Hill Approach Research Articles

Averaging techniques for microstructures with localization bands due to damage progression

AbstractIn multiscale analysis, homogenization methods are needed to up‐scale the micromechanical response obtained from investigating the underlying microstructure to the next higher scale. The standard homogenization schemes are based on volume averaging over the entire microstructure following Hill's approach, which requires that the virtual energies generated on the two involved scales equalize. However, these standard homogenization schemes are not applicable to softening phenomena due to localization, and representativeness of the considered microscale volume is lost. One way to overcome these drawbacks is to perform the volume averaging only within the localizing failure zone. Thereby, representative results can be achieved even in the softening region. In this paper, we apply the failure zone homogenization approach to both, mode I and mode II loading scenarios, as well as mixed‐mode loading of long fiber reinforced plastics. For an accurate description of material failure within the epoxy matrix, a scalar damage model at large strains with gradient enhancement is used, such that the obtained results are mesh‐independent. As a result, we show that for all considered cases representative volume element (RVE) sizes can be determined by using the failure zone homogenization scheme. Nevertheless, the energy distributions of all involved mechanisms have to be considered carefully in order to allow generalizations.

МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ФІЗІОЛОГІЧНОГО ПРОЦЕСУ М’ЯЗОВОГО СКОРОЧЕННЯ

The article discusses improved mathematical models for the physiological process of muscle contraction based on the well-known hypotheses of the functioning of the musculoskeletal system of the human body. In particular, according to the first phenomenological hypothesis of A. Hill, on the basis of rheological models of the components of muscle tissue, a mathematical model was developed for changing the power load of muscle tissue for isometric tetanus and muscle contraction (lengthening) at a constant rate. It has been established that a common drawback of A. Hill's approach is the assumption that the force-speed ratio must be fulfilled instantly after changing the power load. This is inconsistent with the experimental data on the recovery of strength tension after a stepwise change in muscle length. To overcome these disadvantages, A. Huxley's hypothesis was chosen. It is based on the principles of kinetics of the distribution of the binding sites of actin (monomer) with the protein filament (cross bridges). It is assumed that the binding sites on actin are far enough from each other so that only one such binding site is available to each bridge. On the basis of A. Huxley's hypothesis, a mathematical model of muscle tissue strength load was developed, which depends on the distribution function of the number of cross bridges. The results of the comparison of theoretical and experimental studies of the power load on the muscle, based on the developed mathematical models in the form of differential equations, confirmed the adequacy of the use of known theoretical provisions to describe the course of biological processes in muscle tissues.

Reading for Land Susan Hill's The Clay We Are Made Of : Haudenosaunee Land Tenure on the Grand River

Reading for Land Susan Hill's The Clay We Are Made Of:Haudenosaunee Land Tenure on the Grand River Audra Simpson (bio) With this issue, we introduce a new occasional feature in the journal that opens up space for extended consideration of noteworthy new works. Audra Simpson contributes a close examination of how Susan Hill's prize-winning book (NAISA Best First Book, Canadian Historical Association Aboriginal History Group Book Prize, and Ontario Clio Prize, all 2018) constitutes a fieldchange intervention in Haudenosaunee and Indigenous studies. Matthew Cohen reviews Lisa Brooks's new book by way of an interview with the author about her groundbreaking methodology. Jean M. O'Brien and Robert Warrior SUSAN HILL'S PRIZE-WINNING BOOK The Clay We Are Made Of: Haudenosaunee Land Tenure on the Grand River (2017) offers a comprehensive history of land and governance that is rare in its framing, its focus, and its execution, rendering it one of the most important studies to emerge on Haudenosaunee history to date.1 In this book Hill documents the relationships that Haudenosaunee had with lands, peoples, and waters in what is now the North American "Northeast." She moves us through the vicissitudes of the Revolutionary War, documenting Haudenosaunee movement up into the northern points of their hunting territory and their relocation and negotiations with Mississaugas at what would become Six Nations of the Grand River. On the way we run into some of the usual protagonists of Six Nations history: Joseph Brant (Thayendenaga), William Johnson, and John A. MacDonald. Brant's sister and Johnson's wife, Molly Brant, appears briefly, and one of the most chronicled Indigenous women in North America, Pauline Johnson, notably does not make an appearance. These are not ellipses or oversights, as Hill's approach is far from hagiographic; thus, there are very different players in this story. The central concern or protagonist is not a person or an event but a set of [End Page 149] ethics. The ethics of land are the central protagonists in this study, and this makes for a very different kind of history than we have been taught about Six Nations.2 These ethics of land speak through the archives that Hill works with: speeches and letters, council minutes, Indian agent correspondence, and arguments and negotiations. Through Hill's readings we see the process of treaty, of deliberation and decision making regarding property and inheritance in colonial contexts laid bare for us, and it is the burning question—the question of the contradiction between ethics and practice in the teeth of settler-colonial constraint and imperative—that orients her analysis. She asks specifically of this material, "If our relationship to the earth and to land is central why would we negotiate land sharing deals, treaties and, leases and direct sales?" (4). These negotiations over land are in seeming contradiction to Haudenosaunee philosophy and belief. We see how chiefs, clan mothers, and councils tried to maintain land and territory through policy, land tenure practice, and inheritance decisions in the face of rapid and unrelenting attempts to divest them of land and (annuity) money. Gone is the emphasis on militarism, decline and defeat, and then cultural salvage that has marked much of the literature on the Iroquois. Not only is this a sort of story different from the one we have been told, but this is also a model study of how to read archives for Indigenous history, theory, and principle. Hill offers a robust account of the Haudenosaunee eighteenth-century alliance with the British, a relationship based on mutual recognition, on equality. This alliance with the British, however, extends the principles of the earlier seventeenth-century Kaswentha ("Two Row Wampum") Treaty between the Dutch and the Haudenosaunee and transposes it onto relations with the British. But eighteenth-century Haudenosaunee not only treated with British, they maintained their relationships to others in the Confederacy and those in the shadow of the Confederacy. As such, they brought with them protectorate nations like the Nanticokes and Tutelos when they moved to what is now Ontario, but they also brought with them their obligations to people and land. Hill demonstrates how these obligations and relationships with other political orders were...

Spectral and computational features of the binding between riparins and human serum albumin

The green Brazilian bay leaf, a spice much prized in local cuisine (Aniba riparia, Lauraceae), contains chemical compounds presenting benzoyl-derivatives named riparins, which have anti-inflammatory, antimicrobial and anxiolytic properties. However, it is unclear what kind of interaction riparins perform with any molecular target. As a profitable target, human serum albumin (HSA) is one of the principal extracellular proteins, with an exceptional capacity to interact with several molecules, and it also plays a crucial role in the transport, distribution, and metabolism of a wide variety of endogenous and exogenous ligands. To outline the HSA–riparin interaction mechanism, spectroscopy and computational methods were synergistically applied. An evaluation through fluorescence spectroscopy showed that the emission, attributed to Trp 214, at 346 nm decreased with titrations of riparins. A static quenching mechanism was observed in the binding of riparins to HSA. Fluorescence experiments performed at 298, 308 and 318 K made it possible to conduct thermodynamic analysis indicating a spontaneous reaction in the complex formation (ΔG<0). The enthalpy-entropy balance experiment with a molecular modeling calculation revealed that hydrophobic, hydrogen bond and non-specific interactions are present for riparin I–III with HSA. The set of results from fractional fluorescence changes obtained through Schatchard was inconclusive in establishing what kind of cooperativity is present in the interaction. To shed light upon the HSA-riparins complex, Hill's approach was utilized to distinguish the index of affinity and the binding constant. A correspondence between the molecular structures of riparins, due to the presence of the hydroxyl group in the B-ring, with thermodynamic parameters and index of affinity were observed. Riparin III performs an intramolecular hydrogen bond, which affects the Hill coefficient and the binding constant. Therefore, the presence of hydroxyl groups is capable of modulating the interaction between riparins and HSA. Site marker competitive experiments indicated Site I as being the most suitable, and the molecular modeling tools reinforced the experimental results detailing the participation of residues.

A Natural Goodness­of­Fit Test for the Exponential Growth Curve Model Based on the Relative Growth Rate

This paper develops a natural goodness-of-fit test for the exponential growth curve model (EGCM) based on the property of finite differences. The EGCM has wide applications in various scientific fields such as biology, ecology, demography, population dynamics, finance, econometrics etc. Hill (1968, Biometrics, 4, 192-196) proposed a test for the polynomial growth curve model (PGCM) based on finite differences of the size variable. However, the PGCM has limited practical use and does not have any biologically interpretable para.ffieters. In comparison, the exponential model is more realistic and biologically meaningful; a goodness-of-fit test for the EGCM has substantial practical value. Bhattacharya et. al. (2004) generalized Hill's approach to the case of the EGCM based on appropriate finite differences of functions of the size variable. In this paper we present an alternative test for the EGCM by directly modeling the relative growth rate (rather than the size variable itself) and hence avoid the assumptions necessary in Bhattacharya et al (2004). The performance of the theory developed is illustrated with several sets of real data and through simulation. AMS {2000} Subject Classification: 62F03, 62P10.

Approximate rate formulation of non-elastic bifurcation problem for thin-walled structures

Simplified set of equations is derived for solution of a non-elastic bifurcation problem in thin-walled structures. The rate formulation is preferable, and based on the classical Hill's approach. It is shown that for a particular case of small strain the problem can be reduced to a more simple eigenvalue problem. As an example, the approach proposed has been applied to a circular stationary disk subjected to thermal expansion. The material of the disk is assumed to be elastic–perfectly plastic obeying the von Mises yield criterion with its associated flow rule. The influence of the width ratio on the bifurcation behavior has been discussed.

Economic comparison of open and closed nucleus breeding schemes for wool production

Returns on investments in open or closed nucleus breeding schemes to improve clean wool production were examined using Hill's approach of examining the flow of genes through the population. Returns on capital in such schemes are competitive with many alternative investments on the farm if predictions of response are correct. For example, for a typical case considered with heritability of wool weight of 0·4, standard deviation of 0·4 kg, 90% lambs weaned per ewe joined from mature ewes, and 250 cents/kg clean, marginal returns on money invested in labour and materials in the breeding programme in excess of 40% were obtained. The return on the extra investment with an open nucleus using 50% of base-born ewes in the nucleus was about 20%. Returns are sensitive to cost, lambing percentage, price and heritability, the extra returns from the open nucleus becoming more attractive as predicted response or price increases. The value of the gains is not very sensitive to numbers of age groups of ewes or rams. Most of the extra returns go to the commercial flocks, so premiums would need to be paid to the nucleus to provide incentives to maintain the breeding programme.

The Plane Strain Indentation of Anisotropic Aluminium Using a Frictionless Flat Rectangular Punch

In Part 1, the slip-line field solutions and the associated load requirements necessary for the indentation of anisotropic solids are presented. The analysis is based on Hill's approach to the analysis of anisotropic material. All results are recorded in terms of a lumped anisotropic parameter, c. In Part 2, the results of an investigation to determine the anisotropic parameters of a commercially available aluminium are reported. Specimens machined from the aluminium at selected orientations to the anisotropic axes were indented using a nominally frictionless flat rectangular punch. A comparison between the theoretical and experimental indentation loads is given.