Representation Of Quantities Research Articles

ABINIT: Overview and focus on selected capabilities.

abinit is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe-Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the "temperature-dependent effective potential" approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which abinit relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The abinit DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library libpaw. abinit has strong links with many other software projects that are briefly mentioned.

"Few" or "Many"? An Adaptation Level Theory Account for Flexibility in Quantifier Processing.

Quantifiers (e.g., “many,” “some,” “at least seven,” “more than half”) are words characterizing amounts or numerosities by reference to an internal threshold, or degree. For some quantifiers, this degree is not uniquely defined: It varies for external contexts (“many lions”/“many flies”) but may also be shifted within an individual (“many fries” for a hungry/full person). Previous studies showed that manipulation of the degree for one quantifier can impact that of other quantifiers. In this study, we tested whether such changes can occur by mere habituation, as formalized in the Adaptation Level Theory by Helson (1948) for sensory stimuli such as brightness or weight. To this end, participants read a quantifier statement and then judged whether a visual display with varying amounts (20–80%) of blue and yellow circles matched that statement. In Block 1, we identified which proportion of circles of a given color was judged by participants as “many” or “few.” In Block 2, we modified the presentation of stimuli such that (1) only the quantifier “many” was used and (2) only low proportions of circles of a given color were presented, thus changing the base rate at which proportions were encountered together with “many.” The hypothesis was that the internal degree of what is interpreted as “many” would be shifted downward and that this shift would also affect judgments of “few.” Block 3 was identical to Block 1, serving as a test for the expected effect on the degree/threshold for/across all proportions. The findings were as expected: The probability of accepting 40% as “many” was increased during Block 2, indicating adaptation. Likewise, the probability function for “few” was shifted in a parallel fashion around the proportion 40%. These findings complemented earlier studies demonstrating intra-individual flexibility in quantifier processing. They show that this flexibility can even be observed in the absence of explicitly stated verbal contexts or reinforcements, in line with the Adaptation Level Theory formulated originally for magnitudes, i.e., non-linguistic representations of quantities.

On the linear orthobaric-density representation of near-critical solvation quantities: What can we conclude about the accuracy of this paradigm?

In this work, we have derived rigorous expressions for the thermodynamic description of the solvation behavior of a model solute in highly-compressible environments of a real solvent, in order to address the question posed in the title of this manuscript. Toward that end, we first provide the essential statistical thermodynamic foundations to support a fundamentally-based approach for the determination of the Krichevskii parameter of a solute in any solvent, based solely on the knowledge of the corresponding Henry's law constant. Second, we analyze the actual orthobaric-density behavior of lnQ(T,Pσ) and TσlnQ(T,Pσ), when Q=KD∞ and Q=(Hi,jIS/fjo), for an infinitely dilute ideal gas solute in an aqueous solution, a system for which we have complete knowledge of its microscopic and thermodynamic behaviors. Third, we invoke these results to test the assumptions behind the modeling of the orthobaric-density dependence of the Henry's law constant, infinite dilution vapor-liquid distribution, and Ostwald coefficients of real solutes. Fourth, we discuss the implications underlying the interpretation of the regressed orthobaric-density slopes, the accuracy of the resulting effective Krichevskii parameters, and the extension of the current analysis to the orthobaric-density behavior for the corresponding Ostwald coefficient, TσlnLi,j∞(T,Pσ). Finally, we show how the fundamentally-based orthobaric-density linear expressions of lnQ(T,Pσ) for the three Q−quantities converge to the corresponding, empirically-found, TσlnQ(T,Pσ) asymptotic linear representations for near-critical infinitely dilute solutions.

Modeling of multi-physics transients in PEM fuel cells using equivalent circuits for consistent representation of electric, pneumatic, and thermal quantities

Digital simulators of electric networks have been indispensable tools for engineers and researchers engaged in the analysis and design of electric power and energy systems. With the increasing interest to extend electric energy toward multi-energy systems covering multiple energy carriers, there arises a need to also extend the capabilities of today’s simulators. Such an extension is proposed here in the form of a Proton Exchange Membrane Fuel Cell (PEMFC) model that covers the multi-physics transients involved in the flows of the electric current, hydrogen and other gases, and the enthalpy. The modeling makes use of given analogies to allow for a uniform representation of electric, pneumatic, and thermal transients based on electric circuit equivalents. It is shown how these models representing different transients are coupled as part of a PEM fuel cell system. Validation and application are carried out to verify the value of the modeling. The investigations are performed with an electric network simulator of type EMTP (Electromagnetic Transients Program) and so substantiate the possibility of using the latter for studying multi-energy systems.

Reverse engineering cash: Coin designs mark out high value differentials and coin sizes track values logarithmically

Coins are physical representations of monetary values. Like mental or verbal representations of quantities, coins encode sums of money in formats shaped, in part, by cognitive and communicative needs. Studying the coins circulating today, we consider how their design, colour, and size reflect their value. We show that coin designs solve a trade-off between informativeness—the pressure to highlight distinct denominations—and simplicity—the pressure to limit the number of designs that coin users must memorise. Coinage worldwide is more likely to display distinctive graphic designs and distinct colours on pairs of coins with large differences in value, thus minimising the aggregate cost of mistaking one coin for another. Coin size differentials, in contrast, do not seem to indicate greater value differentials, although absolute coin sizes do reflect monetary values. Log-transformed values predict design and colour distinctiveness in coin pairs, as well as absolute coin sizes, better than raw values, consistent with research suggesting that monetary quantities may recruit the “numerosity system” for magnitude representations, thought to track quantities logarithmically. These results show that coins obey similar informational constraints as linguistic and mental representations.

Three-Dimensional Representation of Electrical Circuit Quantities

This letter proposes a new representation of electrical circuit quantities based on three-phase dimensional space, in contrast to the conventional two-dimensional representation. It contributes to an alternative mathematical approach to display the voltage and current waveforms in three-dimensional frame, in which an unbalance displacement angle becomes evident, and can be used as an unbalance metric. It is outside the scope of this letter to propose a new power theory, or state new definitions for the power terms. In fact, such electric power representation can be applied to different power theories. Finally, this letter exemplifies the three-dimensional representation through numerical and illustrative case studies.

Реактансы и другие параметры механических систем

The traditional calculation of mechanisms for forced harmonic oscillations is often a difficult task. Most often, calculators are interested in the steady-state modes of harmonic oscillations. The purpose of this paper is to significantly simplify calculations by replacing the need to solve differential equations with simpler algebraic methods. A complex representation of harmonic and related quantities is used. This approach is widely used in theoretical electrical engineering. Parallel and serial connections of mechanical power consumers are considered. The velocities of elements of mechanical systems and the forces applied to them are determined algebraically from the known parameters of systems and the disturbing harmonic effect. The use of a symbolic (complex) description of mechanical systems under forced harmonic vibrations (in steady-state mode) allowed us to abandon the extremely cumbersome and time-consuming calculation algorithm associated with solving differential equations, and replace it with simpler and more visual algebraic operations. Due to this, the time of calculations is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems under harmonic influences, have substantial methodological significance, since they show quantitative and phase relations between the parameters of systems.

The Small Number System

I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific structure and consequently that there is no domain-general alternative to an innate domain-specific small number system.

АЛГЕБРАИЧЕСКИЕ МЕТОДЫ РАСЧЕТА РАЗВЕТВЛЕННЫХ МЕХАНИЧЕСКИХ СИСТЕМ ПРИ ВЫНУЖДЕННЫХ КОЛЕБАНИЯХ

Parallel-serial and serial-parallel connections of consumers of mechanical power are considered. According to the known parameters of systems and the disturbing harmonic effect, the velocities of the elements of mechanical systems and the forces applied to them are algebraically determined. A comprehensive representation of harmonic and related quantities is used. This approach is widely used in electrical engineering. For the considered branched mechanical schemes, the classical methods based on the solution of second-order differential equations become many times more complicated and require the solution of systems of equations, which are reduced to higher-order differential equations. The use of a symbolic (complex) description of mechanical processes and systems makes it possible to use instead simple and compact algebraic methods, the complexity of which is ten times less.

TASKS AND PRINCIPLES OF ACTIVE DAMPING OF VIBRATION FLIGHTS

The paper considers a model for counteracting seismic effects on a bridge structure created by an active damping device. The essence of the proposed approach is that the active damper plays an auxiliary role as an intermediate device that allows you to determine the necessary hysteresis characteristics of effective damping. Based on the identified optimal hysteresis characteristics, it is possible to determine the parameters of passive dampers intended for direct installation on the protected object. An active damper can be implemented as a device on a specialized test bench, or virtually in numerical experiments. For numerical modeling, a mathematical model of active damping was developed, taking into account the pulsed nature of seismic effects and thereby expanding the limitations inherent in traditional harmonic analysis. In this model, convolutional representations of dynamic quantities are proposed, equivalent to the introduction of a weak measure of dynamic functions in the space of bridge oscillations. This approach is more responsive to the challenges of engineering applications.

On Functional Formulation of the Statistical Theory of Homogeneous Turbulence and the Method of Sceleton Feynman Diagrams

The paper reviews the application of the formalism of a characteristic functional for statistical description of a random velocity field obeying the Navier-Stokes equation for incompressible fluids in the presence of regular and random external forces. The equation in functional derivatives for the characteristic functional is obtained using a representation of the characteristic functional in the form of a functional integral over two fields. From this equation one can obtain equations for various statistical characteristics of the velocity field such as the variance of velocity pulsations (the pair correlation function) or the mean response of velocity field to external forces (Green’s function). The method of skeleton Feynman diagrams is used in the analysis of the equations and of the solution structures. This fact follows directly from the functional formulation of the theory without referring to the commonly used methods of perturbation theory. The vertices of three types arising in the theory formulation appear to be linked. This enables considering the vertex of only one type and simplify the diagrammatic representations of various quantities.

Putting the world in mind: The case of mental representation of quantity

A reoccurring question in cognitive science concerns the way the world is represented. Cognitive scientists quantify the contribution of a physical attribute to a sensation and try to characterize the underlying mechanism. In numerical cognition, the contribution of physical properties to quantity perception in comparison tasks was widely demonstrated albeit leaving the underlying mechanism unclear. Furthermore, it is unclear whether this contribution is related solely to comparison tasks or to a core, general ability. Here we demonstrate that the shape of the convex hull, the smallest convex polygon containing all objects in an array, plays a role in the transfer function between quantity and its mental representation. We used geometric probability to demonstrate that the shape of the convex hull is correlated with quantity in a way that resembles the behavioral enumeration curve of subitizing and estimation. Then, in two behavioral experiments we manipulated the shape of the convex hull and demonstrated its effect on enumeration. Accordingly, we suggest that humans learn the correlation between convex hull shape and numerosity and use it to enumerate.

Temporo-frontal activation during phonological processing predicts gains in arithmetic facts in young children

Behavioral studies have shown discrepant results regarding the role of phonology in predicting math gains. The objective of this study was to use fMRI to study the role of activation during a rhyming judgment task in predicting behavioral gains on math fluency, multiplication, and subtraction skill. We focused within the left middle/superior temporal gyrus and left inferior frontal gyrus, brain areas associated with the storage of phonological representations and with their access, respectively. We ran multiple regression analyses to determine whether activation predicted gains in the three math measures, separately for younger (i.e. 10 years old) and older (i.e 12 years old) children. Results showed that activation in both temporal and frontal cortex only predicted gains in fluency and multiplication skill, and only for younger children. This study suggests that both temporal and frontal cortex activation during phonological processing are important in predicting gains in math tasks that involve the retrieval of facts that are stored as phonological codes in memory. Moreover, these results were specific to younger children, suggesting that phonology is most important in the early stages of math development. When the math task involved subtractions, which relies on quantity representations, phonological processes were not important in driving gains.

On different geometric approaches to the dynamics of finite‐dimensional mechanical systems

AbstractThe language of differential geometry allows a coordinate‐free representation of physical quantities. This led to the development of several geometric theories for the description of finite‐dimensional mechanical systems. These approaches differ in the mathematical concepts they invoke and in the classes of mechanical systems they can describe. This short note aims to give an overview on the following three popular approaches, all of which are limited to time‐independent mechanical systems. While in the first approach, the motion of the mechanical system is considered as a curve in the system's configuration manifold, in the latter two, the corresponding motions are interpreted as curves in the tangent or the cotangent bundle of the configuration manifold.

Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups

In this paper, we start by showing that the intertwining relationship between two minimal Markov semigroups acting on Hilbert spaces implies that any recurrent extensions, in the sense of Itô, of these semigroups satisfy the same intertwining identity. Under mild additional assumptions on the intertwining operator, we prove that the converse also holds. This connection, which relies on the representation of excursion quantities as developed by Fitzsimmons and Getoor (Illinois J. Math. 50 (2006) 413–437), enables us to give an interesting probabilistic interpretation of intertwining relationships between Markov semigroups via excursion theory: two such recurrent extensions that intertwine share, under an appropriate normalization, the same local time at the boundary point. Moreover, in the case when one of the (non-self-adjoint) semigroup intertwines with the one of a quasi-diffusion, we obtain an extension of Krein’s theory of strings by showing that its densely defined spectral measure is absolutely continuous with respect to the measure appearing in the Stieltjes representation of the Laplace exponent of the inverse local time. Finally, we illustrate our results with the class of positive self-similar Markov semigroups and also the reflected generalized Laguerre semigroups. For the latter, we obtain their spectral decomposition and provide, under some conditions, an explicit hypocoercivity $L^{2}$-rate of convergence to equilibrium which is expressed as the spectral gap perturbed by the spectral projection norms.

Automated peak picking using region‐based convolutional neural network for operational modal analysis

Peak picking is used to determine locations of salient peaks in a graphical representation of a physical quantity. It is often used to extract possible natural frequencies from the frequency domain representation of structural responses. One of the challenges in peak picking is to establish a method to automatically distinguish peaks from data containing noise peaks. As selecting peaks intrinsically depends on human perception, algorithms for automated peak picking have exhibited only partial success to date. This paper presents an automated peak picking method that utilizes a region-based convolutional neural network with possible object locations to accurately identify the peaks. A tailored deep learning architecture is proposed, which is subsequently trained using only the peaks numerically generated by computer software. Laboratory and field tests are conducted using acceleration responses obtained from three test structures of beam, truss, and stay cable to verify the identification performance of the proposed peak detector. The proposed peak detector is shown to successfully identify most of the salient peaks with high accuracy.

Improved Parameterization of Ice Particle Size Distributions Using Uncorrelated Mass Spectrum Parameters: Results from GCPEx

AbstractSatellite retrieval algorithms and model microphysical parameterizations require guidance from observations to improve the representation of ice-phase microphysical quantities and processes. Here, a parameterization for ice-phase particle size distributions (PSDs) is developed using in situ measurements of cloud microphysical properties collected during the Global Precipitation Measurement (GPM) Cold-Season Precipitation Experiment (GCPEx). This parameterization takes advantage of the relation between the gamma-shape parameter μ and the mass-weighted mean diameter Dm of the ice-phase PSD sampled during GCPEx. The retrieval of effective reflectivity Ze and ice water content (IWC) from the reconstructed PSD using the μ–Dm relationship was tested with independent measurements of Ze and IWC and overall leads to a mean error of 8% in both variables. This represents an improvement when compared with errors using the Field et al. parameterization of 10% in IWC and 37% in Ze. Current radar precipitation retrieval algorithms from GPM assume that the PSD follows a gamma distribution with μ = 3. This assumption leads to a mean overestimation of 5% in the retrieved Ze, whereas applying the μ–Dm relationship found here reduces this bias to an overestimation of less than 1%. Proper selection of the a and b coefficients in the mass–dimension relationship is also of crucial importance for retrievals. An inappropriate selection of a and b, even from values observed in previous studies in similar environments and cloud types, can lead to more than 100% bias in IWC and Ze for the ice-phase particles analyzed here.

Arabic digits and spoken number words: Timing modulates the cross-modal numerical distance effect

Moving seamlessly between spoken number words and Arabic digits is common in everyday life. In this study, we systematically investigated the correspondence between auditory number words and visual Arabic digits in adults. Auditory number words and visual Arabic digits were presented concurrently or sequentially and participants had to indicate whether they described the same quantity. We manipulated the stimulus onset asynchronies (SOAs) between the two stimuli (Experiment 1: −500 ms to +500 ms; Experiment 2: −200 ms to +200 ms). In both experiments, we found a significant cross-modal distance effect. This effect was strongest for simultaneous stimulus presentation and decreased with increasing SOAs. Numerical distance emerged as the most consistent significant predictor overall, in particular for simultaneous presentation. However, physical similarity between the stimuli was often a significant predictor of response times in addition to numerical distance, and at longer SOAs, physical similarity between the stimuli was the only significant predictor. This shows that SOA modulates the extent to which participants access quantity representations. Our results thus support the idea that a semantic quantity representation of auditory and visual numerical symbols is activated when participants perform a concurrent matching task, while at longer SOAs participants are more likely to rely on physical similarity between the stimuli. We also investigated whether individual differences in the efficiency of the cross-modal processing were related to differences in mathematical performance. Our results are inconclusive about whether the efficiency of cross-format numerical correspondence is related to mathematical competence in adults.

Symbolism overshadows the effect of physical size in supra-second temporal illusions.

The perception of quantities has been suggested to rely on shared, magnitude-based representational systems that preserve metric properties. As such, different quantifiable dimensions that can characterize any given stimulus (e.g., size, speed, or numerosity) have been shown to modulate the perceived duration of these stimuli-a finding that has been attributed to cross-modal interaction among the quantity representations. However, these results are typically based on the isolated effects of a single stimulus dimension, leaving their potential combined effects uncharted. In the present study we aimed to investigate the joint effects of numerical magnitude and physical size on perceived time. In four complementary experiments, participants categorized six durations as "short" or "long," which were presented through combinations of Hindu-Arabic numerals in three font sizes, as well as with simple shapes (rectangles) and unfamiliar symbols (Klingon letters), the sizes of which corresponded to the font sizes of the Hindu-Arabic numerals. Our results showed temporal underestimation for the smallest numeral in the set (3), with no effects of font size on perceived duration. The perceived durations were longest for the physically smallest geometric stimuli (i.e., a rectangle), and the font size of symbol-like stimuli (i.e., Klingon letters) was not found to have an effect on perceived time. Finally, presenting only one numeral (6) instead of the rectangle once again eliminated the relationship between physical size and perceived time, suggesting an overshadowing of physical-size-based influences on temporal choice behavior, presumably by perceived symbolism. Our results point at the complex nature of the interaction between different magnitude representations.

Vector Expression of Units of Physical Quantities

Vector representations of physical quantities in pseudo-Euclidean space are used to discuss several options for an appropriate coordinate system used to express a system of units. The SI system is found to have several issues causing the system of units to be overdetermined and underdetermined. We propose a version of the SI system that takes into account the three-dimensional nature of physical space and eliminates “dimensional isotopes,” i.e., quantities with different physical meaning but identical dimensions in the SI system. We demonstrate that the mathematical expression for the vector norm of a measurement unit, referred to as a “system unit,” can be used to determine whether a unit is within the range of variation in such a system unit.