The image-source method is widely applied to compute room impulse responses (RIRs) of shoebox rooms with arbitrary damping. However, with increasing RIR lengths, the number of image sources grows rapidly, leading to slow computation. We propose a method to estimate the damping density of a damped shoebox room, which in turn can provide the energy decay necessary to model the stochastic late reverberation. The damping density is derived from a modal decomposition that is compliant with the ISM solution. We show that the proposed method gives a more accurate estimate of the energy decay than previous methods and can be efficiently computed regardless of the RIR lengths. While we focus on the derivation and evaluation, the main practical applications of the proposed model include, e.g., the faster synthesis of late reverb and the analysis of multi-slope decays.

The image-source method is widely applied to compute room impulse responses (RIRs) of shoebox rooms with arbitrary absorption. However, with increasing RIR lengths, the number of image sources grows rapidly, leading to slow computation. In this paper, we derive a closed-form expression for the damping density, which characterizes the overall multi-slope energy decay. The omnidirectional energy decay over time is directly derived from the damping density. The resulting energy decay model accurately matches the late reverberation simulated via the image-source method. The proposed model allows the fast stochastic synthesis of late reverberation by shaping noise with the energy envelope. Simulations of various wall damping coefficients demonstrate the model's accuracy. The proposed model consistently outperforms the energy decay prediction accuracy compared to a state-of-the-art approximation method. The paper elaborates on the proposed damping density's applicability to modeling multi-sloped sound energy decay, predicting reverberation time in non-diffuse sound fields, and fast frequency-dependent RIR synthesis.

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or partial differential equations, using established techniques. Recent work has applied the techniques of machine-learning to construct such models automatically from data for the case of systems which have lumped states described by scalar values, such as electrical circuits. In this work, we examine how similar techniques are able to construct models of systems which have spatially distributed rather than lumped states. We describe several novel recurrent neural network structures, and show how they can be thought of as an extension of modal techniques. As a proof of concept, we generate synthetic data for three physical systems and show that the proposed network structures can be trained with this data to reproduce the behavior of these systems.

Molecular communications is a promising framework for the design of controlled-release drug delivery systems. Under this framework, drug carriers, diseased cells, and the channel in between are modeled as transmitters, absorbing receivers, and diffusive channel, respectively. However, existing works on drug delivery systems consider only simple drug carrier models, which limits their practical applicability. In this paper, we investigate diffusion-based spherical matrix-type drug carriers, which are employed in medical applications. In a matrix carrier, the drug molecules are dispersed in the matrix core and diffuse from the inner to the outer layers of the carrier once immersed in a dissolution medium. We derive the channel response of the matrix carrier transmitter for an absorbing receiver. The results are validated by particle-based simulations and compared with commonly used point and transparent spherical transmitters to highlight the necessity of considering practical models. Moreover, we show that a transparent spherical transmitter, with the drug molecules uniformly distributed over the entire volume, is a special case of the considered matrix system. For this case, we provide an analytical expression for the channel response. Furthermore, we derive a criterion for evaluating whether the release process or the channel dynamics are more important for the overall characteristics of the channel response of a drug delivery system. For the limiting regimes, where only the release process or only the channel determine the behavior of the end-to-end system, we propose closed-form approximations for the channel response. Finally, as a scenario of practical relevance, we investigate the channel responses for the release of common therapeutic drugs, e.g., doxorubicin, from a diblock copolymer micelle acting as drug carrier.

The analysis and design of advection-diffusion based molecular communication (MC) systems in cylindrical environments is of particular interest for applications such as micro-fluidics and targeted drug delivery in blood vessels. Therefore, the accurate modeling of the corresponding MC channel is of high importance. The propagation of particles in these systems is caused by a combination of diffusion and flow with a parabolic velocity profile, i.e., laminar flow. The propagation characteristics of the particles can be categorized into three different regimes: The flow dominant regime where the influence of diffusion on the particle transport is negligible, the dispersive regime where diffusion has a much stronger impact than flow, and the mixed regime where both effects are important. For the limiting regimes, i.e., the flow dominant and dispersive regimes, well-known solutions and approximations for particle transport exist. For the mixed regime, approximations, numerical techniques, and particle based simulations are employed. However, the few analytical models that are applicable in all three regimes impose significant constraints on the possible transmitter locations and particle release profiles. In this paper, we develop a more general analytical model for the advection-diffusion problem in cylindrical environments, which is applicable in all three regimes and accounts for general particle release models. The proposed model exhibits a higher accuracy than existing models and is based on a transfer function approach, where the main challenge is the incorporation of laminar flow. The properties of the proposed model are analyzed by numerical evaluation for different scenarios including the uniform and point release of particles. We provide a comparison with particle based simulations and existing analytical models from the literature to demonstrate the validity of the proposed analytical model.

For the purpose of refined fault detection in DC grids, linear models of components, cabling and possible faults can be applied in order to model the first milliseconds after a possible sudden event. Using a semi-analytical model, a factorial analysis of signals at voltage and current sensors is set up - specific signal patterns representing either fault events or changes between normal operation modes are estimated. With these results, refined fault detection methods avoiding false tripping can be implemented and parametrized.

Physical accuracy of virtual acoustics receives increasing attention due to renewed interest in virtual and augmented reality applications. So far, the modeling of vibrating objects as point sources is a common simplification which neglects effects caused by their spatial extent. In this contribution, we propose a technique for the interconnection of a distributed source to a room model, based on a modal representation of source and room. In particular, we derive a connection matrix that describes the coupling between the modes of the source and the room modes in an analytical form. Therefore, we consider the example of a string that is oscillating in a room. Both, room and string rely on well established physical descriptions that are modeled in terms of transfer functions. The derived connection of string and room defines the coupling between the characteristic string and room modes. The proposed structure is analyzed by numerical evaluations and sound examples on the supplementary website.