Temporal Variation In The Carrying Capacity Of A Perennial Grass Population

Density dependence and, therefore, K (carrying capacity, equilibrium population size) are central to understanding and predicting changes in population size (N). Although resource levels certainly fluctuate, K has almost always been treated as constant in both theoretical and empirical studies. We quantified temporal variation in K by fitting extensions of standard population dynamic models to 16 annual censuses of a population of the perennial bunch-grass Bouteloua rigidiseta. Variable-K models provided substantially better fits to the data than did models that varied the potential rate of population increase. The distribution of estimated values of K was skewed, with a long right tail (i.e., a few >jackpot> years). The population did not track K closely. Relatively slow responses to changes in K combined with large, rapid changes in K sometimes caused N to be far from K. In 13%-20% of annual intervals, K was so much larger than N that the population's dynamics were best described by geometric growth and the population was, in effect, unregulated. Explicitly incorporating temporal variation in K substantially improved the realism of models with little increase in model complexity and provided novel information about this population's dynamics. Similar methods would be applicable to many other data sets.Integrative Biolog

Effective speed of sound in phononic crystals

A new formula for the effective quasistatic speed of sound $c$ in 2D and 3D periodic materials is reported. The approach uses a monodromy-matrix operator to enable direct integration in one of the coordinates and exponentially fast convergence in others. As a result, the solution for $c$ has a more closed form than previous formulas. It significantly improves the efficiency and accuracy of evaluating $c$ for high-contrast composites as demonstrated by a 2D example with extreme behavior.Comment: 4 pages, 1 figur

Elastodynamics of radially inhomogeneous spherically anisotropic elastic materials in the Stroh formalism

A method is presented for solving elastodynamic problems in radially inhomogeneous elastic materials with spherical anisotropy, i.e.\ materials such that $c_{ijkl}= c_{ijkl}(r)$ in a spherical coordinate system ${r,\theta,\phi}$. The time harmonic displacement field $\mathbf{u}(r,\theta ,\phi)$ is expanded in a separation of variables form with dependence on $\theta,\phi$ described by vector spherical harmonics with $r$-dependent amplitudes. It is proved that such separation of variables solution is generally possible only if the spherical anisotropy is restricted to transverse isotropy with the principal axis in the radial direction, in which case the amplitudes are determined by a first-order ordinary differential system. Restricted forms of the displacement field, such as $\mathbf{u}(r,\theta)$, admit this type of separation of variables solutions for certain lower material symmetries. These results extend the Stroh formalism of elastodynamics in rectangular and cylindrical systems to spherical coordinates.Comment: 15 page

New limits on anomalous contributions to the Wtb vertex

The authors would like to thank the Center for Theoretical Physics of the Physics Department at the New York City College of Technology, for providing computing power from their High-Performance Computing Cluster. The work of M.C.N. Fiolhais was supported by FCT Grant No. SFRH/BPD/100379/2014. The work of C. M. Pease was partly supported by Macaulay Honors College. The authors would also like to thank Juan Antonio Aguilar-Saavedra and Nuno F. Castro for a long time collaboration.The latest and most precise top quark measurements at the LHC and Tevatron are used to establish new limits on the Wtb vertex. Recent results on the measurements of the W-boson helicity fractions and single top quark production cross section are combined in order to establish new limits at 95% CL (confidence level). The allowed regions for these limits are presented, for the first time, in three-dimensional graphics, for both real and imaginary components of the different anomalous couplings, providing a new perspective on the impact of the combination of different physics observables. These results are also combined with the prospected future measurement of the single top quark production cross section and W-boson helicity fractions at the LHC.The authors would like to thank the Center for Theoretical Physics of the Physics Department at the New York City College of Technology, for providing computing power from their High-Performance Computing Cluster. The work of M.C.N. Fiolhais was supported by FCT Grant No. SFRH/BPD/100379/2014. TheworkofC.M.PeasewaspartlysupportedbyMacaulay Honors College. The authors would also like to thank Juan Antonio Aguilar-Saavedra and Nuno F. Castro for a long time collaboration

Ordering in voter models on networks: Exact reduction to a single-coordinate diffusion

We study the voter model and related random-copying processes on arbitrarily complex network structures. Through a representation of the dynamics as a particle reaction process, we show that a quantity measuring the degree of order in a finite system is, under certain conditions, exactly governed by a universal diffusion equation. Whenever this reduction occurs, the details of the network structure and random-copying process affect only a single parameter in the diffusion equation. The validity of the reduction can be established with considerably less information than one might expect: it suffices to know just two characteristic timescales within the dynamics of a single pair of reacting particles. We develop methods to identify these timescales, and apply them to deterministic and random network structures. We focus in particular on how the ordering time is affected by degree correlations, since such effects are hard to access by existing theoretical approaches.Comment: 37 pages, 10 figures. Revised version with additional discussion and simulation results to appear in J Phys

Soft coronal X-rays from \beta{} Pictoris

A type stars are expected to be X-ray dark, yet weak emission has been detected from several objects in this class. We present new Chandra/HRC-I observations of the A5 V star \beta{} Pictoris. It is clearly detected with a flux of 9+-2 10^{-4} counts/s. In comparison with previous data this constrains the emission mechanism and we find that the most likely explanation is an optically thin, collisionally dominated, thermal emission component with a temperature around 1.1 MK. We interpret this component as a very cool and dim corona, with \log L_X/L_{bol}=-8.2 (0.2-2.0 keV). Thus, it seems that \beta{} Pictoris shares more characteristics with cool stars than previously thought.Comment: accepted by ApJ, 5 pages, 2 figure

X ray based displacement measurement for hostile environments

A new method on noncontacting, high temperature extensometry based on the focus and scanning of x rays is currently under development and shows great promise of overcoming limitations associated with available techniques. The chief advantage is the ability to make undisturbed measurements through stratified or flowing gases, smoke, and flame. The system is based on the ability to focus and scan low energy, hard x rays such as those emanating from copper or molybdenum sources. The x rays are focused into a narrow and intense line image which can be scanned onto targets that fluoresce secondary x ray radiation. The final goal of the system is the ability to conduct macroscopic strain measurements in hostile environments by utilizing two or more fluorescing targets. Current work is limited to displacement measurement of a single target with a resolution of 1.25 micro-m and a target temperature of 1200 C, directly through an open flame. The main advantage of the technique lies in the penetrating nature of x rays which are not affected by the presence of refracting gas layers, smoke, flame, or intense thermal radiation, all of which could render conventional extensometry methods inoperative or greatly compromise their performance

The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

Byzantine Gathering in Networks

This paper investigates an open problem introduced in [14]. Two or more mobile agents start from different nodes of a network and have to accomplish the task of gathering which consists in getting all together at the same node at the same time. An adversary chooses the initial nodes of the agents and assigns a different positive integer (called label) to each of them. Initially, each agent knows its label but does not know the labels of the other agents or their positions relative to its own. Agents move in synchronous rounds and can communicate with each other only when located at the same node. Up to f of the agents are Byzantine. A Byzantine agent can choose an arbitrary port when it moves, can convey arbitrary information to other agents and can change its label in every round, in particular by forging the label of another agent or by creating a completely new one. What is the minimum number M of good agents that guarantees deterministic gathering of all of them, with termination? We provide exact answers to this open problem by considering the case when the agents initially know the size of the network and the case when they do not. In the former case, we prove M=f+1 while in the latter, we prove M=f+2. More precisely, for networks of known size, we design a deterministic algorithm gathering all good agents in any network provided that the number of good agents is at least f+1. For networks of unknown size, we also design a deterministic algorithm ensuring the gathering of all good agents in any network but provided that the number of good agents is at least f+2. Both of our algorithms are optimal in terms of required number of good agents, as each of them perfectly matches the respective lower bound on M shown in [14], which is of f+1 when the size of the network is known and of f+2 when it is unknown