A comparison of methods used to quantify the work of breathing during exercise

The mechanical work of breathing (Wb) is an insightful tool used to assess respiratory mechanics during exercise. There are several different methods used to calculate the Wb, however - each approach having its own distinct advantages/disadvantages. To date, a comprehensive assessment of the differences in the components of Wb between these methods is lacking. We therefore sought to compare the values of Wb during graded exercise as determined via the 4 most popular methods: (i) pressure-volume integration; (ii) the Hedstrand diagram; (iii) the Otis diagram; and the (iv) modified Campbell diagram. Forty-two participants (30 ± 15 years; 16 women) performed graded cycling to volitional exhaustion. Oesophageal pressure-volume loops were obtained throughout exercise. These data were used to calculate the total Wb and, where possible, its subcomponents of inspiratory and expiratory, resistive and elastic Wb, using each of the 4 methods. Our results demonstrate that the components of Wb were indeed different between methods across the minute ventilations engendered by graded exercise (P < 0.05). Importantly, however, no systematic pattern in these differences could be observed. Our findings indicate that the values of Wb obtained during exercise are uniquely determined by the specific method chosen to compute its value - no two methods yield identical results. Because there is currently no "gold-standard" for measuring the Wb, it is emphasized that future investigators be cognizant of the limitations incurred by their chosen method, such that observations made by others may be interpreted with greater context, and transparency.

Conserved charges in general relativity

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved space–time with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner–Sharp mass in the Oppenheimer–Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold.

<i>ConvectiveFoam1.0</i>: development and benchmarking of a infinite-Pr number solver

We developed a new fluid-dynamical numerical model, which we call convectiveFoam, designed to simulate fluids with very large Prandtl number. First we implemented the high-Pr case, in which advection still acts explicitly, and then the Pr → ∞ version, where the momentum equation becomes diagnostic (that is, without time derivatives) and it is formalized as an elliptic problem. The new solver, based on a finite volume integration method, is developed on the OpenFOAM platform and it exhibits a good performance in terms of computational costs and accuracy of the results. Scaling properties show a maximum performance around 16000 cells/core, in agreement with other works developed on the same platform. A systematic validation of the solver was performed for both 2D and 3D geometries, showing that convectiveFoam is able to reproduce the main results of several iso-viscous cases. This new solver can thus simulate idealized configurations of natural geophysical convection, such as in the Earth Mantle where Pr = 1023. This solver represents a starting point for general exploration of the behaviour and parameter dependence of several fluid systems of geological interest.

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

Frequency-domain magnetotelluric footprint analysis for 3D earths

For magnetotelluric (MT) data with a large coverage, inversion interpretation for the whole area is usually impossible, due to the physical limitation of a computer. However, for each MT station, it is only sensitive to a region (called MT footprint) localized immediately underneath the station, much smaller than the whole survey area. Thus the whole large survey area can be subdivided into many sub-areas and inverted using the moving footprint technique efficiently. Therefore, to understand the MT footprint is of great importance for developing such an inversion algorithm. In this paper, we study the influence of frequency, resistivity and existence of anomalous structure in the MT footprint. We first use the finite difference method to evaluate the total electromagnetic (EM) fields, then apply the numerical volume integration of tensor green's function to calculate the total induced fields at the receiver (summation of the contribution for each cell). The footprint is obtained based on the contribution of each cell to the total induced fields. Different models are designed to understand the footprint for MT problems. An increase in frequency or conductivity results in a decrease in the size of footprint. Existence of anomalous bodies within the footprint affects the MT footprint size to a degree, dependent on the overall resistivity. Outside the footprint, the existence of anomalous bodies have little effect on the footprint size and shape.

FVM 1.0: a nonhydrostatic finite-volume dynamical core for the IFS

We present a nonhydrostatic finite-volume global atmospheric model formulation for numerical weather prediction with the Integrated Forecasting System (IFS) at ECMWF and compare it to the established operational spectral-transform formulation. The novel Finite-Volume Module of the IFS (henceforth IFS-FVM) integrates the fully compressible equations using semi-implicit time stepping and non-oscillatory forward-in-time (NFT) Eulerian advection, whereas the spectral-transform IFS solves the hydrostatic primitive equations (optionally the fully compressible equations) using a semi-implicit semi-Lagrangian scheme. The IFS-FVM complements the spectral-transform counterpart by means of the finite-volume discretization with a local low-volume communication footprint, fully conservative and monotone advective transport, all-scale deep-atmosphere fully compressible equations in a generalized height-based vertical coordinate, and flexible horizontal meshes. Nevertheless, both the finite-volume and spectral-transform formulations can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude–latitude coordinates, and physics parameterizations, thereby facilitating their comparison, coexistence, and combination in the IFS. We highlight the advanced semi-implicit NFT finite-volume integration of the fully compressible equations of IFS-FVM considering comprehensive moist-precipitating dynamics with coupling to the IFS cloud parameterization by means of a generic interface. These developments – including a new horizontal–vertical split NFT MPDATA advective transport scheme, variable time stepping, effective preconditioning of the elliptic Helmholtz solver in the semi-implicit scheme, and a computationally efficient implementation of the median-dual finite-volume approach – provide a basis for the efficacy of IFS-FVM and its application in global numerical weather prediction. Here, numerical experiments focus on relevant dry and moist-precipitating baroclinic instability at various resolutions. We show that the presented semi-implicit NFT finite-volume integration scheme on co-located meshes of IFS-FVM can provide highly competitive solution quality and computational performance to the proven semi-implicit semi-Lagrangian integration scheme of the spectral-transform IFS.

FVM 1.0: A nonhydrostatic finite-volume dynamical core formulation for IFS

We present a nonhydrostatic finite-volume global atmospheric model formulation for numerical weather prediction with the Integrated Forecasting System (IFS) at ECMWF, and compare it to the established operational spectral-transform formulation. The novel Finite-Volume Module of IFS (henceforth IFS-FVM) integrates the fully compressible equations using semi-implicit time stepping and non-oscillatory forward-in-time (NFT) Eulerian advection, whereas the spectral-transform IFS solves the hydrostatic primitive equations (optionally the fully compressible equations) using a semi-implicit semi-Lagrangian scheme. The IFS-FVM complements the spectral-transform counterpart by means of the finite-volume discretisation with a local communication footprint, fully conservative and monotone advective transport, all-scale deep-atmosphere fully compressible equations in a generalised height-based vertical coordinate, applicable on flexible meshes. Nevertheless, both the finite-volume and spectral-transform formulations can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude-latitude coordinates, and physical parametrisations, thereby facilitating their comparison, coexistence and combination in IFS. We highlight the advanced semi-implicit NFT finite-volume integration of the fully compressible equations of the novel IFS-FVM considering comprehensive moist-precipitating dynamics with coupling to the IFS cloud parametrisation by means of a generic interface. These developments – including a new horizontal-vertical split NFT MPDATA advective transport scheme, variable time stepping, effective preconditioning of the elliptic Helmholtz solver in the semi-implicit scheme, and a computationally efficient coding implementation – provide a basis for the efficacy of IFS-FVM and its application in global numerical weather prediction. Here, numerical experiments focus on relevant dry and moist-precipitating baroclinic instability at various resolutions. We show that the presented semi-implicit NFT finite-volume integration scheme on co-located meshes of IFS-FVM can provide highly competitive solution quality and computational performance to the proven semi-implicit semi-Lagrangian integration scheme of the spectral-transform IFS.