On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond

An improved understanding of the divergence-free constraint for the incompressible Navier--Stokes equations leads to the observation that a semi-norm and corresponding equivalence classes of forces are fundamental for their nonlinear dynamics. The recent concept of {\em pressure-robustness} allows to distinguish between space discretisations that discretise these equivalence classes appropriately or not. This contribution compares the accuracy of pressure-robust and non-pressure-robust space discretisations for transient high Reynolds number flows, starting from the observation that in generalised Beltrami flows the nonlinear convection term is balanced by a strong pressure gradient. Then, pressure-robust methods are shown to outperform comparable non-pressure-robust space discretisations. Indeed, pressure-robust methods of formal order $k$ are comparably accurate than non-pressure-robust methods of formal order $2k$ on coarse meshes. Investigating the material derivative of incompressible Euler flows, it is conjectured that strong pressure gradients are typical for non-trivial high Reynolds number flows. Connections to vortex-dominated flows are established. Thus, pressure-robustness appears to be a prerequisite for accurate incompressible flow solvers at high Reynolds numbers. The arguments are supported by numerical analysis and numerical experiments.Comment: 43 pages, 18 figures, 2 table

Deformation of polymer films by bending forces

We study the deformation of nano--scale polymer films which are subject to external bending forces by means of computer simulation. The polymer is represented by a generalized bead--spring--model, intended to reproduce characteristic features of n--alkanes. The film is loaded by the action of a prismatic blade which is pressed into the polymer bulk from above and a pair of columns which support the film from below. The interaction between blade and support columns and the polymer is modelled by the repulsive part of a Lennard-Jones potential. For different system sizes as well as for different chainlengths, this nano--scale experiment is simulated by molecular dynamics methods. Our results allow us to give a first characterization of deformed states for such films. We resolve the kinetic and the dynamic stage of the deformation process in time and access the length scale between discrete particle and continuum mechanics behaviour. For the chainlengths considered here, we find that the deformation process is dominated by shear. We observe strangling effects for the film and deformation fluctuations in the steady state.Comment: 15 pages, 8 figure

Experimental investigations on freely exposed ducted radiators

This report deals with the relation between the open areas, the drag, and the air flow as observed on freely exposed, ducted radiators - the air conductivity being modified from zero to one unit. In conjunction with theoretical results, the individual components of the drag of ducted radiators are discussed and general rules established for low-loss ducts. The influence of the wall thickness of the ducts, of the length ratio of the exit, and the effects of sonic velocity on diffusers are dealt with by special measurement

Large-scale Simulation of the Two-dimensional Kinetic Ising Model

We present Monte Carlo simulation results for the dynamical critical exponent $z$ of the two-dimensional kinetic Ising model using a lattice of size $10^6 \times 10^6$ spins. We used Glauber as well as Metropolis dynamics. The $z$-value of $2.16\pm 0.005$ was calculated from the magnetization and energy relaxation from an ordered state towards the equilibrium state at $T_c$.Comment: 6 pages + 2 figures as separate uuencoded compressed tar file, Postscipt also available at http://wwwcp.tphys.uni-heidelberg.de/papers

Diffusion Enhancement in a Periodic Potential under High-Frequency Space-Dependent Forcing

We study the long-time behavior of underdamped Brownian particle moving through a viscous medium and in a systematic potential, when it is subjected to a space-dependent high-frequency periodic force. When the frequency is very large, much larger than all other relevant system-frequencies, there is a Kapitsa time-window wherein the effect of frequency dependent forcing can be replaced by a static effective potential. Our new analysis includes the case when the forcing, in addition to being frequency-dependent, is space-dependent as well. The results of the Kapitsa analysis then lead to additional contributions to the effective potential. These are applied to the numerical calculation of the diffusion coefficient (D) for a Brownian particle moving in a periodic potential. Presented are numerical results, which are in excellent agreement with theoretical predictions and which indicate a significant enhancement of D due to the space-dependent forcing terms. In addition we study the transport property (current) of underdamped Brownian particles in a ratchet potential.Comment: RevTex 6 pages, 5 figure

Brownian motors: current fluctuations and rectification efficiency

With this work we investigate an often neglected aspect of Brownian motor transport: The r\^{o}le of fluctuations of the noise-induced current and its consequences for the efficiency of rectifying noise. In doing so, we consider a Brownian inertial motor that is driven by an unbiased monochromatic, time-periodic force and thermal noise. Typically, we find that the asymptotic, time- and noise-averaged transport velocities are small, possessing rather broad velocity fluctuations. This implies a corresponding poor performance for the rectification power. However, for tailored profiles of the ratchet potential and appropriate drive parameters, we can identify a drastic enhancement of the rectification efficiency. This regime is marked by persistent, uni-directional motion of the Brownian motor with few back-turns, only. The corresponding asymmetric velocity distribution is then rather narrow, with a support that predominantly favors only one sign for the velocity.Comment: 9 pages, 4 figure

Analytical model of brittle destruction based on hypothesis of scale similarity

The size distribution of dust particles in nuclear fusion devices is close to the power function. A function of this kind can be the result of brittle destruction. From the similarity assumption it follows that the size distribution obeys the power law with the exponent between -4 and -1. The model of destruction has much in common with the fractal theory. The power exponent can be expressed in terms of the fractal dimension. Reasonable assumptions on the shape of fragments concretize the power exponent, and vice versa possible destruction laws can be inferred on the basis of measured size distributions.Comment: 10 pages, 3 figure

Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier--Stokes equations

Inf-sup stable FEM applied to time-dependent incompressible Navier--Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the fulfilment of a fundamental invariance principle and velocity error estimates are not corrupted by the pressure approximability. Secondly, Re-semi-robustness means that constants appearing on the right-hand side of kinetic and dissipation energy error estimates (including Gronwall constants) do not explicitly depend on the Reynolds number. Such estimates rely on an essential regularity assumption for the gradient of the velocity, which is discussed in detail. In the sense of best practice, we review and establish pressure- and Re-semi-robust estimates for pointwise divergence-free H1-conforming FEM (like Scott--Vogelius pairs or certain isogeometric based FEM) and pointwise divergence-free H(div)-conforming discontinuous Galerkin FEM. For convection-dominated problems, the latter naturally includes an upwind stabilisation for the velocity which is not gradient-based

Long-term acoustic monitoring at North Sea well site 22/4b

Highlights • First study using long-term passive acoustic monitoring of methane seeps at well blowout site 22/4b. • Seep acoustic temporal variations correlated with ocean tides. • Major acoustic transient event recorded on 8 December 2011 with high temporal resolution. Abstract Marine seeps produce underwater sounds as a result of bubble formation and fragmentation upon emission from the seabed. The frequency content and sound levels of these emissions are related to bubble size distribution and emission flux, providing important information on methane release from the seafloor. Long-term passive acoustic monitoring was used to continuously record seep sounds over a 7-month period within the blowout crater at the abandoned well site, 22/4b, in the central North Sea. Also recorded were water column fluid velocities and near-seafloor water conductivity, temperature, and pressure. Acoustic signatures were primarily from ∼1 to 10 kHz. Key features were relatively broad spectral peaks at about 1.0, 1.5, 2.2, 3.1, 3.6 and 5.1 kHz. Temporal variations in spectral levels were apparently associated with tides. The recordings also documented a series of major episodic events including a large and persistent increase (∼10 dB) in overall sound levels and spectral broadening on 8 December 2011. The acoustic temporal pattern of this event was consistent with other recorded large transient events in the literature, and the major event was correlated with dramatic changes in other measurements, including increased water column fluid velocities, increased pressure and decreased salinity, indicating real changes in emission flux. Observed seabed morphology changes reported elsewhere in this special issue, also likely were related to this event. These data demonstrate the dynamic nature of marine seepage systems, show the value of monitoring systems, and provide direct supporting evidence for a violent formation mechanism of many widespread seep-associated seabed features like pockmarks