Related papers: Quadratic first integrals of constrained autonomou…
In this work, we investigate a skew-symmetric parameterization for energy-preserving quadratic operators. Earlier, [Goyal et al., 2023] proposed this parameterization to enforce energy-preservation for quadratic terms in the context of…
We study cooperative control dynamics with gradient based forcing terms. As a specific example, we focus on source-seeking dynamics with vehicles embedded in an unknown scalar field with a subset of agents having gradient information. As…
The autonomous Duffing oscillator, and its van der Pol modification, are known to admit time-dependent first integrals for specific values of parameters. This corresponds to the existence of Darboux polynomials, and in fact more can be…
Two-dimensional Hamiltonian systems admitting second invariants which are quartic in the momenta are investigated using the Jacobi geometrization of the dynamics. This approach allows for a unified treatment of invariants at both arbitrary…
Achieving optimal steady-state performance in real-time is an increasingly necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for…
Inspired by thermodynamic integration, we propose a method for the calculation of time-independent free energy profiles from history-dependent biased simulations via Mean Force Integration (MFI). MFI circumvents the need for computing the…
Real-time time-dependent density functional theory (TDDFT) is widely considered to be the most accurate available method for calculating electronic stopping powers from first principles, but there have been relatively few assessments of the…
We derive from first principles (without resorting to the replica trick) a density functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the…
We analyze the performance of source-seeking dynamics involving either a single vehicle or multiple flocking-vehicles embedded in an underlying strongly convex scalar field with gradient based forcing terms. For multiple vehicles under…
We develop a rigorous error analysis for coarse-graining of defect-formation free energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the…
Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the…
We construct an effective Quantum Field Theory for the wrapping effects in 1+1 dimensional models of factorised scattering. The recently developed graph-theoretical approach to TBA gives the perturbative desctiption of this QFT. For the…
This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove that for one spatial dimension, various one-step time integrators from the…
We discuss ways that the ring of coefficients for a TQFT can be reduced if one restricts somewhat the allowed cobordisms. When we apply these methods to a TQFT associated to SO(3) at an odd prime p, we obtain a functor from a somewhat…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering amplitudes when there is a separation of scale in a given set of…
The QED(0+1) model describing a quantum mechanical particle on a circle with minimal electromagnetic interaction and with a potential -M cos(phi - theta_M), which mimics the massive Schwinger model, is discussed as a prototype of mechanisms…
We proposed a piecewise quadratic reconstruction method in multiple dimensions, which is in an integrated style, for finite volume schemes to scalar conservation laws. This integrated quadratic reconstruction is parameter-free and…
We study the mode dynamics of a generic quadratic fermionic Hamiltonian under a sudden quench protocol in momentum space. Modes with zero energy at any given time, $t$, are referred to as dynamical critical modes. Among all zero-energy…
As one approaches the continuum limit, $QCD$ systems, investigated via numerical simulations, remain trapped in sectors of field space with fixed topological charge. As a consequence the numerical studies of physical quantities may give…