Pseudoparticle Multipole Method: A Simple Method to Implement High-Accuracy Treecode

In this letter we describe the pseudoparticle multipole method (P2M2), a new method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the Barnes-Hut treecode and FMM. The primary advantage of P2M2 is that it works on GRAPE. GRAPE is a special-purpose hardware for the calculation of gravitational force between particles. Although the treecode has been implemented on GRAPE, we could handle terms only up to dipole, since GRAPE can calculate forces from point-mass particles only. Thus the calculation cost grows quickly when high accuracy is required. With P2M2, the multipole expansion is expressed by particles, and thus GRAPE can calculate high order terms. Using P2M2, we implemented an arbitrary-order treecode on GRAPE-4. Timing result shows GRAPE-4 accelerates the calculation by a factor between 10 (for low accuracy) to 150 (for high accuracy). Even on general-purpose programmable computers, our method offers the advantage that the mathematical formulae and therefore the actual program is much simpler than that of the direct implementation of multipole expansion.Comment: 6 pages, 4 figures, latex, submitted to ApJ Letter

Twisted Elliptic Genera of N=2 SCFTs in Two Dimensions

The elliptic genera of two-dimensional N=2 superconformal field theories can be twisted by the action of the integral Heisenberg group if their U(1) charges are fractional. The basic properties of the resulting twisted elliptic genera and the associated twisted Witten indices are investigated with due attention to their behaviors in orbifoldization. Our findings are illustrated by and applied to several concrete examples. We give a better understanding of the duality phenomenon observed long before for certain Landau-Ginzburg models. We revisit and prove an old conjecture of Witten which states that every ADE Landau-Ginzburg model and the corresponding minimal model share the same elliptic genus. Mathematically, we establish ADE generalizations of the quintuple product identity.Comment: 28 pages; v2 refs adde

Renormalization of 3d quantum gravity from matrix models

Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space-time histories, it is perturbatively non-renormalizable even in three dimensions. By mapping the three-dimensional theory to a two-matrix model with ABAB interaction we show that both the cosmological and the (perturbatively) non-renormalizable gravitational coupling constant undergo additive renormalizations consistent with canonical quantization.Comment: 14 pages, 3 figure

Quantum Electrodynamics at Large Distances II: Nature of the Dominant Singularities

Accurate calculations of macroscopic and mesoscopic properties in quantum electrodynamics require careful treatment of infrared divergences: standard treatments introduce spurious large-distances effects. A method for computing these properties was developed in a companion paper. That method depends upon a result obtained here about the nature of the singularities that produce the dominant large-distance behaviour. If all particles in a quantum field theory have non-zero mass then the Landau-Nakanishi diagrams give strong conditions on the singularities of the scattering functions. These conditions are severely weakened in quantum electrodynamics by effects of points where photon momenta vanish. A new kind of Landau-Nakanishi diagram is developed here. It is geared specifically to the pole-decomposition functions that dominate the macroscopic behaviour in quantum electrodynamics, and leads to strong results for these functions at points where photon momenta vanish.Comment: 40 pages, 11 encapsulated postscript figures, latexed, math_macros.tex can be found on Archive. full postscript available from http://theorl.lbl.gov/www/theorgroup/papers/35972.p

Tracking Control for FES-Cycling based on Force Direction Efficiency with Antagonistic Bi-Articular Muscles

A functional electrical stimulation (FES)-based tracking controller is developed to enable cycling based on a strategy to yield force direction efficiency by exploiting antagonistic bi-articular muscles. Given the input redundancy naturally occurring among multiple muscle groups, the force direction at the pedal is explicitly determined as a means to improve the efficiency of cycling. A model of a stationary cycle and rider is developed as a closed-chain mechanism. A strategy is then developed to switch between muscle groups for improved efficiency based on the force direction of each muscle group. Stability of the developed controller is analyzed through Lyapunov-based methods.Comment: 8 pages, 4 figures, submitted to ACC201

Towards a Non-Perturbative Renormalization of Euclidean Quantum Gravity

A real space renormalization group technique, based on the hierarchical baby-universe structure of a typical dynamically triangulated manifold, is used to study scaling properties of 2d and 4d lattice quantum gravity. In 4d, the $\beta$-function is defined and calculated numerically. An evidence for the existence of an ultraviolet stable fixed point of the theory is presentedComment: 12 pages Latex + 1 PS fi

Scaling Behavior of Ricci Curvature at Short Distance near Two Dimensions

We study the renormalization of the Ricci curvature as an example of generally covariant operators in quantum gravity near two dimensions. We find that it scales with a definite scaling dimension at short distance. The Ricci curvature singularity at the big bang can be viewed as such a scaling phenomenon. The problem of the spacetime singularity may be resolved by the scale invariance of the spacetime at short distance.Comment: 9pages, LaTe