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As it will be shown below, the constitutive equations governing the evolution of the reservoir are strongly nonlinear.
Our approach relies on a stochastic variational inequality governing the evolution between the velocity and the non-linear restoring force.
For an infinite number of non-identical oscillators, one can consider the continuity equation governing the evolution of the probability density of the phases [9, 26, 29].
Soil-forming processes governing the evolution of secondary aluminosilicates in Podzols are however still not fully understood.
Secondly, the laws governing the evolution of the two parameters are analyzed based on 44 moderate and intense immediate rockburst cases in the tunnels of Jinping II.
We demonstrate the principle with a toy computer model and discuss the mathematics governing the evolution of slow degrees of freedom in large Hamiltonian systems.
This is related to the determination of the solution of a particular higher-dimensional PDE governing the evolution of the backstepping-kernel.
These mechanisms are implemented in a phenomenological equation governing the evolution of rod length, with the number density of rods appropriately modified to ensure conservation of surfactant mass.
Mindlin's two-dimensional plate equation is used, from which a system of first-order nonlinear differential equations governing the evolution of the vibration amplitude is obtained.
If we were interested in solutions that were not even, we could include sine terms in (14), substitute into (10), and derive the differential equations governing the evolution of their coefficients.
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The role of function g is to govern the evolution of the model's memory.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com