相关论文: Geometry of Valley Growth

One of the main objectives of the Mars Exploration Program is to search for evidence of past or current life on the planet. To achieve this, Mars exploration has been focusing on regions that may have liquid or frozen water. A set of…

The shape of buildings plays a critical role in the energy efficiency, lifestyles, land use and infrastructure systems of cities. Thus, as most of the world's cities continue to grow and develop, understanding the interplay between the…

Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order…

Modeling of growth (or decay) curves arises in many fields such as microbiology, epidemiology, marketing, and econometrics. Parametric forms like Logistic and Gompertz are often used for modeling such monotonic patterns. While useful for…

We investigate the evolution of axis ratios, roundness (isoperimetric ratio) and the number of static balance points under distance-driven flows. The latter have already been proposed by Aristotle as models of particle shape evolution and…

By measuring the angles at which the Landau levels overlap in tilted magnetic fields (the coincidence method), we determine the splitting of the conduction-band valleys in high-mobility two-dimensional (2D) electrons confined to AlAs…

The coupling between $z$ valleys in the conduction band of a Si quantum well arises from phenomena occurring within several atoms from the interface, thus ruling out a theoretical description based on pure effective mass theory. However,…

The local extremes (i.e., peaks and pits) of the landscape-elevation field play a critical role in energy, water, and nutrient distribution over the region, but the statistical distributions of these points in relation to landscape…

Pit craters are circular to subcircular depressions that lack a rim and ejecta layer and typically have a conical shape. There are several mechanisms that can explain the formation of such depressions and they are associated with collapse…

We describe a categorical approach to finite noncommutative geometries. Objects in the category are spectral triples, rather than unitary equivalence classes as in other approaches. This enables to treat fluctuations of the metric and…

A recent paper [CGT] studies the evolution of star-shaped mean convex hypersurfaces of the Euclidean space by a class of nonhomogeneous expanding curvature flows. In the present paper we consider the same problem in the real, complex and…

A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…

The sliced-Wasserstein flow is an evolution equation where a probability density evolves in time, advected by a velocity field computed as the average among directions in the unit sphere of the optimal transport displacements from its 1D…

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…

Venus may have had both an Earth-like climate as well as extensive water oceans and active (or incipient) plate tectonics for an extended interval of its history. The topographical power spectrum of Venus provides important clues to the…

The formation of vegetation patterns in the arid and the semi-arid climatic zones is studied. Threshold for the biomass of the perennial flora is shown to be a relevant factor, leading to a frozen disordered patterns in the arid zone. In…

Ring-diagram analysis of acoustic waves observed at the photosphere can provide a relatively robust determination of the sub-surface flows at a particular time under a particular region. The depth of penetration of the waves is related to…

We investigate the dynamical evolution of a thermodynamically unstable crystal surface into a hill-and-valley structure. We demonstrate that, for quasi one-dimensional ordering, the equation of motion maps exactly to the modified…

Banded patterns consisting of alternating bare soil and dense vegetation have been observed in water-limited ecosystems across the globe, often appearing along gently sloped terrain with the stripes aligned transverse to the elevation…

Topography is the expression of both internal and external processes of a planetary body. Thus hypsometry (the study of topography) is a way to decipher the dynamic of a planet. For that purpose, the statistics of height and slopes may be…