Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules

Development of a human-structure dynamic interaction model for human sway for use in permanent grandstand design

This paper details a first attempt to develop a simple human-structure dynamic interaction (HSDI) model for vibration serviceability design of permanent grandstands subject to crowd sway. To date, extensive research has been conducted on vertical crowd-induced vibrations to understand interaction mechanisms and enable engineers to account for them. Similar mechanisms have not yet been fully understood or researched in the lateral plane. This, alongside the limited, verified measured response data has led to incomplete design assessment methods. In this work, an effective two-degree-of-freedom spring-mass-damper-actuator system is developed to represent co-ordinated spectators swaying laterally in the side-to-side direction on a real grandstand. The dynamic properties attributed in the constituents of the model are determined by curve fitting of laboratory-scale human sway data and the modal analysis of the grandstand’s finite element model. The comparison of the modelling output against existing serviceability criteria approaches illustrates potential conservatism in current practice. Namely, when the maximum responses and forces were examined as part of the integrated dynamic system a notable drop-out effect was observed. Although further research is required to validate and calibrate the proposed simple human-structure sway model for individuals and crowds, the observations qualitatively determine the significance of explicitly considering human-structure interaction in the design and assessment of permanent grandstands. Such effects may lead to construction cost savings in addition to unwanted limitations on architecture, hospitality areas and spectator circulation

The use of deep friction massage with olive oil as a means of prevention and treatment of sports injuries in ancient times

The aim of this research was to analyse the use of olive oil as a means of prevention and treatment of sports injuries in the ancient world. The method adopted was based on a thorough study of Greek and world literature. Writings of major ancient philosophers and physicians such as Hippocrates, Aristotle, Philostratus, and Lucian have been analysed in depth. According to the results, the use of massage, together with olive oil rub, helped to reduce muscle fatigue, to remove lactic acid, and to prevent the occurrence of sports injuries through flexibility provided to the skin of athletes. The therapeutic use of oil in the ancient world was fully recognized; and as a result Athenian athlothetes (sponsors of sporting events) provided free oil to all sport facilities where athletes could make free use of it [1]

Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT

A density inversion method is presented, to obtain the constrained, optimal, local potential that has a prescribed asymptotic behaviour and reproduces optimally any given ground-state electronic density. This work builds upon the method of [Callow et al., J. Chem. Phys., 2020, 152, 164114.] and differs in the expansion of the screening density in orbital basis element products instead of basis functions of an additional auxiliary set. We demonstrated the method by applying it to densities from DFT, Hartree–Fock, CAS-SCF and RDMFT calculations. For RDMFT, we demonstrate that density inversion offers a viable single-particle description by comparing the ionization potentials for atomic and molecular systems to the corresponding experimental values. Finally, we show that with the present method, accurate correlation potentials can be obtained from the inversion of accurate densities

Effects of oscillation amplitude on motion-induced forces for 5:1 rectangular cylinders

While the 5:1 rectangular cylinder is a benchmark section, studied extensively, there are limited experimental studies commenting on any amplitude-dependence of its motion-induced forces. To this goal, such a cylinder is tested in wind tunnel through a forced vibration protocol for extracting distributed simultaneous pressure measurements under smooth flow conditions and for different heaving, pitching and coupled motion amplitudes. Ordinary flutter derivatives are extracted, and discrepancies due to oscillation amplitude are scrutinized. Spectral analysis is performed for the developing motion-induced forces, and it is found that torsional amplitudes above a threshold would increase higher harmonic frequency content. The phenomenon was also confirmed by means of Probability Density Functions and (PDFs) the Proper Orthogonal Decomposition (POD) of the unsteady wind force. In order to understand the link between the observed amplitude dependence and the flow field variation, the movement of the reattachment point on the cylinder surface is investigated by interpreting statistics of the recorded pressure measurements. The response in terms of instantaneous angle of attack is proven to be incompatible with respect to observations, since equal amplitudes of this variable result to different motion-induced forces

Scaling laws for shaking table testing of reinforced concrete tunnels accounting for post-cracking lining response

This paper proposes a new set of scaling laws for the study of the post-cracking behaviour of lightly reinforced concrete tunnel linings during 1g shaking table testing. The post-cracking behaviour scaling laws are formulated using two non-dimensional parameters: the brittleness number s, which governs the fracturing phenomenon for unreinforced concrete elements and , which plays a primary role for the stability of the process of concrete fracture and steel plastic flow in reinforced concrete elements. The proposed laws allow for the development of an “adequate” experimental model and are validated using numerical analyses of a reinforced tunnel in rock, in both prototype and 1:30 model scale. The adopted experimental set-up is inspired by an existing 1g physical testing campaign on the seismic response of a concrete tunnel in rock and the postulated laws are shown to grant satisfactory similitude between the cracking behaviour of the model and prototype tunnel under two examined earthquake records. The potential of using the proposed laws in 1g tests for Class A predictions of evolving crack patterns in reinforced concrete tunnels is highlighted. The proposed laws are examined under three possible boundary conditions, indicating that both rigid and laminar boxes can still change the behaviour significantly compared to an envisaged free field boundary model. The analysis shows though that for larger soil to lining stiffness ratios, boundary artefacts could be greatly reduced. The present study provides useful recommendations for future 1g tests that did not exist to date, while the proposed scaling laws allow for versatility in the design of novel tunnel lining model test materials