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Thermoelastic problems refer to a coupled phenomenon existing in a wide range of practical applications where elastic responses are influenced by temperature variation. Meanwhile, Moving Morphable Void (MMV) approach receives extensive attentions owing to explicit topological geometric information. In MMV method, a closed B-spline curve defined by several design variables is adopted to describe void material in design domain. In present study, we intend to use the MMV method to topologically optimize the thermoelastic structures under uniform temperature increment and varying temperature field. The weak formulations of heat conduction and elasticity are combined to describe the thermoelastic problems. The optimization mathematical model with the aim of compliance minimization and volume constraint is constructed. The sensitivity of design variables is derived by material derivative method and adjoint sensitivity analysis method. The method of moving asymptote (MMA) algorithm is implemented to update the design variables for finding the best material distribution. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

A consistent finding in sensorimotor adaptation is a persistent undershoot of full compensation, such that performance asymptotes with residual errors greater than seen at baseline. This behaviour has been attributed to limiting factors within the implicit adaptation system, which reaches a sub-optimal equilibrium between trial-by-trial learning and forgetting. However, recent research has suggested that allowing longer motor planning periods prior to movement eliminates these residual errors. The additional planning time allows required cognitive processes to be completed before movement onset, thus increasing accuracy. Here we looked to extend these findings by investigating the relationship between increased motor preparation time and the size of imposed visuomotor rotation (30°, 45° or 60°), with regards to the final asymptotic level of adaptation. We found that restricting preparation time to 0.35 seconds impaired adaptation for moderate and larger rotations, resulting in larger residual errors compared to groups with additional preparation time. However, we found that even extended preparation time failed to eliminate persistent errors, regardless of magnitude of cursor rotation. Thus, the asymptote of adaptation was significantly less than the degree of imposed rotation, for all experimental groups. Additionally, there was a positive relationship between asymptotic error and implicit retention. These data suggest that a prolonged motor preparation period is insufficient to reliably achieve complete adaptation and therefore our results provide support for the proposal that limitations within the implicit learning system contributes to asymptotic adaptation levels.New & NoteworthyResidual errors in sensorimotor adaptation are commonly attributed to an equilibrium between trial-by-trial learning and forgetting. Recent research suggested that allowing sufficient time for mental rotation eliminates these errors. In a number of experimental conditions, we show that while restricted motor preparation time does limit adaptation - consistent with mental rotation - extending preparation time fails to eliminate the residual errors in motor adaptation.

The recent asset pricing literature finds valuation risk is an important determinant of key asset pricing moments. Valuation risk is modelled as a time preference shock within Epstein-Zin recursive utility preferences. While this form of valuation risk appears to fit the data extremely well, we show the preference specification violates an economically meaningful restriction on the weights in the Epstein-Zin time-aggregator. The same model with the corrected preference specification performs nearly as well at matching asset pricing moments, but only if the risk aversion parameter is well above the accepted range of values used in the literature. When the corrected preference specification is combined with Bansal-Yaron long-run risk, the estimated model significantly downgrades the role of valuation risk in determining asset prices. The only significant contribution of valuation risk is to help match the volatility of the risk-free rate.

The moving asymptotes function is widely applied as sequential explicit convex approximation in topology optimization, due to the controllable conservatism and convergence. In virtue of these advantages, it is supposed that the efficiency of optimality criteria method will become higher if constraint functions are approximated by moving asymptotes function instead of linear function. This work presents an optimality criteria method for topology optimization under multiple constraints where the constraint functions are approximated by moving asymptotes function. The dual feasibility condition is customarily adopted to establish explicit update scheme of topological variable, where hypothesis of active topological variable set is avoided, in the case that gradient of objective function is positive. The complementary slackness condition and primal feasibility condition are combined into a simplified dual programming to solve for the Lagrange multipliers, where hypothesis of active constraint set is avoided. Three benchmark examples under multiple displacement, stress, compliance or eigenfrequency constraints are solved by the presented optimality criteria method, the results are compared to the method of moving asymptotes and the optimality criteria method with linear constraint approximation.

Learning similar motor skills in close succession is limited by interference, a phenomenon that takes place early after acquisition when motor memories are unstable. Interference can be bidirectional, as the first memory can be disrupted by the second (retrograde interference), or the second memory can be disrupted by the first (anterograde interference). The heightened plastic state of primary motor cortex after learning is thought to underlie interference, as unstable motor memories compete for neural resources. While time-dependent consolidation processes reduce interference, the passage of time (~6 h) required for memory stabilization limits our capacity to learn multiple motor skills at once. Here, we demonstrate in humans that prolonged training at asymptote of an initial motor skill reduces both retrograde and anterograde interference when a second motor skill is acquired in close succession. Neurophysiological assessments via transcranial magnetic stimulation reflect this online stabilization process. Specifically, excitatory neurotransmission in primary motor cortex increased after short training and decreased after prolonged training at performance asymptote. Of note, this reduction in intracortical excitation after prolonged training was proportional to better skill retention the following day. Importantly, these neurophysiological effects were not observed after motor practice without learning or after a temporal delay. Together, these findings indicate that prolonged training at asymptote improves the capacity to learn multiple motor skills in close succession, and that downregulation of excitatory neurotransmission in primary motor cortex may be a marker of online motor memory stabilization.

This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.

Flow behavior inside rotors can be very complicated and with three-dimensional characteristics. This fact added to a large number of free geometrical parameters that can be varied makes the design of these components a difficult task. Optimization techniques can be applied to generate optimized designs for these machines. In this work, a different approach to design rotors by using topology optimization is proposed. An objective function measured at the boundaries and derived from energy dissipation inside the domain is used with the continuous adjoint approach considering a rotating reference frame for the governing equations. Cyclic boundary conditions are used to represent rotational repeating patterns. The Finite Volume Method is used to solve the direct and adjoint problems, and an implementation of the Globally Convergent Method of Moving Asymptotes (GCMMA) is applied. Numerical examples are presented and an optimized design is compared with a traditional one.

This paper studies the optimization design of sandwich structures with lattice core and viscoelastic layers for suppressing structural resonance response in the frequency domain. A concurrent optimization scheme is proposed to simultaneously optimize the damping material topology in the viscoelastic layers and the size distribution of the lattice core. The damping effect of the viscoelastic layers is simulated as hysteretic damping model, and the full method is used to accurately calculate the dynamic responses. Based on the adjoint method, the corresponding design sensitivities are analytically derived efficiently and the Globally Convergent Method of Moving Asymptotes algorithm is adopted. To ensure a smooth convergence in case of mode switching, the mode tracking technique based on the Modal Assurance Criteria is introduced to track the targeted resonant mode. Numerical examples demonstrate the effect of the concurrent optimization in suppressing structural resonance response.

A full-dimensional global potential energy surface (PES) for the KRb + KRb → K2Rb2* → K2 + Rb2 reaction is reported based on high-level ab initio calculations. The short-range part of the PES is fit with the permutationally invariant polynomial-neural network method, while the long-range parts of the PES in both the reactant and product asymptotes are represented by an asymptotically correct form. The long- and short-range parts are connected with intermediate-range parts to make them smooth. Within a statistical quantum model, this PES reproduces both the measured loss rates of ultracold KRb molecules and the K2 and Rb2 product state distributions, underscoring the important role of tunneling in ultracold chemistry. The PES also correctly predicts the lifetime of the K2Rb2* intermediate complex within the Rice-Ramsperger-Kassel-Marcus limit. It thus provides a reliable platform for future dynamical studies of the prototypical reaction.

Based on the notion of plane asymptote, we introduce the new concept of cone asymptote of a set in the n-dimensional Euclidean space. We discuss the existence and describe some families of cone asymptotes.

The four-parameter logistic (4PL) item response model, which includes an upper asymptote for the correct response probability, has drawn increasing interest due to its suitability for many practical scenarios. This paper proposes a new Gibbs sampling algorithm for estimation of the multidimensional 4PL model based on an efficient data augmentation scheme (DAGS). With the introduction of three continuous latent variables, the full conditional distributions are tractable, allowing easy implementation of a Gibbs sampler. Simulation studies are conducted to evaluate the proposed method and several popular alternatives. An empirical data set was analysed using the 4PL model to show its improved performance over the three-parameter and two-parameter logistic models. The proposed estimation scheme is easily accessible to practitioners through the open-source IRTlogit package.

Objective: To identify differences between asymptote- and rate-based methods for estimating age and size at growth cessation in linear craniofacial measurements. Design: This is a retrospective, longitudinal study. Five linear measurements were collected from lateral cephalograms as part of the Craniofacial Growth Consortium Study (CGCS). Four estimates of growth cessation, including 2 asymptote- (GCasym, GCerr) and 2 rate-based (GCabs, GC10%) methods, from double logistic models of craniofacial growth were compared. Participants: Cephalometric data from participants in 6 historic longitudinal growth studies were included in the CGCS. At least 1749 individuals (870 females, 879 males), unaffected by craniofacial anomalies, were included in all analyses. Individuals were represented by a median of 11 images between 2.5 and 31.3 years of age. Results: GCasym consistently occurred before GCerr and GCabs consistently occurred before GC10% within the rate-based approaches. The ordering of the asymptote-based methods compared to the rate-based methods was not consistent across measurements or between males and females. Across the 5 measurements, age at growth cessation ranged from 13.56 (females, nasion-basion, GCasym) to 24.39 (males, sella-gonion, GCerr). Conclusions: Adolescent growth cessation is an important milestone for treatment planning. Based on our findings, we recommend careful consideration of specific definitions of growth cessation in both clinical and research settings since the most appropriate estimation method may differ according to patients’ needs. The different methods presented here provide useful estimates of growth cessation that can be applied to raw data and to a variety of statistical models of craniofacial growth.

In situ characterization of the saturated hydraulic conductivity (Ks) requires a large number of experiments, sampling, and laboratory measurements that are time-consuming and expensive. Simplified Beerkan Infiltration (SBI) method was developed to estimate an approximate Ks based on the infiltration curve without any sampling procedures. For that purpose, α* parameter, which is used in the calculation of Ks, was commonly set to a fixed value based on soil texture. This approach was not sufficient for an accurate Ks estimation. For a relatively dry soil, a new approach involving an empirical structural parameter was proposed to calculate an approximation of the α* parameter based on the shape of the steady state asymptote of the Beerkan cumulative infiltration. The new α* parameter was tested on simplified Beerkan infiltration (SBI) method in over 32 Beerkan experiments selected from the Soil World Infiltration Global (SWIG) database. The steady state SBI (SSBI) method estimated Ks with an accuracy close to those estimated with the BEST (Beerkan Estimation Soil Transfer) method. The R2 correlation factor for the SSBI method in Ks estimation with BEST intercept and steady methods were 0.982 and 0.994, respectively. For the transient SBI method, the R2 correlation factors calculated with BEST methods were lower; 0.858 and 0.827, respectively. Therefore, the application of the new α* parameter to the steady state simplified Beerkan approach allows an easy, inexpensive way to estimate accurately Ks.

The limits of elastic behaviour change with the nature of the impulse applied to a target and the size of volume interrogated by a measurement, since it is the pre-existing defects sampled within its rise that determine the response observed. This review considers a range of solids of different material classes and tracks the development of the strength of the material during shock loading, from yield at the Hugoniot elastic limit, across the weak shock regime, to its transition to strong shock behaviour. It is shown that at this stress, the weak shock limit (WSL), the shear component of the applied stress exceeds the theoretical strength of the material. Beyond this threshold, there are a number of new responses that confirm a transition from an inhomogeneous to a homogeneous state. Further, whilst strength rises across the weak shock regime, it saturates at the WSL. For instance, failure in shocked glasses transitions from localised fracture initiated at target boundaries to a global failure at this threshold at the theoretical strength. Sapphire′s strength asymptotes to the theoretical strength of the strongest direction in its lattice. Finally, the fourth-power dependence of strain rate upon stress appears to be a consequence of the homogeneous flow in the strong shock regime. This review suggests that µ/2π is a good approximation for the unrelaxed theoretical strength of solids at increasing stresses beyond the WSL. The methodology unfolded here represents a new means to experimentally determine the ultimate shear strength of solids.

This work reports on optimizing the Indirect Indentation Method for measuring the elastic properties of brittle materials by indentation. The method employs a thin metallic film that protects the brittle material by absorbing the inelastic damage causes by the penetrating indenter. It applies hyperbolic identities to the Zhou-Prorok Model for thin film indentation that approach an asymptote as the indenter advances toward the film/substrate interface. The slope of this asymptote has been shown to be directly related to the elastic modulus of the brittle material being tested. A parameter study was conducted and revealed that the method can be optimized when the film Poisson’s ratio is lower than the brittle material tested. This more directly transfers the indenter load to the substrate, enabling it to participate in the composite elastic response earlier in the indentation process. The result is an expanded range of fit of the experimental data to the models linear asymptote, providing more accurate elastic property measurements. Chromium was identified as an ideal film material due to its low Poisson’s ratio, ductility and ability to be deposited onto most ceramics with a strong interface. The improvement was demonstrated on 5 brittle materials with a wide variety of elastic properties; SiC, Al2O3, MgO, SiO2, CaCO3.

Four-parameter models have received increasing psychometric attention in recent years, as a reduced upper asymptote for item characteristic curves can be appealing for measurement applications such as adaptive testing and person-fit assessment. However, applications can be challenging due to the large number of parameters in the model. In this article, we demonstrate in the context of mathematics assessments how the slip and guess parameters of a four-parameter model may often be empirically related. This observation also has a psychological explanation to the extent that both asymptote parameters may be manifestations of a single item complexity characteristic. The relationship between lower and upper asymptotes motivates the consideration of an asymmetric item response theory model as a three-parameter alternative to the four-parameter model. Using actual response data from mathematics multiple-choice tests, we demonstrate the empirical superiority of a three-parameter asymmetric model in several standardized tests of mathematics. To the extent that a model of asymmetry ultimately portrays slips and guesses not as purely random but rather as proficiency-related phenomena, we argue that the asymmetric approach may also have greater psychological plausibility.

Dispersion analysis of Lamb waves propagating in anisotropic functionally graded plates with transverse inhomogeneity reveals that the high frequency asymptotes associated with the interfacial Stoneley waves disappear, while in stratified plates the corresponding high frequency asymptotes exist. The analysis utilizes a variant of the Cauchy sextic formalism coupled with the exponential fundamental matrices for constructing explicit dispersion equation.

A popular parameterized soil water retention curve (SWRC) has a hydraulic conductivity curve associated with it that can have a physically unacceptable infinite slope at saturation. The problem was eliminated before by giving the SWRC a non-zero air entry value. This improved version still has an asymptote at the dry end, which limits its usefulness for dry conditions and causes its integral to diverge for commonly occurring parameter values. We therefore joined the parameterizations' sigmoid midsection to a logarithmic dry section ending at zero water content for a finite matric potential, as was done previously for a power-law-type SWRC. We selected five SWRC parameterizations that had been proven to produce unproblematic near-saturation conductivities and fitted these and our new curve to data from 21 soils. The logarithmic dry branch gave more realistic extrapolations into the dry end of both the retention and the conductivity curves than an asymptotic dry branch. We tested the original curve, its first improvement, and our second improvement by feeding them into a numerical model that calculated evapotranspiration and deep drainage for nine combinations of soils and climates. The new curve was more robust than the other two. The new curve was better able to produce a conductivity curve with a substantial drop during the early stages of drying than the earlier improvement. It therefore generated smaller amounts of more evenly distributed deep drainage compared to the spiked response to rainfall produced by the earlier improvement.

We present an example of demonstration for the basin boundaries in classical rearrangement scattering with particular emphasis on the breakup channel. Whereas the basin boundaries of the other arrangement channels are given by stable manifolds of periodic orbits in the interaction region, the basin boundary of the breakup channel is given by the stable manifold of a particular subset in the set of final asymptotes. The geometry of this boundary surface is presented in detail. Further, we discuss the transition to chaos at the energetic threshold of the breakup channel and the related basin boundary metamorphosis.

Visualizations of reduced-order representations of stratified wakes of Reynolds number $$Re \in \{5,25,100\}\times 10^3$$ are presented at a fixed internal Froude number. The reduced-order representations are constructed by applying proper orthogonal decomposition (POD) to numerical datasets that are high-resolution, three-dimensional and time-dependent. Due to the transient nature of the flow, the dynamics to be represented are highly non-stationary, posing a challenge for the effectiveness of POD. The translational symmetry inherent in the computational configuration is utilized for the POD analysis. This technique turns out to be effective in terms of improving the convergence of energy content represented by the POD modes and enhancing the interpretability of the temporal dynamics. Individual POD modes representing distinct dynamics of various scales are visualized. In the turbulent region, visualizations of the reconstructed vertical vorticity fields suggest that the dominant length scale of flow structures decreases with the modal index. For internal wave motions, visualizations of the reconstructed vertical velocity fields show the opposite trend, as the wavelength of internal waves observed in the wake’s ambient increases with the modal index. The temporal coefficients for a given mode are observed to vary minimally between $$Re = 2.5\times 10^4$$ and $$10^5$$ , suggesting a potential asymptote of the large-scale temporal dynamics in terms of Reynolds number.

Reliability-based design optimization (RBDO) offers a powerful tool to deal with the structural design with heterogeneous interval parameters concurrently. However, it is time-consuming in the practical engineering design. Therefore, a novel sequential moving asymptote method (SMAM) is proposed to improve the computational efficiency for convex model in this study, in which the nested double-loop optimization problem is decoupled to a sequence of deterministic suboptimization problems based on the method of moving asymptotes. In addition, the sensitivity of reliability index is derived, so the finite difference for the nested optimization loop can be avoided to tremendously improve the computational efficiency. Then, the accuracy of the SMAM is proved based on the error analysis. Furthermore, the Kreisselmeier-Steinhauser (KS) function is used to assemble the multiple constraints to deal with the parallel and series RBDO problems. One benchmark mathematical example, three numerical examples, and one complex civil engineering example, i.e., tower crane, are tested to demonstrate the efficiency of the proposed method by comparison with other existing methods, and the results indicate that SMAM offers a general and effective tool for non-probabilistic reliability analysis and optimization.

Allometric scaling laws critically examine structure–function relationships. In estimating the forest biomass carbon and its response under climate change, the issue of scaling has resulted in difficulties when modelling the biomass for different-sized trees, especially large ones, and has not yet been solved in either theory or practice. Here, we propose the concept of a dynamic allometric scaling relationship between stem biomass and above-ground biomass The allometric curve approaches an asymptote with an increase in tree size. An asymptotic allometric equation is presented that has a better fit to the data than the simple power-law allometric equation. The non-constant exponent is determined by the change in the biomass ratio for different organs and is governed by the dynamic allometric coefficient. This study presents a methodological framework to theoretically characterize allometric relationships and provides new insights in understanding the general scaling pattern and carbon sequestration capacity of large trees across global forests. Projecting biomass carbon in forests is challenging due to the modelling of different-sized trees. This Article proposes a dynamic allometric scaling relationship that better fits scaling patterns for large trees and their biomass.

Both the Hilbert transform and the B-spline wavelets are important tools in signal processing, which makes a study of relation between these two subjects be of practical significance. In particular, because the B-spline wavelets have good properties including vanishing moments, symmetry, compact support and so on, we focus on the Hilbert transform of B-spline wavelets in this letter. For this purpose, the B-spline wavelets of order $m$ is described in a piecewise polynomial form firstly. An important property of the Pascal triangle transform is then explored. Based on these results, an explicit form of the Hilbert transform of B-spline wavelet of order $m$ is established. Furthermore, the vanishing moments, symmetry and asymptote behavior of the Hilbert transform of B-spline wavelets are also discussed. To demonstrate the effectiveness of these results, two examples in the case of $m=3$ and $m=4$ are given and the graphs of these two B-spline wavelets as well as their Hilbert transforms are presented. These two cases of $m=3$ and $m=4$ provide two Hilbert transform pairs of wavelets, which can be used in digital image processing.

In this paper, we introduce an extension of our previous paper, A globally convergent version to the Method of Moving Asymptotes, in a multivariate setting. The proposed multivariate version is a globally convergent result for a new method, which consists iteratively of the solution of a modified version of the method of moving asymptotes. It is shown that the algorithm generated has some desirable properties. We state the conditions under which the present method is guaranteed to converge geometrically. The resulting algorithms are tested numerically and compared with several well-known methods.

In analytical geometry an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tend to infinity. Some source includes the requirements that the curve may not cross the line infinitely often but this is unusual for modern definition. In some content such as algebraic geometry an asymptote is defined as a line which is tangent to a curve at infinity. In some case a curve may have a branch or branches extending beyond the finite region. In this case of p be a point on such a branch of the curve, having its coordinates (x,y) and if P moves along the curve, so that at least one of x and y tend to + ∞ and to -∞, then P is said to tend to infinites and this we denote by P → ∞

Research conducted in US schools shows summer learning loss in test scores. If this summer loss is not incorporated into models of student ability growth, assumptions will be violated because fall scores will be overestimated and spring scores will be underestimated, which can be particularly problematic when evaluating teacher or school effectiveness. Statistical methods for summer loss have remained relatively undeveloped and often rely on lagged-time or piecewise models, which commonly saturate the mean structure and become reparameterizations of empirical means. Compound polynomial models have recently been introduced and simultaneously model within-year and between-year growth processes in test scores. However, these models operate with polynomial functions of time, which can have limited interpretative utility. In this article, we propose incorporating seasonality within the dynamic measurement modelling (DMM) framework. DMM reparametrizes non-linear growth models to directly estimate interpretable quantities (e.g. learning capacity as an upper asymptote on growth). Borrowing from ecological models proposed for body mass of cold-climate species, we show how DMM can incorporate seasonality to provide more interpretable parameters as well as to explicitly include summer learning loss as a parameter in the model.

This paper formulates a mathematical model using the extrapolation of load-settlement curves with a rational function for analyzing the capacity of piles obtained from the static load test (SLT). In preliminary analyses, the extrapolation was based on the application of a number of mathematical functions that were gradually eliminated by iterative selection and filtering. The solution was obtained by extrapolation with a rational function. Using a rational function in the extrapolation of the load-settlement curve, a clearly identifiable part is obtained in which the asymptote is vertical, indicating the reached limit state of capacity in the soil and/or in the pile. The probabilistic analysis showed that no unique value for pile capacity was obtained, and that the spectrum of capacity values depends on the probability of occurrence of the corresponding event.

There are growing demands in the robot industry for light structures in order to increase the speed of the robot motion and thus the productivity. Size and shape optimization are carried out previously to achieve minimum traveling time of the robot arm taking into consideration its flexibility. In this work, topology optimization is introduced for obtaining optimum robot arm to achieve minimum traveling time from both structure and control viewpoints. Method of Moving Asymptotes is used as optimization technique, because it can handle arbitrary number of constrains and considered to be a general and flexible optimization method. A comparison is accomplished between the optimal resulted design and its initial design for different dimensions of robot arm neglecting air damping. It is found that the reduction ratio of the travelling time reaches 62% and the reduction ratio of the weight reaches 70%. A comparison between this work using topology optimization of flexible robot arm outperforms the size and the shape optimization when considering the real condition that takes into account the air damping. The optimum topological design in this case gives reduction ratio of travelling time equals 44.8%, while previous work gives 23.5%.

The open porosity of air-saturated acoustical porous materials is estimated from the low-frequency or high-frequency asymptotes of the real part of the dynamic bulk modulus. Combining this technique with the estimation of the static air-flow resistivity from the low-frequency asymptote of the imaginary part of the dynamic mass density and the analytical inversions of the remaining parameters from the dynamic mass density and bulk modulus [methods introduced by Panneton and Olny, J. Acoust. Soc. Am. 119(4), 2027-2040 (2006) and Olny and Panneton 123(2), 814-824 (2008)], this work estimates all six parameters of a Johnson-Champoux-Allard-Lafarge model from impedance tube measurements. A classical two-microphone impedance tube, as well as three- or four-microphone tubes, can be used for these measurements and estimations. Examples of applications and limits of the method are presented and a tool to estimate the open porosity and the static air-flow resistivity is made available online.

The author solves the problem connected with determination of shape of pillars which remain stable under any compression due to barrel distortion. The analysis of cylindrical structures uses the known Leibenson–Ishlinsky stability criterion. The boundary conditions of the problem and its solution are obtained: elasticity in the form of the critical load dependence on the height/radius ratio of pillars. The found asymptote to the curves is associated with the optimized shape of pillars.

A relation connecting stress intensity factors (SIF) with displacement intensity factors (DIF) at the crack front is derived by solving a pseudodifferential equation connecting stress and displacement discontinuity fields for a plane crack in an elastic anisotropic medium with arbitrary anisotropy. It is found that at a particular point on the crack front, the vector valued SIF is uniquely determined by the corresponding DIF evaluated at the same point.

Wood removed in Southwestern US forest restoration treatments currently has limited markets and thus low value. One important property of wood in structural products is its stiffness (measured as modulus of elasticity), which is known to vary systematically within trees. Directly measuring wood stiffness is expensive, time consuming and destructive. Therefore, we tested samples of ponderosa pine (Pinus ponderosa var. scopulorum Engelm.) from northern Arizona destructively in bending and also non-destructively using acoustic velocity (AV) methods. In total, we tested multiple pith-to-bark small clear (2.54 × 2.54 × 40.64 cm) samples from up to four heights in 103 trees. We first measured the standing-tree AV of sample trees, then the AV of small clear samples, and finally measured wood stiffness using three point static bending tests. We found that a Michaelis–Menten curve was a good fit to the radial profile of wood stiffness, with a steep increase outward from the pith that approached an asymptote. The AV of small clear samples, coupled with measured volumetric density values, approximated the static modulus of elasticity values with high accuracy (r2 = 0.86). At the stand level, a model predicting standing tree AV from tree morphology fit the data well (r2 = 0.77). Results indicate that southwestern ponderosa pine contains outerwood with relatively high stiffness that could be suitable for structural products. However, when assessed using wood stiffness, the trees take a long time to reach maturity (~50 years) and thus the corewood proportion is large. AV measurements are a good way to assess variability within and among stands and thus could be employed to segregate the resource by expected stiffness values. Segregation could help identify stands not suitable for structural uses and direct them toward more appropriate products.

When we collect the growth curves of many individuals, orderly variation in the curves is often observed rather than a completely random mixture of various curves. Small individuals may exhibit similar growth curves, but the curves differ from those of large individuals, whereby the curves gradually vary from small to large individuals. It has been recognized that after standardization with the asymptotes, if all the growth curves are the same (anamorphic growth curve set), the growth curve sets can be estimated using nonchronological data; otherwise, that is, if the growth curves are not identical after standardization with the asymptotes (polymorphic growth curve set), this estimation is not feasible. However, because a given set of growth curves determines the variation in the observed data, it may be possible to estimate polymorphic growth curve sets using nonchronological data.In this study, we developed an estimation method by deriving the likelihood function for polymorphic growth curve sets. The method involves simple maximum likelihood estimation. The weighted nonlinear regression and least‐squares method after the log‐transform of the anamorphic growth curve sets were included as special cases.The growth curve sets of the height of cypress (Chamaecyparis obtusa) and larch (Larix kaempferi) trees were estimated. With the model selection process using the AIC and likelihood ratio test, the growth curve set for cypress was found to be polymorphic, whereas that for larch was found to be anamorphic. Improved fitting using the polymorphic model for cypress is due to resolving underdispersion (less dispersion in real data than model prediction).The likelihood function for model estimation depends not only on the distribution type of asymptotes, but the definition of the growth curve set as well. Consideration of these factors may be necessary, even if environmental explanatory variables and random effects are introduced., A growth curve set with an orderly variation is called "polymorphic" growth curve set. It is also recognized that the polymorphic growth curve set cannot be estimated using nonchronological data. However, the growth curve set can be estimated with nonchronological data using a simple maximum likelihood estimation by modeling the probability to observe a given nonchronological data.

Topology optimization approach is considered among the most interesting fields of structural optimization. In this paper topology optimization for compliance minimization using method of moving asymptotes MMA is presented. This method is considered as a general and flexible optimization method, where it can handle any kind of objective function and any number of constraints. The effect of changing the lower and upper asymptotes on the optimization process convergence is studied for seeking the demanded convergence with more stability and minimum time as possible. Topology optimization of different models such as a cantilever beam and simply supported beam for two and three dimensional structure is accomplished. Also a comparison between Method of Moving Asymptotes (MMA) and different methods such as Sequential Quadratic Programming (SQP), Optimality Criteria (OC), and Hybrid Cellular Automata (HCA) is accomplished according to the compliance value, time consumed and the resulted topological shape.

Teak (Tectona grandis L.f.) plantations are increasingly being established in tropical regions to meet a rising demand for its highly valued timber. Teak plantations have been established in the Atlantic Coastal Plain region of Colombia, a region climatically suitable for teak growth by having a monsoon climate with a unimodal precipitation pattern. Tree diameter at breast height (DBH, 1.3 m above ground) and mean top height, periodically measured over a 17-year period in 44 permanent sampling plots of size 0.06 and 0.10 ha, were used in this study. A stochastic differential equation (SDE), along with a Bertalanffy–Richards-type height growth model, was used to model and estimate top height growth of teak plantations in Colombia. Environmental noise and height measurement errors were explicitly considered as the main uncertainty sources of mean top height growth. The best model for estimating mean top height, based on statistical performance and biological rationale, had the asymptote defined as a local parameter and the growth rate and shape specified as global parameters. This model outperformed its counterpart that had the growth rate specified as a local parameter and asymptote and shape as global parameters. The selected model also outperformed alternative approaches such as the mixed-effects model, generalized algebraic difference approach, and the dummy variable method. Estimated trajectories for the mean top height of teak in Colombia are biologically sound based on the measured height series and previous studies in Latin America. Results suggest that most of the uncertainty associated with the mean top height growth of teak plantations in Colombia was largely explained by environmental noise. The best estimated model using the SDE approach can be useful for predicting height growth and evaluating site productivity of teak plantations in Colombia and in neighbouring countries with biophysical characteristics similar to those where teak has been planted in Colombia.

Passive magnetic channel is a kind of beam focusing elements in a cyclotron. It consists of several soft iron bars that are magnetized by the main field in a cyclotron. In this paper, we proposed a topology optimization method to design the pole shape in passive magnetic channel, this method does not require any fixed geometry pattern or initial design. The nonlinear static magnetic finite-element analysis model is used to calculate the objective magnetic field function. Persuade iron material with variable density is used to describe the iron distribution during the iteration. Method of Moving Asymptotes (MMA) is used to optimize the control variable of iron density distribution on magnetic channel cross-section. In three numerical examples, magnetic channels for a 250 MeV superconducting cyclotron is provided, where the design goal is to provide the given magnetic field gradient and bending angle. The relationship between the design goal and the pole shape pattern is discussed. It reveals that magnetic channel pattern with only 2 iron bars is possible for some design goals.

This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology optimization. The formulation allows for initial finite deformations and subsequent small harmonic oscillations. The optimization problem is solved by the method of moving asymptotes, and the gradients are calculated using the adjoint method. Both simple and degenerate eigenfrequencies are considered in the sensitivity analysis. A well-posed topology optimization problem is formulated by filtering the volume fraction field. Numerical issues associated with excessive distortion and spurious eigenmodes in void regions are reduced by removing low volume fraction elements. The optimization objective is to maximize stiffness subject to a lower bound on the fundamental eigenfrequency. Numerical examples show that the eigenfrequencies drastically change with the load magnitude, and that the optimization is able to produce designs with the desired fundamental eigenfrequency.

Recently, different distributions have been generalized using the T-R {Y} framework but the possibility of using Dagum distribution has not been assessed. The T-R {Y} combines three distributions, with one as a baseline distribution, with the strength of each distribution combined to produce greater effect on the new generated distribution. The new generated distributions would have more parameters but would have high flexibility in handling bimodality in datasets and it is a weighted hazard function of the baseline distribution. This paper therefore generalized the Dagum distribution using the quantile function of Lomax distribution. A member of T-Dagum class of distribution called exponentiated-exponential-Dagum {Lomax} (EEDL) distribution was proposed. The distribution will be useful in survival analysis and reliability studies. Different characterizations of the distribution are derived, such as the asymptotes, stochastic ordering, stress-strength analysis, moment, Shannon entropy, and quantile function. Simulated and real data are used and compared favourably with existing distributions in the literature.

This paper aims to propose a quantitative tuning method for active disturbance rejection control (ADRC) that controls the K /( Ts + 1) n -type high-order processes. An asymptote in the Nyquist curve has been observed for the first time and its mathematical expression has been deduced. An asymptote condition is provided in order to derive a parameter tuning rule under the sensitivity constraint. Although this proposed tuning rule is originally designed for a certain type of high-order processes, it can be extended to other types processes that can be approximated into the form of K /( Ts + 1) n . Comparisons with different PID control strategies have been conducted for a range of cases to demonstrate the efficiency of the proposed tuning method. Finally, the effectiveness of the proposed tuning rule is experimentally verified on water tank system that exhibits high-order dynamics. Field tests on the superheater steam temperature control of a circulating fluidized bed power plant further demonstrate its potential for applications in complex industrial processes.

A planar system has been proposed in the paper Rankin et al. (Nonlinear Dyn 66:681–688, 2011) to understand the canard explosion detected in a 6D aircraft ground dynamics model. A specific feature of this minimal 2D system is a critical manifold with a single fold and an asymptote. In this paper, we provide a high-order analytical prediction (in fact, up to any wanted order) of the canard explosion in this system. Using a nonlinear time transformation method, we are able to approximate not only the critical parameter value, but also the critical manifold in the phase space. The comparison of our theoretical results with the corresponding numerical continuations shows a very good agreement.

A global potential energy surface for the lowest quartet state of HN2 is reported for the first time from accurate multi-reference ab initio calculations extrapolated to the complete basis set limit using the double many-body expansion method. All its stationary points are characterized, with the lowest quartet of HN2 predicted to have a bent global minimum 36 kcal mol-1 below the N(4S)+NH(X 3Σ−) asymptote, from which it is barrierlessly achievable. The entire set of calculated ab initio points has been fitted for energies up to 1000 kcal mol-1 above the global minimum with a rmsd of 0.89 kcal mol-1, a gap comprising all identified stationary points. Special care is taken in modeling the involved long-range for ces, and cusps caused by crossing seams. The novel PES will prompt for the calculation of rate constants for several unexplored reactions that are relevant for combustion, plasma and atmospheric chemistry.

In this letter an intuitive measurement based approximation for packet switched network traffic in backbone links is presented. It consists of a sum of independent non-identical Bernoulli sources. The resulting sum has a Poisson binomial distribution which can be approximated to a skewed Gaussian distribution at the asymptote. It can be further approximated to a binomial distribution for predicting congestion by estimating the number of users of the network. The results are verified using samples of traffic data from 42 academic and research institutions.

We consider a user-centric cooperative-cellular network where ${K}$ base stations cooperate to detect the signal from a mobile user in the presence of infinitely many interfering mobiles, using a linear Minimum-Mean-Square-Error (MMSE) receiver. As the number of antennas per base station grows large, it is shown that the uplink spectral efficiency approaches an asymptote that has a simple form, which reveals the relationships between key system parameters. This result generalizes our recently reported findings, which were applicable to mobiles distributed as a Poisson Point Process (PPP), to any model for mobile locations as long as the mobile density exists.

The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical asymptotes of solutions of systems of explosive type. A special case of such systems is the population explosion model. A theorem on the existence of asymptotes is proved. The extension of the numerical method for piecewise smooth systems is described using the Chua system as an example, as well as systems with hysteresis., Comment: Mathematics, 10:8 (2022), 1207

Observance of Stoneley waves at the guided wave dispersion in stratified plates containing layers with alternating contrast physical properties is analyzed by applying Cauchy sextic formalism coupled with the exponential fundamental matrix method. Additional high-frequency asymptotes related to appearing interfacial Stoneley waves are detected and analyzed. Comparison with the case when Stoneley waves do not exist is presented.

The main purpose of this paper is to propose a novel efficient design optimization technique based on the operational quadrature boundary element method (OQBEM) for a simulation study on the material distribution and influence of rotation on the optimal design of rotating anisotropic viscoelastic porous permeable structures. An implicit differentiation method was developed to calculate the design sensitivities of displacements and pore pressure with respect to design variables and the effects of rotation on these sensitivities are also discussed. The optimization problem is solved using the Moving Asymptotes Method (MAM) which requires the calculation of the sensitivities for objective function and constraints by adjoint variable method. The optimum shape design of an elliptical sandwich structure is used as the numerical example to verify the validity and accuracy of the proposed technique.

This study proposes a method for camera calibration using the properties of conic asymptotes, which are combined with the projective invariance, images of the asymptotes, and image of the absolute points to obtain the vanishing line. Constraints for the image of the absolute conic are obtained from a set of orthogonal vanishing points, the homography, and images of the circular points. The proposed calibration algorithm is compared with several other research methods, and its effectiveness and robustness are verified within a certain error range from the results of simulated and real experiments for different eccentricities without loss of generality.

We show that kinematics of charged particles allows us to model the growth of particles' energy by consecutive particle-splits, once a spherical mirror as a perfectly reflective boundary is placed outside a charged black hole. We consider a charged version of the Penrose process, in which a charged particle decays into two fragments, one of them has negative energy and the other has positive energy that is larger than that of the parent particle. The confinement system with the mirror makes the particles' energy amplified each time a split of the parent particle occurs. Thus, the energy is a monotonically increasing function of time. However, the energy does not increase unboundedly, but rather asymptotes to a certain finite value, implying no instability of the system in this respect., 16 pages, 5 figures, typo corrected, miscalculation fixed, version accepted for PRD

We construct new families of $\text{AdS}_2 \times S^2 \times S^2$ solutions with 4 supercharges in Type II supergravities. We show that subclasses of these solutions can be interpreted in terms of defect branes embedded in 4d $\mathcal{N} = 4 $ SYM, or orbifolds thereof. This is explicitly realised by showing that the solutions asymptote locally to $\text{AdS}_5 \times S^5/\mathbb{Z}_n$, in Type IIB, or its T-dual background, in Type IIA. The latter is a Gaiotto-Maldacena geometry realised on an intersection of D4 and NS5 branes. We extend the Type IIA solutions to include D6 branes, and interpret them as describing backreacted baryon vertices within 4d $\mathcal{N} = 2$ CFTs living in D4-NS5-D6 intersections. We propose explicit quiver quantum mechanics in which the defect branes play the role of colour branes, with the D4 branes of the D4-NS5-D6 intersection becoming flavour branes. These quivers are used to compute the degeneracies of the ground states of the dual super conformal quantum mechanics, that are shown to agree with the holographic expressions., 40 pages, 3 figures