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Eigenvalue analysis is widely used for linear instability analysis in both external and internal aerodynamics. It typically involves finding the steady state, linearizing around it to obtain the Jacobian, and then solving for its…
In this paper, we give a new covariation spectral representation of some non stationary symmetric $\alpha$-stable processes (S$\alpha$S). This representation is based on a weaker covariation pseudo additivity condition which is more general…
We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
The basic strategy underlying models of spontaneous wave function collapse (collapse models) is to modify the Schroedinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
Complex fluids subjected to localized microscopic energy inputs, typical of active microrheology setups, exhibit poorly understood nonequilibrium behaviors because of the intricate self-organization of their mesoscopic constituents. In this…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
The linear hydrodynamic stability of a model for confined quasi-two-dimensional granular gases is analyzed. The system exhibits homogeneous hydrodynamics, i.e. there are macroscopic evolution equations for homogeneous states. The stability…
We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore,…
The electromagnetic field distribution as well as the resonating frequency of various modes in superconducting cavities used in particle accelerators for example are sensitive to small geometry deformations. The occurring variations are…
A computational fluid model is developed to study waves and instabilities. A new technique involving initial perturbations in configuration space have been implemented to excite the plasma waves; i.e. the perturbations acting similar to a…
We present linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles two-way coupled to the fluid velocity field via Stokes drag (Saffman 1962). We extend…
Modal and nonmodal analyses of fluid flows provide fundamental insight into the early stages of transition to turbulence. Eigenvalues of the dynamical generator govern temporal growth or decay of individual modes, while singular values of…
We present a general formulation for stability analyses of radiative shocks with multiple cooling processes, longitudinal and transverse perturbations, and unequal electron and ion temperatures. Using the accretion shocks of magnetic…
In order to analyze numerically inverse problems several techniques based on linear and nonlinear stability analysis are presented. These techniques are illustrated on the problem of estimating mobilities and capillary pressure in…
We propose an iterative method to find pointwise growth exponential growth rates in linear problems posed on essentially one-dimensional domains. Such pointwise growth rates capture pointwise stability and instability in extended systems…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…