A significant number of Army soldiers are sufficiently overweight to exceed the maximum weight allowances defined by the Army weight control program (AR600-9). Also, the body weights of a substantial number of soldiers approach the maximum weight allowances. These soldiers should not gain additional weight if they are to meet Army weight allowances. The conventional approach to this overweight problem is assigning soldiers to remedial physical training and mandatory referral for nutrition counseling by a health care provider. An alternative to this conventional approach is to target the entire population of soldiers (population-based intervention) to promote weight loss in overweight soldiers and weight gain prevention in soldiers who are approaching overweight status. To accomplish this objective, the Healthy Eating, Activity, and Lifestyle Training Headquarters (H.E.A.L.T.H.) program was developed. This article describes the rationale for developing the program, the components of the program, and the utilization promotion strategies of the program. The H.E.A.L.T.H. program includes two primary components: (1) a Web site tailored to the standards established in Field Manual 21-20, Physical Fitness Training, Army physical fitness test, and AR600-9, the army weight control program, and (2) a health promotion program designed to promote awareness of the H.E.A.L.T.H. Web site and to facilitate use of the Web site by soldiers and their family members. The Web site is equipped with personalized planning tools and progress tracking over time related to fitness, caloric intake, and lifestyle behavior change goals. The health promotion program includes media advertisements and "ground roots" efforts to facilitate use by soldiers.
The final stage of sedimentation of a spherical particle moving along the axis of a conical vessel containing a viscous incompressible fluid is studied both theoretically by lubrication analysis and experimentally by laser interferometry. The particle settling velocity varies like d5/2, where d is the gap. There is an excellent agreement between this result from lubrication theory and experiment, the upper bound being for a gap of about 1/30 radius and the lower practical bound being at the size of the particle roughness.
We present new stabilization terms for solving the linear transport equation on a cut cell mesh using the discontinuous Galerkin (DG) method in two dimensions with piecewise linear polynomials. The goal is to allow for explicit time stepping schemes, despite the presence of cut cells. Using a method of lines approach, we start with a standard upwind DG discretization for the background mesh and add penalty terms that stabilize the solution on small cut cells in a conservative way. Then, one can use explicit time stepping, even on cut cells, with a time step length that is appropriate for the background mesh. In one dimension, we show monotonicity of the proposed scheme for piecewise constant polynomials and total variation diminishing in the means stability for piecewise linear polynomials. We also present numerical results in one and two dimensions that support our theoretical findings.
Standard numerical methods for hyperbolic PDEs require for stability a CFL-condition which implies that the time step size depends on the size of the elements of the mesh. On cut-cell meshes, elements can become arbitrarily small and thus the time step size cannot take the size of small cut-cells into account but has to be chosen based on the background mesh elements.A remedy for this is the so called DoD (domain of dependence) stabilization for which several favorable theoretical and numerical properties have been shown in one and two space dimensions [4,9]. Up to now the method is restricted to stabilization of cut-cells with exactly one inflow and one outflow face, i.e. triangular cut-cells with a no-flow face (see [4]).We extend the DoD stabilization to cut-cells with multiple in-and outflow faces by properly considering the flow distribution inside the cut-cell. We further prove L 2 -stability for the semi-discrete formulation in space and present numerical results to validate the proposed extension. Copyright line will be provided by the publisher 1 IntroductionTo avoid the mesh generation process of complex geometries, cut-cell methods are an attractive alternative. The general idea is to start with a simple, e.g. structured, background mesh and to cut out the desired geometry. This results in a mesh with unstructured polyhedral cells, called cut-cells. Cut-cells can have an arbitrary shape and can become arbitrarily small, causing the small cell problem. To use explicit time stepping schemes for solving hyperbolic conservation laws, the time step size would need to be chosen based on the smallest cut-cell in the grid to ensure stability, which is in general not feasible.Developing solution approaches to the small cell problem in the context of discontinuous Galerkin (DG) schemes is a very recent research branch, including for example the work in [7,8,10]. In this contribution we focus on the domain of dependence (DoD) stabilization, which was introduced in [4] for the linear transport equation in one and two space dimensions and was extended to non-linear systems in one space dimension in [9]. It is based on a DG scheme in space to allow for higherorder approximations and possesses several desirable theoretical properties. Numerical results show the expected higher-order behavior in smooth flow and robustness around shocks.Up to now, the DoD stabilization in two dimensions has only been used to stabilize small triangular cut-cells for linear advection parallel to a ramp [4,11]. In this setup, the small stabilized cut-cells have exactly one inflow and one outflow face, which was exploited in the design of the stabilization. When moving to non-linear or coupled linear problems, this does not hold true anymore and one has to deal with multiple inflow and outflow faces.In this work, we take the first step in that direction by considering the linear advection equation on a cut-cell mesh with arbitrary flow directions, resulting in triangular cut-cells having 2 inflow and 1 outflow neighbor or reverse. As this ...
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