Related papers: Anisotropic Diffusion-Driven Ergodic Coverage in M…
Autonomous robots are increasingly deployed for long-term information-gathering tasks, which pose two key challenges: planning informative trajectories in environments that evolve across space and time, and ensuring persistent operation…
Applying micro-patterns to surfaces has been shown to impart useful physical properties such as drag reduction and hydrophobicity. However, current manufacturing techniques cannot produce micro-patterned surfaces at scale due to high-cost…
Using multiple mobile robots in search missions offers a lot of benefits, but one needs a suitable and competent motion control algorithm which is able to consider sensors characteristics, the uncertainty of target detection and complexity…
We study the optimal scheduling problem for a Markovian multiclass queueing network with abandonment in the Halfin--Whitt regime, under the long run average (ergodic) risk sensitive cost criterion. The objective is to prove asymptotic…
The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This diffusion term contributes to the highly stiff nature of the…
Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.…
We show that standard algorithms for anisotropic diffusion based on centered differencing (including the recent symmetric algorithm) do not preserve monotonicity. In the context of anisotropic thermal conduction, this can lead to the…
Robots have the potential to perform search for a variety of applications under different scenarios. Our work is motivated by humanitarian assistant and disaster relief (HADR) where often it is critical to find signs of life in the presence…
The divergence of the heat conductivity in the thermodynamic limit is investigated in 2d-lattice models of anharmonic solids with nearest-neighbour interaction from single-well potentials. Two different numerical approaches based on…
In disaster response scenarios, deploying robotic teams effectively is crucial for improving situational awareness and enhancing search and rescue operations. The use of robots in search and rescue has been studied but the question of where…
Recently, ergodic control has been suggested as a means to guide mobile sensors for information gathering tasks. In ergodic control, a mobile sensor follows a trajectory that is ergodic with respect to some information density distribution.…
We investigate one-dimensional driven diffusive systems where particles may also be created and annihilated in the bulk with sufficiently small rate. In an open geometry, i.e., coupled to particle reservoirs at the two ends, these systems…
We analyze the ergodicity of three one-dimensional Hamiltonian systems, with harmonic, quartic and Mexican-hat potentials, coupled to the logistic thermostat. As criteria for ergodicity we employ: the independence of the Lyapunov spectrum…
We propose MADP, a novel diffusion-model-based approach for collaboration in decentralized robot swarms. MADP leverages diffusion models to generate samples from complex and high-dimensional action distributions that capture the…
Heterogeneous diffusion processes can be well described by an overdamped Langevin equation with space-dependent diffusivity $D(x)$. We investigate the ergodic and non-ergodic behavior of these processes in an arbitrary potential well $U(x)$…
We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation…
Anisotropic diffusion is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and the interplay of cosmic rays with the Galactic magnetic field. This diffusion term contributes to the highly stiff nature of…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…
The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrix have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them…