Spectrograms of ship wakes: identifying linear and nonlinear wave signals

A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high speed ferry data have identified additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time-frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. We use a simple weakly nonlinear theory to identify higher order effects in a spectrogram and, while the high speed ferry data is very noisy, we propose that certain additional features in the experimental data are caused by nonlinearity. Finally, we provide a possible explanation for a further discrepancy between the high speed ferry spectrograms and linear theory by accounting for ship acceleration.Comment: 21 pages, 10 figures, submitte

Efficient computation of two-dimensional steady free-surface flows

We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable techniques, these problems are formulated in terms of a coupled system of Bernoulli's equation and an integral equation. When applying a numerical collocation scheme, the Jacobian for the system is dense, as the integral equation forces each of the algebraic equations to depend on each of the unknowns. We present here a strategy for overcoming this challenge, which leads to a numerical scheme that is much more efficient than what is normally employed for these types of problems, allowing for many more grid points over the free surface. In particular, we provide a simple recipe for constructing a sparse approximation to the Jacobian that is used as a preconditioner in a Jacobian-free Newton-Krylov method for solving the nonlinear system. We use this approach to compute numerical results for a variety of prototype problems including flows past pressure distributions, a surface-piercing object and bottom topographies.Comment: 20 pages, 13 figures, under revie

Degradation of Phosphorene in Air: Understanding at Atomic Level

Phosphorene is a promising two dimensional (2D) material with a direct band gap, high carrier mobility, and anisotropic electronic properties. Phosphorene-based electronic devices, however, are found to degrade upon exposure to air. In this paper, we provide an atomic level understanding of stability of phosphorene in terms of its interaction with O2 and H2O. The results based on density functional theory together with first principles molecular dynamics calculations show that O2 could spontaneously dissociate on phosphorene at room temperature. H2O will not strongly interact with pristine phosphorene, however, an exothermic reaction could occur if phosphorene is first oxidized. The pathway of oxidation first followed by exothermic reaction with water is the most likely route for the chemical degradation of the phosphorene-based devices in air

Three\u27s Company: A Constitutional Analysis of Prohibiting Access to Three-Parent In Vitro Fertilization

The 1997 science-fiction film Gattaca tells the story of Vincent Freeman, a “God-child,” “de-gene-erate,” “faith birth.” The film unfolds in a not-too-distant future where genetic modification is commonplace and children’s characteristics and predispositions are routinely decided before birth. A rarity in this world, Vincent is conceived without any genetic modification and, consequently, is born with myopia and a congenital heart defect. His inferior genetic profile has banished him to a new subclass of society, so the only way to achieve his lifelong dream of becoming an astronaut is by impersonating a “valid”—a person with a healthy, genetically-engineered DNA

Three\u27s Company: A Constitutional Analysis of Prohibiting Access to Three-Parent In Vitro Fertilization

The 1997 science-fiction film Gattaca tells the story of Vincent Freeman, a “God-child,” “de-gene-erate,” “faith birth.” The film unfolds in a not-too-distant future where genetic modification is commonplace and children’s characteristics and predispositions are routinely decided before birth. A rarity in this world, Vincent is conceived without any genetic modification and, consequently, is born with myopia and a congenital heart defect. His inferior genetic profile has banished him to a new subclass of society, so the only way to achieve his lifelong dream of becoming an astronaut is by impersonating a “valid”—a person with a healthy, genetically-engineered DNA

Water activities in the Kerala Khondalite Belt

The author and colleagues presented their determinations of water activities in various granulite-facies rocks of the Kerala Khondalite Belt. Using mineral equilibria, thermodynamic data, and assumed geopressure-geotemperature conditions of 5.5 kbar and 750 C, they calculated uniformly low a(H2O) values of about 0.27 over a large geographic region. They suggested that these conditions were produced by the presence of abundant CO2-rich fluids, derived either from deeper levels or from metamorphic reactions involving graphite

Time-frequency analysis of ship wave patterns in shallow water: modelling and experiments

A spectrogram of a ship wake is a heat map that visualises the time-dependent frequency spectrum of surface height measurements taken at a single point as the ship travels by. Spectrograms are easy to compute and, if properly interpreted, have the potential to provide crucial information about various properties of the ship in question. Here we use geometrical arguments and analysis of an idealised mathematical model to identify features of spectrograms, concentrating on the effects of a finite-depth channel. Our results depend heavily on whether the flow regime is subcritical or supercritical. To support our theoretical predictions, we compare with data taken from experiments we conducted in a model test basin using a variety of realistic ship hulls. Finally, we note that vessels with a high aspect ratio appear to produce spectrogram data that contains periodic patterns. We can reproduce this behaviour in our mathematical model by using a so-called two-point wavemaker. These results highlight the role of wave interference effects in spectrograms of ship wakes.Comment: 14 pages, 7 figure

The electrostatic profile of consecutive Cβ atoms applied to protein structure quality assessment.

The structure of a protein provides insight into its physiological interactions with other components of the cellular soup. Methods that predict putative structures from sequences typically yield multiple, closely-ranked possibilities. A critical component in the process is the model quality assessing program (MQAP), which selects the best candidate from this pool of structures. Here, we present a novel MQAP based on the physical properties of sidechain atoms. We propose a method for assessing the quality of protein structures based on the electrostatic potential difference (EPD) of Cβ atoms in consecutive residues. We demonstrate that the EPDs of Cβ atoms on consecutive residues provide unique signatures of the amino acid types. The EPD of Cβ atoms are learnt from a set of 1000 non-homologous protein structures with a resolution cuto of 1.6 Å obtained from the PISCES database. Based on the Boltzmann hypothesis that lower energy conformations are proportionately sampled more, and on Annsen's thermodynamic hypothesis that the native structure of a protein is the minimum free energy state, we hypothesize that the deviation of observed EPD values from the mean values obtained in the learning phase is minimized in the native structure. We achieved an average specificity of 0.91, 0.94 and 0.93 on hg_structal, 4state_reduced and ig_structal decoy sets, respectively, taken from the Decoys `R' Us database. The source code and manual is made available at https://github.com/sanchak/mqap and permanently available on 10.5281/zenodo.7134