Related papers: The Gyro-Kinetic Approximation. An attempt at expl…
We derive a fluid-dynamic model for electron transport near a Dirac point in graphene. The derivation is based on the minimum entropy principle, which is exploited in order to close fluid-dynamic equations for quantum mixed states. To this…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
We describe a method to analyze and decompose the dynamics of a control system on a Lie group subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We develop a method, based on Darboux' and Liouville's works, to find first integrals and/or invariant manifolds for a physically relevant class of dynamical systems, without making any assumption on these elements' form. We apply it to…
Identifying the trajectories of rigid bodies and of interaction forces is essential for a wide range of tasks in robotics, biomechanics, and related domains. These tasks include trajectory segmentation, recognition, and prediction. For…
We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three…
We approximate a chain recurrent dynamical system by periodic dynamical systems. This is similar to the well known Bohr theorem on approximation of almost periodic functions by periodic functions.
The elimination of a fast time scale from the Vlasov equation by Lie-transform methods is an important step in deriving a reduced Vlasov equation such as the drift-kinetic Vlasov equation or the gyrokinetic Vlasov equation. It is shown here…
A finite Larmor radius approximation is derived from the classical Vlasov equation, in the limit of large (and uniform) external magnetic field. We also provide an heuristic derivation of the electroneutrality equation in the finite Larmor…
Painleve analysis and the singular manifold method are the tools used in this paper to perform a complete study of an equation in 2+1 dimensions. This procedure has allowed us to obtain the Lax pair, Darboux transformation and tau functions…
This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
Equivalence transformations play one of the important roles in continuum mechanics. These transformations reduce the original equations to simpler forms. One of the classes of nonlocal equivalence transformations is the class of reciprocal…
Visual-inertial systems rely on precise calibrations of both camera intrinsics and inter-sensor extrinsics, which typically require manually performing complex motions in front of a calibration target. In this work we present a novel…
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…
This research addresses the challenge of performing search missions in dynamic environments, particularly for drifting targets whose movement is dictated by a flow field. This is accomplished through a dynamical system that integrates two…
It's pointed out that the treatment of the resonant electromagnetic perturbation with the Lie transform method adopted in the gyrokinetic theory generates some nonphysical terms in the trajectory equations. By utilizing a modified…
The aim of the causal dynamical triangulations approach is to define nonperturbatively a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. My aim in this paper is to give a concise yet…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…