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.

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

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

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 $\Sigma$ 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 $V_o$, the fiducial cell, whose size $L$ sets the physical scale over which homogeneity is imposed, namely a wavelength cutoff. The reduced theory results from 1) selecting a subset of $V_o$-averaged observables of the full theory; 2) neglecting inhomogeneous $\vec k\neq\mathbf0$ modes with wavelengths $\lambda\geq L$ and $\lambda< L$; 3) neglecting boundary terms encoding interactions between neighbouring cells. The error made is of order $\mathcal O(1/kL)$. As a result, the off-shell structures of the reduced theory depend on the size of $V_o$ and different $V_o$ identify canonically inequivalent theories whose dynamics though is $V_o$-independent. Their quantisation leads then to a family of $V_o$-labeled quantum representations and the quantum version of an active rescaling of $V_o$ 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 $m$, 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 $m\gg1/L$. Finally, a strategy to include inhomogeneities in cosmology is outlined.Comment: 71 + 13 pages, 4 figure