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The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…
Robotics is shifting from rigid, articulated systems to more sophisticated and heterogeneous mechanical structures. Soft robots, for example, have continuously deformable elements capable of large deformations. The flourishing of control…
A system of reduced equations is proposed for the electron motion in the strongly-radiation dominated regime for an arbitrary electromagnetic field configuration. The developed approach is used to analyze various scenarios of an electron…
Discontinuous time derivatives are used to model threshold-dependent switching in such diverse applications as dry friction, electronic control, and biological growth. In a continuous flow, a discon- tinuous derivative can generate multiple…
Weighted finite-state machines are a fundamental building block of NLP systems. They have withstood the test of time -- from their early use in noisy channel models in the 1990s up to modern-day neurally parameterized conditional random…
In this paper, a multi-class Aw-Rascle \textrm{(AR)} model with time fractional order derivative is presented. The conservative form of the proposed model is considered for the natural extension and generalization of equations involved. The…
The appearance of the time derivative of the acceleration in the equation of motion (EOM) of an electric charge is studied. It is shown that when an electric charge is accelerated, a stress force exists in the curved electric field of the…
A description of the motion in noninertial reference frames by means of the inclusion of high time derivatives is studied. Incompleteness of the description of physical reality is a problem of any theory, both in quantum mechanics and…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
Model-based Reinforcement Learning and Control have demonstrated great potential in various sequential decision making problem domains, including in robotics settings. However, real-world robotics systems often present challenges that limit…
The invariance theorems obtained in analytical mechanics and derived from Noether's theorems can be adapted to fluid mechanics. For this purpose, it is useful to give a functional representation of the fluid motion and to interpret the…
Continuous-time trajectory representation has recently gained popularity for tasks where the fusion of high-frame-rate sensors and multiple unsynchronized devices is required. Lie group cumulative B-splines are a popular way of representing…
In recent years, soft robotics simulators have evolved to offer various functionalities, including the simulation of different material types (e.g., elastic, hyper-elastic) and actuation methods (e.g., pneumatic, cable-driven, servomotor).…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
Analytic first and second derivatives of the energy are developed for the fragment molecular orbital method interfaced with molecular mechanics in the electrostatic embedding scheme at the level of Hartree-Fock and density functional…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
Mobile robots, such as ground vehicles and quadrotors, are becoming increasingly important in various fields, from logistics to agriculture, where they automate processes in environments that are difficult to access for humans. However, to…