Asymptotic Relations Research Articles

Two-Dimensional Steady Boussinesq Convection: Existence, Computation and Scaling

This research investigates laser-induced convection through a stream function-vorticity formulation. Specifically, this paper considers a solution to the steady Boussinesq Navier–Stokes equations in two dimensions with a slip boundary condition on a finite box. A fixed-point algorithm is introduced in stream function-vorticity variables, followed by a proof of the existence of steady solutions for small laser amplitudes. From this analysis, an asymptotic relationship is demonstrated between the nondimensional fluid parameters and least upper bounds for laser amplitudes that guarantee existence, which accords with numerical results implementing the algorithm in a finite difference scheme. The findings indicate that the upper bound for laser amplitude scales by O(Re−2Pe−1Ri−1) when Re≫Pe, and by O(Re−1Pe−2Ri−1) when Pe≫Re. These results suggest that the existence of steady solutions is heavily dependent on the size of the Reynolds (Re) and Peclet (Pe) numbers, as noted in previous studies. The simulations of steady solutions indicate the presence of symmetric vortex rings, which agrees with experimental results described in the literature. From these results, relevant implications to thermal blooming in laser propagation simulations are discussed.

Mixed Modes and Asteroseismic Surface Effects. II. Subgiant Systematics

Abstract Models of solar-like oscillators yield acoustic modes at different frequencies than would be seen in actual stars possessing identical interior structure, due to modeling error near the surface. This asteroseismic “surface term” must be corrected when mode frequencies are used to infer stellar structure. Subgiants exhibit oscillations of mixed acoustic (p-mode) and gravity (g-mode) character, which defy description by the traditional p-mode asymptotic relation. Since nonparametric diagnostics of the surface term rely on this description, they cannot be applied to subgiants directly. In Paper I, we generalized such nonparametric methods to mixed modes, and showed that traditional surface-term corrections only account for mixed-mode coupling to, at best, first order in a perturbative expansion. Here, we apply those results, modeling subgiants using asteroseismic data. We demonstrate that, for grid-based inference of subgiant properties using individual mode frequencies, neglecting higher-order effects of mode coupling in the surface term results in significant systematic differences in the inferred stellar masses, and measurable systematics in other fundamental properties. While these systematics are smaller than those resulting from other choices of model construction, they persist for both parametric and nonparametric formulations of the surface term. This suggests that mode coupling should be fully accounted for when correcting for the surface term in seismic modeling with mixed modes, irrespective of the choice of correction used. The inferred properties of subgiants, in particular masses and ages, also depend on the choice of surface-term correction, in a different manner from those of both main-sequence and red giant stars.

Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments

In this paper, we consider the sum Snξ = ξ1 + ... + ξn of possibly dependent and nonidentically distributed real-valued random variables ξ1, ... , ξn with consistently varying distributions. By assuming that collection {ξ1, ... , ξn} follows the dependence structure, similar to the asymptotic independence, we obtain the asymptotic relations for E((Snξ)α1(Snξ > x)) and E((Snξ – x)+)α, where α is an arbitrary nonnegative real number. The obtained results have applications in various fields of applied probability, including risk theory and random walks.

The ropelength of complex knots

The ropelength of a knot is the minimum contour length of a tube of unit radius that traces out the knot in three dimensional space without self-overlap, colloquially the minimum amount of rope needed to tie a given knot. Theoretical upper and lower bounds have been established for the asymptotic relationship between crossing number and ropelength and stronger bounds have been conjectured, but numerical bounds have only been calculated exhaustively for knots and links with up to 11 crossings, which are not sufficiently complex to test these conjectures. Existing ropelength measurements also have not established the complexity required to reach asymptotic scaling with crossing number. Here, we investigate the ropelength of knots and links beyond the range of tested crossing numbers, past both the 11-crossing limit as well as the 16-crossing limit of the standard knot catalogue. We investigate torus knots up to 1023 crossings, establishing a stronger upper bound for T(p, 2) knots and links and demonstrating power-law scaling in T(p, p + 1) below the proven limit. We investigate satellite knots up to 42 crossings to determine the effect of a systematic crossing-increasing operation on ropelength, finding that a satellite knot typically has thrice the ropelength of its companion. We find that ropelength is well described by a model of repeated Hopf links in which each component adopts a minimal convex hull around the cross-section of the others, and derive formulae that heuristically predict the crossing-ropelength relationship of knots and links without free parameters.

On the Optimality of the Greedy Policy for Battery Limited Energy Harvesting Communications

Consider a battery limited energy harvesting communication system with online power control. Assuming independent and identically distributed (i.i.d.) energy arrivals and the harvest-store-use architecture, it is shown that the greedy policy achieves the maximum throughput if and only if the battery capacity is below a certain positive threshold that admits a precise characterization. Simple lower and upper bounds on this threshold are established. The asymptotic relationship between the threshold and the mean of the energy arrival process is analyzed for several examples.

Winter Wheat (Triticum aestivum L.) Tolerance to Mulch.

Mulch from cover crops can effectively suppress weeds in organic corn (Zea mays L.) and soybean (Glycine max L.) as part of cover crop-based rotational no-till systems, but little is known about the feasibility of using mulch to suppress weeds in organic winter small grain crops. A field experiment was conducted in central NY, USA, to quantify winter wheat (Triticum aestivum L.) seedling emergence, weed and crop biomass production, and wheat grain yield across a gradient of mulch biomass. Winter wheat seedling density showed an asymptotic relationship with mulch biomass, with no effect at low rates and a gradual decrease from moderate to high rates of mulch. Selective suppression of weed biomass but not wheat biomass was observed, and wheat grain yield was not reduced at the highest level of mulch (9000 kg ha−1). Results indicate that organic winter wheat can be no-till planted in systems that use mulch for weed suppression. Future research should explore wheat tolerance to mulch under different conditions, and the potential of no-till planting wheat directly into rolled-crimped cover crops.

Spatial components dependence for bidimensional time-constant AR(1) model with alpha -stable noise and triangular coefficients matrix

In this paper, we examine the bidimensional time-constant autoregressive model of order 1 with alpha -stable noise. We focus on the case of the triangular coefficients matrix for which one of the spatial components of the model simplifies to the one-dimensional autoregressive time series. We study the asymptotic behaviour of the cross-codifference and the cross-covariation applied to describe the dependence in time between the spatial components of the model. As a result, we formulate the theorem about the asymptotic relation between both measures, which is consistent with the result that is correct for the case of the non-triangular coefficients matrix.

Asymptotic Input-Output Relationship Predicts Electric Field Effect on Sublinear Dendritic Integration of AMPA Synapses.

An extracellular electric field (EF) induces transmembrane polarizations on extremely inhomogeneous spaces. Evidence shows that EF-induced somatic polarization in pyramidal cells can modulate the neuronal input-output (I/O) function. However, it remains unclear whether and how dendritic polarization participates in the dendritic integration and contributes to the neuronal I/O function. To this end, we built a computational model of a simplified pyramidal cell with multi-dendritic tufts, one dendritic trunk, and one soma to describe the interactions among EF, dendritic integration, and somatic output, in which the EFs were modeled by inserting inhomogeneous extracellular potentials. We aimed to establish the underlying relationship between dendritic polarization and dendritic integration by analyzing the dynamics of subthreshold membrane potentials in response to AMPA synapses in the presence of constant EFs. The model-based singular perturbation analysis showed that the equilibrium mapping of a fast subsystem can serve as the asymptotic subthreshold I/O relationship for sublinear dendritic integration. This allows us to predict the tendency of EF-mediated dendritic integration by showing how EF changes modify equilibrium mapping. EF-induced hyperpolarization of distal dendrites receiving synapses inputs was found to play a key role in facilitating the AMPA receptor-evoked excitatory postsynaptic potential (EPSP) by enhancing the driving force of synaptic inputs. A significantly higher efficacy of EF modulation effect on global AMPA-type dendritic integration was found compared with local AMPA-type dendritic integration. During the generation of an action potential (AP), the relative contribution of EF-modulated dendritic integration and EF-induced somatic polarization was determined to show their collaboration in promoting or inhibiting the somatic excitability, depending on the EF polarity. These findings are crucial for understanding the EF modulation effect on neuronal computation, which provides insight into the modulation mechanism of noninvasive brain modulation.

Asymptotic modeling of electrochemical signaling: Testing Zn in urine for non-invasive bladder cancer diagnosis

A theoretical model on chemical signaling for diagnosis based on the combination of signals for marker and inert and/or interfering metabolites is described. The model yields asymptotic relationships between the intensities of the signals representative of marker and accompanying metabolites compensating concentration fluctuations. The model fits well with voltammetric features associated to the oxidation of different urine metabolites and Zn(II) reduction in the same urine samples after alkaline digestion. As a result, a non-invasive electrochemical detection of urothelial carcinoma (bladder cancer, BC) is reported. Different diagnostic criteria are described all displaying high sensitivity, specificity and positive/negative predictive values. The described methodology was tested by means of an analytical trial with 46 patients with histological and pathologically confirmed BC, 30 healthy controls and 26 patients diagnosed of other urinary pathologies,

Lebesgue constants of Riesz type means of negative order

We give an asymptotic formula for the Lebesgue constants of the Riesz means of negative order in dimension one. The obtained result allows us to extend the asymptotic relations to those for the Lebesgue constants of more general means.

Large-Deflection Nonlinear Mechanics of Curved Cantilevers Under Contact Point Loading

Abstract Presented here is a comprehensive model for hook bending behavior under contact loading conditions, motivated by the relevance of this problem to reusable hook attachment systems in nature and engineering. In this work, a large-deflection model that can describe the bending of hooks, taken as precurved cantilevers with uniform initial curvature, was derived and compared with physical testing. Physical testing was performed with stainless-steel and aluminum hooks shaped as semicircular arcs. The force versus displacement behavior exhibited a linear portion for small displacements but at large displacements there was an asymptotic relation where the force approached some limit and remained flat as further displacement occurred. Comparison with testing showed that the model developed in this paper gave good agreement with the physical testing. Surprisingly, in dimensionless form, all parameters to define the hook transform to approximately linear functions of displacement. Using these linear relations, several equations are presented that allow for rapid calculation of the dimensional force versus displacement for a hook.

An asymptotic relation between the wirelength of an embedding and the Wiener index

An asymptotic relation between the wirelength of an embedding and the Wiener index

Evaluation of sustained release mineral boluses as a long-term nutrient delivery method for beef cattle

Two studies were conducted to evaluate the efficacy of sustained release mineral boluses as an alternative nutrient delivery method for beef cattle. For both studies 16 ruminally-cannulated cows were used in a completely randomized design. In study 1, we evaluated degradation rates of two bolus prototypes and cow age (2-yr-old versus 3-yr-old cows) over an 87-d study period. In study 2, we evaluated two bolus types (90-d degradation target versus 180-d degradation target), as well as two diet qualities contrasting a low-quality high-fiber forage (> 600 g/kg neutral detergent fiber and < 80 g/kg crude protein, dry matter basis) and high-quality low-fiber forage (< 500 g/kg neutral detergent fiber and> 150 g/kg crude protein, dry matter basis). For both Study 1 & 2, intake and digestion periods were conducted to evaluate cow age (study 1) or diet quality (study 2) effects on intake and rumen/reticulum function. In study 1, models containing an asymptotic effect of day and an interaction between day and bolus type were the best supported of the candidate models for bolus degradation rate. Cow age did not affect (P= 0.48) bolus degradation rates (β^ = -0.81 ± 1.13) and degradation rates were greater (P < 0.01) for bolus prototype B compared to bolus A (β^prototype B = -20.39 ± 1.13; β^prototype A = -9.64 ± 0.81). Bolus degradation rate displayed an asymptotic relationship (P < 0.01) to bolus surface area for prototype A (β^ = 5.83 ± 0.57) and a linear relationship (P < 0.01) for prototype B (β^ = 0.001 ± 0.0001). In study 2, models containing a linear effect of day and an interaction between day and diet were the best supported of the candidate models for the degradation rate of the 90-d and 180-d prototype. In addition, both bolus protoypes displayed a diet quality × time interaction (P < 0.01) for bolus degradation rate. Cattle treated with the 90-d bolus and fed a high-quality diet had a greater (P < 0.01) degradation rate (β^High-quality = -2.64 ± 0.08; β^Low-quality = -1.97 ± 0.10) than the cows that were fed a low-quality diet. In contrast, cattle treated with the 180-d bolus had an inverse effect (P < 0.01), with bolus degradation rates greater (β^Low-quality = -0.09 ± 0.007; β^High-quality = -0.04 ± 0.005) with cows on the low-quality diet versus the high-quality diet. Across both studies, two of four bolus prototypes met target release rates at 90 days. However, bolus prototype degradation characteristics varied and were influenced by diet quality.

The Mysterious Souls of Hellé and Debussy’s Toys

Abstract This article is a study of the piano version of Debussy’s La Boîte à joujoux—a musical storybook with illustrations by André Hellé—in the context of literary discourses about the toy. The storybook’s exploration of the nature of toyhood illustrates what Barbara Johnson calls the ‘asymptotic relation between things and persons’. Hellé and Debussy’s characters invite a contribution to philosophical reflections on the role of mechanical bodies as signifying a relationship between subjecthood and objecthood. The characters of La Boîte à joujoux are, I suggest, entirely untroubled by the distinction between interiority and exteriority that haunted the modernist imagination. The final section answers a broader question prompted by the storybook’s opening: how toys could serve as comic ideals of the modern urban citizen.

On the Measure-Theoretic Premises of Bayes Factor and Full Bayesian Significance Tests: a Critical Reevaluation

The Full Bayesian Significance Test (FBST) and the Bayesian evidence value recently have received increasing attention across a variety of sciences including psychology. Ly and Wagenmakers (2021) have provided a critical evaluation of the method and concluded that it suffers from four problems which are mostly attributed to the asymptotic relationship of the Bayesian evidence value to the frequentist p-value. While Ly and Wagenmakers (2021) tackle an important question about the best way of statistical hypothesis testing in the cognitive sciences, it is shown in this paper that their arguments are based on a specific measure-theoretic premise. The identified problems hold only under a specific class of prior distributions which are required only when adopting a Bayes factor test. However, the FBST explicitly avoids this premise, which resolves the problems in practical data analysis. In summary, the analysis leads to the more important question whether precise point null hypotheses are realistic for scientific research, and a shift towards the Hodges-Lehmann paradigm may be an appealing solution when there is doubt on the appropriateness of a precise hypothesis.

Analytical Head Loss Equation of Center-Pivot Irrigation System

Enhancing water use efficiency is essential in irrigated agriculture owing to declining water resources, increasing population, growing water needs, and greater competition among water users. If properly designed and managed, with good operation and maintenance, a center-pivot irrigation system can have high water-application efficiency. One of the design factors for a center-pivot irrigation system is the hydraulic loss in the lateral pipe. In this study, an analytical relationship is presented as a series for calculating the hydraulic loss in the lateral pipe of a center-pivot irrigation system. Given the difficulty and complexity of using a mathematical series, the equation presented in this study and the equation developed by Anwar turn out to be general and asymptotic relations. The final relationships have 0.6% and 0.4% errors, respectively, relative to the series relationships. Due to the high accuracy and ease of use of the asymptotic relationship presented to calculate the hydraulic loss in the lateral pipe, it is recommended for use in designing center-pivot irrigation systems.

Automating Uniformity Trials to Optimize Precision of Agronomic Field Trials

Plot size has an important impact on variation among plots in agronomic field trials, but is rarely considered during the design process. Uniformity trials can inform a researcher about underlying variance, but are seldom used due to their laborious nature. The objective of this research was to describe variation in maize field trials among field plots of varying size and develop a tool to optimize field-trial design using uniformity-trial statistics. Six uniformity trials were conducted in 2015–2016 in conjunction with Iowa State University and WinField United. All six uniformity trials exhibited a negative asymptotic relationship between variance and plot size. Variance per unit area was reduced over 50% with plots 41.8 m2 in size and over 75% when using a plot size &gt;111.5 m2 compared to a 13.9 m2 plot. Plot shape within a fixed plot size did not influence variance. The data illustrated fewer replicates were needed as plot size increased, since larger plots reduced variability. Use of a Shiny web application is demonstrated that allows a researcher to upload a yield map and consider uniformity-trial statistics to inform plot size and replicate decisions.

Season‐specific survival rates and densities of coastal cutthroat trout across stream sizes in southwestern British Columbia

AbstractVariation in seasonal survival rates, densities and growth rates of coastal cutthroat trout (Oncorhynchus clarkii clarkii) were assessed across a size gradient of small, forested streams in the Pacific Northwest. We used a robust, mark‐recapture study, stratified seasonally to estimate monthly survival rates of trout in coastal British Columbia (not including young‐of‐the‐year). Survival estimates showed that the summer season had the lowest monthly survival rates (0.907) across all streams in our study (0.927 remainder of year). Within the size range of the seven small streams studied, low‐flow habitat availability (defined by residual pool depth in summer) was the best predictor of mean monthly survival rates, supporting the hypothesis that trout survival increases with the quantity of aquatic habitat, particularly depths of residual pools. In addition, there was an asymptotic relation between water depth and survival rates, where beyond ~20 cm of residual pool depth, greater depth did not confer greater rates of trout survival. Growth rates in all but the largest stream were also lowest during summer. While densities tended to be higher in streams with greater residual depth, this was not significant. Body mass in a given season was a good predictor of survival to the next sampling period. The distribution and success of resident cutthroat trout populations in small streams appear to be constrained by summer low‐flow periods and specific geomorphologies that support deeper pools.

Attenuation of Rayleigh waves due to surface roughness.

Rayleigh waves are well known to attenuate due to scattering when they propagate over a rough surface. Theoretical investigations have derived analytical expressions linking the attenuation coefficient to statistical surface roughness parameters, namely, the surface's root mean squared height and correlation length and the Rayleigh wave's wavenumber. In the literature, three scattering regimes have been identified-the geometric (short wavelength), stochastic (short to medium wavelength), and Rayleigh (long wavelength) regimes. This study uses a high-fidelity two-dimensional finite element (FE) modelling scheme to validate existing predictions and provide a unified approach to studying the problem of Rayleigh wave scattering from rough surfaces as the same model can be used to obtain attenuation values regardless of the scattering regime. In the Rayleigh and stochastic regimes, very good agreement is found between the theory and FE results both in terms of the absolute attenuation values and for asymptotic power relationships. In the geometric regime, power relationships are obtained through a combination of dimensional analysis and FE simulations. The results here also provide useful insight into verifying the three-dimensional theory because the method used for its derivation is analogous.

A hierarchy of topological systems with completely positive entropy

We define a hierarchy of systems with topological completely positive entropy in the context of countable amenable continuous group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the corresponding level of the aforementioned hierarchy and provide subshifts of finite type for the first three levels. We give necessary and sufficient conditions for entropy pairs by means of the asymptotic relation on systems with the pseudo-orbit tracing property, and thus create a bridge between a result by Pavlov and a result by Meyerovitch. As a corollary, we answer negatively an open question by Pavlov regarding necessary conditions for completely positive entropy.