Boundary Conditions. (i) In its Response to Forecast, Micron may reject the Demand Forecast to the extent the Demand Forecast does not comply with the following boundary conditions:
Boundary Conditions. As boundary conditions, we consider the Euclidean Dirichlet problem for which the induced metric h at ∂M and the corresponding proper length βT , as well as the boundary value of the dilaton ϕb on ∂M are fixed. The gauge parameter ξµ is required to vanish at ∂M, to ensure the boundary condition on h is preserved and the location of the boundary is not disrupted (see for instance [114]). The induced metric h can be arranged to be constant along ∂M by a judicious reparam- eterisation of the boundary time τ . In what follows, we moreover take ϕb to be constant along ∂M. The physical motivation behind this choice of boundary condition stems from the Xxxxxxx-Xxxxxxx prescription for Euclidean black hole thermodynamics [13,14], whereby one views the Euclidean solutions on the disc as contributing to the thermal partition func- tion of the underlying theory.1 We will not necessitate that the boundary is asymptotically (near) AdS2 for large part of our discussion, in line with the considerations of [48]. h b √ Given the solution (1.8) with (1.10), it is clear that a general choice of ϕb and h will not per- mit a real solution to our boundary value problem. For instance, let us consider the dilaton potential with V (ϕ) = −2ϕ, which yields N (r, rh) = r2 − r2. Smoothness of the solution at the origin of the disc moreover fixes rh = 2π/β such that the proper size of the boundary circle is βT = 4π2 − β2r2. Regardless of our choice for ϕb and assuming our solution is real, we have that βT ∈ (0, 2π) which is only a subset of the positive half-line. More markedly, for ϕb = 0, only βT = 2π is permitted. In particular, going from a non-vanishing to a vanishing value of ϕb leads to a discontinuous jump in the allowed set of βT . These restrictions on independent boundary data are a two-dimensional analogue of the obstructions arising when setting up the Dirichlet problem in four-dimensional general relativity [114–117] on manifolds with a boundary. In the case at hand, aside from such restrictions, the Dirichlet problem 1Alternative boundary conditions could fix the trace of the extrinsic curvature K at ∂M or the normal derivative of ϕ at ∂M, or more general combinations thereof. is well-posed due to the absence of locally propagating gravitational degrees of freedom. Nonetheless, we must ensure that the Dirichlet data (βT , ϕb) we consider are indeed sensible.
Boundary Conditions. The boundary conditions of the WHCW model are provided by the Update Model via nesting. This means all major influences on hydrodynamics, including major river discharges, in the outer regions are taken into account.
Boundary Conditions. The lateral and top boundary conditions for trace gases are obtained from daily forecasts with the MACC G-XX XXXXXX global model. Model top boundary concentrations were set to 0.8 μg.m-3 for sulphate and ammonium was set to neutralise the sulphate. Other aerosol species were set to zero. A module was developed for LOTOS-EUROS to include the MACC-AER dust fields as boundary conditions. These dust fields are now used in the operational MACC forecasts as well as MACC analyses since 29 October 2012.
Boundary Conditions. We ascribed a stress field as presented in Figure 14. The outer vertical and the lower horizontal boundaries are roller boundaries, that allow only for boundary parallel movements. The top horizontal boundary has a vertical load of 80 MPa. The pore pressure shows an overpressure of 15 MPa in the PCT which is confined by the low permeable Muschelkalk and decays with depth in the crystalline basement.
Boundary Conditions. 3.1 The work shall be carried out in compliance with all guidelines in use for IPPOG.
Boundary Conditions. The numerical models used for the analysis of landslides have to have a limited extent. These boundaries are artificial, and require suitable boundary conditions. In the case of slow varying, transient problems, the boundary conditions can be of the prescribed displacement type, sometimes combined with zero shear stress. Concerning the pore pressures, the analysts frequently use no flux boundaries. In the case of dynamical problems, suitable radiation or transparent boundary conditions have to be chosen. Otherwise, waves originating within the domain will return to it, resulting sometimes in an unnatural amplification.
