相关论文: Momentum Map and Action-Angle Variables for Nambu …
In this work we investigate the relation between curved momentum space and momentum-dependent gauge fields. While the former is a classic idea that has been shown to be tied to minimal-length models, the latter constitutes a relatively…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work…
Various fluid mechanical systems, governed by nonlinear differential equations, enjoy a hidden, higher-dimensional dynamical Poincar\'e symmetry, which arises owing to their descent from a Nambu-Goto action. Also, for the same reason, there…
A popular approach to analyze the dynamics of high-dimensional many-body systems, such as macromolecules, is to project the trajectories onto a space of slowly-varying collective variables, where subsequent analyses are made, such as…
Quantity of organization in complex networks here is measured as the inverse of the average sum of physical actions of all elements per unit motion multiplied by the Planck's constant. The meaning of quantity of organization is the inverse…
Active materials are capable of converting free energy into directional motion, giving rise to striking dynamical phenomena. Developing a general understanding of their structure in relation to the underlying non-equilibrium physics would…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
Although the idea of the momentum map associated with a symplectic action of a group is already contained in work of Lie, the geometry of momentum maps was not studied extensively until the 1960's. Centering around the relation between…
The motion of atoms and nanoparticles in a trap formed by sequences of counter-propagating light pulses has been analyzed. The atomic state is described by a wave function constructed with the use of the Monte Carlo method, whereas the…
This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…
A different approach will be presented that aims to scrutinize the phase-space trajectories of a general class of Hamiltonian systems with regard to their regular or irregular behavior. The approach is based on the `energy-second-moment…
Negative differential mobility is the phenomenon in which the velocity of a particle decreases when the force driving it increases. We study this phenomenon in Markov jump models where a particle moves in the presence of walls that act as…
Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field…
We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube…
We show that a novel, general phase space mapping Hamiltonian for nonadiabatic systems, which is reminiscent of the renowned Meyer-Miller mapping Hamiltonian, involves a commutator variable matrix rather than the conventional…
We give a generalization of the Nambu mechanics based on vector Hamiltonians theory. It is shown that any divergence-free phase flow in $\mathbb{R}^n$ can be represented as a generalized Nambu mechanics with $n-1$ integral invariants. For…
moment maps arise as a generalization of genuine moment maps on symplectic manifolds when the symplectic structure is discarded, but the relation between the mapping and the action is kept. Particular examples of abstract moment maps had…
This work presents an optimization-based task and motion planning (TAMP) framework that unifies planning for locomotion and manipulation through a shared representation of contact modes. We define symbolic actions as contact mode changes,…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…