Precursor-mediated crystallization process in suspensions of hard spheres

We report on a large scale computer simulation study of crystal nucleation in hard spheres. Through a combined analysis of real and reciprocal space data, a picture of a two-step crystallization process is supported: First dense, amorphous clusters form which then act as precursors for the nucleation of well-ordered crystallites. This kind of crystallization process has been previously observed in systems that interact via potentials that have an attractive as well as a repulsive part, most prominently in protein solutions. In this context the effect has been attributed to the presence of metastable fluid-fluid demixing. Our simulations, however, show that a purely repulsive system (that has no metastable fluid-fluid coexistence) crystallizes via the same mechanism.Comment: 4 figure

Nonequilibrium Temperature and Thermometry in Heat-Conducting Phi-4 Models

We analyze temperature and thermometry for simple nonequilibrium heat-conducting models. We show in detail, for both two- and three-dimensional systems, that the ideal gas thermometer corresponds to the concept of a local instantaneous mechanical kinetic temperature. For the Phi-4 models investigated here the mechanical temperature closely approximates the local thermodynamic equilibrium temperature. There is a significant difference between kinetic temperature and the nonlocal configurational temperature. Neither obeys the predictions of extended irreversible thermodynamics. Overall, we find that kinetic temperature, as modeled and imposed by the Nos\'e-Hoover thermostats developed in 1984, provides the simplest means for simulating, analyzing, and understanding nonequilibrium heat flows.Comment: 20 pages with six figures, revised following review at Physical Review

Elephant Grass

Elephant Grass, sometimes known as Napier\u27s Fodder, is a hardy, palatable and nutritious plant which under good conditions will give heavy yields. When once established it will remain as a permanent stand so long as it receives good treatment. It grows well in many parts of Western Australia and up to date appears to be free from attack by pests and diseases. * (Revised from Leaflet No. 600, by H. G. Elliott

Towards a method for rigorous development of generic requirements patterns

We present work in progress on a method for the engineering, validation and verification of generic requirements using domain engineering and formal methods. The need to develop a generic requirement set for subsequent system instantiation is complicated by the addition of the high levels of verification demanded by safety-critical domains such as avionics. Our chosen application domain is the failure detection and management function for engine control systems: here generic requirements drive a software product line of target systems. A pilot formal specification and design exercise is undertaken on a small (twosensor) system element. This exercise has a number of aims: to support the domain analysis, to gain a view of appropriate design abstractions, for a B novice to gain experience in the B method and tools, and to evaluate the usability and utility of that method.We also present a prototype method for the production and verification of a generic requirement set in our UML-based formal notation, UML-B, and tooling developed in support. The formal verification both of the structural generic requirement set, and of a particular application, is achieved via translation to the formal specification language, B, using our U2B and ProB tools

Genetic structure and genetic diversity of Swietenia macrophylla (Meliaceae): implications for sustainable forest management in Mexico

The genetic structure and genetic diversity of Mexican populations of Swietenia macrophylla were evaluated. In Mexico, this neotropical tree reaches its northernmost distribution limit. The relationship between genetic diversity and geographic position (longitude, latitude) of four populations was described. The mean genetic and pairwise genetic differentiations were estimated to study the geographic pattern in the genetic structure. The mean overall values for observed heterozygosis (Ho), expected heterozygosis (He) and fixation coefficient (Fis) were 0.41, 0.71 and 0.449 respectively. The mean values per population of Ho, He and Fis correlated with latitude only. The genetic differentiation between populations revealed by the coefficient of differentiation (Fst= 0.047) was statistically significant (p=0.0001). Unweighted pair group method analysis showed that the extent of pairwise genetic differentiation increased with latitudinal position of populations, although no isolation by distance was observed (r=0.76, p=0.15). Results were discussed in the context of the marginal distribution of Mexican populations. Implications of the results on the conservation of S. macrophylla , particularly for populations located in the Mayan zone were discussed

Velocity autocorrelation functions of hard-sphere fluids: Long-time tails upon undercooling

Molecular dynamics simulations are employed to obtain the velocity autocorrelation function (VAF) for hard spheres, spanning a wide range of volume fractions from dilute to high-density metastable fluids. For all volume fractions below freezing, Alder's classical positive 3/2 long-time tail is observed. For volume fractions from 0.45 to 0.48 the VAF becomes negative, before becoming positive and decaying with the positive 3/2 long-time tail. At the freezing volume fraction (0.494) the Alder 3/2 tail is not observed. At higher volume fractions a negative tail with an exponent of 5/2 emerges, which coincides with the long-time tail of a Lorentz gas

How hard is a colloidal 'hard-sphere' interaction?

Poly-12-hydroxystearic acid (PHSA) is widely used as a coating on colloidal spheres to provide a "hard-sphere-type" interaction. These hard spheres have been widely used in fundamental studies of nucleation, crystallization, and glass formation. Most authors describe the interaction as "nearly" hard sphere. In this paper we directly measure this interaction, using layers of PHSA adsorbed onto mica sheets in a surfaces force apparatus. We find that the layers, in appropriate solvents, have no long-range interaction. When the solvent is decahydronaphthalene (decalin), the repulsion rises from zero to the maximum measurable over a distance range of 15-20 nm. The data is converted to equivalent forces between spheres of different diameters, and modeled using a hard core potential. Using zeroth-order perturbation theory and computer simulation, we demonstrate that the equation of state does not deviate from that of a perfect hard-sphere system under any relevant experimental conditions

New Langevin and Gradient Thermostats for Rigid Body Dynamics

We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.Comment: 16 pages, 4 figure

Asymptotic analysis for the generalized langevin equation

Various qualitative properties of solutions to the generalized Langevin equation (GLE) in a periodic or a confining potential are studied in this paper. We consider a class of quasi-Markovian GLEs, similar to the model that was introduced in \cite{EPR99}. Geometric ergodicity, a homogenization theorem (invariance principle), short time asymptotics and the white noise limit are studied. Our proofs are based on a careful analysis of a hypoelliptic operator which is the generator of an auxiliary Markov process. Systematic use of the recently developed theory of hypocoercivity \cite{Vil04HPI} is made.Comment: 27 pages, no figures. Submitted to Nonlinearity

Destructive harvesting of wild honey in Miombo woodlands affects keystone elements in the ecosystem

Protected areas cover 13% of the world's terrestrial surface. With increasing demands on land and with challenges of land degradation and climate change, conflicts between conservation and use are on the rise, particularly in developing countries. Effective management of these conflicts requires viable livelihood options for local land users which are in line with nature conservation goals. Consolidation of nature conservation guidelines with local land use practices may be particularly challenging where keystone species are affected or where land uses have the potential for leading to ecosystem changes. This can be an issue even in ecosystems like savannahs, where fire largely defines ecosystem structure. The Miombo woodlands, covering around 2.4 million km2 of land, harbour important diversity and are crucial for livelihoods of around 75 million people in southern Africa. As a result of various pressures, cover and biomass of Miombo woodlands are declining throughout their range. Honey harvesting is an important land use in Miombo areas, both economically and culturally. Wild bees use cavities in trees for their colonies. Harvesting practices in some places include felling of trees with honeycombs to collect the honey and setting fire for pacifying bees. This leads to starvation and death of bee colonies. Given that most tree species are bee pollinated, trees with cavities colonised by wild bees can be classified as keystone elements in these ecosystems. Although ecologically far reaching, the effects of this harvesting practice on tree population structures in Miombo woodlands have seldom been studied. We characterised the ecological effects of destructive harvesting of wild honey on tree population structure and tree species distribution in Miombo woodlands in the Niassa wildlife reserve in Mozambique. The results show that forest structure and tree diversity differed along honey harvesting intensity gradients, with the highest number of fire tolerant tree species in areas with high honey harvesting intensity, which also showed the lowest tree regeneration density and Shannon diversity. Options for reconciling livelihoods with ecosystem maintenance do exist and include non-destructive harvesting based on climbing trees with locally produced ropes and leaving larval combs behind so the colony could continue to grow