1,394 research outputs found
A Complexity View of Rainfall
We show that rain events are analogous to a variety of nonequilibrium
relaxation processes in Nature such as earthquakes and avalanches. Analysis of
high-resolution rain data reveals that power laws describe the number of rain
events versus size and number of droughts versus duration. In addition, the
accumulated water column displays scale-less fluctuations. These statistical
properties are the fingerprints of a self-organized critical process and may
serve as a benchmark for models of precipitation and atmospheric processes.Comment: 4 pages, 5 figure
On two 10th order mock theta identities
We give short proofs of conjectural identities due to Gordon and McIntosh
involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan Journa
Mandelbrot's stochastic time series models
I survey and illustrate the main time series models that Mandelbrot introduced into time series analysis in the 1960s and 1970s. I focus particularly on the members of the additive fractional stable family including LĂ©vy flights and fractional Brownian motion (fBm), noting some of the less wellâknown aspects of this family, such as the cases when the selfâsimilarity exponent H and the Hurst exponent J differ. I briefly discuss the role of multiplicative models in modeling the physics of cascades. I then recount the still littleâknown story of Mandelbrot's work on fractional renewal models in the late 1960s, explaining how these differ from their more familiar fBm counterpart and form a âmissing linkâ between fBm and the problem of random change points. I conclude by highlighting the frontier problem of damped fractional models
Shape complexity and fractality of fracture surfaces of swelled isotactic polypropylene with supercritical carbon dioxide
We have investigated the fractal characteristics and shape complexity of the
fracture surfaces of swelled isotactic polypropylene Y1600 in supercritical
carbon dioxide fluid through the consideration of the statistics of the islands
in binary SEM images. The distributions of area , perimeter , and shape
complexity follow power laws , , and , with the scaling ranges spanning
over two decades. The perimeter and shape complexity scale respectively as
and in two scaling regions delimited by . The fractal dimension and shape complexity increase when the temperature
decreases. In addition, the relationships among different power-law scaling
exponents , , , , and have been derived analytically,
assuming that , , and follow power-law distributions.Comment: RevTex, 6 pages including 7 eps figure
Components of multifractality in the Central England Temperature anomaly series
We study the multifractal nature of the Central England Temperature (CET)
anomaly, a time series that spans more than 200 years. The series is analyzed
as a complete data set and considering a sliding window of 11 years. In both
cases, we quantify the broadness of the multifractal spectrum as well as its
components defined by the deviations from the Gaussian distribution and the
influence of the dependence between measurements. The results show that the
chief contribution to the multifractal structure comes from the dynamical
dependencies, mainly the weak ones, followed by a residual contribution of the
deviations from Gaussianity. However, using the sliding window, we verify that
the spikes in the non-Gaussian contribution occur at very close dates
associated with climate changes determined in previous works by component
analysis methods. Moreover, the strong non-Gaussian contribution found in the
multifractal measures from the 1960s onwards is in agreement with global
results very recently proposed in the literature.Comment: 21 pages, 10 figure
A Bulloch Tapestry
The title for this collection was inspired by a poem by Rita Turner Wall. The poem is included in this book, along with articles by C.D. Sheley, Daniel Good, James D. Morgan, Gregory Alan Baker, Paul T. Marlott, and Charles Bonds, David R. Williams. Topics covered by these articles are the history of the Bill Olliff House; the historical geography of Arcola, New Hope, and Denmark, Georgia; the lives of Luetta Leverette Moore and Amanda Love Smith; and the letters of Confederate soldier Asbury Wesley Hodges. Also included are letters to Union soldier Perry Lovejoy, submitted by Bill Lovejoy and transcribed by Evelyn Mabry. The index to this collection was compiled by Julius Ariail.https://digitalcommons.georgiasouthern.edu/bchs-pubs/1001/thumbnail.jp
Shopping centre siting and modal choice in Belgium: a destination based analysis
Although modal split is only one of the elements considered in decision-making on new shopping malls, it remarkably often arises in arguments of both proponents and opponents. Today, this is also the case in the debate on the planned development of three major shopping malls in Belgium. Inspired by such debates, the present study focuses on the impact of the location of shopping centres on the travel mode choice of the customers. Our hypothesis is that destination-based variables such as embeddedness in the urban fabric, accessibility and mall size influence the travel mode choice of the visitors. Based on modal split data and location characteristics of seventeen existing shopping centres in Belgium, we develop a model for a more sustainable siting policy. The results show a major influence of the location of the shopping centre in relation to the urban form, and of the size of the mall. Shopping centres that are part of a dense urban fabric, measured through population density, are less car dependent. Smaller sites will attract more cyclists and pedestrians. Interestingly, our results deviate significantly from the figures that have been put forward in public debates on the shopping mall issue in Belgium
Actually existing Silk Roads
This article explores the relevance of the concept of Silk Road for understandings patterns of trade and exchange between China, Eurasia and the Middle East. It is based on ethnographic fieldwork in the city of Yiwu, in Chinaâs Zhejiang Province. Yiwu is a node in the global distribution of Chinese âsmall commoditiesâ and home to merchants and traders from across Asia and beyond. The article explores the role played by traders from Afghanistan in connecting the city of Yiwu to markets and trading posts in the world beyond. It seeks to bring attention to the diverse types of networks involved in such forms of trade, as well as their emergence and development over the past thirty years
Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by
certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of
the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is
invariant under the action of certain differential operators which include half
the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit
clusters of size at most k: they vanish when k+1 of their variables are
identified, and they do not vanish when only k of them are identified. We
generalize most of these properties to superspace using orthogonal
eigenfunctions of the supersymmetric extension of the trigonometric
Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular,
we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at
\alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span
an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N
commuting variables and N anticommuting variables. We prove that the ideal
{\mathcal I}^{(k,r)}_N is stable with respect to the action of the
negative-half of the super-Virasoro algebra. In addition, we show that the Jack
superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting
variables are equal, and conjecture that they do not vanish when only k of them
are identified. This allows us to conclude that the standard Jack polynomials
with prescribed symmetry should satisfy similar clustering properties. Finally,
we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for
the subspace of symmetric superpolynomials in N variables that vanish when k+1
commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we
present exceptions to an often made statement concerning the clustering
property of the ordinary Jack polynomials for (k,r,N)-admissible partitions
(see Footnote 2); 2) Conjecture 14 is substantiated with the extensive
computational evidence presented in the new appendix C; 3) the various tests
supporting Conjecture 16 are reporte
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