The Classical Heisenberg Model on the Centred Pyrochlore Lattice

The centred pyrochlore lattice is a novel geometrically frustrated lattice, realized in the metal-organic framework Mn(ta)$_2$ (arXiv:2203.08780) where the basic unit of spins is a five site centred tetrahedron. Here, we present an in-depth theoretical study of the $J_1-J_2$ classical Heisenberg model on this lattice, using a combination of mean-field analytical methods and Monte Carlo simulations. We find a rich phase diagram with low temperature states exhibiting ferrimagnetic order, partial ordering, and a highly degenerate spin liquid with distinct regimes of low temperature correlations. We discuss in detail how the regime displaying broadened pinch points in its spin structure factor is consistent with an effective description in terms of a fluid of interacting charges. We also show how this picture holds in two dimensions on the analogous centred kagome lattice and elucidate the connection to the physics of thin films in ($d+1$) dimensions. Furthermore, we show that a Coulomb phase can be stabilized on the centred pyrochlore lattice by the addition of further neighbour couplings. This demonstrates the centred pyrochlore lattice is an experimentally relevant geometry which naturally hosts emergent gauge fields in the presence of charges at low energies.Comment: 29 pages, 9 figures, resubmission to SciPost with minor revision

Satisfaction with the oral health services. A qualitative study among non-commissioned officers in the Malaysian armed forces

Patient satisfaction is critical for the growth and prosperity of any oral health service or practice. The success of any oral health service can be assessed by an evaluation of the degree of satisfaction/dissatisfaction of its patients. Objective The aim of this study is to assess satisfaction/dissatisfaction with the oral health services among Non-Commissioned Officers (NCOs) in the Malaysian Armed Forces (MAF). Method A qualitative study using the Nominal Group Technique was undertaken. Eighty subjects from the Rasah Camp, Seremban were randomly selected from four lists, namely privates, male and female corporals and sergeants and were Grouped into 10 discussion groups of eight participants each. Of the 10 groups, four groups comprised male corporals.. three groups of privates, two groups of sergeants and one group of female corporals. Two separate discussion sessions were conducted to elicit factors/items causing dissatisfaction and satisfaction expressed by the participants. Every participant then scored all the factors perceived as important by members of the group. The score ranged from 0-9 i.e., the least to the most important. Scores were weighted, and the weighted score of every participant for each item was added. The ratings of the factors were determined by comparing the sum Of the weighted scores. Results The six most important factors/items rated in the satisfaction discussion were modern equipment (9.07), friendly dentist (8.27), pleasant surgery (8.23), good quality treatment (7.93), friendly staff (7.18) and pain alleviation (6.07). These factors were further regrouped into three broad categories i.e. (1) Clinic set-Lip, (2) Patient-personnel interaction (PPI) and (3) Technical competency (TC). In the dissatisfaction discussion six factors/items were rated i.e. long waiting time (10.39), sequence of treatment not followed (7.18), non-availability of dentist (7.16), unfriendly staff (7.05), poor quality treatment (6.80) and restricted time for treatment (5.98). The three most important categories in the dissatisfaction discussion were (1) Administrative efficiency, (2) PPI and (3) TC. Conclusion A conceptual model was developed to explain the factors affecting patients' satisfaction/dissatisfaction with the oral health services. It is recommended that a questionnaire Survey be undertaken to validate and reflect the entire population of the MAF. Remedial measures highlighted in the areas of dissatisfaction should be addressed accordingly based on the quantitative study

Particle-Based Monte-Carlo Simulations of Steady-State Mass Transport at Intermediate Péclet Numbers

Conventional approaches for simulating steady-state distributions of dilute particles under diffusive and advective transport involve solving the diffusion and advection equations in at least two dimensions. Here, we present an alternative computational strategy by combining a particle-based rather than a field-based approach with the initialisation of particles in proportion to their flux. This method allows accurate prediction of the steady state and is applicable even at intermediate and high Péclet numbers (Pe>1) swhere traditional particle-based Monte-Carlo methods starting from randomly initialised particle distributions fail. We demonstrate that generating a flux of particles according to a predetermined density and velocity distribution at a single fixed time and initial location allows for accurate simulation of mass transport under flow. Specifically, upon initialisation in proportion to their flux, these particles are propagated individually and detected by summing up their Monte-Carlo trajectories in predefined detection regions. We demonstrate quantitative agreement of the predicted concentration profiles with the results of experiments performed with fluorescent particles in microfluidic channels under continuous flow. This approach is computationally advantageous and readily allows non-trivial initial distributions to be considered. In particular, this method is highly suitable for simulating advective and diffusive transport in microfluidic devices, for instance in the context of diffusive sizing.Financial support from the Biotechnology and Biological Sciences Research Council (BBSRC), the European Research Council (ERC), the Frances and Augustus Newman Foundation as well as the Swiss National Science Foundation is gratefully acknowledged

Particle-Based Monte-Carlo Simulations of Steady-State Mass Transport at Intermediate Péclet Numbers

Conventional approaches for simulating steady-state distributions of dilute particles under diffusive and advective transport numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we present an alternative computational strategy by combining a particle-based rather than a field-based approach with the initialisation of particles in proportion to their flux. This method allows accurate prediction of the steady state and is applicable even at intermediate and high Péclet numbers (Pe>1) where traditional particle-based Monte-Carlo methods starting from randomly initialised particle distributions fail. We demonstrate that generating a flux of particles according to a predetermined density and velocity distribution at a single fixed time and initial location allows for accurate simulation of mass transport under flow. Specifically, upon initialisation in proportion to their flux, these particles are propagated individually and detected by summing up their Monte-Carlo trajectories in predefined detection regions. We demonstrate quantitative agreement of the predicted concentration profiles with the results of experiments performed with fluorescent particles in microfluidic channels under continuous flow. This approach is computationally advantageous and readily allows non-trivial initial distributions to be considered. In particular, this method is highly suitable for simulating advective and diffusive transport in microfluidic devices, for instance in the context of diffusive sizing.Financial support from the Biotechnology and Biological Sciences Research Council (BBSRC), the European Research Council (ERC), the Frances and Augustus Newman Foundation as well as the Swiss National Science Foundation is gratefully acknowledged

Frustration on a centered pyrochlore lattice in metal-organic frameworks

Geometric frustration inhibits magnetic systems from ordering, opening a window to unconventional phases of matter. The paradigmatic frustrated lattice in three dimensions to host a spin liquid is the pyrochlore, although there remain few experimental compounds thought to realize such a state. Here, we go beyond the pyrochlore via molecular design in the metal-azolate framework [Mn(II)(ta)2], which realizes a closely related centered pyrochlore lattice of Mn spins with S=5/2. Despite a Curie-Weiss temperature of −21 K indicating the energy scale of magnetic interactions, [Mn(II)(ta)2] orders at only 430 mK, putting it firmly in the category of highly frustrated magnets. Comparing magnetization and specific-heat measurements to numerical results for a minimal Heisenberg model, we predict that this material displays distinct features of a classical spin liquid with a structure factor reflecting Coulomb physics in the presence of charges

Integrability of Lie systems through Riccati equations

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.Comment: Corrected typo

MMP-1 activation contributes to airway smooth muscle growth and asthma severity

Introduction: Matrix metalloproteinase-1 and mast cells are present in the airways of people with asthma. We hypothesised that matrix metalloproteinase-1 could be activated by mast cells and increase asthma severity. Methods: Patients with stable asthma and healthy controls underwent spirometry, methacholine challenge, bronchoscopy and their airway smooth muscle cells were grown in culture. A second asthma group and controls had symptom scores, spirometry and bronchoalveolar lavage before and after rhinovirus-induced asthma exacerbations. Extra-cellular matrix was prepared from decellularised airway smooth muscle cultures. Matrix metalloproteinase-1 protein and activity were assessed. Results: Airway smooth muscle cells generated pro-matrix metalloproteinase-1 which was proteolytically activated by mast cell tryptase. Airway smooth muscle treated with activated mast cell supernatants produced extra-cellular matrix which enhanced subsequent airway smooth muscle growth by 1.5 fold (p<0.05) which was dependent on matrix metalloproteinase-1 activation. In asthma, airway pro-matrix metalloproteinase-1 was 5.4 fold higher than control subjects (p=0.002). Mast cell numbers were associated with airway smooth muscle proliferation and matrix metalloproteinase-1 protein associated with bronchial hyper-responsiveness. During exacerbations, matrix metalloproteinase-1 activity increased and was associated with fall in FEV1 and worsening asthma symptoms. Conclusions: Matrix metalloproteinase-1 is activated by mast cell tryptase resulting in a pro-proliferative extra-cellular matrix. In asthma, mast cells are associated with airway smooth muscle growth, matrix metalloproteinase-1 levels are associated with bronchial hyper-responsiveness and matrix metalloproteinase-1 activation with exacerbation severity. Our findings suggest that airway smooth muscle/mast cell interactions contribute to asthma severity by transiently increasing matrix metalloproteinase activation, airway smooth muscle growth and airway responsiveness