Condition Zero is a fail-safe procedure the Martian Congressional Republic Navy (MCRN) enacts during boarding procedures. It states should any of the three critical areas of the ship be lost to boarders the bridge, Combat Information Center (CIC), or engineering the ship is to be detonated (self-destructed) immediately. As these areas are considered vital to ship operation or hold critical strategic value (in the case of the CIC), should these areas fall into enemy hands the Captain (or surviving command officer) should consider the ship lost and initiate Condition zero to prevent the enemy from capturing the ship or otherwise using the ship to enemy advantage.
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We study the diffusion of classical particles in channels with varying boundaries. The problem is characterized by the Neumann boundary condition (zero normal current) in contrast to the Dirichlet boundary condition (zero function) for "quantum confinement" problems. Eliminating transverse modes, we derive an effective diffusion equation that describes particle propagation in the space of reduced dimension in the presence of a frozen drift field. The latter stems from boundary variations of the original boundary problem. Boundary variations may thus result in an appreciable change of the particle transport and, in particular, in a nonlinear response to an external field. We show also that there is a difference between the nonlinear responses of open and closed channels.
Kelvin-Voigt constitutive law, Signorini condition, zero gap function, weak formulation, existence, uniqueness, evolution equations, maximal monotone operators, semi-discrete numerical scheme, convergence, regularity, optimal order error estimates
A series of diesel fuel fire experiments were conducted in the Pittsburgh Research Center's Safety Research Coal mine (SRCM) to determine products-of-combustion (POC) spread rates along a single entry under zero imposed airflow conditions. Six experiments with an average fire intensity of 330 kW and three experiments with an average fire intensity of 30 kW were conducted in a 180 m long entry which had an average 2 m heights and 4 m width. POC spread rates were measured by the response time of diffusion type CO detectors, positioned at 30 m intervals, to CO concentrations 5 ppm above ambient. For the 330 kW fires, average POC spread rates of 0.22, 0.13, and 0.06 m/s were determined at 30, 60, and 90 m distances from the fire. For the 30 kW fires these average spread rates were reduced to 0.08, 0.04, and 0.04 m/s. The measured maximum roof layer temperature 30 m from two of the 330 kW fire was 30 and 36 degrees C, which is less than the 57 degrees C alarm point of a typical mine thermal sensor. It was determined that smoke detectors can be more effective for mine fire detection than CO detectors. The experimentally determined POC spread rates can be used to provide guidance for specification of sensor spacing to improve early fire detection at zero or very low air flows.
However, as we demonstrate explicitly in this paper, there exists a possibility of such matter distributions which lead to nonzero average values of the first-order metric corrections. Namely, in the framework of the mechanical approach to cosmological problems at the late stage of the Universe evolution we give a concrete example of a rest mass density profile for which the standard formula determining the scalar perturbations results in their nonzero average values. Since exactly this formula underlies the modern N-body simulations which play an extremely important role for the structure formation analysis, the discovered weak point must be eliminated in order to be fully confident in their predictions. We suggest avoiding this challenge without exceeding the limits of the conventional ΛCDM model, by cutting off the nonrelativistic gravitational potentials of cosmic bodies/inhomogeneities (e.g., galaxies).
In order to determine the gravitational potential φ corresponding to the given sphere, one can solve the Poisson equation (2.2) with the appropriate boundary conditions φ(R) = 0, dφ/dr(R) = 0 or use the standard prescription (2.8). The result is the same: inside the sphere (the region I)
meaning that the standard prescription (2.8) can lead to unreasonable nonzero average values of cosmological perturbations. One can naively suppose that the result (3.3) is true only for the considered region of the finite volume V, while averaging over the infinite volume saves the situation. This argumentation is apparently wrong since there is an infinite number of such regions in the model under consideration, and each of them makes a nonzero (negative) contribution when averaging over the infinite volume. Thus, the average value will be again nonzero (negative).
Of course, since the function Φ describes the deviation of the metric coefficients in (2.1) from the corresponding average quantities, its own average value must be equal to zero: Φ=0. The same statement must hold true for φ, δεrad, etc. The discovered indubitable disadvantage of the formula (2.8) should not be ignored in the modern N-body simulations (along with [11, 12]; see [16]).
therefore, φ=0, as it certainly should be. Thus, the use of the finite-range gravitational potential (3.4) instead of the infinite-range one (2.8) leads to reasonable zero average values of cosmological perturbations. This advantage of the proposed formula (3.4) in comparison with (2.8) may be taken into account when simulating the behavior of N-body systems.
Let us mention that in the framework of the extension of the ΛCDM model, assuming the presence in the Universe of the additional constituent (namely, quintessence) with the linear equation of state εq = ωqpq with the constant parameter ωq = - 1/3, the discussed problem of nonzero average values of cosmological perturbations in the case of the infinite-range gravitational potential is resolved in a different manner: quintessence fluctuations around a point-like nonrelativistic matter inhomogeneity cause the Yukawa form of its potential instead of the Newtonian one, and the average value of the total potential produced by all inhomogeneities is really zero [20], irrespective of the interaction range and its cutoff.
The other extension, assuming a negative spatial curvature, is also characterized by the potential of a point-like inhomogeneity, similar to the Yukawa one, so the average value of the total potential is again zero [2].
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