Related papers: The Least Action-Augmented Lanchester Model
AI planning algorithms have addressed the problem of generating sequences of operators that achieve some input goal, usually assuming that the planning agent has perfect control over and information about the world. Relaxing these…
I report on our construction and analysis of the effective low energy Lagrangian for the Minimal Walking Technicolor (MWT) model. The parameters of the effective Lagrangian are constrained by imposing modified Weinberg sum rules and by…
This paper investigates the contact structures and dynamics of stochastic vector bundles, leading to the formulation of the least constraint theorem. It is found that the probability space of stochastic vector bundles possesses an…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
The aim of the article is to develop the stochastic interpretation of quantum mechanics by E. Nelson on the basis of balancing the intra-systemic contradiction (i.e., antisymmetry) between "order" and "chaos". For the set task, it is…
Learning by interaction is the key to skill acquisition for most living organisms, which is formally called Reinforcement Learning (RL). RL is efficient in finding optimal policies for endowing complex systems with sophisticated behavior.…
Very often when studying non-equilibrium systems one is interested in analysing dynamical behaviour that occurs with very low probability, so called rare events. In practice, since rare events are by definition atypical, they are often…
We construct models where initial and boundary conditions can be found from the fundamental rules of physics, without the need to assume them, they will be derived from the action principle. Those constraints are established from physical…
In this paper, we consider a first-order mean field game model motivated by crowd motion in which agents evolve in a (not necessarily compact) metric space and wish to reach a given target set. Each agent aims to minimize the sum of their…
In several domains of physics, including first principle simulations and classical models for polarizable systems, the minimization of an energy function with respect to a set of auxiliary variables must be performed to define the dynamics…
Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum,…
A method for constructing general null Lagrangians and their higher harmonics is presented for dynamical systems with one degree of freedom. It is shown that these Lagrangians can be used to obtain non-standard Lagrangians, which give…
It is well known that, in the five-dimensional scenario of braneworld and space-time-mass theories, geodesic motion in 5D is observed to be non-geodesic in 4D. Usually, the discussion is purely geometric and based on the dimensional…
In nonequilibrium classical thermostatistics, the state of a system may be described by not only dynamical/thermodynamical variables but also a kinetic distribution function. This "double structure" bears some analogy with that in quantum…
This paper presents a formulation of Lagrangian dynamics of constrained mechanical systems in terms of reduced quasi-velocities and quasi-forces that can be used for simulation, analysis, and control purposes. In this formulation, Cholesky…
Armed conflict data display scaling and universal dynamics in both social and physical properties like fatalities and geographic extent. We propose a randomly branching, armed-conflict model that relates multiple properties to one another…
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…
The usefulness of persistent excitation is well-known in the control community. Thanks to a persistently excited adaptive tracking control, we show that it is possible to avoid the strong controllability assumption recently proposed in the…