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For classical discrete system under constant composition typically referred to substitutional alloys, we examine local nonlinearity in canonical average phi . We have respectively investigated the local and global behavior of nonlinearity…

For classical discrete systems with constant composition (typically referred to substitutional alloys) under thermodynamically equilibrium state, macroscopic structure should in principle depend on temperature and many-body interaction…

For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…

For classical discrete system under constant composition, typically reffered to as substitutional alloys, canonical average acts as nonlinear map F from a set of potential energy surface U to that of microscopic configuration in…

For classical discrete system under constant composition, typically reffered to as substitutional alloys, correspondence between interatomic many-body interactions and structure in thermodynamic equilibrium exhibit profound, complicated…

For classical discrete systems under constant composition (specifically substitutional alloys), canonical average acts as a map from a set of many-body interatomic interactions to a set of configuration in thermodynamic equilibrium, which…

In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…

When we consider classical discrete systems under constant composition, their stable configuration in thermodynamic equilibrium can be typically obtained through the well-known canonica average phi. In configurational thermodynamics, phi as…

For classical discrete systems under constant composition (typically reffered to as substitutional alloys), canonical average can act as a map from a set of many-body interatomic interactions to that of configuration in thermodynamic…

This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…

To observe synchronization in a large network of classical or quantum systems demands both excellent control of the interactions between the nodes and very accurate preparation of the initial conditions due to the involved nonlinearities…

Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…

This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…

The erratic nature of chaotic behavior is thought to erode the stability of periodic behavior, including topological oscillations. However, we discover that in the presence of chaos, non-trivial topology not only endures but also provides…

Open quantum-system dynamics can follow exponential decay, non-exponential relaxation, or oscillatory dynamics, depending on the system-environment coupling. We study a lattice with a boundary defect that transitions between these regimes,…

We study the dynamical and chaotic behavior of a disordered one-dimensional elastic mechanical lattice which supports translational and rotational waves. The model used in this work is motivated by the recent experimental results of B. Deng…

Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…

This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…

Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…

Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…