Variational bounds for the shear viscosity of gelling melts

We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $\eta$, which implies that it diverges algebraically with a critical exponent $k\ge 2\nu-\beta$. Here, $\nu$ and $\beta$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark-Houwink relation for the shear viscosity of isolated clusters of fixed size.Comment: 5 pages; CHANGES: typos corrected, some references added; version as publishe

Diverse cytomotive actins and tubulins share a polymerization switch mechanism conferring robust dynamics

Protein filaments are used in myriads of ways to organize other molecules within cells. Some filament-forming proteins couple the hydrolysis of nucleotides to their polymerization cycle, thus powering the movement of other molecules. These filaments are termed cytomotive. Only members of the actin and tubulin protein superfamilies are known to form cytomotive filaments. We examined the basis of cytomotivity via structural studies of the polymerization cycles of actin and tubulin homologs from across the tree of life. We analyzed published data and performed structural experiments designed to disentangle functional components of these complex filament systems. Our analysis demonstrates the existence of shared subunit polymerization switches among both cytomotive actins and tubulins, i.e., the conformation of subunits switches upon assembly into filaments. These cytomotive switches can explain filament robustness, by enabling the coupling of kinetic and structural polarities required for cytomotive behaviors and by ensuring that single cytomotive filaments do not fall apart

Quantum Mechanical Aspects of Cell Microtubules: Science Fiction or Realistic Possibility?

Recent experimental research with marine algae points towards quantum entanglement at ambient temperature, with correlations between essential biological units separated by distances as long as 20 Angstr\"oms. The associated decoherence times, due to environmental influences, are found to be of order 400 fs. This prompted some authors to connect such findings with the possibility of some kind of quantum computation taking place in these biological entities: within the decoherence time scales, the cell "quantum calculates" the optimal "path" along which energy and signal would be transported more efficiently. Prompted by these experimental results, in this talk I remind the audience of a related topic proposed several years ago in connection with the possible r\^ole of quantum mechanics and/or field theory on dissipation-free energy transfer in microtubules (MT), which constitute fundamental cell substructures. Quantum entanglement between tubulin dimers was argued to be possible, provided there exists sufficient isolation from other environmental cell effects. The model was based on certain ferroelectric aspects of MT. In the talk I review the model and the associated experimental tests so far and discuss future directions, especially in view of the algae photo-experiments.Comment: 31 pages latex, 11 pdf figures, uses special macros, Invited Plenary Talk at DICE2010, Castello Pasquini, Castiglioncello (Italy), September 13-18 201

Hierarchical Graph Transformation

If systems are specified by graph transformation, large graphs should be structured in order to be comprehensible. In this paper, we present an approach for the rule-based transformation of hierarchically structured (hyper)graphs. In these graphs, distinguished hyperedges contain graphs that can be hierarchical again. Our framework extends the well-known double-pushout approach from at to hierarchical graphs. In particular, we show how pushouts and pushout complements of hierarchical graphs and graph morphisms can be constructed recursively. Moreover, we make rules more expressive by introducing variables which allow to copy and to remove hierarchical subgraphs in a single rule application

Optimal design of multi-channel microreactor for uniform residence time distribution

Multi-channel microreactors can be used for various applications that require chemical or electrochemical reactions in either liquid, gaseous or multi phase. For an optimal control of the chemical reactions, one key parameter for the design of such microreactors is the residence time distribution of the fluid, which should be as uniform as possible in the series of microchannels that make up the core of the reactor. Based on simplifying assumptions, an analytical model is proposed for optimizing the design of the collecting and distributing channels which supply the series of rectangular microchannels of the reactor, in the case of liquid flows. The accuracy of this analytical approach is discussed after comparison with CFD simulations and hybrid analytical-CFD calculations that allow an improved refinement of the meshing in the most complex zones of the flow. The analytical model is then extended to the case of microchannels with other cross-sections (trapezoidal or circular segment) and to gaseous flows, in the continuum and slip flow regimes. In the latter case, the model is based on second-order slip flow boundary conditions, and takes into account the compressibility as well as the rarefaction of the gas flow

Microstructure-based simulations of the viscous densification of snow and firn

Accurate models for the viscous densification of snow (understood here as a density below 550 kg m−3) and firn (a density above 550 kg m−3) under mechanical stress are of primary importance for various applications, including avalanche prediction and the interpretation of ice cores. Formulations of snow and firn compaction in models are still largely empirical instead of using microstructures from micro-computed tomography to numerically compute the mechanical behavior directly from the physics at the microscale. The main difficulty of the latter approach is the choice of the correct rheology/constitutive law governing the deformation of the ice matrix, which is still controversially discussed. Being aware of these uncertainties, we conducted a first systematic attempt of microstructure-based modeling of snow and firn compaction. We employed the finite element suite Elmer FEM using snow and firn microstructures from different sites in the Alps and Antarctica to explore which ice rheologies are able to reproduce observations. We thereby extended the ParStokes solver in Elmer FEM to facilitate parallel computing of transverse isotropic material laws for monocrystalline ice. We found that firn densification can be reasonably well simulated across different sites assuming a polycrystalline rheology (Glen's law) that is traditionally used in glacier or ice sheet modeling. In contrast, for snow, the observations are in contradiction with this rheology. To further comprehend this finding, we conducted a sensitivity study on different ice rheologies. None of the material models is able to explain the observed high compactive viscosity of depth hoar compared to rounded grains having the same density. While, on one hand, our results re-emphasize the limitations of our current mechanical understanding of the ice in snow, they constitute, on the other hand, a confirmation of the common picture of firn as a foam of polycrystalline ice through microstructure-based simulations.</p

Interactive Evolution and Exploration within Latent Level-Design Space of Generative Adversarial Networks

Generative Adversarial Networks (GANs) are an emerging form of indirect encoding. The GAN is trained to induce a latent space on training data, and a real-valued evolutionary algorithm can search that latent space. Such Latent Variable Evolution (LVE) has recently been applied to game levels. However, it is hard for objective scores to capture level features that are appealing to players. Therefore, this paper introduces a tool for interactive LVE of tile-based levels for games. The tool also allows for direct exploration of the latent dimensions, and allows users to play discovered levels. The tool works for a variety of GAN models trained for both Super Mario Bros. and The Legend of Zelda, and is easily generalizable to other games. A user study shows that both the evolution and latent space exploration features are appreciated, with a slight preference for direct exploration, but combining these features allows users to discover even better levels. User feedback also indicates how this system could eventually grow into a commercial design tool, with the addition of a few enhancements.Comment: GECCO 202

Critical Dynamics of Gelation

Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation $k=\phi-\beta$ for the critical exponent of the shear viscosity. Here $\beta$ is the thermal exponent for the gel fraction and $\phi$ is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results.Comment: 34 pages, 2 figures (revtex, amssymb); revised version (minor changes

Shear viscosity of a crosslinked polymer melt

We investigate the static shear viscosity on the sol side of the vulcanization transition within a minimal mesoscopic model for the Rouse-dynamics of a randomly crosslinked melt of phantom polymers. We derive an exact relation between the viscosity and the resistances measured in a corresponding random resistor network. This enables us to calculate the viscosity exactly for an ensemble of crosslinks without correlations. The viscosity diverges logarithmically as the critical point is approached. For a more realistic ensemble of crosslinks amenable to the scaling description of percolation, we prove the scaling relation $k=\phi-\beta$ between the critical exponent $k$ of the viscosity, the thermal exponent $\beta$ associated with the gel fraction and the crossover exponent $\phi$ of a random resistor network.Comment: 8 pages, uses Europhysics Letters style; Revisions: results extende