Related papers: Generalization of the least uncomfortable journey …
This paper is devoted to the study of directional minimal time functions that specify the minimal time for a vector to reach an object following its given direction. We provide a careful analysis of general and generalized differentiation…
The essentially unique reduction of the Euler-Poinsot problem may be performed in different sets of variables. Action-angle variables are usually preferred because of their suitability for approaching perturbed rigid-body motion. But they…
This paper uses Pontryagin methods to analyze pulse-and-glide driving for different nominal vehicle speeds. There is significant literature supporting the fact that pulse-and-glide has the potential to reduce fuel consumption compared to…
The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…
The paper considers the problem of constructing program control for an object described by a system with a quasidifferentiable right-hand side. The control aim is to bring the system from a given initial position to a given final state in…
We construct a theory of particles moving in curved both momentum space and spacetime, being a generalization of Relative Locality. We find that in order to construct such theory, with desired symmetries, including the general coordinate…
In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…
We investigate a dynamic inverse problem using a regularization which implements the so-called Wasserstein-$1$ distance. It naturally extends well-known static problems such as lasso or total variation regularized problems to a (temporally)…
General models of network navigation must contain a deterministic or drift component, encouraging the agent to follow routes of least cost, as well as a random or diffusive component, enabling free wandering. This paper proposes a…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
In train routing, the headway is the minimum distance that must be maintained between successive trains for safety and robustness. We introduce a model for train routing that requires a fixed headway to be maintained between trains, and…
In this paper we study a variant of the branched transportation problem, that we call multi-material transport problem. This is a transportation problem, where distinct commodities are transported simultaneously along a network. The cost of…
When there are significant service disruptions in public transit systems, passengers usually need guidance to find alternative paths. This paper proposes a path recommendation model to mitigate congestion during public transit disruptions.…
Motion prediction of surrounding vehicles is one of the most important tasks handled by a self-driving vehicle, and represents a critical step in the autonomous system necessary to ensure safety for all the involved traffic actors. Recently…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
The $n$-body problem with a purely repulsive Coulomb interaction is considered. It is shown that for large times $t$ the distance between any two particles grows linearly in $t$. The trajectory of each particle is asymptotically a straight…
Implementing virtual fixtures in guiding tasks constrains the movement of the robot's end effector to specific curves within its workspace. However, incorporating guiding frameworks may encounter discontinuities when optimizing the…
We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with…