In this paper, a time dependent one-dimensional linear advection diffusion equation with Dirichlet homogeneous boundary conditions and an initial sine function is solved analytically by separation of variables and numerically by the finite element method.
In real heterogeneous materials, the simultaneous presence of instantaneous mechanisms (elasticity) and time dependent ones (non-linear viscoplasticity) leads to a complex space time coupling between the mechanical fields, difficult to represent in a simple and efficient way.
Trip time dependent on tides.
By generalizing the well developed time-independent full quantum mechanical theory in real space to the time-dependent one, we show that various sideband-transmission phenomena could be observed.
Two constitutive relationships were adopted for the shear connection, i.e., a linear-elastic one, and a new time-dependent one, to account for the long-term effects produced in the complex stress state of the concrete surrounding the shear connectors.
A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium.
We consider the time-dependent one-dimensional nonlinear Schrödinger equation with pointwise singular potential.
The results of time-dependent one-dimensional modelling of a dielectric barrier discharge (DBD) in a nitrogen oxygen water vapor mixture at atmospheric pressure are presented.
This model integrates time-dependent, one-dimensional energy and mass conservation equations describing a propellant block with combustion inside an enclosed gas pocket.
A time-dependent one-dimensional model of the active magnetic regenerator (AMR) that takes into account most of the physical and practical design problems for the AMR is developed as a highly nonlinear system of partial differential equations.
