2,017 research outputs found
Degree Distribution of Competition-Induced Preferential Attachment Graphs
We introduce a family of one-dimensional geometric growth models, constructed
iteratively by locally optimizing the tradeoffs between two competing metrics,
and show that this family is equivalent to a family of preferential attachment
random graph models with upper cutoffs. This is the first explanation of how
preferential attachment can arise from a more basic underlying mechanism of
local competition. We rigorously determine the degree distribution for the
family of random graph models, showing that it obeys a power law up to a finite
threshold and decays exponentially above this threshold.
We also rigorously analyze a generalized version of our graph process, with
two natural parameters, one corresponding to the cutoff and the other a
``fertility'' parameter. We prove that the general model has a power-law degree
distribution up to a cutoff, and establish monotonicity of the power as a
function of the two parameters. Limiting cases of the general model include the
standard preferential attachment model without cutoff and the uniform
attachment model.Comment: 24 pages, one figure. To appear in the journal: Combinatorics,
Probability and Computing. Note, this is a long version, with complete
proofs, of the paper "Competition-Induced Preferential Attachment"
(cond-mat/0402268
Robust Bain distortion in the premartensite phase of platinum substituted Ni2MnGa magnetic shape memory alloy
The premartensite phase of shape memory and magnetic shape memory alloys
(MSMAs) is believed to be a precursor state of the martensite phase with
preserved austenite phase symmetry. The thermodynamic stability of the
premartensite phase and its relation to the martensitic phase is still an
unresolved issue, even though it is critical to the understanding of the
functional properties of MSMAs. We present here unambiguous evidence for
macroscopic symmetry breaking leading to robust Bain distortion in the
premartensite phase of 10% Pt substituted Ni2MnGa. We show that the robust Bain
distorted premartensite (T2) phase results from another premartensite (T1)
phase with preserved cubic-like symmetry through an isostructural phase
transition. The T2 phase finally transforms to the martensite phase with
additional Bain distortion on further cooling. Our results demonstrate that the
premartensite phase should not be considered as a precursor state with the
preserved symmetry of the cubic austenite phase
The power of choice in network growth
The "power of choice" has been shown to radically alter the behavior of a
number of randomized algorithms. Here we explore the effects of choice on
models of tree and network growth. In our models each new node has k randomly
chosen contacts, where k > 1 is a constant. It then attaches to whichever one
of these contacts is most desirable in some sense, such as its distance from
the root or its degree. Even when the new node has just two choices, i.e., when
k=2, the resulting network can be very different from a random graph or tree.
For instance, if the new node attaches to the contact which is closest to the
root of the tree, the distribution of depths changes from Poisson to a
traveling wave solution. If the new node attaches to the contact with the
smallest degree, the degree distribution is closer to uniform than in a random
graph, so that with high probability there are no nodes in the network with
degree greater than O(log log N). Finally, if the new node attaches to the
contact with the largest degree, we find that the degree distribution is a
power law with exponent -1 up to degrees roughly equal to k, with an
exponential cutoff beyond that; thus, in this case, we need k >> 1 to see a
power law over a wide range of degrees.Comment: 9 pages, 4 figure
Pterodactyl: Thermal Protection System for Integrated Control Design of a Mechanically Deployed Entry Vehicle
The need for precision landing of high mass payloads on Mars and the return of sensitive samples from other planetary bodies to specific locations on Earth is driving the development of an innovative NASA technology referred to as the Deployable Entry Vehicle (DEV). A DEV has the potential to deliver an equivalent science payload with a stowed diameter 3 to 4 times smaller than a traditional rigid capsule configuration. However, the DEV design does not easily lend itself to traditional methods of directional control. The NASA Space Technology Mission Directorate (STMD)s Pterodactyl project is currently investigating the effectiveness of three different Guidance and Control (G&C) systems actuated flaps, Center of Gravity (CG) or mass movement, and Reaction Control System (RCS) for use with a DEV using the Adaptable, Deployable, Entry, and Placement Technology (ADEPT) design. This paper details the Thermal Protection System (TPS) design and associated mass estimation efforts for each of the G&C systems. TPS is needed for the nose cap of the DEV and the flaps of the actuated flap control system. The development of a TPS selection, sizing, and mass estimation method designed to deal with the varying requirements for the G&C options throughout the trajectory is presented. The paper discusses the methods used to i) obtain heating environments throughout the trajectory with respect to the chosen control system and resulting geometry; ii) determine a suitable TPS material; iii) produce TPS thickness estimations; and, iv) determine the final TPS mass estimation based on TPS thickness, vehicle control system, vehicle structure, and vehicle payload
Toward the co-production of hydro-climatic services: learning from research and practice
The India-UK Water Centre (IUKWC) promotes cooperation and collaboration between the complementary priorities of NERC-MoES water security research.
This State of Science Brief was produced as an output from an India–UK Water Centre supported Researcher Exchange on the co-production of hydro-climatic services hosted at Watershed Organisation Trust (WOTR) in Pune, India from 28 April – 18 May 2017
Consolidating learning about stakeholder engagement from research and practice: toward the development of hydro-climatic services. Report of research exchange April-May 2017
The India-UK Water Centre (IUKWC) promotes cooperation and collaboration between the complementary priorities of NERC-MoES water security research.
This report documents and discusses activities carried out under a Researcher Exchange funded
by the India-UK Water Centre (IUKWC) on the topic of “Consolidating Learning About Stakeholder
Engagement from Research and Practice: Toward the Development of Hydro-climatic Services.”
This exchange enabled Dr. Meaghan Daly, from University of Leeds, UK to conduct a three week
exchange hosted by Mr. Crispino Lobo and Dr. Marcella D’Souza at the Watershed Organisation
Trust (WOTR) in Pune, India from 28 April–18 May 2017. This report provides background on the
rationale for conducting the research exchange on the topic of stakeholder engagement within
hydro-climatic services, as well as a review of the objectives. This is followed by a description
of the activities carried out under the exchange and a brief summary of themes and outcomes
arising from a mini-workshop conducted on the topic of user engagement within development of
hydro-climatic services in the future
Mass transfer dynamics in double degenerate binary systems
We present a numerical study of the mass transfer dynamics prior to the
gravitational wave-driven merger of a double white dwarf system. Recently,
there has been some discussion about the dynamics of these last stages,
different methods seemed to provide qualitatively different results. While
earlier SPH simulations indicated a very quick disruption of the binary on
roughly the orbital time scale, more recent grid-based calculations find
long-lived mass transfer for many orbital periods. Here we demonstrate how
sensitive the dynamics of this last stage is to the exact initial conditions.
We show that, after a careful preparation of the initial conditions, the
reportedly short-lived systems undergo mass transfer for many dozens of orbits.
The reported numbers of orbits are resolution-biased and therefore represent
only lower limits to what is realized in nature. Nevertheless, the study shows
convincingly the convergence of different methods to very similar results.Comment: 5 pages, 3 figures, for associated movie files, see
http://pandora.jacobs-university.de/~mdan/WD_coalescences.htm, to appear in
Journal of Physics Conference Proceedings for the 16th European White Dwarf
Worksho
Correlated multiplexity and connectivity of multiplex random networks
Nodes in a complex networked system often engage in more than one type of
interactions among them; they form a multiplex network with multiple types of
links. In real-world complex systems, a node's degree for one type of links and
that for the other are not randomly distributed but correlated, which we term
correlated multiplexity. In this paper we study a simple model of multiplex
random networks and demonstrate that the correlated multiplexity can
drastically affect the properties of giant component in the network.
Specifically, when the degrees of a node for different interactions in a duplex
Erdos-Renyi network are maximally correlated, the network contains the giant
component for any nonzero link densities. In contrast, when the degrees of a
node are maximally anti-correlated, the emergence of giant component is
significantly delayed, yet the entire network becomes connected into a single
component at a finite link density. We also discuss the mixing patterns and the
cases with imperfect correlated multiplexity.Comment: Revised version, 12 pages, 6 figure
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