Related papers: Hamiltonian structure of compartmental epidemiolog…
We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The proposed Hamiltonian couples the given system to auxiliary…
We here discuss the outcome of an hypothetic experiments of populations dynamics, where a set of independent realizations is made available. The importance of ensemble average is clarified with reference to the registered time evolution of…
Asymptotic properties of statistical estimators play a significant role both in practice and in theory. However, many asymptotic results in statistics rely heavily on the independent and identically distributed (iid) assumption, which is…
It is well known that the dynamics of a Hamiltonian system depends crucially on whether or not it possesses nonlinear resonances. In the generic case, the set of nonlinear resonances consists of independent clusters of resonantly…
The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…
Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual coupling (direct, semidirect and matched-pair products) as…
A study of changes in the transmission of a disease, in particular, a new disease like COVID-19, requires very flexible models which can capture, among others, the effects of non-pharmacological and pharmacological measures, changes in…
We address a simple connection between results of Hamiltonian nonlinear dynamical theory and thermostatistics. Using a properly defined dynamical temperature in low-dimensional symplectic maps, we display and characterize long-standing…
We study the algebraic structure of the eigenvalues of a Hamiltonian that corresponds to a many-body fermionic system. As the Hamiltonian is quadratic in fermion creation and/or annihilation operators, the system is exactly integrable and…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
To forecast the time dynamics of an epidemic, we propose a discrete stochastic model that unifies and generalizes previous approaches to the subject. Viewing a given population of individuals or groups of individuals with given health state…
Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…
We consider nonholonomic systems with symmetry possessing a certain type of first integrals that are linear in the velocities. We develop a systematic method for modifying the standard nonholonomic almost Poisson structure that describes…
Port-Hamiltonian systems theory provides a structured approach to modelling, optimization and control of multiphysical systems. Yet, its relationship to thermodynamics seems to be unclear. The Hamiltonian is traditionally thought of as…
In this paper we develope, in a geometric framework, a Hamilton-Jacobi Theory for general dynamical systems. Such a theory contains the classical theory for Hamiltonian systems on a cotangent bundle and recent developments in the framework…
Simulating the spread of infectious diseases in human communities is critical for predicting the trajectory of an epidemic and verifying various policies to control the devastating impacts of the outbreak. Many existing simulators are based…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
The symmetric top is a special case of the general top, and canonical Poisson structure on $T^*SE(3)$ is the common method of its description. This structure is invariant under the right action of $SO(3)$, but the Hamiltonian of the…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…