Defining the ‘modified Griffin plot’ in vortex-induced vibration: revealing the effect of Reynolds number using controlled damping

In the present work, we study the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow. We employ a technique to accurately control the structural damping, enabling the system to take on both negative and positive damping. This permits a systematic study of the effects of system mass and damping on the peak vibration response. Previous experiments over the last 30 years indicate a large scatter in peak-amplitude data ($A^*$) versus the product of mass–damping ($\alpha$), in the so-called ‘Griffin plot’. A principal result in the present work is the discovery that the data collapse very well if one takes into account the effect of Reynolds number ($\mbox{\textit{Re}}$), as an extra parameter in a modified Griffin plot. Peak amplitudes corresponding to zero damping ($A^*_{{\alpha}{=}0}$), for a compilation of experiments over a wide range of $\mbox{\textit{Re}}\,{=}\,500-33000$, are very well represented by the functional form $A^*_{\alpha{=}0} \,{=}\, f(\mbox{\textit{Re}}) \,{=}\, \log(0.41\,\mbox{\textit{Re}}^{0.36}$). For a given $\mbox{\textit{Re}}$, the amplitude $A^*$ appears to be proportional to a function of mass–damping, $A^*\propto g(\alpha)$, which is a similar function over all $\mbox{\textit{Re}}$. A good best-fit for a wide range of mass–damping and Reynolds number is thus given by the following simple expression, where $A^*\,{=}\, g(\alpha)\,f(\mbox{\textit{Re}})$: \[ A^* \,{=}\,(1 - 1.12\,\alpha + 0.30\,\alpha^2)\,\log (0.41\,\mbox{\textit{Re}}^{0.36}). \] In essence, by using a renormalized parameter, which we define as the ‘modified amplitude’, $A^*_M\,{=}\,A^*/A^*_{\alpha{=}0}$, the previously scattered data collapse very well onto a single curve, $g(\alpha)$, on what we refer to as the ‘modified Griffin plot’. There has also been much debate over the last three decades concerning the validity of using the product of mass and damping (such as $\alpha$) in these problems. Our results indicate that the combined mass–damping parameter ($\alpha$) does indeed collapse peak-amplitude data well, at a given $\mbox{\textit{Re}}$, independent of the precise mass and damping values, for mass ratios down to $m^*\,{=}\,1$.

The Mechanical Genome in Regulation and Infection

Biological information storage and retrieval is a dynamic process that requires the genome to undergo dramatic structural rearrangements. Recent advances in single-molecule techniques have allowed precise quantification of the nano-mechanical properties of DNA [1, 2], and direct in vivo observation of molecules in action [3]. In this work, we will examine elasticity in protein-mediated DNA looping, whose structural rearrangement is essential for transcriptional regulation in both prokaryotes and eukaryotes. We will look at hydrodynamics in the process of viral DNA ejection, which mediates information transfer and exchange and has prominent implications in evolution. As in the case of Kepler's laws of planetary motion leading to Newton's gravitational theory, and the allometric scaling laws in biology revealing the organizing principles of complex networks [4], experimental data collapse in these biological phenomena has guided much of our studies and urged us to find the underlying physical principles.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

O Modelo de Ising inomogêneo: uma interrupção contínua entre as redes quadrada e triangular.

The ferromagnetic and antiferromagnetic Ising model on a two dimensional inhomogeneous lattice characterized by two exchange constants (J1 and J2) is investigated. The lattice allows, in a continuous manner, the interpolation between the uniforme square (J2 = 0) and triangular (J2 = J1) lattices. By performing Monte Carlo simulation using the sequential Metropolis algorithm, we calculate the magnetization and the magnetic susceptibility on lattices of differents sizes. Applying the finite size scaling method through a data colappse, we obtained the critical temperatures as well as the critical exponents of the model for several values of the parameter α = J2 J1 in the [0, 1] range. The ferromagnetic case shows a linear increasing behavior of the critical temperature Tc for increasing values of α. Inwhich concerns the antiferromagnetic system, we observe a linear (decreasing) behavior of Tc, only for small values of α; in the range [0.6, 1], where frustrations effects are more pronunciated, the critical temperature Tc decays more quickly, possibly in a non-linear way, to the limiting value Tc = 0, cor-responding to the homogeneous fully frustrated antiferromagnetic triangular case.

Income and poverty in a developing economy

We present a stochastic agent-based model for the distribution of personal incomes in a developing economy. We start with the assumption that incomes are determined both by individual labour and by stochastic effects of trading and investment. The income from personal effort alone is distributed about a mean, while the income from trade, which may be positive or negative, is proportional to the trader's income. These assumptions lead to a Langevin model with multiplicative noise, from which we derive a Fokker-Planck (FP) equation for the income probability density function (IPDF) and its variation in time. We find that high earners have a power law income distribution while the low-income groups have a Levy IPDF. Comparing our analysis with the Indian survey data (obtained from the world bank website: http://go.worldbank.org/SWGZB45DN0) taken over many years we obtain a near-perfect data collapse onto our model's equilibrium IPDF. Using survey data to relate the IPDF to actual food consumption we define a poverty index (Sen A. K., Econometrica., 44 (1976) 219; Kakwani N. C., Econometrica, 48 (1980) 437), which is consistent with traditional indices, but independent of an arbitrarily chosen "poverty line" and therefore less susceptible to manipulation. Copyright © EPLA, 2010.

Out-of-equilibrium dynamical fluctuations in glassy systems

"In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models with short-ranged quenched interactions. The key ingredient for such scaling properties is shown to be the development of a criticallike dynamical correlation length, and not other microscopic details. This robust data collapse may be described in terms of a time-evolving "extreme value" distribution. We develop a theory to describe both the form and evolution of these distributions based on a effective sigma model approach."

Geotechnical Data and Numerical Analysis of Edifice Collapse and Related Hazards at Pacaya Volcano, Guatemala

The continual eruptive activity, occurrence of an ancestral catastrophic collapse, and inherent geologic features of Pacaya volcano (Guatemala) demands an evaluation of potential collapse hazards. This thesis merges techniques in the field and laboratory for a better rock mass characterization of volcanic slopes and slope stability evaluation. New field geological, structural, rock mechanical and geotechnical data on Pacaya is reported and is integrated with laboratory tests to better define the physical-mechanical rock mass properties. Additionally, this data is used in numerical models for the quantitative evaluation of lateral instability of large sector collapses and shallow landslides. Regional tectonics and local structures indicate that the local stress regime is transtensional, with an ENE-WSW sigma 3 stress component. Aligned features trending NNW-SSE can be considered as an expression of this weakness zone that favors magma upwelling to the surface. Numerical modeling suggests that a large-scale collapse could be triggered by reasonable ranges of magma pressure (greater than or equal to 7.7 MPa if constant along a central dyke) and seismic acceleration (greater than or equal to 460 cm/s2), and that a layer of pyroclastic deposits beneath the edifice could have been a factor which controlled the ancestral collapse. Finally, the formation of shear cracks within zones of maximum shear strain could provide conduits for lateral flow, which would account for long lava flows erupted at lower elevations.

Emplacement of pyroclastic deposits offshore Montserrat : insights from 3D seismic data

During the current (1995-present) eruptive phase of the Soufrière Hills volcano on Montserrat, voluminous pyroclastic flows entered the sea off the eastern flank of the island, resulting in the deposition of well-defined submarine pyroclastic lobes. Previously reported bathymetric surveys documented the sequential construction of these deposits, but could not image their internal structure, the morphology or extent of their base, or interaction with the underlying sediments. We show, by combining these bathymetric data with new high-resolution three dimensional (3D) seismic data, that the sequence of previously detected pyroclastic deposits from different phases of the ongoing eruptive activity is still well preserved. A detailed interpretation of the 3D seismic data reveals the absence of significant (> 3. m) basal erosion in the distal extent of submarine pyroclastic deposits. We also identify a previously unrecognized seismic unit directly beneath the stack of recent lobes. We propose three hypotheses for the origin of this seismic unit, but prefer an interpretation that the deposit is the result of the subaerial flank collapse that formed the English's Crater scarp on the Soufrière Hills volcano. The 1995-recent volcanic activity on Montserrat accounts for a significant portion of the sediments on the southeast slope of Montserrat, in places forming deposits that are more than 60. m thick, which implies that the potential for pyroclastic flows to build volcanic island edifices is significant.

Multi-stage collapse events in the South Soufrière Hills, Montserrat as recorded in marine sediment cores

We present new evidence for sector collapses of the South Soufrière Hills (SSH) edifice, Montserrat during the mid-Pleistocene. High-resolution geophysical data provide evidence for sector collapse, producing an approximately 1 km3 submarine collapse deposit to the south of SSH. Sedimentological and geochemical analyses of submarine deposits sampled by sediment cores suggest that they were formed by large multi-stage flank failures of the subaerial SSH edifice into the sea. This work identifies two distinct geochemical suites within the SSH succession on the basis of trace-element and Pb-isotope compositions. Volcaniclastic turbidites in the cores preserve these chemically heterogeneous rock suites. However, the subaerial chemostratigraphy is reversed within the submarine sediment cores. Sedimentological analysis suggests that the edifice failures produced high-concentration turbidites and that the collapses occurred in multiple stages, with an interval of at least 2 ka between the first and second failure. Detailed field and petrographical observations, coupled with SEM image analysis, shows that the SSH volcanic products preserve a complex record of magmatic activity. This activity consisted of episodic explosive eruptions of andesitic pumice, probably triggered by mafic magmatic pulses and followed by eruptions of poorly vesiculated basaltic scoria, and basaltic lava flows.

Submarine record of volcanic island construction and collapse in the Lesser Antilles arc: First scientific drilling of submarine volcanic island landslides by IODP Expedition 340

IODP Expedition 340 successfully drilled a series of sites offshore Montserrat, Martinique and Dominica in the Lesser Antilles from March to April 2012. These are among the few drill sites gathered around volcanic islands, and the first scientific drilling of large and likely tsunamigenic volcanic island-arc landslide deposits. These cores provide evidence and tests of previous hypotheses for the composition and origin of those deposits. Sites U1394, U1399, and U1400 that penetrated landslide deposits recovered exclusively seafloor sediment, comprising mainly turbidites and hemipelagic deposits, and lacked debris avalanche deposits. This supports the concepts that i/ volcanic debris avalanches tend to stop at the slope break, and ii/ widespread and voluminous failures of preexisting low-gradient seafloor sediment can be triggered by initial emplacement of material from the volcano. Offshore Martinique (U1399 and 1400), the landslide deposits comprised blocks of parallel strata that were tilted or microfaulted, sometimes separated by intervals of homogenized sediment (intense shearing), while Site U1394 offshore Montserrat penetrated a flat-lying block of intact strata. The most likely mechanism for generating these large-scale seafloor sediment failures appears to be propagation of a decollement from proximal areas loaded and incised by a volcanic debris avalanche. These results have implications for the magnitude of tsunami generation. Under some conditions, volcanic island landslide deposits composed of mainly seafloor sediment will tend to form smaller magnitude tsunamis than equivalent volumes of subaerial block-rich mass flows rapidly entering water. Expedition 340 also successfully drilled sites to access the undisturbed record of eruption fallout layers intercalated with marine sediment which provide an outstanding high-resolution data set to analyze eruption and landslides cycles, improve understanding of magmatic evolution as well as offshore sedimentation processes.

Late Svecofennian leucogranites of southern Finland : Chronicles of an orogenic collapse

Leucogranite magmatism occurred in southern Finland during the later stages of the Paleoproterozoic Svecofennian orogeny. The leucogranites are considered to have formed from pre-existing crustal rocks that have undergone anatexis in the extensional stage of the orogeny, following continental collision and resultant crustal thickening. The leucogranites have been studied in the field using petrographic and mineralogical methods, elemental and isotope geochemistry on whole rocks and minerals, and U-Pb geochronology. On outcrop scale, these granites typically form heterogeneous, layered, sheet-like bodies that migmatize their country rocks. All of the leucogranites are peraluminous and rich in SiO2, but otherwise display significant geochemical variation. Their Nd isotope composition ranges from fairly juvenile to very unradiogenic, and the Hf isotope composition of their zircon shows a varying degree of mixing in the source, the zircon populations becoming more heterogeneous and generally less radiogenic towards the east. The leucogranites have been dated using U-Pb isotopic analyses, utilizing thermal ionization mass spectrometry, secondary ion mass spectrometry, and laser ablation multicollector ICP mass spectrometry on zircon and monazite. The results show that the granites were emplaced between 1.85 Ga and 1.79 Ga, which is a considerably longer period than has traditionally been perceived for these rocks. The rocks tend to become younger towards the east. Single crystal data also display a wide array of inherited zircons, especially in the eastern part of the leucogranite belt. The most common inherited age groups are ~2.8 2.5 Ga, ~2.1 2.1 Ga, and ~1.9 Ga. Magmatic zircon and monazite usually record similar ages for any one sample.Thermobarometric calculations indicate that the leucogranites in the Veikkola area of southcentral Finland were formed from relatively low-temperature melts, and emplaced at 17-25 km depth, i.e. at mid-crustal level. It is likely that these conditions apply to the Svecofennian leucogranites in general. Large differences in the Hf and Nd isotope compositions, emplacement ages, and distributions of inherited zircon ages show that these granites were formed from different types of source rocks, which probably included both sedimentary and igneous rocks.

Averting biodiversity collapse in tropical forest protected areas

The rapid disruption of tropical forests probably imperils global biodiversity more than any other contemporary phenomenon(1-3). With deforestation advancing quickly, protected areas are increasingly becoming final refuges for threatened species and natural ecosystem processes. However, many protected areas in the tropics are themselves vulnerable to human encroachment and other environmental stresses(4-9). As pressures mount, it is vital to know whether existing reserves can sustain their biodiversity. A critical constraint in addressing this question has been that data describing a broad array of biodiversity groups have been unavailable for a sufficiently large and representative sample of reserves. Here we present a uniquely comprehensive data set on changes over the past 20 to 30 years in 31 functional groups of species and 21 potential drivers of environmental change, for 60 protected areas stratified across the world's major tropical regions. Our analysis reveals great variation in reserve `health': about half of all reserves have been effective or performed passably, but the rest are experiencing an erosion of biodiversity that is often alarmingly widespread taxonomically and functionally. Habitat disruption, hunting and forest-product exploitation were the strongest predictors of declining reserve health. Crucially, environmental changes immediately outside reserves seemed nearly as important as those inside in determining their ecological fate, with changes inside reserves strongly mirroring those occurring around them. These findings suggest that tropical protected areas are often intimately linked ecologically to their surrounding habitats, and that a failure to stem broad-scale loss and degradation of such habitats could sharply increase the likelihood of serious biodiversity declines.

Folding of Protein L with Implications for Collapse in the Denatured State Ensemble

A fundamental question in protein folding is whether the coil to globule collapse transition occurs during the initial stages of folding (burst phase) or simultaneously with the protein folding transition. Single molecule fluorescence resonance energy transfer (FRET) and small-angle X-ray scattering (SAXS) experiments disagree on whether Protein L collapse transition occurs during the burst phase of folding. We study Protein L folding using a coarse-grained model and molecular dynamics simulations. The collapse transition in Protein L is found to be concomitant with the folding transition. In the burst phase of folding, we find that FRET experiments overestimate radius of gyration, R-g, of the protein due to the application of Gaussian polymer chain end-to-end distribution to extract R-g from the FRET efficiency. FRET experiments estimate approximate to 6 angstrom decrease in R-g when the actual decrease is approximate to 3 angstrom on guanidinium chloride denaturant dilution from 7.5 to 1 M, thereby suggesting pronounced compaction in the protein dimensions in the burst phase. The approximate to 3 angstrom decrease is close to the statistical uncertainties of the R-g data measured from SAXS experiments, which suggest no compaction, leading to a disagreement with the FRET experiments. The transition-state ensemble (TSE) structures in Protein L folding are globular and extensive in agreement with the Psi-analysis experiments. The results support the hypothesis that the TSE of single domain proteins depends on protein topology and is not stabilized by local interactions alone.

Quantifying Earthquake Collapse Risk of Tall Steel Moment Frame Buildings Using Rupture-to-Rafters Simulations

There is a sparse number of credible source models available from large-magnitude past earthquakes. A stochastic source model generation algorithm thus becomes necessary for robust risk quantification using scenario earthquakes. We present an algorithm that combines the physics of fault ruptures as imaged in laboratory earthquakes with stress estimates on the fault constrained by field observations to generate stochastic source models for large-magnitude (Mw 6.0-8.0) strike-slip earthquakes. The algorithm is validated through a statistical comparison of synthetic ground motion histories from a stochastically generated source model for a magnitude 7.90 earthquake and a kinematic finite-source inversion of an equivalent magnitude past earthquake on a geometrically similar fault. The synthetic dataset comprises of three-component ground motion waveforms, computed at 636 sites in southern California, for ten hypothetical rupture scenarios (five hypocenters, each with two rupture directions) on the southern San Andreas fault. A similar validation exercise is conducted for a magnitude 6.0 earthquake, the lower magnitude limit for the algorithm. Additionally, ground motions from the Mw7.9 earthquake simulations are compared against predictions by the Campbell-Bozorgnia NGA relation as well as the ShakeOut scenario earthquake. The algorithm is then applied to generate fifty source models for a hypothetical magnitude 7.9 earthquake originating at Parkfield, with rupture propagating from north to south (towards Wrightwood), similar to the 1857 Fort Tejon earthquake. Using the spectral element method, three-component ground motion waveforms are computed in the Los Angeles basin for each scenario earthquake and the sensitivity of ground shaking intensity to seismic source parameters (such as the percentage of asperity area relative to the fault area, rupture speed, and risetime) is studied.

Under plausible San Andreas fault earthquakes in the next 30 years, modeled using the stochastic source algorithm, the performance of two 18-story steel moment frame buildings (UBC 1982 and 1997 designs) in southern California is quantified. The approach integrates rupture-to-rafters simulations into the PEER performance based earthquake engineering (PBEE) framework. Using stochastic sources and computational seismic wave propagation, three-component ground motion histories at 636 sites in southern California are generated for sixty scenario earthquakes on the San Andreas fault. The ruptures, with moment magnitudes in the range of 6.0-8.0, are assumed to occur at five locations on the southern section of the fault. Two unilateral rupture propagation directions are considered. The 30-year probabilities of all plausible ruptures in this magnitude range and in that section of the fault, as forecast by the United States Geological Survey, are distributed among these 60 earthquakes based on proximity and moment release. The response of the two 18-story buildings hypothetically located at each of the 636 sites under 3-component shaking from all 60 events is computed using 3-D nonlinear time-history analysis. Using these results, the probability of the structural response exceeding Immediate Occupancy (IO), Life-Safety (LS), and Collapse Prevention (CP) performance levels under San Andreas fault earthquakes over the next thirty years is evaluated.

Furthermore, the conditional and marginal probability distributions of peak ground velocity (PGV) and displacement (PGD) in Los Angeles and surrounding basins due to earthquakes occurring primarily on the mid-section of southern San Andreas fault are determined using Bayesian model class identification. Simulated ground motions at sites within 55-75km from the source from a suite of 60 earthquakes (Mw 6.0 − 8.0) primarily rupturing mid-section of San Andreas fault are considered for PGV and PGD data.