Influence of the 6061 Aluminium Alloy Thermo-Viscoplastic Behaviour on the Load-Area Relation of a Contact

The contact between solids in metal-forming operations often involves temperature-dependent viscoplasticity of the workpiece. In order to estimate the real contact area in such contexts, both the topography and the deformation behaviour should be taken into account. In this work, a deterministic approach is used to represent asperities in appropriately shaped quadratic surfaces. Such geometries are implemented in indentation finite element simulations, in which the indented material has thermo-viscoplastic properties. By creating a database of simulation data, investigations in terms of contact load and area for the specifically shaped asperities allow for an analysis on the influence of the material properties on the load–area relation of the contact. The temperature and viscoplasticity greatly define how much load is supported by a substrate due to an indenting asperity, but the description of the deformation behaviour at small values of strain and strain rate is also relevant. The pile-up and sink-in regions are very dependent on the thermo-viscoplastic conditions and material model, which consequently affect the real contact area calculation. The interplay between carried load and contact area of a full surface analysis indicates the role that different sized asperities play in the contact under different thermomechanical conditions.

Energy sharing based on microscopic level densities

The transformation of a moderately excited heavy nucleus into two excited fission fragments is modeled as a strongly damped evolution of the nuclear shape. The resulting Brownian motion in the multi-dimensional deformation space is guided by the shape-dependent level density which has been calculated microscopically for each of nearly ten million shapes (given in the three-quadratic-surfaces parametrization) by using a previously developed combinatorial method that employs the same single-particle levels as those used for the calculation of the pairing and shell contributions to the five-dimensional macroscopic-microscopic potential-energy surface. The stochastic shape evolution is followed until a small critical neck radius is reached, at which point the mass, charge, and shape of the two proto-fragments are extracted. The available excitation energy is divided statistically on the basis of the microscopic level densities associated with the two distorted fragments. Specific fragment structure features may cause the distribution of the energy disvision to deviate significantly from expectations based on a Fermi-gas level density. After their formation at scission, the initially distorted fragments are being accelerated by their mutual Coulomb repulsion as their shapes relax to their equilibrium forms. The associated distortion energy is converted to additional excitation energy in the fully accelerated fragments. These subsequently undergo sequential neutron evaporation which is calculated using again the appropriate microscopic level densities. The resulting dependence of the mean neutron multiplicity on the fragment mass, as well as the dependence of on the initial excitation energy of the fissioning compound nucleus, exhibit features that are similar to the experimentally observed behavior, suggesting that the microscopic energy sharing mechanism plays an important role in low-energy fission.

Linear Twin Quadratic Surface Support Vector Regression

Twin support vector regression (TSVR) generates two nonparallel hyperplanes by solving a pair of smaller-sized problems instead of a single larger-sized problem in the standard SVR. Due to its efficiency, TSVR is frequently applied in various areas. In this paper, we propose a totally new version of TSVR named Linear Twin Quadratic Surface Support Vector Regression (LTQSSVR), which directly uses two quadratic surfaces in the original space for regression. It is worth noting that our new approach not only avoids the notoriously difficult and time-consuming task for searching a suitable kernel function and its corresponding parameters in the traditional SVR-based method but also achieves a better generalization performance. Besides, in order to make further improvement on the efficiency and robustness of the model, we introduce the 1-norm to measure the error. The linear programming structure of the new model skips the matrix inverse operation and makes it solvable for those huge-sized problems. As we know, the capability of handling large-sized problem is very important in this big data era. In addition, to verify the effectiveness and efficiency of our model, we compare it with some well-known methods. The numerical experiments on 2 artificial data sets and 12 benchmark data sets demonstrate the validity and applicability of our proposed method.

On equidistant lines of given line configurations

The equidistant set of a collection F of lines in 3-space is the set of those points whose distances to the lines in F are all equal. We present many examples and results related to the lines possibly contained in the equidistant set of F. In particular, we determine the possible numbers of lines in the equidistant set of a collection of n lines for every {n>0} . For example, if {n=3} , then the possible number of such lines is either 4 or 2 or 1 or 0. In a natural way, our results are connected with properties of special types of (ruled) surfaces. For example, we obtain also results on the number of lines in the intersection of quadratic surfaces.