Some calculations on the ground and lowest-triplet state of the helium isoelectronic sequence with the nucleus in motion

The method described in the preceding paper for the solution of two-electron atoms, which was used to calculate the 1 1S and 2 3S states of helium and heliumlike atoms within the fixed-nucleus approximation, has been applied to the case where all three particles are in relative motion. The solutions in the present case automatically include the effects of the mass polarization term and are compared with the results obtained for the term by using first-order perturbation theory with the fixed-nucleus wave functions. The input data for a particular atom consist of the atomic number, as before, but now the corresponding mass of the nucleus must be given also. Nonrelativistic energies with the nuclear mass included in the calculation have been obtained for the 1 1S and 2 3S states for Z ranging from 1 to 10. The energy with the nucleus in motion can be expressed only to eight significant figures (SF's) given the accuracy with which the relevant physical constants are known at present. All the results given here are computed as if these constants were known to ten SF's so that errors not incurred due to rounding. Convergence of the energies to ten SF's for both the singlet and triplet state was reached with a matrix of size 444 for Z values from 2 to 10. Convergence for the H- ion was a little slower

Dielectric response with short-ranged electrostatics.

The dielectric nature of polar liquids underpins much of their ability to act as useful solvents, but its description is complicated by the long-ranged nature of dipolar interactions. This is particularly pronounced under the periodic boundary conditions commonly used in molecular simulations. In this article, the dielectric properties of a water model whose intermolecular electrostatic interactions are entirely short-ranged are investigated. This is done within the framework of local molecular-field theory (LMFT), which provides a well-controlled mean-field treatment of long-ranged electrostatics. This short-ranged model gives a remarkably good performance on a number of counts, and its apparent shortcomings are readily accounted for. These results not only lend support to LMFT as an approach for understanding solvation behavior, but also are relevant to those developing interaction potentials based on local descriptions of liquid structure.Royal Commission for the Exhibition of 185

The Many Faces of Heterogeneous Ice Nucleation: Interplay Between Surface Morphology and Hydrophobicity

What makes a material a good ice nucleating agent? Despite the importance of heterogeneous ice nucleation to a variety of fields, from cloud science to microbiology, major gaps in our understanding of this ubiquitous process still prevent us from answering this question. In this work, we have examined the ability of generic crystalline substrates to promote ice nucleation as a function of the hydrophobicity and the morphology of the surface. Nucleation rates have been obtained by brute-force molecular dynamics simulations of coarse-grained water on top of different surfaces of a model fcc crystal, varying the water-surface interaction and the surface lattice parameter. It turns out that the lattice mismatch of the surface with respect to ice, customarily regarded as the most important requirement for a good ice nucleating agent, is at most desirable but not a requirement. On the other hand, the balance between the morphology of the surface and its hydrophobicity can significantly alter the ice nucleation rate and can also lead to the formation of up to three different faces of ice on the same substrate. We have pinpointed three circumstances where heterogeneous ice nucleation can be promoted by the crystalline surface: (i) the formation of a water overlayer that acts as an in-plane template; (ii) the emergence of a contact layer buckled in an ice-like manner; and (iii) nucleation on compact surfaces with very high interaction strength. We hope that this extensive systematic study will foster future experimental work aimed at testing the physiochemical understanding presented herein.Comment: Main + S

Democratization in a passive dendritic tree: an analytical investigation

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius

Generalized Model of Resonant Polymer-Coated Microcantilevers in Viscous Liquid Media

Expressions describing the resonant frequency and quality factor of a dynamically driven, polymer-coated microcantilever in a viscous liquid medium have been obtained. These generalized formulas are used to describe the effects the operational medium and the viscoelastic coating have on the device sensitivity when used in liquid-phase chemical sensing applications. Shifts in the resonant frequency are normally assumed proportional to the mass of sorbed analyte in the sensing layer. However, the expression for the frequency shift derived in this work indicates that the frequency shift is also dependent on changes in the sensing layer’s loss and storage moduli, changes in the moment of inertia, and changes in the medium of operation’s viscosity and density. Not accounting for these factors will lead to incorrect analyte concentration predictions. The derived expressions are shown to reduce to well-known formulas found in the literature for the case of an uncoated cantilever in a viscous liquid medium and the case of a coated cantilever in air or in a vacuum. The theoretical results presented are then compared to available chemical sensor data in aqueous and viscous solutions

Stabilization of AgI's polar surfaces by the aqueous environment, and its implications for ice formation.

Silver iodide is one of the most potent inorganic ice nucleating particles known, a feature generally attributed to the excellent lattice match between its basal Ag-(0001) and I-(000-1) surfaces, and ice. This crystal termination, however, is a type-III polar surface, and its surface energy therefore diverges with crystal size unless a polarity compensation mechanism prevails. In this simulation study, we investigate to what extent the surrounding aqueous environment is able to provide such polarity compensation. On its own, we find that pure H2O is unable to stabilize the AgI crystal in a physically reasonable manner, and that mobile charge carriers such as dissolved ions, are essential. In other words, proximate dissolved ions must be considered an integral part of the heterogeneous ice formation mechanism. The simulations we perform utilize recent advances in simulation methodology in which appropriate electric and electric displacement fields are imposed. A useful by-product of this study is the direct comparison to the commonly used Yeh-Berkowitz method that this enables. Here we find that naive application of the latter leads to physically unreasonable results, and greatly influences the structure of H2O in the contact layer. We therefore expect these results to be of general importance to those studying polar/charged surfaces in aqueous environments.T. S. is supported by a departmental studentship (No. RG84040) sponsored by the Engineering and Sciences Research Council (EPSRC) of the United Kingdom. We are grateful for computational support from the UK Materials and Molecular Modelling Hub, which is partially funded by EPSRC (EP/P020194), for which access was obtained via the UKCP consortium and funded by EPSRC grant ref EP/P022561/1. S. J. C. is supported by a Royal Commission for the Exhibition of 1851 Research Fellowship