相关论文: Differential Geometry applied to Acoustics : Non L…

"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 survey the close relationship between sound and light rays and geometry. In the case where the medium is at rest, the geometry is the classical geometry of Riemann. In the case where the medium is moving, the more general geometry known…

This study aims to make use of two concepts in the field of aeroacoustics; an analogy with relativity, and Geometric Algebra. The analogy with relativity has been investigated in physics and cosmology, but less has been done to use this…

Room acoustics is commonly regarded and studied as an applied subdiscipline of engineering acoustics. It is likely for this reason that many textbooks and lecture notes on the topic provide a too brief, unsystematic, and incomplete physical…

We consider acoustic propagation in an irrotational vortex, using the technical machinery of differential geometry to investigate the ``acoustic geometry'' that is probed by the sound waves. The acoustic space-time curvature of a constant…

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…

Caustic formation occurs within a ray skeleton as optical or acoustic fields propagate in a medium with variable refractive properties and are unphysical, their presence being an artifact of the ray approximation of the field, and methods…

Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…

We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.

Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field…

We discuss certain aspects of the combinatorial approach to the differential geometry of non-abelian gerbes, due to W. Messing and the author (arXiv:math.AG/0106083), and give a more direct derivation of the associated cocycle equations.…

Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent geometric model for music perception in order to rationalize, explain and predict psycho-acoustic phenomena. The space of…

Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…

We introduce an alternative formalization of curved spaces in which the concept of a pointwise affine space, as defined here, replaces that of a manifold. New or modified definitions of familiar notions from differential geometry such as…

Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…

Many physically important mechanical systems may be described with a Lie group $G$ as configuration space. According to the well-known Noether's theorem, underlying symmetries of the Lie group may be used to considerably reduce the…

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field.…

Geometric acoustics is an efficient framework for room acoustics modeling, governed by the canonical time-dependent rendering equation. Acoustic radiance transfer (ART) solves the equation by discretization, modeling time- and…

We reanalyze the problem of existence of longitudinal normals inside symmetry planes of piezoelectric crystals belonging to the symmetry class mm2. The equations determining components of longitudinal normals situated outside symmetry…