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Scale Invariant (scale + invariant)

Distribution by Scientific Domains

Physics and Astronomy	50%

Selected Abstracts

The role of spatial scale and the perception of large-scale species-richness patterns

ECOLOGY LETTERS, Issue 2 2005
Carsten Rahbek
Abstract Despite two centuries of exploration, our understanding of factors determining the distribution of life on Earth is in many ways still in its infancy. Much of the disagreement about governing processes of variation in species richness may be the result of differences in our perception of species-richness patterns. Until recently, most studies of large-scale species-richness patterns assumed implicitly that patterns and mechanisms were scale invariant. Illustrated with examples and a quantitative analysis of published data on altitudinal gradients of species richness (n = 204), this review discusses how scale effects (extent and grain size) can influence our perception of patterns and processes. For example, a hump-shaped altitudinal species-richness pattern is the most typical (c. 50%), with a monotonic decreasing pattern (c. 25%) also frequently reported, but the relative distribution of patterns changes readily with spatial grain and extent. If we are to attribute relative impact to various factors influencing species richness and distribution and to decide at which point along a spatial and temporal continuum they act, we should not ask only how results vary as a function of scale but also search for consistent patterns in these scale effects. The review concludes with suggestions of potential routes for future analytical exploration of species-richness patterns. [source]

Nonlocal quantum gravity and the size of the universe

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6-7 2004
M. Reuter
Motivated by the conjecture that the cosmological constant problem is solved by strong quantum effects in the infrared we use the exact flow equation of Quantum Einstein Gravity to determine the renormalization group behavior of a class of nonlocal effective actions. They consist of the Einstein-Hilbert term and a general nonlinear function Fk(V) of the Euclidean spacetime volume V. For the V + V ln V -invariant the renormalization group running enormously suppresses the value of the renormalized curvature which results from Planck-size parameters specified at the Planck scale. One obtains very large, i.e., almost flat universes without finetuning the cosmological constant. A critical infrared fixed point is found where gravity is scale invariant. [source]

On circuit models for quantum-classical networks,

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5-6 2007
Árpád I. Csurgay
Abstract Physics is not scale invariant, and today the scale of atoms and molecules challenges designers of machines in which quantum effects have dominant sway. What role could circuit theory play in designing machines described by quantum-classical models? Classical equivalent circuits do exist for systems composed of metal contacted and wired devices, such as resonant tunneling diodes, single electron transistors, metal,insulator,metal diodes, etc. circuits, but not for quantum-entangled networks, such as multi-quantum-state atoms. If devices were not contacted and wired by macroscopic metals, i.e. devices were classically field coupled, then generalized circuit models can be introduced. Case studies have been presented on the role of circuit models in quantum-classical systems. However, there are no ideal circuit elements capable of capturing the port properties of quantum-mechanical and/or quantum-optical subsystems and their coupling to classical waveguides or cavities. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Conductance distribution at criticality: one-dimensional Anderson model with random long-range hopping

ANNALEN DER PHYSIK, Issue 12 2009
A. Méndez
Abstract We study numerically the conductance distribution function w(T) for the one-dimensional Anderson model with random long-range hopping described by the Power-law Banded Random Matrix model at criticality. We concentrate on the case of two single-channel leads attached to the system. We observe a smooth transition from localized to delocalized behavior in the conductance distribution by increasing b, the effective bandwidth of the model. Also, for b < 1 we show that w(ln T/Ttyp) is scale invariant, where Ttyp = exp , ln T , is the typical value of T. Moreover, we find that for T < Ttyp, w(ln T/Ttyp) shows a universal behavior proportional to (T/Ttyp) -1/2. [source]