1,858 research outputs found
A multiple scales approach to evaporation induced Marangoni convection
This paper considers the stability of thin liquid layers of binary mixtures of a volatile (solvent) species and a non-volatile (polymer) species. Evaporation leads to a depletion of the solvent near the liquid surface. If surface tension increases for lower solvent concentrations, sufficiently strong compositional gradients can lead to Bénard-Marangoni-type convection that is similar to the kind which is observed in films that are heated from below. The onset of the instability is investigated by a linear stability analysis. Due to evaporation, the base state is time dependent, thus leading to a non-autonomous linearised system, which impedes the use of normal modes. However, the time scale for the solvent loss due to evaporation is typically long compared to the diffusive time scale, so a systematic multiple scales expansion can be sought for a finite dimensional approximation of the linearised problem. This is determined to leading and to next order. The corrections indicate that sufficient separation of the top eigenvalue from the remaining spectrum is required for the validity of the expansions, but not the magnitude of the eigenvalues themselves. The approximations are applied to analyse experiments by Bassou and Rharbi with polystyrene/toluene mixtures [Langmuir 2009 (25) 624–632]
A thin film model for corotational Jeffreys fluids under strong slip
We derive a thin film model for viscoelastic liquids under strong slip which
obey the stress tensor dynamics of corotational Jeffreys fluids.Comment: 3 pages, submitted to Eur. Phys. J.
Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
The physical interpretation and eventual fate of gravitational singularities
in a theory surpassing classical general relativity are puzzling questions that
have generated a great deal of interest among various quantum gravity
approaches. In the context of loop quantum gravity (LQG), one of the major
candidates for a non-perturbative background-independent quantisation of
general relativity, considerable effort has been devoted to construct effective
models in which these questions can be studied. In these models, classical
singularities are replaced by a "bounce" induced by quantum geometry
corrections. Undesirable features may arise however depending on the details of
the model. In this paper, we focus on Schwarzschild black holes and propose a
new effective quantum theory based on polymerisation of new canonical phase
space variables inspired by those successful in loop quantum cosmology. The
quantum corrected spacetime resulting from the solutions of the effective
dynamics is characterised by infinitely many pairs of trapped and anti-trapped
regions connected via a space-like transition surface replacing the central
singularity. Quantum effects become relevant at a unique mass independent
curvature scale, while they become negligible in the low curvature region near
the horizon. The effective quantum metric describes also the exterior regions
and asymptotically classical Schwarzschild geometry is recovered. We however
find that physically acceptable solutions require us to select a certain subset
of initial conditions, corresponding to a specific mass (de-)amplification
after the bounce. We also sketch the corresponding quantum theory and
explicitly compute the kernel of the Hamiltonian constraint operator.Comment: 50 pages, 10 figures; v2: journal version, minor comment and
references added; v3: minor corrections in section 5.3 to match journal
versio
A note on the Hamiltonian as a polymerisation parameter
In effective models of loop quantum gravity, the onset of quantum effects is
controlled by a so-called polymerisation scale. It is sometimes necessary to
make this scale phase space dependent in order to obtain sensible physics. A
particularly interesting choice recently used to study quantum corrected black
hole spacetimes takes the generator of time translations itself to set the
scale. We review this idea, point out errors in recent treatments, and show how
to fix them in principle.Comment: 7 pages, 2 figures; v2: journal version, minor clarification
Life-cycle assessment in eco-labelling: Between standardisation and local appropriation
Over the last decades the demand for green and fair products by consumers has steadily increased and governments have undertaken greater efforts to devise green policies as well as to create incentives for industry to lessen the environmental impact of production processes (Finkbeiner, et al. 2006). Companies and large-scale multinational corporations, as well as national governments and local businesses are thus increasingly urged to account for the ecological footprint they leave behind and to actively improve their environmental performance. There exists a large variety of different scientific methods to analyse the environmental impact of a certain product, service or policy – for instance Environmental Impact Assessment (EIA) or Risk Assessment. However, amongst the multiplicity of methods, life cycle assessment (LCA) has become one of the most prominent approaches, since it is considered to be the methodology that encompasses the widest range of possible environmental impacts. This chapter seeks to shed light on the tension between standardisation and local appropriation, in order to show that a certain degree of local responsiveness is necessary for the effectiveness of the method.
Slip vs viscoelasticity in dewetting thin films
Ultrathin polymer films on non-wettable substrates display dynamic features
which have been attributed to either viscoelastic or slip effects. Here we show
that in the weak and strong slip regime effects of viscoelastic relaxation are
either absent or not distinguishable from slip effects. Strong-slip modifies
the fastest unstable mode in a rupturing thin film, which questions the
standard approach to reconstruct the effective interface potential from
dewetting experiments.Comment: 4 pages, submitted to Eur. Phys. J.
A new generalized domain decomposition strategy for the efficient parallel solution of the FDS-pressure equation. Part I: Theory, Concept and Implementation
Due to steadily increasing problem sizes and accuracy requirements as well as storage restrictions on single-processor systems, the efficient numerical simulation
of realistic fire scenarios can only be obtained on modern high-performance computers based on multi-processor architectures. The transition to those systems
requires the elaborate parallelization of the underlying numerical concepts which must guarantee the same result as a potentially corresponding serial execution and preserve the convergence order of the original serial method. Because
of its low degree of inherent parallelizm, especially the efficient parallelization of the elliptic pressure equation is still a big challenge in many simulation programs for fire-induced flows such as the Fire Dynamics Simulator (FDS). In order to avoid losses of accuracy or numerical instabilities, the parallelization process must definitely take into account the strong global character of the physical pressure. The current parallel FDS solver is based on a relatively coarse-grained parallellization concept which can’t guarantee these requirements in all cases.
Therefore, an alternative parallel pressure solver, ScaRC, is proposed which ensures a high degree of global coupling and a good computational performance at the same time. Part I explains the theory, concept and implementation of this
new strategy, whereas Part II describes a series of validation and verification tests to proof its correctness
Controlled topological transitions in thin film phase separation
In this paper the evolution of a binary mixture in a thin-film geometry with
a wall at the top and bottom is considered. By bringing the mixture into its
miscibility gap so that no spinodal decomposition occurs in the bulk, a slight
energetic bias of the walls towards each one of the constituents ensures the
nucleation of thin boundary layers that grow until the constituents have moved
into one of the two layers. These layers are separated by an interfacial region
where the composition changes rapidly. Conditions that ensure the separation
into two layers with a thin interfacial region are investigated based on a
phase-field model. Using matched asymptotic expansions a corresponding
sharp-interface problem for the location of the interface is established.
It is then argued that this newly created two-layer system is not at its
energetic minimum but destabilizes into a controlled self-replicating pattern
of trapezoidal vertical stripes by minimizing the interfacial energy between
the phases while conserving their area. A quantitative analysis of this
mechanism is carried out via a thin-film model for the free interfaces, which
is derived asymptotically from the sharp-interface model.Comment: Submitted 23/12/201
On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC
We study the homogeneous minisuperspace reduction within the canonical
framework for a scalar field theory and gravity. Symmetry reduction is
implemented via second class constraints for the field modes over a
partitioning of the non-compact spatial slice into disjoint cells. The
canonical structure of the resulting homogeneous theories is obtained via the
associated Dirac bracket which can only be defined on a finite number of cells
homogeneously patched together and agrees with the full theory Poisson bracket
for the averaged fields. This identifies a finite region , the fiducial
cell, whose size sets the physical scale over which homogeneity is imposed,
namely a wavelength cutoff. The reduced theory results from 1) selecting a
subset of -averaged observables of the full theory; 2) neglecting
inhomogeneous modes with wavelengths and
; 3) neglecting boundary terms encoding interactions between
neighbouring cells. The error made is of order . As a result,
the off-shell structures of the reduced theory depend on the size of and
different identify canonically inequivalent theories whose dynamics
though is -independent. Their quantisation leads then to a family of
-labeled quantum representations and the quantum version of an active
rescaling of is implemented via a suitable dynamics-preserving
isomorphism between the different theories. We discuss the consequences for
statistical moments, fluctuations, and semiclassical states in both a standard
and polymer quantisation. For a scalar field of mass , we also sketch the
quantum reduction and identify a subsector of the QFT where the results of
the"first reduced, then quantised" theories can be reproduced with good
approximation as long as . Finally, a strategy to include
inhomogeneities in cosmology is outlined.Comment: 71 + 13 pages, 4 figure
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