Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost

Diffusion of hard disks and rodlike molecules on surfaces

We study the submonolayer diffusion of hard disks and rodlike molecules on smooth surfaces through numerical simulations and theoretical arguments. We concentrate on the behavior of the various diffusion coefficients as a function of the two-dimensional (2D) number density ρ in the case where there are no explicit surface-particle interactions. For the hard disk case, we find that while the tracer diffusion coefficient DT(ρ) decreases monotonically up to the freezing transition, the collective diffusion coefficient DC(ρ) is wholly determined by the inverse compressibility which increases rapidly on approaching freezing. We also study memory effects associated with tracer diffusion, and present theoretical estimates of DT(ρ) from the mode-mode coupling approximation. In the case of rigid rods with short-range repulsion and no orientational ordering, we find behavior very similar to the case of disks with the same repulsive interaction. Both DT(ρ) and the angular diffusion coefficient DR(ρ) decrease with ρ. Also in this case DC(ρ) is determined by inverse compressibility and increases rapidly close to freezing. This is in contrast to the case of flexible chainlike molecules in the lattice-gas limit, where DC(ρ) first increases and then decreases as a function of the density due to the interplay between compressibility and mobility.Peer reviewe

Many-particle diffusion in continuum: Influence of a periodic surface potential

We study the diffusion of Brownian particles with a short-range repulsion on a surface with a periodic potential through molecular dynamics simulations and theoretical arguments. We concentrate on the behavior of the tracer and collective diffusion coefficients DT(θ) and DC(θ), respectively, as a function of the surface coverage θ. In the high friction regime we find that both coefficients are well approximated by the Langmuir lattice-gas results for up to θ≈0.7 in the limit of a strongly binding surface potential. In particular, the static compressibility factor within DC(θ) is very accurately given by the Langmuir formula for 0⩽θ⩽1. For higher densities, both DT(θ) and DC(θ)show an intermediate maximum which increases with the strength of the potential amplitude. In the low friction regime we find that long jumps enhance blocking and DT(θ) decreases more rapidly for submonolayer coverages. However, for higher densities DT(θ)/DT(0) is almost independent of friction as long jumps are effectively suppressed by frequent interparticle collisions. We also study the role of memory effects for many-particle diffusion.Peer reviewe

Height, social position and coronary heart disease incidence: the contribution of genetic and environmental factors

Background: The associations between height, socioeconomic position (SEP) and coronary heart disease (CHD) incidence are well established, but the contribution of genetic factors to these associations is still poorly understood. We used a polygenic score (PGS) for height to shed light on these associations. Methods: Finnish population-based health surveys in 1992-2011 (response rates 65-93%) were linked to population registers providing information on SEP and CHD incidence up to 2019. The participants (N=29 996; 54% women) were aged 25-75 at baseline, and there were 1767 CHD incident cases (32% in women) during 472 973 person years of follow-up. PGS-height was calculated based on 33 938 single-nucleotide polymorphisms, and residual height was defined as the residual of height after adjusting for PGS-height in a linear regression model. HRs of CHD incidence were calculated using Cox regression. Results: PGS-height and residual height showed clear gradients for education, social class and income, with a larger association for residual height. Residual height also showed larger associations with CHD incidence (HRs per 1 SD 0.94 in men and 0.87 in women) than PGS-height (HRs per 1 SD 0.99 and 0.97, respectively). Only a small proportion of the associations between SEP and CHD incidence was statistically explained by the height indicators (6% or less). Conclusions: Residual height associations with SEP and CHD incidence were larger than for PGS-height. This supports the role of material and social living conditions in childhood as contributing factors to the association of height with both SEP and CHD risk

Influence of hydrodynamics on many-particle diffusion in 2D colloidal suspensions

We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective diffusion coefficients $D_T(\rho) / D_0$ and $D_C(\rho) / D_0$, where $D_0$ is the single-particle diffusion coefficient, as a function of the density of the colloids $\rho$. At low Schmidt numbers $Sc={\cal O}(1)$, we find that hydrodynamics has essentially no effect on the behaviour of $D_T(\rho)/D_0$. At larger $Sc$, $D_T(\rho)/D_0$ is enhanced at all densities, although the differences compared to the case without hydrodynamics are minor. The collective diffusion coefficient, on the other hand, is much more strongly coupled to hydrodynamical conservation laws and is distinctly different from the purely dissipative case

The effect of a probiotic blend on gastrointestinal symptoms in constipated patients: A double blind, randomised, placebo controlled 2-week trial

Selected strains of lactobacilli and bifidobacteria are known to ameliorate constipation-related symptoms and have previously shown efficacy on digestive health. In this clinical trial, the safety and effectiveness of a probiotic blend containing lactobacilli and bifidobacteria were evaluated in adults with self-reported bloating and functional constipation. Constipation was diagnosed by the Rome III criteria. A total of 156 adults were randomised into this double-blind and placebo-controlled trial. Participants consumed the combination of Lactobacillus acidophilus NCFM (1010 cfu), Lactobacillus paracasei Lpc-37 (2.5×109 cfu), Bifidobacterium animalis subsp. lactis strains Bl-04 (2.5×109 cfu), Bi-07 (2.5×109 cfu) and HN019 (1010 cfu) (n=78), or placebo (microcrystalline cellulose) (n=78) for two weeks. After treatment the following were measured: primary outcome of bloating and secondary outcomes of colonic transit time, bowel movement frequency, stool consistency, other gastrointestinal symptoms (flatulence, abdominal pain, and burbling), constipation-related questionnaires (PAC-SYM and PAC-QoL) and product satisfaction. Faecal recovery of consumed strains was determined. The enrolled population was defined as constipated, however, the initial bloating severity was lower than in previous similar studies. No clinically significant observations related to the safety of the product were reported. Product efficacy was not shown in the primary analysis for bloating nor for the secondary efficacy analyses. The placebo functioned similarly as the probiotic product. In post-hoc analysis, a statistically significant decrease in flatulence in favour of the probiotic group was observed; day 7 (intention-to-treat (ITT): P=0.0313; per-protocol (PP): 0.0253) and on day 14 (ITT: P=0.0116; PP: P=0.0102) as measured by area under the curve (AUC) analysis. The mean AUC of all symptoms decreased in favour of the probiotic group, indicating less digestive discomfort. The study was registered at the ISRCTN registry (ISRCTN41607808)