A hierarchy of models for simulating experimental results from a 3D heterogeneous porous medium

In this work we examine the dispersion of conservative tracers (bromide and fluorescein) in an experimentally-constructed three-dimensional dual-porosity porous medium. The medium is highly heterogeneous ($\sigma_Y^2=5.7$), and consists of spherical, low-hydraulic-conductivity inclusions embedded in a high-hydraulic-conductivity matrix. The bi-modal medium was saturated with tracers, and then flushed with tracer-free fluid while the effluent breakthrough curves were measured. The focus for this work is to examine a hierarchy of four models (in the absence of adjustable parameters) with decreasing complexity to assess their ability to accurately represent the measured breakthrough curves. The most information-rich model was (1) a direct numerical simulation of the system in which the geometry, boundary and initial conditions, and medium properties were fully independently characterized experimentally with high fidelity. The reduced models included; (2) a simplified numerical model identical to the fully-resolved direct numerical simulation (DNS) model, but using a domain that was one-tenth the size; (3) an upscaled mobile-immobile model that allowed for a time-dependent mass-transfer coefficient; and, (4) an upscaled mobile-immobile model that assumed a space-time constant mass-transfer coefficient. The results illustrated that all four models provided accurate representations of the experimental breakthrough curves as measured by global RMS error. The primary component of error induced in the upscaled models appeared to arise from the neglect of convection within the inclusions. Interestingly, these results suggested that the conventional convection-dispersion equation, when applied in a way that resolves the heterogeneities, yields models with high fidelity without requiring the imposition of a more complex non-Fickian model.Comment: 27 pages, 9 Figure

The sodium-potassium pump controls the intrinsic firing of the cerebellar Purkinje neuron

In vitro, cerebellar Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting, and quiescence. The bimodal pattern consists of tonic spiking and quiescence. It is unclear how these firing patterns are generated and what determines which firing pattern is selected. We have constructed a realistic biophysical Purkinje cell model that can replicate these patterns. In this model, Na+/K+ pump activity sets the Purkinje cell's operating mode. From rat cerebellar slices we present Purkinje whole cell recordings in the presence of ouabain, which irreversibly blocks the Na+/K+ pump. The model can replicate these recordings. We propose that Na+/K+ pump activity controls the intrinsic firing mode of cerbellar Purkinje cells

Solvent fluctuations induce non-Markovian kinetics in hydrophobic pocket-ligand binding

We investigate the impact of water fluctuations on the key-lock association kinetics of a hydrophobic ligand (key) binding to a hydrophobic pocket (lock) by means of a minimalistic stochastic model system. It describes the collective hydration behavior of the pocket by bimodal fluctuations of a water-pocket interface that dynamically couples to the diffusive motion of the approaching ligand via the hydrophobic interaction. This leads to a set of overdamped Langevin equations in 2D-coordinate-space, that is Markovian in each dimension. Numerical simulations demonstrate locally increased friction of the ligand, decelerated binding kinetics, and local non-Markovian (memory) effects in the ligand's reaction coordinate as found previously in explicit-water molecular dynamics studies of model hydrophobic pocket-ligand binding [1,2]. Our minimalistic model elucidates the origin of effectively enhanced friction in the process that can be traced back to long-time decays in the force-autocorrelation function induced by the effective, spatially fluctuating pocket-ligand interaction. Furthermore, we construct a generalized 1D-Langevin description including a spatially local memory function that enables further interpretation and a semi-analytical quantification of the results of the coupled 2D-system

Velocity map imaging of the dynamics of the CH3 + HCl -> CH4 + Cl reaction using a dual molecular beam method

International audienceThe reactions CH3 + HCl → CH4 + Cl(²P_3/2) and CD₃ + HCl → CD₃H + Cl(²P_3/2) have been studied by photo-initiation (by CH₃I or CD₃I photolysis at 266 nm) in a dual molecular beam apparatus. Product Cl(²P</sub>3/2</sub>) atoms were detected using resonance enhanced multi-photon ionisation and velocity map imaging, revealing product translational energy and angular scattering distributions in the centre-of-mass frame. Image analysis is complicated by the bimodal speed distribution of CH₃ (and CD₃) radicals formed in coincidence with I(²P_3/2) and I(²P_1/2) atoms from CH₃I (CD₃I) photodissociation, giving overlapping Newton diagrams with displaced centre of mass velocities. The relative reactivities to form Cl atoms are greater for the slower CH₃ speed group than the faster group by factors of ~1.5 for the reaction of CH₃ and ~2.5 for the reaction of CD₃, consistent with the greater propensity of the faster methyl radicals to undergo electronically adiabatic reactions to form Cl(²P_1/2). The average fraction of the available energy becoming product translational energy is = 0.48 ± 0.05 and 0.50 ± 0.03 for reaction of the faster and slower sets of CH₃ radicals, respectively. The Cl atoms are deduced to be preferentially forward scattered with respect to the HCl reagents, but the angular distributions from the dual beam imaging experiments require correction for under-detection of forward scattered Cl products

Re-defining the Empirical ZZ Ceti Instability Strip

We use the new ZZ Ceti stars (hydrogen atmosphere white dwarf variables; DAVs) discovered within the Sloan Digital Sky Survey (Mukadam et al. 2004) to re-define the empirical ZZ Ceti instability strip. This is the first time since the discovery of white dwarf variables in 1968 that we have a homogeneous set of spectra acquired using the same instrument on the same telescope, and with consistent data reductions, for a statistically significant sample of ZZ Ceti stars. The homogeneity of the spectra reduces the scatter in the spectroscopic temperatures and we find a narrow instability strip of width ~950K, from 10850--11800K. We question the purity of the DAV instability strip as we find several non-variables within. We present our best fit for the red edge and our constraint for the blue edge of the instability strip, determined using a statistical approach.Comment: 14 pages, 5 pages, ApJ paper, accepte

Generating functionals for computational intelligence: the Fisher information as an objective function for self-limiting Hebbian learning rules

Generating functionals may guide the evolution of a dynamical system and constitute a possible route for handling the complexity of neural networks as relevant for computational intelligence. We propose and explore a new objective function, which allows to obtain plasticity rules for the afferent synaptic weights. The adaption rules are Hebbian, self-limiting, and result from the minimization of the Fisher information with respect to the synaptic flux. We perform a series of simulations examining the behavior of the new learning rules in various circumstances. The vector of synaptic weights aligns with the principal direction of input activities, whenever one is present. A linear discrimination is performed when there are two or more principal directions; directions having bimodal firing-rate distributions, being characterized by a negative excess kurtosis, are preferred. We find robust performance and full homeostatic adaption of the synaptic weights results as a by-product of the synaptic flux minimization. This self-limiting behavior allows for stable online learning for arbitrary durations. The neuron acquires new information when the statistics of input activities is changed at a certain point of the simulation, showing however, a distinct resilience to unlearn previously acquired knowledge. Learning is fast when starting with randomly drawn synaptic weights and substantially slower when the synaptic weights are already fully adapted

Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models

In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d=1,...,5, affects the behaviour of the specific heat C and its microcanonical relative, the entropy derivative -dS/dU. In dimensions 4 and 5 the boundary has a strong effect on the critical region of the model and for cyclic boundaries in dimension 5 we find that the model displays a quasi first order phase transition with a bimodal energy distribution. The latent heat decreases with increasing systems size but for all system sizes used in earlier papers the effect is clearly visible once a wide enough range of values for K is considered. Relations to recent rigorous results for high dimensional percolation and previous debates on simulation of Ising models and gauge fields are discussed.Comment: 12 pages, 27 figure

Folding thermodynamics of model four-strand antiparallel beta-sheet proteins

The thermodynamic properties for three different types of off-lattice four-strand beta-sheet protein models interacting via a hybrid Go-type potential have been investigated. Discontinuous molecular dynamic simulations have been performed for different sizes of the bias gap g, an artificial measure of a model protein's preference for its native state. The thermodynamic transition temperatures are obtained by calculating the squared radius of gyration, the root-mean-squared pair separation fluctuation, the specific heat, the internal energy of the system, and the Lindemann disorder parameter. In spite of the simplicity, the protein-like heteropolymers have shown a complex set of protein transitions as observed in experimental studies. Starting from high temperature, these transitions include a collapse transition, a disordered-to-ordered globule transition, a folding transition, and a liquid-to-solid transition. These transitions strongly depend on the native-state geometry of the model proteins and the size of the bias gap. A strong transition from the disordered globule state to the ordered globule state with large energy change and a weak transition from the ordered globule state to the native state with small energy change were observed for the large gap models. For the small gap models no native structures were observed at any temperature, all three beta-sheet proteins fold into a partially-ordered globule state which is geometrically different from the native state. For small bias gaps at even lower temperatures, all protein motions are frozen indicating an inactive solid-like phase.Comment: PDF file, 32 pages including 13 figure page