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In this paper, we investigate the interior inverse source problem for the Helmholtz equation with attenuation in the plane from boundary Cauchy data of multiple frequencies when the source term is assumed to be compactly supported in an arbitrary domain Ω with sufficiently smooth boundary. The main goal of this paper is to understand the dependence of increasing stability on the attenuation factor or constant damping. Using Fourier transform with respect to the wave numbers, explicit bounds for the analytic continuation and Hankel function and exact observability and Carleman estimates for the wave equation led us to our goal which is an increasing stability estimates with larger wave numbers interval. [ABSTRACT FROM AUTHOR]

Using the split-step Fourier transform method, we numerically investigate the generation of breathing solitons in the propagation and interactions of Airy–Gaussian (AiG) beams in a cubic–quintic nonlinear medium in one transverse dimension. We show that the propagation of single AiG beams can generate stable breathing solitons that do not accelerate within a certain initial power range. The propagation direction of these breathing solitons can be controlled by introducing a launch angle to the incident AiG beams. When two AiG beams accelerated in opposite directions interact with each other, different breathing solitons and soliton pairs are observed by adjusting the phase shift, the beam interval, the amplitudes, and the light field distribution of the initial AiG beams. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study double-slit diffraction at the nanometric scale. We treat the time evolution of a Gaussian wave packet in quantum mechanics traveling until it reaches a double-slit wall. A detailed investigation and analysis of the diffraction phenomenon and its progress is developed by numerically solving the Schrödinger equation. This is written using a potential intended to model the wall. It is solved by using finite differences in the time domain method, so that the probability amplitude, ψ, is obtained as a function of the spatial coordinates at discretized times. Then, the probability density, ρ, is found in a straightforward way and used to plot graphics or make videos. Furthermore, the time evolution of the wave packet is registered at several fixed points to acquire local information. Fourier transforms are calculated to complement the knowledge obtained. Students interested in didactic approaches, or in applications for nanodevices, could find interest in this approach. [ABSTRACT FROM AUTHOR]

Numerical differentiation is commonly used by a number of science students and researchers for data analysis. The differentiation of vectors of data points representing discrete samples of some underlying signal can be implemented in a computer using the central differencing scheme or the fast Fourier transform (FFT)-based approach. We point out that a simple extension of the continuous Fourier transform derivative identity to the discrete case, however, gives rise to results that are inconsistent with the central differencing scheme. In particular, for functions with step-like discontinuities, the numerical derivative computed with the FFT-based approach is corrupted by ringing artifacts. We describe the idea of a modified wave number for FFT-based numerical differentiation which leads to results that are consistent with the central differencing scheme. Modified wave number identities for numerical computation of both first and second order derivatives are described. The pitfalls of using a simplistic extension of the derivative identity for continuous Fourier transform to the discrete case and the methodology to avoid them are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed. [ABSTRACT FROM AUTHOR]

Collective scattering of spatially coherent radiation by separated point emitters induces inter-particle forces. For particles close to nano-photonic structures as, for example, nano-fibers, hollow core fibers or photonic waveguides, this pair-interaction induced by monochromatic light is periodic and virtually of infinite range. Here we show that the shape and range of the optical interaction potential can be precisely controlled by spectral design of the incoming illumination. If each particle is only weakly coupled to the confined guided modes the forces acting within a particle ensemble can be decomposed to pairwise interactions. These forces can be tailored to almost arbitrary spatial dependence as they are related to Fourier transforms with coefficients controlled by the intensities and frequencies of the illuminating lasers. We demonstrate the versatility of the scheme by highlighting some examples of unconventional pair potentials. Implementing these interactions in a chain of trapped quantum particles could be the basis of a versatile quantum simulator with almost arbitrary all-to-all interaction control. [ABSTRACT FROM AUTHOR]

Airy beams have gained attention due to their exotic properties of seemingly bending around obstacles, self-healing and being resistant to diffraction. Regular Airy beams are often generated by imposing cubic spatial phase on a Gaussian beam and Fourier transforming the resulting field with a lens. In this paper, we analyze the so-called hyperbolic Airy (HA) beams that are formed behind the cubic phase element, i.e. with no Fourier lens in the setup. We use an ultra-broadband supercontinuum laser source in combination with transmissive (refractive) and reflective cubic phase elements to create white-light HA beams. The resulting beams are sampled with a SEA TADPOLE spatial-spectral interferometer to record the hyperspectral beam profile and reconstruct a three-dimensional spatio-temporal impulse response of the cubic phase elements. We show that nondispersing beams are produced in reflective geometry, while the main lobe of the HA beam created with a refractive phase element suffered from lateral dispersion. [ABSTRACT FROM AUTHOR]

We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show mathematically that the Fourier transforms of eigenimages derived from PCA applied to an ensemble of images in the spatial domain are identical to the eigenvectors of PCA applied to the ensemble of the Fourier transforms of the images, which suggests that this approach may be applied to modeling the sparse interferometric Fourier-visibilities produced by an array such as the Event Horizon Telescope. We also show that the simulations in the spatial domain can themselves be compactly represented with a PCA-derived basis of eigenimages, which allows for detailed comparisons to be made between variable observations and time-dependent models, as well as for detection of outliers or rare events within a time series of images. Furthermore, we demonstrate that the spectrum of PCA eigenvalues is a diagnostic of the power spectrum of the structure and, hence, of the underlying physical processes in the simulated and observed images. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a method of selectively enhancing the single mode signal of a Lamb wave by using a meander-coil electromagnetic acoustic transducer (EMAT) with a new magnetic configuration. We use the Lamb antisymmetric (A0) mode and symmetric (S0) mode as an example for analysis. The analytical expression of the magnitude of the spatial Fourier transform of the Lorentz force generated by different meander coils is used to determine the optimal driving frequency for single mode generation. The numerical calculation is used to characterize the new magnetic configuration and the conventional EMAT magnet. Experimental examinations of each meander coil in combination with the conventional and new magnetic configuration show that the Lamb wave signal can be selectively enhanced by choosing the appropriate driving frequency and coil parameters through using the improved meander-coil EMAT. [ABSTRACT FROM AUTHOR]

We present a spectral approach to perform nanoindentation simulations using three-dimensional nodal discrete dislocation dynamics. The method relies on a two step approach. First, the contact problem between an indenter of arbitrary shape and an isotropic elastic half-space is solved using a spectral iterative algorithm, and the contact pressure is fully determined on the half-space surface. The contact pressure is then used as a boundary condition of the spectral solver to determine the resulting stress field produced in the simulation volume. In both stages, the mechanical fields are decomposed into Fourier modes and are efficiently computed using fast Fourier transforms. To further improve the computational efficiency, the method is coupled with a subcycling integrator and a special approach is devised to approximate the displacement field associated with surface steps. As a benchmark, the method is used to compute the response of an elastic half-space using different types of indenter. An example of a dislocation dynamics nanoindentation simulation with complex initial microstructure is presented. [ABSTRACT FROM AUTHOR]

Entanglement is a fundamental resource at the basis of quantum-enhanced performances in several applications, such as quantum algorithms and quantum metrology. In these contexts, Fourier interferometers implement a relevant class of unitary evolutions which can be embedded in a large variety of protocols. For instance, in the single-particle regime it can be adopted to implement the quantum Fourier transform, while in the multi-particle scenario it can be employed to generate quantum states possessing useful entanglement for quantum phase estimation purposes, or as a tool to verify genuine multi-photon interference. In this article, we study experimentally the dynamics of single-photon and two-photon input states during the evolution provided by a 8-mode Fourier transformation, implemented by exploiting a three-dimensional architecture enabled by the femtosecond laser micromachining technology. In such a way, we fabricated three devices to study the evolution after each step of the decomposition. We observe that the probability distributions obey a step-by-step majorization relationship, where the quantum state occupies a progressively larger portion of the Hilbert space. Such behaviour can be related to the majorization principle, which has been conjectured as a necessary condition for quantum speedup. [ABSTRACT FROM AUTHOR]

In this work, the results of an analysis of the response of a near-resonant series resistance−inductance−capacitance (RLC) electric circuit with time-dependent forcing frequency by means of a wavelet cross-correlation approach are reported. In particular, it is shown how the wavelet approach enables frequency and time analysis of the circuit response to be carried out simultaneously—this procedure not being possible by Fourier transform, since the frequency is not stationary in time. A series RLC circuit simulation is performed by using the Simulation Program with Integrated Circuits Emphasis (SPICE), in which an oscillatory sinusoidal voltage drive signal of constant amplitude is swept through the resonant condition by progressively increasing the frequency over a 20-second time window, linearly, from 0.32 Hz to 6.69 Hz. It is shown that the wavelet cross-correlation procedure quantifies the common power between the input signal (represented by the electromotive force) and the output signal, which in the present case is a current, highlighting not only which frequencies are present but also when they occur, i.e. providing a simultaneous time-frequency analysis. The work is directed toward graduate Physics, Engineering and Mathematics students, with the main intention of introducing wavelet analysis into their data analysis toolkit. [ABSTRACT FROM AUTHOR]

In isotropic homogeneous media, far fields of time-harmonic electromagnetic waves radiated by compactly supported volume currents, and elastic waves radiated by compactly supported body force densities can be modelled in very similar fashions. Both are projected restricted Fourier transforms of vector-valued source terms. In this work we generalize two types of uncertainty principles recently developed for far fields of scalar-valued time-harmonic waves in Griesmaier and Sylvester (2017 SIAM J. Appl. Math. 77 154–80) to this vector-valued setting. These uncertainty principles yield stability criteria and algorithms for splitting far fields radiated by collections of well-separated sources into the far fields radiated by individual source components, and for the restoration of missing data segments. We discuss proper regularization strategies for these inverse problems, provide stability estimates based on the new uncertainty principles, and comment on reconstruction schemes. A numerical example illustrates our theoretical findings. [ABSTRACT FROM AUTHOR]

We study the Wigner crystallization on partially filled topological flat bands of kagome, honeycomb and checkerboard lattices. We identify the Wigner crystals (WCs) by analyzing the Cartesian and angular Fourier transform of the pair correlation density of the many-body ground state obtained using exact diagonalization. The crystallization strength, measured by the magnitude of the Fourier peaks, increases with decreasing particle density. The Wigner crystallization observed by us is a robust and general phenomenon, existing in all three lattice models for a broad range of filling factors and interaction parameters. The shape of the resulting WCs is determined by the boundary conditions of the chosen plaquette. It is to a large extent independent on the underlying lattice, including its topology, and follows the behavior of classical point particles. [ABSTRACT FROM AUTHOR]

One of the key issues in unraveling the mystery of high TC superconductivity in the cuprates is to understand the normal state outside the superconducting dome. Here we perform scanning tunneling microscopy and spectroscopy measurements on a heavily overdoped, non-superconducting (Bi, Pb)2Sr2CuO6+δ cuprate. Spectroscopic imaging reveals dispersive quasiparticle interferences (QPIs) and the Fourier transforms uncover the evolution of momentum space topology. More interestingly, we observe nanoscale patches of static charge order with periodicity. Both the dispersive QPI and static charge order can be qualitatively explained by theoretical calculations, which reveal the unique electronic structure of strongly overdoped cuprate. [ABSTRACT FROM AUTHOR]

In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain Ω with a sufficiently smooth boundary. Using the Fourier transform in the frequency domain, bounds for the Hankel functions and for scattering solutions in the complex plane, improving bounds for the analytic continuation, and the exact observability for the wave equation led us to our goals which are a sharp uniqueness and increasing stability estimate when the wave number interval is growing. [ABSTRACT FROM AUTHOR]

The underlying mechanism of the spectral cleaning effect of the cross-polarized wave (XPW) generation process was theoretically investigated. This study shows that the spectral noise of an input spectrum can be removed in the XPW generation process and that the spectral cleaning effect depends on the characteristics of the input pulses, such as the chirp and Fourier-transform-limited duration of the initial pulse, and the modulation amplitude and frequency of the spectral noise. Though these factors codetermine the output spectrum of the XPW generation process, the spectral cleaning effect is mainly affected by the initial pulse chirp. The smoothing of the spectrum in the XPW generation process leads to a significant enhancement of the coherent contrast. [ABSTRACT FROM AUTHOR]

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain approaches to show uniqueness in determining the spatial function from wave fields on a large sphere over a finite time interval. The stability estimate of the temporal function from the data of one receiver and the uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivates inversion schemes that can be easily implemented. A Landweber iterative algorithm for recovering the spatial function and a non-iterative inversion scheme based on the uniqueness proof for recovering the temporal function are proposed. Numerical examples are demonstrated in both two and three dimensions. [ABSTRACT FROM AUTHOR]

We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks. [ABSTRACT FROM AUTHOR]

In this reply, we respond to the comments of Mustafaev et al to our paper ‘Information hidden in the velocity distribution of ions and the exact kinetic Bohm criterion’ (Plasma Sources Science and Technology26 055003). The objections about the validity and the correctness of the analysis in the paper are addressed through providing some of the omitted calculations and extending the discussions on certain aspects of the contents. [ABSTRACT FROM AUTHOR]

We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. [ABSTRACT FROM AUTHOR]

In the present work, we develop a low-cost and simple experiment to visualise Fourier’s synthesis using a short, soft, and light plastic coiled spring oscillating in a horizontal plane, and a basic camera (120 fps). It is shown that the spring obeys a linear wave differential equation, as gravitational influence is neglected. A nonlinear criterion is evaluated to determine if magnitudes of the parameters in the initial conditions satisfy the linear wave equation. Our setup promotes some desirable characteristics that make Fourier’s synthesis experiments feasible, visual, and enlightening: (i) it requires few, common, and cheap resources, and the experiment can be carried out even in a high-school laboratory; (ii) since the spring’s tension is small (∼1 N, on average), the frequencies of normal modes are low (close to 2 Hz), and therefore, it is possible to record the oscillations just with the camera and extract a considerable number of position and time data in just one cycle; (iii) when the video is loaded in the Tracker free software, it can be reproduced in slow motion. Since the frequencies involved are low, an interesting and instructive temporal sequence of images of the spring displaying the typical trapezoidal shape appears clearly; (iv) the tools associated with the Tracker software tools can yield the relevant oscillation parameters, such as the damping constant, amplitudes, frequencies, and phases; and (v) it is possible to carry out superposition of a snapshot of the spring in Tracker at any time, and to draw the related Fourier synthesis graphs. The visual match between the shape of the spring and the theoretical graph is remarkable, and can be enhanced by adding the damping term. [ABSTRACT FROM AUTHOR]

Polycrystalline undoped and Sb doped BaSnO3 powder samples, BaSn1−xSbxO3 (0 ≤ x ≤ 0.1) have been prepared by hydrogen peroxide assisted method. Hydrogen is incorporated into BaSn1−xSbxO3 to tune the defect and optical properties of the parent oxide. Three localized vibrational modes at 2800–3000 cm−1 in Fourier transform infrared spectra originate from positive and neutral charge states of hydrogen. The observation of strong Raman lines indicate a local structural distortion in a cubic phase of BaSnO3. X-ray photoelectron studies indicate Sn4+ and Sb5+ oxidation states of Sn and Sb in doped samples. The replacement of Sn4+ by Sb5+ enhances the optical band gap from 3.14 ± 0.24 eV in undoped to 3.25 ± 0.20 eV in the 10% Sb-doped sample. Hydrogen impurities act as electron donors and also increase the optical band gap. The overall band gap enhancement has been explained by the Burstein-Moss band filling effect. Two electron paramagnetic resonance signals, corresponding to two kinds of oxygen vacancy centres, are strongly influenced by Sb and hydrogen dopants. [ABSTRACT FROM AUTHOR]

We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium. [ABSTRACT FROM AUTHOR]

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs. [ABSTRACT FROM AUTHOR]

During edge localised mode (ELM) crashes in KSTAR deuterium plasmas, bursts of spectrally structured ion cyclotron emission (ICE) are detected. Usually the ICE spectrum chirps downwards during an ELM crash, on sub-microsecond timescales. For KSTAR ICE where the separation of spectral peak frequencies is close to the proton cyclotron frequency at the outer plasma edge, we show that the driving population of energetic ions is likely to be a subset of the 3 MeV fusion protons, born centrally on deeply passing orbits which drift from the core to the edge plasma. We report first principles modelling of this scenario using a particle-in-cell code, which evolves the full orbit dynamics of large numbers of energetic protons, thermal deuterons, and electrons self-consistently with the electric and magnetic fields. The Fourier transform of the excited fields in the nonlinear saturated regime of the simulations is the theoretical counterpart to the measured ICE spectra. Multiple simulation runs for different, adjacent, values of the plasma density under KSTAR edge conditions enable us to infer the theoretical dependence of ICE spectral structure on the local electron number density. By matching this density dependence to the observed time-dependence of chirping ICE spectra in KSTAR, we obtain sub-microsecond time resolution of the evolving local electron number density during the ELM crash. [ABSTRACT FROM AUTHOR]

Quantitative detection of defects in atomic structures is of great significance to evaluating product quality and exploring quality improvement process. In this study, a Fourier transform filtered sampling Moiré technique was proposed to visualize and detect defects in atomic arrays in a large field of view. Defect distributions, defect numbers and defect densities could be visually and quantitatively determined from a single atomic structure image at low cost. The effectiveness of the proposed technique was verified from numerical simulations. As an application, the dislocation distributions in a GaN/AlGaN atomic structure in two directions were magnified and displayed in Moiré phase maps, and defect locations and densities were detected automatically. The proposed technique is able to provide valuable references to material scientists and engineers by checking the effect of various treatments for defect reduction. [ABSTRACT FROM AUTHOR]

We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the method of accumulated spectrograms (the sum of the spectrograms corresponding to large eigenvalues). We derive a sharp bound for the rate of convergence of the accumulated spectrogram, improving on recent results. [ABSTRACT FROM AUTHOR]

The most important quantitative aspects of computational structural crystallography can be introduced in a satisfactory way using 1D truncated and periodic Gaussian functions to represent the atoms in a crystal lattice. This paper describes in detail and demonstrates 1D structural crystallography starting with the definition of such truncated Gaussians. The availability of the computer programme CRONE makes possible the repetition of the examples provided in the paper as well as the creation of new ones. [ABSTRACT FROM AUTHOR]

A critical challenge in the observation of the redshifted 21 cm line is its separation from bright Galactic and extragalactic foregrounds. In particular, the instrumental leakage of polarized foregrounds, which undergo significant Faraday rotation as they propagate through the interstellar medium, may harmfully contaminate the 21 cm power spectrum. We develop a formalism to describe the leakage due to instrumental widefield effects in visibility-based power spectra measured with redundant arrays, extending the delay-spectrum approach presented in Parsons et al. We construct polarized sky models and propagate them through the instrument model to simulate realistic full-sky observations with the Precision Array to Probe the Epoch of Reionization. We find that the leakage due to a population of polarized point sources is expected to be higher than diffuse Galactic polarization at any k mode for a 30 m reference baseline. For the same reference baseline, a foreground-free window at k > 0.3 h Mpc−1 can be defined in terms of leakage from diffuse Galactic polarization even under the most pessimistic assumptions. If measurements of polarized foreground power spectra or a model of polarized foregrounds are given, our method is able to predict the polarization leakage in actual 21 cm observations, potentially enabling its statistical subtraction from the measured 21 cm power spectrum. [ABSTRACT FROM AUTHOR]

Seismic data interpolation and denoising plays a key role in seismic data processing. These problems can be understood as sparse inverse problems, where the desired data are assumed to be sparsely representable within a suitable dictionary. In this paper, we present a new method based on a data-driven tight frame (DDTF) of Kronecker type (KronTF) that avoids the vectorization step and considers the multidimensional structure of data in a tensor-product way. It takes advantage of the structure contained in all different modes (dimensions) simultaneously. In order to overcome the limitations of a usual tensor-product approach we also incorporate data-driven directionality. The complete method is formulated as a sparsity-promoting minimization problem. It includes two main steps. In the first step, a hard thresholding algorithm is used to update the frame coefficients of the data in the dictionary; in the second step, an iterative alternating method is used to update the tight frame (dictionary) in each different mode. The dictionary that is learned in this way contains the principal components in each mode. Furthermore, we apply the proposed KronTF to seismic interpolation and denoising. Examples with synthetic and real seismic data show that the proposed method achieves better results than the traditional projection onto convex sets method based on the Fourier transform and the previous vectorized DDTF methods. In particular, the simple structure of the new frame construction makes it essentially more efficient. [ABSTRACT FROM AUTHOR]

Aiming at the threats to the active laser detection systems of electro-optical devices due to the cat-eye effect, a novel solution is put forward to realize retro-reflection reduction in this paper. According to the demands of both cat-eye effect reduction and the image quality maintenance of electro-optical devices, a symmetric phase mask is achieved from a stationary phase method and a fast Fourier transform algorithm. Then, based on a comparison of peak normalized cross-correlation (PNCC) between the different defocus parameters, the optimal imaging position can be obtained. After modification with the designed phase mask, the cat-eye effect peak intensity can be reduced by two orders of magnitude while maintaining good image quality and high modulation transfer function (MTF). Furthermore, a practical design example is introduced to demonstrate the feasibility of our proposed approach. [ABSTRACT FROM AUTHOR]

Eccentric binaries known as heartbeat stars experience strong dynamical tides as the stars pass through periastron, providing a laboratory to study tidal interactions. We measure the rotation periods of 24 heartbeat systems, using the Kepler light curves to identify rotation peaks in the Fourier transform. Where possible, we compare the rotation period to the pseudosynchronization period derived by Hut. Few of our heartbeat stars are pseudosynchronized with the orbital period. For four systems, we were able to identify two sets of rotation peaks, which we interpret as the rotation from both stars in the binary. Most stars in our sample have rotation rates larger than the pseudosynchronization period while a single target rotates much faster than this rate. The majority of the systems have a rotation period that is approximately times the pseudosynchronization period, suggesting that other physical mechanisms strongly influence the star’s evolution. [ABSTRACT FROM AUTHOR]

Astronomical objects frequently exhibit structure over a wide range of scales whereas many telescopes, especially interferometer arrays, only sample a limited range of spatial scales. To properly image these objects, images from a set of instruments covering the range of scales may be needed. These images then must be combined in a manner to recover all spatial scales. This paper describes the feathering technique for image combination in the Fourier transform plane. Implementations in several packages are discussed and example combinations of single dish and interferometric observations of both simulated and celestial radio emission are given. [ABSTRACT FROM AUTHOR]

Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise. [ABSTRACT FROM AUTHOR]

Consider the incidence of a time-harmonic electromagnetic plane wave onto a biperiodic dielectric grating, where the surface is assumed to be a small and smooth perturbation of a plane. The diffraction is modeled as a transmission problem for Maxwell’s equations in three dimensions. This paper concerns the inverse diffraction problem which is to reconstruct the grating surface from either the diffracted field or the transmitted field. A novel approach is developed to solve the challenging nonlinear and ill-posed inverse problem. The method requires only a single incident field and is realized via the fast Fourier transform. Numerical results show that it is simple, fast, and stable to reconstruct biperiodic dielectric grating surfaces with super-resolved resolution. [ABSTRACT FROM AUTHOR]

Arterial stiffness is found to be an early indicator of many cardiovascular diseases. Among various techniques, shear wave elastography has emerged as a promising tool for estimating local arterial stiffness through the observed dispersion of guided waves. In this paper, we develop efficient models for the computational simulation of guided wave dispersion in arterial walls. The models are capable of considering fluid-loaded tubes, immersed in fluid or embedded in a solid, which are encountered in in vitro/ex vivo, and in vivo experiments. The proposed methods are based on judiciously combining Fourier transformation and finite element discretization, leading to a significant reduction in computational cost while fully capturing complex 3D wave propagation. The developed methods are implemented in open-source code, and verified by comparing them with significantly more expensive, fully 3D finite element models. We also validate the models using the shear wave elastography of tissue-mimicking phantoms. The computational efficiency of the developed methods indicates the possibility of being able to estimate arterial stiffness in real time, which would be beneficial in clinical settings. [ABSTRACT FROM AUTHOR]

We experimentally measure the sodium D-lines from the multibubble sonoluminescence in sodium hydroxide aqueous solution. The asymmetric overlapping D-lines are successfully decomposed based on the Fourier transform analysis. The line broadening of the decomposed sodium D-lines shows the effective temperature of 3600–4500 K and the pressure of 560–1000 atm during sonoluminescence. [ABSTRACT FROM AUTHOR]

A spectrogram of a singer’s vibrato presents a striking way to introduce students to frequency, Fourier spectra, and modulation. Vibrato is discussed from the perspectives of the physicist and the musician. A dramatic spectrogram is included where coauthor soprano Michel suppresses her vibrato so that acoustical characteristics can be compared to the same note sung with vibrato. A video (Ruiz 2017 Video: vibrato http://mjtruiz.com/ped/vibrato/) is provided of this demonstration. [ABSTRACT FROM AUTHOR]

Measurement-based one-way quantum computation, which uses cluster states as resources, provides an efficient model to perform computation. However, few of the continuous variable (CV) quantum algorithms and classical algorithms based on one-way quantum computation were proposed. In this work, we propose a method to implement the classical Hadamard transform algorithm utilizing the CV cluster state. Compared with classical computation, only half operations are required when it is operated in the one-way CV quantum computer. As an example, we present a concrete scheme of four-mode classical Hadamard transform algorithm with a four-partite CV cluster state. This method connects the quantum computer and the classical algorithms, which shows the feasibility of running classical algorithms in a quantum computer efficiently. [ABSTRACT FROM AUTHOR]

Realizing the logic operations with small-scale states is pursued to improve the utilization of quantum resources and to simplify the experimental setup. We propose a scheme to realize a general single-mode Gaussian operation with a two-mode entangled state by utilizing only one nondegenerate optical parametric amplifier and by adjusting four angle parameters. The fidelity of the output mode can be optimized by changing one of the angle parameters. This scheme would be utilized as a basic efficient element in the future large-scale quantum computation. [ABSTRACT FROM AUTHOR]

The complex conjugate ambiguity in Fourier domain optical coherence tomography (FDOCT) is a major roadblock that prevents full-detector resolution for the depth scan in single shot operation for the individual A-scan. Current techniques to eliminate this problem involve changing the experimental set-up, usually complicating the OCT system. In this work we show that the standard FDOCT spectrum data when resampled appropriately can be cast exactly in terms of type-1 discrete cosine transform (DCT). Additionally, a sparse reconstruction method in the DCT domain enables image recovery with full-detector resolution, thus effectively doubling the depth scan resolution. In a realistic simulation study we demonstrate full-detector resolution for a discrete reflective target by successfully resolving closely spaced reflective peaks that cannot be separated using the standard Fourier transform based reconstruction. Experimental results on reflective glass sheet targets further validate the methodology. The results of the proposed technique suggest that full resolution FDOCT systems may be implemented practically without additional hardware costs and system complexity. [ABSTRACT FROM AUTHOR]

This work focuses on the calculation of the large-volume behaviour of form factors of local operators in the XXZ spin-1/2 chain taken between the ground state and an excited state containing bound states. The analysis is rigorous and builds on various fine properties of the string solutions to the Bethe equations and certain technical hypotheses. These technical hypotheses are satisfied for a generic excited state. The results obtained in this work pave the way for extracting, starting from the first principles, the large-distance and long-time asymptotic behaviour of the XXZ chain’s two-point functions just as the so-called edge singularities of their Fourier transforms. [ABSTRACT FROM AUTHOR]

A superoscillating function is defined by the property that it oscillates faster than its fastest Fourier components. This is mathematically possible because the coefficients of the linear combinations of the band limited components depend on the number of components. This phenomenon was discovered in the context of quantum physics, but it has important applications in a variety of areas, including metrology, antenna theory, and a new theory of superresolution in optics. In this paper we study the evolution of superoscillatory functions in uniform electric field by the Schrödinger equation where we assume that the Hamiltonian contains a even polynomial of the linear momentum p. This includes the classical case but also relativistic corrections of any order. Moreover, we extend our results to the case of several variables using the theory of superoscillating functions in several variables. We conclude by discussing a comparison of our work with the existing literature. [ABSTRACT FROM AUTHOR]

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys. [ABSTRACT FROM AUTHOR]

Image coaddition is one of the most basic operations that astronomers perform. In Paper I, we presented the optimal ways to coadd images in order to detect faint sources and to perform flux measurements under the assumption that the noise is approximately Gaussian. Here, we build on these results and derive from first principles a coaddition technique that is optimal for any hypothesis testing and measurement (e.g., source detection, flux or shape measurements, and star/galaxy separation), in the background-noise-dominated case. This method has several important properties. The pixels of the resulting coadded image are uncorrelated. This image preserves all the information (from the original individual images) on all spatial frequencies. Any hypothesis testing or measurement that can be done on all the individual images simultaneously, can be done on the coadded image without any loss of information. The PSF of this image is typically as narrow, or narrower than the PSF of the best image in the ensemble. Moreover, this image is practically indistinguishable from a regular single image, meaning that any code that measures any property on a regular astronomical image can be applied to it unchanged. In particular, the optimal source detection statistic derived in Paper I is reproduced by matched filtering this image with its own PSF. This coaddition process, which we call proper coaddition, can be understood as the maximum signal-to-noise ratio measurement of the Fourier transform of the image, weighted in such a way that the noise in the entire Fourier domain is of equal variance. This method has important implications for multi-epoch seeing-limited deep surveys, weak lensing galaxy shape measurements, and diffraction-limited imaging via speckle observations. The last topic will be covered in depth in future papers. We provide an implementation of this algorithm in MATLAB. [ABSTRACT FROM AUTHOR]

We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small- and large-scale dynamo properties, as well as the inverse cascade of magnetic helicity, in the most general minimal subset of interacting velocity and magnetic fields on a closed Fourier triad. We mainly focus on the dependency of magnetic field growth as a function of the distribution of kinetic and magnetic helicities among the three interacting wavenumbers. By combining direct numerical simulations of the full magnetohydrodynamics equations with the helical Fourier decomposition, we numerically confirm that in the kinematic dynamo regime the system develops a large-scale magnetic helicity with opposite sign compared to the small-scale kinetic helicity, a sort of triad-by-triad α-effect in Fourier space. Concerning the small-scale perturbations, we predict theoretically and confirm numerically that the largest instability is achived for the magnetic component with the same helicity of the flow, in agreement with the Stretch–Twist–Fold mechanism. Vice versa, in the presence of Lorentz feedback on the velocity, we find that the inverse cascade of magnetic helicity is mostly local if magnetic and kinetic helicities have opposite signs, while it is more nonlocal and more intense if they have the same sign, as predicted by the analytical approach. Our analytical and numerical results further demonstrate the potential of the helical Fourier decomposition to elucidate the entangled dynamics of magnetic and kinetic helicities both in fully developed turbulence and in laminar flows. [ABSTRACT FROM AUTHOR]

The problem of recovering a signal of finite duration from a piece of its Fourier transform was solved at Bell Labs in the 1960’s, by exploiting a ‘miracle’: a certain naturally appearing integral operator commutes with an explicit differential one. Here we show that this same miracle holds in a matrix valued version of the same problem. [ABSTRACT FROM AUTHOR]

Astronomical radio signals are subjected to phase dispersion while traveling through the interstellar medium. To optimally detect a short-duration signal within a frequency band, we have to precisely compensate for the unknown pulse dispersion, which is a computationally demanding task. We present the “fast dispersion measure transform” algorithm for optimal detection of such signals. Our algorithm has a low theoretical complexity of , where Nf, Nt, and NΔ are the numbers of frequency bins, time bins, and dispersion measure bins, respectively. Unlike previously suggested fast algorithms, our algorithm conserves the sensitivity of brute-force dedispersion. Our tests indicate that this algorithm, running on a standard desktop computer and implemented in a high-level programming language, is already faster than the state-of-the-art dedispersion codes running on graphical processing units (GPUs). We also present a variant of the algorithm that can be efficiently implemented on GPUs. The latter algorithm’s computation and data-transport requirements are similar to those of a two-dimensional fast Fourier transform, indicating that incoherent dedispersion can now be considered a nonissue while planning future surveys. We further present a fast algorithm for sensitive detection of pulses shorter than the dispersive smearing limits of incoherent dedispersion. In typical cases, this algorithm is orders of magnitude faster than enumerating dispersion measures and coherently dedispersing by convolution. We analyze the computational complexity of pulsed signal searches by radio interferometers. We conclude that, using our suggested algorithms, maximally sensitive blind searches for dispersed pulses are feasible using existing facilities. We provide an implementation of these algorithms in Python and MATLAB. [ABSTRACT FROM AUTHOR]

We study the incommensurate charge ordered states in the model using the Gutzwiller mean field theory on large systems. In particular, we explore the properties of incommensurate charge modulated states referred to as nodal pair density waves (nPDW) in the literature. nPDW states intertwine site and bond charge order with modulated d-wave pair order, and are characterized by a nonzero amplitude of uniform pairing; they also manifest a dominant intra-unit cell d-density wave form factor. To compare with a recent scanning tunneling microscopy (STM) study (Hamidian et al 2015 Nat. Phys.12 150) of the cuprate superconductor BSCCO-2212, we compute the continuum local density of states (LDOS) at a typical STM tip height using the Wannier function based approach. By Fourier transforming Cu and O sub-lattice LDOS we also obtain bias-dependent intra-unit cell form factors and spatial phase difference. We find that in the nPDW state the behavior of form factors and spatial phase difference as a function of energy agrees remarkably well with the experiment.This is in contrast to commensurate charge modulated states, which we show do not agree with experiment. We propose that the nPDW states are good candidates for the charge density wave phase observed in the superconducting state of underdoped cuprates. [ABSTRACT FROM AUTHOR]