Bishop Independence on the Surface of a Square Prism

Bishop Independence concerns determining the maximum number of bishops that can be placed on a board such that no bishop can attack any other bishop. This paper presents the solution to the bishop independence problem, determining the bishop independence number, for all sizes of boards on the surface of a square prism.

How a ball free to orbit in a circular track mitigates the galloping of a square prism

Transverse galloping is a type of flow-induced vibration (FIV) that leads to critical design considerations for engineering structures. A purely nonlinear energy sink (NES) composed of a ball free to rotate in a circular track experimentally mitigated the galloping of a square in a previous study. The current study introduces a model for simulating the dynamics of the square prism coupled with a ball-in-track (BIT) NES and predicting the system behaviour at high flow speeds beyond the limits of the previously presented experiments. Numerical simulations employ the fitting of experimental data as inputs to define parameters. Wind tunnel static experiments provide the galloping force coefficient [[EQUATION]] relative to the prism angle of attack. Additionally, free rotation tests allow evaluating the ball damping coefficient [[EQUATION]] as a function of its mass and the NES track radius. The result of the rotation tests provides a critical angular speed beyond which the ball damping increases non-linearly. We point out the damping variation as an advantage of the BIT-NES; less damping at low angular velocities helps the ball start its rotation, while relatively large damping at higher speeds dissipates more energy from the vibrating system. Numerical results exhibit four response modes for the NES; oscillatory at low flow speeds, intermittent within a small range of higher flow speeds, rotational at higher flow speeds, and ineffective regime at flow speeds out of the NES effective range. Modelling the primary mass as a parametric excitation source for the NES provides an analytical estimation of the boundary between the oscillatory and intermittent regimes. Furthermore, we advance an analytical analysis of the power flow across the integrated prism-NES system to explain the NES behaviour and predict the limit of its effective range.

Solution NMR and racemic crystallography provide insights into a novel structural class of cyclic plant peptides

Head-to-tail cyclic and disulfide-rich peptides are natural products with applications in drug design. Among these are the PawS-Derived Peptides (PDPs) produced in seeds of the daisy plant family. PDP-23 is a unique member of this class in that it is twice the typical size and adopts two β-hairpins separated by a hinge region. The β-hairpins - both stabilised by a single disulfide bond - fold together into a V-shaped tertiary structure creating a hydrophobic core. In water two PDP-23 molecules merge their hydrophobic cores to form a square prism quaternary structure. Here, we synthesised PDP-23 and its enantiomer comprising all D-amino acids, which allowed us to confirm these solution NMR structural data by racemic crystallography. Furthermore, we discovered the related PDP-24. NMR analysis showed that PDP-24 does not form a dimeric structure and it has poor water solubility, but in less polar solvents adopts near identical secondary and tertiary structure to PDP-23. The natural role of these peptides in plants remains enigmatic, as we did not observe any antimicrobial or insecticidal activity. However, the plasticity of these larger PDPs and their ability to change structure under different conditions makes them appealing peptide drug scaffolds.

EXPERIMENTAL INVESTIGATION OF AN ACOUSTIC METAMATERIAL BARRIER DESIGN COMPOSED OF A SQUARE PRISM WITHIN A HEXAGONAL RECESS

This paper presents an experimental investigation of an acoustic barrier composed out of an acousticmetamaterial unit cell. The design of the unit cell consists of a square prism, acting as a resonator,within a hexagonal recess manufactured out of a single material. Two materials were used tomanufacture the unit cell: PolyMide Polycarbonate and Polylite Polylactic Acid. The acousticperformance of the unit cell was quantified for both materials using the acoustic absorptioncoefficient and acoustic transmission loss values for frequencies between 100 Hz and 5,000Hz. Theexperimental results indicate that the design reduced the peak absorption coefficient for bothmaterials while also introducing two additional peaks at around 1,500 Hz and at 4,000 Hz. Changesto the absorption coefficient values were observed for frequencies above 1,000 Hz while minimalchanges were observed for frequencies below 1,000 Hz. These results indicate that the proposeddesign, is able to widen the effective frequency band, or stop band for acoustic absorption forfrequencies above 1,000 Hz compared to the absorption coefficient of the material. The experimentalresults also indicate that the design increases the peak transmission loss by about 7 dB at 4,000 Hz.For sounds below 3,000 Hz, the design will only change the transmission loss by about 3 dB forfrequencies between 100 Hz to 3,000 Hz. These results indicate that the acoustic metamaterial design,consisting of resonator in a recess manufactured out of a single material, is able to broaden theeffective frequency range for sound absorption for frequencies between 1,000 Hz and 4,000 Hz andat increasing the transmission loss values for frequencies between 3,000 Hz and 5,000 Hz. It can beconcluded that the resonator in recess metamaterial design, manufactured out of a single material,can be used to increase the stop band for acoustic absorption for frequencies above 1,000 Hz and toincrease the transmission loss for frequencies above 3,000 Hz.

Assessment of turbulence models for low Reynolds number flows and their computational costs, Part 2: Square prism in cross flow

The accuracy of six turbulent flow modeling techniques in an unsteady solution is evaluated against experimental data for a square prism in cross flow. The selected models; SST, SST-SAS, RSM, PANS-SST, DES and LES models are the same as those presented in Part 1 of this study, which focused on flow in a staggered tube bank. For this geometry, the SST model proved to be effective at capturing the averaged Nusselt values per side of the square with relatively low computational costs. The SST model however showed poorer fidelity to the local Nusselt number profile compared to the experimental data. The LES approach provided a more accurate representation of the local Nusselt number but the computational cost was significantly higher. The PANS modification to the SST model did provide a noticeable improvement in accuracy at a reasonable cost while the SAS modification did not see the same improvement. These conclusions are generally consistent with those found for the staggered tube bank in Part 1 of this study. This study can be used as a guide for the industrial user to select a turbulence model for a similar problem with a low Reynolds number and significant flow separation.

Finite Element Analysis Study on Lattice Structure Fabricated Recycled Polystyrene from Post-used Styrofoam Waste

Lattice structure design widely applicable for 3D printed components. This research investigated the lattice structure with different shape and relative density using Finite Element Analysis (FEA) simulation. The material used for the lattice structure was the recycled polystyrene made from post-used Styrofoam. The research assessed the mechanical behaviour of lattice structure with either triangular prism and square prism with FEA simulation and numerical mathematical modelling, such as stiffness to-mass ratio, maximum von Misses stress and effective Young’s modulus. The finding FEA shows a good agreement with result from numerical mathematic modelling. The FEA results show lattice structure with triangular prism exhibited lowest value of maximum von Misses stress with maximum stiffness-to-mass value compared to lattice structure square prism. The finding from this work provided an early prediction on mechanical properties of lattice structure fabricated from recycled polystyrene.

The Centroid Solid Angle and Probability Models of Square Prism Dice Rolls

Past studies have indicated that the centroid solid angle is related to probabilities of square prism dice rolls. We explain how it is relevant to these probabilities and how to use the spherical projection to calculate the centroid solid angles for the faces on a square prism. These values are then used in a statistical analysis in the quest of constructing a mathematical probability model. The proposed model is based on the principle that the probability of ending up on a particular resting aspect is proportional to the centroid solid angle of that aspect and inversely proportional to a power of the centroid height in that aspect. Using a power of 2.427, this proposed model fits our data of over 60,000 non-symmetrical square prism dice rolls of various sizes (unequal heights and widths) with the largest magnitude Z-score of 1.01. Different powers can potentially describe other situations; e.g. different surfaces, larger dice, heavier dice, etc.