Packing Fractions and Maximum Angles of Stability of Granular Materials

In two-dimensional rotating drum experiments, we find two separate influences of the packing fraction of a granular heap on its stability. For a fixed grain shape, the stability increases with packing fraction. However, in determining the relative stability of different grain shapes, those with the lowest average packing fractions tend to form the most stable heaps. We also show that only the configuration close to the surface of the pile figures prominently.Comment: 4 pages, 4 figure

Grain size dependence of barchan dune dynamics

The dependence of the barchan dune dynamics on the size of the grains involved is investigated experimentally. Downsized barchan dune slices are observed in a narrow water flow tube. The relaxation time from an initial symmetric triangular heap towards an asymmetric shape attractor increases with dune mass and decreases with grain size. The dune velocity increases with grain size. In contrast, the velocity scaling and the shape of the barchan dune is independent of the size of the grains

Vagueness

In ordinary conversation, we describe all sorts of different things as vague: you can have vague plans, vague ideas and vague aches and pains. In philosophy of language, in contrast, it is parts of language – words, expressions and so on – that are said to be vague. One classic example of a vague term is the word ‘heap’. A single grain clearly does not make a heap, and a million grains (when arranged in the right way) does make a heap, but where exactly does the boundary lie? How many grains do you need to make a heap? There seems to be no precise answer to this question, and because the term is imprecise in this way, we call it vague. Vague terms are extremely common in natural language. The term ‘bald’ is vague, because there is no precise number of hairs that mark the boundary between ‘bald’ and ‘not bald’; the term ‘hot’ is vague because there is no precise temperature that something must reach to count as hot – and so on. As we have seen, adjectives can be vague, but so can nouns, adverbs and perhaps all parts of language. To find terms which are precise rather than vague, we need to look to the languages of logic and mathematics. We can use vague terms to construct paradoxes known as sorites paradoxes. From an obviously true premise, such as that a collection of 1 million grains (in a certain arrangement) is a heap, together with the claim that ‘heap’ has no sharp boundary, we can derive the absurd conclusion that just 1 grain counts as a heap. Any theory of vagueness must offer some solution to this paradox. Some of the most popular theories of vagueness include supervaluationism, the degree theory of truth and the epistemic theory, and many of the available theories demand a radical rethink of classical accounts of logic and language

The implications of vagueness

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references (leaves 29-30).If grains of sand are added, one by one, to a growing collection of sand on an otherwise empty table, there will eventually be a "heap" of sand on the table. It seems impossible, however, to specify the precise point at which the collection becomes a heap. One grain of sand is certainly not a heap of sand. Does two grains comprise a heap? Can the collection be called a heap at three grains, at 10 grains, or at 500 grains? The commonly used term "heap" is vague -- there is no clear line, which demarcates the heaps from the non-heaps. The difficulty presented by this vagueness becomes clear when we examine the sorites paradox, a very old philosophical problem, which is centered around the premise that the term "heap" has no precise definition. If it is impossible to specify exactly which objects are heaps and which objects are not heaps, how do we continue to use the term with such impunity? Is it possible for a system of logic to model the use of vague terms, if their application is often "neither true nor false," or, "only a matter of interpretation?" How are we to understand the role of vagueness within language

On the Borders of Vagueness and the Vagueness of Borders

This article argues that resolutions to the sorites paradox offered by epistemic and supervaluation theories fail to adequately account for vagueness. After explaining the paradox, I examine the epistemic theory defended by Timothy Williamson and discuss objections to his semantic argument for vague terms having precise boundaries. I then consider Rosanna Keefe's supervaluationist approach and explain why it fails to accommodate the problem of higher-order vagueness. I conclude by discussing how fuzzy logic may hold the key to resolving the sorites paradox without positing indefensible borders to the correct application of vague terms

The effect of processing route on properties of HfNbTaTiZr high entropy alloy

High entropy alloys (HEA) have been one of the most attractive groups of materials for researchers in the last several years. Since HEAs are potential candidates for many (e.g., refractory, cryogenic, medical) applications, their properties are studied intensively. The most frequent method of HEA synthesis is arc or induction melting. Powder metallurgy is a perspective technique of alloy synthesis and therefore in this work the possibilities of synthesis of HfNbTaTiZr HEA from powders were studied. Blended elemental powders were sintered, hot isostatically pressed, and subsequently swaged using a special technique of swaging where the sample is enveloped by a titanium alloy. This method does not result in a full density alloy due to cracking during swaging. Spark plasma sintering (SPS) of mechanically alloyed powders resulted in a fully dense but brittle specimen. The most promising result was obtained by SPS treatment of gas atomized powder with low oxygen content. The microstructure of HfNbTaTiZr specimen prepared this way can be refined by high pressure torsion deformation resulting in a high hardness of 410 HV10 and very fine microstructure with grain size well below 500 nm.Web of Science1223art. no. 402