Complementary Fraction Research Articles

An evolutionary Cournot model with limited market knowledge

In this paper we analyze a dynamic game of Cournot competition with heterogeneous firms choosing between two different adaptive behavioral rules in deciding output strategies. The underlying oligopoly structure is standard: using a constant return to scale technology, N firms produce homogeneous goods, which are sold in a market characterized by constant price elasticity. In this setup, we assume that a fraction of firms employs a quite rough rule of thumb, the so-called Local Monopolistic Approximation (LMA), whereas the complementary fraction plays Best Reply (BR), a more demanding strategy in terms of information and computation requirements. The model is first considered with exogenously fixed fractions of firms in the two complementary groups. Then it is generalized by considering an endogenous evolutionary switching process between the two behavioral strategies based on profit-driven replicator dynamics. The role of the number of firms, information costs and inertia (or anchoring attitude) in production decisions is analyzed, as well as the influence in the evolutionary process of random noise in the demand function and memory of past profits. Global properties of the oligopoly with evolutionary pressure between behavioral rules are discussed, with particular regard to cases in which the Nash equilibrium is unstable.

The binomial Gini inequality indices and the binomial decomposition of welfare functions

In the context of Social Welfare and Choquet integration, we briefly review, on the one hand, the generalized Gini welfare functions and inequality indices for populations of n≥2 individuals, and on the other hand, the Möbius representation framework for Choquet integration, particularly in the case of k-additive symmetric capacities. We recall the binomial decomposition of OWA functions due to Calvo and De Baets and we examine it in the restricted context of generalized Gini welfare functions, with the addition of appropriate S-concavity conditions. We show that the original expression of the binomial decomposition can be formulated in terms of two equivalent functional bases, the binomial Gini welfare functions and the Atkinson–Kolm–Sen (AKS) associated binomial Gini inequality indices, according to Blackorby and Donaldson's correspondence formula. The binomial Gini pairs of welfare functions and inequality indices are described by a parameter j=1,…,n, associated with the distributional judgements involved. The j-th generalized Gini pair focuses on the (n−j+1)/n poorest fraction of the population and is insensitive to income transfers within the complementary richest fraction of the population.

Temperature-dependent location of a weakly segregated block copolymer in binary blends of block copolymers

The phase behaviors of binary blends of poly(styrene-b-butadiene) block copolymers were investigated by a small-angle X-ray scattering technique. The blends were composed of weakly segregated one in a random micellar phase and the other in a cylindrical phase with similar molecular weights and complementary volume fractions. Morphologies, domain spacings, and order–disorder transition temperatures of the blends indicated that the junctions of the constituent block copolymers share the interface at low temperatures. The domain spacing decreased as temperature increased in a blend with a small amount of the weakly segregated block copolymer. In the cases of the blends with a large amount of the weakly segregated constituent, domain spacing increased with increasing temperature. These results implied that some of the weakly segregated block copolymer moved from the interface to one microdomain at higher temperatures. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 470–476

Integrated biological–chemical approach for the isolation and selection of polyaromatic mutagens in surface waters

Many environmental mutagens, including polyaromatic compounds are present in surface waters, often in complex mixtures and at low concentrations. The present study provides and applies a novel, integrated approach to isolate polyaromatic mutagens in river water using a sample from the River Elbe. The sample was taken downstream of industrial discharges using blue rayon (BR) as a passive sampler that selectively adsorbs polyaromatic compounds and was subjected to effect-directed fractionation in order to characterise the compounds causing the detected effect(s). The procedure relies on three complementary fractionation steps, the Ames fluctuation assay with strains TA98, YG1024 and YG1041 with and without S9 activation and analytical screening. Several mutagenic fractions were isolated by combining mutagenicity testing with fractionation. The enhanced mutagenicity in the nitroreductase and/or O-acetyltransferase overexpressing strains YG1024 and YG1041 strains suggested amino- and/or nitro-compounds causing mutagenicity in several fractions. Analytical screening of mutagenic fractions with LC-HRMS/MS provided a list of molecular formulas typically containing one to ten nitrogen and at least two oxygen atoms supporting the presence of amino and nitro-compounds in the mutagenic fractions.

Alexander duality in experimental designs

If F is a full factorial design and D is a fraction of F, then for a given monomial ordering, the algebraic method gives a saturated polynomial basis for D which can be used for regression. Consider now an algebraic basis for the complementary fraction of D in F, built under the same monomial ordering. We show that the basis for the complementary fraction is the Alexander dual of the first basis, constructed by shifting monomial exponents. For designs with two levels, the Alexander dual uses the traditional definition for simplicial complexes, while for designs with more than two levels, the dual is constructed with respect to the basis for the design F. This yields various new constructions for designs, where the basis and linear aberration can easily be read from the duality.

Role of general melt convection in the development of cryptic layering of intrusive complexes at cratons

The role of melt movement is discussed with reference to the development of phase and cryptic magmatic layering. Differences in the evolution of unmoving and moving melt are controlled by the corresponding types of local equilibria: mosaic and volumetric, respectively. Unmoving melt crystallizes within its marginal gradient zone containing suspension of crystals, and this process gradually extends to the whole melt volume in the chamber. Mineral grains nucleate in the homogeneous melt ahead of the crystallization front. Each crystallization center is immediately surrounded by a locally equilibrated isolated diffusion cell, and hence, only complementary gravitational fractionation of the solid phase from a melt of unchanging composition can take place in unmoving melt. This is the reason for the absence of cryptic layering in the crystallization products. Phase layering is generated by the overlap of batch fractionation with the participation of phase convection, which disturbs the even character of the former, on the continuous process of melt equilibrium crystallization within isolated diffusion cells. Moving melt undergoes in-situ fractional crystallization within a narrow marginal gradient layer. Its composition and temperature systematically change in the course of its consolidation, and this results in the cryptic layering of the crystallization products. The phase layering is controlled by the crystallization sequence of phases on the liquidus at decreasing temperature and by the self-sustained oscillatory process of nucleation in the undercooled melt in the course of cotectic crystallization. It is demonstrated that the origin of layered rock series of the Moncha Tundra and Monchegorsk massifs and one of the world’s largest Stillwater Complex was formed by the crystallization of unmoving melt. Intrusive massifs in the Imandra gabbroid complex in the Monchegorsk district and the Pilgujarvi gabbro-wehrlite complex in the Pechenga district, Kola Peninsula, the Burakovka Massif in southern Karelia, and the Bushveld Complex in South Africa were formed with the participation of overall melt convection. The compositional variations of bodies filling fractures in the root zone of the Monchegorsk Pluton were controlled by the fractional crystallization of mantle melt at the walls of magma conduits during melt ascent to upper crustal levels and provide evidence of variations in the melt velocity.

Mining the surface proteome of tomato (Solanum lycopersicum) fruit for proteins associated with cuticle biogenesis

The aerial organs of plants are covered by the cuticle, a polyester matrix of cutin and organic solvent-soluble waxes that is contiguous with the polysaccharide cell wall of the epidermis. The cuticle is an important surface barrier between a plant and its environment, providing protection against desiccation, disease, and pests. However, many aspects of the mechanisms of cuticle biosynthesis, assembly, and restructuring are entirely unknown. To identify candidate proteins with a role in cuticle biogenesis, a surface protein extract was obtained from tomato (Solanum lycopersicum) fruits by dipping in an organic solvent and the constituent proteins were identified by several complementary fractionation strategies and two mass spectrometry techniques. Of the ∼200 proteins that were identified, a subset is potentially involved in the transport, deposition, or modification of the cuticle, such as those with predicted lipid-associated protein domains. These include several lipid-transfer proteins, GDSL-motif lipase/hydrolase family proteins, and an MD-2-related lipid recognition domain-containing protein. The epidermal-specific transcript accumulation of several of these candidates was confirmed by laser-capture microdissection and quantitative reverse transcription-PCR (qRT-PCR), together with their expression during various stages of fruit development. This indicated a complex pattern of cuticle deposition, and models for cuticle biogenesis and restructuring are discussed.

Multiple environmental determinants of regional species richness and effects of geographic range size

Understanding patterns of species richness at broad geographic extents remains one of the most challenging yet necessary scientific goals of our time. Many hypotheses have been proposed to account for spatial variation in species richness; among them, environmental determinants have played a central role. In this study, we use data on regional bat species richness in the New World to study redundancy and complementarity of three environmental hypotheses: energy, heterogeneity and seasonality. We accomplish this by partitioning variation in species richness among components associated with unique and combined effects of variables from each hypotheses, and by partitioning the overall richness gradient into gradients of species with varying breadths of geographic distribution.These three environmental hypotheses explain most variation in the species richness gradient of all bats, but do not account for all positive spatial autocorrelation at short distances. Although environmental predictors are highly redundant, energy and seasonality explain different and complementary fractions of variation in species richness of all bats. On the other hand, heterogeneity variables contribute little to explain this gradient. However, results change dramatically when richness is estimated for groups of species with different sizes of geographic distribution. First, the amount of variation explained by environment decreases with a decrease in range size; this suggests that richness gradients of small‐ranged species can not be explained as easily as those of broadly distributed species, as has been implied by analyses that do not consider differences in range size among species. Second, the relative contribution of environmental predictors to explained variation also changes with change in range size. Seasonality and energy are good predictors of species with broad distributions, but they loose almost all explanatory power for richness of species with small ranges. In contrast, heterogeneity, which is a relatively poor predictor of richness of species with large ranges, becomes the main predictor of richness gradients of species with restricted distributions. This suggests that range size is a different dimension on which heterogeneity and other environmental characteristics are complementary to each other. Our results suggest that determinants of species richness gradients might be complex, or at least more complex than many studies have previously suggested.

NMR Investigation of the Dynamics of Confined Water in Nafion-Based Electrolyte Membranes at Subfreezing Temperatures

The dynamical characteristics and the thermal analysis of water absorbed in filler-free Nafion and in silica or zirconia phosphate Nafion composites, between 20 and -50 degrees C, were investigated by NMR and DSC techniques. Self-diffusion coefficients and longitudinal NMR relaxation times (T(1)) put in evidence a fraction of water freezing at subzero temperatures. The complementary water fraction remains in the liquid state at least down to -50 degrees C. The freezing point (T(f)) depends on the initial water uptake of the electrolyte membrane and, for similar uptake values, water mobility is favorite in composites systems respect to the filler-free Nafion. By DSC thermograms the hydration water molecules number per sulfonic group in the filler-free Nafion was estimated, obtaining 8 molecules/SO(3)(-) group. In the Nafion/Zr(HPO(4))(2) composite, instead, the number of hydration water is about 20 molecules/ionic group, because of the acid nature of the zirconia particles. Below T(f), the presence of this nonfreezable water fraction allows proton transport, and therefore ensures ionic conductivity also at subzero temperatures.

Imaging igneous rocks on the North Atlantic rifted continental margin

SUMMARY Extruded basalt flows with thicknesses of several kilometres occur ubiquitously along the rifted continental margins of the northern North Atlantic. Their total volume exceeds 1 million km 3 , and may reach several million cubic kilometres. Intruded igneous rock comprising the complementary melt fraction to that extruded at the surface should exist in the lower crust with a volume at least as large as that of the extrusive basalts. To image the extrusive and intrusive igneous rocks on the continental margin near the Faroe Islands, in 2002 we shot a 375 km long deep-penetration seismic profile across the margin using 85 ocean bottom seismometers for wide-angle acquisition and shot a separate reflection profile using a 12 km streamer for optimal imaging. By using large airgun sources tuned to produce low frequency energy we were able to constrain the seismic velocity structure of the whole crust. We imaged not only layering and structure within the extrusive basalts, but also lower-crustal intrusions on the continent–ocean transition (COT). Combination of good velocity control on the lower-crust together with direct imaging of the extrusive basalts enables us to constrain the volumes of extrusive and intrusive igneous rocks produced near the Faroe Islands to be 340–420 and 560–780 km 3 per kilometre along strike, respectively. The COT marked both by high-velocity intrusions and lower-crustal layering is surprisingly narrow, with only 50 km separating unstretched continental crust from fully oceanic crust. In contrast, the extruded basalts flow up to 150 km landward at the paleo-surface.

SU-FF-T-43: Feasibility of Using Radioactive Bone Cement to Treat Vertebral Metastases

Purpose: To evaluate the feasibility of using radioactive bone cement to delivertherapeuticradiation to the vertebral body without undue risk to the spinal cord, i.e. vertebral brachytherapy.Method and Materials: CT‐scan based Monte Carlo N‐Particle radiation transport models, consisting of a three‐dimensional rectangular lattice of 0.625×0.625×1.25‐mm voxels, were created of a T‐12 human cadaveric vertebra. Trabecular and cortical bone were both represented by a spectrum of thirty complementary volume fractions of solid cortical bone and bone marrow, and all soft tissue was represented as a single material. A cylindrical volume of radioactive bone cement was simulated within the model, and two candidate radioisotopes were studied: P‐32 and Sr‐89. Thirty million particle histories were simulated (MCNPX v.2.5.0) to characterize the dose distribution within the vertebral body. Results: The dose distributions for both radioisotopes were axisymmetric about the cement implant and rapidly decreased with increasing distance from the cement. Initial activities of 0.94 mCi and 0.51 mCi for P‐32 and Sr‐89, respectively, would deliver >300 Gy to bone within 1.6 mm of the cement implant and >80 Gy to bone within 2.8 mm, while keeping the dose at 3.4 mm under 45 Gy. Conclusion: The predicted dose distributions show that a therapeuticradiationdose would be delivered to all bone within ∼3 mm of the cement without undue risk to tissue beyond 3.4 mm (such as the spinal cord), indicating preliminary feasibility of this technique. With further development, this technology may yield a clinically‐feasible procedure that would eliminate the need for 10 radiotherapy sessions, making it convenient for the patient, while potentially improving the clinical outcome by delivering a higher dose to the tumor and a lower dose to the spinal cord than conventional radiotherapy. Conflict of Interest (only if applicable): Research sponsored by Bone‐Rad Therapeutics, Inc.

Risk assessment in man and mouse.

Human and mouse subjects tried to anticipate at which of 2 locations a reward would appear. On a randomly scheduled fraction of the trials, it appeared with a short latency at one location; on the complementary fraction, it appeared after a longer latency at the other location. Subjects of both species accurately assessed the exogenous uncertainty (the probability of a short versus a long trial) and the endogenous uncertainty (from the scalar variability in their estimates of an elapsed duration) to compute the optimal target latency for a switch from the short- to the long-latency location. The optimal latency was arrived at so rapidly that there was no reliably discernible improvement over trials. Under these nonverbal conditions, humans and mice accurately assess risks and behave nearly optimally. That this capacity is well-developed in the mouse opens up the possibility of a genetic approach to the neurobiological mechanisms underlying risk assessment.

Na − photolysis in THF: Charge transfer to solvent studied from the donors perspective in <10fs detail

Two and three pulse photolysis experiments on terahydrofuran (THF) solutions of Na(-), utilizing hyperspectral probing, are described. The objective is to probe the extent and duration of energetic correlations between the primary charge transfer to solvent (CTTS) fragments which are an e(-) and Na(0). The latter is characterized by an intense visible absorption spectrum with fine structure reflecting the atom's immediate solvent environment. Pump-probe experiments with approximately 6 fs pulses show that for the majority of irradiated ions, the electron ejection and production of unperturbed Na(0) is effectively over in approximately 15 fs, with no precursors. Three pulse experiments further demonstrate this to be true for nearly all ions irradiated at 3 eV. Thus, the 400 nm data provide a detailed spectral record of the formation and subsequent solvation and polarization of neutral sodium bubbles in THF. Measures are presented for parametrizing the ensuing spectral evolution. In contrast, exciting at 1.5 eV, the red edge of the CTTS band leads to charge transfer with less than unity quantum efficiency. The complementary fraction of absorbing ions is photostable at 800 nm, presumably due to preferential solvent stabilization. Prompt secondary irradiation at 2 microm can complete ionization of that population leading to additional generation of Na(0) but exhibiting much more pronounced spectral structure. Thus, at low photon energies, a short lived correlated and bound electronic excited state is produced with significant yield. These results are discussed in terms of classical models for CTTS spectra, as well as more recent simulations and experiments concerning CTTS in this and other related systems.

On the structure of competitive societies

We model the dynamics of social structure by a simple interacting particle system. The social standing of an individual agent is represented by an integer-valued fitness that changes via two offsetting processes. When two agents interact one advances: the fitter with probability p and the less fit with probability 1-p. The fitness of an agent may also decline with rate r. From a scaling analysis of the underlying master equations for the fitness distribution of the population, we find four distinct social structures as a function of the governing parameters p and r. These include: (i) a static lower-class society where all agents have finite fitness; (ii) an upwardly-mobile middle-class society; (iii) a hierarchical society where a finite fraction of the population belongs to a middle class and a complementary fraction to the lower class; (iv) an egalitarian society where all agents are upwardly mobile and have nearly the same fitness. We determine the basic features of the fitness distributions in these four phases.

New quantum states in the fractional quantum Hall effect regime

It is shown that the new fractional values of the filling factor observed experimentally in the fractional quantum Hall effect (FQHE) regime, ν=4/11, 4/13, 5/13, 5/17, 6/17, 3/8, and 3/10 (and also the complementary fractions 5/8 and 7/11), which do not fit the standard composite fermion model, can be described in the framework of an expanded systematics of the quantum states of the FQHE, based on Halperin’s conjecture of the coexistence of free electrons and bound electron pairs in two-dimensional (2D) systems in the thermodynamic limit. The possibility of existence of bound triplet “Cooper” pairs in a completely polarized state at the lowest spin Landau level may be due to the electron–phonon interaction of 2D electrons with 2D surface acoustic and optical phonons localized near the interface in semiconductor heterostructures. The proposed expanded systematics includes as particular cases the Laughlin model, the early hierarchical models of the FQHE, and the composite fermion model, including certain generalizations of it, and permits a description of absolutely all of the observed fractional values of ν, including fractions with even denominators (in particular, ν=3/8 and 3/10) and also predicts the possibility of existence of new “exotic” fractions (e.g., ν=5/14, 5/16, and 3/20).

Magnetism and charge ordering inFe3O2BO3studied byFe57Mössbauer spectroscopy

The homometallic $\mathrm{Fe}$ ludwigite ${\mathrm{Fe}}_{3}{\mathrm{O}}_{2}{\mathrm{BO}}_{3}$, is an oxyborate with a chain structure of oxygen octahedra occupied by ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ with four different crystallographic sites. We report $^{57}\mathrm{Fe}$ M\ossbauer spectroscopic studies on the magnetic spin arrangements and on the charge ordering in ${\mathrm{Fe}}_{3}{\mathrm{O}}_{2}{\mathrm{BO}}_{3}$, between $4$ and $450\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. From the temperature dependence of the isomer shifts and quadrupole interactions, together with the information from previous x-ray and transport data, we are able to discuss the structural arrangement of ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ and the dynamics of the electronic configurations. Below ${T}_{N1}=112\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ the M\ossbauer spectra show the onset of antiferromagnetic order only for a fraction of the $\mathrm{Fe}$ ions, the complementary fraction remaining paramagnetic down to $74\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Below $74\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ all the sample becomes magnetically ordered, and an increase and a canting of the magnetic hyperfine field for each $\mathrm{Fe}$ ion is observed. This canting is related to the presence of weak ferromagnetism, as proposed from magnetization measurements. Below $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ antiferromagnetic order is found. From M\ossbauer spectra taken under applied external magnetic fields, there is strong evidence for magnetic short-range order above ${T}_{N1}$ involving ferromagnetic clusters. The observed magnetic transitions appear to be clearly related to charge ordering.

Simulation of interaction between two non-depolarizing muscle relaxants: generation of an additive or a supra-additive neuromuscular block.

To examine in a model of neuromuscular transmission the interaction between two non-depolarizing muscle relaxants. An additive or a supra-additive interaction was evaluated as a function of the affinities of acetylcholine and the muscle relaxants for the two binding sites at a single receptor. Affinity of acetylcholine for site1 was postulated to be higher than for site2. Muscle relaxants may display a similar pattern of affinities, a higher affinity for site2, or the affinities may be identical. Receptors with both sites occupied by acetylcholine are activated and, if their concentration at an end plate surpasses the critical threshold, initiate contraction of the associated muscle fiber. The number of contracting muscle fibers determines twitch strength of the whole muscle. Neuromuscular block (NMB) = 1--twitch. NMB was simulated for muscle relaxants acting as single agents or in three types of combinations. (a) Complementary fractions of equieffective concentrations. (b) Variable combinations of equieffective concentrations producing NMB equal to NMB produced by the single muscle relaxant (isobolographic analysis), and (c) NMB-vs.-concentration relationship of single agents and of their combination in a fixed ratio. Additive interaction was simulated for pairs of muscle relaxants displaying identical ratios of affinities. All other pairs produce a supra-additive interaction, more prominent, the more divergent the patterns of affinities. The slopes of NMB-vs.-concentration curves were steeper for supra-additive combinations than for single agents. The simulations define conditions leading to additive or supra-additive interaction and suggest an experimental design suitable to test the results.

Fraction of Design Space Plots for Assessing Mixture and Mixture-Process Designs

Variance dispersion graphs are useful tools for evaluating various types of designs, including mixture and mixture-process designs. They allow an experimenter to see patterns of scaled prediction variances (SPV) throughout a design space. We introduce a complementary fraction of design space (FDS) plot that provides additional information on the distribution of the SPV throughout a design space. These plots display the fraction of design space where the SPV is less than or equal to specific values. The FDS plots for combined mixture-process experiments also show which of the two types of variables has more influence on the SPV. The FDS plots for mixture and mixture-process experiments are developed and then demonstrated with several examples.

The relationships between half-life (t1/2) and mean residence time (MRT) in the two-compartment open body model.

In the one-compartment model following i.v. administration the mean residence time (MRT) of a drug is always greater than its half-life (t(1/2)). However, following i.v. administration, drug plasma concentration (C) versus time (t) is best described by a two-compartment model or a two exponential equation:C=Ae(-alpha t)+Be(-beta t), where A and B are concentration unit-coefficients and alpha and beta are exponential coefficients. The relationships between t(1/2) and MRT in the two-compartment model have not been explored and it is not clear whether in this model too MRT is always greater than t(1/2). In the current paper new equations have been developed that describe the relationships between the terminal t(1/2) (or t(1/2 beta)) and MRT in the two-compartment model following administration of i.v. bolus, i.v. infusion (zero order input) and oral administration (first order input). A critical value (CV) equals to the quotient of (1-ln2) and (1-beta/alpha) (CV=(1-ln2)/(1-beta/alpha)=0.307/(1-beta/alpha)) has been derived and was compared with the fraction (f(1)) of drug elimination or AUC (AUC-area under C vs t curve) associated with the first exponential term of the two-compartment equation (f(1)=A/alpha/AUC). Following i.v. bolus, CV ranges between a minimal value of 0.307 (1-ln2) and infinity. As long as f(1)<CV,MRT>t(1/2) and vice versa, and when f(1)=CV, then MRT=t(1/2). Following i.v. infusion and oral administration the denominator of the CV equation does not change but its numerator increases to (0.307+beta T/2) (T-infusion duration) and (0.307+beta/ka) (ka-absorption rate constant), respectively. Examples of various drugs are provided. For every drug that after i.v. bolus shows two-compartment disposition kinetics the following conclusions can be drawn (a) When f(1)<0.307, then f(1)<CV and thus, MRT>t(1/2). (b) When beta/alpha>ln2, then CV>1>f(1) and thus(,) MRT>t(1/2). (c) When ln2>beta/alpha>(ln4-1), then 1>CV>0.5 and thus, in order for t(1/2)>MRT, f(1) has to be greater than its complementary fraction f(2) (f(1)>f(2)). (d) When beta/alpha<(ln4-1), it is possible that t(1/2)>MRT even when f(2)>f(1), as long as f(1)>CV. (e) As beta gets closer to alpha, CV approaches its maximal value (infinity) and therefore, the chances of MRT>t(1/2) are growing. (f) As beta becomes smaller compared with alpha, beta/alpha approaches zero, the denominator approaches unity and consequently, CV gets its minimal value and thus, the chances of t(1/2)>MRT are growing. (g) Following zero and first order input MRT increases compared with i.v. bolus and so does CV and thus, the chances of MRT>t(1/2) are growing.

Stellar Rotation in Young Clusters: The First 4 Million Years

To investigate what happens to angular momentum during the earliest observable phases of stellar evolution, we searched the literature for periods (P), projected rotational velocities (v sin i), and supporting data on K5–M2 stars (corresponding to masses 0.25–1 M⊙) from the Orion Nebula Cluster and environs, ρ Ophiuchi, TW Hydra, Taurus-Auriga, NGC 2264, Chamaeleon, Lupus, and η Chamaeleonis. We combine these measures of rotation with the stellar R (as determined from Lbol and Teff) to compare the data with two extreme cases: conservation of stellar angular velocity and conservation of stellar angular momentum. Analysis of the P data set suggests that the frequency distribution of periods among the youngest and oldest stars in the sample is indistinguishable, while the v sin i data set reveals a decrease in mean v sin i as a function of age. Both results suggest that a significant fraction of all pre–main-sequence (PMS) stars must evolve at nearly constant angular velocity during the first ~3–5 Myr after they begin their evolution down the convective tracks. Hence, the angular momenta of a significant fraction of pre–main-sequence (PMS) stars must be tightly regulated during the first few million years after they first become observable. This result seems surprising at first glance, because observations of young main-sequence stars reveal a population (30%–40%) of rapidly rotating stars that must begin to spin up at ages t 5 Myr. To determine whether these apparently contradictory results are reconcilable, we use simple models along with our data set to place limits on (1) the fraction of PMS stars that must be regulated, and (2) the complementary fraction that could spin up as a function of time but escape statistical detection given the broad distribution of stellar rotation rates. These models include (1) instantaneous release at the stellar birthline of a given fraction of stars, with the remaining fraction regulated for 10 Myr; (2) all stars regulated initially, with the released fraction varying linearly with time, and timescales for release of half the stars varying from 0.5 to 5 Myr (i.e., all released by 1 to 10 Myr); and (3) a hybrid model that invokes assumptions (1) and (2). In all cases, we find that a modest population (30%–40%) of PMS stars could be released within the first 1 Myr and still produce period distributions statistically consistent with the observed data. This population is large enough to account for the rapid rotators observed among young main-sequence stars of comparable mass. The limits placed by our models on the fraction of regulated and released stars as a function of time are also consistent with the lifetime of accretion disks as inferred from near-IR excesses, and hence with the hypothesis that disk locking accounts for rotation regulation during early PMS phases.