78,193 research outputs found
Replica Condensation and Tree Decay
We give an intuitive method--using local, cyclic replica symmetry--to isolate
exponential tree decay in truncated (connected) correlations. We give an
expansion and use the symmetry to show that all terms vanish, except those
displaying {\em replica condensation}. The condensation property ensures
exponential tree decay.
We illustrate our method in a low-temperature Ising system, but expect that
one can use a similar method in other random field and quantum field problems.
While considering the illustration, we prove an elementary upper bound on the
entropy of random lattice surfaces
Scaling functions for nonequilibrium fluctuations: A picture gallery
The emergence of non-gaussian distributions for macroscopic quantities in
nonequilibrium steady states is discussed with emphasis on the effective
criticality and on the ensuing universality of distribution functions. The
following problems are treated in more detail: nonequilibrium interface
fluctuations (the problem of upper critical dimension of the
Kardar-Parisi-Zhang equation), roughness of signals displaying Gaussian 1/f
power spectra (the relationship to extreme-value statistics), effects of
boundary conditions (randomness of the digits of pi).Comment: Invited contribution at SPIE conference on Fluctuations and Noise,
Santa Fe, 2003; 9 pages, 6 figure
Topological characterization of antireflective and hydrophobic rough surfaces: are random process theory and fractal modeling applicable?
The random process theory (RPT) has been widely applied to predict the joint
probability distribution functions (PDFs) of asperity heights and curvatures of
rough surfaces. A check of the predictions of RPT against the actual statistics
of numerically generated random fractal surfaces and of real rough surfaces has
been only partially undertaken. The present experimental and numerical study
provides a deep critical comparison on this matter, providing some insight into
the capabilities and limitations in applying RPT and fractal modeling to
antireflective and hydrophobic rough surfaces, two important types of textured
surfaces. A multi-resolution experimental campaign by using a confocal
profilometer with different lenses is carried out and a comprehensive software
for the statistical description of rough surfaces is developed. It is found
that the topology of the analyzed textured surfaces cannot be fully described
according to RPT and fractal modeling. The following complexities emerge: (i)
the presence of cut-offs or bi-fractality in the power-law power-spectral
density (PSD) functions; (ii) a more pronounced shift of the PSD by changing
resolution as compared to what expected from fractal modeling; (iii) inaccuracy
of the RPT in describing the joint PDFs of asperity heights and curvatures of
textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured
surfaces in case of special surface treatments, not accounted by fractal
modeling.Comment: 21 pages, 13 figure
A Method for the Perceptual Optimization of Complex Visualizations
A common problem in visualization applications is the display of one surface overlying another. Unfortunately, it is extremely difficult to do this clearly and effectively. Stereoscopic viewing can help, but in order for us to be able to see both surfaces simultaneously, they must be textured, and the top surface must be made partially transparent. There is also abundant evidence that all textures are not equal in helping to reveal surface shape, but there are no general guidelines describing the best set of textures to be used in this way. What makes the problem difficult to perceptually optimize is that there are a great many variables involved. Both foreground and background textures must be specified in terms of their component colors, texture element shapes, distributions, and sizes. Also to be specified is the degree of transparency for the foreground texture components. Here we report on a novel approach to creating perceptually optimal solutions to complex visualization problems and we apply it to the overlapping surface problem as a test case. Our approach is a three-stage process. In the first stage we create a parameterized method for specifying a foreground and background pair of textures. In the second stage a genetic algorithm is applied to a population of texture pairs using subject judgments as a selection criterion. Over many trials effective texture pairs evolve. The third stage involves characterizing and generalizing the examples of effective textures. We detail this process and present some early results
Optical Diffraction from Fractals with a Structural Transition
A macroscopic characterization of fractals showing up a structural transition
from dense to multibranched growth is made using optical diffraction theory.
Such fractals are generated via the numerical solution of the 2D Poisson and
Biharmonic equations and are compared to more 'regular'irreversible clusters
such as diffusion limited and Laplacian aggregates. The optical diffraction
method enables to identify a decrease of the fractal dimension above the
structural point.Comment: LaTex file; 6 figures upon request to [email protected]**.
IC/94/7
Sedimentology and kinematics of a large, retrogressive growth-fault system in Upper Carboniferous deltaic sediments, western Ireland
Growth faulting is a common feature of many deltaic environments and is vital in determining local sediment dispersal and accumulation, and hence in controlling the resultant sedimentary facies distribution and architecture. Growth faults occur on a range of scales, from a few centimetres to hundreds of metres, with the largest growth faults frequently being under-represented in outcrops that are often smaller than the scale of feature under investigation. This paper presents data from the exceptionally large outcrops of the Cliffs of Moher, western Ireland, where a growth-fault complex affects strata up to 60 m in thickness and extends laterally for 3 km. Study of this Namurian (Upper Carboniferous) growth-fault system enables the relationship between growth faulting and sedimentation to be detailed and permits reconstruction of the kinematic history of faulting. Growth faulting was initiated with the onset of sandstone deposition on a succession of silty mudstones that overlie a thin, marine shale. The decollement horizon developed at the top of the marine shale contact for the first nine faults, by which time aggradation in the hangingwall exceeded 60 m in thickness. After this time, failure planes developed at higher stratigraphic levels and were associated with smaller scale faults. The fault complex shows a dominantly landward retrogressive movement, in which only one fault was largely active at any one time. There is no evidence of compressional features at the base of the growth faults, thus suggesting open-ended slides, and the faults display both disintegrative and non-disintegrative structure. Thin-bedded, distal mouth bar facies dominate the hangingwall stratigraphy and, in the final stages of growth-fault movement, erosion of the crests of rollover structures resulted in the highest strata being restricted to the proximity of the fault. These upper erosion surfaces on the fault scarp developed erosive chutes that were cut parallel to flow and are downlapped by the distal hangingwall strata of younger growth faults
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