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A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…
Peculiar velocities are analyzed through cosmological perturbations in the Newtonian longitudinal gauge characterized by irrotational shear-free congruences in an Eulerian frame. We show that non-trivial peculiar velocity fields can be…
In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…
Shearlets are a relatively new directional multi-scale framework for signal analysis, which have been shown effective to enhance signal discontinuities such as edges and corners at multiple scales. In this work we address the problem of…
This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The…
Shear flows are ubiquitously present in space and astrophysical plasmas. This paper highlights the central idea of the non-thermal acceleration of charged particles in shearing flows and reviews some of the recent developments. Topics…
A second derivative-based moment method is proposed for describing the thickness and shape of the region where viscous forces are dominant in turbulent boundary layer flows. Rather than the fixed location sublayer model presently employed,…
Machining processes are most accurately described using complex dynamical systems that include nonlinearities, time delays, and stochastic effects. Due to the nature of these models as well as the practical challenges which include…
Forced advection of passive tracer, $\theta $, in nonlinear relaxational medium by large scale (Batchelor problem) incompressible velocity field at scales less than the correlation length of the flow and larger than the diffusion scale is…
This article describes two independent developments aimed at improving the Particle Tracking Method for measurements of flow or particle velocities. First, a stereoscopic multicamera calibration method that does not require any optical…
Scene flow depicts the dynamics of a 3D scene, which is critical for various applications such as autonomous driving, robot navigation, AR/VR, etc. Conventionally, scene flow is estimated from dense/regular RGB video frames. With the…
This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale observations on the flow field. A relaxation-based approach is…
Scene flow estimation, which extracts point-wise motion between scenes, is becoming a crucial task in many computer vision tasks. However, all of the existing estimation methods utilize only the unidirectional features, restricting the…
Viscous and gravitational flow instabilities cause a displacement front to break up into finger-like fluids. The detection and evolutionary analysis of these fingering instabilities are critical in multiple scientific disciplines such as…
We consider strongly-convex-strongly-concave saddle point problems assuming we have access to unbiased stochastic estimates of the gradients. We propose a stochastic accelerated primal-dual (SAPD) algorithm and show that SAPD sequence,…
This paper investigates the nature of the development of vortex shedding for two-dimensional unsteady flow of an incompressible fluid at the rear stagnation point.
A two-dimensional inviscid incompressible fluid is governed by simple rules. Yet, to characterise its long-time behaviour is a knotty problem. The fluid evolves according to Euler's equations: a non-linear Hamiltonian system with infinitely…
In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term of the form $\alpha/t$. For positive values of $\alpha$,…
This study develops a comprehensive description of local streamline geometry and uses the resulting shape features to characterize velocity gradient ($A_{ij}$) dynamics. The local streamline geometric shape parameters and scale-factor…
We introduce a new technique to visualize complex flowing phenomena by using concepts from shape analysis. Our approach uses techniques that examine the intrinsic geometry of manifolds through their heat kernel, to obtain representations of…