Numerical simulation of stochastic vortex tangles

We present the results of simulation of the chaotic dynamics of quantized vortices in the bulk of superfluid He II. Evolution of vortex lines is calculated on the base of the Biot-Savart law. The dissipative effects appeared from the interaction with the normal component, or/and from relaxation of the order parameter are taken into account. Chaotic dynamics appears in the system via a random forcing, e.i. we use the Langevin approach to the problem. In the present paper we require the correlator of the random force to satisfy the fluctuation-disspation relation, which implies that thermodynamic equilibrium should be reached. In the paper we describe the numerical methods for integration of stochastic differential equation (including a new algorithm for reconnection processes), and we present the results of calculation of some characteristics of a vortex tangle such as the total length, distribution of loops in the space of their length, and the energy spectrum.Comment: 8 pages, 5 figure

The sensitivity of the vortex filament method to different reconnection models

We present a detailed analysis on the effect of using different algorithms to model the reconnection of vortices in quantum turbulence, using the thin-filament approach. We examine differences between four main algorithms for the case of turbulence driven by a counterflow. In calculating the velocity field we use both the local induction approximation (LIA) and the full Biot-Savart integral. We show that results of Biot-Savart simulations are not sensitive to the particular reconnection method used, but LIA results are.Comment: 9 pages, 9 figure

Identification of Kelvin waves: numerical challenges

Kelvin waves are expected to play an essential role in the energy dissipation for quantized vortices. However, the identification of these helical distortions is not straightforward, especially in case of vortex tangle. Here we review several numerical methods that have been used to identify Kelvin waves within the vortex filament model. We test their validity using several examples and estimate whether these methods are accurate enough to verify the correct Kelvin spectrum. We also illustrate how the correlation dimension is related to different Kelvin spectra and remind that the 3D energy spectrum E(k) takes the form 1/k in the high-k region, even in the presence of Kelvin waves.Comment: 6 pages, 5 figures. The final publication is available at http://www.springerlink.co

A note on the propagation of quantized vortex rings through a quantum turbulence tangle:energy transport or energy dissipation?

We investigate quantum vortex ring dynamics at scales smaller than the inter-vortex spacing in quantum turbulence. Through geometrical arguments and high-resolution numerical simulations, we examine the validity of simple estimates for the mean free path and the structure of vortex rings post-reconnection. We find that a large proportion of vortex rings remain coherent objects where approximately 75% of their energy is preserved. This leads us to consider the effectiveness of energy transport in turbulent tangles. Moreover, we show that in low density tangles, appropriate for the ultra-quantum regime, ring emission cannot be ruled out as an important mechanism for energy dissipation. However at higher vortex line densities, typically associated with the quasi-classical regime, loop emission is expected to make a negligible contribution to energy dissipation, even allowing for the fact that our work shows rings can survive multiple reconnection events. Hence the Kelvin wave cascade seems the most plausible mechanism leading to energy dissipatio

Tree method for quantum vortex dynamics

We present a numerical method to compute the evolution of vortex filaments in superfluid helium. The method is based on a tree algorithm which considerably speeds up the calculation of Biot-Savart integrals. We show that the computational cost scales as Nlog{(N) rather than N squared, where $N$ is the number of discretization points. We test the method and its properties for a variety of vortex configurations, ranging from simple vortex rings to a counterflow vortex tangle, and compare results against the Local Induction Approximation and the exact Biot-Savart law.Comment: 12 pages, 10 figure

A Fine-Mapping Study of 7 Top Scoring Genes from a GWAS for Major Depressive Disorder

Major depressive disorder (MDD) is a psychiatric disorder that is characterized -amongst others- by persistent depressed mood, loss of interest and pleasure and psychomotor retardation. Environmental circumstances have proven to influence the aetiology of the disease, but MDD also has an estimated 40% heritability, probably with a polygenic background. In 2009, a genome wide association study (GWAS) was performed on the Dutch GAIN-MDD cohort. A non-synonymous coding single nucleotide polymorphism (SNP) rs2522833 in the PCLO gene became only nominally significant after post-hoc analysis with an Australian cohort which used similar ascertainment. The absence of genome-wide significance may be caused by low SNP coverage of genes. To increase SNP coverage to 100% for common variants (m.a.f.>0.1, r2>0.8), we selected seven genes from the GAIN-MDD GWAS: PCLO, GZMK, ANPEP, AFAP1L1, ST3GAL6, FGF14 and PTK2B. We genotyped 349 SNPs and obtained the lowest P-value for rs2715147 in PCLO at P = 6.8E−7. We imputed, filling in missing genotypes, after which rs2715147 and rs2715148 showed the lowest P-value at P = 1.2E−6. When we created a haplotype of these SNPs together with the non-synonymous coding SNP rs2522833, the P-value decreased to P = 9.9E−7 but was not genome wide significant. Although our study did not identify a more strongly associated variant, the results for PCLO suggest that the causal variant is in high LD with rs2715147, rs2715148 and rs2522833