Canonical Configuration Research Articles

Social attention as a general mechanism? Demonstrating the influence of stimulus content factors on social attentional biasing.

Humans spontaneously attend to faces and eyes. Recent findings, however, suggest that this social attentional biasing may not be driven by the social value of faces but by general factors, like stimulus content, visual context, or task settings. Here, we investigated whether the stimulus content factors of global luminance, featural configuration, and perceived attractiveness may independently drive social attentional biasing. Six experiments were run. In each, participants completed a dot-probe task where the presentation of a face, a house, and two neutral images was followed by the presentation of a response target at one of those locations. Experiments 1 and 2 assessed social attentional biasing when the face had higher overall global luminance. Experiments 3 and 4 assessed social attentional biasing when the face (but not the comparison house) retained the typical canonical configuration of internal features. Experiments 5 and 6 examined social attentional biasing when the face was more attractive than the house. Experiments 1, 3, and 5 measured manual responses when participants were instructed to maintain fixation. Experiments 2, 4, and 6 measured both manual and oculomotor responses when no instructions about eye movements were provided. The results indicated no reliable social attentional biasing in Experiments 1 to 5, however, a reliable saccadic bias toward the eyes of attractive upright faces was found in Experiment 6. Together, these results show that perceived facial attractiveness may be an important general factor in social attentional biasing. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Effects of curvature on soot formation in steady and unsteady counterflow diffusion flames

A numerical study has been conducted in order to understand the effects of flame curvature on soot formation in laminar non-premixed flames. For the fundamental understanding, the canonical configuration of a counterflow diffusion flame is employed as it exhibits the essential combustion physics associated with non-premixed flames. Numerical results for the steady counterflow ethylene flames confirmed that the response of soot in curved flames is governed by the intricate coupling between flow convection, soot kinetics, and differential transport of soot impacting the rates of soot formation sub-processes. The sensitivity of the soot formation in curved flames to the strain rate variation is also analyzed to understand their competing effects. Furthermore, the dynamic response of soot formation to the unsteady curvature is investigated by imposing harmonic oscillations to the curvature. Numerical results revealed that for an increase in the frequency of curvature oscillations, the soot formation gets attenuated and amplitudes of the induced oscillations exhibit large phase-shift with respect to imposed fluctuations. The higher characteristic time scales of larger-sized particles proved to control the overall dynamic response of soot under unsteady fluctuations of curvature. To examine the dynamic response of soot formation under a more complex case of flow-flame-soot interaction, the unsteady analysis of flames is extended by subjecting them to the simultaneous strain rate and curvature oscillations. The correlation between imposed frequencies and variability of soot formation response under fluctuating strain rate and curvature is elaborated.

Canonical finger-numeral configurations facilitate the processing of Arabic numerals in adults: An Event-Related Potential study

Various studies claim that early-learned, culture-typical (canonical) finger configurations used to communicate or represent numerosity, have stronger connections to numerical concepts stored in long-term memory than cultural-unfamiliar finger configurations, thereby allowing for faster access to their numerical meaning. The current study investigated whether presentation of canonical finger configurations gesturing numerosities 1–4 or 6–9 would facilitate young adults’ behavioral and neural processing of Arabic numerals. Thirty-one adults performed a number comparison task in which they had to decide whether simultaneously presented Arabic numerals and canonical or non-canonical finger configurations showed the same or a different numerosity, while measuring their performance and Event-Related Potentials (ERPs). The results showed faster responses when comparisons involved canonical (versus non-canonical) finger configurations, but only on numerosity-congruent trials where finger configuration and Arabic numeral matched in number identity. Canonical, and small-number finger configurations 1–4 in general (irrespective of their canonicity), also elicited enhanced amplitude of the early right-parietal P2p, and the later centro-parietal P3 on numerosity-congruent trials. We suggest these P2p and P3 findings respectively reflect facilitated numerical access and easier categorization of canonical finger-numeral configurations. The current results provide behavioral and neurophysiological evidence for the embodiment of culture-specific, canonical, finger-numeral configurations, and their link with other number representations in the adult brain, likely emerging from their more frequent use in daily life communication and/or in early childhood during number symbol acquisition.

Negative refraction for anti-plane elastic waves in canonical quasicrystalline laminates

Elastic anti-plane shear waves can be refracted negatively when they are transmitted across an interface between a homogeneous substrate and a transverse periodic laminate. To achieve pure negative refraction, the frequency of the source should be lower than the upper limit of the second transition zone of the harmonic spectrum of the laminate. An effective way to control the location of transition zones is to consider a canonical configuration for the laminate, a concept that originates from the properties of quasicrystalline sequences among which the Fibonacci one is a particular case. We give a detailed account of the classification in three families of canonical configurations and the role of canonical frequency. We exploit the knowledge of the scaling factor of the self-similar structure of the layout of transition zones for laminates of this kind to provide a quantitative tool to predict the relevant frequencies to accomplish negative refraction. We also investigate how the change of other parameters of the elementary cell may affect the values of those frequencies. The obtained results show that the features of quasicrystalline sequences may be profitably exploited for the realisation of elastic metamaterials.

Influence of Vibration–Dissociation Coupling and Number of Reactions in Hypersonic Nonequilibrium Flows

Abstract During the atmospheric cruising of a hypersonic vehicle, the thermal and chemical nonequilibrium effects characterize the flow field within the shock layer. Therefore an understanding of nonequilibrium flow is essential for the efficient design of a hypersonic vehicle. The present numerical study uses various canonical configurations to study the thermochemical nonequilibrium effects in hypersonic flows. The present study investigates the influence of the vibration–dissociation (V–D) coupling method and the number of reactions on shock standoff distance (SSD), vibrational relaxation process, and surface properties. A finite volume method-based solver using the open-source platform openfoam has been developed to analyze the thermochemical nonequilibrium effects in the hypersonic flow field. The current results show that thermal and chemical nonequilibrium flow assumptions significantly affect SSD, and hence these assumptions are necessary to study the cases with a higher degree of nonequilibrium. The number of reactions influences the vibrational relaxation of diatomic gases in the air. At the same time, the V–D coupling method used to calculate reaction rate constants has a negligible impact on the vibrational relaxation process. Moreover, the V–D coupling method and the number of reactions marginally affect surface pressure. However, in the case of surface heat flux, the 11 reaction model predicts higher peak values than the 17 reaction model.

Data driven forecast of concurrent flame spread in micro-gravity

This paper presents a methodology that combines data assimilation and physical modelling of flame spread for fire growth forecast. The concurrent flame spreading over a flat solid sample in the absence of buoyant flows is considered as a simple canonical fire spread configuration. To predict flame spread rate and flame length evolution, the analytical solution to the two-dimensional boundary layer non-premixed combustion problem is combined with a CFD model which delivers the structure of the flow away from the fuel surface. In the process, two coefficients which intervene in the gas and solid heat transfer equations are assimilated using the pyrolysis length data as a flame spread rate surrogate input to absorb the shortcomings of the modelling. The robustness of the overall method is evaluated through convergence assessment of these two assimilated variables for different initial guesses, and for different values of the input invariants. Validation over large-scale microgravity data provides confidence in this approach, and demonstrates its potential to deliver flame spread predictions from initial measurements at a reduced computational cost. However, discrepancies between flame length measurements and predictions question the degree of correlation between pyrolysis and flame lengths.

Coriolis force effects on radial convection in a cylindrical annulus

Thermal convection under the influence of rotation appears in a wide range of engineering and geophysical applications, and has been investigated extensively both experimentally and numerically utilizing different canonical configurations. The problem of radial convection in a cylindrical annulus, studied in the present work, has received less attention than other configurations, such as rotating Rayleigh-Bénard convection. It has long been known that rotation has a stabilizing effect and, in the limit of strong rotation, a two-dimensional flow emerges, resulting in reduced heat transfer rates. Here, direct numerical simulations are performed for buoyancy-driven flows in a cylindrical annulus bounded by two parallel disks with and without rotation. By maintaining a radial gravity term analogous to a centrifugal acceleration even in the stationary cases, it is possible to isolate the effect of the Coriolis force on the flow. As expected, when rotation is imposed the flow is characterized by large-scale structures and the heat transfer rates are significantly reduced. Turbulence statistics are presented for the mean temperature profiles, temperature and velocity fluctuations, turbulent kinetic energy budgets, and Reynolds stress anisotropy tensor. It is shown that rotation significantly affects the distribution of turbulent kinetic energy throughout the radial direction, in particular away from the cylindrical surfaces. The anisotropy maps reveal that the turbulence is quasi-two-dimensional in the rotating cases, even for the highest value of Ra considered, whereas without rotation the core region approaches the isotropic limit with increasing Ra.

A Computational Study of RNA Tetraloop Thermodynamics, Including Misfolded States.

An important characteristic of RNA folding is the adoption of alternative configurations of similar stability, often referred to as misfolded configurations. These configurations are considered to compete with correctly folded configurations, although their rigorous thermodynamic and structural characterization remains elusive. Tetraloop motifs found in large ribozymes are ideal systems for an atomistically detailed computational quantification of folding free energy landscapes and the structural characterization of their constituent free energy basins, including nonnative states. In this work, we studied a group of closely related 10-mer tetraloops using a combined parallel tempering and metadynamics technique that allows a reliable sampling of the free energy landscapes, requiring only knowledge that the stem folds into a canonical A-RNA configuration. We isolated and analyzed unfolded, folded, and misfolded populations that correspond to different free energy basins. We identified a distinct misfolded state that has a stability very close to that of the correctly folded state. This misfolded state contains a predominant population that shares the same structural features across all tetraloops studied here and lacks the noncanonical A-G base pair in its loop portion. Further analysis performed with biased trajectories showed that although this competitive misfolded state is not an essential intermediate, it is visited in most of the transitions from unfolded to correctly folded states. Moreover, the tetraloops can transition from this misfolded state to the correctly folded state without requiring extensive unfolding.

Local combustion regime identification using machine learning

A new combustion regime identification methodology using the neural networks as supervised classifiers is proposed and validated. As a first proof of concept, a binary classifier is trained with labelled thermochemical states obtained as solutions of prototypical one-dimensional models representing premixed and nonpremixed regimes. The trained classifier is then used to associate the regime to any given thermochemical state originating from a multi-dimensional reacting flow simulation that shares similar operating conditions with the training problems. The classification requires local information only, i.e. no gradients are required, and operates on reduced-dimension thermochemical states, in order to cope with experimental data as well. The validity of the approach is assessed by employing a two-dimensional laminar edge flame data as a canonical configuration exhibiting multi-regime combustion behaviour. The method is readily extendable to additional classes to identify criticality phenomena, such as local extinction and re-ignition. It is anticipated that the proposed classifier tool will be useful in the development of turbulent multi-regime combustion closure models in large scale simulations.

Lagrangian approach for modal analysis of fluid flows

Common modal decomposition techniques for flow-field analysis, data-driven modelling and flow control, such as proper orthogonal decomposition and dynamic mode decomposition, are usually performed in an Eulerian (fixed) frame of reference with snapshots from measurements or evolution equations. The Eulerian description poses some difficulties, however, when the domain or the mesh deforms with time as, for example, in fluid–structure interactions. For such cases, we first formulate a Lagrangian modal analysis (LMA) ansatz by a posteriori transforming the Eulerian flow fields into Lagrangian flow maps through an orientation and measure-preserving domain diffeomorphism. The development is then verified for Lagrangian variants of proper orthogonal decomposition and dynamic mode decomposition using direct numerical simulations of two canonical flow configurations at Mach 0.5, i.e. the lid-driven cavity and flow past a cylinder, representing internal and external flows, respectively, at pre- and post-bifurcation Reynolds numbers. The LMA is demonstrated for several situations encompassing unsteady flow without and with boundary and mesh deformation as well as non-uniform base flows that are steady in Eulerian but not in Lagrangian frames. We show that application of LMA to steady non-uniform base flow yields insights into flow stability and post-bifurcation dynamics. LMA naturally leads to Lagrangian coherent flow structures and connections with finite-time Lyapunov exponents. We examine the mathematical link between finite-time Lyapunov exponents and LMA by considering a double-gyre flow pattern. Dynamically important flow features in the Lagrangian sense are recovered by performing LMA with forward and backward (adjoint) time procedures.

Geometry and dynamics of passive scalar structures in compressible turbulent mixing

We present a structure-based numerical analysis of passive scalar mixing in decaying homogeneous isotropic turbulence (DHIT) and shock-turbulence interaction canonical configurations. The analysis focuses on the temporal evolution of ensembles of passive scalar structures, initialized as spheres of different sizes relative to the Taylor microscale. An algorithm is introduced to track the evolution of each individual structure and the interactions with other structures in the ensemble, relating changes in the surface geometry and the underlying physical processes (turbulent transport, scalar dissipation, and shock compression). The tracking algorithm is applied to datasets from shock-capturing direct numerical simulations of DHIT, with Taylor microscale Reynolds number Reλ=40 and turbulence Mach number Mt=0.2, and STI cases in which the turbulence is processed by a shock wave at Mach numbers M = 1.5 and 3.0. Temporal surface convolution increases for initially larger structures, resulting in a higher probability of locally hyperbolic geometries where breakup into smaller structures occurs. Shock-induced deformation of the structures amplifies breakup processes, enhancing mixing, particularly for larger structures. Mixing enhancement by the shock is manifested as an amplification of the surface-averaged scalar gradient, which increases for initially larger structures. The alignment between the scalar gradient and the most extensional strain-rate eigendirection on the scalar isosurfaces also increases across the shock. Larger magnitudes of the scalar gradient and its alignment with the most compressive strain-rate eigendirection correlate with flatter surface regions. Shock-induced structure compression increases the area coverage of flat regions, where the amplification of scalar gradient is localized.

Design and calibration of permanent magnet probes for the local measurement of velocity and temperature in a liquid metal backward facing step flow

The simultaneous and local measurement of velocity and the temperature of a non-isothermal liquid metal flow has been an ongoing research topic over decades. The motivation is to obtain a detailed panorama of a liquid metal flow for the validation of turbulent heat flux models. So-called permanent magnet probes were used in the past for the local measurement of velocity and temperature profiles in liquid sodium in rather canonical flow configurations. The next step is to measure velocity and temperature profiles in a more complex flow geometry, namely a vertical confined backward facing step. For this, the permanent magnet probe must be adapted regarding its design, calibration procedure and temperature correction method. Particularly, considering that for this experiment the eutectic alloy of gallium, indium and tin was used as a working fluid, instead of liquid sodium, as in the mentioned past experiments. The main design aspects for a permanent magnet probe found in the literature are summarized and applied to the present probe. A calibration strategy for the probe was developed and implemented for the measurement of mean velocity profiles. A wetting procedure for the probe is proposed. The measured probe sensitivity for all six used probes agrees well with the theoretical estimations. The highest uncertainty contribution to measured sensitivity is related to the typical wetting issues of gallium–indium–tin. Future implementation of permanent magnet probes in general gallium–indium–tin experiments can make use of the developed know-how shared in this work.Graphic abstract

Quantifying the impact of heat loss, stretch and preferential diffusion effects to the anchoring of bluff body stabilized premixed flames

The response of a premixed flame subjected to either flame stretch (and associated Lewis number effects) or heat loss has been well documented in the literature and has enabled a good understanding of canonical configurations such as flat burner-stabilized, counter flow and tubular flames. However, in practical burners, flames are simultaneously subjected to stretch, heat transfer with the flame holder and preferential diffusion effects. For such flames, usually the collective effect of underlying contributions is studied and individual effects are only treated in a qualitative manner. In this paper, our objective is to use flame stretch theory to separate and quantify the underlying contributions from flame stretch, preferential diffusion and heat transfer with the flame holder to the flame speed of bluff body stabilized flames. It is shown that the theory adequately predicts the flame displacement speed in comparison to the results from the numerical simulations. Using the quantification of contributions, an overall stabilization mechanism for H2 enriched CH4-air mixtures is discussed. The role of competing contributions from preferential diffusion and heat loss is highlighted especially near the flame base region where the flame speed is heavily impacted by all the effects. Insights are also given for low Lewis number flashback prone flames.

Interpretation preferences in contexts with three antecedents: examining the role of prominence in German pronouns

AbstractThis paper focuses on the relational notion of prominence, in which entities of equal type are ranked according to certain prominence-lending features. In German two demonstrative forms, “der” and “dieser”, can function like personal pronouns in English. It has been proposed that processing “der” involves computing a prominence hierarchy of the prior referents, and excluding the referent with the highest prominence rank. The demonstrative “dieser” has not been extensively tested. In the current study, personal and demonstrative pronominal forms were investigated following ditransitive contexts, where three potential antecedents are available, in two rating experiments. The personal pronoun showed flexibility in that it received equally high ratings for all three antecedents in canonical configurations. The ratings fordieserfollowed a graded sensitivity to thematic role prominence, with lowest scores when referring to prominent antecedents (agents) and the highest scores for the least prominent antecedents (patients), with scores for the medium prominence candidate (recipients) differing from both.Derfollowed a similar but not identical pattern, with a less marked difference between lower prominence candidates. Positional information also has a strong influence on demonstratives. In sum, final interpretation is sensitive to fine-grained differences in prominence hierarchies.

Shock-Wave/Boundary-Layer Interactions on an Axisymmetric Body at Mach 2

The flow physics associated with shock-wave/boundary-layer interactions (SBLIs) on an axisymmetric body, simulating a projectile near an aircraft, is of significant interest to the aerodynamic community. The main objective of this experimental study is to investigate SBLIs on an axisymmetric configuration involving curved surfaces as compared to two-dimensional and three-dimensional (3-D) canonical configurations with flat surfaces. The experiments were carried out at Mach 2, and the planar shock wave was generated using a wedge-shaped shock generator with a turn angle of 10 deg. Measurements include steady and unsteady pressures, surface oil flow, and shadowgraph flow visualizations on the axisymmetric body. Results of the surface flow visualizations and steady pressure contours show that the separation on the body is an open-type region similar to that observed for 3-D SBLI canonical configurations. Flow separation on the surface is driven by pressure gradients caused by both the impingement of the oblique shock and the curvature of the body. Unsteady pressure measurements reveal that the shock impingement on the surface is governed by large-amplitude pressure fluctuations beneath the shock foot and flow reattachment regions.

An experimental multiparameter investigation on the thermochemical structures of benchmark ethylene and propane counterflow diffusion flames and implications to their numerical modeling

Counterflow diffusion flame is a canonical non-premixed flame configuration that is suitable for studying complex combustion chemistries such as soot formation. An important objective of such studies is to build predictive kinetic models. For validation of these models, complete and accurate experimental characterization of the flames are essential. Existing counterflow flame- based soot studies focused primarily on the determination of soot volume fraction, while simultaneous measurements of temperature, species concentrations and in particular flow fields were less common. Here we performed an experimental multiparameter investigation for a comprehensive characterization of the most important physical and chemical properties of four benchmark ethylene and propane counterflow flames, with the intention to provide data with sufficient details for the setup of corresponding numerical simulations and the evaluation of the resulted numerical data. Particle image velocimetry, tunable diode laser absorption spectrometry, microprobe sampling with gas chromatography, laser light extinction, laser induced incandescence are the techniques used respectively to measure flow fields, temperature, gas-phase species, and soot. Special attention was given to the effects of radial profiles of nozzle exit velocity on the quasi-one-dimensional counterflow simulation, whose results were compared against both the experiments and two-dimensional simulation. Probe effects on speciation were also quantitatively evaluated by comparing CO2 mole fraction as measured with the intrusive probe sampling as well as an independent optical technique. Our specially chosen ethylene and propane flames offered a direct experimental evidence that a flame producing higher concentration of benzene can have a significantly lower sooting tendency. It is hoped that the present comprehensive dataset can serve as a useful validation target for future high-fidelity gas-phase and soot models. It is also our intention that we provide sufficient details regarding the experimental apparatus and associated measurement techniques so that interested readers can reproduce our experimental data.

Ignition and flame stabilisation of primary reference fuel sprays at engine-relevant conditions

This study aims to investigate the underlying processes governing ignition and flame stabilisation in compression-ignition (CI) engine-relevant conditions. The experiments feature a canonical configuration with a single fuel jet injected into a constant-volume combustion chamber. Primary reference fuels (PRFs), including PRF100 (neat iso-octane, a gasoline surrogate), PRF80 (a blend of 80 vol.% iso-octane and 20 vol.% n-heptane) and PRF0 (neat n-heptane, a diesel surrogate), were tested to simulate changes in fuel ignition quality inside a quiescent steady environment with an ambient density of 22.8 kg/m3 and an O2 concentration of 15 vol.%. The ambient gas temperatures were controlled at 1150 K (PRF100), 1120 K (PRF80) and 900 K (PRF0), in order to adapt to the fuel reactivity so that a constant ignition delay of 1.15 ms can be achieved for all blends. This approach was employed in order to substantially reduce the effect of fuel-oxidiser mixing prior to ignition while highlighting the effect of fuel chemistry on the ignition process and flame evolution. Under the test conditions of this study, optical imaging reveals that the blends with higher iso-octane content exhibit a faster spreading of combustion after ignition and establish a steady lifted flame that is closer to the nozzle. Imaging by CH2O-PLIF indicates that blends with higher iso-octane content produce CH2O that is distributed across larger portions of the jet at an earlier timing when compared to neat n-heptane that shows a propagating first-stage ignition through the fuel jet. Supporting unsteady flamelet calculations are presented to investigate the effect of chemistry and turbulent mixing. The flamelet calculations agree qualitatively in several respects to the experiments, especially in the spatial and temporal trends for CH2O production and consumption. Synthesis of the flamelet and experimental results suggests that for the iso-octane-containing fuels, CH2O is formed via single-stage ignition reactions rather than exhibiting the typical two-stage ignition behaviour which is found in the pure n-heptane fuel case. Furthermore, the flamelet calculations suggest high-temperature ignition occurs first in lean mixtures in the iso-octane-containing fuel cases, but in rich mixtures for the PRF0 case. If autoignition is the mode of flame stabilisation, this provides an explanation for why the PRF100 and PRF80 cases stabilise further upstream, since lean mixtures have longer residence times, experience lower scalar dissipation rate, and may be more likely to be exposed to a supporting peripheral reservoir of hot products, should one exist. Overall, this study provides insights into the roles of fuel chemistry and turbulent mixing on the ignition and combustion behaviour of PRFs under engine-relevant conditions.

Effects of stretch-chemistry interaction on chemical pathways for strained and curved hydrogen/air premixed flames

In most combustion scenarios, stretch-chemistry interaction can directly alter the flame structure and combustion properties of a flammable mixture. In this study, the effects of stretch-chemistry interaction on chemical pathways of hydrogen oxidation are numerically investigated by considering laminar Inwardly Propagating Flames (IPF) and Outwardly Propagating Flames (OPF). One-dimensional transient simulations considering detailed chemistry and transport are conducted for different hydrogen/air mixtures with Lewis numbers well below and above unity. It is observed that the chemical pathways are affected by both flame stretch and flame propagation process. The relative roles of dominant elementary reactions vary with the Lewis number. In IPF and OPF, the negative and positive stretch rate are found to have opposite effects on the chemical pathway. When the relative importance of a reaction is enhanced by the positive stretch in OPF, it is weakened by the negative stretch in IPF. Furthermore, the chemical pathways obtained in this study are compared with other canonical flame configurations in previous work. It is observed that the relative importance of individual reaction is similar in different flame configurations, while disagreement is noticed in the quantitative contributions to the heat release and radical production. The disagreement is due to the different combinations of strain and curvature embodied in the stretch rate. To illustrate the individual role of the two stretch components respectively originating from hydrodynamic strain and flame curvature, a recently developed composition space model is used to decouple the influence of strain and curvature. It is found that these two stretch components have different effects upon chemical pathways. Overall, the hydrogen chemical pathway is more sensitive to the stretch originating from the curved flame propagation than to the flow field strain rate. Though the stretch rate is sufficient to characterize the flame chemistry for fuel-rich hydrogen/air flames with a negative stretch rate, more specific information on strain and curvature is required for fuel-lean and stoichiometric hydrogen/air flames.

Electrophysiological evidence for internalized representations of canonical finger-number gestures and their facilitating effects on adults\u2019 math verification performance

Fingers facilitate number learning and arithmetic processing in early childhood. The current study investigated whether images of early-learned, culturally-typical (canonical), finger montring patterns presenting smaller (2,3,4) or larger (7,8,9) quantities still facilitate adults’ performance and neural processing in a math verification task. Twenty-eight adults verified solutions to simple addition problems that were shown in the form of canonical or non-canonical finger-number montring patterns while measuring Event Related Potentials (ERPs). Results showed more accurate and faster sum verification when sum solutions were shown by canonical (versus non-canonical) finger patterns. Canonical finger montring patterns 2–4 led to faster responses independent of whether they presented correct or incorrect sum solutions and elicited an enhanced early right-parietal P2p response, whereas canonical configurations 7–9 only facilitated performance in correct sum solution trials without evoking P2p effects. The later central-parietal P3 was enhanced to all canonical finger patterns irrespective of numerical range. These combined results provide behavioral and brain evidence for canonical cardinal finger patterns still having facilitating effects on adults’ number processing. They further suggest that finger montring configurations of numbers 2–4 have stronger internalized associations with other magnitude representations, possibly established through their mediating role in the developmental phase in which children acquire the numerical meaning of the first four number symbols.

Development of an interface thickening method for the direct numerical simulation of compressible liquid–vapor flows in the framework of the second gradient theory

This study presents a method to perform direct numerical simulation (DNS), in the sense of turbulence, of two-phase flows with interfaces. It is based on the compressible diffuse interface model introduced by the second gradient theory. This model assumes a continuous variation of the thermodynamic variables in the interface and add to their description a dependency on the density gradient. The interface widths as predicted by the model fall way below the typical relevant turbulent scales. We propose here a thermodynamically consistent method to thicken the interface in order to perform calculations on typical DNS meshes. The modified model has been integrated and validated on canonical configurations. It has then been applied to more complex cases such as colliding three-dimensional droplets and the breakup of two-dimensional liquid jets.