The aim of this paper is to provide and numerically test in the presence of measurement noise a procedure for target classification in wave imaging based on comparing frequency-dependent distribution descriptors with precomputed ones in a dictionary of learned distributions. Distribution descriptors for inhomogeneous objects are obtained from the scattering coefficients. First, we extract the scattering coefficients of the (inhomogeneous) target from the perturbation of the reflected waves. Then, for a collection of inhomogeneous targets, we build a frequency-dependent dictionary of distribution descriptors and use a matching algorithm in order to identify a target from the dictionary up to some translation, rotation and scaling.

The classical Monge–Kantorovich (MK) problem as originally posed is concerned with how best to move a pile of soil or rubble to an excavation or fill with the least amount of work relative to some cost function. When the cost is given by the square of the Euclidean distance, one can define a metric on densities called the Wasserstein distance. In this note, we formulate a natural matrix counterpart of the MK problem for positive-definite density matrices. We prove a number of results about this metric including showing that it can be formulated as a convex optimisation problem, strong duality, an analogue of the Poincaré–Wirtinger inequality and a Lax–Hopf–Oleinik–type result.

The present paper is devoted to the study of the existence, the uniqueness and the stability of transition fronts of non-local dispersal equations in time heterogeneous media of bistable type under the unbalanced condition. We first study space non-increasing transition fronts and prove various important qualitative properties, including uniform steepness, stability, uniform stability and exponential decaying estimates. Then, we show that any transition front, after certain space shift, coincides with a space non-increasing transition front (if it exists), which implies the uniqueness, up-to-space shifts and monotonicity of transition fronts provided that a space non-increasing transition front exists. Moreover, we show that a transition front must be a periodic travelling front in periodic media and asymptotic speeds of transition fronts exist in uniquely ergodic media. Finally, we prove the existence of space non-increasing transition fronts, whose proof does not need the unbalanced condition.

Steady two-dimensional fluid flow over an obstacle is solved using complex variable methods. We consider the cases of rectangular obstacles, such as large boulders, submerged in a potential flow. These may arise in geophysics, marine and civil engineering. Our models are applicable to initiation of motion that may result in subsequent transport. The local flow depends on the obstacle shape, slowing down in confining corners and speeding up in expanding corners. The flow generates hydrodynamic forces, drag and lift, and their associated moments, which differ around each face. Our model replaces the need for ill-defined drag and lift coefficients with geometry-dependent functions. We predict smaller flow velocities to initiate motion. We show how a joint-bound boulder can be transported against gravity, and analyse the influence of a wake region behind an isolated boulder.

Switched server systems are mathematical models of manufacturing, traffic and queueing systems that have being studied since the early 1990s. In particular, it is known that typically the dynamics of such systems is asymptotically periodic: each orbit of the system converges to one of its finitely many limit cycles. In this article, we provide an explicit example of a switched server system with exotic behaviour: each orbit of the system converges to the same Cantor attractor. To accomplish this goal, we bring together recent advances in the understanding of the topological dynamics of piecewise contractions and interval exchange transformations (IETs) with flips. The ultimate result is a switched server system whose Poincaré map is semiconjugate to a minimal and uniquely ergodic IET with flips.

We consider Fokker–Planck equations with tilted periodic potential in the subcritical regime and characterise the spatio-temporal dynamics of the partial masses in the limit of vanishing diffusion. Our convergence proof relies on suitably defined substitute masses and bounds the approximation error using the energy-dissipation relation of the underlying Wasserstein gradient structure. In the appendix, we also discuss the case of an asymmetric double-well potential and derive the corresponding limit dynamics in an elementary way.