Maria Cameron
Fast and accurate simulation of dynamical systems is a fundamental challenge across scientific and engineering domains. Traditional numerical integrators often face a trade-off between accuracy and computational efficiency, while existing…
As the need for higher performance from biological and electronic sensors continues to outpace current technologies, new strategies for designing, developing, and implementing novel sensor systems are emerging. A recently introduced…
Hydrocarbon pyrolysis is a complex chemical reaction system at extreme temperature and pressure conditions involving large numbers of chemical reactions and chemical species. Only two kinds of atoms are involved: carbons and hydrogens. Its…
In addition to translational and rotational symmetries, clusters of identical interacting particles possess permutational symmetry. Coarse-grained models for such systems are instrumental in identifying metastable states, providing an…
We obtain asymptotically sharp error estimates for the consistency error of the Target Measure Diffusion map (TMDmap) (Banisch et al. 2020), a variant of diffusion maps featuring importance sampling and hence allowing input data drawn from…
Many processes in nature such as conformal changes in biomolecules and clusters of interacting particles, genetic switches, mechanical or electromechanical oscillators with added noise, and many others are modeled using stochastic…
An experimental arrangement and a set of experiments are developed to generate empirical evidence of the effect of noise on a rotating, macro-scale cantilever structure. The experiment is a controlled representation of a rotating machinery…
The dynamics of mechanical systems such as turbomachinery with multiple blades are often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibrational modes, and…
Hydrocarbon pyrolysis is a complex process involving large numbers of chemical species and types of chemical reactions. Its quantitative description is important for planetary sciences, in particular, for understanding the processes…
We present a new algorithm, the efficient jet marching method (EJM), for computing the quasipotential and its gradient for two-dimensional SDEs. The quasipotential is a potential-like function for nongradient SDEs that gives asymptotic…
The study of noise-driven transitions occurring rarely on the time-scale of systems modeled by SDEs is of crucial importance for understanding such phenomena as genetic switches in living organisms and magnetization switches of the Earth.…
Nongradient stochastic differential equations (SDEs) with position-dependent and anisotropic diffusion are often used in biological modeling. The quasi-potential is a crucial function in the Large Deviation Theory that allows one to…
The quasi-potential is a key function in the Large Deviation Theory. It characterizes the difficulty of the escape from the neighborhood of an attractor of a stochastic non-gradient dynamical system due to the influence of small white…
We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size $N$ onto stochastic networks, computing transition probabilities…
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…
We consider stochastic networks with pairwise transition rates of the exponential form where the temperature T is a small parameter. Such networks arise in physics and chemistry and serve as mathematically tractable models of complex…
A set of analytical and computational tools based on transition path theory (TPT) is proposed to analyze flows in complex networks. Specifically, TPT is used to study the statistical properties of the reactive trajectories by which…