Scalar Quantity Research Articles

Numerical Simulations for Calibration Setup for Dynamic Contrast-Enhanced Ultrasonography Imaging Protocol.

This study presents an investigation of an innovative microfluidic flow separator using both numerical and experimental approaches to calibrate contrast-enhanced ultrasound scanners. Numerical simulations were conducted using Lagrangian particles tracking and passive scalar transport methodologies using the OpenFOAM software. The experimental validation confirmed the accuracy of the numerical simulations, particularly at an imposed total pressure of , showing an excellent agreement in particle distributions. The study emphasizes the computational efficiency and modeling of passive scalar transport, providing valuable understanding into the behavior of scalar quantities in microfluidic systems. An optimized diffusion coefficient value of was identified, showing its critical role in achieving accurate simulation results and optimizing the performance of microfluidic flow separators for contrast-enhanced ultrasound scanner calibration.

A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra.

The use of machine learning (ML) algorithms in molecular simulations has become commonplace in recent years. There now exists, for instance, a multitude of ML force field algorithms that have enabled simulations approaching ab initio level accuracy at time scales and system sizes that significantly exceed what is otherwise possible with traditional methods. Far fewer algorithms exist for predicting rotationally equivariant, tensorial properties such as the electric polarizability. Here, we introduce a kernel ridge regression algorithm for machine learning of the polarizability tensor. This algorithm is based on the bond polarizability model and allows prediction of the tensor components at the cost similar to that of scalar quantities. We subsequently show the utility of this algorithm by simulating gas phase Raman spectra of biphenyl and malonaldehyde using classical molecular dynamics simulations of these systems performed with the recently developed MACE-OFF23 potential. The calculated spectra are shown to agree very well with the experiments and thus confirm the expediency of our algorithm as well as the accuracy of the used force field. More generally, this work demonstrates the potential of physics-informed approaches to yield simple yet effective machine learning algorithms for molecular properties.

Pulsar-wind nebulae meeting the circumstellar media of their progenitors

A significative fraction of high-mass stars sail away through the interstellar medium of the galaxies. Once they evolved and died via a core-collapse supernova, a magnetised, rotating neutron star (a pulsar) is usually left over. The immediate surroundings of the pulsar is the pulsar wind, which forms a nebula whose morphology is shaped by the supernova ejecta and channelled into the circumstellar medium of the progenitor star in the pre-supernova time. Irregular pulsar-wind nebulae display a large variety of radio appearances, screened by their interacting supernova blast wave, or harbour asymmetric up–down emission. Here, we present a series of 2.5-dimensional (2 dimensions for the scalar quantities plus a toroidal component for the vectors) black non-relativistic magneto-hydrodynamical simulations exploring the evolution of the pulsar-wind nebulae generated by a red supergiant and a Wolf-Rayet massive supernova progenitor, moving with Mach number $M=1$ and $M=2$ into the warm phase of the Galactic plane. black In such a simplified approach, the progenitor's direction of motion, the local ambient medium magnetic field, and the progenitor and pulsar axis of rotation, are all aligned; this restricted our study to peculiar pulsar-wind nebula of high-equatorial-energy flux. We find that the reverberation of the termination shock of the pulsar-wind nebulae, when sufficiently embedded into its dead stellar surroundings and interacting with the supernova ejecta, is asymmetric and differs greatly as a function of the past circumstellar evolution of its progenitor, which reflects into their projected radio synchrotron emission. This mechanism is particularly at work in the context of remnants involving slowly moving or very massive stars. We find that the mixing of material in plerionic core-collapse supernova remnants is strongly affected by the asymmetric reverberation in their pulsar-wind nebulae.

An Improved Scheme for the Finite Difference Approximation of the Advective Term in the Heat or Solute Transport Equations

AbstractTransport equations are widely used to describe the evolution of scalar quantities subject to advection, dispersion and, possibly, reactions. Numerical methods are required to solve these equations in applications, adopting either the advective or conservative formulations. Conservative formulations are usually preferred in practice because they conserve mass. Advective formulations do not, but have received more mathematical attention and are required for Lagrangian solution methods. To obtain an advective formulation that conserves mass, we subtract the discretized fluid flow equation, multiplied by concentration, from the conservative form of the transport equation. The resulting scheme not only conserves mass, but is also elegant in that it can be interpreted as averaging the advective term at cell interfaces, instead of approximating it at cell centers as in traditional centered schemes. The two schemes are identical when fluid velocity is constant, and both have second-order convergence, but the truncation errors are slightly different. We argue that the error terms appearing in the proposed scheme actually imply an improved representation of subgrid spreading/contraction and acceleration/deceleration caused by variable velocity. We compare the proposed and traditional schemes on several problems with variable velocity caused by recharge, discharge or evaporation, including two newly developed analytical solutions. The proposed method yields results that are slightly, but consistently, better than the traditional scheme, while always conserving mass (i.e., mass at the end equals mass at the beginning plus inputs minus outputs), which the traditional centered finite differences scheme does not. We conclude that this scheme should be preferred in finite difference solutions of transport.

Direct observation of the neural computations underlying a single decision

Neurobiological investigations of perceptual decision-making have furnished the first glimpse of a flexible cognitive process at the level of single neurons. Neurons in the parietal and prefrontal cortex are thought to represent the accumulation of noisy evidence, acquired over time, leading to a decision. Neural recordings averaged over many decisions have provided support for the deterministic rise in activity to a termination bound. Critically, it is the unobserved stochastic component that is thought to confer variability in both choice and decision time. Here, we elucidate this drift-diffusion signal on individual decisions. We recorded simultaneously from hundreds of neurons in the lateral intraparietal cortex of monkeys while they made decisions about the direction of random dot motion. We show that a single scalar quantity, derived from the weighted sum of the population activity, represents a combination of deterministic drift and stochastic diffusion. Moreover, we provide direct support for the hypothesis that this drift-diffusion signal approximates the quantity responsible for the variability in choice and reaction times. The population-derived signals rely on a small subset of neurons with response fields that overlap the choice targets. These neurons represent the integral of noisy evidence. Another subset of direction-selective neurons with response fields that overlap the motion stimulus appear to represent the integrand. This parsimonious architecture would escape detection by state-space analyses, absent a clear hypothesis.

Direct observation of the neural computations underlying a single decision.

Neurobiological investigations of perceptual decision-making have furnished the first glimpse of a flexible cognitive process at the level of single neurons. Neurons in the parietal and prefrontal cortex are thought to represent the accumulation of noisy evidence, acquired over time, leading to a decision. Neural recordings averaged over many decisions have provided support for the deterministic rise in activity to a termination bound. Critically, it is the unobserved stochastic component that is thought to confer variability in both choice and decision time. Here, we elucidate this drift-diffusion signal on individual decisions. We recorded simultaneously from hundreds of neurons in the lateral intraparietal cortex of monkeys while they made decisions about the direction of random dot motion. We show that a single scalar quantity, derived from the weighted sum of the population activity, represents a combination of deterministic drift and stochastic diffusion. Moreover, we provide direct support for the hypothesis that this drift-diffusion signal approximates the quantity responsible for the variability in choice and reaction times. The population-derived signals rely on a small subset of neurons with response fields that overlap the choice targets. These neurons represent the integral of noisy evidence. Another subset of direction-selective neurons with response fields that overlap the motion stimulus appear to represent the integrand. This parsimonious architecture would escape detection by state-space analyses, absent a clear hypothesis.

Analysis of a Dry Friction Force Law for the Covariant Optimal Control of Mechanical Systems with Revolute Joints

This contribution shows a geometric optimal control procedure to solve the trajectory generation problem for the navigation (generic motion) of mechanical systems with revolute joints. The mechanical system is analyzed as a nonlinear Lagrangian system affected by dry friction at the joint level. Rayleigh’s dissipation function is used to model this dissipative effect of joint-level friction, and regarded as a potential. Rayleigh’s potential is an invariant scalar quantity from which friction forces derive and are represented by a smooth model that approaches the traditional Coulomb’s law in our proposal. For the optimal control procedure, an invariant cost function is formed with the motion equations and a Riemannian metric. The goal is to minimize the consumed energy per unit time of the system. Covariant control equations are obtained by applying Pontryagin’s principle, and time-integrated using a Finite Elements Method-based solver. The obtained solution is an optimal trajectory that is then applied to a mechanical system using a proportional–derivative plus feedforward controller to guarantee the trajectory tracking control problem. Simulations and experiments confirm that including joint-level friction forces at the modeling stage of the optimal control procedure increases performance, compared with scenarios where the friction is not taken into account, or when friction compensation is performed at the feedback level during motion control.

A Single Compartment Relaxed Eddy Accumulation Method

AbstractThe relaxed eddy accumulation (REA) method is a widely‐known technique that measures turbulent fluxes of scalar quantities. The REA technique has been used to measure turbulent fluxes of various compounds, such as methane, ethene, propene, butene, isoprene, nitrous oxides, ozone, and others. The REA method requires the accumulation of scalar concentrations in two separate compartments that conditionally sample updrafts and downdraft events. It is demonstrated here that the assumptions behind the conventional or two‐compartment REA approach allow for one‐compartment sampling, therefore called a one compartment or 1‐C‐REA approach, thereby expanding its operational utility. The one‐compartment sampling method is tested across various land cover types and atmospheric stability conditions, and it is found that the one‐compartment REA can provide results comparable to those determined from conventional two‐compartment REA. This finding enables rapid expansion and practical utility of REA in studies of surface‐atmosphere exchanges, interactions, and feedbacks.

OAM degree of coherence.

A new, to the best of our knowledge, scalar quantity characterizing radial correlations among all the orbital angular momentum (OAM) modes present in a random beam is introduced. It is given by the maximum value of the interference fringe contrasts produced by the filtered pairs of the OAM modes. This new measure is termed the OAM degree of coherence (DOC) in similarity with the electromagnetic (EM) degree of coherence which describes two-point correlations in polarization components of the electric field. The theoretical development is augmented by several numerical examples. Moreover, the possibility of combining the OAM and the EM degrees of coherence in one quantity is also outlined.

Investigating the missing-wedge problem in small-angle X-ray scattering tensor tomography across real and reciprocal space.

Small-angle-scattering tensor tomography is a technique for studying anisotropic nanostructures of millimetre-sized samples in a volume-resolved manner. It requires the acquisition of data through repeated tomographic rotations about an axis which is subjected to a series of tilts. The tilt that can be achieved with a typical setup is geometrically constrained, which leads to limits in the set of directions from which the different parts of the reciprocal space map can be probed. Here, we characterize the impact of this limitation on reconstructions in terms of the missing wedge problem of tomography, by treating the problem of tensor tomography as the reconstruction of a three-dimensional field of functions on the unit sphere, represented by a grid of Gaussian radial basis functions. We then devise an acquisition scheme to obtain complete data by remounting the sample, which we apply to a sample of human trabecular bone. Performing tensor tomographic reconstructions of limited data sets as well as the complete data set, we further investigate and validate the missing wedge problem by investigating reconstruction errors due to data incompleteness across both real and reciprocal space. Finally, we carry out an analysis of orientations and derived scalar quantities, to quantify the impact of this missing wedge problem on a typical tensor tomographic analysis. We conclude that the effects of data incompleteness are consistent with the predicted impact of the missing wedge problem, and that the impact on tensor tomographic analysis is appreciable but limited, especially if precautions are taken. In particular, there is only limited impact on the means and relative anisotropies of the reconstructed reciprocal space maps.

Functional Time Series Models for K-Step Prediction of Sugar Production: A Case Study of Eswatini, Kenya, and South Africa

Sugar, produced from cane or beet, is a vital energy source and a globally traded commodity. Most business happens in a futures exchange market where speculators, hedgers, and institutional consumers and producers, make decisions based on their understanding of the future supply and demand situation. Sugar is sometimes bought and sold before the cane or beet is planted. Hence, improving sugar production forecast accuracy is vital to maximize gains and enable effective planning. The study considered the annual sugar production total as a function of the monthly output rather than a scalar quantity and analyzed historical data using three functional time series techniques. In particular, the methods used for k-steps and dynamic updating prediction of sugar production include Local Polynomial Regression (LPR), Ridge Regression (RR), and Penalized Least Squares (PLS). The performance of the three models was compared to that of the automatic ARIMA method using the Mean Squared Error (MSE) and the Mean Absolute Percentage Error (MAPE) measures to establish the suitability of each technique in sugar production forecasting. The LPR, RR, and PLS outperformed the ARIMA method in all three cases. However, the prediction accuracy was lower for highly volatile datasets from countries that overly depend on rainfall for cane development.

CuGBasis: High-performance CUDA/Python library for efficient computation of quantum chemistry density-based descriptors for larger systems.

CuGBasis is a free and open-source CUDA®/Python library for efficient computation of scalar, vector, and matrix quantities crucial for the post-processing of electronic structure calculations. CuGBasis integrates high-performance Graphical Processing Unit (GPU) computing with the ease and flexibility of Python programming, making it compatible with a vast ecosystem of libraries. We showcase its utility as a Python library and demonstrate its seamless interoperability with existing Python software to gain chemical insight from quantum chemistry calculations. Leveraging GPU-accelerated code, cuGBasis exhibits remarkable performance, making it highly applicable to larger systems or large databases. Our benchmarks reveal a 100-fold performance gain compared to alternative software packages, including serial/multi-threaded Central Processing Unit and GPU implementations. This paper outlines various features and computational strategies that lead to cuGBasis's enhanced performance, guiding developers of GPU-accelerated code.

Dynamic range and optimization strategies for radiochromic film calibration using gradient radiation fields.

This investigation aimed to optimize gradient positioning for radiochromic film calibration to facilitate a uniform distribution of calibration points. The study investigated the influence of various parameters on gradient dose profiles generated by a physical wedge, assessing their impact on the field's dose dynamic range, a scalar quantity representing the span of absorbed doses. Numerical parameterization of the physical wedge profile was used to visualize and quantify the impact of field size, depth, and energy on the dynamic range of dose gradients. This concept enabled the optimization of the gradient positioning and estimation of the necessary number of exposures for the desired calibration dose range. An optimization algorithm based on histogram bin height minimization was developed and presented. The maximum dynamic range was achieved with a 20 20 field size at 5 cm depth. Optimization of wedge gradient positioning yielded the most uniform dose distribution with 7 exposures for the [1,10] Gy range and 8 exposures for the [1,20] Gy range. Film calibration using gradients centered at 1.6, 3, 3.5, and 7 Gy central axis (CAX), obtained through optimized gradient positioning, was showcased. The presented work demonstrates the potential for an improved film calibration process, with efficient material utilization and enhanced dosimetric accuracy for clinical applications. While the method was described for the use of a physical wedge, the methodology can be easily extended to the use of a more convenient dynamicwedge.

Geodesic metrics for RBF approximation of some physical quantities measured on sphere

The radial basis function (RBF) approximation is a rapidly developing field of mathematics. In the paper, we are concerned with the measurement of scalar physical quantities at nodes on sphere in the 3D Euclidean space and the spherical RBF interpolation of the data acquired. We employ a multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 considered in Cartesian coordinates. Attention is paid to geodesic metrics that define the distance of two points on a sphere. The choice of a particular geodesic metric function is an important part of the construction of interpolation formula.We show the existence of an interpolation formula of the type considered. The approximation formulas of this type can be useful in the interpretation of measurements of various physical quantities. We present an example concerned with the sampling of anisotropy of magnetic susceptibility having extensive applications in geosciences and demonstrate the advantages and drawbacks of the formulas chosen, in particular the strong dependence of interpolation results on condition number of the matrix of the system considered and on round-off errors in general.

Speed as an expression and texture of space: Theory at play in a movement activity

In recent years, following new materialist, posthumanist and non-representational turns, human geography has increasingly understood the worlds it studies as vital, immediate and emergent. As part of this vision, studies have empirically animated and theoretically articulated various expressions/textures in the movement of space, including its rhythms, shapes, timings, repetitions, sensuousness and infections. Speed is one such expression/texture that has received some empirical attention but, in comparison to most others, it has not been so thoroughly theorized. In response, this article conducts a reconnaissance into speed, its intentions being to convey some foundational theoretical understandings of speed and, through empirical research, show these at play in social contexts. Specifically, naturalistic participant observations of forms of the movement activity of cycling are used to animate how (1) speed can be represented and affective as a scalar quantity, (2) all objects possess speeds and affect other speeds, (3) speeds and objects are known through relative positions and speeds, (4) speeds create rates of happening, (5) speeds occur in all expressions/textures of space and (6) the accelerating world is engaged at relational speeds. From this reconnaissance, to assist future research on speed, the article closes with some suggested avenues for further inquiry.

Algorithm to Produce a Density Field with Given Two, Three, and Four-Point Correlation Functions

Abstract Here we show how to produce a 3D density field with a given set of higher-order correlation functions. Our algorithm enables producing any desired two-point, three-point, and four-point functions, including odd-parity for the latter. We note that this algorithm produces the desired correlations about a set of “primary” points, matched to how the spherical-harmonic-based algorithms ENCORE and CADENZA measure them. These “primary points” must be used as those around which the correlation functions are measured. We also generalize the algorithm to i) N-point correlations with N > 4, ii) dimensions other than 3, and iii) beyond scalar quantities. This algorithm should find use in verifying analysis pipelines for higher-order statistics in upcoming galaxy redshift surveys such as DESI, Euclid, Roman, and Spherex, as well as intensity mapping. In particular it may be helpful in searches for parity violation in the 4PCF of these samples, for which producing initial conditions for N-body simulations is both costly and highly model-dependent at present, and so alternative methods such as that developed here are desirable.

Hybrid compressible lattice Boltzmann method for supersonic flows with strong discontinuities

Within the framework of the hybrid recursive regularized lattice Boltzmann (HRR-LB) model, we propose a novel hybrid compressible LB method to ensure the conservation of total energy in simulating compressible flows with strong discontinuities. This method integrates a LB solver to handle the mass and momentum conservation equations via collision-streaming steps on standard lattices, while a finite volume method (FVM) is employed for the conservation of the total energy equation. The flux reconstruction in the FVM is achieved through a momentum coupled method (MCM). The interface momentum, crucial for reconstructing the convective fluxes and determining the upwind extrapolation of passive scalar quantities in MCM, is derived from the LB method. The validity and accuracy of the proposed method are evaluated through six test cases: (I) isentropic vortex convection in subsonic and supersonic regimes; (II) non-isothermal acoustic pulse; (III) one-dimensional Riemann problems; (IV) two-dimensional Riemann problem; (V) double Mach reflection of a Mach 10 shock wave; and (VI) shock–vortex interaction. Numerical results demonstrate that this method surpasses the previous HRR-LB model by Guo et al. [“Improved standard thermal lattice Boltzmann model with hybrid recursive regularization for compressible laminar and turbulent flows,” Phys. Fluids 32, 126108 (2020)] in terms of accuracy and robustness when dealing with strong shock waves.

A dynamic scale-mixture model of motion in natural scenes.

Some of the most important tasks of visual and motor systems involve estimating the motion of objects and tracking them over time. Such systems evolved to meet the behavioral needs of the organism in its natural environment, and may therefore be adapted to the statistics of motion it is likely to encounter. By tracking the movement of individual points in movies of natural scenes, we begin to identify common properties of natural motion across scenes. As expected, objects in natural scenes move in a persistent fashion, with velocity correlations lasting hundreds of milliseconds. More subtly, but crucially, we find that the observed velocity distributions are heavy-tailed and can be modeled as a Gaussian scale-mixture. Extending this model to the time domain leads to a dynamic scale-mixture model, consisting of a Gaussian process multiplied by a positive scalar quantity with its own independent dynamics. Dynamic scaling of velocity arises naturally as a consequence of changes in object distance from the observer, and may approximate the effects of changes in other parameters governing the motion in a given scene. This modeling and estimation framework has implications for the neurobiology of sensory and motor systems, which need to cope with these fluctuations in scale in order to represent motion efficiently and drive fast and accurate tracking behavior.

Closed-loop coupling of a dynamic wake model with a wind inflow estimator

The estimation of turbine flow evolution provided by low-fidelity dynamic wake models, such as FLORIDyn, can be improved by the introduction of a Kalman filter based on power production measurements. However, it is not possible to infer any information about which side of an impinged rotor is affected by the wake only by the observed power, being itself a single scalar quantity. In this paper, a new closed-loop formulation of the FLORIDyn model is investigated: wind speed estimates, given by a blade load-based wind observer, are implemented into a Kalman Filter, providing information about the position of the wake over the rotor plane. The FLORIDyn model augmented with the wind flow estimator is tested in a layout of two aligned turbines and compared to a corresponding CFD simulation. The results of the proposed approach show an improved ability to predict wind flow quantities and the wake centerline position compared to the open-loop version of the model.

Modeling and Experimental Validation of High‐Flow Fluid‐Driven Membrane Valves for Hyperactuated Soft Robots

Herein, the design, modeling, and validation of high‐flow, fluid‐driven, membrane valves tailored specifically for applications in soft robotic systems are described. Targeting the piping problem in hyper‐actuated soft robots, two fluid‐driven membrane valve designs that can admit flows of up to while weighing less than are introduced. A mathematical model to predict fluid flow by representing the displacement of the membrane as a scalar quantity influenced by the balance of pressures applied across the valve's ports is established. The model incorporates six parameters with direct physical relevance, enhancing its usefulness in valve design and system integration. In an experimental validation, flow rates with deviations within 4% are predicted and the onset of flow is correctly identified with an error rate of less than 1%. In addition, applications of these valves for flow amplification and for the creation of a fluid‐driven oscillator are experimentally demonstrated. This research contributes to the advancement of soft robotics by providing a tool for designing, optimizing, and controlling fluid‐driven systems and it lays the groundwork for the future development of embedded, fluid‐controlled valve networks that can be used to realize hyper‐actuated soft robotic systems.