Mutual information for examining correlations in DNA

This paper examines two methods for finding whether long-range correlations exist in DNA: a fractal measure and a mutual information technique. We evaluate the performance and implications of these methods in detail. In particular we explore their use comparing DNA sequences from a variety of sources. Using software for performing in silico mutations, we also consider evolutionary events leading to long range correlations and analyse these correlations using the techniques presented. Comparisons are made between these virtual sequences, randomly generated sequences, and real sequences. We also explore correlations in chromosomes from different species.Comment: 8 pages, 3 figure

Estimates of frequency-dependent compressibility from a quasistatic double-porosity model

Gassmann's relationship between the drained and undrained bulk modulus of a porous medium is often used to relate the dry bulk modulus to the saturated bulk modulus for elastic waves, because the compressibility of air is considered so high that the dry rock behaves in a drained fashion and the frequency of elastic waves is considered so high that the saturated rock behaves in an undrained fashion. The bulk modulus calculated from ultrasonic velocities, however, often does not match the Gassmann prediction. Mavko and Jizba examined how local flow effects and unequilibrated pore pressures can lead to greater stiffnesses. Their conceptual model consists of a distribution of porosities obtained from the strain-versus-confining-pressure behavior. Stiff pores that close at higher confining pressures are considered to remain undrained (unrelaxed) while soft pores drain even for high-frequency stress changes. If the pore shape distribution is bimodal, then the rock approximately satisfies the assumptions of a double-porosity, poroelastic material. Berryman and Wang [1995] established linear constitutive equations and identified four different time scales of ow behavior: (1) totally drained, (2) soft pores are drained but stiff pores are undrained, (3) soft and stiff pores are locally equilibrated, but undrained beyond the grain scale, and (4) both soft and stiff pores are undrained. The relative magnitudes of the four associated bulk moduli will be examined for all four moduli and illustrated for several sandstones

Target characterization using decomposition of the time-reversal operator: electromagnetic scattering from small ellipsoids

Decomposition of the time-reversal operator for an array, or equivalently the singular value decomposition of the multistatic response matrix, has been used to improve imaging and localization of targets in complicated media. Typically, each singular value is associated with one scatterer even though it has been shown in several cases that a single scatterer can generate several singular values. In earlier papers Chambers and Berryman [1, 2] showed that a small spherical scatterer can generate up to six singular values depending on the array geometry and sphere composition. It was shown that the existence and characteristics of multiple singular values for each scatterer can, in principle, be used to determine certain properties of the scatterers, e.g. conducting or non-conducting material. In this paper, we extend this analysis to non-spherical targets and show how orientation information about the target may be obtained from the spectrum of singular values. The general properties of the decomposition for small non-spherical dielectric (and possibly conductive) targets in an electromagnetic field are derived and detailed results are obtained for the specific cases of non-magnetic and perfectly conducting needles and disks. It is shown that scatterer orientation can be estimated by tracking the singular values of a linear array as it is rotated around its midpoint

Long-Term Variations in the Growth and Decay Rates of Sunspot Groups

Using the combined Greenwich (1874-1976) and Solar Optical Observatories Network (1977-2009) data on sunspot groups, we study the long-term variations in the mean daily rates of growth and decay of sunspot groups. We find that the minimum and the maximum values of the annually averaged daily mean growth rates are ~52% per day and ~183% per day, respectively, whereas the corresponding values of the annually averaged daily mean decay rates are ~21% per day and ~44% per day, respectively. The average value (over the period 1874-2009) of the growth rate is about 70% more than that of the decay rate. The growth and the decay rates vary by about 35% and 13%, respectively, on a 60-year time-scale. From the beginning of Cycle 23 the growth rate is substantially decreased and near the end (2007-2008) the growth rate is lowest in the past about 100 years.Comment: 1 table, 13 figures, accepted by Solar Physic

Simulations of dynamic crack propagation in brittle materials using nodal cohesive forces and continuum damage mechanics in the distinct element code LDEC

Experimental data indicates that the limiting crack speed in brittle materials is less than the Rayleigh wave speed. One reason for this is that dynamic instabilities produce surface roughness and microcracks that branch from the main crack. These processes increase dissipation near the crack tip over a range of crack speeds. When the scale of observation (or mesh resolution) becomes much larger than the typical sizes of these features, effective-medium theories are required to predict the coarse-grained fracture dynamics. Two approaches to modeling these phenomena are described and used in numerical simulations. The first approach is based on cohesive elements that utilize a rate-dependent weakening law for the nodal cohesive forces. The second approach uses a continuum damage model which has a weakening effect that lowers the effective Rayleigh wave speed in the material surrounding the crack tip. Simulations in this paper show that while both models are capable of increasing the energy dissipated during fracture when the mesh size is larger than the process zone size, only the continuum damage model is able to limit the crack speed over a range of applied loads. Numerical simulations of straight-running cracks demonstrate good agreement between the theoretical predictions of the combined models and experimental data on dynamic crack propagation in brittle materials. Simulations that model crack branching are also presented

Numerical model for granular compaction under vertical tapping

A simple numerical model is used to simulate the effect of vertical taps on a packing of monodisperse hard spheres. Our results are in agreement with an experimantal work done in Chicago and with other previous models, especially concerning the dynamics of the compaction, the influence of the excitation strength on the compaction efficiency, and some ageing effects. The principal asset of the model is that it allows a local analysis of the packings. Vertical and transverse density profiles are used as well as size and volume distributions of the pores. An interesting result concerns the appearance of a vertical gradient in the density profiles during compaction. Furthermore, the volume distribution of the pores suggests that the smallest pores, ranging in size between a tetrahedral and an octahedral site, are not strongly affected by the tapping process, in contrast to the largest pores which are more sensitive to the compaction of the packing.Comment: 8 pages, 15 figures (eps), to be published in Phys. Rev. E. Some corrections have been made, especially in paragraph IV

Packing of Compressible Granular Materials

3D Computer simulations and experiments are employed to study random packings of compressible spherical grains under external confining stress. Of particular interest is the rigid ball limit, which we describe as a continuous transition in which the applied stress vanishes as (\phi-\phi_c)^\beta, where \phi is the (solid phase) volume density. This transition coincides with the onset of shear rigidity. The value of \phi_c depends, for example, on whether the grains interact via only normal forces (giving rise to random close packings) or by a combination of normal and friction generated transverse forces (producing random loose packings). In both cases, near the transition, the system's response is controlled by localized force chains. As the stress increases, we characterize the system's evolution in terms of (1) the participation number, (2) the average force distribution, and (3) visualization techniques.Comment: 4 pages, 7 figures, to appear in Phys. Rev. Let

Random Packings of Frictionless Particles

We study random packings of frictionless particles at T=0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows and its peak approaches random close-packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.Comment: 4 pages, 3 figure