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Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
Nonlinear optical generation from a crystalline material can reveal the symmetries of both its lattice structure and underlying ordered electronic phases and can therefore be exploited as a complementary technique to diffraction based…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Here we present a new perspective to the breakdown of ferromagnetic order in two-dimensional spin-lattice models employing the rotation of the underlying lattice. Using an Ising spin system on a square lattice as a prototype, we demonstrate…
A transfer-matrix algorithm is presented herein as a beginning to study the transmission characteristics of coherent light through three-dimensional periodic microstructures, in which the structures are treated as two-dimensional-layer…
This study presents a nonlinear signal processing method for accurate radar-based heartbeat interval estimation by exploiting the periodicity of higher-order harmonics inherent in heartbeat signals. Unlike conventional approaches that…
When analyzing non-Hermitian lattice systems, the standard eigenmode decomposition utilized for the analysis of Hermitian systems must be replaced by Jordan decomposition. This approach enables us to identify the correct number of the left…
The calculation of the transfer matrix for a large non-periodic multilayered system may become unstable in the presence of absorption. We discuss the origin of this instability and we explore two methods to overcome it: the use of a total…
Chains of resonators in the form of spring-mass systems have long been known to exhibiting interesting properties such as band gaps. Such features can be leveraged to manipulate the propagation of waves such as the filtering of specific…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
This paper extends the RRT* algorithm, a recently developed but widely-used sampling-based optimal motion planner, in order to effectively handle nonlinear kinodynamic constraints. Nonlinearity in kinodynamic differential constraints often…
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
We show the possibility of controlling the dynamical behavior of a single fiber ring (SFR) resonator system with the fiber being an amplified (gain) channel and the ring being attenuated (loss) nonlinear dielectric medium. Our model is…
This paper describes the development of beam dynamic simulation code for cyclotron. Starting from a description of beam dynamics in the cyclotron, lattice functions were determined and the solutions for the 2nd-order nonlinear Hamiltonian…
This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical systems. This non-intrusive formulation constrains the…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial…
Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order…