Space Distribution Research Articles

Generating realistic infrared spectra using artificial neural networks

AbstractArtificial spectra were generated to match the different acid solubility properties of the rocks. The purpose of generating artificial spectra was to increase the number of samples available for future data processing with a convolutional neural network. The samples were collected from different geological matrices during targeted rock tests to support industrial applications. The inherent characteristics of the samples are their uneven distribution in the parameter space of the features and their limited availability for data‐intensive studies. Both data set characteristics constrain the prediction performance of the machine learning methods to estimate the unknown solubility of samples in the chosen acids. If the sample multiplication techniques are performed without considering the relationship between solubility of samples and their infrared spectra, the synthetic samples adversely impact the efficacy of the prediction method. By utilizing a dimensionality reduction technique (principal component analysis) and a neural network, we established a relationship between the solubility of the samples and their infrared spectra. Infrared spectra of the samples used for learning the model could be efficiently reproduced and infrared spectra of created samples could be generated. The reliability of the applied method has been shown by the comparison of the original and artificial spectra through a mean Pearson correlation coefficient and by comparing the closest neighbors to each other. This method can be used to create new samples and their infrared spectra, where different constraints must be met and the samples must be connected to the infrared spectrum.

Computational modeling of interval distributions in tonal space reveals paradigmatic stylistic changes in Western music history

Diachronic stylistic changes in music are to a large extent affected by composers’ different choices, for example regarding the usage of tones, intervals, and harmonies. Analyzing the tonal content of pieces of music and observing them over time is thus informative about large-scale historical changes. In this study, we employ a computational model that formalizes music-theoretic conceptualizations of tonal space, and use it to infer the most likely interval distributions for pieces in a large corpus of music, represented as so-called ‘bags of tonal pitch classes’. Our results show that tonal interval relations become increasingly complex, that the interval of the perfect fifth dominates compositions for centuries, and that one can observe a stark increase in the usage of major and minor thirds during the 19th century, which coincides with the emergence of extended tonality. In complementing prior research on the historical evolution of tonality, our study thus demonstrates how example-based music theory can be informed by quantitative analyses of large corpora and computational models.

A real-time intelligent monitoring method for indoor evacuee distribution based on deep learning and spatial division

Providing real-time and detailed indoor evacuee distribution information is of great significance for the on-site formulating and dynamic adjustment of indoor emergency evacuation strategies. However, due to limitations in hardware costs and privacy protection, existing video surveillance and other evacuee counting methods cannot achieve real-time and accurate monitoring of the number and distribution of evacuees in all indoor areas. To solve the problem, using video data from an indoor surveillance system as a data source, an intelligent monitoring method for indoor pedestrian real-time distribution based on deep learning and spatial division is proposed. Firstly, the whole indoor area is divided many subareas according to the layout of indoor space and the size of spatial units. Then, deep learning detection and tracking algorithms are used to detect and track evacuees to achieve the number of evacuees at the boundary of each subarea and their movement directions; Finally, the numbers of evacuees entering and leaving each subarea are counted to obtain the spatial distribution information of evacuees. The experimental results show that within an appropriate monitoring distance, the proposed method achieves an average F1 score of 91.85% for evacuee counting at the boundaries of each subarea, with a processing speed of 22 FPS. More comprehensive and accurate real-time monitoring of evacuee distribution in the entire indoor space can be achieved, including no covered areas of cameras. It not only helps to formulate on-site emergency evacuation in case of a fire, but also enhances the daily operation and management capabilities of buildings.

An Introduction to Extended Gevrey Regularity

Gevrey classes are the most common choice when considering the regularities of smooth functions that are not analytic. However, in various situations, it is important to consider smoothness properties that go beyond Gevrey regularity, for example, when initial value problems are ill-posed in Gevrey settings. In this paper, we consider a convenient framework for studying smooth functions that possess weaker regularity than any Gevrey function. Since the available literature on this topic is scattered, our aim is to provide an overview of extended Gevrey regularity, highlighting its most important features. Additionally, we consider related dual spaces of ultra distributions and review some results on micro-local analysis in the context of extended Gevrey regularity. We conclude the paper with a few selected applications that may motivate further study of the topic.

Drag reduction characteristics of the placoid scale array skin sup-ported by micro Stewart mechanism based on penalty immersed boundary method

Sharkskin performs an excellent flow drag reduction property, leading to numerous biomimetic research to obtain artificial drag reduction structures for underwater vehicles. The existing work mainly focused on replicating or simplifying the morphology of the placoid scale, however, such bionic structures cannot fully reproduce the drag reduction effects of sharks swimming in natural environments. This is because the existing research has not considered the influence of the multi-degree freedom motion characteristics of the placoid scale. Therefore, a new bionic drag reduction skin is proposed by combining micro Stewart mechanisms and placoid scales, where the micro Stewart mechanism is able to achieve the multi-degree freedom motion characteristics. The numerical results indicate that micro Stewart mechanisms inhibit the generation and development of the streamwise and spanwise vortex structures in the bionic placoid scale array, which can delay flow separation and improve the drag reduction effect of the placoid scale array. Compared with the bionic placoid scale skin and the blade groove skin without multi-degree freedom motion foundation, the new bionic skin achieves relative drag reduction efficiency of 15.78 % and 14.18 % at maximum, respectively, by reasonably adjusting the bionic skin parameters including the leg stiffness, leg damping, upper platform mass, upper platform center of mass height of the micro Stewart mechanism and the skin element distribution spacing. The research presents a novel sharkskin bionics design and reveals the mechanism of skin drag reduction to some extent.

Dynamic evolution and trend prediction in coupling coordination between urban and rural space utilization efficiency based local and tele-coupling model

Optimizing the pattern of territorial space utilization is one of the key tasks to achieve the sustainable development goals. With the accelerating rate of global urbanization, the understanding of territorial space utilization efficiency, role and potential is a prerequisite for alleviating contradictions in urban and rural space distribution. The city cluster is the main form of organization for urban development in future, so the study attempted to explore the urban and rural space utilization efficiency (URSUE) in Chengdu-Chongqing urban agglomeration (CCEC) from coupling coordination degree (CCD) perspective. Considering the gradual increase in the trend of remote interactions between URSUE, we further introduced the Local and Tele-coupling coordination (LTCCD) model that takes into account interactive development relationship between different systems. The results of the study show that: In CCEC, the more economically developed cities indicated that urban spatial utilization efficiency lags behind rural spatial utilization efficiency; The LTCCD in the geographic center region will indicate a higher level but the LTCCD in the economic core cities is higher compared with their CCD level, especially in Chengdu City. This suggests that the LTCCD model is better able to take into account regional development correlations and spatial spillovers effect. This study attempts to explore several key issues of urban-rural spatial allocation in the process of urbanization development and to provide guidance for the territorial space utilization planning in urban agglomerations.

Stochastic quantisation of Yang–Mills–Higgs in 3D

We define a state space and a Markov process associated to the stochastic quantisation equation of Yang–Mills–Higgs (YMH) theories. The state space S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{S}$\\end{document} is a nonlinear metric space of distributions, elements of which can be used as initial conditions for the (deterministic and stochastic) YMH flow with good continuity properties. Using gauge covariance of the deterministic YMH flow, we extend gauge equivalence ∼ to S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{S}$\\end{document} and thus define a quotient space of “gauge orbits” O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathfrak {O}$\\end{document}. We use the theory of regularity structures to prove local in time solutions to the renormalised stochastic YMH flow. Moreover, by leveraging symmetry arguments in the small noise limit, we show that there is a unique choice of renormalisation counterterms such that these solutions are gauge covariant in law. This allows us to define a canonical Markov process on O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathfrak {O}$\\end{document} (up to a potential finite time blow-up) associated to the stochastic YMH flow.

Enhanced Acceleration and Escape of Hydrogen Pickup Ions Upstream from Mars by Interplanetary Shocks

The pickup process of newly ionized hydrogen (H) from the Martian extended exosphere represents an important H+ escape channel on Mars. It is generally believed that interplanetary (IP) shocks can accelerate the pickup ions and, in turn, affect the pickup process. However, the underlying processes inherent to the acceleration are not yet fully understood. Here, we concentrate on the dynamic processes involved in acceleration arising from IP shock compression. We examine two typical IP shock events characterized by a sudden increase in the average energy of upstream H+ pickup ions across the shock. The H+ pickup ions continuously enter the field of view of Supra-Thermal And Thermal Ion Composition or Solar Wind Ion Analyzer on board the Mars Atmosphere and Volatile EvolutioN spacecraft in a narrow angular range. Moreover, they correspond to a similar part of their respective ring distributions in velocity space. By comparing measured and theoretical H+ pickup ion energies, we attribute the more energetic H+ pickup ions to the enhanced convection electric field acceleration caused by the shock compression. An increase in the guiding center drift speed across the shock implies a higher escape rate of the H+ pickup ions. Furthermore, the pitch-angle scattering could facilitate the escape of the higher energy H+ pickup ions from Mars. The results may shed light on the understanding of the energization and escape of planetary pickup ions in the solar system.

Reconstructing phase space of injection beam based on the measurement of accumulated beam: A novel tomography algorithm and its applications

The measurement of phase space has always been an important topic in the field of accelerator physics, playing an indispensable role in understanding the beam dynamics. The phase space distribution of the injected beam is crucial for optimizing the multiturn accumulation injection process in synchrotrons. However, directly and accurately measuring the phase space distribution is a challenging task. In this study, we propose an innovative tomographic algorithm based on the measurement data of the accumulated beam profile obtained from the wall current monitor (WCM) in a synchrotron, to reconstruct the longitudinal phase space of the injected beam. Simulations were conducted for various initial distribution scenarios, and the results showed that this algorithm can achieve a difference of about 4% in the rms momentum spread between the initial and reconstructed phase space distribution of the injected beam. This algorithm has been applied to the China Spallation Neutron Source and successfully measured the momentum spread of the injected beam. Machine studies considering the phase error of the injected beam showed a high consistency between the reconstructed beam profiles and the measurement results from the WCM on Rapid Cycling Synchrotron. The research results demonstrate that this algorithm can be an effective approach for measuring the momentum distribution of the injected beam in a synchrotron. Furthermore, this method also has the potential to be extended to reconstruct the transverse phase space of the injected beam. Published by the American Physical Society 2024

Special affine Fourier transform of tempered distributions and pseudo-differential operators

The primary aim is to develop a new class of pseudo-differential operators by incorporating the Special Affine Fourier Transform (SAFT) and some of its fundamental properties in Schwartz and tempered distribution space. The secondary aim is to explore the utility of the SAFT in constructing a new generalized heat equation and derive its analytical solution. Further, we have investigated particular cases of the proposed generalized heat equation. Furthermore, we have visually illustrated solutions of this equation via MATLAB R2023b.

An essay on semiclassical analysis for microlocal singularities, turbulence intensity and integration of singularities by Schrödinger equation in probabilistic behavior

The Schrödinger equation governs the probabilistic behavior of quantum particles through the wave function. Microlocal singularities denote regions with significantly high probability density or abrupt changes therein. By visualizing the probability distribution in time and space, we discern regions with higher probability density, indicative of potential microlocal singularities. These regions probably correspond to areas with a greater probability of particle presence. Such analysis aligns with Theorem 1, predicting characteristics of microlocal singularities of wave functions. Furthermore, Theorem 2 postulates that semiclassical path integrals along these singularities contribute significantly to solving the Schrödinger equation. Interpreting the temporal evolution of the probability density in the probability distribution visualization reveals the propagation of the particle over time. Regions of high density mean likely presence of particles at specific times, aligning with the predictions of Theorem 2. Consequently, the analysis of the contribution of high-density regions to the temporal evolution of the wave function resembles semi-classical path integral calculations. Thus, our findings demonstrate that visualization of probability distributions obtained from the numerical resolution of the Schrödinger equation allows a comprehensive interpretation of the behavior of quantum particles, consistent with the theorems.

Free entropy minimizing persuasion in a predictor–corrector dynamic

Persuasion is the process of changing an agent’s belief distribution from a given (or estimated) prior to a desired posterior. A common assumption in the acceptance of information or misinformation as fact is that the (mis)information must be consistent with or familiar to the individual who accepts it. We model the process as a control problem in which the state is given by a (time-varying) belief distribution following a predictor–corrector dynamic. Persuasion is modeled as the corrector control signal with the performance index defined using the Fisher–Rao information metric, reflecting a fundamental cost associated to altering the agent’s belief distribution. To compensate for the fact that information production arises naturally from the predictor dynamic (i.e., expected beliefs change) we modify the Fisher–Rao metric to account just for information generated by the control signal. The resulting optimal control problem produces non-geodesic paths through distribution space that are compared to the geodesic paths found using the standard free entropy minimizing Fisher metric in several example belief models: a Kalman Filter, a Boltzmann distribution and a joint Kalman/Boltzmann belief system.

Velocity-space distribution function of fast ions in a sawtoothing plasma

This study explores the influence of sawtooth oscillations on the velocity space distribution of fast ions in tokamak plasma discharges. The relevant Fokker–Planck equation for fast ions is solved analytically. Two distinct effects arising from the temperature drop associated with a sawtooth crash and their impact on the distribution function of fast ions are considered. The first effect involves the modulation of the fusion alpha particle source on the timescale of the sawtooth period, linked to the drop in fusion yield resulting from the sawtooth temperature relaxations. The second effect is tied to the increase of the slowing-down time during the sawtooth ramp, causing particles born later in the sawtooth cycle to experience reduced slowing down compared to those born right after the crash, creating an accumulation-like mechanism at higher energies. In regimes where the sawtooth period is shorter than the fast ion slowing-down time, the combined influence of these effects gives rise to fast ion distribution functions that transiently exhibit positive slopes in velocity space.

Interactions between different birds of prey as a random point process

The two-dimensional (2D) Coulomb gas is a one-parameter family of random point processes, depending on the inverse temperature β. Based on previous work, it is proposed as a simple statistical measure to quantify the intra- and interspecies repulsion among three different highly territorial birds of prey. Using data from the area of the Teutoburger Wald over 20 years, we fit the nearest-neighbour and next-to-nearest neighbour spacing distributions between the respective nests of the goshawk, eagle owl and the previously examined common buzzard to β of the Coulomb gas. Within each species, the repulsion measured in this way deviates significantly from the Poisson process of independent points in the plane. In contrast, the repulsion amongst each of two species is found to be considerably lower and closer to Poisson. Methodologically, we investigate the influence of the terrain, of a shorter interaction range given by the 2D Yukawa interaction, and the statistical independence of the time moving average we use for the yearly ensembles of occupied nests. We also check that an artificial random displacement of the original nest positions of the order of the mean level spacing quickly destroys the repulsion measured by β > 0. A simple, approximate analytical expression for the nearest-neighbour spacing distribution derived from non-Hermitian random matrix theory proves to be very useful.

Complex-valued Wigner entropy of a quantum state

It is common knowledge that the Wigner function of a quantum state may admit negative values, so that it cannot be viewed as a genuine probability density. Here, we examine the difficulty in finding an entropy-like functional in phase space that extends to negative Wigner functions and then advocate the merits of defining a complex-valued entropy associated with any Wigner function. This quantity, which we call the complex Wigner entropy, is defined via the analytic continuation of Shannon’s differential entropy of the Wigner function in the complex plane. We show that the complex Wigner entropy enjoys interesting properties, especially its real and imaginary parts are both invariant under Gaussian unitaries (displacements, rotations, and squeezing in phase space). Its real part is physically relevant when considering the evolution of the Wigner function under a Gaussian convolution, while its imaginary part is simply proportional to the negative volume of the Wigner function. Finally, we define the complex-valued Fisher information of any Wigner function, which is linked (via an extended de Bruijn’s identity) to the time derivative of the complex Wigner entropy when the state undergoes Gaussian additive noise. Overall, it is anticipated that the complex plane yields a proper framework for analyzing the entropic properties of quasiprobability distributions in phase space.

Turbulent System Dynamics: An Introduction to Spectral Decomposition and External Forcing in Sobolev Spaces

Turbulent systems represent a complex and ubiquitous phenomenon in various natural and engineered environments. This study investigates the dynamics of turbulent systems through the lens of four fundamental theorems. The first theorem establishes a spectral decomposition of the velocity correlation function, shedding light on the coherent and incoherent structures within turbulent flows. The second theorem delves into the energy distribution in Sobolev spaces, providing insights into the regularity and properties of turbulent solutions. Expanding on these findings, the third theorem explores the influence of external forcing on energy distribution, elucidating how external factors shape turbulent behavior. Building upon these insights, the fourth theorem integrates the concepts from the previous theorems, describing the interplay between spectral decomposition, energy distribution, and external forcing effects in turbulent systems. This comprehensive analysis offers a deeper understanding of turbulent dynamics, with implications for fields such as fluid mechanics, atmospheric science, and engineering. By elucidating the underlying mechanisms governing turbulent behavior, this study paves the way for improved modeling, prediction, and control of turbulent systems in various practical applications.

M3D-K simulations of beam-driven instabilities in an energetic particle dominant KSTAR discharge

We perform a systematic simulation study of energetic passing particle-driven instabilities in KSTAR using the kinetic-MHD hybrid code M3D-K. Linear simulation results show that the observed n = 1 mode in the early phase of the discharge is the low-frequency fishbone driven by energetic passing beam ions. The mode frequency computed is in a good agreement with the experimental measurement. Nonlinear simulations show that the frequency of the n = 1 mode jumps up to a higher value corresponding to the β-induced Alfvén eigenmode (BAE). In the later phase of the discharge, the simulated n = 5 mode is identified as a BAE in its linear phase. In the nonlinear phase, the n = 5 mode exhibits a similar frequency jump to a higher value of an energetic particle (EP) mode after mode saturation. Analysis of perturbed beam ion distributions in phase space shows that these new modes in nonlinear stages are driven by new resonances due to nonlinearly evolved beam ion distributions. Further simulations of a beam beta scan for the n = 5 mode show that the frequency jump disappears for a sufficiently small beam beta or beam ion drive. This result may explain the non-existence of frequency jump in the experiment. Finally, the impact of toroidal rotation on mode characteristics is investigated, showing that it has a marginal influence on EP driven modes.

Investigation of physics-informed deep learning for the prediction of parametric, three-dimensional flow based on boundary data

The placement of temperature sensitive and safety-critical components is crucial in the automotive industry. It is therefore inevitable, even at the design stage of new vehicles, that these components are assessed for potential safety issues. However, with increasing number of design proposals, risk assessment using Computational Fluid Dynamics (CFD) quickly becomes expensive. We therefore present a parameterized surrogate model for the prediction of three-dimensional flow fields in aerothermal vehicle simulations. The proposed physics-informed neural network (PINN) design is aimed at learning families of flow solutions according to a geometric variation. The novelty of our method compared to existing works in the field of PINN lies in the extension of parametric flow prediction to three-dimensional space by applying a mini-batch based Quasi-Newton optimization. We contribute a parametric minibatch training algorithm which enables the utilization of the large datasets necessary for the three-dimensional flow modeling. Further, we introduce a continuous resampling algorithm that allows to represent domain variations, while operating on one static dataset of reduced size. In scope of this work, we could show that our nondimensional, multivariate scheme can be efficiently extended to predict the velocity and pressure distribution in three-dimensional space for different design scenarios and geometric scales. Every feature of our methodology is tested individually and verified against conventional CFD simulations. Finally, we apply our proposed method in context of an exemplary real-world automotive application.

A grasp of police research: characteristics of empirical research on police careers based on multiple scoping reviews

PurposeThis article provides an overview of the literature characteristics of empirical research on topics related to police careers from 2000 to 2021. Methodology, distribution in time and space and types of publication are presented. Recommendations for new research avenues are given.Design/methodology/approachEight scoping reviews on specific topics were carried out by criminology students under the close guidance and supervision of the first author, an academic researcher. The reviews followed the same procedure, enabling an overarching reflection.FindingsThe scoping reviews resulted in 179 unique publications for analysis. It appears that the topic of police professional competencies is studied more often in the field of police careers (n = 55), in contrast to informal learning in police training (n = 4) which was studied the least frequently. Since 2012, there has been a noticeable increase in the number of publications. Publications in scientific journals are by far the most common (n = 153), as is a quantitative research design (n = 123). All topics have been studied in Europe and North America.Research limitations/implicationsMore qualitative research and international dissemination of empirical results are recommended to gain a deeper understanding of police careers. As for the limitations, specific topics were selected, which limits the scope of the findings. Working with students for data collection has its benefits in terms of workload, but comes with potential limitations in terms of quality. It is recommended to conduct a screening using the four-eyed principle, as was done here by the first and second authors. Additionally, the review protocol (e.g. keywords and databases) has an influence on the outcome. Different choices may lead to different results.Originality/valueA comprehensive analysis of police career literature is made based on eight scoping reviews that followed the same procedure. It allows to study the literature in a broad sense rather than studying one topic in depth.

Permeability anisotropy analysis of two-phase flow during hydrate dissociation process

Natural gas hydrate (NGH) is a versatile and energy source. But in the actual extraction process, NGH in the reservoir will be out of phase equilibrium conditions and dissociate. This will induce alterations in permeability characteristics of reservoir and will exert a significant influence on the assessment of hydrate reservoir capacity. In the research, an innovative CT triaxial system was used to obtain the micro-structure of sediment specimen during hydrate dissociation. The anisotropy of absolute permeability (k), capillary pressure (Pc) and relative permeability (kr) were also analyzed using the pore network model (PNM). As demonstrated by the results, k increases gradually in all three directions during the dissociation. Pc gradually decreases. The degree of anisotropy of both Pc and gas-water relative permeability (krg and krw) gradually decreases. The impact of hydrate dissociation on the kr anisotropy during primary gas flooding surpasses that observed during secondary water flooding. As hydrate saturation decreases, the krw increases and the krg decreases in the horizontal directions. The krw does not change significantly and the krg increases in the vertical direction. Along the length of the sample, the distribution of hydrate and pore space exhibits heterogeneity across the sections. This inhomogeneous distribution will lead to anisotropy in permeability.