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