19,790 research outputs found
Pareto optimality in house allocation problems
We study Pareto optimal matchings in the context of house allocation problems. We present an O(\sqrt{n}m) algorithm, based on Gales Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is NP-hard, though approximable within a factor of 2. We then show that there exist Pareto optimal matchings of all sizes between a minimum and maximum cardinality Pareto optimal matching. Finally, we introduce the concept of a signature, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching
Evolution of magnetic states in frustrated diamond lattice antiferromagnetic Co(Al1-xCox)2O4 spinels
Using neutron powder diffraction and Monte-Carlo simulations we show that a
spin-liquid regime emerges at $all compositions in the diamond-lattice
antiferromagnets Co(Al1-xCox)2O4. This spin-liquid regime induced by
frustration due to the second-neighbour exchange coupling J2, is gradually
superseded by antiferromagnetic collinear long-range order (k=0) at low
temperatures. Upon substitution of Al3+ by Co3+ in the octahedral B-site the
temperature range occupied by the spin-liquid regime narrows and TN increases.
To explain the experimental observations we considered magnetic anisotropy D or
third-neighbour exchange coupling J3 as degeneracy-breaking perturbations. We
conclude that Co(Al1-xCox)2O4 is below the theoretical critical point
J2/J1=1/8, and that magnetic anisotropy assists in selecting a collinear
long-range ordered ground state, which becomes more stable with increasing x
due to a higher efficiency of O-Co3+-O as an interaction path compared to
O-Al3+-O
Direct measurement of the phase coherence length in a GaAs/GaAlAs square network
The low temperature magnetoconductance of a large array of quantum
coherentloops exhibits Altshuler-Aronov-Spivak oscillations which
periodicitycorresponds to 1/2 flux quantum per loop.We show that the
measurement of the harmonics content in a square networkprovides an accurate
way to determine the electron phase coherence length in units of the
lattice length without any adjustableparameters.We use this method to determine
in a network realised from a 2Delectron gas (2DEG) in a GaAS/GaAlAs
heterojunction. The temperaturedependence follows a power law from
1.3 K to 25 mK with nosaturation, as expected for 1D diffusive electronic
motion andelectron-electron scattering as the main decoherence mechanism.Comment: Additional experimental data in version
Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders
We have studied the quantum oscillations of the conductance for arrays of
connected mesoscopic metallic rings, in the presence of an external magnetic
field. Several geometries have been considered: a linear array of rings
connected with short or long wires compared to the phase coherence length,
square networks and hollow cylinders. Compared to the well-known case of the
isolated ring, we show that for connected rings, the winding of the Brownian
trajectories around the rings is modified, leading to a different harmonics
content of the quantum oscillations. We relate this harmonics content to the
distribution of winding numbers. We consider the limits where coherence length
is small or large compared to the perimeter of each ring
constituting the network. In the latter case, the coherent diffusive
trajectories explore a region larger than , whence a network dependent
harmonics content. Our analysis is based on the calculation of the spectral
determinant of the diffusion equation for which we have a simple expression on
any network. It is also based on the hypothesis that the time dependence of the
dephasing between diffusive trajectories can be described by an exponential
decay with a single characteristic time (model A) .
At low temperature, decoherence is limited by electron-electron interaction,
and can be modelled in a one-electron picture by the fluctuating electric field
created by other electrons (model B). It is described by a functional of the
trajectories and thus the dependence on geometry is crucial. Expressions for
the magnetoconductance oscillations are derived within this model and compared
to the results of model A. It is shown that they involve several
temperature-dependent length scales.Comment: 35 pages, revtex4, 25 figures (34 pdf files
Precision Spectroscopy of Molecular Hydrogen Ions: Towards Frequency Metrology of Particle Masses
We describe the current status of high-precision ab initio calculations of
the spectra of molecular hydrogen ions (H_2^+ and HD^+) and of two experiments
for vibrational spectroscopy. The perspectives for a comparison between theory
and experiment at a level of 1 ppb are considered.Comment: 26 pages, 13 figures, 1 table, to appear in "Precision Physics of
Simple Atomic Systems", Lecture Notes in Physics, Springer, 200
A dynamical trichotomy for structured populations experiencing positive density-dependence in stochastic environments
Positive density-dependence occurs when individuals experience increased
survivorship, growth, or reproduction with increased population densities.
Mechanisms leading to these positive relationships include mate limitation,
saturating predation risk, and cooperative breeding and foraging. Individuals
within these populations may differ in age, size, or geographic location and
thereby structure these populations. Here, I study structured population models
accounting for positive density-dependence and environmental stochasticity i.e.
random fluctuations in the demographic rates of the population. Under an
accessibility assumption (roughly, stochastic fluctuations can lead to
populations getting small and large), these models are shown to exhibit a
dynamical trichotomy: (i) for all initial conditions, the population goes
asymptotically extinct with probability one, (ii) for all positive initial
conditions, the population persists and asymptotically exhibits unbounded
growth, and (iii) for all positive initial conditions, there is a positive
probability of asymptotic extinction and a complementary positive probability
of unbounded growth. The main results are illustrated with applications to
spatially structured populations with an Allee effect and age-structured
populations experiencing mate limitation
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