We study –both in theory and practice– the use of momentum motions in classic iterative hard thresholding (IHT) methods. By simply modifying plain IHT, we investigate its convergence behavior on convex optimization criteria with non-convex constraints, under standard assumptions. In diverse scenaria, we observe that acceleration in IHT leads to significant improvements, compared to state of the...

We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation-the geotryptic state. A priori error estimates for the linearized momentum and free surface...

Antennas radiate (vector) momentum as well as energy, but if the radiation pattern is symmetric, the total radiated momentum is zero. Consider a simple antenna array that consists of two short linear dipole antennas whose centers are λ/4 apart and whose conductors point along the line of centers of the antennas. If the two antennas are excited with a 90◦ phase difference, deduce the asymmetric ...

The spin angular momentum in an elliptically polarized beam of light plays several noteworthy roles in optical traps. It contributes to the linear momentum density in a nonuniform beam, and thus to the radiation pressure exerted on illuminated objects. It can be converted into orbital angular momentum, and thus can exert torques even on optically isotropic objects. Its curl, moreover, contribut...

The well-known effect of the linear damping on the moving nonlinear Schrödinger soliton (even when there is a supply of energy via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex traveling with zero momentum at a nonzero...

I describe an elementary way of introducing electromagnetic field momentum. By considering a system of a long solenoid and line charge, the dependence of the field momentum on the electric and magnetic fields can be deduced. I obtain the electromagnetic angular momentum for a point charge and magnetic monopole pair partially through dimensional analysis and without using vector calculus identit...

Recent research suggests the importance of controlling rotational dynamics of a humanoid robot in balance maintenance and gait. In this paper, we present a novel balance strategy that controls both linear and angular momentum of the robot. The controller’s objective is defined in terms of the desired momenta, allowing intuitive control of the balancing behavior of the robot. By directly determi...