Unexpected symmetry in the nodal structure of the he atom

The nodes of even simple wave functions are largely unexplored. Motivated by their importance to quantum simulations of fermionic systems, we have found unexpected symmetries in the nodes of several atoms and molecules. Here, we report on helium. We find that in both ground and excited states the nodes have simple forms. In particular, they have higher symmetry than the wave functions they come from. It is of great interest to understand the source of these new symmetries. For the quantum simulations that motivated the study, these symmetries may help circumvent the fermion sign problem

Analysis of mesoscale effects in high-shear granulation through a computational fluid dynamics-population balance coupled compartment model

There is a need for mesoscale resolution and coupling between flow-field information and the evolution of particle properties in high-shear granulation. We have developed a modelling framework that compartmentalizes the high-shear granulation process based on relevant process parameters in time and space. The model comprises a coupled-flow-field and population-balance solver and is used to resolve and analyze the effects of mesoscales on the evolution of particle properties. A Diosna high-shear mixer was modelled with microcrystalline cellulose powder as the granulation material. An analysis of the flow-field solution and compartmentalization allows for a resolution of the stress and collision peak at the impeller blades. Different compartmentalizations showed the importance of resolving the impeller region, for aggregating systems and systems with breakage. An independent study investigated the time evolution of the flow field by changing the particle properties in three discrete steps that represent powder mixing, the initial granulation stage mixing and the late stage granular mixing. The results of the temporal resolution study show clear changes in collision behavior, especially from powder to granular mixing, which indicates the importance of resolving mesoscale phenomena in time and space

Beyond Blobs in Percolation Cluster Structure: The Distribution of 3-Blocks at the Percolation Threshold

The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly-connected ``links'' and multiply-connected ``blobs.'' Here we decompose blobs into objects known in graph theory as 3-blocks. A 3-block is a graph that cannot be separated into disconnected subgraphs by cutting the graph at 2 or fewer vertices. Clusters, blobs, and 3-blocks are special cases of $k$-blocks with $k=1$, 2, and 3, respectively. We study bond percolation clusters at the percolation threshold on 2-dimensional square lattices and 3-dimensional cubic lattices and, using Monte-Carlo simulations, determine the distribution of the sizes of the 3-blocks into which the blobs are decomposed. We find that the 3-blocks have fractal dimension $d_3=1.2\pm 0.1$ in 2D and $1.15\pm 0.1$ in 3D. These fractal dimensions are significantly smaller than the fractal dimensions of the blobs, making possible more efficient calculation of percolation properties. Additionally, the closeness of the estimated values for $d_3$ in 2D and 3D is consistent with the possibility that $d_3$ is dimension independent. Generalizing the concept of the backbone, we introduce the concept of a ``$k$-bone'', which is the set of all points in a percolation system connected to $k$ disjoint terminal points (or sets of disjoint terminal points) by $k$ disjoint paths. We argue that the fractal dimension of a $k$-bone is equal to the fractal dimension of $k$-blocks, allowing us to discuss the relation between the fractal dimension of $k$-blocks and recent work on path crossing probabilities.Comment: All but first 2 figs. are low resolution and are best viewed when printe

Student perspectives on creating a positive classroom dynamic: science education in prison

Detailed student perspectives on their involvement in prison education are limited in published literature, yet such contributions are invaluable to education practitioners wanting to create inclusive learning environments. This article focuses on the student experience of taking part in a science outreach programme teaching science in prison in England, which was designed to build confidence in students who face challenges in accessing education pathways. Here, former students share their experiences of the programme, as well as other education courses in prison, and offer guidance on best practices for those engaging in outreach or research with the prison population. In particular, their reflections highlight that by creating and maintaining an environment that is accessible, inclusive and relatable, students from all backgrounds are able to engage in course content, and overcome hidden barriers to accessing education. Furthermore, based on their lived experience, the students offer practical advice with regard to improving future access to education in prison. The aim of this article is to give a voice to students in prison about their education experience, highlighting which aspects of this outreach programme (and other education courses) were impactful for them

Correlated sampling in quantum Monte Carlo: a route to forces

In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate numerical forces and potential energy surfaces in diffusion Monte Carlo. It employs a novel coordinate transformation, earlier used in variational Monte Carlo, to greatly reduce the statistical error. Results are presented for first-row diatomic molecules.Comment: 5 pages, 2 postscript figure

Proof for an upper bound in fixed-node Monte Carlo for lattice fermions

We justify a recently proposed prescription for performing Green Function Monte Carlo calculations on systems of lattice fermions, by which one is able to avoid the sign problem. We generalize the prescription such that it can also be used for problems with hopping terms of different signs. We prove that the effective Hamiltonian, used in this method, leads to an upper bound for the ground-state energy of the real Hamiltonian, and we illustrate the effectiveness of the method on small systems.Comment: 14 pages in revtex v3.0, no figure

Monte Carlo Calculations for Liquid 4^4He at Negative Pressure

A Quadratic Diffusion Monte Carlo method has been used to obtain the equation of state of liquid $^4$He including the negative pressure region down to the spinodal point. The atomic interaction used is a renewed version (HFD-B(HE)) of the Aziz potential, which reproduces quite accurately the features of the experimental equation of state. The spinodal pressure has been calculated and the behavior of the sound velociy around the spinodal density has been analyzed.Comment: 10 pages, RevTex 3.0, with 4 PostScript figures include

Quasi one dimensional 4^4He inside carbon nanotubes

We report results of diffusion Monte Carlo calculations for both $^4$He absorbed in a narrow single walled carbon nanotube (R = 3.42 \AA) and strictly one dimensional $^4$He. Inside the tube, the binding energy of liquid $^4$He is approximately three times larger than on planar graphite. At low linear densities, $^4$He in a nanotube is an experimental realization of a one-dimensional quantum fluid. However, when the density increases the structural and energetic properties of both systems differ. At high density, a quasi-continuous liquid-solid phase transition is observed in both cases.Comment: 11 pages, 3ps figures, to appear in Phys. Rev. B (RC

Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. One consequence is that in the constrained-path method the so-called mixed estimator for the energy is not an upper bound to the exact energy, as previously claimed. Several ways of producing an energy upper bound are given, and relevant methodological aspects are illustrated with simple examples.Comment: 28 pages, REVTEX, 5 ps figure

The Detection of Incipient Caries with Tracer Dyes

The purpose of this study was to determine the increase in color contrast produced by the use of a tracer dye in detection of incipient caries lesions with transillumination. Twenty four caries-free first premolars were immersed in an acid gelatin for production of artificial incipient caries lesions. After the lesions had developed, these teeth were photographed by transillumination. Two photographs were taken of each tooth. The first photograph showed the lesion without dye. A blue tracer dye was then added and absorbed by the lesion, and a second photograph was taken. The data on the color difference were obtained by use of a reflectance colorimeter and showed a four-fold increase between the lesion and surrounding area with the dye. A two-way analysis of variance was used for the statistical interpretation. The color difference between the lesion without the dye and then with the dye was significant. The use of the blue tracer dye, therefore, significantly increased the contrast in the images of the artificial incipient lesions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68289/2/10.1177_00220345890680021101.pd