This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dyt = dωt − ∇V (yt)dt, y0 = 0. When d = 1 and V reflects media characterized by an infinite number of spatial scales V (x) = ∞ k=0 Uk(x/Rk), where Uk are smooth functions of period 1, Uk(0) = 0, and Rk grows exponentially fast with k, we can show that yt has an anomalous slow behavior and obtain ...

The assessment of biotic responses to habitat disturbance and fragmentation generally has been limited to analyses at a single spatial scale. Furthermore, methods to compare responses between scales have lacked the ability to discriminate among patterns related to the identity, strength, or direction of associations of biotic variables with landscape attributes. We present an examination of the...

Demographically, cities throughout the world seem to be expanding rather than shrinking. However a closer look at recent urban population change among the world’s largest urban agglomerations of one million people or more reveals that between 2000 and 2005, 30 out of 414 cities experienced zero to negative average annual growth (U.N. 2005). Recently, this internationalized pattern of city contr...

This webpage is about how to compare species diversity (using only species richness or species richness and abundance) among sites/habitats/communities. Some people call this beta diversity and others call it complementarity, turnover, similarity, dissimilarity, etc. Often, these terms are used interchangeably and at a variety of spatial scales. Methods for making these comparisons are used in ...

– ... yielding [ ] the result that the decay rate on spatial scales of about 1000 km (about 10 times larger than the ion inertial length) [which] is higher ... Reply: Done. (page 1, lines 4–5) – ... of plasma physical (and not fluid mechanical) [processes]. Reply: Done. (page 1, line 7) Introduction – ... [A] Fourier representation of the two-time[] two-point... Reply: Done. (page 1, line 11) –...

We consider the homogenization of nonlinear random parabolic operators. Depending on the ratio between time and spatial scales different homogenization regimes are studied and the homogenization procedure is carried out. The parameter dependent auxiliary problem is investigated and used in the construction of the homogenized operator.

This paper studies the index system of land parcel generalization which is crucial in land use data generalization. We discuss the macro and micro indices of land use data generalization with consideration of spatial scales and landscape pattern. To quantitatively relate the indices and scale and landscape pattern metrics, land use data samples have been collected at multiple spatial scales in ...

We present a formalism to calculate the probability distribution function of a scalar field coarse-grained over some spatial scales with a Gaussian filter at finite temperature. As an application, we investigate the role of subcritical fluctuations in the electroweak phase transition in the minimal standard model. It is concluded that the universe was in a mixed state of true and false vacua al...

The development of the complex and multi-dimensional urban socio-economic system creates impacts on natural capital and human capital, which range from a local to a global scale. An emergy-based multiple spatial scale analysis framework and a rigorous accounting method that can quantify the values of human-made and natural capital losses were proposed in this study. With the intent of comparing...

Since various behavioral movement patterns are likely to be valid within different, unique ranges of spatial and temporal scales (e.g., instantaneous, diurnal, or seasonal) with the corresponding spatial extents, a cross-scale approach is needed for accurate classification of behaviors expressed in movement. Here, we introduce a methodology for the characterization and classification of behavio...