Higher Derivative Field Theories: Degeneracy Conditions and Classes

We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze which (non)trivial classes of solutions this allows for. It is shown explicitly how Lorentz invariance avoids the propagation of "half" degrees of freedom. Moreover, for a large class of theories, we construct the field redefinitions and/or (extended) contact transformations that put the theory in a manifestly first order form. Finally, we identify which class of theories cannot be brought to first order form by such transformations.Comment: 26 pages, 1 figure. v2: minor changes, references added, matches version published in JHE

Simulations and experiments of short intense envelope solitons of surface water waves

The problem of existence of stable nonlinear groups of gravity waves in deep water is revised by means of laboratory and numerical simulations with the focus on intense waves. Wave groups with steepness up to $A_{cr} \omega_m^2 /g \approx 0.30$ are reproduced in laboratory experiments ($A_{cr}$ is the wave crest amplitude, $\omega_m$ is the mean angular frequency and $g$ is the gravity acceleration). We show that the groups remain stable and exhibit neither noticeable radiation nor structural transformation for more than 60 wave lengths or about 15-30 group lengths. These solitary wave patterns differ from the conventional envelope solitons, as only a few individual waves are contained in the group. Very good agreement is obtained between the laboratory results and strongly nonlinear numerical simulations of the potential Euler equations. The envelope soliton solution of the nonlinear Schr\"odinger equation is shown to be a reasonable first approximation for specifying the wavemaker driving signal. The short intense envelope solitons possess vertical asymmetry similar to regular Stokes waves with the same frequency and crest amplitude. Nonlinearity is found to have remarkably stronger effect on the speed of envelope solitons in comparison to the nonlinear correction to the Stokes wave velocity.Comment: Under review in Physics of Fluid

Polyethylene under tensile load: strain energy storage and breaking of linear and knotted alkanes probed by first-principles molecular dynamics calculations

The mechanical resistance of a polyethylene strand subject to tension and the way its properties are affected by the presence of a knot is studied using first-principles molecular dynamics calculations. The distribution of strain energy for the knotted chains has a well-defined shape that is very different from the one found in the linear case. The presence of a knot significantly weakens the chain in which it is tied. Chain rupture invariably occurs just outside the entrance to the knot, as is the case for a macroscopic rope.Comment: 8 pages, 11 figures, to appear on J. Chem. Phy

Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship

Similar self-organizing scale-invariant properties characterize early cancer invasion and long range species spread

Occupancy of new habitats through dispersion is a central process in nature. In particular, long range dispersal is involved in the spread of species and epidemics, although it has not been previously related with cancer invasion, a process that involves spread to new tissues. We show that the early spread of cancer cells is similar to the species individuals spread and that both processes are represented by a common spatio-temporal signature, characterized by a particular fractal geometry of the boundaries of patches generated, and a power law-scaled, disrupted patch size distribution. We show that both properties are a direct result of long-distance dispersal, and that they reflect homologous ecological processes of population self-organization. Our results are significant for processes involving long-range dispersal like biological invasions, epidemics and cancer metastasis.Comment: 21 pages, 2 figure

Influence of a knot on the strength of a polymer strand

Many experiments have been done to determine the relative strength of different knots, and these show that the break in a knotted rope almost invariably occurs at a point just outside the `entrance' to the knot. The influence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties. Knot theory applied to the topology of macromolecules indicates that the simple trefoil or `overhand' knot is likely to be present with high probability in any long polymer strand. Fragments of DNA have been observed to contain such knots in experiments and computer simulations. Here we use {\it ab initio} computational methods to investigate the effect of a trefoil knot on the breaking strength of a polymer strand. We find that the knot weakens the strand significantly, and that, like a knotted rope, it breaks under tension at the entrance to the knot.Comment: 3 pages, 4 figure

Genome analyses of the sunflower pathogen Plasmopara halstedii provide insights into effector evolution in downy mildews and Phytophthora.

BACKGROUND: Downy mildews are the most speciose group of oomycetes and affect crops of great economic importance. So far, there is only a single deeply-sequenced downy mildew genome available, from Hyaloperonospora arabidopsidis. Further genomic resources for downy mildews are required to study their evolution, including pathogenicity effector proteins, such as RxLR effectors. Plasmopara halstedii is a devastating pathogen of sunflower and a potential pathosystem model to study downy mildews, as several Avr-genes and R-genes have been predicted and unlike Arabidopsis downy mildew, large quantities of almost contamination-free material can be obtained easily. RESULTS: Here a high-quality draft genome of Plasmopara halstedii is reported and analysed with respect to various aspects, including genome organisation, secondary metabolism, effector proteins and comparative genomics with other sequenced oomycetes. Interestingly, the present analyses revealed further variation of the RxLR motif, suggesting an important role of the conservation of the dEER-motif. Orthology analyses revealed the conservation of 28 RxLR-like core effectors among Phytophthora species. Only six putative RxLR-like effectors were shared by the two sequenced downy mildews, highlighting the fast and largely independent evolution of two of the three major downy mildew lineages. This is seemingly supported by phylogenomic results, in which downy mildews did not appear to be monophyletic. CONCLUSIONS: The genome resource will be useful for developing markers for monitoring the pathogen population and might provide the basis for new approaches to fight Phytophthora and downy mildew pathogens by targeting core pathogenicity effectors