2,479 research outputs found
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 are comparably accurate than non-pressure-robust
methods of formal order 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
of the two-dimensional kinetic Ising model using a lattice of size spins. We used Glauber as well as Metropolis dynamics. The
-value of was calculated from the magnetization and energy
relaxation from an ordered state towards the equilibrium state at .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
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
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
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
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