We study a one-dimensional transport equation with nonlocal velocity which was recently considered in the work of Córdoba, Córdoba and Fontelos [4]. We show that in the subcritical and critical cases the problem is globally well-posed with arbitrary initial data in Hmax{3/2−γ,0}. While in the supercritical case, the problem is locally well-posed with initial data in H3/2−γ , and is globally wel...

Many real-world problems can be expressed in terms of states and actions that modify the world to reach a certain goal. Such problems can be solved by automated planning. Numeric planning supports numeric quantities such as resources or physical properties in addition to the propositional variables from classical planning. We approach numeric planning with heuristic search and introduce adaptat...

n an 1881 study of ferromagnetism [37], James A. Ewing coined the term hysteresis, which means “to lag behind” in Greek. In Figure 1, which is reproduced from [1], the horizontal axis is the magnitude of the average magnetic field H in a soft-iron ring, while the vertical axis is the magnitude of the average magnetic flux density B. The plot was obtained by varying the magnetic field in a quasi...

When an ion moves across the interface of two immiscible electrolytes it moves together with the ion-induced protrusion of one solvent into the other. For an infinitely slow motion of an ion the height of the protrusion, heq , is a function of the position of the ion z. Due to a finite relaxation time the protrusion may not be able to spontaneously follow the motion of the ion, and this will ca...

2D Free-surface hydraulic modeling tools are commonly used to assess flood hazard for production of maximal water depth (hmax) maps, as support for flood risk assessment. High Resolution (HR) topographic data are big data getting commonly available and used by hydraulic modeling community. Topographical information and its strategy of inclusion in models, are inputs of great importance for over...

Acoustic Doppler velocity profiler (ADVP) measurements of instantaneous threedimensional velocity profiles over the entire turbulent boundary layer height, δ, of rough-bed open-channel flows at moderate Reynolds numbers show the presence of large scale coherent shear stress structures (called LC3S herein) in the zones of uniformly retarded streamwise momentum. LC3S events over streamwise distan...

The two-dimensional velocity potential associated with the scattering of linear waves in water of finite but non-uniform depth is shown to be unique for Khmax ≤ 1. Here hmax is the maximum depth of the fluid and K = ω2/g, where ω is the angular frequency and g is the acceleration due to gravity. Uniqueness is established by proving that the homogeneous boundary value problem for the velocity po...

Factored planning decouples planning tasks into subsets (factors) of state variables. The traditional focus is on handling complex cross-factor interactions. Departing from this, we introduce a form of target-profile factoring, forcing the crossfactor interactions to take the form of a fork, with several leaf factors and one potentially very large root factor. We show that forward state space s...