Related papers: Mapping dynamical systems into chemical reactions
In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the…
This paper analyses the behaviour of a second order DPCM (Differential Pulse Code Modulation) transmission system when the nonlinear characteristic of the quantizer is taken into consideration. In this way, qualitatively new properties of…
In this paper we study the control co-design (CCD) synthesis problem for a class of systems with parabolic partial differential equation (PDE) dynamics. We formulate CCD problem and finally derive an approximate CCD problem with matrix…
Causal dynamics models (CDMs) have demonstrated significant potential in addressing various challenges in reinforcement learning. To learn CDMs, recent studies have performed causal discovery to capture the causal dependencies among…
This paper reports on the state-of-the-art in application of multidimensional scaling (MDS) techniques to create semantic maps in linguistic research. MDS refers to a statistical technique that represents objects (lexical items, linguistic…
We investigate the emergence of chimera and cluster states possessing asymmetric dynamics in globally coupled systems, where the trajectories of oscillators belonging to different subpopulations exhibit different dynamical properties. In an…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
We present QDK/Chemistry, a software toolkit for quantum chemistry workflows targeting quantum computers. The toolkit addresses a key challenge in the field: while quantum algorithms for chemistry have matured considerably, the…
Basic problems of the semiclassical microscopic modelling of strongly interactingsystems are discussed within the framework of Quantum Molecular Dynamics (QMD). This model allows to study the influence of several types of nucleonic…
In this paper, we consider the quasi-gas-dynamic (QGD) model in a multiscale environment. The model equations can be regarded as a hyperbolic regularization and are derived from kinetic equations. So far, the research on QGD models has been…
In the theory of open quantum systems, divisibility of the system dynamical maps is related to memory effects in the dynamics. By decomposing the system Hilbert space as a direct sum of several Hilbert spaces, we study the relationship…
The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for…
Chemical plants are complex and dynamical systems consisting of many components for manipulation and sensing, whose state transitions depend on various factors such as time, disturbance, and operation procedures. For the purpose of…
Quantitative susceptibility mapping (QSM) has gained broad interests in the field by extracting biological tissue properties, predominantly myelin, iron and calcium from magnetic resonance imaging (MRI) phase measurements in vivo. Thereby,…
Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments. For combustion, the number of reactions can be significant (over 100) and due to…
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…
We present the first quantum-centric simulations of noncovalent interactions using a supramolecular approach. We simulate the potential energy surfaces (PES) of the water and methane dimers, featuring hydrophilic and hydrophobic…
This chapter gives a self-contained review of the how standard open quantum system Hamiltonians can be mapped analytically onto representations in which the environments appear as one dimensional harmonic chains with nearest neighbour…
Equations of motion that recognize biochemical patterns are described. The equations are partial differential equations in a continuous multiple component system in which adequate initial and boundary conditions are given. The biochemical…
Long lived quasi-stationary states (QSSs) are a signature characteristic of long-range interacting systems both in the classical and in the quantum realms. Often, they emerge after a sudden quench of the Hamiltonian internal parameters and…