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Nonlinear eigenvalue problems arise in a wide range of physical systems, in which system parameters depend on the eigenvalue. Such systems have been proposed to exhibit an extreme sensitivity of their spectra to boundary conditions, which…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
In this paper, we use dynamical systems to analyze stability of desynchronization algorithms at equilibrium. We start by illustrating the equilibrium of a dynamic systems and formalizing force components and time phases. Then, we use Linear…
The dissipative dynamics of two interacting qubits coupled to independent reservoirs at nonzero temperatures is investigated, paying special attention to the entanglement evolution. The counter-rotating terms in the qubit-qubit interaction…
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy…
Flutter stability is a dominant design constraint of modern gas and steam turbines. To further increase the feasible design space, flutter-tolerant designs are currently explored, which may undergo Limit Cycle Oscillations (LCOs) of…
The temperature-dependence of dynamical properties (e.g., the asymptotic diffusion coefficient and the sub-diffusive exponent) are calculated for charges and excitons in one-dimensional systems subject to static and dynamic disorder. These…
We provide an efficient method to approximate the covariance between decision variables and uncertain parameters in solutions to a general class of stochastic nonlinear complementarity problems. We also develop a sensitivity metric to…
Rocket engine combustors are prone to transverse instabilities that are characterized by large amplitude high frequency oscillations in the acoustic pressure and the heat release rate. We study the coupled interaction between the acoustic…
We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…
We present a method to increase the resolution of measurements of a physical system and subsequently predict its time evolution using thermodynamics-aware neural networks. Our method uses adversarial autoencoders, which reduce the…
Nonlinear non-stationary equation describing evolution of weakly curved premixed flames with arbitrary gas expansion, subject to the Landau-Darrieus instability, is derived. The new equation respects all the conservation laws to be…
This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred…
A boundary value problem, which could represent a transcendent temperature conduction problem with evaporation in a part of the boundary, was studied to determine unknown thermophysical parameters, which can be constants or time dependent…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…
In this work, we consider a nonlinear vibrating Timoshenko system with thermoelasticity with second sound. We recall first the results of well-posdness and regularity and the asymptotic behavior of the energy obtained in \cite{Ayadi}. Then,…
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…
The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…
A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures occuring in Taylor-Couette and…