A deductive statistical mechanics approach for granular matter

We introduce a deductive statistical mechanics approach for granular materials which is formally built from few realistic physical assumptions. The main finding is an universal behavior for the distribution of the density fluctuations. Such a distribution is the equivalent of the Maxwell-Boltzmann's distribution in the kinetic theory of gasses. The comparison with a very extensive set of experimental and simulation data for packings of monosized spherical grains, reveals a remarkably good quantitative agreement with the theoretical predictions for the density fluctuations both at the grain level and at the global system level. Such agreement is robust over a broad range of packing fractions and it is observed in several distinct systems prepared by using different methods. The equilibrium distributions are characterized by only one parameter ($k$) which is a quantity very sensitive to changes in the structural organization. The thermodynamical equivalent of $k$ and its relation with the `granular temperature' are also discussed.Comment: 15 pages, 6 figure

Rose Marie

https://digitalcommons.library.umaine.edu/mmb-vp/6133/thumbnail.jp

Quantum Measurement and the Aharonov-Bohm Effect with Superposed Magnetic Fluxes

We consider the magnetic flux in a quantum mechanical superposition of two values and find that the Aharonov-Bohm effect interference pattern contains information about the nature of the superposition, allowing information about the state of the flux to be extracted without disturbance. The information is obtained without transfer of energy or momentum and by accumulated nonlocal interactions of the vector potential $\vec{A}$ with many charged particles forming the interference pattern, rather than with a single particle. We suggest an experimental test using already experimentally realized superposed currents in a superconducting ring and discuss broader implications.Comment: 6 pages, 4 figures; Changes from version 3: corrected typo (not present in versions 1 and 2) in Eq. 8; Changes from version 2: shortened abstract; added refs and material in Section IV. The final publication is available at: http://link.springer.com/article/10.1007/s11128-013-0652-

Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems

Switches in real systems take many forms, such as impacts, electronic relays, mitosis, and the implementation of decisions or control strategies. To understand what is lost, and what can be retained, when we model a switch as an instantaneous event, requires a consideration of so-called hidden terms. These are asymptotically vanishing outside the switch, but can be encoded in the form of nonlinear switching terms. A general expression for the switch can be developed in the form of a series of sigmoid functions. We review the key steps in extending the Filippov's method of sliding modes to such systems. We show how even slight nonlinear effects can hugely alter the behaviour of an electronic control circuit, and lead to `hidden' attractors inside the switching surface.Comment: 12 page

Deformation of lamellar TiAl alloys by longitudinal twinning

© 2016 Elsevier Ltd. The occurrence of longitudinal twinning in the engineering alloy Ti-45Al-2Nb-2Mn (at.%)-0.8 vol.% TiB2 has been studied by measuring the changes in crystallographic orientation within individual lamellae during microcompression. Twinning in this alloy appeared to be a nucleation-limited process with the twins growing from lamellar boundaries at resolved shear stresses as low as 100 MPa, consistent with observations elsewhere. However, instead of forming twins ∼ 10-200 nm in thickness, as in polysynthetically twinned crystals, the longitudinal twins in this alloy were initiated at a lamellar boundary and then spread through the whole lamella.The work was supported by the EPSRC / Rolls-Royce Strategic Partnership (EP/H500375/1). Alberto Palomares Garcia, Claire Davis and Robert Jones are acknowledged for discussions and help with the TEM respectively

Upward Three-Dimensional Grid Drawings of Graphs

A \emph{three-dimensional grid drawing} of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional grid drawings with small bounding box volume. We prove that every $n$-vertex graph with bounded degeneracy has a three-dimensional grid drawing with $O(n^{3/2})$ volume. This is the broadest class of graphs admiting such drawings. A three-dimensional grid drawing of a directed graph is \emph{upward} if every arc points up in the z-direction. We prove that every directed acyclic graph has an upward three-dimensional grid drawing with $(n^3)$ volume, which is tight for the complete dag. The previous best upper bound was $O(n^4)$. Our main result is that every $c$-colourable directed acyclic graph ($c$ constant) has an upward three-dimensional grid drawing with $O(n^2)$ volume. This result matches the bound in the undirected case, and improves the best known bound from $O(n^3)$ for many classes of directed acyclic graphs, including planar, series parallel, and outerplanar

Measurement of enhanced ductility in nanolayered ceramics via micro-compression testing and digital image correlation

The use of ceramic or intermetallic structures in industrial applications is limited by their brittleness. However, it has been shown that nanolayered ceramics, such as the MAX phases, show unusually high levels of plasticity, with resolved shear yield stresses being reported to be as low as 77 MPa [1]. Our aim is to show that the origin of this behaviour is related to electron density shifts between layers, which enable eased dislocation movement compared to non-layered ceramics [2]. For an accurate study of this effect, and to prove its generality, a reliable determination of the onset of plastic deformation in form of dislocation movement is crucial. Please click Additional Files below to see the full abstract

Comparison of Two Different Pasture Species Compositions for Recovery of Deep Soil Nitrogen during Winter

Surplus nitrate (NO3-) beneath animal urine patches is highly vulnerable to leaching, particularly during winter when soil drainage is often highest. Most common pastures in New Zealand (i.e. Lolium perenne) have relatively shallow root systems and produce low dry matter (DM) yields during winter months. Recent investigations suggest that alternative pasture species may be able to recover more soil nitrogen (N) during winter and consequently reduce NO3- leaching losses (Moir et al., 2013; Malcolm et al., 2014; 2015). However, further work is required to better understand the importance of root system architecture and plant growth of these alternative species during this cool period. The objective was to determine the ability of L. multiflorum (Italian ryegrass) and F. arundinacea (tall fescue)-based pastures to recover mineral-N from different soil depths under simulated winter conditions and determine the relative importance of plant growth/metabolic activity and root system architecture

The topological susceptibility and f_pi from lattice QCD

We study the topological susceptibility, chi, in QCD with two quark flavours using lattice field configurations that have been produced with an O(a) improved quark action. We find clear evidence for the expected suppression at small quark mass, and examine the variation of chi with this mass. The resulting estimate of the pion decay constant, f_pi = 105 +/- 6 ^{+18}_{-10} MeV, is consistent with the experimental value of ~93 MeV. We compare chi to the large-N_c prediction and find consistency over a large range of quark masses. We discuss the benefits of the non-perturbative action improvement scheme and of the stategy of keeping the lattice spacing (nearly) fixed as the quark mass is varied. We compare our results with other studies and suggest why such a quark mass dependence has not always been seen.Comment: LaTeX. Supercedes our preprint hep-ph/0004180. Version to appear in Phys. Lett.

Stable Speckle Patterns for Nano-scale Strain Mapping up to 700 °C

The digital image correlation (DIC) of speckle patterns obtained by vapour-assisted gold remodelling at 200 – 350 °C has already been used to map plastic strains with submicron resolution. However, it has not so far proved possible to use such patterns for testing at high temperatures. Here we demonstrate how a gold speckle pattern can be made that is stable at 700 °C, to study deformation in a commercial TiAl alloy (Ti-45Al-2Nb- 2Mn(at%)-0.8 vol% TiB$_2$). The pattern is made up of a uniformly sized random array of Au islands as small as 15 nm in diameter, depending on reconstruction parameters, with a sufficiently small spacing to be suitable for nano-scale, nDIC, strain mapping at a subset size of 60 × 60 nm$^2$ . It can be used at temperatures up to 700 °C for many hours, for high cycle fatigue testing for instance. There is good particle attachment to the substrate. It can withstand ultra-sound cleaning, is thermally stable and has a high atomic number contrast for topography-free backscatter electron imaging.EPSRC / Rolls-Royce Strategic Partnership (EP/M005607/1