Related papers: Exploring Fourier methods with beer bottles
The water bottle flip experiment is a recreational, non-conventional illustration of the conservation of angular moment. When a bottle partially filled with water is thrown in a rotational motion, water redistributes throughout the bottle,…
We describe a semiconductor multilayer structure based in acoustic phonon cavities and achievable with MBE technology, designed to display acoustic phonon Bloch oscillations. We show that forward and backscattering Raman spectra give a…
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
The properties of 3D Bose-Einstein condensate have been studied with variational and numerical methods. In the variational approach, we use the super-Gaussian trial function, and it is demonstrated that this trial function gives a good…
Experiments in mechanics can often be timed by the sounds they produce. In such cases, digital audio recordings provide a simple way of measuring time intervals with an accuracy comparable to that of photogate timers. We illustrate this…
We study the possibility of occurrence of vibrational resonance in a softening Duffing oscillator in the underdamped and overdamped cases both theoretically as well as numerically. The oscillator is driven by two periodic forces.…
A recently developed enhanced Fourier law is applied to the problem of extracting thermal properties of materials from frequency-domain thermoreflectance (FDTR) experiments. The heat transfer model comprises contributions from two phonon…
Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward…
We describe a method to probe the spectral fluctuations of a transition over broad ranges of frequencies and timescales with the high spectral resolution of Fourier spectroscopy, and a temporal resolution as high as the excited state…
We have developed a senior undergraduate experiment that illustrates frequency stabilization techniques using radio-frequency electronics. The primary objective is to frequency stabilize a voltage controlled oscillator to a cavity resonance…
The interaction between the fractional order parameter and the damping parameter can play a relevant role for introducing different dynamical behaviors in a physical system. Here, we study the Duffing oscillator with a fractional damping…
The frequency-dependent attenuation of broadband acoustics is often confronted in many different areas. However, the related time domain simulation is rarely found in literature due to enormous technical difficulty. The currently popular…
Acoustic room modes and the Green's function mode expansion are well-known for rectangular rooms with perfectly reflecting walls. First-order approximations also exist for nearly rigid boundaries; however, current analytical methods fail to…
To study the dynamical behaviour of the engineering and physical systems, we often need to capture their continuous behaviour, which is modeled using differential equations, and perform the frequency-domain analysis of these systems.…
Modeling optical field propagation in highly scattering and birefringent medium is of important interest to many photonic research branches. Despite the existence of numerical electromagnetic simulation tools and beam propagation method…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
In this paper we show that the discrete Fourier transform can be performed by scattering a coherent particle or laser beam off a two-dimensional potential that has the shape of rings or peaks. After encoding the initial vector into the…
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…
We study the low-energy limit of a quarter-filled one-dimensional Mott insulator. We analytically determine the local density of states in the presence of a strong impurity potential, which is modeled by a boundary. To this end we calculate…