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Examples of the determination of unknown velocity profiles by tracer techniques utilizing the probe are presented.
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In the SBAS approach, we minimized the norm of the unknown velocity vector, where each component corresponds to a specific period, resulting in a time series of velocity field smoothed in time.
The 2-D space of the unknown velocity can be modeled as an N vx × N vy search space such that each point in the discretized space represents a hypothetical target velocity vector, where N vx and N vy denote the number of discrete points used to represent the entire target velocity space along the x-axis and y-axis, respectively.
ν is the kinematic viscosity of the fluid, u is the unknown velocity field of the fluid, p the pressure, and (alpha>0) a length scale parameter characterizing the elasticity of the fluid, (f t-rho(t),u(t-rho(t)))) the external f t-rhoerm which contains a memory effect during a fixed interval of time of length (h>0),u t-rhoho(t)) a given adequate delay function.
where u, π, θ and ϕ denote unknown velocity field, pressure scalar, temperature of the fluid and the order parameter, respectively.
where u, π, and θ denote unknown velocity vector field, pressure scalar and temperature of the fluid.
Then to address the case in the presence of external disturbance and lack of velocity measurement, a finite-time convergent observer is constructed to estimate both the unknown velocity information and the disturbance in a finite time.
The technique assumes a moving transmitter at an unknown location (and with an unknown velocity vector).
Similarly, wavefields reconstructed in unknown velocity using data recorded with dense arrays can be described as having a random character due to the inconsistent interference of wave components.
This requires solving a single linear system that combines the unknown velocities of the structure with the unknown pressures of the fluid.
Recall that one of our main concerns is whether mathematical models can be built that supports doubly periodic traveling patterns (with a priori unknown velocities and periodicities).
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