Mesh-free canonical tensor products for six-dimensional density matrix: computation of kinetic energy

The computation of a six-dimensional density matrix is the crucial step for the evaluation of kinetic energy in electronic structure calculations. For molecules with heavy nuclei, one has to consider a very refined mesh in order to deal with the nuclear cusps. This leads to high computational time and needs huge memory for the computation of the density matrix. To reduce the computational complexity and avoid discretization errors in the approximation, we use mesh-free canonical tensor products in electronic structure calculations. In this paper, we approximate the six-dimensional density matrix in an efficient way and then compute the kinetic energy. Accuracy is examined by comparing our computed kinetic energy with the exact computation of the kinetic energy.     

Investigation of the potential of asymptotic homogenization for elastic composites via a three-dimensional computational study

Asymptotic homogenization is employed assuming a sharp length scale separation between the periodic structure (fine scale) and the whole composite (coarse scale). A classical approach yields the linear elastic-type coarse scale model, where the effective elastic coefficients are computed solving fine scale periodic cell problems. We generalize the existing results by considering an arbitrary number of subphases and general periodic cell shapes. We focus on the stress jump conditions arising in the cell problems and explicitly compute the corresponding interface loads. The latter represent a key driving force to obtain nontrivial cell problems solutions whenever discontinuities of the coefficients between the host medium (matrix) and the subphases occur. The numerical simulations illustrate the geometrically induced anisotropy and foster the comparison between asymptotic homogenization and well established Eshelby based techniques. We show that the method can be routinely implemented in three dimensions and should be applied to hierarchical hard tissues whenever the precise shape and arrangement of the subphases cannot be ignored. Our numerical results are benchmarked exploiting the semi-analytical solution which holds for cylindrical aligned fibers.     

Virtual-Point-Based asymptotic tracking control of 4WS vehicles

This paper studies the lateral and longitudinal path tracking control of four-wheel steering vehicles. By the introduction of virtual points, a robust and adaptive path tracking control strategy is proposed to simultaneously counteract modeling uncertainties, unexpected disturbances, and coupling effects. An adaptive model-based feedforward adaptive term and the robust integral of the sign of the error (RISE) feedback term can be used to yield an asymptotic tracking result, which improve the tracking performance and reduce the control effort. The stability of closed-loop system is analyzed using a Lyapunov-based method. Simulation results are provided to demonstrate the performance of the proposed controller under different driving conditions.     

Data Fusion-based resilient control system under DoS attacks: A game theoretic approach

In this paper, the resilient control under the Denial-of-Service (DoS) attack is rebuilt within the framework of Joint Directors of Laboratories (JDL) data fusion model. The JDL data fusion process is characterized by the so-called Game-in-Game approach, where decisions are made at different layers. The interactions between different JDL levels are considered which take the form of Packet Delivery Rate of the communication channel. Some criterions to judge whether the cyber defense system is able to protect the underlying control system is provided. Finally, a numerical example is proposed to verify the validity of the proposed method.     

Calibration of imprecise and inaccurate numerical models considering fidelity and robustness: a multi-objective optimization-based approach

Traditionally, model calibration is formulated as a single objective problem, where fidelity to measurements is maximized by adjusting model parameters. In such a formulation however, the model with best fidelity merely represents an optimum compromise between various forms of errors and uncertainties and thus, multiple calibrated models can be found to demonstrate comparable fidelity producing non-unique solutions. To alleviate this problem, the authors formulate model calibration as a multi-objective problem with two distinct objectives: fidelity and robustness. Herein, robustness is defined as the maximum allowable uncertainty in calibrating model parameters with which the model continues to yield acceptable agreement with measurements. The proposed approach is demonstrated through the calibration of a finite element model of a steel moment resisting frame.     

Leon Battista Alberti as Author of <Emphasis Type="Italic">Hypnerotomachia Poliphili</Emphasis>

The enigmatic Hypnerotomachia Poliphili published anonymously in 1499 has long posed puzzles for historians and other scholars. This present text argues that the volume can credibly be attributed, not to Francesca Colonna as is often done, but to the Renaissance humanist and polymath Leon Battista Alberti. Evidence for this is found in the unravelling of arithmogrammatical evidence sprinkled throughout the work, similar to those found in other of Alberti’s works.     

Creating geometrically robust designs for highly sensitive problems using topology optimization

Resonance and wave-propagation problems are known to be highly sensitive towards parameter variations. This paper discusses topology optimization formulations for creating designs that perform robustly under spatial variations for acoustic cavity problems. For several structural problems, robust topology optimization methods have already proven their worth. However, it is shown that direct application of such methods is not suitable for the acoustic problem under consideration. A new double filter approach is suggested which makes robust optimization for spatial variations possible. Its effect and limitations are discussed. In addition, a known explicit penalization approach is considered for comparison. For near-uniform spatial variations it is shown that highly robust designs can be obtained using the double filter approach. It is finally demonstrated that taking non-uniform variations into account further improves the robustness of the designs.