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Velocity autocorrelation functions (VACFs) were calculated using the molecular dynamics method in the TIP4P/2005 and SPC/E water models of 157 464 molecules at temperatures ranging from 250 to 370 K. The large size of the models and the high accuracy of the calculations allow us to reliably compute the long-time tails of the VACFs, showing that they systematically change shape from hydrodynamic (argon-like) at high temperatures to that typical of supercooled liquids at low temperatures. These tails in the range of 2–10 ps can be well fitted by a combination of two power functions: At−3/2 – Bt−β (A, B > 0, β ≈ 2). It is found that the amplitude of the hydrodynamic asymptote, A, approaches zero as the temperature decreases, thereby rendering the negative power-law decay,−Bt−2, the dominant term within the specified time interval. The presence of a negative −Bt−2 decay in the time interval of 2–10 ps determines the specific shape of the VACF long-time tail of water, distinguishing it from ordinary simple liquids. The amplitude B, which is always non-zero, demonstrates a slight increase with rising temperature. At medium temperatures, weak but well-defined damped oscillations are observed on the VACF in the 0.5–2 ps interval. [ABSTRACT FROM AUTHOR]

An ab initio molecular orbital study has been performed to explore the structural rearrangement and dissociation of SiH 4 + radical cation at the X ̃ 2 T 2 ground electronic state. All stationary points located on the lowest adiabatic sheet of Jahn–Teller (JT) split X ̃ 2 T 2 state are fully optimized and characterized by performing harmonic vibrational frequency calculations. The structural rearrangement is predicted to start with JT distortions involving the doubly-degenerate (e) and triply-degenerate (t2) modes. The e mode reduces the initial Td symmetry of the SiH 4 + ground state to a D2d saddle point, which eventually dissociates into the SiH 3 + ( 2 A 1 ) + H products via C3v local minimum. In turn, an e-type bending of αH-Si-H yields the SiH 2 + ( 2 A 1 ) + H2 products through the first C3v local minimum and then the Cs(2A′) global minimum. In the alternative pathway, the t2 mode distorts the initial Td symmetry into a loosely bound C3v local minimum, which further dissociates into the SiH 3 + ( 2 A 1 ) + H asymptote via totally symmetric Si–H stretching mode, and SiH 2 + ( 2 A 1 ) + H2 products via H–Si–H bending (e) mode through the Cs(2A′) global minimum. It is further predicted that the Cs global minimum interconverts equivalent structures via a C2v transition structure. In addition, the two dissociation products are found to be connected by a second C2v transition structure. [ABSTRACT FROM AUTHOR]

The new continuous class of probability distribution named the Power Burr X-T (PBX-T) family is proposed in this paper. The essential characteristics of the PBX-T family of distributions, i.e. conventional moments and associated procedures, stress-strength reliability, and Rényi entropy, are derived and studied. Some special models belonging to the new family have been comprehensively explored concerning their shapes. Extensive simulations have been conducted to compare the maximum likelihood (ML) estimates with other classical estimators. It is found that the mean squared errors and the bias of the ML estimates are relatively least for large samples. Moreover, real-life applications from medical and engineering fields have been used to demonstrate the potentiality and adequacy of the suggested sub-models from the PBX-T family. The values of observed goodness-of-fit measures show that the sub-models of the suggested family of distributions are superior in adequacy parallel to the other generalized models. [ABSTRACT FROM AUTHOR]

This study investigated the effect of therapeutic community programming and aftercare treatment completion on rearrest rates in the Southwest United States across 25 years. The asymptote of rearrest trajectories did not occur until 10 years post-release, although this varied by risk classification. Treatment receipt was not related to 25-year rearrest trajectories. However, people classified as higher risk were more likely to be rearrested than those classified a low risk while controlling for treatment receipt. Aftercare completion extended the time to arrest; individuals completing an aftercare program were less likely to be arrested, and high-risk participants that completed aftercare showed a similar rearrest trajectory as low-risk participants. [ABSTRACT FROM AUTHOR]

Direct use of the likelihood function typically produces severely biased estimates when the dimension of the parameter vector is large relative to the effective sample size. With linearly separable data generated from a logistic regression model, the loglikelihood function asymptotes and the maximum likelihood estimator does not exist. We show that an exact analysis for each regression coefficient produces half-infinite confidence sets for some parameters when the data are separable. Such conclusions are not vacuous, but an honest portrayal of the limitations of the data. Finite confidence sets are only achievable when additional, perhaps implicit, assumptions are made. Under a notional double-asymptotic regime in which the dimension of the logistic coefficient vector increases with the sample size, the present paper considers the implications of enforcing a natural constraint on the vector of logistic transformed probabilities. We derive a relationship between the logistic coefficients and a notional parameter obtained as a probability limit of an ordinary least-squares estimator. The latter exists even when the data are separable. Consistency is ascertained under weak conditions on the design matrix. [ABSTRACT FROM AUTHOR]

A rapid and appropriate evaluation of the crack asymptote coefficients is essential for estimating the fracture growth in rock materials with inherent cracks and discontinuities. In the present study, the extended finite element method (XFEM), implemented with free coarse mesh, is used in conjunction with the finite element over‐deterministic (FEOD) method to determine the stress intensity factors (SIFs) and T‐stress for mixed‐mode I/II in‐plane loading of cracked rock specimens. Then, the generalized strain energy density (GSED) criterion is employed to estimate both fracture load and crack initiation angle for two types of rock pre‐cracked specimens. The predictions of the GSED criterion are then benchmarked against the experimental results, here obtained from three‐point bend tests on Neyriz marble. It is shown that such an approach to evaluate the fracture load dramatically reduces the computational cost and effort, meanwhile guaranteeing high accuracy and robustness. Highlights: XFEM is combined with FEOD to obtain stress fields around the crack tip.A new method for extracting test samples from rock cores is introduced.Various mixed‐mode fracture tests are conducted on rock samples.The results are satisfying even with unstructured coarse mesh. [ABSTRACT FROM AUTHOR]

Topology optimization is a mathematical method used to determine the optimal design of a structure to achieve desirable functional performance. Traditional single-material topology optimization can be extended to include multiple materials, offering greater design freedom, and the potential for superior layouts. Additive manufacturing technologies have become powerful tools to build up such multi-material solutions. However, inherent limitations in these processes must be considered in the optimal design. One significant challenge in additive manufacturing is the trapping of either unmelted or non-solidified powder, or in some cases, support structures in enclosed voids. This study investigates a gradient-based 3D bi-material topology optimization method that considers not only the volume fraction of each material and total mass constraints but also an additional virtual temperature constraint to avoid enclosed voids. To this end, the virtual temperature method is extended to identify and mitigate enclosed voids in bi-material structures. An efficient and straightforward technique is proposed for interpolating the elemental virtual heat conduction matrix and the elemental thermal load. Additionally, a discrete material optimization approach is employed to interpolate the elemental stiffness matrix. The problem formulation and sensitivities are thoroughly discussed. The method of moving asymptotes is used to update the design variables, which are the element densities of each material. 3D numerical results are presented to demonstrate the capability and feasibility of the proposed implementation, thereby providing superior performing designs with minimal impact on the structural performance. [ABSTRACT FROM AUTHOR]

AbstractInconsistent topologies and oscillations during iterations are commonly observed when solving stress-constrained problems, indicating inadequate stability in topology optimization. The trust region based moving asymptotes (TRMA) method is proposed in this paper. To comprehensively investigate the stability of the TRMA method, the Trinity Evaluation Framework is proposed in this paper. It focuses on three types of dependencies in topology optimization, i.e. mesh dependence, parameter dependence, and initial topology dependence. The corresponding evaluation vector is proposed to measure the stability of the TRMA method. Numerical examples are given, indicating strong stability of the TRMA method in topology optimization of stress-constrained problems. [ABSTRACT FROM AUTHOR]

Hyperbolic relations between independent and dependent variables are ubiquitous in the experimental analysis of behavior, mentioned in over 150 articles in the Journal of the Experimental Analysis of Behavior. There are two principal forms of hyperbolae: The first describes the relation between response rate and reinforcement rate on variable‐interval schedules of reinforcement; it rises asymptotically toward a maximum. The second describes the relation between the current equivalent value of an incentive and its delay or (im)probability; it falls from a maximum toward an asymptote of 0. Where do these come from? What do their parameters mean? How are they related? This article answers the first two questions and addresses the last. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design. The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads. The topology optimization formula is combined with the ordered solid isotropic material with penalization (ordered-SIMP) multi-material interpolation model. The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function. Furthermore, the sequential optimization and reliability assessment (SORA) is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization (DTO) problem. Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point (MPP). In each cycle, the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle. The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method (MMA) is used to update design variables. Finally, the validity and feasibility of the method are verified by the numerical example of L-shape beam design, T-shape structure design, steering knuckle, and 3D T-shaped beam. [ABSTRACT FROM AUTHOR]

The prediction of mechanical behavior and fatigue life is of major importance for design and for replacing costly and time-consuming tests. The proposed approach for polymers is a combination of a fatigue model and a governing constitutive model, which is formulated using the Haward–Thackray viscoplastic model (1968) and is capable of capturing large deformations. The fatigue model integrates high- and low-cycle fatigue and is based on the concept of damage evolution and a moving endurance surface in the stress space, therefore memorizing the load history without requesting vague cycle-counting approaches. The proposed approach is applicable for materials in which the fatigue development is ductile, i.e., damage during the formation of microcracks controls most of the fatigue life (up to 90%). Moreover, damage evolution shows a certain asymptote at the ultimate of the low-cycle fatigue, a second asymptote at the ultimate of the high-cycle fatigue (which is near zero), and a curvature of how rapidly the transition between the asymptotes is reached. An interesting matter is that similar to metals, many polymers satisfy these constraints. Therefore, all the model parameters for fatigue can be given in terms of the Basquin and Coffin–Manson model parameters, i.e., satisfying well-defined parameters. [ABSTRACT FROM AUTHOR]

Topology optimization is an appealing technique for optimal layout of active controllers of structures. However, the existing methods are mainly restricted to deterministic excitations, and the optimal control law involved is determined by use of the classical optimal control (COC) method, in which the sensitivities of the gain matrix with respect to the design variables need to be determined by solving the Riccati sensitivity equation numerically. In this study, a reliability-based topology optimization framework is proposed for optimal layout of active controllers of structures under nonstationary random excitations. The optimization problem is formulated as the minimization of the failure probability of the structure subjected to a specified maximum number of controllers. To avoid solving the Riccati equation, an explicit optimal control (EOC) method is first employed to derive the closed-form optimal control law in terms of the position parameters of controllers. The statistical moments of the optimal control forces and structural responses under random excitations are then obtained explicitly by the operation rules of moments, and the first-passage dynamic reliability of the structure can be formulated using the level-crossing theory. On this basis, the sensitivities of the structural failure probability with respect to the position parameters of controllers can be derived analytically by the direct differential method. Finally, the explicit formulations of the response statistics and the relevant sensitivities are incorporated into a gradient-based method of moving asymptotes (MMA) for topology optimization of the layout of controllers in conjunction with the solid isotropic material with penalization (SIMP) technique. Two numerical examples are presented to demonstrate the feasibility of the proposed topology optimization framework. [ABSTRACT FROM AUTHOR]

This article explores cinematic representations of American military interventions in Iraq and Afghanistan, examining documentary and fiction films from American, Iraqi, and Afghan perspectives. The article argues that these films often fail to communicate meaningfully with domestic and international audiences effectively, instead remaining 'asymptotic' or 'uroboric' in their rhetorical and communicative impact. I highlight the ethical challenge faced by filmmakers, whether situated in the West or in the Middle East, of turning the 'traumatic mirror' back on themselves, and the difficulties in achieving successful communication and self-reflexivity. The post-9/11 era is marked by a complex intersection of realpolitik, public performatives, and moral commitments, with long-standing tensions between West and non-West persisting in new forms. Cinematic representations of these interventions serve as a window into the traumatic legacies of these conflicts and the ongoing struggle for ethical representation, as well as a lens on the rhetorics of cinema. [ABSTRACT FROM AUTHOR]

In order to explicitly and smoothly implement fluid-based topology optimization for improving the performance and manufacturing efficiency of flow systems, the moving morphable void (MMV) method is employed to optimize the steady-state navier-stokes (NS) flow for minimizing the dissipation energy under a volume constraint. To this end, a MMV-based Brinkman term is proposed to penalize the velocity in solid area, which can expand the region controlled by the NS flow equilibrium equation from fluid to whole design domain, and can also establish the relationship between design variables and governing equations. Then, a MMV-based optimization model of NS flow is proposed and the design variables are updated by the method of moving asymptotes according to the sensitivity analysis. In benchmark examples, we can precisely track the topology boundary with detailed geometric information without the intuitive geometric judgement error. Also, by means of contrasting the results of proposed method with previous work, the effectiveness and advantages of the MMV method can be confirmed. [ABSTRACT FROM AUTHOR]

Thermo-elastic systems have a wide range of applications in various engineering fields. Traditional single-objective topology optimization (TO) design of thermos-elastic structures is difficult to achieve the combined optimum of multiple properties, and the non-periodic TO design of results are complex and difficult to fabricate. This paper introduces a multi-objective TO formulation based on density for designing thermo-elastic structures with periodic constraints, aiming to overcome the aforementioned issues. This paper assesses two competing weighted objective functions, the first function corresponds to structural and thermal compliance, while the second pertains to regional temperature and global stress. To solve the optimization issue, we utilize the p-norm function with a modified coefficient for evaluating the maximum temperature and stress values. Additionally, the adjoint variable method is employed to evaluate the sensitivity of various objectives, while the method of moving asymptotes (MMA) is used to update the design variables. Then the influence of different weight coefficients and subregion numbers regarding thermos-elastic coupled analysis is demonstrated through numerical examples. The results show that the complexity of the subregion features decreases as the number of subregions increases, and that changing both the number of subregions and the weighting coefficients results in changes in the overall structural performance. Finally, the geometric model is reconstructed using the TO results, and the structural performance is validated through the simulation of the reconstructed model. The results indicate that the TO results obtained by the method of this paper have predefined performance. [ABSTRACT FROM AUTHOR]

Inclusion of contact in mechanical designs opens a large range of design possibilities, this includes classical designs with contact, such as gears, couplings, switches, clamps etc. However, incorporation of contact in topology optimization is challenging, as classical contact models are not readily applicable when the boundaries are not defined. This paper aims to address the limitations of contact in topology optimization by extending the third medium contact method for topology optimization problems with internal contact. When the objective is to maximize a given contact load for a specified displacement, instabilities may arise as an optimum is approached. In order to alleviate stability problems as well as provide robustness of the optimized designs, a tangent stiffness requirement is introduced to the design objective. To avoid a non-physical exploitation of the third medium in optimized designs, small features are penalized by evaluating the volume constraint on a dilated design. The present work incorporates well-established methods in topology optimization including Helmholtz PDE filtering, threshold projection, Solid Isotropic Material Interpolation with Penalization, and the Method of Moving Asymptotes. Three examples are used to illustrate how the approach exploits internal contact in the topology optimization of structures subjected to large deformations. [ABSTRACT FROM AUTHOR]

In their research, the authors actively exploit different branches of geometry. For geometric constructions, computer algebra approaches and systems are used. Currently, we are interested in computer geometry, more specifically, the implementation of computer graphics. The use of the projective space and homogeneous coordinates has actually become a standard in modern computer graphics. In other words, the problem is reduced to the application of analytic projective geometry. The authors failed to find a computer algebra system that could implement projective geometry in its entirety. Therefore, it was decided to partially implement computer algebra for visualization of algebraic relations. For this purpose, the Asymptote system was employed. [ABSTRACT FROM AUTHOR]

Abstract—During the magnetotelluric studies in North Vietnam, simultaneous Phase Roll Out from Quadrant effect was detected in the behavior of impedance phases Zxy and Zyx at one of the sounding sites, CTH, in the Cam Thuy district, Thanh Hoa province. The investigation of this phenomenon has shown that it is accompanied by negative (directed upwards) components of the Umov–Poynting vector of electromagnetic energy flux in the entire range of the recorded periods of magnetotelluric variations. This energy flux direction remains unchanged when the initial coordinate system is rotated by angles of 45° and 60°. Another characteristic feature of this phenomenon is an unusual behavior of the apparent resistivity curves: the apparent resistivity magnitudes increase starting from a period of 200 s up to a period of 104 s, and this increase occurs practically along the asymptote. The analysis of the magnetotelluric field polarization and phase tensor asymmetry parameter (skew angle) β has shown that the section is characterized by significant three-dimensional (3D) distortions which manifest themselves by β values ranging between 20° and 90°. [ABSTRACT FROM AUTHOR]

In this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund's filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications. [ABSTRACT FROM AUTHOR]

Purpose: To quantify the effects of the intrinsic signal pattern, image acquisition conditions, and data analysis conditions on diffusion‐tensor MRI (DTMRI) tractography–based muscle architecture estimates using a sampling–reconstruction assessment framework. Methods: Numerical models of muscles were constructed with realistic architectural properties. DTMRI signals were computed at signal‐to‐noise ratio (SNR) of 24–96 and common voxel sizes. Fiber tracking was performed, and the results were compared with the known architectural properties. Results: SNR exerted the most significant impact on the outcome. The outcome variables approached asymptotes at SNR ≈ 54. Large in‐plane voxel dimensions reduced the similarity between reconstructed fibers and the known architectural properties. Higher order polynomials helped reconstruct fibers with more complicated geometry but overfit noise for less complex geometries. The intrinsic fiber curvature also affected the robustness of polynomial smoothing to SNR. Other conditions, such as the fiber dimensionality, voxel aspect ratio, and slice thickness, did not affect the outcomes. Conclusion: SNR ≥ 54 is recommended for accurate muscle architecture characterization using DTMRI. Averaged across all simulated conditions, the greatest percent errors under SNR = 54 were −5.6% and −4.0% for the pennation angle and fiber‐tract length estimates, respectively. For fiber tracts with intermediate intrinsic curvature, the greatest percent error for the curvature estimate was 9.8% for SNR = 54. Smaller in‐plane voxel size (≤1.5 mm) is preferred to minimize the estimation error in architectural properties. If necessary, slice thickness may be adjusted within typical ranges to achieve sufficient SNR when slices are aligned near the fiber direction. Third‐order polynomial fitting is appropriate for smoothing fiber tracts. [ABSTRACT FROM AUTHOR]

The asymptotic structure of null and spatial infinities of asymptotically flat spacetimes plays an essential role in discussing gravitational radiation, gravitational memory effect, and conserved quantities in General Relativity (GR). Bondi, Metzner and Sachs (BMS) established that the asymptotic symmetry group for asymptotically simple spacetimes is the infinite-dimensional BMS group. Given that null infinity is divided into two sets: past null infinity I− and future null infinity I+ , one can identify two independent symmetry groups: BMS− at I− and BMS+ at I+. Associated with these symmetries are the so-called BMS charges. A recent conjecture by Strominger suggests that the generators of BMS− and BMS+ and their associated charges are related via an antipodal reflection map near spatial infinity. To verify this matching, an analysis of the gravitational field near spatial infinity is required. This task is complicated due to the singular nature of spatial infinity for spacetimes with non-vanishing ADM mass. Different frameworks have been introduced in the literature to address this singularity, e.g. Friedrich's cylinder, Ashtekar-Hansen's hyperboloid and Ashtekar-Romano's asymptote at spatial infinity. This paper reviews the role of Friedrich's formulation of spatial infinity in the investigation of the matching of the spin-2 charges on Minkowski spacetime and in the full GR setting. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'. [ABSTRACT FROM AUTHOR]

This paper investigates a reversible investment problem with finite horizon, in which a social planner aims to determine the project's capacity level to minimize the expected total costs. These costs depend on the demand for the good, the supply in terms of production capacity, and the proportional costs. The issue of irreversible investment has been examined by Han and Yi [Commun. Nonlinear Sci. Numer. Simul., 109 (2022), 106302]. Mathematically, the reversible investment problem can be formulated as a singular stochastic control problem. The value function satisfies a two-dimensional parabolic variational inequality subject to gradient constraint, which leads to two time-dependent free boundaries representing optimal investment and disinvestment strategies. We employ a partial differential equation approach to characterize the continuity, monotonicity, and horizontal asymptotes of free boundaries, as well as establish the C2,1 regularity of the value function. To the best of our knowledge, the approach to analyze the behavior of free boundaries is novel in the literature. [ABSTRACT FROM AUTHOR]

Using spread complexity and spread entropy, we study non-unitary quantum dynamics. For non-hermitian Hamiltonians, we extend the bi-Lanczos construction for the Krylov basis to the Schrödinger picture. Moreover, we implement an algorithm adapted to complex symmetric Hamiltonians. This reduces the computational memory requirements by half compared to the bi-Lanczos construction. We apply this construction to the one-dimensional tight-binding Hamiltonian subject to repeated measurements at fixed small time intervals, resulting in effective non-unitary dynamics. We find that the spread complexity initially grows with time, followed by an extended decay period and saturation. The choice of initial state determines the saturation value of complexity and entropy. In analogy to measurement-induced phase transitions, we consider a quench between hermitian and non-hermitian Hamiltonian evolution induced by turning on regular measurements at different frequencies. We find that as a function of the measurement frequency, the time at which the spread complexity starts growing increases. This time asymptotes to infinity when the time gap between measurements is taken to zero, indicating the onset of the quantum Zeno effect, according to which measurements impede time evolution. [ABSTRACT FROM AUTHOR]

In this paper, we set up the numerical S-matrix bootstrap by using the crossing symmetric dispersion relation (CSDR) to write down Roy equations for the partial waves. As a motivation behind examining the local version of the CSDR, we derive a new crossing symmetric, 3-channels-plus-contact-terms representation of the Virasoro-Shapiro amplitude in string theory that converges everywhere except at the poles. We then focus on gapped theories and give novel analytic and semi-analytic derivations of several bounds on low-energy data. We examine the high-energy behaviour of the experimentally measurable rho-parameter, introduced by Khuri and Kinoshita and defined as the ratio of the real to the imaginary part of the amplitude in the forward limit. Contrary to expectations, we find numerical evidence that there could be multiple changes in the sign of this ratio before it asymptotes at high energies. We compare our approach with other existing numerical methods and find agreement, with improvement in convergence. [ABSTRACT FROM AUTHOR]

A new method is proposed to optimize the configurations of vertical ground heat exchangers using topology optimization and the method of moving asymptotes. The problem formulation minimizes the required number of boreholes of a given length with simultaneous constraints on the entering fluid temperature in cooling and heating mode. The method relies on the adaptation of the alternative ASHRAE design method and a new analytical formulation for the calculation of g -functions based on a boundary condition of equal average fluid temperature. The method is applied to large bore fields consisting of more than a hundred boreholes. The paper also studies the effect of different types of domains and ground load profiles on the optimized configurations. It is shown that the shape of the domain has minimal impact on the optimized configurations. A higher density of boreholes on the perimeter of the domain compared to the center is recommended in the case where one operation mode is dominant. A uniform configuration is better suited when the load profile is balanced. [ABSTRACT FROM AUTHOR]

Ecological Niche Models (ENMs) are often used to project species distributions within alien ranges and in future climatic scenarios. However, ENMs depend on species‐environment equilibrium, which may be absent for actively expanding species. We present a novel framework to estimate whether species have reached environmental equilibrium in their native and alien ranges. The method is based on the estimation of niche breadth with the accumulation of species occurrences. An asymptote will indicate exhaustive knowledge of the realised niches. We demonstrate the CNA framework for 26 species of mammals, amphibians, and birds. Possible outcomes of the framework include: (1) There is enough data to quantify the native and alien realised niches, allowing us to calculate niche expansion between the native and alien ranges, also indicating that ENMs can be reliably projected to new environmental conditions. (2) The data in the native range is not adequate but an asymptote is reached in the alien realised niche, indicating low confidence in our ability to evaluate niche expansion in the alien range but high confidence in model projections to new environmental conditions within the alien range. (3) There is enough data to quantify the native realised niche, but not enough knowledge about the alien realised niche, hindering the reliability of projections beyond sampled conditions. (4) Both the native and alien ranges do not reach an asymptote, and thus few robust conclusions about the species' niche or future projections can be made. Our framework can be used to detect species' environmental equilibrium in both the native and alien ranges, to quantify changes in the realised niche during the invasion processes, and to estimate the likely accuracy of model projections to new environmental conditions. [ABSTRACT FROM AUTHOR]

In this article, a joint topology optimization procedure is executed to design phononic crystals (PnCs) with a maximized band gap. First, the band gap of two-dimensional PnCs is calculated using a finite element model under the plane strain assumption for easy and efficient optimization. In the numerical computation of the band gaps, the band structures of in-plane and out-of-plane modes are analyzed and verified using COMSOL. Then, the density-based and feature-driven methods are sequentially used to design the unit cell of the PnCs with single-phase material. A stiffness constraint is added to ensure the continuity of the material inside the unit cell, and a boundary constraint guarantees continuity amongst the unit cells. The optimization problem is solved through the Method of Moving Asymptotes (MMA), and reconfigurable manufacturing PnC is obtained via joint topology optimization. Lastly, the band structures and vibration modes of the reconstructed model are analyzed. Research results show that the optimal PnCs generate broadband vibrations by localized resonance and have negative refraction characteristics. This research also confirms that the joint topology optimization is an efficient approach for designing novel elastic metamaterials. [ABSTRACT FROM AUTHOR]

Using a horizontal batch dry bead mill newly developed by our company, talc raw material was ground in air, and its grinding performance and mechanochemical effect on the sample were evaluated from various perspectives. First, the average diameter of the ground product as a grinding performance decreases with the increase in grinding time or power source unit, reaching the submicron size. In addition, when mill operation is continued, talc changes fine particle aggregation and crystal structure change due to mechanochemical effects, and the phenomenon of detachment of the (OH) group around Mg in the crystals becomes remarkable. The flowability of the ground product is inhibited by the withdrawal of (OH) from the talc crystal, but this flowability is restored when it is dried. When the power source unit in the grinding approaches 3 kWh/kg2 it asymptotes to the maximum value of 9% in the weight reduction percentage. [ABSTRACT FROM AUTHOR]

The relevance of this study is the importance of investigating mathematical models and systems to optimize oil production in forecasting and regulating well stock in fuzzy environments. The purpose was to assess the practical application of Markov chain models and fuzzy set theory to optimize oil production. This study specifically analyzed operating and idle well stocks in Kazakhstan's Kenkiyak oil field using a Markov chain system of equations. Fuzzy set theory was then applied to model linguistic relationships between oil production parameters like depth and porosity. The Markov model successfully predicted linear asymptotes of well stock over time and assessed impacts of changing repair crew productivity. The fuzzy approach effectively modeled the dependence of production efficiency on depth and reservoir rock porosity. Results showed a 15% improvement in forecasting accuracy and a 10% increase in production efficiency. This demonstrates the value of mathematical models in optimizing real)world oil production processes and their ability to enhance management system performance. The models provide oil field designers with tools to better regulate well stock and staff operations. [ABSTRACT FROM AUTHOR]

The concept of forest productivity is biologically complex. In forest masses, it is indirectly estimated via dominant height growth models and site indices. The aim of this study was to develop a dominant height model for Gmelina arborea using data from 129 monitoring plots. 9 dynamic equations were generated from the Hossfeld and Bertalanffy-Richards theoretical models, which were individually fitted and cross-validated. Among the evaluated models, the Bertalanffy-Richards model (parameter c) stood out. This model showed a logical biological trend, with polymorphic curves and a unique asymptote. The selected model is an important tool for the management of G. arborea forest plantations in areas with site characteristics similar to those of this study. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to increase the energy efficiency of gated Johnson counters by eliminating the redundant switching consumption of the unused counter-chain cells. Two techniques that aim to achieve this goal are analysed and show that efficiency improves almost exponentially as the counter resolution increases up to a limiting asymptote. To demonstrate the effectiveness of the proposed approach, a 5-bit Johnson counter architecture with 16 stages is designed. The design is extensively analysed and simulated up to 1 GHz clock frequency and implemented into single channel SS-ADC as part of CIS realized in a 0.11µm 1P4M BSI CMOS process. The obtained results show that the proposed approach trades energy efficiency for the area and is practically suitable only for counters with resolution = 8 bits. [ABSTRACT FROM AUTHOR]

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The paper focuses on analyzing the first asymptote of hitting time functions in relation to dynamical partitions. We study the circle maps with quadratic irrational rotations whose continued fractions exhibit eventual periodicity. The main aim of this paper is to establish that the sequence of distribution functions of rescaled hitting times determined by dynamical partitions, converges to finite limit points. Moreover, it is proved that the limit functions of these distribution functions are piecewise linear distribution functions. [ABSTRACT FROM AUTHOR]

This paper discusses the Topp-Leone-G power series class of distributions. The greatest attention is paid to the investigation of intrinsic characteristic "saturation" to the horizontal asymptote in the Hausdorff sense. Some estimates for the value of the Hausdorff distance are obtained. We present a new family of recurrence generated adaptive functions with corresponding applications. The usefulness of the obtained results is demonstrated in a simulation study of some real data sets from the medical sector and insurance. Some suitable software modules within the programming environment CAS MATHEMATICA are proposed. [ABSTRACT FROM AUTHOR]

This article proposes an augmented Lagrangian-based topology optimization approach to minimize the volume fraction subject to multiple nodal displacement constraints. The proposed method puts the multiple constraint equations in the objective function and transforms it into a sequence of unconstrained optimization problems. This study explains the theoretical aspects of the employed augmented Lagrangian approach in depth. Sensitivity expression in terms of design variables is identified by exercising the differentiate-then-discretize mechanism, and utilizes a moving asymptote algorithm to sort out a sequence of optimization subproblems. The optimized results are compared and analysed with those from conventional aggregation-based topology optimization. However, the predefined aggregation approach indicates a dependency on the supplied parameters. The numerical two- and three-dimensional examples reveal the viability and reliability of the suggested augmented Lagrangian scheme, which shows advantages in terms of robustness and efficiency. [ABSTRACT FROM AUTHOR]

In the H-mode regime of diverted tokamaks, the presence of strong pressure gradients in the pedestal gives rise to a sizable bootstrap current, together with the Ohmic and Pfirsch–Schlueter currents, close to the separatrix. For such equilibria, the presence of finite current density close to the separatrix requires the reexamination of equilibrium properties. It is almost universally assumed that the two branches of the separatrix (the stable and unstable manifolds) are straight as they cross at the X-point. However, the opposite angles of the plasma-filled segment and vacuum one cannot be equal if the current density does not vanish at the separatrix on the plasma side. We solve this difficulty by chipping off a thin layer of plasma edge so that the sharp corner of the plasma-filled segment becomes a hyperbola. Using the conformal transformation, we found that in the assumption of a hyperbolic boundary, the X point moves beyond the plasma boundary to fall in the vacuum region. An acute angle of the plasma-filled segment leads to an obtuse opposite angle of vacuum segment and vice versa. In the case of an acute angle of the plasma-filled segment, the new X point shifts inside the X point formed by the asymptotes of a hyperbolic boundary; in the case of an obtuse angle of the plasma-filled segment, the new X point shifts outside the X point formed by the asymptotes of a hyperbolic plasma boundary. The results are important for understanding the X point features, which affect the tokamak edge stability and transport. [ABSTRACT FROM AUTHOR]

We reveal limitations of several standard coupled-cluster (CC) methods with perturbation-theory based noniterative or approximate iterative treatments of triple excitations when applied to the determination of highly accurate potential energy curves (PECs) of ionic dimers, such as the X Σ g + 2 electronic ground state of Rb2+. Such computations are of current interest for the understanding of ion–atom interactions in the ultracold regime. We demonstrate that these CC methods lead to an unphysical long-range barrier for the Rb2+ system. The barrier is small but spoils the long-range behavior of the PEC. The effect is also found for other X2+ systems, such as X = Li, Na, and K. Calculations using a flexible framework for obtaining leading perturbative triples corrections derived using an analytic CC singles and doubles energy derivative formulation demonstrate that the origin of this problem lies in the use of T ̂ 3 amplitudes obtained from approximate CC singles, doubles, and triples amplitude equations. It is shown that the unphysical barrier is related to a symmetry instability of the underlying Hartree–Fock mean-field solution, leading to orbitals representing two +0.5-fold charged ions in the limit of separated fragments. This, in turn, leads to a wrong 1/R asymptote of the interaction potential computed by perturbation-based CC approximations. Physically meaningful perturbative corrections in the long-range tail of the PEC may instead be obtained using symmetry-broken reference determinants. [ABSTRACT FROM AUTHOR]

We reveal limitations of several standard coupled-cluster (CC) methods with perturbation-theory based noniterative or approximate iterative treatments of triple excitations when applied to the determination of highly accurate potential energy curves (PECs) of ionic dimers, such as the X Σ g + 2 electronic ground state of Rb2+. Such computations are of current interest for the understanding of ion–atom interactions in the ultracold regime. We demonstrate that these CC methods lead to an unphysical long-range barrier for the Rb2+ system. The barrier is small but spoils the long-range behavior of the PEC. The effect is also found for other X2+ systems, such as X = Li, Na, and K. Calculations using a flexible framework for obtaining leading perturbative triples corrections derived using an analytic CC singles and doubles energy derivative formulation demonstrate that the origin of this problem lies in the use of T ̂ 3 amplitudes obtained from approximate CC singles, doubles, and triples amplitude equations. It is shown that the unphysical barrier is related to a symmetry instability of the underlying Hartree–Fock mean-field solution, leading to orbitals representing two +0.5-fold charged ions in the limit of separated fragments. This, in turn, leads to a wrong 1/R asymptote of the interaction potential computed by perturbation-based CC approximations. Physically meaningful perturbative corrections in the long-range tail of the PEC may instead be obtained using symmetry-broken reference determinants. [ABSTRACT FROM AUTHOR]

Tree height (H) and stem diameter at breast height (DBH) (H-D) relationship is correlated with timber yield and quality as well as stability of forest and is crucial in forest management and genetic breeding. It is influenced by not only environmental factors such as site quality and climate factors but also genetic control that is mostly neglected. A dataset of H and DBH of 25 provenances of Betula alnoides Buch.–Ham. ex D. Don at four sites was used to model the H-D relationship. The dummy variable nonliner mixed-effect equations were applied to evaluate the effects of sites and provenances on variations of the H-D relationship and to select superior provenances of B. alnoides. Weibull equation was selected as the base model for the H-D relationship. The sites affected asymptotes of the H-D curves, and the provenance effect on asymptotes of the H-D curves varied across sites. Taking above-average DBH and lower asymptote of the H-D curves as indicators, five excellent provenances were screened out at each site with a rate of 20%. Their selection gains of individual volume ranged from 1.99% to 29.81%, and their asymptote parameter (kj) and H-D ratio were 7.17%–486.05% and 3.07–4.72% lower than the relevant total means at four sites, respectively. Genetic selection based on the H-D relationship could promote selection efficiency of excellent germplasms and was beneficial for the large-sized timber production of B. alnoides. [ABSTRACT FROM AUTHOR]

The artwork of sculptor, draftsperson, and installation artist Michael Richards (1963 – 2001) challenges prevalent assumptions about the physical properties, and therefore the aesthetic application, of suspension in Black cultural production. As an African American of Jamaican and Costa Rican descent, Richards grappled with questions of citizenship, racism, and freedom, frequently using motifs of flight and gravity. Although Richards created his work before his untimely death in the September 11 attacks on the World Trade Center, his piece titled Tar and Feather nevertheless anticipates the possibilities, and important limitations, of suspension as a theoretical framework. When placed in conversation with the theoretical discourse that now exists surrounding suspension, Richards's material sculptures and archival sketches posthumously anticipate the limits of conventional strategies for Black possibility. This paper argues that Tar and Feather illustrates the asymptotic imbrication of blackness and freedom, which renders the plot as both a diagram of forces and an abstract aesthetic geography from which to create. [ABSTRACT FROM AUTHOR]

This paper primarily analyzes the one-parameter generalized logistic (1PGlogit) model, which is a generalized model containing other one-parameter item response theory (IRT) models. The essence of the 1PGlogit model is the introduction of a generalized link function that includes the probit, logit, and complementary log-log functions. By transforming different parameters, the 1PGlogit model can flexibly adjust the speed at which the item characteristic curve (ICC) approaches the upper and lower asymptote, breaking the previous constraints in one-parameter IRT models where the ICC curves were either all symmetric or all asymmetric. This allows for a more flexible way to fit data and achieve better fitting performance. We present three simulation studies, specifically designed to validate the accuracy of parameter estimation for a variety of one-parameter IRT models using the Stan program, illustrate the advantages of the 1PGlogit model over other one-parameter IRT models from a model fitting perspective, and demonstrate the effective fit of the 1PGlogit model with the three-parameter logistic (3PL) and four-parameter logistic (4PL) models. Finally, we demonstrate the good fitting performance of the 1PGlogit model through an analysis of real data. [ABSTRACT FROM AUTHOR]

The method of designing cell structures with variable-density cells based on erode-dilate operators was applied to the optimization of thermal structures. A series of variable-density microstructures with the same topology definition but different volume fractions were obtained with erode-dilate operators. Then, the thermal conductivity of the variable-density cells was extracted and the equivalent thermal conductivity fitting curve was obtained. After this, the method of moving asymptotes was used to update macro design variables, and the variable-density microstructure was implanted into the macroscopic unit of the corresponding volume fraction to complete the assembly. Numerical examples were given to compare and analyze the thermal compliance, the mean temperature, the variance and other parameters of the temperature fields with different optimization methods. The results show that, variable-density cell structures have better heat dissipating performance than traditional single-scale cell structures and periodic cell structures. [ABSTRACT FROM AUTHOR]

We show that by a simple modification of the Bernstein operators one can obtain a polynomial approximation of unbounded functions which admit an asymptote at an end point of the interval and we give a typical example. We define a certain modulus of continuity which allow to give a quantitative result for the degree of approximation and to make more explicit the class of functions which can be approximate. Finally we show that these operators could be transformed in order to obtain linear positive operators for approximation of functions on interval $ [0, \infty) $. The scheme used in this paper is applicable in more general cases. [ABSTRACT FROM AUTHOR]

We have measured the merged-beams rate coefficient for the titular isotope exchange reactions as a function of the relative collision energy in the range of ∼ 3 meV–10 eV. The results appear to scale with the number of available sites for deuteration. We have performed extensive theoretical calculations to characterize the zero-point energy corrected reaction path. Vibrationally adiabatic minimum energy paths were obtained using a combination of unrestricted quadratic configuration interaction of single and double excitations and internally contracted multireference configuration interaction calculations. The resulting barrier height, ranging from 68 meV to 89 meV, together with the various asymptotes that may be reached in the collision, was used in a classical over-the-barrier model. All competing endoergic reaction channels were taken into account using a flux reduction factor. This model reproduces all three experimental sets quite satisfactorily. In order to generate thermal rate coefficients down to 10 K, the internal excitation energy distribution of each H 3 + isotopologue is evaluated level by level using available line lists and accurate spectroscopic parameters. Tunneling is accounted for by a direct inclusion of the exact quantum tunneling probability in the evaluation of the cross section. We derive a thermal rate coefficient of < 1 × 1 0 − 12 c m 3 s − 1 for temperatures below 44 K, 86 K, and 139 K for the reaction of D with H 3 + , H 2 D + , and D 2 H + , respectively, with tunneling effects included. The derived thermal rate coefficients exceed the ring polymer molecular dynamics prediction of Bulut et al. [J. Phys. Chem. A 123, 8766 (2019)] at all temperatures. [ABSTRACT FROM AUTHOR]

We report on the experimental observation of the B+2Σ+ state of MgAr+ located below the Mg+(3p²P3/2) + Ar(¹S0) dissociation asymptote. Using the technique of isolated-core multiphoton Rydberg-dissociation spectroscopy, we have recorded rotationally resolved spectra of the B+2Σ+(v′) ← X+ ²Σ+(v″ = 7) transitions, which extend from the vibrational ground state (v′ = 0) to the dissociation continuum above the Mg+(3p²P3/2) + Ar(¹S0) dissociation threshold. The analysis of the rotational structure reveals a transition from Hund’s angular-momentum-coupling case (b) at low v′ values to case (c) at high v′ values caused by the spin–orbit interaction. Measurements of the kinetic-energy release and the angular distribution of the Mg+ fragments detected in the experiments enabled the characterization of the dissociation mechanisms. The vibrational levels of the B+ state above v′ = 6 are subject to predissociation into the Mg+(3p²P1/2) + Ar(¹S0) continuum, and the fragment angular distributions exhibit anisotropy β parameters around 0.5, whereas direct dissociation into the continuum above the Mg+(3p²P3/2) + Ar(¹S0) asymptote is characterized by β parameters approaching 2. Molecular ions excited to the B+ state with v′ = 0–6 efficiently absorb a second photon to the repulsive part of the ²Σ+ state associated with the Mg+(3d ²D3/2,5/2) + Ar(¹S0) continua. The interpretation of the data is validated by the results of ab initio calculations of the low-lying electronic states of MgAr+, which provided initial evidence for the existence of bound vibrational levels of the B+ state and for the photodissociation mechanisms of its low vibrational levels. [ABSTRACT FROM AUTHOR]

In this paper, we consider compliance minimization problems within the variable-thickness approach for the rib-stiffened plates subjected to a transverse loading. It is known, that such optimization problems are usually not well posed and their solutions become strongly mesh-dependent. To overcome this issue, we introduce additional regularization constraint on the thickness gradient and evaluate the convergence and efficiency of considered method. Variable thickness is defined based on topology optimization approach introducing additional design variables in the nodes of the shell-type elements. Numerical solutions are provided by using finite element simulations within Mindlin–Reissner theory and method of moving asymptotes. Possibility for the well-converged optimal solutions for the benchmark problems with rib-stiffened panels loaded by the systems of concentrated forces is shown. Parametric studies are provided to analyse the effects of the shape functions order, values of penalty factors and initial conditions for the plate thickness. Recommendations for the optimal settings of the considered method are established. Theoretical and experimental assessments on the advantages and accuracy of the variable-thickness approach are given based on comparison of the obtained solutions to the standard design for the plates with regular stiffening. [ABSTRACT FROM AUTHOR]

In the 1960s, Birch proved that the traces of Frobenius for elliptic curves taken at random over a large finite field is modeled by the semicircular distribution (i.e. the usual Sato–Tate for non-CM elliptic curves). In analogy with Birch's result, a recent paper by Ono, the author, and Saikia proved that the limiting distribution of the normalized Frobenius traces A λ ⁢ (p) of a certain family of K ⁢ 3 surfaces X λ with generic Picard rank 19 is the O ⁢ (3) distribution. This distribution, which we denote by 1 4 ⁢ π ⁢ f ⁢ (t) , is quite different from the semicircular distribution. It is supported on [ - 3 , 3 ] and has vertical asymptotes at t = ± 1 . Here we make this result explicit. We prove that if p ≥ 5 is prime and - 3 ≤ a < b ≤ 3 , then | # ⁢ { λ ∈ 픽 p : A λ ⁢ (p) ∈ [ a , b ] } p - 1 4 ⁢ π ⁢ ∫ a b f ⁢ (t) ⁢ 푑 t | ≤ 98.28 p 1 / 4 . As a consequence, we are able to determine when a finite field 픽 p is large enough for the discrete histograms to reach any given height near t = ± 1 . To obtain these results, we make use of the theory of Rankin–Cohen brackets in the theory of harmonic Maass forms. [ABSTRACT FROM AUTHOR]