Simple Scaling Properties Research Articles

Fold analysis of crumpled sheets using microcomputed tomography.

Hand-crumpled paper balls involve intricate structure with a network of creases and vertices, yet show simple scaling properties, which suggests self-similarity of the structure. We investigate the internal structure of crumpled papers by the microcomputed tomography (micro-CT) without destroying or unfolding them. From the reconstructed three-dimensional (3D) data, we examine several power laws for the crumpled square sheets of paper of the sizes L=50-300mm and obtain the mass fractal dimension D_{M}=2.7±0.1 by the relation between the mass and the radius of gyration of the balls and the fractal dimension 2.5≲d_{f}≲2.8 for the internal structure of each crumpled paper ball by the box counting method in the real space and the structure factors in the Fourier space. The data for the paper sheets are consistent with D_{M}=d_{f}, suggesting that the self-similarity in the structure of each crumpled ball gives rise to the similarity among the balls with different sizes. We also examine the cellophane sheets and the aluminium foils of the size L=200mm and obtain 2.6≲d_{f}≲2.8 for both of them. The micro-CT also allows us to reconstruct 3D structure of a line drawn on the crumpled sheets of paper. The Hurst exponent for the root-mean-square displacement along the line is estimated as H≈0.9 for the length scale shorter than the scale of the radius of gyration, beyond which the line structure becomes more random with H∼0.5.

Speed of traveling waves for monotone reaction–diffusion systems as a function of diffusion coefficients

Traveling waves form a basic class of solutions to reaction–diffusion equations, which can describe a large number of phenomena. The basic property characterizing traveling wave solutions is their speed of propagation. In this study we analyze its dependence on the diffusivities of the interacting agents. We show that this dependence is subject to some relations, which can be derived by simple scaling properties. We augment our findings by an investigation of reaction–diffusion systems describing intercellular calcium dynamics in the presence of buffer molecules. We establish some mathematical results concerning the behavior of the velocity of traveling waves in the case of fast buffer kinetics, (paying special attention to the vicinity of zero speed), and present outcomes of numerical simulations showing how complicated the interplay between the diffusion coefficients of calcium and buffering molecules can be, especially in models with more than one kind of buffer molecules.

Characterizing extreme rainfalls and constructing confidence intervals for IDF curves using Scaling‐GEV distribution model

AbstractThis article compares the performances of three fitting methods (SLmom, S1NCM, and S3NCM) to account for temporal characteristics of Annual Maximum Precipitations (AMPs) on daily and sub‐daily time scales using scaling General Extreme Value (GEV) distribution at a local site. Based on simple scaling properties of AMPs, the temporal downscaling model (called Scaling‐GEV) with parameter estimation methods are used to estimate sub‐daily AMPs from observed daily data. The feasibility and accuracy of the suggested method were assessed using rainfall data available from Dorval in Quebec (Canada) and Seoul (South Korea) for the period 1961–1990. Presence of simple scaling properties of AMPs for two stations has shown that it is feasible to use the temporal downscaling method for describing the linkage between AMPs of different time scales. Numerical and graphical analyses revealed that the Scaling‐GEV distribution by the Three‐Non central moments (NCM) method (S3NCM) provides the most accurate estimates compared to observed data amongst three fitting methods. In addition, this study suggested a modified bootstrap technique to determine confidence intervals (CIs) CIs of extreme rainfall series using the simple scaling properties of extreme rainfalls and only daily AMPs. Although the CIs were constructed by only daily AMPs and the simple scaling properties, the observed sub‐daily AMPs are generally within the 95% CI estimated.

Spatial chirp control of high-intensity 4D pulse focusing for laser-matter interactions

Spatial chirp can be manipulated to control the focusing conditions for materials processing. Our double-ABCD nonparaxial analysis helps to understand and exploit the mechanisms for intensity localization, pulse front tilt, and grating formation, and includes initial spectral phase and detuning of the wavelength crossing plane. We also present a novel method for creating high density, high intensity interference patterns with crossed beams that have no relative pulse front tilt. 1. Non-paraxial double ABCD tracing The properties of space-time focused beams are strongly dependent of the nature of the spatial overlap of the frequency components. The analysis of optical systems with spatial chirp is therefore critical both for understanding the unusual properties of these beams and for designing systems to exploit these properties for materials processing. In a recent paper, we developed an analytical approach to calculate the propagation of spatially chirped beams. A ray is traced that represents the central axis of the Gaussian beamlet for each frequency component. Since one form of the calculation is nonparaxial, the beamlet angles can be large and the calculation is valid over a wider range of conditions than direct Fresnel propagation. Our technique explains, for example, how the evolution of the beamlet radius of curvature leads to an axial variation of the spectral chirp through the focus, contributing to the axial intensity localization. It also allows the derivation of simple scaling properties of the beam, showing that the improvement of the localization over the confocal parameter of the focused beamlets depends primarily on the degree of spatial chirp, not on the initial pulse duration or the focal length.

Localization properties of covariant Lyapunov vectors for quasi-one-dimensional hard disks

The Lyapunov exponent spectrum and covariant Lyapunov vectors are studied for a quasi-one-dimensional system of hard disks as a function of density and system size. We characterize the system using the angle distributions between covariant vectors and the localization properties of both Gram-Schmidt and covariant vectors. At low density there is a kinetic regime that has simple scaling properties for the Lyapunov exponents and the average localization for part of the spectrum. This regime shows strong localization in a proportion of the first Gram-Schmidt and covariant vectors and this can be understood as highly localized configurations dominating the vector. The distribution of angles between neighboring covariant vectors has characteristic shapes depending upon the difference in vector number, which vary over the continuous region of the spectrum. At dense gas- or liquid-like densities the behavior of the covariant vectors are quite different. The possibility of tangencies between different components of the unstable manifold and between the stable and unstable manifolds is explored but it appears that exact tangencies do not occur for a generic chaotic trajectory.

Autonomous multi-sensor micro-system for measurement of ocean water salinity

This paper describes the design, fabrication and application of a micro-fabricated salinity sensor system. The theoretical electrochemical behaviour is described using electrical equivalent diagrams and simple scaling properties are investigated analytically and numerically using finite element method (FEM). The chip design and fabrication is described and measurement results of two different electrode designs are presented. The 4 mm × 4 mm multi-sensor allows for salinity determination with an accuracy of ± 0.5 psu through determination of the electrical conductivity, temperature and pressure with accuracies of ± 0.6 mS, ± 0.065 ° C and ± 0.05 bar, respectively.

K-string tensions at finite temperature and integrable models

It has recently been pointed out that simple scaling properties of Polyakov correlation functions of gauge systems in the confining phase suggest that the ratios of k-string tensions in the low temperature region is constant up to terms of order T^3. Here we argue that, at least in a three-dimensional Z_4 gauge model, the above ratios are constant in the whole confining phase. This result is obtained by combining numerical experiments with known exact results on the mass spectrum of an integrable two-dimensional spin model describing the infrared behaviour of the gauge system near the deconfining transition.

The conformal anomaly of k-strings

Simple scaling properties of correlation functions of a confining gauge theory in d-dimensions lead to the conclusion that k-string dynamics is described, in the infrared limit, by a two-dimensional conformal field theory with conformal anomaly c=(d-2)T_k/T_1, where T_k is the k-string tension. This result applies to any gauge theory with stable k-strings. We check it in a 3D Z_4 gauge model at finite temperature, where a string effect directly related to c can be clearly identified.

A SIMPLE SCALING CHARATERISTICS OF RAINFALL IN TIME AND SPACE TO DERIVE INTENSITY DURATION FREQUENCY RELATIONSHIPS

The properties of time and space scale invariance of rainfall are investigated and applied to Intensity-Duration-Frequency (IDF) relationships. The hypothesis of the simple scaling is examined in time and space in Yodo River basin and the simple scaling properties in time are confirmed, which is used to derive IDF relationships for short-duration rainfall of several hours from the statistical characteristics of daily data only. The derived IDF matches well with the one derived from historical observed data. Also, the simple scaling properties in space are examined. It is found that two ranges less than 1000 km 2 and more than 1000 km 2 show different scale properties.

Particle production in nuclear collisions over a broad centrality range from the PHOBOS experiment

The PHOBOS collaboration has studied the pseudorapidity and transverse momentum distributions of charged particles produced in heavy ion collisions. Results from Au+Au collisions at various center-of-mass energies and over a broad range of centrality are presented here. The data are compared to Cu+Cu, p+p and d+Au collisions at corresponding energies and centralities. The data are found to exhibit simple scaling properties such as the observed factorization of collision energy and geometry dependences. The presented data help us distinguish between models of particle production in relativistic heavy ion collisions.

Sheared Force Networks: Anisotropies, Yielding, and Geometry

A scenario for the yielding of granular matter is presented by considering the ensemble of force networks for a given contact network and applied shear stress tau. As tau is increased, the probability distribution of contact forces becomes highly anisotropic, the difference between average contact forces along minor and major axes grows, and the allowed networks span a shrinking subspace of all force networks. Eventually, contacts start to break, and at the maximal shear stress the packing becomes effectively isostatic. The size of the allowed subspace exhibits simple scaling properties, which lead to a prediction for the yield stress for packings of an arbitrary contact number.

Studies of multiplicity in relativistic heavy-ion collisions

In this talk I'll review the present status of charged particle multiplicity measurements from heavy-ion collisions. The characteristic features of multiplicity distributions obtained in Au+Au collisions will be discussed in terms of collision centrality and energy and compared to those of p+p collisions. Multiplicity measurements of d+Au collisions at 200 GeV nucleon-nucleon center-of-mass energy will also be discussed. The results will be compared to various theoretical models and simple scaling properties of the data will be identified.

Uniform Thin Film Electrodeposition onto Large Circular Wafer Substrates

A wafer-scale electrochemical flow cell specially suited for uniform thin-film electrodeposition is presented. The cell consists of a porous disk injector set parallel and coaxial to a working disk electrode with a narrow separation gap between them. The porous injector was designed to supply a uniform axial flow of electrolyte onto the surface of the working disk electrode. The mass transfer characteristics of the cell and the current distribution on the working disk electrode were studied for various operating conditions, geometric parameters and bath chemistries. The experimental results confirmed the simple scaling properties that were theoretically predicted. It has also been shown that this cell can provide nearly uniform current distribution on the working electrode under conditions of both migration and convective-diffusive mass transfer control. The results indicate that this cell is suitable for uniform thin-film electrodeposition onto large circular wafer substrates.

Simple scaling properties of Canadian annual average streamflow

The spatial scaling properties of Canadian annual average streamflow (abbreviated as AASF) are assessed using both the product moments (PMs) and the probability weighted moments (PWMs) of AASF across the entire country and in its sub-climatic regions. By the PMs, the log relationship between the kth moments of AASF and the drainage area can be almost represented by a perfect straight line across the entire country and in its sub-climatic regions, whose regression parameters are a linear function of the moment order. By the PWMs, the logarithm of the kth PWM is a linear function of the logarithm of drainage area for the entire country and its sub-climatic regions, where its slope (or scale exponent) in a region is constant and is independent of the order. These results indicate that Canadian AASF exhibits simple scaling and drainage area alone may describe most of the variability in the moments of AASF. The third approach, based on the log linearity between quantiles and drainage area, is applied to Region 2, also demonstrate simple scaling of AASF in that region, as concluded from using PMs and PWMs methods, which indicates that all three methods are consistent. The simple scaling results provide a basis for using the index flood method to conduct regional frequency analysis of AASF in Canada.

Mode coupling in the nonlinear response of black holes

We study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes.

Traveling waves in a model of influenza A drift

Between major pandemics, the influenza A virus changes its antigenic properties by accumulating point mutations (drift) mainly in the RNA genes that code for the surface proteins hemagglutinin (HA) and neuraminidase (NA). The successful strain (variant) that will cause the next epidemic is selected from a reduced number of progenies that possess relatively high transmissibility and the ability to escape from the immune surveillance of the host. In this paper, we analyse a one-dimensional model of influenza A drift (Z. Angew. Math. Mech. 76 (2) (1996) 421) that generalizes the classical SIR model by including mutation as a diffusion process in a phenotype space of variants. The model exhibits traveling wave solutions with an asymptotic wave speed that matches well those obtained from numerical simulations. As exact solutions for these waves are not available, asymptotic estimates for the amplitudes of infected and recovered classes are provided through an exponential approximation based on the smallness of the diffusion constant. Through this approximation, we find simple scaling properties to several parameters of relevance to the epidemiology of the disease.

Rayleigh instability of charged droplets in the presence of counterions

The classical instability of a charged spherical droplet is reconsidered in the presence of counterions. An ensemble of such droplets is studied within a simplified cell model. Screening of the electric field by the counterions is found to increase the equilibrium droplet size. Furthermore, if the ions can enter the droplet, a first-order phase transition occurs upon increasing Bjerrum length, surface tension or droplet density, leading to a phase separation. Simple scaling properties of the free energy give the shape of the phase boundary and show the system to be scale-invariant there. Pearl-necklace structures of hydrophobic polyelectrolytes are discussed as an application.

Stochastic heterostructures and diodium in B/N-doped carbon nanotubes.

Carbon nanotubes are one dimensional and very narrow. These obvious facts imply that, under doping with boron and nitrogen, microscopic doping inhomogeneity is much more important than for bulk semiconductors. We consider the possibility of exploiting such fluctuations to create interesting devices. Using the self-consistent tight-binding technique, we study heavily doped highly compensated nanotubes, revealing the spontaneous formation of structures resembling chains of random quantum dots, or nanoscale diodelike elements in series. We also consider truly isolated impurities, revealing simple scaling properties of bound state sizes and energies.

Mesoscopic magnetization fluctuations for metallic grains close to the Stoner instability

This paper is devoted to the magnetic properties of isolated mesoscopic grains. We demonstrate that under very general conditions the electron-electron interactions in such grains can be taken into account by a simple interaction Hamiltonian. This Hamiltonian involves only three coupling constants, which correspond to charging, exchange interaction, and superconducting correlations. The most important condition for such a description is that Thouless conductance of each grain is large. Under this condition sample-to-sample fluctuations of the coupling constants can be neglected. However, the thermodynamic properties can still remain sample specific due to the one-electron part of the Hamiltonian. If the grain is made from a material that is close to the threshold of ferromagnetic instability, the mesoscopic fluctuations of the magnetization are especially strong. Moreover, the situation becomes multistable: free energy of each grain as a function of the magnetization is characterized by a large number of local minima. We analyze the statistics of these minima and show that it possesses simple scaling properties. Numerical simulations confirm this scaling.

Monopole, quadrupole and pairing: a shell model view

The three main contributions to the nuclear Hamiltonian–monopole, quadrupole and pairing–are analyzed in a shell model context. The first has to be treated phenomenologically, while the other two can be reliably extracted from the realistic interactions. Due to simple scaling properties, the realistic quadrupole and pairing interactions eliminate the tendency to collapse of their conventional counterparts, while retaining their basic simplicity.