相关论文: Jet Methods in Time-Dependent Lagrangian Biomechan…

This talk discusses various aspects of the structure of space-time presenting mechanisms leading to the explanation of the "rigidity" of the manifold and to the emergence of time, i.e. of the Lorentzian signature. The proposed ingredient is…

The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…

This paper extends our recently developed Life Space Foam (LSF) model of motivated cognitive dynamics \cite{IA}. LSF uses adaptive path integrals to generate Lewinian force--fields on smooth manifolds, in order to characterize the dynamics…

In these three lectures we will discuss some fundamental aspects of the theory of self-adjoint extensions of the covariant Laplace-Beltrami and Dirac operators on compact Riemannian manifolds with smooth boundary emphasizing the relation…

In dynamics and vibrations, the concept of bandwidth for linear time-invariant systems is widely recognized as a measure of the dispersion of frequency content around resonance. Similarly, the time constant is associated with the rate of…

We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…

An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…

In this article we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics. To achieve this goal, we identify the phase space invariant manifolds using…

We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known…

Multi-step pathways, constituted of a sequence of reconfigurations, are central to a wide variety of natural and man-made systems. Such pathways autonomously execute in self-guided processes such as protein folding and self-assembly, but…

In this work, we analyze the evolution of the phase-space structures of KCN molecular system as a function of the vibrational energy using Lagrangian descriptors. For low energies, the motion is mostly regular around the absolute minimum of…

With this paper, a consistent and comprehensive treatise on the foundations of the extended Hamilton-Lagrange formalism will be presented. In this formalism, the system's dynamics is parametrized along a system evolution parameter $s$, and…

For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first…

We consider time-dependence of dynamical transport, following a recent study of the stadium billiard in which classical transmission and reflection probabilities were shown to exhibit exponential or algebraic decay depending on the choice…

We extend the port-Hamiltonian framework defined with respect to a Lagrangian submanifold and a Dirac structure by augmenting the Lagrangian submanifold with the space of external variables. The new pair of conjugated variables is called…

Let F be a smooth real manifold with a linear connection in the tangent bundle. How can we extend the coefficients of the connection to bi-differential operators that incorporate the original structure at zero order? Take a constant mapping…

A time-varying bivariate copula joint model, which models the repeatedly measured longitudinal outcome at each time point and the survival data jointly by both the random effects and time-varying bivariate copulas, is proposed in this…

Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…

Nature offers remarkable examples of complex photonic architectures such as those responsible for the iridescent colors of butterfly wings that emerge spontaneously during growth, well before any centralized control takes place. Arising…

This paper proposes a novel maneuvering technique for the complex-Laplacian-based formation control. We show how to modify the original weights that build the Laplacian such that a designed steady-state motion of the desired shape emerges…