相关论文: Symbolic Computations for Nonlinear Resonances
The aim of this paper is to present a symbolic computational algorithm that will allow us to deal with the feedback stabilization problem for continuous nonlinear polynomial systems. The overall approach is based on a methodology that…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
Though many safety-critical software systems use floating point to represent real-world input and output, programmers usually have idealized versions in mind that compute with real numbers. Significant deviations from the ideal can cause…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
We study a large class of strongly interacting condensate-like materials, which can be characterized by a normalizable complex-valued function. A quantum wave equation with logarithmic nonlinearity is known to describe such systems, at…
By numerical simulation of exact equations of motion (in terms of conformal variables) for planar non-stationary potential flows of an ideal fluid with a free surface over a strongly non-uniform bottom profile, the effect of nonlinear…
Quantum algorithms for computing classical nonlinear maps are widely known for toy problems but might not suit potential applications to realistic physics simulations. Here, we propose how to compute a general differentiable invertible…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
We consider several electronic circuits, which represent dynamical systems with hyperbolic chaotic attractors of Smale-Williams type, and demonstrate results of their simulation using the software package NI Multisim 10. The developed…
Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such…
A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
This paper presents causal block-diagram models to represent the equations of motion of multi-body systems in a very compact and simple closed form. Both the forward dynamics (from the forces and torques imposed at the various…
A nonlinear kinetic equation for nonrelativistic quantum plasma with electromagnetic interaction of particles is obtained in the Hartree's mean-field approximation. It is cast in a convenient form of Vlasov-Boltzmann-type equation with…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…
Models based on non-Hermitian Hamiltonians can exhibit a range of surprising and potentially useful phenomena. Physical realizations typically involve couplings to sources of incoherent gain and loss; this is problematic in quantum…
Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a…
We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with…
Nonlinear systems, transforming an input signal into a high-dimensional output feature space, can be used for non-conventional computing. This approach, however, requires a change of system parameters during training rather than…