Tracing the Dark Matter Sheet in Phase Space

The primordial velocity dispersion of dark matter is small compared to the velocities attained during structure formation. The initial density distribution is close to uniform and it occupies an initial sheet in phase space that is single valued in velocity space. Because of gravitational forces this three dimensional manifold evolves in phase space without ever tearing, conserving phase-space volume and preserving the connectivity of nearby points. N-body simulations already follow the motion of this sheet in phase space. This fact can be used to extract full fine-grained phase-space-structure information from existing cosmological N-body simulations. Particles are considered as the vertices of an unstructured three dimensional mesh, moving in six dimensional phase-space. On this mesh, mass density and momentum are uniquely defined. We show how to obtain the space density of the fluid, detect caustics, and count the number of streams as well as their individual contributions to any point in configuration-space. We calculate the bulk velocity, local velocity dispersions, and densities from the sheet - all without averaging over control volumes. This gives a wealth of new information about dark matter fluid flow which had previously been thought of as inaccessible to N-body simulations. We outline how this mapping may be used to create new accurate collisionless fluid simulation codes that may be able to overcome the sparse sampling and unphysical two-body effects that plague current N-body techniques.Comment: MNRAS submitted; 17 pages, 19 figures; revised in line with referee's comments, results unchange

The finite-temperature Monte Carlo method and its application to superfluid helium clusters

We review the use of the path integral Monte Carlo (PIMC) methodology to the study of finite-size quantum clusters, with particular emphasis on recent applications to pure and impurity-doped He clusters. We describe the principles of PIMC, the use of the multilevel Metropolis method for sampling particle permutations, and the methods used to accurately incorporate anisotropic molecule-helium interactions into the path integral scheme. Applications to spectroscopic studies of embedded atoms and molecules are summarized, with discussion of the new concepts of local and nanoscale superfluidity that have been generated by recent PIMC studies of the impurity-doped He clusters.Comment: P. Huang, Y. Kwon, and K. B. Whaley, in "Quantum Fluids in Confinement", Vol. 4 of "Advances in Quantum Many-Body Theories", edited by E. Krotscheck and J. Navarro (World Scientific, Singapore, 2002), in pres

Microscopic two-fluid theory of rotational constants of the OCS-H2_2 complex in 4^4He droplets

We present a microscopic quantum analysis for rotational constants of the OCS-H$_2$ complex in helium droplets using the local two-fluid theory in conjunction with path integral Monte Carlo simulations. Rotational constants are derived from effective moments of inertia calculated assuming that motion of the H$_2$ molecule and the local non-superfluid helium density is rigidly coupled to the molecular rotation of OCS and employing path integral methods to sample the corresponding H$_2$ and helium densities. The rigid coupling assumption for H$_2$-OCS is calibrated by comparison with exact calculations of the free OCS-H$_2$ complex. The presence of the H$_2$ molecule is found to induce a small local non-superfluid helium density in the second solvation shell which makes a non-negligible contribution to the moment of inertia of the complex in helium. The resulting moments of inertia for the OCS-H$_2$ complex embedded in a cluster of 63 helium atoms are found to be in good agreement with experimentally measured values in large helium droplets. Implications for analysis of rotational constants of larger complexes of OCS with multiple H$_2$ molecules in helium are discussed.Comment: 11 pages, 5 figures, accepted for publication in J. Chem. Phy

Optimal sensing for fish school identification

Fish schooling implies an awareness of the swimmers for their companions. In flow mediated environments, in addition to visual cues, pressure and shear sensors on the fish body are critical for providing quantitative information that assists the quantification of proximity to other swimmers. Here we examine the distribution of sensors on the surface of an artificial swimmer so that it can optimally identify a leading group of swimmers. We employ Bayesian experimental design coupled with two-dimensional Navier Stokes equations for multiple self-propelled swimmers. The follower tracks the school using information from its own surface pressure and shear stress. We demonstrate that the optimal sensor distribution of the follower is qualitatively similar to the distribution of neuromasts on fish. Our results show that it is possible to identify accurately the center of mass and even the number of the leading swimmers using surface only information

Dense Motion Estimation for Smoke

Motion estimation for highly dynamic phenomena such as smoke is an open challenge for Computer Vision. Traditional dense motion estimation algorithms have difficulties with non-rigid and large motions, both of which are frequently observed in smoke motion. We propose an algorithm for dense motion estimation of smoke. Our algorithm is robust, fast, and has better performance over different types of smoke compared to other dense motion estimation algorithms, including state of the art and neural network approaches. The key to our contribution is to use skeletal flow, without explicit point matching, to provide a sparse flow. This sparse flow is upgraded to a dense flow. In this paper we describe our algorithm in greater detail, and provide experimental evidence to support our claims.Comment: ACCV201

A particle filter to reconstruct a free-surface flow from a depth camera

We investigate the combined use of a Kinect depth sensor and of a stochastic data assimilation method to recover free-surface flows. More specifically, we use a Weighted ensemble Kalman filter method to reconstruct the complete state of free-surface flows from a sequence of depth images only. This particle filter accounts for model and observations errors. This data assimilation scheme is enhanced with the use of two observations instead of one classically. We evaluate the developed approach on two numerical test cases: a collapse of a water column as a toy-example and a flow in an suddenly expanding flume as a more realistic flow. The robustness of the method to depth data errors and also to initial and inflow conditions is considered. We illustrate the interest of using two observations instead of one observation into the correction step, especially for unknown inflow boundary conditions. Then, the performance of the Kinect sensor to capture temporal sequences of depth observations is investigated. Finally, the efficiency of the algorithm is qualified for a wave in a real rectangular flat bottom tank. It is shown that for basic initial conditions, the particle filter rapidly and remarkably reconstructs velocity and height of the free surface flow based on noisy measurements of the elevation alone

Path integral Monte Carlo simulation of global and local superfluidity in liquid 4^{4}He reservoirs separated by nanoscale apertures

We present a path integral Monte Carlo study of the global superfluid fraction and local superfluid density in cylindrically-symmetric reservoirs of liquid $^{4}$He separated by nanoaperture arrays. The superfluid response to both translations along the axis of symmetry (longitudinal response) and rotations about the cylinder axis (transverse response) are computed, together with radial and axial density distributions that reveal the microscopic inhomogeneity arising from the combined effects of the confining external potential and the $^4$He-$^4$He interatomic potentials. We make a microscopic determination of the length-scale of decay of superfluidity at the radial boundaries of the system by analyzing the local superfluid density distribution to extract a displacement length that quantifies the superfluid mass displacement away from the boundary. We find that the longitudinal superfluid response is reduced in reservoirs separated by a septum containing sufficiently small apertures compared to a cylinder with no intervening aperture array, for all temperatures below $T_{\lambda}$. For a single aperture in the septum, a significant drop in the longitudinal superfluid response is seen when the aperture diameter is made smaller than twice the empirical temperature-dependent $^4$He healing length, consistent with the formation of a weak link between the reservoirs. Increasing the diameter of a single aperture or the number of apertures in the array results in an increase of the superfluid density toward the expected bulk value.Comment: 12 pages, 6 figure

A statistical analysis of particle trajectories in living cells

Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of single molecules in living cells. Such inference allows to determine the organization and function of the cell. The trajectories of particles in the cells, computed with tracking algorithms, can be modelled with diffusion processes. Three types of diffusion are considered : (i) free diffusion; (ii) subdiffusion or (iii) superdiffusion. The Mean Square Displacement (MSD) is generally used to determine the different types of dynamics of the particles in living cells (Qian, Sheetz and Elson 1991). We propose here a non-parametric three-decision test as an alternative to the MSD method. The rejection of the null hypothesis -- free diffusion -- is accompanied by claims of the direction of the alternative (subdiffusion or a superdiffusion). We study the asymptotic behaviour of the test statistic under the null hypothesis, and under parametric alternatives which are currently considered in the biophysics literature, (Monnier et al,2012) for example. In addition, we adapt the procedure of Benjamini and Hochberg (2000) to fit with the three-decision test setting, in order to apply the test procedure to a collection of independent trajectories. The performance of our procedure is much better than the MSD method as confirmed by Monte Carlo experiments. The method is demonstrated on real data sets corresponding to protein dynamics observed in fluorescence microscopy.Comment: Revised introduction. A clearer and shorter description of the model (section 2