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We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the…
The bistable states and separation hysteresis in curved compression ramp (CCR) flows, and the corresponding aerothermal characteristics (including wall friction, pressure and heat flux), are studied numerically and theoretically. Direct…
We use a hydrodynamic model to study the space-time evolution transverse to the beam direction in ultrarelativistic heavy-ion collisions with nonzero impact parameters. We focus on the influence of early pressure on the development of…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
In this paper, we analyze the robustness of the PSO-based approach to parameter estimation of robot dynamics presented in Part One. We have made attempts to make the PSO method more robust by experimenting with potential cost functions. The…
We consider the problem of analyzing the probabilistic performance of first-order methods when solving convex optimization problems drawn from an unknown distribution only accessible through samples. By combining performance estimation…
Mirroring their role in electrical and optical physics, two-dimensional crystals are emerging as novel platforms for fluid separations and water desalination, which are hydrodynamic processes that occur in nanoscale environments. For…
Collisionless plasma shocks are efficient sources of non-thermal particle acceleration in space and astrophysical systems. We use hybrid (kinetic ions -- fluid electrons) simulations to examine the non-linear feedback of the self-generated…
In this work, an adaptive predictive control scheme for linear systems with unknown parameters and bounded additive disturbances is proposed. In contrast to related adaptive control approaches that robustly consider the parametric…
We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the…
The goal of this note is to provide a theoretical explanation for the saturation of the drag coefficient in strong wind conditions. The hydrodynamic model under consideration takes into account the important effects of airborne droplets of…
We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the dependent response is also (potentially) a…
Simulations with an adaptive time-dependent bias, such as metadynamics, enable an efficient exploration of the conformational space of a system. However, the dynamic information of the system is altered by the bias. With infrequent…
Molecular dynamics simulations yield large amounts of trajectory data. For their durable storage and accessibility an efficient compression algorithm is paramount. State of the art domain-specific algorithms combine quantization, Huffman…
We explore the possibility that a single relativistic shock, where the gas dynamics is coupled with radiation, can fit the light curves of long GRBs. For this we numerically solve the one dimensional relativistic radiation hydrodynamics…
The shock formation process in shock tubes has been extensively studied; however, significant gaps remain in understanding the effects of the diaphragm rupture process on the resulting flow non-uniformities. Existing models predicting the…
The histogram reweighting technique, widely used to analyze Monte Carlo data, is shown to be applicable to dynamic properties obtained from Molecular Dynamics simulations. The theory presented here is based on the fact that the correlation…
With the growing number of wind farms over the last decades and the availability of large datasets, research in wind-farm flow modeling - one of the key components in optimizing the design and operation of wind farms - is shifting towards…