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The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic…
A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting "boundary" and "interior" subsystems. This view is…
Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of this class of problems is the…
The attachment-line boundary layer is critical in hypersonic flows because of its significant impact on heat transfer and aerodynamic performance. In this study, high-fidelity numerical simulations are conducted to analyze the subcritical…
We present a generative modeling framework for synthesizing physically feasible two-dimensional incompressible flows under arbitrary obstacle geometries and boundary conditions. Whereas existing diffusion-based flow generators either ignore…
Optimality Theory is a constraint-based theory of phonology which allows constraints to be violated. Consequently, implementing the theory presents problems for declarative constraint-based processing frameworks. On the basis of two…
Laminar-turbulent transition in shock wave-boundary-layer interactions (SWBLI) remains a major challenge for hypersonic vehicle design, with implications for drag, heat transfer, and structural loads. Linear optimal perturbation analyses…
We study the transition to turbulence in a flat plate boundary layer by means of visibility analysis of velocity time-series extracted across the flow domain. By taking into account the mutual visibility of sampled values, visibility graphs…
This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…
In Kalman filtering, unknown inputs are often estimated by augmenting the state vector, which introduces reliance on fictitious input models. In contrast, minimum-variance unbiased methods estimate inputs and states separately, avoiding…
We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and…
Sensory observations about the world are invariably ambiguous. Inference about the world's latent variables is thus an important computation for the brain. However, computational constraints limit the performance of these computations.…
Stacked cross-correlation functions have become ubiquitous in the ambient seismic imaging and monitoring community as approximations to the Green's function between two receivers. While theoretical understanding of this approximation to the…
In this paper we present a framework for investigating coloured noise in reaction-diffusion systems. We start by considering a deterministic reaction-diffusion equation and show how external forcing can cause temporally correlated or…
Accurate prediction of mixing transition induced by interfacial instabilities is vital for engineering applications, but has remained a great challenge for decades. For engineering practices, Reynolds-averaged Navier-Stokes simulation…
The laminar-to-turbulent transition remains a fundamental and enduring challenge in fluid mechanics. Its complexity arises from the intrinsic nonlinearity and extreme sensitivity to external disturbances. This transition is critical in a…
Motivated by risk assessment of coastal flooding, we consider time-consuming simulators with a spatial output. The aim is to perform sensitivity analysis (SA), quantifying the influence of input parameters on the output. There are three…
We study the mixing processes inside a forced fountain using data from direct numerical simulation. The outer boundary of the fountain with the ambient is a turbulent/non-turbulent interface. Inside the fountain, two internal boundaries,…
The transient growth of disturbances made possible by the non-normality of the linearized Navier-Stokes equations plays an important role in bypass transition for many shear flows. Transient growth is typically quantified by the maximum…
Statistical mechanics is used to study unrealizable generalization in two large feed-forward neural networks with binary weights and output, a perceptron and a tree committee machine. The student is trained by a teacher being larger, i.e.…