Potential one-forms for hyperk\"ahler structures with torsion

It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperk\"ahler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic condition on their torsion.Comment: 16 pages, Latex, no figure

Cellular solid behaviour of liquid crystal colloids. 1. Phase separation and morphology

We study the phase ordering colloids suspended in a thermotropic nematic liquid crystal below the clearing point Tni and the resulting aggregated structure. Small (150nm) PMMA particles are dispersed in a classical liquid crystal matrix, 5CB or MBBA. With the help of confocal microscopy we show that small colloid particles densely aggregate on thin interfaces surrounding large volumes of clean nematic liquid, thus forming an open cellular structure, with the characteristic size of 10-100 micron inversely proportional to the colloid concentration. A simple theoretical model, based on the Landau mean-field treatment, is developed to describe the continuous phase separation and the mechanism of cellular structure formation.Comment: Latex 2e (EPJ style) EPS figures included (poor quality to comply with space limitations

Cautionary Tales on Synthetic Controls in Survival Analyses

Synthetic control (SC) methods have gained rapid popularity in economics recently, where they have been applied in the context of inferring the effects of treatments on standard continuous outcomes assuming linear input-output relations. In medical applications, conversely, survival outcomes are often of primary interest, a setup in which both commonly assumed data-generating processes (DGPs) and target parameters are different. In this paper, we therefore investigate whether and when SCs could serve as an alternative to matching methods in survival analyses. We find that, because SCs rely on a linearity assumption, they will generally be biased for the true expected survival time in commonly assumed survival DGPs -- even when taking into account the possibility of linearity on another scale as in accelerated failure time models. Additionally, we find that, because SC units follow distributions with lower variance than real control units, summaries of their distributions, such as survival curves, will be biased for the parameters of interest in many survival analyses. Nonetheless, we also highlight that using SCs can still improve upon matching whenever the biases described above are outweighed by extrapolation biases exhibited by imperfect matches, and investigate the use of regularization to trade off the shortcomings of both approaches.Comment: To appear in the 3rd Conference on Causal Learning and Reasoning (CLeaR 2024

Experimental neutrino physics in a nuclear landscape

There are profound connections between neutrino physics and nuclear experiments. Exceptionally precise measurements of single and double beta-decay spectra illuminate the scale and nature of neutrino mass and may finally answer the question of whether neutrinos are their own antimatter counterparts. Neutrino-nucleus scattering underpins oscillation experiments and probes nuclear structure, neutrinos offer a rare vantage point into collapsing stars and nuclear fission reactors, and techniques pioneered in neutrino nuclear-physics experiments are advancing quantum-sensing technologies. In this article, we review current and planned efforts at the intersection of neutrino and nuclear experiments.Comment: 22 pages, 4 figures, 1 table. Submitted as a contribution to "The liminal position of Nuclear Physics: from hadrons to neutron stars" issue of Philosophical Transactions

First-principles calculations of step formation energies and step interactions on TiN(001)

We study the formation energies and repulsive interactions of monatomic steps on the TiN(001) surface, using density functional total-energy calculations. The calculated formation energy of [100] oriented steps agree well with recently reported experimental values; these steps are shown to have a rumpled structure, with the Ti atoms undergoing larger displacements than the N atoms. For steps that are parallel to [110], our calculations predict a nitrogen (N) termination, as the corresponding formation energy is several hundred meV/\AA \ smaller than that of Ti-terminated steps

Influence of polydispersity on the critical parameters of an effective potential model for asymmetric hard sphere mixtures

We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential (R. Roth {\em et al}, Phys. Rev. E{\bf 62} 5360 (2000)) designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: $q\equiv\sigma_s/\bar\sigma_b=0.1$ and $q=0.05$. We find that inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems.Comment: 11 pages, 10 figure

Critical phenomena in colloid-polymer mixtures: interfacial tension, order parameter, susceptibility and coexistence diameter

The critical behavior of a model colloid-polymer mixture, the so-called AO model, is studied using computer simulations and finite size scaling techniques. Investigated are the interfacial tension, the order parameter, the susceptibility and the coexistence diameter. Our results clearly show that the interfacial tension vanishes at the critical point with exponent 2\nu ~ 1.26. This is in good agreement with the 3D Ising exponent. Also calculated are critical amplitude ratios, which are shown to be compatible with the corresponding 3D Ising values. We additionally identify a number of subtleties that are encountered when finite size scaling is applied to the AO model. In particular, we find that the finite size extrapolation of the interfacial tension is most consistent when logarithmic size dependences are ignored. This finding is in agreement with the work of Berg et al.[Phys. Rev. B, V47 P497 (1993)]Comment: 13 pages, 16 figure

Thermal roughening of an SOS-model with elastic interaction

We analyze the effects of a long-ranged step-step interaction on thermal roughening within the framework of a solid-on-solid model of a crystal surface by means of Monte Carlo simulation. A repulsive step-step interaction is modeled by elastic dipoles located on sites adjacent to the steps. In order to reduce the computational effort involved in calculating interaction energy based on long-ranged potentials, we employ a multi-grid scheme. As a result of the long-range character of the step interaction, the roughening temperature increases drastically compared to a system with short-range cutoff as a consequence of anti-correlations between surface defects