A consistent nonlocal scheme based on filters for the homogenization of heterogeneous linear materials with non-separated scales

In this work, the question of homogenizing linear elastic, heterogeneous materials with periodic microstructures in the case of non-separated scales is addressed. A framework if proposed, where the notion of mesoscopic strain and stress fields are defined by appropriate integral operators which act as low-pass filters on the fine scale fluctuations. The present theory extends the classical linear homogenization by substituting averaging operators by integral operators, and localization tensors by nonlocal operators involving appropriate Green functions. As a result, the obtained constitutive relationship at the mesoscale appears to be nonlocal. Compared to nonlocal elastic models introduced from a phenomenological point of view, the nonlocal behavior has been fully derived from the study of the microstructure. A discrete version of the theory is presented, where the mesoscopic strain field is approximated as a linear combination of basis functions. It allows computing the mesoscopic nonlocal operator by means of a finite number of transformation tensors, which can be computed numerically on the unit cell.     

Diagnostic value of elastosonography for thyroid microcarcinoma

Objective

To assess the diagnostic value of elastosonography for thyroid microcarcinoma (TMC), particularly with regard to elasticity score (ES) and strain ratio (SR).

Methods

Conventional ultrasound and elastosonography were performed for 487 thyroid micronodules before surgery. We set the histology as the reference standard. The ES and SR values, as well as their diagnostic threshold and efficiency, were compared and analyzed by the receiver-operating characteristic (ROC) curve. Additional comparisons between TMC patients with and without extracapsular extension were also performed.

Results

Statistically significant differences (P < 0.05) in both ES and SR values were detected among the TMC and benign groups. The area under the ROC curve of SR was significantly greater than that of ES (0.956 and 0.844, respectively; P < 0.05). Using ES ? 3 and SR ? 3.65 as diagnostic threshold values, the diagnostic sensitivity, specificity, and accuracy of ES for differentiating benign and malignant nodules were 79.9%, 72.3%, and 80.5%, respectively, whereas those of SR were 86.6%, 85.3%, and 89.4%, respectively. The maximum diameter, microcalcification status, aspect ratio, bilateral cervical lymph node metastasis, and SR values of nodules with extracapsular extension (A1 subgroup) were greater than those of nodules without extracapsular extension (A2 subgroup).

Conclusions

Elasticity imaging technology not only can help differentiate between benign and malignant thyroid micronodules but also allow SR values to provide accurate and objective information on tissue hardness and to predict TMC extracapsular extension or even bilateral cervical lymph node metastasis.     

A new type of full multigrid method for the elasticity eigenvalue problem

This paper introduces a new type of full multigrid method for the elasticity eigenvalue problem. The main idea is to avoid solving large scale elasticity eigenvalue problem directly by transforming the solution of the elasticity eigenvalue problem into a series of solutions of linear boundary value problems defined on a multilevel finite element space sequence and some small scale elasticity eigenvalue problems defined on the coarsest correction space. The involved linear boundary value problems will be solved by performing some multigrid iterations. Besides, some efficient techniques such as parallel computing and adaptive mesh refinement can also be absorbed in our algorithm. The efficiency and validity of the multigrid methods are verified by several numerical experiments.     

On a phase field model of Cahn–Hilliard type for tumour growth with mechanical effects

Mechanical effects have mostly been neglected so far in phase field tumour models that are based on a Cahn–Hilliard approach. In this paper we study a macroscopic mechanical model for tumour growth in which cell–cell adhesion effects are taken into account with the help of a Ginzburg–Landau type energy. In the overall model an equation of Cahn–Hilliard type is coupled to the system of linear elasticity and a reaction–diffusion equation for a nutrient concentration. The highly non-linear coupling between a fourth-order Cahn–Hilliard equation and the quasi-static elasticity system lead to new challenges which cannot be dealt within a gradient flow setting which was the method of choice for other elastic Cahn–Hilliard systems. We show existence, uniqueness and regularity results. In addition, several continuous dependence results with respect to different topologies are shown. Some of these results give uniqueness for weak solutions and other results will be helpful for optimal control problems.     

分散控制对供需网节点的影响研究——复杂性的观点

供应链作为供需网的一个节点,传统在对供需系统研究上,往往假设存在一个全局控制中心,通过对系统的整体控制,达到系统的稳定均衡;但当所处理事物是复杂的,决策分散在系统各结点中,势必会影响到传统对系统的描述。在传统供应链研究模型的基础上,引入逆向回流收益分享,并构建加入未销售产品处理收益的供应链收入共享模型,推导认为在分散决策下供应链系统并不能总是最优;进一步,通过对契约模型的差分化,求解不动点,并通过Simulink编程数值计算,分析得出受决策周期的影响,系统均衡点并不容易达到,随着初值参数的改变,系统甚至出现浑沌。由此,探讨了基于复杂性下分散控制对当前管理现象认知及研究的意义。     

Method of Riemann surfaces for an inverse antiplane problem in an n-connected domain

ABSTRACT

An inverse problem of the theory of harmonic functions for an n-connected domain is analyzed. The problem is equivalent to a problem of antiplane elasticity on determination of the profiles of n uniformly stressed inclusions. The inclusions are in ideal contact with the surrounding matrix, the stress field inside the inclusions is uniform, and at infinity the body is subjected to antiplane uniform shear. The exterior of the inclusions, an n-connected domain, is treated as the image by a conformal map of an n-connected slit domain with the slits lying in the same line. The inverse problem is solved by quadratures by reducing it to two Riemann-Hilbert problems on a Riemann surface of genus n?1. Samples of two and three symmetric and non-symmetric uniformly stressed inclusions are reported.     

Edge effects in Hypar nets

Edge effects in hyperbolic paraboloidal nets are analyzed using a model that features the elastic resistance of the fibers of the net to flexure and twist in addition to the extensional elasticity of the conventional membrane theory of networks.     

Spring-network model of red blood cell: From membrane mechanics to validation

Red blood cell membrane is highly elastic and proper modeling of this elasticity is essential for biomedical applications that involve computational experiments with blood flow. Inseparable and often some of the most difficult parts of modeling process are verification and validation. In this work, we present a revised model, which uses a spring network to represent the cell membrane immersed in a fluid and has been successfully used in blood flow simulations. We demonstrate the validation steps by first deriving the theoretical relations between the bulk properties of elastic membranes—shear modulus and area compressibility modulus—and parameters of the model that enter the nonlinear stretching and local area conservation computational moduli. We verify the theoretically derived relations using computer simulations of deformable triangular mesh. We calibrate the model by performing a computational version of the optical tweezers experiment. And finally, we validate the modeled cell behavior by investigating the cell rotation frequency when it is subjected to shear flow and cell deformation in narrow channels. The supplementary material contains an extensive dataset that can be used for setting different elastic properties for each cell in simulations of dense suspensions, while still conforming to the biological data. This work contains a complete model development process: From modelling of basic mechanical concepts (the spring network) and advanced biomechanical concepts (such as elasticity of the membrane), through calibration process towards the final stage of model validation.     

Locking-free nonconforming finite elements for three-dimensional elasticity problem

Two locking-free nonconforming finite elements are presented for three-dimensional elasticity problem with pure displacement boundary condition. Convergence rate of the elements are uniformly optimal with respect to λ. The energy norm and L² norm errors are O(h²) and O(h³), respectively. Lastly, a numerical experiment is carried out, which coincides with the theoretical analysis.