Learning Efficient Navigation in Vortical Flow Fields

Efficient point-to-point navigation in the presence of a background flow field is important for robotic applications such as ocean surveying. In such applications, robots may only have knowledge of their immediate surroundings or be faced with time-varying currents, which limits the use of optimal control techniques for planning trajectories. Here, we apply a novel Reinforcement Learning algorithm to discover time-efficient navigation policies to steer a fixed-speed swimmer through an unsteady two-dimensional flow field. The algorithm entails inputting environmental cues into a deep neural network that determines the swimmer's actions, and deploying Remember and Forget Experience replay. We find that the resulting swimmers successfully exploit the background flow to reach the target, but that this success depends on the type of sensed environmental cue. Surprisingly, a velocity sensing approach outperformed a bio-mimetic vorticity sensing approach by nearly two-fold in success rate. Equipped with local velocity measurements, the reinforcement learning algorithm achieved near 100% success in reaching the target locations while approaching the time-efficiency of paths found by a global optimal control planner.Comment: 6 pages, 6 figure

Nonlinear effects in E⊗(b1+b2)\otimes(b_1+b_2) Jahn-Teller model: Variational approach with excited phonon states and mode correlations

Interplay of nonlinear and quantum effects in the ground state of the E$\otimes (b_1+b_2)$ Jahn-Teller model was investigated by the {\it variational approach and exact numerical simulations}. They result in the recognition of (i) importance of the admixture of {\it the first excited state of the displaced harmonic oscillator} of the symmetric phonon mode in the ground state of the system in the selftrapping-dominated regime; (ii) existence of {\it the region of localized $b_1$-undisplaced oscillator states} in the tunneling-dominated regime. The effect (i) occurs owing to significant decrease of the ground state energy on account of the overlapping contribution of the symmetric phonon mode between the states of the same parity. This contribution considerably improves variational results especially in the selftrapping-dominated regime. Close to the E$\otimes$e limit, the nonlinear effects of {\it two-mode correlations} turn to be effective due to the rotational symmetry of this case. In the tunneling-dominated regime the phonon wave functions behave like the strongly localized harmonic oscillator ground state and the effect (i) looses its significance.Comment: 28 pages,6 figure

Electronic structure, magnetism and superconductivity of MgCNi3_{3}

The electronic structure of the newly discovered superconducting perovskite MgCNi$_3$ is calculated using the LMTO and KKR methods. The states near the Fermi energy are found to be dominated by Ni-d. The Stoner factor is low while the electron-phonon coupling constant is estimated to be about 0.7, which suggests that the material is a conventional type of superconductor where T$_C$ is not affected by magnetic interactions. However, the proximity of the Fermi energy to a large peak in the density of states in conjunction with the reported non-stoichiometry of the compound, has consequences for the stability of the results.Comment: 3 pages, 4 figure

Nesting properties and anomalous band effect in MgB2

First principle FLAPW band calculations of the new superconductor MgB2 were performed and the polarization function P12(Q) between the two p-bands mainly formed of boron pz-orbital was calculated. We found that P12(Q) is substantially enhanced around Q=(0,0,p/c), which supports the two-band mechanism of superconductivity for MgB2. P12(Q) peaks at Qz ~ 0.3(2p/c) and Qz \~ 0.5(2p/c). These two peaks are related to the nesting of these Fermi surfaces, but significantly deviates from the position expected from the simplest tight-binding bands for the p-bands. From the calculations for different lattice parameters, we have found significant dependences on the isotopic species of B and on the pressure effect of the polarization function in accordance with the respective changes of Tc in the above-mentioned framework.Comment: 15 pages, 7 graphs. to be published in J. Phys. Soc. Jpn. 70_, No.

Nonradiative Electronic Deexcitation Time Scales in Metal Clusters

The life-times due to Auger-electron emission for a hole on a deep electronic shell of neutral and charged sodium clusters are studied for different sizes. We consider spherical clusters and calculate the Auger-transition probabilities using the energy levels and wave functions calculated in the Local-Density-Approximation (LDA). We obtain that Auger emission processes are energetically not allowed for neutral and positively charged sodium clusters. In general, the Auger probabilities in small Na$_N^-$ clusters are remarkably different from the atomic ones and exhibit a rich size dependence. The Auger decay times of most of the cluster sizes studied are orders of magnitude larger than in atoms and might be comparable with typical fragmentation times.Comment: 11 pages, 4 figures. Accepted for publication in Phys. Rev.

A critical assessment of the Self-Interaction Corrected Local Density Functional method and its algorithmic implementation

We calculate the electronic structure of several atoms and small molecules by direct minimization of the Self-Interaction Corrected Local Density Approximation (SIC-LDA) functional. To do this we first derive an expression for the gradient of this functional under the constraint that the orbitals be orthogonal and show that previously given expressions do not correctly incorporate this constraint. In our atomic calculations the SIC-LDA yields total energies, ionization energies and charge densities that are superior to results obtained with the Local Density Approximation (LDA). However, for molecules SIC-LDA gives bond lengths and reaction energies that are inferior to those obtained from LDA. The nonlocal BLYP functional, which we include as a representative GGA functional, outperforms both LDA and SIC-LDA for all ground state properties we considered.Comment: 14 pages, 5 figure

Electronic structure of undoped and potassium doped coronene investigated by electron energy-loss spectroscopy

We performed electron energy-loss spectroscopy studies in transmission in order to obtain insight into the electronic properties of potassium intercalated coronene, a recently discovered superconductor with a rather high transition temperature of about 15\,K. A comparison of the loss function of undoped and potassium intercalated coronene shows the appearance of several new peaks in the optical gap upon potassium addition. Furthermore, our core level excitation data clearly signal filling of the conduction bands with electrons.Comment: 15 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1102.328

Magnetic Ordering and Superconductivity in the RE2_2Ir3_3Ge5_5 (RE = Y, La-Tm, Lu) System

We find that the compounds for RE = Y, La-Dy, crystallize in the tetragonal Ibam (U$_2$Co$_3$Si$_5$ type) structure whereas the compounds for RE = Er-Lu, crystallize in a new orthorhombic structure with a space group Pmmn. Samples of Ho$_2$Ir$_3$Ge$_5$ were always found to be multiphase. The compounds for RE = Y to Dy which adopt the Ibam type structure show a metallic resistivity whereas the compounds with RE = Er, Tm and Lu show an anomalous behavior in the resistivity with a semiconducting increase in $\rho$ as we go down in temperature from 300K. Interestingly we had earlier found a positive temperature coefficient of resistivity for the Yb sample in the same temperature range. We will compare this behavior with similar observations in the compounds RE$_3$Ru$_4$Ge$_{13}$ and REBiPt. La$_2$Ir$_3$Ge$_5$ and Y$_2$Ir$_3$Ge$_5$ show bulk superconductivity below 1.8K and 2.5K respectively. Our results confirm that Ce$_2$Ir$_3$Ge$_5$ shows a Kondo lattice behavior and undergoes antiferromagnetic ordering below 8.5K. Most of the other compounds containing magnetic rare-earth elements undergo a single antiferromagnetic transition at low temperatures (T$\leq$12K) while Gd$_2$Ir$_3$Ge$_5$, Dy$_2$Ir$_3$Ge$_5$ and Nd$_2$Ir$_3$Ge$_5$ show multiple transitions. The T$_N$'s for most of the compounds roughly scale with the de Gennes factor. which suggests that the chief mechanism of interaction leading to the magnetic ordering of the magnetic moments may be the RKKY interaction.Comment: 25 pages, 16 figure

Crystal Structures and Electronic Properties of Haloform-Intercalated C60

Using density functional methods we calculated structural and electronic properties of bulk chloroform and bromoform intercalated C60, C60 2CHX3 (X=Cl,Br). Both compounds are narrow band insulator materials with a gap between valence and conduction bands larger than 1 eV. The calculated widths of the valence and conduction bands are 0.4-0.6 eV and 0.3-0.4 eV, respectively. The orbitals of the haloform molecules overlap with the $\pi$ orbitals of the fullerene molecules and the p-type orbitals of halogen atoms significantly contribute to the valence and conduction bands of C60 2CHX3. Charging with electrons and holes turns the systems to metals. Contrary to expectation, 10 to 20 % of the charge is on the haloform molecules and is thus not completely localized on the fullerene molecules. Calculations on different crystal structures of C60 2CHCl3 and C60 2CHBr3 revealed that the density of states at the Fermi energy are sensitive to the orientation of the haloform and C60 molecules. At a charging of three holes, which corresponds to the superconducting phase of pure C60 and C60 2CHX3, the calculated density of states (DOS) at the Fermi energy increases in the sequence DOS(C60) < DOS(C60 2CHCl3) < DOS(C60 2CHBr3).Comment: 11 pages, 7 figures, 4 table

Arbitrary Choice of Basic Variables in Density Functional Theory. II. Illustrative Applications

Our recent theory (Ref. 1) enables us to choose arbitrary quantities as the basic variables of the density functional theory. In this paper we apply it to several cases. In the case where the occupation matrix of localized orbitals is chosen as a basic variable, we can obtain the single-particle equation which is equivalent to that of the LDA+U method. The theory also leads to the Hartree-Fock-Kohn-Sham equation by letting the exchange energy be a basic variable. Furthermore, if the quantity associated with the density of states near the Fermi level is chosen as a basic variable, the resulting single-particle equation includes the additional potential which could mainly modify the energy-band structures near the Fermi level.Comment: 27 page