When Does a Polynomial Over a Finite Field Permute the Elements of the Field?

We present a class of indecomposable polynomials of non prime-power degree over the finite field of two elements which are permutation polynomials on infinitely many finite extensions of the field. The associated geometric monodromy groups are the simple ...

A New Finite Element Method for Strain Gradient Theories and Applications to Fracture Analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J2 deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip.

H4 exponential finite-difference scheme for convective diffusion-equations

Perturbations are applied to the convective coefficients and source term of a convection-diffusion equation so that second-order corrections may be applied to a second-order exponential scheme. The basic Structure of the equations in the resulting fourth-order scheme is identical to that for the second order. Furthermore, the calculations are quite simple as the second-order corrections may be obtained in a single pass using a second-order scheme. For one to three dimensions, the fourth-order exponential scheme is unconditionally stable. As examples, the method is applied to Burgers' and other fluid mechanics problems. Compared with schemes normally used, the accuracies are found to be good and the method is applicable to regions with large gradients.

A simple method to simulate shrinkage-induced cracking in cement-based composites by lattice-type modeling

A new numerical procedure is proposed to investigate cracking behaviors induced by mismatch between the matrix phase and aggregates due to matrix shrinkage in cement-based composites. This kind of failure processes is simplified in this investigation as a purely spontaneous mechanical problem, therefore, one main difficulty during simulating the phenomenon lies that no explicit external load serves as the drive to propel development of this physical process. As a result, it is different from classical mechanical problems and seems hard to be solved by using directly the classical finite element method (FEM), a typical kind of "load -> medium -> response" procedures. As a solution, the actual mismatch deformation field is decomposed into two virtual fields, both of which can be obtained by the classical FEM. Then the actual response is obtained by adding together the two virtual displacement fields based on the principle of superposition. Then, critical elements are detected successively by the event-by-event technique. The micro-structure of composites is implemented by employing the generalized beam (GB) lattice model. Numerical examples are given to show the effectiveness of the method, and detailed discussions are conducted on influences of material properties.

A simple closed aquatic ecosystem (CAES) for space

A closed aquatic ecosystem (CAES) was developed to stud), the effects of microgravity on the function of closed ecosystems aboard the Chinese retrieved satellite and on the spacecraft SHENZHOU-II. These systems housed a small freshwater snail (Bulinus australianus) and an autotrophic green algae (Chlorella pyrenoidosa). The results of the test on the satellite were that the concentration of algae changed little, but that the snails died during the experiments. We then sought to optimize the function of the control system, the cultural conditions and the data acquisition system and carried out an experiment on the spacecraft SHENZHOU-II. Using various sensors to monitor the CAES, real-time data regarding the operation of the CAES in microgravity was acquired. In addition, all on-board Ig centrifuge was included to identify gravity-related factors. It was found that microgravity is the major factor affecting the operation of the CAES in space. The change in biomass of the primary producer during each day in microgravity was larger than that of the control groups. The mean biomass concentration per day in the microgravity group decreased, but that of the control groups increased for several days and then leveled off. Space effects on the biomass of a primary producer may be a result of microgravity effects leading to increasing metabolic rates of the consumer combined with decreases in photosynthesis. (c) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

A model for scattering due to interface roughness in finite quantum wells

A model for scattering due to interface roughness in finite quantum wells (QWs) is developed within the framework of the Boltzmann transport equation and a simple and explicit expression between mobility limited by interface roughness scattering and barrier height is obtained. The main advantage of our model is that it does not involve complicated wavefunction calculations, and thus it is convenient for predicting the mobility in thin finite QWs. It is found that the mobility limited by interface roughness is one order of amplitude higher than the results derived by assuming an infinite barrier, for finite barrier height QWs where x = 0.3. The mobility first decreases and then flattens out as the barrier confinement increases. The experimental results may be explained with monolayers of asperity height 1-2, and a correlation length of about 33 angstrom. The calculation results are in excellent agreement with the experimental data from AlxGa1-xAs/GaAs QWs.

constructing finite algebras with falcon

The generation of models and counterexamples is an important form of reasoning. In this paper, we give a formal account of a system, called FALCON, for constructing finite algebras from given equational axioms. The abstract algorithms, as well as some implementation details and sample applications, are presented. The generation of finite models is viewed as a constraint satisfaction problem, with ground instances of the axioms as constraints. One feature of the system is that it employs a very simple technique, called the least number heuristic, to eliminate isomorphic (partial) models, thus reducing the size of the search space. The correctness of the heuristic is proved. Some experimental data are given to show the performance and applications of the system.

Assessment of genetic diversities of selected Laminaria (Laminariales, Phaeophyta) gametophytes by inter-simple sequence repeat analysis

Inter-simple sequence repeat (ISSR) analysis was used to assess genetic diversity among 10 pairs of male and female Laminaria gametophytes. A total of 58 amplification loci was obtained from 10 selected ISSR primers, of which 34 revealed polymorphism among the gametophytes. Genetic distances were calculated with the Dice coefficient ranging from 0.006 to 0.223. A dendrogram based on the unweighted pair-group method arithmetic (UPGMA) average showed that most male and female gametophytes of the same species were clustered together and that 10 pairs of gametophytes were divided into four groups. This was generally consistent with the taxonomic categories. The main group consisted of six pairs of gametophytes, which were selected from Laminaria japonica Aresch. by intensive inbreeding through artificial hybridization. One specific marker was cloned, but was not converted successfully into a sequence characterized amplified region (SCAR) marker. Our results demonstrate the feasibility of applying ISSR markers to evaluate Laminaria germplasm diversities.