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In a system with one conserved charge the charge diffusion is modified by non-linear self-interactions within an effective field theory (EFT) of diffusive fluctuations. We include the slowest ultraviolet (UV) mode, constructing a…
A function has been proposed to evaluate the electron density model constructed by inverse Fourier transform using the observed structure amplitudes and trial phase set. The strategy of this function is applying an imaginary electron…
In capillary electrophoresis, sample ions migrate along a micro-capillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity…
We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel…
We study a reduced hydrodynamic formulation of paraxial vector beam propagation in which the beam intensity, optical phase, and spatially-dependent polarization are coupled through a nonlinear dispersive system. While prior analytical work…
The diffraction pattern of a single non-periodic compact object, such as a molecule, is continuous and is proportional to the square modulus of the Fourier transform of that object. When arrayed in a crystal, the coherent sum of the…
Flame Propagation is used as a prototypical example of expanding fronts that wrinkle without limit in radial geometries but reach a simple shape in channel geometry. We show that the relevant scaling laws that govern the radial growth can…
We address a numerical instability that arises in the directionally split computation of hydrodynamic flows when shock fronts are parallel to a grid plane. Transverse oscillations in pressure, density and temperature are produced that are…
Convolution neural networks have achieved remarkable performance in many tasks of computing vision. However, CNN tends to bias to low frequency components. They prioritize capturing low frequency patterns which lead them fail when suffering…
We derive a formula for the non-coherent wave field propagation in terms of the Fourier transformation. As a result, we find a theoretical solution of the inverse problem of image propagation in non-coherent case. However, the practical…
This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a…
A K-mirror rotates the wavefront of an incident optical field. However, the rotation always introduces polarization changes in the transmitted field. This is a serious concern for applications ranging from astronomical image derotation to…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
We propose an optimized optical vector network analyzer with automatic polarization control to stabilize the reference arm polarization throughout the sweep range. We demonstrate this technique, successfully removing the…
Process of the nonlinear deformation of the shallow water wave in a basin of constant depth is studied. The characteristics of the first breaking are analyzed in details. The Fourier spectrum and steepness of the nonlinear wave is…
We show how spatial dispersion can be used as a mechanism to customize the longitudinal profiles of electric fields inside modulated wire media, using a fast and remarkably accurate 1D inhomogeneous model. This customization gives fine…
The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles, as in a Free Electron Laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article,…
Mean-variance portfolio decisions that combine prediction and optimisation have been shown to have poor empirical performance. Here, we consider the performance of various shrinkage methods by their efficient frontiers under different…
Recent experimental studies indicate that visual cognition is accompanied by slowly propagating biophysical travelling waves in cortical tissue. Here we propose polarization waves as a coherent physical framework for visual cognition. We…
In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability…