Related papers: A Dynamic Theory-Based Method for the Computation …
Entropy production (EP) is a central measure in nonequilibrium thermodynamics, as it can quantify the irreversibility of a process as well as its energy dissipation in special cases. Using the time-reversal asymmetry in a system's path…
A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless…
This paper addresses the synthesis of interval observers for partially unknown nonlinear systems subject to bounded noise, aiming to simultaneously estimate system states and learn a model of the unknown dynamics. Our approach leverages…
Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and its many different families of unstable periodic orbits…
This paper develops the high-order entropy stable (ES) finite difference schemes for multi-dimensional compressible Euler equations with the van der Waals equation of state (EOS) on adaptive moving meshes. Semi-discrete schemes are first…
Non-equilibrium thermodynamics provides a general framework for understanding non-equilibrium processes, particularly in small systems that are typically far from equilibrium and dominated by fluctuations. However, the experimental…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as discretization. The error estimator…
Nonlinear state estimation (SE), with the goal of estimating complex bus voltages based on all types of measurements available in the power system, is usually solved using the iterative Gauss-Newton method. The nonlinear SE presents some…
A pendulum prepared perfectly inverted and motionless is a prototype of unstable equilibria and corresponds to an unstable hyperbolic fixed point in the dynamical phase space. Unstable fixed points are central to understanding Hamiltonian…
Text embeddings are essential components in modern NLP pipelines. Although numerous embedding models have been proposed, no single model consistently dominates across domains and tasks. This variability motivates the use of ensemble…
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
We present a new empirical pseudopotential (EPM) calculation approach to simulate the million atom nanostructured semiconductor devices under potential bias using the periodic boundary conditions. To treat the non-equilibrium condition,…
An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The…
In this paper, we present an open-source, automated, and multi-faceted computational-statistical platform to obtain synthetic homogeneous isotropic turbulent flow and passive scalar transport. A parallel implementation of the well-known…
We describe computational tools that have been developed to simulate dynamical mass transfer in semi-detached, polytropic binaries that are initially executing synchronous rotation upon circular orbits. Initial equilibrium models are…
We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an…