4,532 research outputs found
On the Exponentials of Some Structured Matrices
In this note explicit algorithms for calculating the exponentials of
important structured 4 x 4 matrices are provided. These lead to closed form
formulae for these exponentials. The techniques rely on one particular Clifford
Algebra isomorphism and basic Lie theory. When used in conjunction with
structure preserving similarities, such as Givens rotations, these techniques
extend to dimensions bigger than four.Comment: 19 page
Models of the circumstellar medium of evolving, massive runaway stars moving through the Galactic plane
At least 5 per cent of the massive stars are moving supersonically through
the interstellar medium (ISM) and are expected to produce a stellar wind bow
shock. We explore how the mass loss and space velocity of massive runaway stars
affect the morphology of their bow shocks. We run two-dimensional axisymmetric
hydrodynamical simulations following the evolution of the circumstellar medium
of these stars in the Galactic plane from the main sequence to the red
supergiant phase. We find that thermal conduction is an important process
governing the shape, size and structure of the bow shocks around hot stars, and
that they have an optical luminosity mainly produced by forbidden lines, e.g.
[OIII]. The Ha emission of the bow shocks around hot stars originates from near
their contact discontinuity. The H emission of bow shocks around cool
stars originates from their forward shock, and is too faint to be observed for
the bow shocks that we simulate. The emission of optically-thin radiation
mainly comes from the shocked ISM material. All bow shock models are brighter
in the infrared, i.e. the infrared is the most appropriate waveband to search
for bow shocks. Our study suggests that the infrared emission comes from near
the contact discontinuity for bow shocks of hot stars and from the inner region
of shocked wind for bow shocks around cool stars. We predict that, in the
Galactic plane, the brightest, i.e. the most easily detectable bow shocks are
produced by high-mass stars moving with small space velocities.Comment: 22 pages, 24 figure
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Energetic and Environmental Constraints on the Community Structure of Benthic Microbial Mats in Lake Fryxell, Antarctica.
Ecological communities are regulated by the flow of energy through environments. Energy flow is typically limited by access to photosynthetically active radiation (PAR) and oxygen concentration (O2). The microbial mats growing on the bottom of Lake Fryxell, Antarctica, have well-defined environmental gradients in PAR and (O2). We analyzed the metagenomes of layers from these microbial mats to test the extent to which access to oxygen and light controls community structure. We found variation in the diversity and relative abundances of Archaea, Bacteria and Eukaryotes across three (O2) and PAR conditions: high (O2) and maximum PAR, variable (O2) with lower maximum PAR, and low (O2) and maximum PAR. We found distinct communities structured by the optimization of energy use on a millimeter-scale across these conditions. In mat layers where (O2) was saturated, PAR structured the community. In contrast, (O2) positively correlated with diversity and affected the distribution of dominant populations across the three habitats, suggesting that meter-scale diversity is structured by energy availability. Microbial communities changed across covarying gradients of PAR and (O2). The comprehensive metagenomic analysis suggests that the benthic microbial communities in Lake Fryxell are structured by energy flow across both meter- and millimeter-scales
Group projector generalization of dirac-heisenberg model
The general form of the operators commuting with the ground representation
(appearing in many physical problems within single particle approximation) of
the group is found. With help of the modified group projector technique, this
result is applied to the system of identical particles with spin independent
interaction, to derive the Dirac-Heisenberg hamiltonian and its effective space
for arbitrary orbital occupation numbers and arbitrary spin. This gives
transparent insight into the physical contents of this hamiltonian, showing
that formal generalizations with spin greater than 1/2 involve nontrivial
additional physical assumptions.Comment: 10 page
The Role and Sources of Individual Differences in Critical-Analytic Thinking: a Capsule Overview
Critical-analytic thinking is typically conceived as a meta-construct that arises at the junction of a problem state (i.e., a situation that requires analysis that challenges previous assumptions) and an individual (i.e., an entity with the capacity to exercise critical-analytic thinking). With regard to the latter, there is a substantial body of research focusing on developmental and educational prerequisites for critical-analytic thinking. A less studied aspect of critical-analytic thinking pertains to individual differences, particularly in the set of foundational or componential cognitive skills that embody this construct. The bottom line here is whether, all else being equal (i.e., the same situation and the same developmental/educational stage), there is variation in whether, when, and how people think critically/analytically. We argue that there is unequivocal evidence for both the existence and importance of individual differences in critical-analytic thinking. This review focuses on theoretical and empirical evidence, identifying the cognitive processes that serve as the sources of these individual differences and capturing these processes’ differential contributions to both the critical and analytic components of this construct.National Institutes of Health (U.S.) (Grant HD079143
Stein Points
An important task in computational statistics and machine learning is to approximate a posterior distribution with an empirical measure supported on a set of representative points . This paper focuses on methods where the selection of points is essentially deterministic, with an emphasis on achieving accurate approximation when is small. To this end, we present `Stein Points'. The idea is to exploit either a greedy or a conditional gradient method to iteratively minimise a kernel Stein discrepancy between the empirical measure and . Our empirical results demonstrate that Stein Points enable accurate approximation of the posterior at modest computational cost. In addition, theoretical results are provided to establish convergence of the method
On positive solutions and the Omega limit set for a class of delay differential equations
This paper studies the positive solutions of a class of delay differential
equations with two delays. These equations originate from the modeling of
hematopoietic cell populations. We give a sufficient condition on the initial
function for such that the solution is positive for all time .
The condition is "optimal". We also discuss the long time behavior of these
positive solutions through a dynamical system on the space of continuous
functions. We give a characteristic description of the limit set of
this dynamical system, which can provide informations about the long time
behavior of positive solutions of the delay differential equation.Comment: 15 pages, 2 figure
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