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We study the Asymmetric Brownian Energy, a model of heat conduction defined on the one-dimensional finite lattice with open boundaries. The system is shown to be dual to the Symmetric inclusion process with absorbing boundaries. The proof…

This paper establishes trace-formulae for a class of operators defined in terms of the functional calculus for the Laplace operator on divergence-free vector fields with relative and absolute boundary conditions on Lipschitz domains in…

Platooning has emerged as a promising strategy for improving fuel efficiency in automated vehicle systems, with significant implications for reducing emissions and operational costs. While existing literature on vehicle platooning primarily…

We study the thermal partition function of quantum field theories on arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We demonstrate that the equations of…

The quasipotential is a natural generalization of the concept of energy functions to non-equilibrium systems. In the analysis of rare events in stochastic dynamics, it plays a central role in characterizing the statistics of transition…

For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…

Platooning has been exploited as a method for vehicles to minimize energy consumption. In this article, we present a constraint-driven optimal control framework that yields emergent platooning behavior for connected and automated vehicles…

This paper considers the use of recently proposed optimal transport-based multivariate test statistics, namely rank energy and its variant the soft rank energy derived from entropically regularized optimal transport, for the unsupervised…

We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…

We focus on Optimal Transport PDE on the unit sphere $\mathbb{S}^2$ with a particular type of cost function $c(x,y) = F(x \cdot y, x \cdot \hat{e}, y \cdot \hat{e})$ which we call cost functions with preferential direction, where $\hat{e}…

This paper studies the properties of solutions to a class of elliptic and parabolic problems involving the fractional Laplacian. By applying the mountain pass theorem, we prove the existence of bounded classical positive solutions in the…

The occurrence of an inverse current, where the sign of the induced current is opposite to the applied force, is a highly counterintuitive phenomenon. We show that inverse currents in coupled transport (ICC) of energy and particle can occur…

We study the modifications to the fragmentation pattern of partons into charged particles in the presence of a hot and dense Quark Gluon Plasma. To this end, we analyze the perturbative renormalization group equations of the track…

The motion of a charged particle in a straight magnetic field ${\bf B} = B(y)\,\wh{\sf z}$ with a constant perpendicular gradient is solved exactly in terms of elliptic functions and integrals. The motion can be decomposed in terms of a…

Hydrodynamic transport coefficients may be evaluated from first principles in a weakly coupled scalar field theory at arbitrary temperature. In a theory with cubic and quartic interactions, the infinite class of diagrams which contribute to…

We present a low-temperature experimental test of the fluctuation theorem for electron transport through a double quantum dot. The rare entropy-consuming system trajectories are detected in the form of single charges flowing against the…

We provide experimental validation, in a pair of vehicles, of a recently introduced predictor-based cooperative adaptive cruise control (CACC) design, developed for achieving delay compensation in heterogeneous vehicular platoons subject to…

The electrostatic force on a charge above a neutral conductor is generally attractive. Surprisingly, that force becomes repulsive in certain geometries (Levin & Johnson 2011), a result that follows from an energy theorem in electrostatics.…

We analyze the dynamics of a classical particle in a spatially periodic potential under the influence of a periodic in time uniform force. It was shown in [S.Flach, O.Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000)] that…

In this paper, we prove that the dynamical model of a quadrotor subject to linear rotor drag effects is differentially flat in its position and heading. We use this property to compute feed-forward control terms directly from a reference…