behaviour, however, is suggested to arise because the TiN particles are undeformable. The Orowan stress always therefore has to be exceeded before the network model of dislocation creep can be at all appropriate. However, the measured variations in dislocation density with stress imply that the creep rate can be correlated with the dislocation density, as in the network model, if the effects of plastic relaxation are taken into account.

Theory of dislocation cell sizes in deformed metals

Preceding theoretical investigations have demonstrated that dislocation cell structures in deformed polycrystalline materials result from the strain energy reduction of glide dislocations which have become mutually trapped. However, it had been hitherto not possible to give a theoretical reason for the cell sizes actually observed nor for the fact that the average dislocation link length in the cell walls is a constant fraction of the average cell diameter during stage II work hardening. A theory is presented to close this gap. For the example of the simplest known type of dislocation cell structure of very low energy, namely a three-dimensional checkerboard pattern of cubic cells with a common axis of misorientation but alternating sense of rotation, it is shown that the experimentally observed cell sizes and link lengths represent the minimum total strain energy for a fixed dislocation content. This occurs because with shrinking cell size the remnant longer-range cell stresses decrease while the short-range dislocation stresses, i.e. the dislocation line energy, increases whereas the reverse is true when at constant dislocation content the cell size increases.