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In this article we provide various analytical and numerical methods for calculating the average drift of magnetically trapped particles across field lines in complex geometries, and we compare these methods against each other. To evaluate bounce-integrals, we introduce a generalisation of the trapezoidal rule which is able to circumvent integrable singularities. We contrast this method with more standard quadrature methods in a parabolic magnetic well and find that the computational cost is significantly lower for the trapezoidal method, though at the cost of accuracy. With numerical routines in place, we next investigate conditions on particles which cross the computational boundary, and we find that important differences arise for particles affected by this boundary, which can depend on the specific implementation of the calculation. Finally, we investigate the bounce-averaged drifts in the optimized stellarator NCSX. From investigating the drifts, one can readily deduce important properties, such as what subset of particles can drive trapped-particle modes, and in what regions radial drifts are most deleterious to the stability of such modes., Comment: 12 pages, 6 figures

This work is concerned with homogenization problems for elliptic equations of the type \[ \begin{cases} \mathfrak{L}_{\delta} u_{\delta} + \lambda u_{\delta} = f_{\delta} \qquad \text{in} \;\; D, \\ \qquad \quad \;\, u = 0 \qquad \, \text{on} \;\; \partial D, \end{cases} \] where $\delta > 0$, $\lambda \in \mathbb{R}$, $D$ is a bounded open set in $\mathbb{R}^{d}$, and $f_{\delta} \in H^{-1}(D)$. The operator $ \mathfrak{L}_{\delta} u = -{\rm div} \left( A^\delta \nabla u + C^\delta u \right) + B^\delta \nabla u +k^\delta u $ involved uniformly bounded diffusion coefficients $A^\delta$, where drifts $B^\delta$, $C^\delta$ and potential $k^\delta$ are possibly unbounded. An application to homogenization of the corresponding diffusion processes is also discussed., Comment: 38 pages

We study the quantitative homogenization of linear second order elliptic equations in non-divergence form with highly oscillating periodic diffusion coefficients and with large drifts, in the so-called ``centered'' setting where homogenization occurs and the large drifts contribute to the effective diffusivity. Using the centering condition and the invariant measures associated to the underlying diffusion process, we transform the equation into divergence form with modified diffusion coefficients but without drift. The latter is in the standard setting for which quantitative homogenization results have been developed systematically. An application of those results then yields quantitative estimates, such as the convergence rates and uniform Lipschitz regularity, for equations in non-divergence form with large drifts., Comment: 16 pages

Consider the motion of a Brownian particle in $n$ dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, exactly $k$ of the coordinate processes get a (known) non-zero drift permanently. Given that the position of the Brownian particle is being observed in real time, the problem is to detect the time at which the $k$ coordinate processes get the drift as accurately as possible. We solve this problem in the most uncertain scenario when the random/unobservable time is (i) exponentially distributed and (ii) independent from the initial motion without drift. The solution is expressed in terms of a stopping time that minimises the probability of a false early detection and the expected delay of a missed late detection. The elliptic case $k=1$ has been settled in Ernst and Peskir (2022) where the hypoelliptic case $1 < k < n$ resolved in the present paper was left open (the case $k = n$ reduces to the classic case $n=1$ having a known solution). We also show that the methodology developed solves the problem in the general case where exactly $k$ is relaxed to any number of the coordinate processes getting the drift. To our knowledge this is the first time that such a multi-dimensional hypoelliptic problem has been solved exactly in the literature., Comment: 26 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2007.14786

It has been shown in \cite{Tong:2022gpg} that shallow water in the Euler description admits a dual gauge theory formulation. We show in the Lagrange description this gauge symmetry is a manifestation of the 2 dimensional area-preserving diffeomorphisms. We find surface charges associated with the gauge symmetry and their algebra, and study their physics in the shallow water system. In particular, we provide a reinterpretation of the Kelvin circulation theorem in terms of conserved charges. In the linear shallow water case, the charges form a u(1) current algebra with level proportional to the Coriolis parameter over the height of the fluid. We also study memory effect for the gauge theory description of the linearized shallow water and show Euler, Stokes and Darwin drifts can be understood as a memory effect and/or change of the surface charges in the gauge theory description., Comment: 28 pages, 2 figures, minor improvements, references added

We show the existence and uniqueness as well as boundedness of weak solutions to linear elliptic equations with $L^2$-drifts of negative divergence and singular zero-order terms which are positive. Our main target is to show the $L^r$-contraction properties of the unique weak solutions. Indeed, using the Dirichlet form theory, we construct a sub-Markovian $C_0$-resolvent of contractions and identify it to the weak solutions. Furthermore, we derive an $L^1$-stability result through an extended version of the $L^1$-contraction property., Comment: 15 pages, manuscript submitted after acceptance

Millions of vulnerable consumer IoT devices in home networks are the enabler for cyber crimes putting user privacy and Internet security at risk. Internet service providers (ISPs) are best poised to play key roles in mitigating risks by automatically inferring active IoT devices per household and notifying users of vulnerable ones. Developing a scalable inference method that can perform robustly across thousands of home networks is a non-trivial task. This paper focuses on the challenges of developing and applying data-driven inference models when labeled data of device behaviors is limited and the distribution of data changes (concept drift) across time and space domains. Our contributions are three-fold: (1) We collect and analyze network traffic of 24 types of consumer IoT devices from 12 real homes over six weeks to highlight the challenge of temporal and spatial concept drifts in network behavior of IoT devices; (2) We analyze the performance of two inference strategies, namely "global inference" (a model trained on a combined set of all labeled data from training homes) and "contextualized inference" (several models each trained on the labeled data from a training home) in the presence of concept drifts; and (3) To manage concept drifts, we develop a method that dynamically applies the ``closest'' model (from a set) to network traffic of unseen homes during the testing phase, yielding better performance in 20% of scenarios., Comment: Submitted to IEEE IoT Journal

The High Field High Density Region (HFSFD) has been experimentally observed in both divertor and limiter tokamak devices. In order to numerically reproduced the HFSHD region in the limiter tokamak device J-TEXT, we first performed SOLPS-ITER simulations on the J-TEXT limiter tokamak with the activation of drifts, which is associated with the HFSHD region. The validated physical models, which is from ASDEX Upgrade (AUG) divertor modelling including full drifts and currents, were applied. Through a gas puffing rate scan, both attached and detached regimes were numerically obtained in the AUG divertor and J-TEXT limiter. The key plasma parameters in the J-TEXT limiter are evaluated with and without drifts that have a qualitative performance like AUG except the roll-overment of the total ion flux at the targets. The drift effects on the target profiles are investigated in which the maximum electron temperature at the outer targets is 15eV and 5eV respectively. When the outer targets are attached in the J-TEXT limiter and AUG divertor, the drifts result in the partial detachment of the inner targets. In the detached regimes, the drifts decrease the electron temperature on AUG divertor targets. However, for the J-TEXT limiter, the electron temperature only decreases at the far SOL region. The effect of drifts on the neutral density is also presented.

The transport properties of gapless edge modes at boundaries between topologically distinct domains are of fundamental and technological importance. Therefore, it is crucial to gain a better understanding of topological edge states and their response to interparticle interactions. Here, we experimentally study long-distance quantised Hall drifts in a harmonically confined topological pump of non-interacting and interacting ultracold fermionic atoms. We find that quantised drifts halt and reverse their direction when the atoms reach a critical slope of the confining potential, revealing the presence of a topological boundary. The drift reversal corresponds to a band transfer between a band with Chern number $C = +1$ and a band with $C = -1$ via a gapless edge mode, in agreement with the bulk-edge correspondence for non-interacting particles. We establish that a non-zero repulsive Hubbard interaction leads to the emergence of an additional edge in the system, relying on a purely interaction-induced mechanism, in which pairs of fermions are split.

High precision lightcurves combined with eclipse mapping techniques can reveal the horizontal and vertical structure of a planet's thermal emission and the dynamics of hot Jupiters. Someday, they even may reveal the surface maps of rocky planets. However, inverting lightcurves into maps requires an understanding of the planet, star and instrumental trends because they can resemble the gradual flux variations as the planet rotates (ie. partial phase curves). In this work, we simulate lightcurves with baseline trends and assess the impact on planet maps. Baseline trends can be erroneously modeled by incorrect astrophysical planet map features, but there are clues to avoid this pitfall in both the residuals of the lightcurve during eclipse and sharp features at the terminator of the planet. Models that use a Gaussian process or polynomial to account for a baseline trend successfully recover the input map even in the presence of systematics but with worse precision for the m=1 spherical harmonic terms. This is also confirmed with the ThERESA eigencurve method where fewer lightcurve terms can model the planet without correlations between the components. These conclusions help aid the decision on how to schedule observations to improve map precision. If the m=1 components are critical, such as measuring the East/West hotspot shift on a hot Jupiter, better characterization of baseline trends can improve the m=1 terms' precision. For latitudinal North/South information from the remaining mapping terms, it is preferable to obtain high signal-to-noise at ingress/egress with more eclipses., Comment: AJ, accepted, 22 pages

This paper presents a dual receding horizon output feedback controller for a general non linear stochastic system with imperfect information. The novelty of this controller is that stabilization is treated, inside the optimization problem, as a negative drift constraint on the control that is taken from the theory of stability of Markov chains. The dual effect is then created by maximizing information over the stabilizing controls which makes the global algorithm easier to tune than our previous algorithm. We use a particle filter for state estimation to handle nonlinearities and multimodality. The performance of this method is demonstrated on the challenging problem of terrain aided navigation.

The purpose of this paper is twofold. Firstly, we prove transportation inequalities ${\bf T_2}(C)$ on the space of continuous paths with respect to the uniform metric for the law of the solution to a class of non-linear monotone stochastic partial differential equations (SPDEs) driven by the Wiener noise. Furthermore, we also establish the ${\bf T_1}(C)$ property for such SPDEs but with merely locally monotone coefficients, including the stochastic Burgers type equation and stochastic $2$-D Navier-Stokes equation.

The nonequilibrium Fokker-Planck dynamics with a non-conservative drift field, in dimension $N\geq 2$, can be related with the non-Hermitian quantum mechanics in a real scalar potential $V$ and in a purely imaginary vector potential -$iA$ of real amplitude $A$. Since Fokker-Planck probability density functions may be obtained by means of Feynman's path integrals, the previous observation points towards a general issue of "magnetically affine" propagators, possibly of quantum origin, in real and Euclidean time. In below we shall follow the $N=3$ "magnetic thread", within which one may keep under a computational control formally and conceptually different implementations of magnetism (or surrogate magnetism) in the dynamics of diffusion processes. We shall focus on interrelations (with due precaution to varied, not evidently compatible, notational conventions) of: (i) the pertinent non-conservatively drifted diffusions, (ii) the classic Brownian motion of charged particles in the (electro)magnetic field, (iii) diffusion processes arising within so-called Euclidean quantum mechanics (which from the outset employs non-Hermitian "magnetic" Hamiltonians), (iv) limitations of the usefulness of the Euclidean map $\exp(-itH_{quant}) \rightarrow \exp(-tH_{Eucl})$, regarding the probabilistic significance of inferred (path) integral kernels in the description of diffusion processes., Comment: 28 pp. Title and Abstract modified, sections VI and VII written anew

Real-time monitoring of human behaviours, especially in e-Health applications, has been an active area of research in the past decades. On top of IoT-based sensing environments, anomaly detection algorithms have been proposed for the early detection of abnormalities. Gradual change procedures, commonly referred to as drift anomalies, have received much less attention in the literature because they represent a much more challenging scenario than sudden temporary changes (point anomalies). In this paper, we propose, for the first time, a fully unsupervised real-time drift detection algorithm named DynAmo, which can identify drift periods as they are happening. DynAmo comprises a dynamic clustering component to capture the overall trends of monitored behaviours and a trajectory generation component, which extracts features from the densest cluster centroids. Finally, we apply an ensemble of divergence tests on sliding reference and detection windows to detect drift periods in the behavioural sequence., Comment: Accepted to IEEE TKDE

Gravitational waves with frequencies below 1~nHz are notoriously difficult to detect. With periods exceeding current experimental lifetimes, they induce slow drifts in observables rather than periodic correlations. Observables with well-known intrinsic contributions provide a means to probe this regime. In this work, we demonstrate the viability of using observed pulsar timing parameters to discover such "ultralow" frequency gravitational waves, presenting two complementary observables for which the systematic shift induced by ultralow-frequency gravitational waves can be extracted. Using existing data for these parameters, we search the ultralow frequency regime for continuous-wave signals, finding a sensitivity near the expected prediction from inspirals of supermassive black holes. We do not see an excess in the data, setting a limit on the strain of $ 1.3 \times 10 ^{ - 12} $ at $ 450~{\rm pHz} $ with a sensitivity dropping approximately quadratically with frequency until $ 10~{\rm pHz}$. Our search method opens a new frequency range for gravitational wave detection and has profound implications for astrophysics, cosmology, and particle physics., Comment: 20 pages, 4 figures, 4 appendices; v2: updated to match PRL

We consider a generalization of classical results of Freidlin and Wentzell to the case of time dependent dissipative drifts. We show the convergence of diffusions with multiplicative noise in the zero limit of a diffusivity parameter to the related dynamical systems. The solution to the associated transport equation is obtained as an application., Comment: arXiv admin note: text overlap with arXiv:2205.01750

We study the solvability of singular Abreu equations which arise in the approximation of convex functionals subject to a convexity constraint. Previous works established the solvability of their second boundary value problems either in two dimensions, or in higher dimensions under either a smallness condition or a radial symmetry condition. Here, we solve the higher dimensional case by transforming singular Abreu equations into linearized Monge-Amp\`ere equations with drifts. We establish global H\"older estimates for the linearized Monge-Amp\`ere equation with drifts under suitable hypotheses, and then use them to the regularity and solvability of the second boundary value problem for singular Abreu equations in higher dimensions. Many cases with general right-hand side will also be discussed., Comment: v2: final version to appear in JEMS