Caustics in turbulent aerosols: an excitable system approach

Aerosol particles are inertial particles. They cannot follow the surrounding fluid in a region of high vorticity. These encounters render the particle velocity field v locally compressible. Caustics occur if the trace of the gradient matrix \sigma of the field v locally diverges. For three-dimensional isotropic and homogeneous turbulence, the dynamics of the gradient matrix can be expressed in terms of three geometric invariants. In the present paper we establish a parametrisation of this problem where the dynamics takes the form of an excitable stochastic dynamical system with a three-dimensional phase space. The deterministic part of the dynamics is solved analytically. We show that the deterministic system has a globally attractive stable fixed point. Small noise induces excursions from the fixed point that typically relax straight back towards the fixed point. Caustics emerge as non-trivial return to a global fixed point when noise excites a trajectory across a stability threshold. The relaxation to the global fixed point will then involve at least one, and it may involve two or even three divergences of Tr \sigma. Based on a combination of analytical insights and numerical analysis, we determine the rate of occurrence, duration and relative observation probability of caustic events in turbulent aerosols. Our analysis reveals that each approach towards a divergence proceeds along a straight line in the phase space of the dynamical system, which can help identify caustics. Moreover, there are infinite ways in which caustics can arise, namely whenever Tr \sigma tends to negative infinity, so that no two caustics look the same

A probabilistic particle tracking framework for guided and Brownian motion systems with high particle densities

This paper presents a new framework for particle tracking based on a Gaussian Mixture Model (GMM). It is an extension of the state-of-the-art iterative reconstruction of individual particles by a continuous modeling of the particle trajectories considering the position and velocity as coupled quantities. The proposed approach includes an initialization and a processing step. In the first step, the velocities at the initial points are determined after iterative reconstruction of individual particles of the first four images to be able to generate the tracks between these initial points. From there on, the tracks are extended in the processing step by searching for and including new points obtained from consecutive images based on continuous modeling of the particle trajectories with a Gaussian Mixture Model. The presented tracking procedure allows to extend existing trajectories interactively with low computing effort and to store them in a compact representation using little memory space. To demonstrate the performance and the functionality of this new particle tracking approach, it is successfully applied to a synthetic turbulent pipe flow, to the problem of observing particles corresponding to a Brownian motion (e.g., motion of cells), as well as to problems where the motion is guided by boundary forces, e.g., in the case of particle tracking velocimetry of turbulent Rayleigh-Bénard convection

pyPTV - a complete framework to reconstruct physical flow fields from camera images

We introduce a novel probability-based Particle Tracking Velocimetry (PTV) and Data Assimilation (DA) framework called pyPTV. It is an open-source project under continuous development and is completely written in the programming language Python. The framework provides a complete routine for processing measurement data suitable for PTV. Starting from raw camera images, pyPTV includes image processing, calibration, and a novel PTV algorithm to reconstruct individual seeding particle trajectories (tracks) in a Lagrangian frame of view. In addition, post-processing algorithms are implemented to refine the tracks. The framework includes interpolation and DA algorithms, that allow the user to generate physical flow fields in an Eulerian frame of view. The velocity field of the particle tracks is corrected to be solenoidal, and the pressure field is estimated. The implemented debugging scripts help fix problems with each subroutine during processing. To verify the method, a synthetic test case of turbulent Rayleigh-Bénard (RB) convection (Pr = 6.9, Ra = 1E10) in a cubic cell is generated by direct numerical simulation with massless tracer particles. A reconstruction accuracy of over 65% with 95% correct tracks is achieved at tracer particle densities of about 0.1 pp

The Fragmented Mitochondrial Ribosomal RNAs of Plasmodium falciparum

The mitochondrial genome in the human malaria parasite Plasmodium falciparum is most unusual. Over half the genome is composed of the genes for three classic mitochondrial proteins: cytochrome oxidase subunits I and III and apocytochrome b. The remainder encodes numerous small RNAs, ranging in size from 23 to 190 nt. Previous analysis revealed that some of these transcripts have significant sequence identity with highly conserved regions of large and small subunit rRNAs, and can form the expected secondary structures. However, these rRNA fragments are not encoded in linear order; instead, they are intermixed with one another and the protein coding genes, and are coded on both strands of the genome. This unorthodox arrangement hindered the identification of transcripts corresponding to other regions of rRNA that are highly conserved and/or are known to participate directly in protein synthesis.The identification of 14 additional small mitochondrial transcripts from P. falciparum and the assignment of 27 small RNAs (12 SSU RNAs totaling 804 nt, 15 LSU RNAs totaling 1233 nt) to specific regions of rRNA are supported by multiple lines of evidence. The regions now represented are highly similar to those of the small but contiguous mitochondrial rRNAs of Caenorhabditis elegans. The P. falciparum rRNA fragments cluster on the interfaces of the two ribosomal subunits in the three-dimensional structure of the ribosome.All of the rRNA fragments are now presumed to have been identified with experimental methods, and nearly all of these have been mapped onto the SSU and LSU rRNAs. Conversely, all regions of the rRNAs that are known to be directly associated with protein synthesis have been identified in the P. falciparum mitochondrial genome and RNA transcripts. The fragmentation of the rRNA in the P. falciparum mitochondrion is the most extreme example of any rRNA fragmentation discovered

Genomic Relationships, Novel Loci, and Pleiotropic Mechanisms across Eight Psychiatric Disorders

Genetic influences on psychiatric disorders transcend diagnostic boundaries, suggesting substantial pleiotropy of contributing loci. However, the nature and mechanisms of these pleiotropic effects remain unclear. We performed analyses of 232,964 cases and 494,162 controls from genome-wide studies of anorexia nervosa, attention-deficit/hyper-activity disorder, autism spectrum disorder, bipolar disorder, major depression, obsessive-compulsive disorder, schizophrenia, and Tourette syndrome. Genetic correlation analyses revealed a meaningful structure within the eight disorders, identifying three groups of inter-related disorders. Meta-analysis across these eight disorders detected 109 loci associated with at least two psychiatric disorders, including 23 loci with pleiotropic effects on four or more disorders and 11 loci with antagonistic effects on multiple disorders. The pleiotropic loci are located within genes that show heightened expression in the brain throughout the lifespan, beginning prenatally in the second trimester, and play prominent roles in neurodevelopmental processes. These findings have important implications for psychiatric nosology, drug development, and risk prediction.Peer reviewe

A probabilistic particle tracking framework for high particle densities

A framework for particle tracking velocimetry at high particle densities (HD-PTV) based on a Gaussian Mixture Model (GMM) is presented. This new approach is validated by tracking synthetic particles generated for a generalized turbulent pipe flow defining the ground truth. For a step size per time step of δS = 14 px and a particles per pixel (ppp) density of 0:09 the framework tracks about 90% of the ground truth particles (percentage of matched particles, pmp) already after 9 time steps without generating any ghost particles. For a lower step size of δS = 7 px, corresponding to a higher temporal resolution of the flow, and the lowest investigated particle density ppp = 0:02 a constant pmp close to 100% is reported. A decrease on pmp to 80% is found for the highest ppp = 0; 11 - corresponding to about 45000 particles in total. Increasing the step size per time step to δS = 14 px results in a similar sloping curve and pmp that are generally 5% lower compared to the lower step size. The approach is further successfully applied to a well-known experimental tracking problem, i.e. particle tracking in turbulent Rayleigh-Bénard convection, for which the motion of about 28500 particles is tracked. With track lengths up to 250 times steps the occuring structures and velocities are investigated and agree well with previous studies based on tomographic particle image velocimetry using the same data. Thus, it is concluded that the presented HD-PTV framework is an appropriate tool for the flow analysis even at high particle densitie

Probabilistic high-density Particle-Tracking-Velocimetry of turbulent flow structures in a cubic Rayleigh-Bénard convection cell.

We apply a new probabilistic python-based high-density Particle-Tracking-Velocimetry (pyHDPTV) method and the commercial Shake-The-Box (STB) algorithm from LaVision (DaVis v10.2.0) to measured data of a turbulent RayleighBénard (RB) convection in a cubic cell. The measurement was performed in water (Prandtl number Pr = 7) with a seeding particle densities of 0,04 ppp at the hard turbulence regime with Rayleigh number Ra = 1 · 1E10. The comparison of the two PTV approaches reveals that the probabilistic pyHDPTV method leads to similar qualitative flow structures as with the state-of-the-art STB method. However, the pyHDPTV framework leads to better quantitative results such as longer track lengths, more active tracks and a higher track density over the whole measurement volume