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Here, the solution is derived from a closed-form quadratic programme, leading to tractable matrix representations.
The non-stationary solution is derived from the solution in the case of a moving load with a deterministic amplitude.
The weak form is discretized using the isoparametric finite element approximation, while the analytical solution is derived from the strong form.
The Navier's analytical solution is derived from the strong form, while the weak form is discretized using the isoparametric finite element approximation.
The analytical solution is derived from the simplified one-dimensional governing equation of unsaturated flow for an infinitely long monolithic cover by taking the exponential forms of the soil water characteristic curve and the hydraulic conductivity curve into account.
The solution is derived from first principles, and is evolved from the well known [Timoshenko, A. 1925. Analysis of bi-metal thermostats. Journal of the Optical Society of America, 11, 233 255] bimetal thermostat analysis.
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Pressure distributions, solution concentration and velocity of CO2 gas and solution are derived from the simulations.
Necessary and sufficient conditions for existence of a solution are derived from the abstract principle of maximum.
The solution was derived from a limit equilibrium analysis where a straight failure plane to ground surface is assumed above the cavern and shear resistant force on the failure plane induced by cohesion and friction angle of overburden rock mass is considered.
The temperature-dependent activity coefficient for aqueous CO2 was derived from the empirical relationship established by Drummond (1981), and the temperature-dependent activity of water in NaCl solution was derived from the formulation of Bethke (2008).
The standard curve of a HCPT solution was derived from the following equation: y = 10.7 x + 0.0056 (r = 0.9999).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com