Locating Image Sources from Multiple Spatial Room Impulse Responses

Measured spatial room impulse responses have been used to compare acoustic spaces. One way to analyze and render such responses is to apply parametric methods, yet those methods have been bound to single measurement locations. This paper introduces a method that locates image sources from spatial room impulse responses measured at multiple source and receiver positions. The method aligns the measurements to a common coordinate frame and groups stable direction-of-arrival estimates to find image source positions. The performance of the method is validated with three case studies—one small room and two concert halls. The studies show that the method is able to locate the most prominent image sources even in complex spaces, providing new insights into available Spatial Room Impulse Response (SRIR) data and a starting point for six degrees of freedom (6DoF) acoustic rendering.

LOWER BOUNDS ALONG STABLE MANIFOLDS

It is well known that along any stable manifold the dynamics travels with an exponential rate. Moreover, this rate is close to the slowest exponential rate along the stable direction of the linearization, provided that the nonlinear part is sufficiently small. In this note, we show that whenever there is also a fastest finite exponential rate along the stable direction of the linearization, similarly we can establish a lower bound for the speed of the nonlinear dynamics along the stable manifold. We consider both cases of discrete and continuous time, as well as a nonuniform exponential behaviour.

Magnetic control of continuum devices

In this paper we apply Cosserat rod theory to catheters with permanent magnetic components that are subject to spatially varying magnetic fields. The resulting model formulation captures the magnetically coupled catheter behavior and provides numerical solutions for rod equilibrium configurations in real-time. The model is general, covering cases with different catheter geometries, multiple magnetic components, and various boundary constraints. The necessary Jacobians for quasi-static, closed-loop control using an electromagnetic coil system and a motorized advancer are derived and incorporated into a visual-feedback controller. We address the issue of solution bifurcations caused by the magnetic field by proposing an additional, stabilizing control method that makes use of system redundancies. We demonstrate the effectiveness of the model by performing 3D tip-position trajectories with root-mean-square distance errors of 2.7 mm in open-loop, 0.30 mm in closed-loop, and 0.42 mm in stabilizing closed-loop modes. The stabilizing controller achieved on average a factor of 1.6 increase in the restoring wrenches for the least stable direction.

Initiation and directional control of period-1 rotation for a parametric pendulum

We study a time-delayed feedback control for initiating period-1 rotations of a vertically excited parametric pendulum from arbitrary initial conditions. The possibility of controlling the direction of rotation has also been explored. We start with a simple linear time-delayed control for which the control gain corresponding to the most stable period-1 rotation has been obtained using the Floquet theory. This control increases the basins of attraction of rotations, but they do not encompass the full initial condition space. We modify our control law by using a switched control gain that destabilizes all the oscillatory solutions, and the entire initial condition space becomes the basin of attraction of either the clockwise or the anticlockwise rotation. By a suitable modification of the switching condition, we can choose a preferential stable direction of rotation. Hence, we can initiate either clockwise or anticlockwise rotation for a parametric pendulum from arbitrary initial conditions. Performance of our controller in achieving this objective has been demonstrated for different sets of parameters to establish its effectiveness.

Flexible periodic points

We define the notion of ${\it\varepsilon}$-flexible periodic point: it is a periodic point with stable index equal to two whose dynamics restricted to the stable direction admits ${\it\varepsilon}$-perturbations both to a homothety and a saddle having an eigenvalue equal to one. We show that an ${\it\varepsilon}$-perturbation to an ${\it\varepsilon}$-flexible point allows us to change it to a stable index one periodic point whose (one-dimensional) stable manifold is an arbitrarily chosen $C^{1}$-curve. We also show that the existence of flexible points is a general phenomenon among systems with a robustly non-hyperbolic two-dimensional center-stable bundle.

Singularities of the susceptibility of a Sinai–Ruelle–Bowen measure in the presence of stable–unstable tangencies

Let ρ be a Sinai–Ruelle–Bowen (SRB or ‘physical’) measure for the discrete time evolution given by a map f , and let ρ ( A ) denote the expectation value of a smooth function A . If f depends on a parameter, the derivative δρ ( A ) of ρ ( A ) with respect to the parameter is formally given by the value of the so-called susceptibility function Ψ ( z ) at z =1. When f is a uniformly hyperbolic diffeomorphism, it has been proved that the power series Ψ ( z ) has a radius of convergence r ( Ψ )>1, and that δρ ( A )= Ψ (1), but it is known that r ( Ψ )<1 in some other cases. One reason why f may fail to be uniformly hyperbolic is if there are tangencies between the stable and unstable manifolds for ( f , ρ ). The present paper gives a crude, non-rigorous, analysis of this situation in terms of the Hausdorff dimension d of ρ in the stable direction. We find that the tangencies produce singularities of Ψ ( z ) for | z |<1 if d <1/2, but only for | z |>1 if d >1/2. In particular, if d >1/2, we may hope that Ψ (1) makes sense, and the derivative δρ ( A )= Ψ (1) thus has a chance to be defined.

STOCHASTIC STABILITY OF NON-UNIFORMLY HYPERBOLIC DIFFEOMORPHISMS

We prove that the statistical properties of random perturbations of a diffeomorphism with dominated splitting having mostly contracting center-stable direction and non-uniformly expanding center-unstable direction are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic stability of such dynamical systems. We show that a certain C2-open class of non-uniformly hyperbolic diffeomorphisms introduced by Alves, Bonatti and Viana in [2] are stochastically stable.