Related papers: On Gaussian Beams Described by Jacobi's Equation
A continuous-time white Gaussian channel can be formulated using a white Gaussian noise, and a conventional way for examining such a channel is the sampling approach based on the Shannon-Nyquist sampling theorem, where the original…
The 'vertical modes and horizontal rays' method, commonly applied for simulating acoustic wave propagation in shallow water is advanced in this research. Our approach to this method involves the use of the so-called space-time rays, which…
We introduce a new class of optical beams, which feature a spatial profile akin to an ``inverted pin''. In particular, we asymptotically find that close to the axis the transverse amplitude profile of such beams takes the form of a Bessel…
The parameter space for continuous gravitational waves (GWs) can be divided into amplitude parameters (signal amplitude, inclination and polarization angles describing the orientation of the source, and an initial phase) and phase-evolution…
During the Gaussian Splatting optimization process, the scene's geometry can gradually deteriorate if its structure is not deliberately preserved, especially in non-textured regions such as walls, ceilings, and furniture surfaces. This…
"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the…
We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…
Quantum Gaussian channels are fundamental models for communication and information processing in continuous-variable quantum systems. This work addresses both foundational aspects and physical implementation pathways for these channels.…
This work focuses on the interaction of an acoustical quasi-Gaussian beam centered on a rigid immovable sphere, during which at least three physical phenomena arise, namely, the (axial) acoustic scattering, the instantaneous force, and the…
A sharp bending scheme for the self-collimation of acoustic waves is proposed by simply truncating the sonic crystals. An all-angle and wide-band 90{\deg}-bending wave guide is demonstrated with nearly perfect transmissions for Gaussian…
An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It differs significantly from the equations proposed by Szabo. Dispersion and attenuation associated with the…
We survey the state of the art for the proof of the quantum Gaussian optimizer conjectures of quantum information theory. These fundamental conjectures state that quantum Gaussian input states are the solution to several optimization…
We show that introducing an exponential cut-off on a suitable Sobolev norm facilitates the proof of quasi-invariance of Gaussian measures with respect to Hamiltonian PDE flows and allows us to establish the exact Jacobi formula for the…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
We investigate the broadband turbulent dynamics of attached and separated flows over a Gaussian bump, focusing on the origin of low-frequency coherent structures. The analysis combines time-resolved experimental measurements with…
We compare two sets of multimode quantum channels acting on a finite collection of harmonic oscillators: (a) the set of linear bosonic channels, whose action is described as a linear transformation at the phase space level; and (b) Gaussian…
The Gaussian curvature $K$ is a fundamental geometric quantity discovered by Gauss in the case of surfaces embedded in $\mathbb{R}^3$. One can naturally extend the definition of the Gaussian curvature to arbitrary submanifolds of…
A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the…
The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct metric spaces. They are particularly useful in areas such as…
General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws…