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Searching similarity between a pair of shapes or data is an important problem in data analysis and visualization. The problem of computing similarity measures using scalar topology has been studied extensively and proven useful in the shape and data matching. Even though multi-field or multivariate (consists of multiple scalar fields) topology reveals richer topological features, research on building tools for computing similarity measures using multi-field topology is still in its infancy. In the current article, we propose a novel similarity measure between two piecewise-linear multi-fields based on their multi-resolution Reeb spaces - a newly developed data-structure that captures the topology of a multi-field. Overall, our method consists of two steps: (i) building a multi-resolution Reeb space corresponding to each of the multi-fields and (ii) proposing a similarity measure between two multi-resolution Reeb spaces by computing a list of topologically consistent matching pairs (of nodes) and the similarity between them. We demonstrate the effectiveness of the proposed similarity measure in detecting topological features from real time-varying multi-field data in two application domains - one from computational physics and one from computational chemistry.

Colormapping is an effective and popular visualization technique for analyzing patterns in scalar fields. Scientists usually adjust a default colormap to show hidden patterns by shifting the colors in a trial-and-error process. To improve efficiency, efforts have been made to automate the colormap adjustment process based on data properties (e.g., statistical data value or histogram distribution). However, as the data properties have no direct correlation to the spatial variations, previous methods may be insufficient to reveal the dynamic range of spatial variations hidden in the data. To address the above issues, we conduct a pilot analysis with domain experts and summarize three requirements for the colormap adjustment process. Based on the requirements, we formulate colormap adjustment as an objective function, composed of a boundary term and a fidelity term, which is flexible enough to support interactive functionalities. We compare our approach with alternative methods under a quantitative measure and a qualitative user study (25 participants), based on a set of data with broad distribution diversity. We further evaluate our approach via three case studies with six domain experts. Our method is not necessarily more optimal than alternative methods of revealing patterns, but rather is an additional color adjustment option for exploring data with a dynamic range of spatial variations.

This article considers the fully distributed leaderless synchronization in a complex network by only utilizing local neighboring information to design and tune the coupling strength of each node such that the synchronization problem can be solved without involving any global information of the network. For an undirected network, a fully distributed synchronization algorithm is presented to adjust the coupling strength of each node based on a simple adaptive law. When the topology of a network is directed, two different types of adaptive algorithms are developed to achieve synchronization in a fully distributed manner, where the coupling strength of each node is designed to be either the sum or product of two non-negative scalar functions. The fully distributed leaderless synchronization of a directed network is investigated in a leader-follower framework, where the leader subnetwork is analyzed by using the techniques from constrained Rayleigh quotients and the follower subnetwork is addressed by employing the properties of nonsingular M -matrices. Simulations are given to illustrate the theoretical results.

This paper analyzes a Susceptible-Infected-Susceptible (SIS) model of epidemic propagation over hypergraphs and, motivated by an important special case, we refer to the model as to the simplicial SIS model. Classically, the multi-group SIS model has assumed pairwise interactions of contagion across groups and thus has been vastly studied in the literature. It is only recently that a renewed special attention has been drawn to the study of contagion dynamics over higher-order interactions and over more general graph structures, like simplexes. Previous work on mean-field approximation scalar models of the simplicial SIS model has indicated that a new dynamical behavior domain, compared to the classical SIS model, appears due to the newly introduced higher order interaction terms: both a disease-free equilibrium and an endemic equilibrium co-exist and are both locally asymptotically stable. This paper formally establishes that bistability (as a new epidemiological behavior) also appears in the multi-group simplicial SIS model. We give sufficient conditions over the model's parameters for the appearance of this and the other behavioral domains present in the classical

The present work has been able to relate the magnetic field produced to the basic physical ionization process and derive a general expression for the same starting from the fundamental retarded scalar and vector potentials (Leinard-Weichert potentials).

Optimal sensor and actuator selection is a central challenge in high-dimensional estimation and control. Nearly all subsequent control decisions are affected by these sensor/actuator locations, and optimal placement amounts to an intractable brute-force search among the combinatorial possibilities. In this work, we exploit balanced model reduction and greedy optimization to efficiently determine sensor and actuator selections that optimize observability and controllability. In particular, we determine locations that optimize scalar measures of observability and controllability via greedy matrix QR pivoting on the dominant modes of the direct and adjoint balancing transformations. Pivoting runtime scales linearly with the state dimension, making this method tractable for high-dimensional systems. The results are demonstrated on the linearized Ginzburg-Landau system, for which our algorithm approximates known optimal placements computed using costly gradient descent methods., Comment: 8 pages, 6 figures

We present a gentle approach to the justification of effective media approximations, for PDE's set outside the union of $n \gg 1$ spheres with low volume fraction. To illustrate our approach, we consider three classical examples: the derivation of the so-called strange term, made popular by Cioranescu and Murat, the derivation of the Brinkman term in the Stokes equation, and a scalar analogue of the effective viscosity problem. Under some separation assumption on the spheres, valid for periodic and random distributions of the centers, we recover effective models as $n$ goes to infinity by simple arguments., 20 pages. Final version, to appear in Asympt. Anal

In this paper, we investigate the relationships between proper efficiency and the solutions of a general scalarization problem in multi-objective optimization. We provide some conditions under which the solutions of the dealt with scalar program are properly efficient and vice versa. We also show that, under some conditions, if the considered general scalar problem is unbounded, then the original multi-objective problem does not have any properly efficient solution. In another part of the work, we investigate a general transformation of the objective functions which preserves proper efficiency. We show that several important results existing in the literature are direct consequences of the results of the present paper.

This article proposes a new scalar control scheme for variable speed drives of induction motors with an adaptive starting control. Besides centrifugal pumps, blowers, and fans, it expands the scalar control application field to move, for instance, a class of conveyor belts with nominal torque loading. An adaptive passivity-based controller designed for a class of nonlinear systems encompassing the dynamical machine model keeps a constant stator starting current. The proposed methodology uses information from the motor nameplate. Hence, it keeps a simple control scheme, not needing parameter estimates, neither adjusting controllers nor variable observers depending on them. Experimental results with a 10 HP downscaled laboratory prototype validate the proposed control strategy effectiveness. It shows rated-starting torque capabilities and fast speed response. Moreover, it shows lower stator current consumption than previous scalar control schemes

This article opens a conversation between anthropological studies of the Mediterranean and of postsocialism in order to propose the notion of a “scalar gaze” as an analytical approach useful for capturing veering practices in their social complexity. The article argues that favors (veze/štela,, lit. relations, connections) in contemporary Bosnia and Herzegovina were a practice through which people fulfilled the demands of capitalist economy to be active, rather than a pre-capitalist excess that prevented “proper” development of the country into a neoliberal democracy. Zooming in and out and looking sideways between moral reasoning, internationally supervised structural changes of the job markets, and electoral politics, this article explores how the relational labor of favors reproduced moral selves, as well as hierarchy and inequality.

International audience; This article deals with robust fixed-time stability and stabilization. First, new global robust fixed-time stability results are proposed for scalar systems by using constant and variable exponent coefficients. Then, they are applied to global robust fixed-time stabilization of a class of uncertain nonlinear second order systems by using sliding mode control. All the results are illustrated in simulation.

Parameter estimation is defined as the process to adjust or optimize the model parameter using observations. A long-term problem in ensemble-based parameter estimation methods is that the parameters are assumed to be constant during model integration. This assumption will cause underestimation of parameter ensemble spread, such that the parameter ensemble tends to collapse before an optimal solution is found. In this work, a two-stage inflation method is developed for parameter estimation, which can address the collapse of parameter ensemble due to the constant evolution of parameters. In the first stage, adaptive inflation is applied to the augmented states, in which the global scalar parameter is transformed to fields with spatial dependence. In the second stage, extra multiplicative inflation is used to inflate the scalar parameter ensemble to compensate for constant parameter evolution, where the inflation factor is determined according to the spread growth ratio of model states. The observation system simulation experiment with CESM shows that the second stage of the inflation scheme plays a crucial role in successful parameter estimation. With proper multiplicative inflation factors, the parameter estimation can effectively reduce the parameter biases, providing more accurate analyses.

This paper presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, our argument establishes the optimality of Gaussian codebooks and hence, a closed-form formula for the optimal rate region. The second problem is Wyner’s common information and a generalization thereof, where conditional independence is generalized to a limit on the conditional mutual information. We present full explicit solutions for the scalar as well as the vector case.

Magnetomotive ultrasound is an emerging technique that enables detection of magnetic nanoparticles. This has implications for ultrasound molecular imaging, and potentially addresses clinical needs regarding determination of metastatic infiltration of the lymphatic system. Contrast is achieved by a time-varying magnetic field that sets nanoparticle-laden regions in motion. This motion is governed by vector-valued mechanical and magnetic forces. Understanding how these forces contribute to observed displacement patterns is important for the interpretation of magnetomotive ultrasound images. Previous studies have captured motion adjacent to nanoparticle-laden regions that was attributed to diamagnetism. While diamagnetism could give rise to a force, it cannot fully account for the observed displacements in magnetomotive ultrasound. To isolate explanatory variables of the observed displacements, a finite element model is set up. Using this model, we explore potential causes of the unexplained motion by comparing numerical models with earlier experimental findings. The simulations reveal motion outside particle-laden regions that could be attributed to mechanical coupling and the principle of mass conservation. These factors produced a motion that counterbalanced the time-varying magnetic excitation, and whose extent and distribution was affected by boundary conditions as well as compressibility and stiffness of the surroundings. Our findings emphasize the importance of accounting for the vector-valued magnetic force in magnetomotive ultrasound imaging. In an axisymmetric geometry, that force can be represented by a simple scalar expression, an oversimplification that rapidly becomes inaccurate with distance from the symmetry axis. Additionally, it results in an underestimation of the vertical force component by up to 30%. We therefore recommend using the full vector-valued force to capture the magnetic interaction. This study enhances our understanding of how forces govern magnetic nanoparticle displacement in tissue, contributing to accurate analysis and interpretation of magnetomotive ultrasound imaging.

A moisture advection scheme is an essential module of a numerical weather/climate model representing the horizontal transport of water vapor. The Piecewise Rational Method (PRM) scalar advection scheme in the Global/Regional Assimilation and Prediction System (GRAPES) solves the moisture flux advection equation based on PRM. Computation of the scalar advection involves boundary exchange, and computation of higher bandwidth requirements is complicated and time-consuming in GRAPES. Recently, Graphics Processing Units (GPUs) have been widely used to solve scientific and engineering computing problems owing to advancements in GPU hardware and related programming models such as CUDA/OpenCL and Open Accelerator (OpenACC). Herein, we present an accelerated PRM scalar advection scheme with Message Passing Interface (MPI) and OpenACC to fully exploit GPUs' power over a cluster with multiple Central Processing Units (CPUs) and GPUs, together with optimization of various parameters such as minimizing data transfer, memory coalescing, exposing more parallelism, and overlapping computation with data transfers. Results show that about 3.5 times speedup is obtained for the entire model running at medium resolution with double precision when comparing the scheme's elapsed time on a node with two GPUs (NVIDIA P100) and two 16-core CPUs (Intel Gold 6142). Further, results obtained from experiments of a higher resolution model with multiple GPUs show excellent scalability.

Private individual information are increasingly exposed through high-dimensional and high-order data, with the wide deployment of learning techniques. These data are typically expressed in form of tensors, but there is no principled way to guarantee privacy for tensor-valued queries. Conventional differential privacy is typically applied to scalar values without a precise definition on the shape of the queried data. Realizing that the conventional mechanisms do not take the data structural information into account, we propose Tensor Variate Gaussian (TVG), a new (,δ)-differential privacy mechanism for tensor-valued queries. We further introduce two mechanisms based on TVG with an improved utility by imposing the unimodal differentially-private noise. With the utility space available, the proposed mechanisms can be instantiated with an optimized utility, and the optimization problem has a closed-form solution scalable to large-scale problems. Finally, we experimentally test our mechanisms on a variety of datasets and models, demonstrating that TVG is superior than other state-of-the-art mechanisms on tensor-valued queries.

In this paper, a novel model to investigate leakage of gaseous working fluid in pressured devices with lubricating oil was created with Lattice Boltzmann method and Shan-Chen multiphase model. A method to adapt actual pressure-density relation into the lattice via a self-adapting timestep and simplify the simulation of compressible fluid was developed. A model to simulate two-phased leakage with lubricating oil was created with a combination of Shan-Chen model and passive scalar model. The model can realize the phase distribution simulation in the leakage field without causing the pressure and the inter-phase interactions to overlap. This model is also able to be combined with other multiphase models. After a group of preliminary tests of the model, the characteristics of phase distribution and leakage were investigated qualitatively. Five types of phase distribution in the simulation results were classified, which are: uniformed distribution, sphered drips, gas channel, blocked channel and slug bubbles. The results of simulations show good conformance with actual leakage patterns. Preliminary discussions about the leakage features are made upon the results. However, these simulation results are only qualitative and cannot show the quantitative features in leakages. More experimental investigations should be carried out to realize correlations to the model.

Due to the broad successes of deep learning, many CPU-centric artificial intelligent computing systems employ specialized devices such as GPUs, FPGAs, and ASICs, which can be named as Deep Learning Processing Units (DLPUs), for processing computation-intensive deep learning tasks. The separation between the scalar control operations mapped on CPUs and the vector computation operations mapped on DLPUs causes the frequent and costly interactions between CPUs and DLPUs, leading to the Interaction Wall. Moreover, the increasing algorithm complexity and DLPU computation speed would further aggravate the interaction wall substantially.

This article proposes a new maximum torque per ampere (MTPA) control strategy for an induction motor (IM) controlled by the scalar ( v / f ) method. In scalar control, constant air-gap flux control is generally adopted for IM drives to provide the same torque capability in all operating ranges. However, this control method results in poor motor efficiency due to excessive stator current at light loads. This work proposes a new MTPA control method to minimize the stator current amplitude based on reactive power without measuring the rotor mechanical speed, resulting in improved system efficiency at light loads. In addition, this method proposes an online machine parameter compensation method. Thus, this proposed method is robust to parameter variations. Simulation and experimental results are provided to verify the performance of this MTPA control strategy.

We extend the theory of lower and upper solutions to planar systems of ordinary differential equations with separated boundary conditions, both in the well-ordered and in the non-well-ordered cases. We are able to deal with general Sturm–Liouville boundary conditions in the well-ordered case, and we analyze the Dirichlet problem in the non-well-ordered case. Our results apply in particular to scalar second order differential equations, including those driven by the mean curvature operator. Higher dimensional systems are also treated, with the same approach.

Neutron stars are known to host extremely powerful magnetic fields. Among other effects, one of the consequences of harbouring such fields is the deformation of the neutron star structure, leading, together with rotation, to the emission of continuous gravitational waves. On the one hand, the details of their internal magnetic fields are mostly unknown. Likewise, their internal structure, encoded by the equation of state, is highly uncertain. Here we present a study of axisymmetric models of isolated magnetised neutron stars, for various realistic equations of state considered viable by observations and nuclear physics constraints. We show that it is possible to find simple relations between the magnetic deformation of a neutron star, its Komar mass and its circumferential radius. Such relations are quasi-universal, meaning that they are mostly independent on the equation of state of the neutron star and only slightly dependent on the magnetic field configuration. Being formulated in terms of potentially observable quantities, as we discuss, our results could help to constrain the magnetic properties of the neutron star interior and to better assess the detectability of continuous gravitational waves by isolated neutron stars, without knowing their equation of state. Our results are derived both in general relativity and in scalar-tensor theories - one of the most promising extensions of general relativity - in this case by considering also the scalar charge. We show that even in this case general relations hold that account for deviations from general relativity, that could potentially be used to set constraints on the gravitational theory., Comment: Accepted for publication in A&A; minor language corrections

A waveguide with a constant, simply connected section S is considered under the condition that the substance filling the waveguide is characterized by permittivity and permeability that vary smoothly over the section S, but are constant along the waveguide axis. Ideal conductivity conditions are assumed on the walls of the waveguide. On the basis of the previously found representation of the electromagnetic field in such a waveguide using 4 scalar functions, namely, two electric and two magnetic potentials, Maxwells equations are rewritten with respect to the potentials and longitudinal components of the field. It appears possible to exclude potentials from this system and arrive at a pair of integro-differential equations for longitudinal components alone that split into two uncoupled wave equations in the optically homogeneous case. In an optically inhomogeneous case, this approach reduces the problem of finding the normal modes of a waveguide to studying the spectrum of a quadratic self-adjoint operator pencil.

In weakly coupled neural oscillator networks describing brain dynamics, the coupling delay is often distributed. We present a theoretical framework to calculate the phase response curve of distributed-delay induced limit cycles with infinite-dimensional phase space. Extending previous works, in which non-delayed or discrete-delay systems were investigated, we develop analytical results for phase response curves of oscillatory systems with distributed delay using Gaussian and log-normal delay distributions. We determine the scalar product and normalization condition for the linearized adjoint of the system required for the calculation of the phase response curve. As a paradigmatic example, we apply our technique to the Wilson-Cowan oscillator model of excitatory and inhibitory neuronal populations under the two delay distributions. We calculate and compare the phase response curves for the Gaussian and log-normal delay distributions. The phase response curves obtained from our adjoint calculations match those compiled by the direct perturbation method, thereby proving that the theory of weakly coupled oscillators can be applied successfully for distributed-delay-induced limit cycles. We further use the obtained phase response curves to derive phase interaction functions and determine the possible phase locked states of multiple inter-coupled populations to illuminate different synchronization scenarios. In numerical simulations, we show that the coupling delay distribution can impact the stability of the synchronization between inter-coupled gamma-oscillatory networks.

We concern $C^2$-compactness of the solution set of the boundary Yamabe problem on smooth compact Riemannian manifolds with boundary provided that their dimensions are $4$, $5$ or $6$. By conducting a quantitative analysis of a linear equation associated with the problem, we prove that the trace-free second fundamental form must vanish at possible blow-up points of a sequence of blowing-up solutions. Applying this result and the positive mass theorem, we deduce the $C^2$-compactness for all $4$-manifolds (which may be non-umbilic). For the $5$-dimensional case, we also establish that a sum of the second-order derivatives of the trace-free second fundamental form is non-negative at possible blow-up points. We essentially use this fact to obtain the $C^2$-compactness for all $5$-manifolds. Finally, we show that the $C^2$-compactness on $6$-manifolds is true if the trace-free second fundamental form on the boundary never vanishes., Comment: 29 pages, This version treats general 5-manifolds as well, Comments are welcome

International audience; This paper is concerned with the in-domain stabilization of a class of block diagonal infinite-dimensional systems in the presence of an uncertain and time-varying delay in the distributed control input. Two actuation schemes are considered. The first one assumes a control input that is fully distributed over the domain. The second one assumes that the control input is finite-dimensional, acting over the domain via a bounded operator. In both cases, the control design strategy consists in a predictor feedback law synthesized on a finite-dimensional truncated LTI model capturing the unstable dynamics of the original infinitedimensional system. The predictor feedback law is designed based on the knowledge of the nominal value of the uncertain and time-varying input delay. In the second actuation scheme, the case of distinct input delays in the different scalar control input channels is considered. Index Terms-Delayed distributed actuation, partial differential equations, predictor feedback law. H. Lhachemi and R. Shorten acknowledge the support of Science Foundation Ireland (Grant numbers 16/RC/3872 and 16/IA/4610) and I-Form industry partners. C. Prieur acknowledges the support from MIAI@Grenoble Alpes, (ANR-19-P3IA-0003).

The brushless doubly-fed machine (BDFM) has two stator windings with different pole numbers, supplied with different frequencies. Therefore, the distribution of magnetic fields in stator and rotor iron is complex. In addition, the stator flux density distribution is non-sinusoidal and has a DC offset at the natural speed. This makes the use of conventional hysteresis models utilised for sinusoidal fields impractical for the BDFM. In this paper a new hysteresis model is proposed for the BDFM stator iron based on the scalar Preisach model. The rotational characteristics of the magnetic fields in the BDFM are also considered and their effects in generating iron losses are assessed. 2-D time-stepping finite element (FE) models are developed for a prototype D160 BDFM to estimate iron losses and are validated by experiments.

A second-order time stepping scheme is developed for the binary fluid-surfactant phase field model coupled with hydrodynamics by using the scalar auxiliary variable approach and pressure correction method. The free energy contains a double-well potential, a nonlinear coupling entropy and a Flory-Huggins potential. By introducing one scalar auxiliary variable, the system is transformed into an equivalent form so that the nonlinear terms can be treated semi-explicitly. The scheme is linear and decoupled; thus, they can be solved eciently. We further prove that the semidiscretized scheme in time is unconditionally energy stable. Numerical experiments are performed to validate the accuracy and energy stability of the proposed scheme.

A novel functional regression model was introduced in this research in which, the predictor is a curve linked to a scalar fuzzy response variable. An absolute error-based penalized method with SCAD loss function was also proposed to evaluate the unknown components of the model. For this purpose, a concept of fuzzy-valued function was developed and discussed. Then, a fuzzy large number notion was proposed to estimate the fuzzy-valued function. The performance of the proposed method was examined by some common goodness-of-fit criteria. The efficiency of the proposed method was then evaluated through two numerical examples; a simulation study and an applied example in the scope of watershed management. The proposed method was also compared with several common fuzzy regression models in cases where the functional data were converted to scalar ones.

Drawing on and developing literatures on automobilities, vertical urbanisms and the use of storylines to understand mega transport projects, we imagine infrastructure as a shifting assemblage of actors, storylines and material objects and practices. In the case of motorway building, this requires an understanding of how competing storylines about how both the infrastructure itself and the city it is located in are mobilised and politicised across diverse local geographies and multiple scales as the process proceeds. Our case study focuses on WestConnex, a 33 km motorway being built in Sydney, Australia. Similar to other major transport infrastructure projects, WestConnex morphed over time, growing in ambition, budget, complexity, debate and by enrolling new actors.

By combining multilayer perceptrons (MLPs) and radial basis function neural networks (RBF-NNs), an efficient multilayer RBF network is proposed in this work for regression problems. As an extension to the existing multilayer RBF network (RBF-MLP-I), the new multilayer RBF network (RBF-MLP-II) first nonlinearly transforms the multi-dimensional input data by adopting a set of multivariate basis functions. Then, linear weighted sums of these basis functions, i.e., the RBF approximations, are computed in the first hidden layer and used as the features of this layer. Subsequently, in the following hidden layers, each feature of the preceding hidden layer is fed into a univariate RBF characterized by the trainable scalar center and width, and then, RBF approximations are also applied to these basis functions. Finally, the features of the last hidden layer are linearly transformed to approximate the target output data. RBF-MLP-II reduces the number of parameters in basis functions and thus the network complexity of RBF-MLP-I. Verified by four regression problems, it is demonstrated that the proposed RBF-MLP-II exhibits the best approximation accuracy and fastest training convergence compared to conventional MLPs, RBF-NNs, and RBF-MLP-I.

Analytic and numerical techniques are presented for computing gravitational production of scalar particles in the limit that the inflaton mass is much larger than the Hubble expansion rate at the end of inflation. These techniques rely upon adiabatic invariants and time modeling of a typical inflaton field which has slow and fast time variation components. A faster computation time for numerical integration is achieved via subtraction of slowly varying components that are ultimately exponentially suppressed. The fast oscillatory remnant results in production of scalar particles with a mass larger than the inflationary Hubble expansion rate through a mechanism analogous to perturbative particle scattering. An improved effective Boltzmann collision equation description of this particle production mechanism is developed. This model allows computation of the spectrum using only adiabatic invariants, avoiding the need to explicitly solve the inflaton equations of motion., 37 pages, 5 figures

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

In this study, we develop high-order time-accurate, efficient, and energy stable schemes for solving the conservative Swift–Hohenberg equation that can be used to describe the L 2 -gradient flow based phase-field crystal dynamics. By adopting a modified exponential scalar auxiliary variable approach, we first transform the original equations into an expanded system. Based on the expanded system, the first-, second-, and third-order time-accurate schemes are constructed using the backward Euler formula, second-order backward difference formula (BDF2), and third-order backward difference formula (BDF3), respectively. The energy dissipation law can be easily proved with respect to a modified energy. In each time step, the local variable is updated by solving one elliptic type equation and the non-local variables are explicitly computed. The whole algorithm is totally decoupled and easy to implement. Extensive numerical experiments in two- and three-dimensional spaces are performed to show the accuracy, energy stability, and practicability of the proposed schemes.

Low-frequency radar tomography is an important subsurface imaging method for future planetary missions to solar system small bodies. We derive angular and radial sampling criteria for monostatic and bistatic radar tomography algorithms that are based on monochromatic free-space backprojection and spherical apertures. We use the vector Born approximation to highlight the degeneracy of monochromatic bistatic source/receiver direction pair measurements in k-space. Analytical expressions are then derived for the scalar point target response of different spherical sampling geometries. We also derive the angular sampling step and total number of sampling points required to fully reconstruct the point target response for monostatic, bistatic, and non-degenerate k-space spherical apertures. These are evaluated for object sizes and radar operating frequencies expected in small body tomography. We also analyze and derive expressions for the coherence loss of spherical apertures due to random errors in a sensor’s radial position, which provides requirements on the a posteriori ephemeris knowledge. Finally, we derive a vector backprojection algorithm suitable for focusing quad-pol scattering matrix (S-matrix) data that is tested using full-wave S-matrix simulations of dielectric point targets. This work is intended to aid radar instrument performance analysis and inform the design and architecture of future instruments and missions.

The level-set method is widely used for high-accuracy 3-D topography simulations in process technology computer-aided design (TCAD) because of its robustness to topological changes introduced by the involved complicated physical phenomena. Particularly challenging are material flow processes, such as oxidation, reflow, and silicidation, as these require the solution of intricate physical models and the extension of the model-dependent velocity fields to the entire simulation domain at every time step to accurately compute the advection. This velocity extension, thus, introduces yet another computational burden at every time step, which is significant when considering that high-accuracy material flow simulations can easily require several hundred time steps and are applied multiple times in cutting-edge fabrication processes of integrated circuits. In this work, a shared-memory parallel scalar and vector velocity extension algorithm for level-set-based material flow simulations on hierarchical meshes is introduced, allowing to further reduce the turnaround time of TCAD workflows. The performance is evaluated by investigating a representative material flow simulation of 3-D thermal oxidation of silicon. A parallel speedup of 7.1 for the vector-valued extension and 6.6 for the scalar-valued extension is achieved for ten threads; the latter outperforms a previous approach by up to 60%.

Non-spherical particles can be found in many industrial processes. Unfortunately, scalar shape parameters are often insufficient to predict their complex behavior. Therefore, this study used convolutional neural networks (CNN), which are able to interpret abstract shape features to derive the flow and packing behavior. For training data generation, experimentally validated Discrete Element Method simulations of silo filling and discharge were conducted. The subsequent training of the neural network was achieved with extensive input data augmentation. The CNN was then applied for the investigation of common shapes like ellipsoids or frustums for validation. The trained network showed good accordance to literature and high predictive robustness. Finally, the CNN assessed various food grains and tablet shapes. The network predicted the densest packing and best flowability for rounded lentils, whereas long rice kernels showed poor flow behavior. For pharmaceutical tablets, rounded and hexagonal shapes were predicted to yield denser packings than plain cylinders.

This article presents a robust stabilizer designed to damp low-frequency electromechanical oscillations which occurs in induction machines controlled by scalar control when operating at low speed and light load. The robust stabilizer design is based on the linear parameter varying (LPV) approach. A discrete LPV model is identified to allow the design of the robust LPV controller. Experimental tests are performed on a 7.5-kW induction motor dynamometer using an industrial inverter driver. The results show satisfactory improvement of the motor performance with the damping controller activated.

In this paper, the dispersion of a solute in blood flow in a tube has been discussed. Treating blood as thixotropic fluid modell, the presence of homogeneous chemical reaction has been considered in the analysis by adopting Taylor’s approach, and the effects of various parameters on the equivalent dispersion coefficient have been studied. It is seen that the dispersion coefficient decreases as the reaction rate constant increases, for given parameters of non-Newtonian fluids. A comparative study of the equivalent dispersion coefficient among Newtonian and other non-Newtonian modells is made. One of the remarkable results is that the increase in the scalar structural parameter of materials or thixotropic parameter leads to yield a decreasing trend in the equivalent dispersion coefficient. The present analytical study provides useful information of the physiological process in the circulatory system.

Landau-Ginzburg $\phi^4$ field theory is usually applied to systems for understanding continuous phase transitions at critical points. Here we analyze the thermal field using a similar free energy description from a statistical field theory perspective, and study fluctuations in such a field with a particular focus on realizing the thermal Casimir effect. Initially, we qualitatively describe the emergence of the Casimir-like effect using mean-field approximation and further derive it using coarse-graining of perturbative renormalization procedure in the vicinity of Gaussian-fixed point. These results may lead to further the understanding of the Casimir effect from scalar fields without employing the concept of zero-point energy in a cosmological sense., Comment: 9 pages, Added more clarification and references in this version

Discrete mechanics proposes an alternative formulation of the equations of mechanics where the Navier-Stokes and Navier-Lam\'e equations become approximations of the equation of discrete motion. It unifies the fields of fluid and solid mechanics by extending the fields of application of these equations to all space and time scales. This article presents the essential differences induced by the abandonment of the notion of continuous medium and global frame of reference. The results of the mechanics of continuous medium validated by fluid and solid observations are not questioned. The concept of continuous medium is not invalidated, the discrete formulation proposed simply widens the spectrum of the applications of the classical equations. The discrete equation of motion introduces several important modifications, in particular the fundamental law of the dynamics on an element of volume becomes a law of conservation of the accelerations on an edge. The acceleration considered as an absolute quantity is written as a sum of two components, one soledoidal the other irrotational according to a local orthogonal Helmholtz-Hodge decomposition. The mass is abandoned and replaced by the compression and rotation energies represented by the scalar and vectorial potentials of the acceleration. The equation of motion and all the physical parameters are expressed only with two fundamental units, those of length and time. The essential differences between the two approaches are listed and some of them are discussed in depth. This is particularly the case with the known paradoxes of the Navier-Stokes equation or the importance of inertia for the Navier-Lam\'e equation., Comment: 16 pages, 5 figures

Nuclear magnetic resonance (NMR) experiments are frequently complicated by the presence of homonuclear scalar couplings. For the growing body of biomolecular 13C-detected NMR methods, one-bond 13C-13C couplings significantly reduce sensitivity and resolution. The solution to this problem has typically been to perform virtual decoupling by recording multiple spectra and taking linear combinations. Here, we propose an alternative method of virtual decoupling using deep neural networks, which only requires a single spectrum and gives a significant boost in resolution while reducing the minimum effective phase cycles of the experiments by at least a factor of 2. We successfully apply this methodology to virtually decouple in-phase CON (13CO-15N) protein NMR spectra, 13C-13C correlation spectra of protein side chains, and 13Cα-detected protein 13Cα-13CO spectra where two large homonuclear couplings are present. The deep neural network approach effectively decouples spectra with a high degree of flexibility, including in cases where existing methods fail, and facilitates the use of simpler pulse sequences.

In this work, we consider the numerical computation for the two-dimensional generalized nonlinear Schrodinger equations with wave operator. Based on the scalar auxiliary variable (SAV) approach, the original problem is transformed into an equivalent one, which corresponds to the energy-conservation laws. We present an energy-conserving and linearly implicit three-level scheme for the equivalent system. The energy-conserving property, boundedness of the numerical solution and convergence analysis in the discrete maximum norm are derived, which has not restricted to specific forms of cubic nonlinear term f and not needed the sharply restriction on mesh size. Finally, numerical experiments on several models confirm our theoretical results.

We present a system to visualize multiple time-dependent scalar fields defined on 3D surfaces as they arise from numerical simulations. Domain experts want to understand correlations between multiple scalar fields to verify underlying processes. However, existing visualization techniques require high exploration effort to perceive temporal changes and relations of multiple fields on 3D surfaces. This makes analysis time-consuming and carries a high risk of overlooking regions with specific correlations. Therefore, we introduce a novel concept to facilitate exploration of multiple time-dependent scalar fields simultaneously. The basic idea is to use a novel glyph-based depiction, called skyline visualization, which is inspired by the skyscraper metaphor from information visualization. The skyscrapers are represented by 2D and 3D bar charts, where their floors show the temporal behavior of scalar fields of the corresponding surface region. The user can interact with the skyline visualization to see at which surface areas the scalar fields take on striking values or whether correlations exist between them. Furthermore, the user can immediately see in which regions scalar fields change strongly over time or show strongly inverted behavior. We evaluated our system with several CFD engineers, radiologists and visualization experts. Compared to existing systems, they were able to find regions of interest quickly and with high accuracy.

We investigate the effect of admitting signed measures as a datum at the scalar Chern-Simons equation -\Delta u + {\rm e}^u({\rm e}^u-1) =\mu\quadin \Omega with the Dirichlet boundary condition. Approximating $\mu$ by a sequence $(\mu_n)_{n \in\mathbb N}$ of $L^1$ functions or finite signed measures such that this equation has a solution $u_n$ for each $n\in\mathbb{N}$, we are interested in establishing the convergence of the sequence $(u_n)_{n\in\mathbb{N}}$ to a function $u^#$ and describing the form of the measure which appears on the right-hand side of the scalar Chern-Simons equation solved by $u^#$.

In this letter, we present a holographic metasurface (HMS) based on an orthogonally discrete unit-cell. The proposed unit-cell possesses discrete surface impedance tuning abilities in two orthogonal directions, providing flexible beam formation as a scalar unit-cell and polarization control as a tensor unit-cell. Operation principle and design formulas for generating independently linearly polarized beams and circularly polarized beams using the orthogonal components are concluded. Two example antennas utilizing this HMS are measured to demonstrate the beam formation and polarization control abilities at 11.0 GHz. The first example antenna generates dual beams with independently linear polarizations whereas the second example antenna generates dual beams with independently circular polarizations. Our letter indicates that there exists a middle type of HMS between scalar and tensor HMSs.

We generalize the unifying relations for tree amplitudes to the $1$-loop Feynman integrands. By employing the $1$-loop CHY formula, we construct differential operators which transmute the $1$-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, include Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at $1$-loop level is established. Under the well known unitarity cut, the $1$-loop level operators will factorize into two tree level operators. Such factorization is also discussed., Comment: 42 pages, 3 figures, 4 tables

In this paper, a multi-scale modelling approach has been developed to predict the progressive damage and failure behaviour of 2D woven SiC/SiC composites. At the tow scale, non-linear tow properties have been determined by a micromechanics-based damage model, in which two scalar damage variables were introduced to characterize the fibre-dominated and matrix-dominated damage, respectively. Based on periodic boundary conditions, a meso-scale unit cell model has been established to simulate the macroscopic stress-strain responses and progressive damage processes of the composite under uniaxial tensile, compressive and in-plane shear loadings, respectively. In the numerical method, the non-linear properties of constituent materials have been implemented by the user defined subroutine, USDFLD of the finite element package, Abaqus. The numerical results and their comparisons with experimental stress-strain curves have been presented. The failure mechanisms of the composite under each loading have been also discussed. The high efficiency and prediction accuracy of the model make it possible to analyse large scale woven composites.

This article investigates the consensus tracking of exponentially unstable multiagent systems with time-varying input delay. The truncated predictor feedback approach is utilized for designing delay-dependent state and output feedback protocols. And the explicit conditions that can realize consensus tracking are established in terms of parametric Lyapunov equations and scalar inequalities. Besides, the protocol design algorithms under the maximum allowable delay and the maximum convergence rate are, respectively, provided. Compared with the existing results, the salient characteristic of the current results is to reveal the quantitative relationship among the time delay, unstable plant, network topologies, and the convergence rate. Specifically, for achieving the consensus tracking, the synchronization force from network connectivity needs to dominate the anti-synchronization force from unstable open-loop poles and input delays; the maximum allowable input delay is inversely proportional to the sum of the unstable open-loop poles; the convergence rate becomes smaller as the input delay bounds or/and the sum of the unstable poles in plant increase. Numerical simulations confirm the effectiveness of the proposed theoretical design.

Turf was widely used as a building material in the Roman period, especially in military architecture. Despite this, few studies have investigated properties of turf in construction, and fewer still have applied micromorphology to ancient turf walls. This study details the methods and results from a combined macro- and micro-scale analysis, using samples from the well-preserved ramparts at Vindolanda, a fort associated with Hadrian’s Wall. Our work not only proposes a refined methodology for the wider geoarchaeological study of turf walls, but also provides new, deeper insight into the properties of turf as a building material.

Quantization and compression of neural network parameters using the uniform scalar quantization is carried out in this paper. The attractiveness of the uniform scalar quantizer is reflected in a low complexity and relatively good performance, making it the most popular quantization model. We present a design approach for the memoryless Laplacian source with zero-mean and unit variance, which is based on iterative rule and uses the minimal mean-squared error distortion as a performance criterion. In addition, we derive closed-form expressions for SQNR (Signal to Quantization Noise Ratio) in a wide dynamic range of variance of input data. To show effectiveness on real data, the proposed quantizer is used to compress the weights of neural networks using bit rates from 9 to 16 bps (bits/sample) instead of standardly used 32 bps full precision bit rate. The impact of weights compression on the NN (neural network) performance is analyzed, indicating good matching with the theoretical results and showing negligible decreasing of the prediction accuracy of the NN even in the case of high variance-mismatch between the variance of NN weights and the variance used for the design of quantizer, if the value of the bit-rate is properly chosen according to the rule proposed in the paper.