816,243 research outputs found
Automating the determination of wave speed using the pu-loop method
The PU-loop (pressure-velocity loop) is a method for determining wave speed and relies on the linear relationship between the pressure and velocity in the absence of reflected waves. This linearity of the PU-loop during early systole, which is directly related to wave speed, has always been established by eye. This paper presents a new technique that establishes this linearity and thus determining wave speed online. Pressure and flow were measured in the ascending aorta of 11 anesthetised dogs. The slope of the PU-loop, indicating wave speed was determined by eye and by using the new technique. The difference between the slopes of the two methods is in the order of 3%. The new technique is convenient and allows for the online assessment of wave speed, which could be used as a bedside tool for the assessment of arterial compliance
Inverse obstacle problem for the non-stationary wave equation with an unknown background
We consider boundary measurements for the wave equation on a bounded domain
or on a compact Riemannian surface, and introduce a method to
locate a discontinuity in the wave speed. Assuming that the wave speed consist
of an inclusion in a known smooth background, the method can determine the
distance from any boundary point to the inclusion. In the case of a known
constant background wave speed, the method reconstructs a set contained in the
convex hull of the inclusion and containing the inclusion. Even if the
background wave speed is unknown, the method can reconstruct the distance from
each boundary point to the inclusion assuming that the Riemannian metric tensor
determined by the wave speed gives simple geometry in . The method is based
on reconstruction of volumes of domains of influence by solving a sequence of
linear equations. For \tau \in C(\p M) the domain of influence is
the set of those points on the manifold from which the distance to some
boundary point is less than .Comment: 4 figure
Propagation of Delayed Lattice Differential Equations without Local Quasimonotonicity
This paper is concerned with the traveling wave solutions and asymptotic
spreading of delayed lattice differential equations without quasimonotonicity.
The spreading speed is obtained by constructing auxiliary equations and using
the theory of lattice differential equations without time delay. The minimal
wave speed of invasion traveling wave solutions is established by presenting
the existence and nonexistence of traveling wave solutions
Sensitivity of helioseismic travel-times to the imposition of a Lorentz force limiter in computational helioseismology
The rapid exponential increase in the Alfv\'en wave speed with height above
the solar surface presents a serious challenge to physical modelling of the
effects of magnetic fields on solar oscillations, as it introduces a
significant CFL time-step constraint for explicit numerical codes. A common
approach adopted in computational helioseismology, where long simulations in
excess of 10 hours (hundreds of wave periods) are often required, is to cap the
Alfv\'en wave speed by artificially modifying the momentum equation when the
ratio between Lorentz and hydrodynamic forces becomes too large. However,
recent studies have demonstrated that the Alfv\'en wave speed plays a critical
role in the MHD mode conversion process, particularly in determining the
reflection height of the upward propagating helioseismic fast wave. Using
numerical simulations of helioseismic wave propagation in constant inclined
(relative to the vertical) magnetic fields we demonstrate that the imposition
of such artificial limiters significantly affects time-distance travel times
unless the Alfv\'en wave-speed cap is chosen comfortably in excess of the
horizontal phase speeds under investigation.Comment: 8 pages, 5 figures, accepted by ApJ
Regularization strategy for inverse problem for 1+1 dimensional wave equation
An inverse boundary value problem for a 1+1 dimensional wave equation with
wave speed is considered. We give a regularisation strategy for
inverting the map where is the
hyperbolic Neumann-to-Dirichlet map corresponding to the wave speed . More
precisely, we consider the case when we are given a perturbation of the
Neumann-to-Dirichlet map , where corresponds to the measurement errors, and reconstruct an approximate wave
speed . We emphasize that may not not be in the
range of the map . We show that the reconstructed wave speed
satisfies . Our
regularization strategy is based on a new formula to compute from
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