Related papers: Mapping dynamical systems into chemical reactions
Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded…
The study of the phase space of multidimensional systems is one of the central open problems in dynamical systems. Being able to distinguish chaoticity from regularity in nonlinear dynamical systems, as well as to determine the subspace of…
The paper presents amended basic map of states of chemical systems in discrete thermodynamics of chemical equilibria. Uniting two previously found basic map types in one and covering a wider range of situations, it allows us to obtain more…
In alloy thermodynamics, stochastically disordered state (SDS), where each lattice point is stochastically occupied by constituents according to given composition, is typically referred to investigating physical properties for homogeneously…
The paper presents new thermodynamic paradigm of chemical equilibrium, setting forth comprehensive basics of Discrete Thermodynamics of Chemical Equilibria (DTd). Along with previous results by the author during the last decade, this work…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
Suggestion of modifications of finite-dimensional QED models are proposed for interpreting chemical reactions in terms of artificial atoms and molecules on quantum dots placed in optical cavities. Moving both photons and atoms is possible…
Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks…
A collision model (CM) is a framework to describe open quantum dynamics. In its {\it memoryless} version, it models the reservoir $\mathcal R$ as consisting of a large collection of elementary ancillas: the dynamics of the open system…
The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully…
The chemistry of an astrophysical environment is closely coupled to its dynamics, the latter often found to be complex. Hence, to properly model these environments a 3D context is necessary. However, solving chemical kinetics within a 3D…
We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
Encoding time-series with Linear Dynamical Systems (LDSs) leads to rich models with applications ranging from dynamical texture recognition to video segmentation to name a few. In this paper, we propose to represent LDSs with…
Quantum dynamics simulations (QDSs) are one of the most highly anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation algorithms is commonly time dependent so that long time dynamics…
Computational feasibility of turbulent reacting flows hinges on the reduction of large chemical kinetics systems to smaller more manageable reaction sets. Recently, several sophisticated reduction techniques have been developed but they…
Quantum many-body scar (QMBS) in kinetically constrained quantum systems challenges the conventional eigenstate thermalization hypothesis (ETH). We develop an effective open-system description for constrained dynamics and introduce the…
The quasi-steady-state assumption (QSSA) is an approximation that is widely used in chemistry and chemical engineering to simplify reaction mechanisms. The key step in the method requires a solution by radicals of a system of multivariate…
We investigate classes of interacting systems that allow for a mapping to disordered noninteracting systems. As we show, such a mapping is possible for interacting systems with a suppressed density of states at the chemical potential,…