Boltzmann noticed that his transport equation predicts special cases in which gases never reach thermal equilibrium. One example is the monopole breathe mode of atoms confined in a perfectly isotropic three-dimensional (3D) harmonic potential1. Such a complete absence of damping had not been observed in nature, and this anomaly weakened Boltzmann’s then-controversial claim to have established a...

The 30 Hz flicker electroretinogram (ERG) response was studied in seven patients with Schubert-Bornschein complete-type congenital stationary night blindness (SB-CSNB) by measuring conventional peak implicit times and by harmonic analysis. Responses were elicited with xenon photostrobe flashes. The fundamental flicker component showed a significant increased phase lag (P = 0.002), even though t...

Environment-mapped rendering of Lambertian isotropic surfaces is common, and a popular technique is to use a quadratic spherical harmonic expansion. This compact irradiance map representation is widely adopted in interactive applications like video games. However, many materials are anisotropic, and shading is determined by the local tangent direction, rather than the surface normal. Even for v...

The split integration symplectic method (SISM) for molecular dynamics (MD) integration using normal mode analysis based on a factorization of the Liouville propagator is presented. This approach is quite distinct from others that use fractional-step methods, owing to the analytical treatment of high-frequency motions. The method involves splitting the total Hamiltonian of the system into a harm...

In western tonal music, musical phrases end with an explicit harmonic consequent which is highly expected. As such expectation is a consequence of musical background, cerebral processing of incongruities of musical grammar might be a function of expertise. We hypothesized that a subtle incongruity of standard closure should evoke a profound and rapid reaction in an expert's brain. If such a rea...

The possibility of unidirectional motion of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least biharmonic) and of zero mean, is presented. The dependence of the kink mean velocity on system parameters is investigated numerically and the results are compared with a perturbation analysis based on a point-particle represen...

Harmonic analysis, and in particular the relation between function smoothness and approximate sparsity of its wavelet coefficients, has played a key role in signal processing and statistical inference for low dimensional data. In contrast, harmonic analysis has thus far had little impact in modern problems involving high dimensional data, or data encoded as graphs or networks. The main contribu...

Designs and simulation studies for harmonic cascades, consisting of multiple stages of harmonic generation in free electron lasers (FELs), are presented as part of the LUX R&D project to design ultrafast, high photon energy light sources for basic science. Beam energies of 1.1, 2.1, and 3.1 GeV, corresponding to each pass through a recirculating linac, have independent designs for the harmonic ...

Ringing, the high-frequency response of a structure to relatively low-frequency waves, has been a great concern in offshore engineering. To investigate this phenomenon, we solve the third-harmonic diffraction problem using a three-dimensional higher-order panel method in the low-frequency range. In this thesis, the boundary integral equations are derived from two different theories , based on c...

Nonlinear vibration behavior of beam is an important issue of structural engineering. In this study, a mathematical modeling of a forced nonlinear vibration of Euler-Bernoulli beam resting on nonlinear elastic foundation is presented. The nonlinear vibration behavior of the beam is investigated by using a modified multi-level residue harmonic balance method. The main advantage of the method is ...