Occupation Density Research Articles

The Paradox of Global Multireference Diagnostics.

Modern computational chemistry methods are a useful tool for modeling many chemical systems, but they are challenged by multireference species (e.g., transition metals). A variety of diagnostics have been formulated to identify such cases. They are typically developed by analyzing multireference characters of small molecules, and many provide an average picture of the entire system. We caution the use of such diagnostics for large systems because large systems may include parts with varying degrees of multireference characters. Specifically, a small but highly multireference component may yield a large error in absolute terms, which may be masked in an average value over the entire molecule. As the calculation of molecular relative energies often concerns errors in absolute terms, such a false sense of safety may be detrimental. A prospective means to tackle this challenge is to use fractional occupation density to identify potentially problematic components in a system and then examine this moiety with higher-level computations on appropriately constructed smaller models.

Fluctuations of the Occupation Density for a Parking Process

Consider the following simple parking process on Λn:={-n,…,n}d,d≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _n:= \\{-n, \\ldots , n\\}^d,d\\ge 1$$\\end{document}: at each step, a site i is chosen at random in Λn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _n$$\\end{document} and if i and all its nearest neighbor sites are empty, i is occupied. Once occupied, a site remains so forever. The process continues until all sites in Λn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _n$$\\end{document} are either occupied or have at least one of their nearest neighbors occupied. The final configuration (occupancy) of Λn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _n$$\\end{document} is called the jamming limit and is denoted by XΛn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\\Lambda _n}$$\\end{document}. Ritchie (J Stat Phys 122:381–398, 2006) constructed a stationary random field on Zd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}^d$$\\end{document} obtained as a (thermodynamic) limit of the XΛn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\\Lambda _n}$$\\end{document}’s as n tends to infinity. As a consequence of his construction, he proved a strong law of large numbers for the proportion of occupied sites in the box Λn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _n$$\\end{document} for the random field X. Here we prove the central limit theorem, the law of iterated logarithm, and a gaussian concentration inequality for the same statistics. A particular attention will be given to the case d=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=1$$\\end{document}, in which we also obtain new asymptotic properties for the sequence XΛn,n≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\\Lambda _n},n\\ge 1$$\\end{document}.

Relation between occupation density and ambient noise in open plan offices: a study based on field measurements

Although progress has been made over the last decade on the issue of well-being in open-plan offices, recent surveys show that employees are still dissatisfied with their working environment, particularly the noise environment, remains. However, standards exist to help ensure that open-plan offices are designed to provide the best possible working environment. But, because of the scope of these standards, their recommendations can be contradictory. For example, the French ergonomics standard NF X35-102 makes recommendations on the sizing of workstations, likely to lead to office occupancy densities that are incompatible with the ambient noise level objectives defined in the ISO 22955 standard. To resolve these contradictions, a field measurement protocol was implemented. It consists in (1) a real-time count of the number of people in the office, (2) a measurement of ambient noise, (3) a questionnaire assessing employees' perception of their physical working environment. The data collected in several French companies will make it possible to establish relationships between the ambient noise level, the occupancy density and the perception of noise levels. This paper presents an occupancy sensor developed for this study and measurements of ambient noise level and occupancy ratio during a working day in an open-plan office.

Modelling cultural responses to disease spread in Neolithic Trypillia mega-settlements

As zoonotic diseases coevolved with early agriculture, social distancing within dense human settlements could have conferred a selective advantage in terms of infection risk. Here, we consider the case of Trypillia mega-settlements after 4000 BC, as virulent diseases began affecting humans in the Black Sea region. Through epidemiological susceptible-infected-recovered-susceptible (SIRS) models situated on clustered networks and on a site plan of a Trypillia mega-settlement, we show the adaptive benefits of decreasing either occupation density or the frequency of interactions with other communities across the settlement. We explore critical thresholds in these parameters that may shed light on the fluctuations of population densities at Trypillia mega-settlements before and after approximately 3600 BCE. Our findings suggest that disease was probably a significant driver of human settlement patterns by late Neolithic times.

A class of processes defined in the white noise space through generalized fractional operators

The generalization of fractional Brownian motion in the white and grey noise spaces has been recently carried over, following the Mandelbrot–Van Ness representation, through Riemann–Liouville type fractional operators. Our aim is to extend this construction by means of more general fractional derivatives and integrals, which we define as Fourier-multiplier operators and then specialize by means of Bernstein functions. More precisely, we introduce a general class of kernel-driven processes which encompasses, as special cases, a number of models in the literature, including fractional Brownian motion, tempered fractional Brownian motion, Ornstein–Uhlenbeck process. The greater generality of our model, with respect to the previous ones, allows a higher flexibility and a wider applicability. We derive here some properties of this class of processes (such as continuity, occupation density, variance asymptotics and persistence) according to the conditions satisfied by the Fourier symbol of the operator or the Bernstein function chosen. On the other hand, these processes are proved to display short- or long-range dependence, if obtained by means of a derivative or an integral type operator, respectively, regardless of the kernel used in their definition. Finally, this kind of construction allows us to define the corresponding noise and to solve a Langevin-type integral equation.

Effect of Oriented External Electric Fields on the Electronic Properties of Linear Acenes: A Thermally Assisted Occupation DFT Study.

Recently, oriented external electric fields (OEEFs) have earned much attention due to the possibility of tuning the properties of electronic systems. From a theoretical perspective, one can resort to electronic structure calculations to understand how the direction and strength of OEEFs affect the properties of electronic systems. However, for multi-reference (MR) systems, calculations employing the popular Kohn-Sham density functional theory with the traditional semilocal and hybrid exchange-correlation energy functionals can yield erroneous results. Owing to its decent compromise between accuracy and efficiency for MR systems at the nanoscale (i.e., MR nanosystems), in this study, thermally assisted occupation density functional theory (TAO-DFT) is adopted to explore the electronic properties of n-acenes (n = 2-10), containing n linearly fused benzene rings, in OEEFs, where the OEEFs of various electric field strengths are applied along the long axes of n-acenes. According to our TAO-DFT calculations, the ground states of n-acenes in OEEFs are singlets for all the cases examined. The effect of OEEFs is shown to be significant on the vertical ionization potentials and vertical electron affinities of ground-state n-acenes with odd-number fused benzene rings. Moreover, the MR character of ground-state n-acenes in OEEFs increases with the increase in the acene length and/or the electric field strength.

Isotropization of a longitudinally expanding system of scalar fields in the 2PI formalism

Motivated by isotropization of QCD matter in the initial stages of heavy-ion collisions, we consider a system of scalar fields that undergoes a boost invariant longitudinal expansion. We use the framework of the two-particle irreducible (2PI) effective action, which is close to the underlying quantum field theory, and resum self-energy corrections up to three loops. The resulting 2PI equations of motion are expressed in terms of the Milne coordinates to account for longitudinal expansion. By solving numerically these equations of motion, we can extract the occupation density and the effective mass generated by in-medium interactions. At the largest values of the coupling considered in this study, we observe the onset of isotropization both in the occupation number and in the momentum dependence of the effective mass.

Theoretical Analysis of Superior Photodegradation of Methylene Blue by Cerium Oxide/Reduced Graphene Oxide vs. Graphene.

Density functional theory and a semi-empirical quantum chemical approach were used to evaluate the photocatalytic efficiency of ceria (CeO2) combined with reduced graphene oxide (rGO) and graphene (GP) for degrading methylene blue (MB). Two main aspects were examined: the adsorption ability of rGO and GP for MB, and the separation of photogenerated electrons and holes in CeO2/rGO and CeO2/GP. Our results, based on calculations of the adsorption energy, population analysis, bond strength index, and reduced density gradient, show favorable energetics for MB adsorption on both rGO and GP surfaces. The process is driven by weak, non-covalent interactions, with rGO showing better MB adsorption. A detailed analysis involving parameters like fractional occupation density, the centroid distance between molecular orbitals, and the Lewis acid index of the catalysts highlights the effective charge separation in CeO2/rGO compared to CeO2/GP. These findings are crucial for understanding photocatalytic degradation mechanisms of organic dyes and developing efficient photocatalysts.

Developing a prediction model in a lightweight packaging waste sorting plant using sensor-based sorting data combined with data of external near-infrared and LiDAR sensors.

Sensor-based material flow monitoring allows for continuously high output qualities, through quality management and process control. The implementation in the waste management sector, however, is inhibited by the heterogeneity of waste and throughput fluctuations. In this study, challenges and possibilities of using different types of sensors in a lightweight packaging waste sorting plant are investigated. Three external sensors have been mounted on different positions in an Austrian sorting plant: one Light Detection and Ranging (LiDAR) sensor for monitoring the volume flow and two near-infrared (NIR) sensors for measuring the pixel-based material composition and occupation density. Additionally, the data of an existing sensor-based sorter (SBS) were evaluated. To predict the newly introduced parameter material-specific occupation density (MSOD) of multi-coloured polyethylene terephthalate (PET) preconcentrate, different machine learning models were evaluated. The results indicate that using SBS data for both monitoring of throughput fluctuations caused by different bag opener settings as well as monitoring the material composition is feasible, if the pre-set teach-in is suitable. The ridge regression model based on SBS was comparable (RMSE = 3.59 px%, R² = 0.57) to the one based on NIR and LiDAR (RMSE = 3.1 px%, R² = 0.68). The demonstrated feasibility of the implementation at plant scale highlights the opportunities of sensor-based material flow monitoring for the waste management sector and paves the way towards a more circular plastics economy.

Reply to the Comments on Planar Tetracoordinate Hydrogen: Pushing the Limit of Multicentre Bonding

AbstractRecently, Huo et al. has commented on our communication (Angew. Chem. Int. Ed. 2024, 63, e202317312, DOI: 10.1002/anie.202317312), regarding the multireference character (MRC) of our proposed cluster. Their argument is based on small HOMO–LUMO gap, fractional occupation density (FOD) and CASPT2(12,13) calculations. They also proposed that the singlet planar In4H+ cluster cannot be observed. We present our calculations which reveals that some of their arguments are based on wrong interpretation of data and inadequate use of methodology. While we certainly agree with the strong physical ground of FOD, CASSF and CASPT2 methodology, we believe that such analysis for clusters is not adequate.

Gibbs Properties of the Bernoulli Field on Inhomogeneous Trees under the Removal of Isolated Sites

We consider the i.i.d. Bernoulli field p with occupation density p 2 (0; 1) on a possibly non-regular countably in finite tree with bounded degrees. For large p, we show that the quasilocal Gibbs property, i.e. compatibility with a suitable quasilocal speci fication, is lost under the deterministic transformation which removes all isolated ones and replaces them by zeros, while a quasilocal specifi cation does exist at small p. Our results provide an example for an independent field in a spatially nonhomogeneous setup which loses the quasilocal Gibbs property under a local deterministic transformation.

Electronic Properties of Graphene Nano-Parallelograms: A Thermally Assisted Occupation DFT Computational Study.

In this computational study, we investigate the electronic properties of zigzag graphene nano-parallelograms (GNPs), which are parallelogram-shaped graphene nanoribbons of various widths and lengths, using thermally assisted occupation density functional theory (TAO-DFT). Our calculations revealed a monotonic decrease in the singlet-triplet energy gap as the GNP length increased. The GNPs possessed singlet ground states for all the cases examined. With the increase of GNP length, the vertical ionization potential and fundamental gap decreased monotonically, while the vertical electron affinity increased monotonically. Some of the GNPs studied were found to possess fundamental gaps in the range of 1-3 eV, lying in the ideal region relevant to solar energy applications. Besides, as the GNP length increased, the symmetrized von Neumann entropy increased monotonically, denoting an increase in the degree of the multi-reference character associated with the ground state GNPs. The occupation numbers and real-space representation of active orbitals indicated that there was a transition from the nonradical nature of the shorter GNPs to the increasing polyradical nature of the longer GNPs. In addition, the edge/corner localization of the active orbitals was found for the wider and longer GNPs.

Fall Risk Prediction in Community Dwelling Hong Kong Elderly Chinese Based on their 12-Month Prospective Fall History, Longest Pre-Retirement Occupation and Bone Mineral Density

Background: Falls are common among older adults worldwide. This study aimed to investigate and predict fall risk based on the fall incidence, longest pre-retirement occupation and bone mineral density in community dwelling Hong Kong Chinese elderly. Methods: 3,983 subjects consisting of 2,000 men (aged 72.39±5.01) and 1,983 women (aged 72.58±5.4) of community dwelling Hong Kong Chinese at age 65 or above were recruited. The subjects’ fall history in a 12-month prospective cohort, longest pre-retirement occupations, bone mineral density (BMD) level, and physical capability by the Physical Activity Scale for the Elderly Questionnaire were evaluated with their fall history four-monthly by telephone contacts. Results: Fall incidence per 1,000 person-years in women and men was 245.75 and 158.60 in osteoporosis, 246.99 and 152.98 in osteopenia, and 252.35 and 182.57 in normal BMD respectively (p<0.001). Women had higher fall incidence than in men (p<0.001). Older age (73.3± 5.2) had 2 or more falls than no fall in younger age (72.1± 4.8) [RR (95% CI) 1.21 (1.14, 1.28) per 5 years increase]. PASE scores were 92.0±48.8 in older age and 98.4±49.9 in younger age [RR (95% CI): 0.93 (0.87, 0.99) per 50-unit increase]. Pre-retired longest occupation in Building/Maintenance jobs showed the lowest fall risk [RR (95% CI): 0.58 (0.37, 0.90)], followed by Business/Finance [RR (95% CI): 0.80 (0.68, 0.95)] and Art/Design/Office [RR (95% CI): 0.81 (0.68, 0.97)] as compared to Management jobs as a standard reference. Conclusion: Women had a higher fall risk than men due to their decreasing physical capability with increasing age in Hong Kong Chinese. Longest pre-retired occupation with physically demanding jobs showed the lowest fall risk.

Unsettling in Norrland

This research uses film, photography and projection to analyse the changing space of Northern Sweden (Norrland). This peripheral region is one of the most rapidly reconfiguring spaces in Europe, with on-going programmes of corporate and state investment to exploit space and natural resources for settlement and extraction.
 The images are part of an archive of the moving of buildings, a common practice in the region. Buildings are moved in relation to changing environmental conditions and now urban land values and global property speculation. It is understood to be a distinct process of what David Harvey has described as “remaking capitalism’s geography”1
 Images analyse the material conditions, ideology and power in this frontier economy. The project considers an architecture of de-growth2, challenging ideas of the expanding urbanisation of Norrland. As land values and modes of occupation change, buildings are displaced from the urban centre to increase occupation density through speculative investment. This process displaces social space and previous land formations. The city of Kiruna has been entirely displaced by expanding mine workings. The practice of relocation also has the capacity to shift large-scale historic architectures, as a distinct form of caretaking.
 In this moment of new waves of investment in mining and forestry, of urbanisation of parts of the region, predicated on an underlying and largely uncontested agenda of ‘development’, the archive offers other conceptions of space and architectural production.
 The images consider the wrenching of a house from its location and moving it to another location, documenting this process of detachment. It records the re-arrangements of space between land and building. Displacement is illuminated through projections to unsettle, by superimposing architectures onto previous conditions. Keywords: Unsettling, de-growth, relocation, house-moving, displacement.
 Cover image: Robin Serjeant, “Midwinter projection inside the house.”, Degernäs, December 2021, Film stills

Towards digital twins of waste sorting plants: Developing data-driven process models of industrial-scale sensor-based sorting units by combining machine learning with near-infrared-based process monitoring

Sorting plants are crucial for effective recycling, but their optimization can be challenging due to the heterogeneity of waste streams. We introduce a novel approach to holistically optimize sorting plants using digital twins containing data-driven process models. To demonstrate their technical feasibility, we developed a data-driven process model for industrial-scale sensor-based sorting (SBS) units by combining near-infrared process monitoring with machine learning. Our results indicate a sorting performance change (F1-score) in the SBS unit by 0.22 a% for +1% occupation density and +0.19 a% for +1 wt% target material share. An artificial neural network predicted the SBS behavior with a 3.0% mean absolute error. Our case study demonstrates the potential of data-driven process models for digital twins by clarifying the influence of throughput fluctuations on SBS performance and simulating different SBS cascade designs, thus paving the way towards improved design and operation of sorting plants and a more circular future.

The percolating cluster is invisible to image recognition with deep learning

We study the two-dimensional site-percolation model on a square lattice. In this paradigmatic model, sites are randomly occupied with probability p; a second-order phase transition from a non-percolating to a fully percolating phase appears at occupation density pc , called percolation threshold. Through supervised deep learning approaches like classification and regression, we show that standard convolutional neural networks (CNNs), known to work well in similar image recognition tasks, can identify pc and indeed classify the states of a percolation lattice according to their p content or predict their p value via regression. When using instead of p the spatial cluster correlation length ξ as labels, the recognition is beginning to falter. Finally, we show that the same network struggles to detect the presence of a spanning cluster. Rather, predictive power seems lost and the absence or presence of a global spanning cluster is not noticed by a CNN with a local convolutional kernel. Since the existence of such a spanning cluster is at the heart of the percolation problem, our results suggest that CNNs require careful application when used in physics, particularly when encountering less-explored situations.

Real-Time Extension of TAO-DFT.

Thermally assisted occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Moreover, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

Occupation density of every chess piece by phases, levels of game, outcomes and phase-space according to their entropy differences

In this paper, we statistically analyze the density of each chess piece in four square concentric frames for different skill levels (according to the Elo ranking system), phases (opening, middlegame and endgame) and outcomes. The results indicate a tendency for pawns, knights and bishops to move towards the central areas, particularly during the opening phase. Additionally, we identified intrinsic entropy patterns for each piece throughout the entire game, independent of player skill level. We constructed a phase-space from entropy delay time series to provide probabilistic predictions for game outcomes.

Electronic and optical properties of metal decorated graphitic carbon nitride M/g‐C3N4 (M = K, Ca, Ga, Ni, Cu): A theoretical study

AbstractThe influence of single metal doping (K, Ca, Ga, Ni, Cu) on the electronic and optical characteristics of graphitic carbon nitride (g‐C3N4) was explored utilizing a semi‐empirical tight‐binding‐based quantum chemistry technique (GFN2‐xTB). The calculated results of interaction energy, analyzing the charge transfer, and the bond order revealed that chemical bonds were formed between the metal atom and g‐C3N4. Furthermore, the bond formation between doped metal atoms with g‐C3N4 is predominantly covalent, except for K. The fractional occupation density analysis of the M/g‐C3N4 systems shows different distributions of active electrons across the material systems. The frontier molecular orbitals (HOMO, LUMO) distribution utilized to assess the photogenerated electron and hole recombination of the catalytic systems. Due to the efficient separation of the photogenerated electron‐hole pairs, Ni/g‐C3N4 exhibits the highest photocatalytic activity among the studied systems. On the basis of more extensive electronic and optical property calculations including ionization potential, electron affinity, global electrophilicity index, band gap energy, and UV‐VIS spectra, the Ni/g‐C3N4 photocatalyst's high activity can be explained and interpreted.

Explaining population booms and busts in Mid-Holocene Europe

Archaeological evidence suggests that the population dynamics of Mid-Holocene (Late Mesolithic to Initial Bronze Age, ca. 7000–3000 BCE) Europe are characterized by recurrent booms and busts of regional settlement and occupation density. These boom-bust patterns are documented in the temporal distribution of 14C dates and in archaeological settlement data from regional studies. We test two competing hypotheses attempting to explain these dynamics: climate forcing and social dynamics leading to inter-group conflict. Using the framework of spatially-explicit agent-based models, we translated these hypotheses into a suite of explicit computational models, derived quantitative predictions for population fluctuations, and compared these predictions to data. We demonstrate that climate variation during the European Mid-Holocene is unable to explain the quantitative features (average periodicities and amplitudes) of observed boom-bust dynamics. In contrast, scenarios with social dynamics encompassing density-dependent conflict produce population patterns with time scales and amplitudes similar to those observed in the data. These results suggest that social processes, including violent conflict, played a crucial role in the shaping of population dynamics of European Mid-Holocene societies.