Convergent Patterns Research Articles

The influence of Mach number and overpressure on the structure of supersonic gas jets

ABSTRACT The Mach number is the primary parameter in determining the intrinsic driving properties, and effect on the environment of a supersonic jet. In the most basic form, a jet is released when a wall of a large high-pressure gas reservoir is punctured. The resulting high-pressure jet contains a configuration of shocks that continue to disturb the environment after the initial bow shock has passed. Here, we perform numerical simulations to determine the properties attributable to pure adiabatic hydrodynamic effects, taking a uniform stream out of a circular nozzle. We take a range of Mach numbers that, along with the jet overpressure, determine the flow pattern and shock locations. We distinguish conditions that generate Mach shock discs rather than a diamond pattern of oblique regular reflections. Potential observational diagnostics explored include the disc size, the distance from the nozzle, and oscillations in shock positions. Rapid oscillations occur in the divergent–convergent pattern through a feedback/hysteresis effect promoted by the ambient medium. The underlying flow patterns are independent of relative jet density, but heavy jets display both lower amplitude and lower frequency oscillations. We also study the energy transferred into the environment. Overpressured jets may contribute to noise and sound wave generation through screeching. However, these oscillations in the near-field are not sufficiently significant to regulate star and galaxy formation. We expect that upcoming high dynamic range and resolution observations will increasingly detect the shock patterns as jet gas transits from protostellar and galactic cores.

Research on airflow convergence patterns and air distribution characteristics under multi-column attachment ventilation

Multi-column attachment ventilation (M-CAV) is usually delivered to the occupied zone by floor-attached airflows in large spaces. However, after the floor-attached airflow converges, the original air distribution will change, which will have an important impact on the traditional air distribution design. In this paper, airflow convergence patterns and air distribution characteristics in the most common double-column and tri-column layouts are studied by experiments and computational fluid dynamics (CFD) simulations. A 1:3 scaled-down model was established for velocity experiments and flow field visualization, and the results were used to verify and optimize the CFD model. The results indicated a seagull-like convergence flow pattern under the symmetric double-column layout. Under the axisymmetric layout with different column spacings, the floor-attached airflow in the half-open air outlet mode exhibited full convergence with the merging point (point MP) and combined point (point CP), partial convergence with point MP, and non-convergence without point MP and point CP. Under the centrosymmetric layout, an M-shaped velocity distribution was formed, and no airflow converged. For equal-velocity conditions, the dimensionless convergence axial velocity distributions for different air supply velocities was approximately consistent. In the fully-open air outlet mode, the floor-attached airflow could be divided into the collision-dominated region, the combined collision and convergence-dominated region, and the convergence-dominated region based on the forms of airflow interaction. For unequal-velocity conditions, the high-velocity airflow restricted the diffusion of the low-velocity airflow.

When tainted money should fund public goods: fundraising professional and public moral preferences.

Philanthropy is essential to public goods such as education and research, arts and culture, and the provision of services to those in need. Providers of public goods commonly struggle with the dilemma of whether to accept donations from morally tainted donors. Ethicists also disagree on how to manage tainted donations. Forgoing such donations reduces opportunities for societal well-being and advancement; however, accepting them can damage institutional and individual reputations. Half of professional fundraisers have faced tainted donors, but only around a third of their institutions had relevant policies (n = 52). Here, we draw on two large samples of US laypeople (ns = 2,019; 2,566) and a unique sample of experts (professional fundraisers, n = 694) to provide empirical insights into various aspects of tainted donations that affect moral acceptability: the nature of the moral taint (criminal or morally ambiguous behavior), donation size, anonymity, and institution type. We find interesting patterns of convergence (rejecting criminal donations), divergence (professionals' aversion to large tainted donations), and indifference (marginal role of anonymity) across the samples. Laypeople also applied slightly higher standards to universities and museums than to charities. Our results provide evidence of how complex moral trade-offs are resolved differentially, and can thus motivate and inform policy development for institutions dealing with controversial donors.

Multimodal meaning-making of aggression in English song narrative: A cognitive-pragmatic perspective

This article addresses cognitive and pragmatic aspects of the multimodal meaning-making of AGGRESSION in the English song narrative. The cognitive-pragmatic foundations integrate cognitive and pragmatic aspects with multimodal ones, which allows to explain how signs of different modes and semiotic resources instantiate the concept and which cognitive features are decisive for (re)construction of meaning by performers and viewers. Cognitive features have verbal and non-verbal implementation through visual and auditory modes. The verbal semiotic resource, implemented through auditory and visual modes, contains lexical and pragmatic means of direct/indirect realization of aggression. Lexical means include words that name/describe/express aggression, as well as lexemes that acquire the aggressive meaning in a certain context. Pragmatic means are represented by expressive statements realizing threat, order, reproach, and accusation. The non-verbal semiotic resource is also represented through both modes and is characterized by semiotic heterogeneity, including prosodic/mimic/gestural features, various aspects of performers’ appearance, music clip design and lighting. They include hoarse voice/high exalted vocals/screaming; aggressive look/bulging eyes/wide open mouth/tense distorted face; active movements/fight; dark clothes/ dark make-up/tattoos. The musical component is characterized by the lower register, alternating consonance and dissonance, and a fast tempo. The lighting includes the play of light and shadow, and flashes. The construction of aggression appears as a result of the integration of semiotic elements into a multimodal blend, which is an emergent entity. Semantic relations between the blend components are based on the complementarity or contradiction of their elements, which makes it possible to single out convergent and divergent constructive patterns.

Gene-rich plastid genomes of two parasitic red algal species, Laurencia australis and L. verruciformis (Rhodomelaceae, Ceramiales), and a taxonomic revision ofJanczewskia.

Parasitic red algae are an interesting system for investigating the genetic changes that occur in parasites. These parasites have evolved independently multiple times within the red algae. The functional loss of plastid genomes can be investigated in these multiple independent examples, and fine-scale patterns may be discerned. The only plastid genomes from red algal parasites known so far are highly reduced and missing almost all photosynthetic genes. Our study assembled and annotated plastid genomes from the parasites Janczewskia tasmanica and its two Laurencia host species (Laurencia elata and one unidentified Laurencia sp. A25) from Australia and Janczewskia verruciformis, its host species (Laurencia catarinensis), and the closest known free-living relative (Laurencia obtusa) from the Canary Islands (Spain). For the first time we show parasitic red algal plastid genomes that are similar in size and gene content to free-living host species without any gene loss or genome reduction. The only exception was two pseudogenes (moeB and ycf46) found in the plastid genome of both isolates of J. tasmanica, indicating potential for future loss of these genes. Further comparative analyses with the three highly reduced plastid genomes showed possible gene loss patterns, in which photosynthetic gene categories were lost followed by other gene categories. Phylogenetic analyses did not confirm monophyly of Janczewskia, and the genus was subsumed into Laurencia. Further investigations will determine if any convergent small-scale patterns of gene loss exist in parasitic red algae and how these are applicable to other parasitic systems.

Associating Multimodal Neuroimaging Abnormalities With the Transcriptome and Neurotransmitter Signatures in Schizophrenia.

Schizophrenia is a multidimensional disease. This study proposes a new research framework that combines multimodal meta-analysis and genetic/molecular architecture to solve the consistency in neuroimaging biomarkers of schizophrenia and whether these link to molecular genetics. We systematically searched Web of Science, PubMed, and BrainMap for the amplitude of low-frequency fluctuations (ALFF) or fractional ALFF, regional homogeneity, regional cerebral blood flow, and voxel-based morphometry analysis studies investigating schizophrenia. The pooled-modality, single-modality, and illness duration-dependent meta-analyses were performed using the activation likelihood estimation algorithm. Subsequently, Spearman correlation and partial least squares regression analyses were conducted to assess the relationship between identified reliable convergent patterns of multimodality and neurotransmitter/transcriptome, using prior molecular imaging and brain-wide gene expression. In total, 203 experiments comprising 10 613 patients and 10 461 healthy controls were included. Multimodal meta-analysis showed that brain regions of significant convergence in schizophrenia were mainly distributed in the frontotemporal cortex, anterior cingulate cortex, insula, thalamus, striatum, and hippocampus. Interestingly, the analyses of illness-duration subgroups identified aberrant functional and structural evolutionary patterns: Lines from the striatum to the cortical core networks to extensive cortical and subcortical regions. Subsequently, we found that these robust multimodal neuroimaging abnormalities were associated with multiple neurobiological abnormalities, such as dopaminergic, glutamatergic, serotonergic, and GABAergic systems. This work links transcriptome/neurotransmitters with reliable structural and functional signatures of brain abnormalities underlying disease effects in schizophrenia, which provides novel insight into the understanding of schizophrenia pathophysiology and targeted treatments.

Accuracy of Different Electronic Basis Set Families for Anharmonic Molecular Vibrations: A Comprehensive Benchmark Study.

In this work, the accuracy and convergence of different electronic basis set families for the computation of anharmonic molecular vibrational spectroscopic calculations are benchmarked. A series of 39 different basis sets from different families following their hierarchy are assessed on VSCF and VSCF-PT2 algorithms with commonly used MP2 and DFT based B3LYP-D potentials for a set of molecular systems. Such an effort has been validated in a previous work ( J. Phys. Chem. A 2020, 124, 9203-9221) with split-valence basis sets for fundamentals and intensities. Here, fundamental transitions, vibrationally excited states, and intensities are compared with the experimental data to estimate the accuracy for a series of Jensen, Dunning, Calendar, Karlsruhe, and Sapporo basis set families. The convergence of basis sets are also compared with the large ANO basis set. Comprehensive statistical error analysis in terms of accuracy and precision was carried out to assess the performance of each basis set. It is observed that the improvement for the calculated harmonic and anharmonic values from the smaller basis sets to the medium (i.e., triple-ξ) is considerable. Beyond this, from medium to large basis sets, the convergence is slow and mostly posits nearly converged values. Basis sets with and without diffuse functions offer characteristically different accuracies and convergence patterns. Finally, recommendations are given on the choice of basis set chosen as black-box which can balance between accuracy and computational time, estimation of the errors, and their selections especially for large molecules.

The Changing Shape of Spatial Income Disparities in the United States

Spatial income disparities have increased in the US since 1980, a pattern linked to major social, economic, and political challenges. Yet, today’s spatial inequality, and how it relates to the past, remains insufficiently well understood. The primary contribution of this article is to demonstrate a deep polarization in the American spatial system—yet one whose character differs from that commonly reported on in the literature. The increase in spatial inequality since 1980 is almost entirely driven by a small number of populous, economically important, and resiliently high-income superstar city-regions. But we also show that the rest of the system exhibits a long-run pattern of income convergence over the study period. A secondary contribution is historical: today’s superstars have sat durably atop the urban hierarchy since at least 1940. Third, we describe six distinctive pathways of development that regions follow between 1940 and 2019, with certain locations catching up, falling behind, and surging ahead. We explore the role played by initial endowments in driving locations down these pathways, finding population, education, industrial structure, and immigrant attraction to be key distinguishing features. These insights are enabled by a fourth contribution: methodologically, we use group-based trajectory modeling—an approach new to the field that integrates top-down and bottom-up views of the evolving national spatial system. We conclude by exploring implications for the mid-twenty-first century.

Basis Set Effects on the Stabilities and Interaction Energies of Small Amide Molecules Adsorbed on Kaolinite Surface

Adsorptions of small amide molecules, acetamide (AA) and N-methyl-acetamide (NMA) on the surface of kaolinite are investigated in this study. The focus is on the basis set effects towards the stabilities and the interaction energies of the molecules on the Al–O surface. With a fixed B3LYP functional, we increased the size of the basis sets for the single-point calculations, to find the converged interaction energies and obtain the relative stabilities. We found that, under the direct usage of Pople-type and Dunning’s correlation consistent basis sets, it is not possible to achieve the pattern of convergence for the interaction energies and the relative stabilities. Compared to the complete basis set (CBS) extrapolation scheme, the double zeta basis sets deviated the most, in the range of 21 to 27%, while it is from 1 to 7% for the triple zeta basis sets. Based on the results, we suggest using 6-311++G(2df,2pd) or cc-pVQZ for energy-related quantities. Compared to AA, NMA attached more strongly by 0.5 eV on the surface of Al–O.

Temporal–Spatial Variations and Convergence Analysis of Land Use Eco-Efficiency in the Urban Agglomerations of the Yellow River Basin in China

Achieving synergistic development of efficient urban land use and the natural environment is crucial in promoting green urbanization. The assessment of land use eco-efficiency (LUEE) and its temporal–spatial changes provides an effective means of quantifying the relationship between the urban ecological environment and land use. Targeting 55 selected cities in the Yellow River Basin (YRB), in this study, we utilize the Super-EBM method to gauge the LUEE. We explore the temporal patterns and the spatial convergence of LUEE utilizing kernel density estimation and spatial econometric methods. Considering the resource and environmental costs of land use, we assumed the industrial pollutant emissions generated during urban land use as the undesired outputs and designed a framework for measuring the level of LUEE under double constraints, which theoretically revealed the formation process and spatial convergence mechanism of LUEE. The results show the following: (1) Throughout the sample period, the LUEE of the YRB urban agglomeration decreased from 0.158 in 2009 to 0.094 in 2020, indicating a decreasing spatial disparity in LUEE over time. Notably, the Lanxi urban cluster exhibited the largest gap in LUEE, whereas the Guanzhong Plain urban agglomeration displayed the smallest gap. The hyper-variable density exceeded the inter-group gap as the main factor leading to the difference in LUEE. (2) Although the LUEE of urban agglomerations has increased, there still exists a noticeable polarization phenomenon. (3) The LUEE of YRB demonstrates a pattern of conditional convergence and exerts a significant spatial spillover effect. Over time, the LUEE of YRB will tend towards an individual steady state. The findings have implications for strengthening linkage and synergy among cities in YRB, promoting factor integration across administrative regions, and formulating heterogeneous policies.

Individual identity information persists in learned calls of introduced parrot populations.

Animals can actively encode different types of identity information in learned communication signals, such as group membership or individual identity. The social environments in which animals interact may favor different types of information, but whether identity information conveyed in learned signals is robust or responsive to social disruption over short evolutionary timescales is not well understood. We inferred the type of identity information that was most salient in vocal signals by combining computational tools, including supervised machine learning, with a conceptual framework of "hierarchical mapping", or patterns of relative acoustic convergence across social scales. We used populations of a vocal learning species as a natural experiment to test whether the type of identity information emphasized in learned vocalizations changed in populations that experienced the social disruption of introduction into new parts of the world. We compared the social scales with the most salient identity information among native and introduced range monk parakeet (Myiopsitta monachus) calls recorded in Uruguay and the United States, respectively. We also evaluated whether the identity information emphasized in introduced range calls changed over time. To place our findings in an evolutionary context, we compared our results with another parrot species that exhibits well-established and distinctive regional vocal dialects that are consistent with signaling group identity. We found that both native and introduced range monk parakeet calls displayed the strongest convergence at the individual scale and minimal convergence within sites. We did not identify changes in the strength of acoustic convergence within sites over time in the introduced range calls. These results indicate that the individual identity information in learned vocalizations did not change over short evolutionary timescales in populations that experienced the social disruption of introduction. Our findings point to exciting new research directions about the robustness or responsiveness of communication systems over different evolutionary timescales.

On the Difference in Cycling Pattern on Linear and Higher-Order Effect Designs

D-optimality is a design criterion that seeks to maximize the determinant of the information matrix, or equivalently minimize the determinant of the inverse information matrix of the design. This design criterion results in maximizing the differential Shannon information content of the parameter estimates. Cycling, a phenomenal problem associated with the construction of optimal designs, impedes the rate of convergence to such desired optimum, whenever it occurs in a variance exchange process. Different polynomial functions may have varying effects on the pattern of convergence due to cycling. This paper seeks to determine the nature and extent to which the influence of cycling affects the pattern of convergence on Linear, Interactive, and Quadratic order effect designs. The variance exchange algorithmic search method was adopted based on the philosophy of numerically searching the design space for optimum designs. Two and three-variable response functions are used in the investigation of even and odd-sized point designs. Generated data from designs of sizes 10 and 11 were employed in the investigation. Numerical illustrations were given to ascertain the pattern of convergence on each of the degree polynomial designs. The computations and graphs were conducted in R version 4.1.1 (2021). The results show that cycling patterns differ with respect to the degree of the response function whether it is of even or odd-sized design, or has two or three variables. The result will enable researchers to find appropriate measures to accommodate the challenge posed by cycling.

Investigating the Change Pattern in Adsorption Properties of Soil Media for Non-Polar Organic Contaminants under the Impact of Freezing and Thawing

The adsorption of petroleum hydrocarbons by soils in the unsaturated zone determines the amount that goes into the groundwater. However, the intricate behavior of petroleum hydrocarbon adsorption in soil media under the influence of freeze–thaw conditions in globally prevalent seasonally frozen regions remains unclear. Alkanes as a non-polar compound are an important part of petroleum hydrocarbons. We conducted field-scale seasonal freeze-thaw experiments using n-dodecane to quantify the dynamic patterns and influencing factors of the physicochemical properties of soil media and their adsorption capacity for petroleum hydrocarbons during different freeze–thaw cycles. Our findings demonstrated that, as the number of natural freeze–thaw cycles increased, the proportion of soil micro-agglomerates rose rapidly, thereby expanding the available adsorption sites and enhancing the adsorption capacity for non-polar organic pollutants. The rise in sorption capacity for the outdoor freeze–thaw experimental group surpassed that of the indoor room-temperature control group by an impressive 75.57%, showing the enhancement of the adsorption capacity for non-polar organic pollutants. Conversely, the decline in soil organic matter content during the later stages of the freeze–thaw process hampered its adsorption performance for non-polar organic pollutants. The decrease in sorption capacity for the outdoor freeze–thaw experimental group surpassed that of the indoor room temperature control group by 77.97%. By shedding light on the adsorption mechanisms of non-polar organic pollutants in soils subjected to freeze–thaw conditions, our research facilitated a comprehensive understanding and predictive modeling of this process. Furthermore, our study provided a scientific foundation for exploring the convergence and migration transformation patterns of other organic compounds in petroleum-contaminated areas within seasonally frozen regions.

Brain network analysis reveals convergent and divergent aberrations between mild stroke patients with cortical and subcortical infarcts during cognitive task performing.

Although consistent evidence has revealed that cognitive impairment is a common sequela in patients with mild stroke, few studies have focused on it, nor the impact of lesion location on cognitive function. Evidence on the neural mechanisms underlying the effects of mild stroke and lesion location on cognitive function is limited. This prompted us to conduct a comprehensive and quantitative study of functional brain network properties in mild stroke patients with different lesion locations. Specifically, an empirical approach was introduced in the present work to explore the impact of mild stroke-induced cognitive alterations on functional brain network reorganization during cognitive tasks (i.e., visual and auditory oddball). Electroencephalogram functional connectivity was estimated from three groups (i.e., 40 patients with cortical infarctions, 48 patients with subcortical infarctions, and 50 healthy controls). Using graph theoretical analysis, we quantitatively investigated the topological reorganization of functional brain networks at both global and nodal levels. Results showed that both patient groups had significantly worse behavioral performance on both tasks, with significantly longer reaction times and reduced response accuracy. Furthermore, decreased global and local efficiency were found in both patient groups, indicating a mild stroke-related disruption in information processing efficiency that is independent of lesion location. Regarding the nodal level, both divergent and convergent node strength distribution patterns were revealed between both patient groups, implying that mild stroke with different lesion locations would lead to complex regional alterations during visual and auditory information processing, while certain robust cognitive processes were independent of lesion location. These findings provide some of the first quantitative insights into the complex neural mechanisms of mild stroke-induced cognitive impairment and extend our understanding of underlying alterations in cognition-related brain networks induced by different lesion locations, which may help to promote post-stroke management and rehabilitation.

Comparing alignment toward American, British, and Indian English text-to-speech (TTS) voices: influence of social attitudes and talker guise

Text-to-speech (TTS) voices, which vary in their apparent native language and dialect, are increasingly widespread. In this paper, we test how speakers perceive and align toward TTS voices that represent American, British, and Indian dialects of English and the extent that social attitudes shape patterns of convergence and divergence. We also test whether top-down knowledge of the talker, manipulated as a “human” or “device” guise, mediates these attitudes and accommodation. Forty-six American English-speaking participants completed identical interactions with 6 talkers (2 from each dialect) and rated each talker on a variety of social factors. Accommodation was assessed with AXB perceptual similarity by a separate group of raters. Results show that speakers had the strongest positive social attitudes toward the Indian English voices and converged toward them more. Conversely, speakers rate the American English voices as less human-like and diverge from them. Finally, speakers overall show more accommodation toward TTS voices that were presented in a “human” guise. We discuss these results through the lens of the Communication Accommodation Theory (CAT).

Multi combination pattern labeling by using deep learning for chameleon rotary machine environment

Rotary machines are constructed and operated in diverse industrial environments and operate according to various specifications and characteristics. When rotary machinery constructed under dynamic real world environments is in operation, various types of vibrations are generated depending on the normal or defective state of the machinery. In this way, Numerous studies have been conducted on vibration analysis for diagnosing the state of rotary machinery. However, Without performing robust data cleansing and comprehensive labeling of the internal and external state of complex machinery, the analysis process of the condition monitoring system faces difficulties in accurately identifying the various and complex states of rotary machines and making decisions in the dynamic real world. To overcome these limitations, this paper proposes Multi Combination Pattern Labeling (MCPL) method. By simultaneously considering the complex internal and external states of rotary machines, MCPL generates detailed vibration frequency pattern criteria and labels for each state. Based on these complex pattern classifications, it is able to classify various types of abnormal states. The MCPL generates FFT patterns and spectrogram patterns by considering the simultaneous internal and external states of the rotary machine. Extracting internal and external patterns, each pattern is combined for identifying convergence patterns, named MCP. Each MCP proceeds labeling process, named MCPL, then MCPL dataset is structured. MCPL dataset is verified based on Deep Neural Network (DNN) and Convolutional Neural Network (CNN). By utilizing the DNN and CNN techniques to derive MCPL from MCP, it becomes possible to perform unbiased state diagnosis across a variety of patterns, based on the complex patterns of the internal and external states of the rotating machinery. Presenting high accuracy and stable results, MCPL are able to classify rotary machine states and detect anomalies under the convergence environment. Our source code and utilized data are available on https://github.com/JEJESBSB/Journal-of-Big-Data.

Convergent patterns in multitrophic biodiversity effects on yield across ecosystems.

Convergent patterns in multitrophic biodiversity effects on yield across ecosystems.

Rapid Evolution of Glycan Recognition Receptors Reveals an Axis of Host-Microbe Arms Races beyond Canonical Protein-Protein Interfaces.

Detection of microbial pathogens is a primary function of many mammalian immune proteins. This is accomplished through the recognition of diverse microbial-produced macromolecules including proteins, nucleic acids, and carbohydrates. Pathogens subvert host defenses by rapidly changing these structures to avoid detection, placing strong selective pressures on host immune proteins that repeatedly adapt to remain effective. Signatures of rapid evolution have been identified in numerous immunity proteins involved in the detection of pathogenic protein substrates, but whether similar signals can be observed in host proteins engaged in interactions with other types of pathogen-derived molecules has received less attention. This focus on protein-protein interfaces has largely obscured the study of fungi as contributors to host-pathogen conflicts, despite their importance as a formidable class of vertebrate pathogens. Here, we provide evidence that mammalian immune receptors involved in the detection of microbial glycans have been subject to recurrent positive selection. We find that rapidly evolving sites in these genes cluster in key functional domains involved in carbohydrate recognition. Further, we identify convergent patterns of substitution and evidence for balancing selection in one particular gene, MelLec, which plays a critical role in controlling invasive fungal disease. Our results also highlight the power of evolutionary analyses to reveal uncharacterized interfaces of host-pathogen conflict by identifying genes, like CLEC12A, with strong signals of positive selection across mammalian lineages. These results suggest that the realm of interfaces shaped by host-microbe conflicts extends beyond the world of host-viral protein-protein interactions and into the world of microbial glycans and fungi.

Contextualising the temporal dimension in multilingual identity construction: A longitudinal Q methodological study with Chinese LOTE-learning public high school students

Multilingual identity construction is a diachronic, non-linear and constantly evolving process which is influenced by a complex range of contextual and temporal factors. Yet the temporal dimension seldom receives explicit empirical attention and remains under-theorised. Meanwhile, the dynamics of multilingual identity development are rarely explored at the cohort (i.e., whole-class) level. Underpinned by complex dynamic systems theory, this study tracks the evolution of multilingual identity positions in a class of Japanese-learning public high school students in China using longitudinal Q methodology. Three rounds of Q sorting and Q-based interviews were administered over the course of one academic year. The findings testified the enrichment and concretisation of students' multilingual identity with the accumulation of their Japanese learning experience. A range of sociocultural factors with changing saliencies impacted the students’ identity development, giving rise to group-level patterns of convergences and divergences at different timepoints. We argue that the temporal axis should be explicitly conceptualised in multilingual identity research. A temporal model of multilingual identity development is proposed to better contextualise and construe the continuity and shifts of multilingual identity at both individual and group levels.

Few-body model approach to the lowest bound S-state of non-symmetric exotic atoms and ions

Lowest bound S-state energy of Coulombic three-body systems (N Z+ μ − e −) consisting of a positively charged nucleus of charge number Z (N Z+), a negatively charged muon (μ −) and an electron (e −), is investigated in the framework of few-body (i.e., two- and three-body) cluster model approach. For the three-body cluster model, we adopted the hyperspherical harmonics expansion (HHE) method. An approximated two-body model calculation is also performed for all the three-body systems considered here. A Yukawa-type screened Coulomb potential with an arbitrary screening parameter (λ) is chosen for the two-body subsystems of the three-body system. In the resulting Schrödinger equation (SE), the three-body relative wave function is expanded in the complete set of hyperspherical harmonics (HH). The use of the orthonormality of HH in the SE leads to a set of coupled differential equations (CDEs) which are solved numerically for a manageable basis size to get the energy (E). The pattern of convergence in energy relative to increasing basis size is also investigated. Results are compared with some of those found in the literature.