Gradient based microphone arrays, the horizontal sound field’s plane wave decomposition, and the corresponding circular harmonics decomposition are reviewed. Further, a general relation between directivity patterns of the horizontal sound field gradients and the circular harmonics of any order is derived. Based on this relation, a number of example differential microphone arrays are analyzed, i...

Biological rhythms such as circadian rhythms, biochemical rhythms and neural oscillators are based on the mathematical model of the theory of harmonic oscillators. These are solutions of certain second-order differential equations. They can also be viewed as spherical harmonics on the circle in the two-dimensional Euclidean space. The spherical harmonics on (n-1)-spheres and, more generally, th...

Nonperturbative high-order harmonic conversion of high-intensity, ultrafast laser pulses in gases represents a unique means to generate high-brightness, coherent XUV, and soft X-ray radiation. We review the physics controlling the spatial qualities of harmonic radiation and recent experimental measurements of high-order harmonic spatial profiles. We also examine the factors controlling the spat...

By generating broadband high-harmonic pulses from neon and compensating for attosecond chirp by the material dispersion of argon, the generation of near transform-limited 63 as pulses was achieved. The spectral phase analysis showed that, without proper compensation, the attosecond chirp of the broadband harmonics caused splitting of attosecond high-harmonic pulses in addition to pulse broadeni...

It is well established that electrical-stimulation frequency is crucial to determining the scale of induced neuromodulation, particularly when attempting to modulate corticospinal excitability. However, the modulatory effects of stimulation frequency are not only determined by its absolute value but also by other parameters such as power at harmonics. The stimulus pulse shape further influences...

Jaydeep P. Bardhan and Matthew G. Knepley Dept. of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago IL 60612 Computation Institute, The University of Chicago, Chicago IL 60637 Abstract We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are us...

By lifting full Yang-Mills theory to R4 × S2 , Mason et al. obtained MHV vertices by gauge transformation. Their Lagrangian depended on long intricate twistor manipulations. Spinor S2 harmonics give a one page proof, eliminating all the CP3 apparatus.

Nowadays with increasing use of numerous nonlinear loads, voltage and current harmonics in power systems are one of the most important problems power engineers encounter. Many of these nonlinear loads, because of their dynamic natures, inject time-varying harmonics into power system. Common techniques applied for harmonics measurement and assessment such as FFT have significant errors in presen...