37,524 research outputs found
Spin-1 Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies
Using density matrix renormalization group calculations, ground state
properties of the spin-1 Heisenberg chain with exchange and single-ion
anisotropies in an external field are studied. Our findings confirm and refine
recent results by Sengupta and Batista, Physical Review Letters 99, 217205
(2007) (2007), on the same model applying Monte Carlo techniques. In
particular, we present evidence for two types of biconical (or supersolid) and
for two types of spin-flop (or superfluid) structures. Basic features of the
quantum phase diagram may be interpreted qualitatively in the framework of
classical spin models.Comment: Ref. 1 corrected (also in the abstract
Quantum Heisenberg antiferromagnetic chains with exchange and single--ion anisotropies
Using density matrix renormalization group calculations, ground state
properties of the spin-1 Heisenberg chain with exchange and quadratic
single-ion anisotropies in an external field are studied, for special choices
of the two kinds of anisotropies. In particular, the phase diagram includes
antiferromagnetic, spin-liquid (or spin-flop), (10), and supersolid (or
biconical) phases. Especially, new features of the spin-liquid and supersolid
phases are discussed. Properties of the quantum chains are compared to those of
corresponding classical spin chains.Comment: 4 pages, 5 figures, ICM0
Searching for Globally Optimal Functional Forms for Inter-Atomic Potentials Using Parallel Tempering and Genetic Programming
We develop a Genetic Programming-based methodology that enables discovery of
novel functional forms for classical inter-atomic force-fields, used in
molecular dynamics simulations. Unlike previous efforts in the field, that fit
only the parameters to the fixed functional forms, we instead use a novel
algorithm to search the space of many possible functional forms. While a
follow-on practical procedure will use experimental and {\it ab inito} data to
find an optimal functional form for a forcefield, we first validate the
approach using a manufactured solution. This validation has the advantage of a
well-defined metric of success. We manufactured a training set of atomic
coordinate data with an associated set of global energies using the well-known
Lennard-Jones inter-atomic potential. We performed an automatic functional form
fitting procedure starting with a population of random functions, using a
genetic programming functional formulation, and a parallel tempering
Metropolis-based optimization algorithm. Our massively-parallel method
independently discovered the Lennard-Jones function after searching for several
hours on 100 processors and covering a miniscule portion of the configuration
space. We find that the method is suitable for unsupervised discovery of
functional forms for inter-atomic potentials/force-fields. We also find that
our parallel tempering Metropolis-based approach significantly improves the
optimization convergence time, and takes good advantage of the parallel cluster
architecture
Multi-Task Policy Search for Robotics
© 2014 IEEE.Learning policies that generalize across multiple tasks is an important and challenging research topic in reinforcement learning and robotics. Training individual policies for every single potential task is often impractical, especially for continuous task variations, requiring more principled approaches to share and transfer knowledge among similar tasks. We present a novel approach for learning a nonlinear feedback policy that generalizes across multiple tasks. The key idea is to define a parametrized policy as a function of both the state and the task, which allows learning a single policy that generalizes across multiple known and unknown tasks. Applications of our novel approach to reinforcement and imitation learning in realrobot experiments are shown
Design of helicopter rotor blades for optimum dynamic characteristics
The mass and stiffness distributions for helicopter rotor blades are tailored in such a way to give a predetermined placement of blade natural frequencies. The optimal design is pursued with respect of minimum weight, sufficient inertia, and reasonable dynamic characteristics. Finite element techniques are used as a tool. Rotor types include hingeless, articulated, and teetering
Classical and quantum anisotropic Heisenberg antiferromagnets
We study classical and quantum Heisenberg antiferromagnets with exchange
anisotropy of XXZ-type and crystal field single-ion terms of quadratic and
cubic form in a field. The magnets display a variety of phases, including the
spin-flop (or, in the quantum case, spin-liquid) and biconical (corresponding,
in the quantum lattice gas description, to supersolid) phases. Applying
ground-state considerations, Monte Carlo and density matrix renormalization
group methods, the impact of quantum effects and lattice dimension is analysed.
Interesting critical and multicritical behaviour may occur at quantum and
thermal phase transitions.Comment: 13 pages, 14 figures, conferenc
Growth of Intermediate-Mass Black Holes in Globular Clusters
We present results of numerical simulations of sequences of binary-single
scattering events of black holes in dense stellar environments. The simulations
cover a wide range of mass ratios from equal mass objects to 1000:10:10 solar
masses and compare purely Newtonian simulations to simulations in which
Newtonian encounters are interspersed with gravitational wave emission from the
binary. In both cases, the sequence is terminated when the binary's merger time
due to gravitational radiation is less than the arrival time of the next
interloper. We find that black hole binaries typically merge with a very high
eccentricity (0.93 < e < 0.95 pure Newtonian; 0.85 < e < 0.90 with
gravitational wave emission) and that adding gravitational wave emission
decreases the time to harden a binary until merger by ~ 30% to 40%. We discuss
the implications of this work for the formation of intermediate-mass black
holes and gravitational wave detection.Comment: 28 pages including 9 figures, submitted to Ap
Design of helicopter rotor blades for optimum dynamic characteristics
The possibilities and limitations of tailoring blade mass and stiffness distributions to give an optimum blade design in terms of weight, inertia, and dynamic characteristics are discussed. The extent that changes in mass of stiffness distribution can be used to place rotor frequencies at desired locations is determined. Theoretical limits to the amount of frequency shift are established. Realistic constraints on blade properties based on weight, mass, moment of inertia, size, strength, and stability are formulated. The extent that the hub loads can be minimized by proper choice of E1 distribution, and the minimum hub loads which can be approximated by a design for a given set of natural frequencies are determined. Aerodynamic couplings that might affect the optimum blade design, and the relative effectiveness of mass and stiffness distribution on the optimization procedure are investigated
Fractal Markets Hypothesis and the Global Financial Crisis: Scaling, Investment Horizons and Liquidity
We investigate whether fractal markets hypothesis and its focus on liquidity
and invest- ment horizons give reasonable predictions about dynamics of the
financial markets during the turbulences such as the Global Financial Crisis of
late 2000s. Compared to the mainstream efficient markets hypothesis, fractal
markets hypothesis considers financial markets as com- plex systems consisting
of many heterogenous agents, which are distinguishable mainly with respect to
their investment horizon. In the paper, several novel measures of trading
activity at different investment horizons are introduced through scaling of
variance of the underlying processes. On the three most liquid US indices -
DJI, NASDAQ and S&P500 - we show that predictions of fractal markets hypothesis
actually fit the observed behavior quite well.Comment: 11 pages, 3 figure
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