Two Dimensional and Time Varying Spatial Domains

A two-dimensional, unsteady, transonic, irrotational, inviscid flow of a perfect gas with constant specific heats is considered. The analysis involves perturbations from a uniform sonic isentropic flow. The governing perturbation potential equations are derived for various orders of the ratio of the characteristic time associated with a temporal flow disturbance to the time taken by a sonic disturbance to traverse the transonicregime. The case where this ratio is large compared to one is studied in detail. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady chimel flows with either stationary or time-varying wall shapes. Numerical computations are presented showing the temporal changes in flow structure as a disturbance dies out exponentially for the following typical nozzle flows: simple accelerating (Meyer) flow and flow with supersonic pockets (Taylor and limiting Taylor flow).

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Time-Varying Channel Estimation Using Two-Dimensional Channel Orthogonalization and Superimposed Training

IEEE Transactions on Signal Processing ◽

10.1109/tsp.2012.2195658 ◽

2012 ◽

Vol 60 (8) ◽

pp. 4439-4443 ◽

Cited By ~ 11

Author(s):

Roberto Carrasco-Alvarez ◽

R. Parra-Michel ◽

Aldo G. Orozco-Lugo ◽

Jitendra K. Tugnait

Keyword(s):

Channel Estimation ◽

Time Varying ◽

Two Dimensional ◽

Superimposed Training ◽

Time Varying Channel

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Analytic reconstruction of a two-dimensional velocity field from an observed diffusive scalar

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.301 ◽

2019 ◽

Vol 871 ◽

pp. 755-774

Author(s):

Arjun Sharma ◽

Irina I. Rypina ◽

Ruth Musgrave ◽

George Haller

Keyword(s):

Velocity Field ◽

Ocean Circulation ◽

Incompressible Flows ◽

Circulation Model ◽

Scalar Fields ◽

Navier Stokes ◽

Two Dimensional ◽

Velocity Measurements ◽

Ocean Circulation Model ◽

Spatial Domains

Inverting an evolving diffusive scalar field to reconstruct the underlying velocity field is an underdetermined problem. Here we show, however, that for two-dimensional incompressible flows, this inverse problem can still be uniquely solved if high-resolution tracer measurements, as well as velocity measurements along a curve transverse to the instantaneous scalar contours, are available. Such measurements enable solving a system of partial differential equations for the velocity components by the method of characteristics. If the value of the scalar diffusivity is known, then knowledge of just one velocity component along a transverse initial curve is sufficient. These conclusions extend to the shallow-water equations and to flows with spatially dependent diffusivity. We illustrate our results on velocity reconstruction from tracer fields for planar Navier–Stokes flows and for a barotropic ocean circulation model. We also discuss the use of the proposed velocity reconstruction in oceanographic applications to extend localized velocity measurements to larger spatial domains with the help of remotely sensed scalar fields.

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Linear Approximations for Swing Leg Motion During Gait

Journal of Biomechanical Engineering ◽

10.1115/1.3138470 ◽

1984 ◽

Vol 106 (2) ◽

pp. 137-143 ◽

Cited By ~ 5

Author(s):

W. H. Lee ◽

J. M. Mansour

Keyword(s):

Linear Systems ◽

System Analysis ◽

Linear Time ◽

Time Varying ◽

Two Dimensional ◽

State Variables ◽

Linear Time Invariant ◽

Linear Time Invariant Systems ◽

Leg Motion ◽

Time Invariant

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.

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