Normal Rack Grid Generation Method for Screw Machines with Large Helix Angles

Improving the efficiency of the screw machine is highly significant for industry. Numerical simulation is an important tool in developing these machines. The 3D computational fluid dynamic simulation can give a valuable insight into the flow parameters of screw machines. However, it is currently difficult to generate high quality computational grids required for screw rotors with large helix angle. This is mainly due to the excessively high cell skewness of the rotors with large helix angel, which would introduce errors in numerical simulation. This paper presents a novel grid generation algorithm used for the screw rotors with large helix angel. This method is based on the principles developed for the grid generation in transverse cross-section. Such mesh is generated by SCORGTM using normal rack grid generation method which means numerical meshes are generated in a plane normal to the pitch helix line. The mesh lines are then parallel to the helix line and thus an orthogonal mesh will be produced. The main flow and leakage flow directions are orthogonal to the mesh, potentially reducing numerical diffusion. This developed algorithm could also be employed for single screw machines

Fractionalization and confinement in the U(1) and Z2Z_2 gauge theories of strongly correlated systems

Recently, we have elucidated the physics of electron fractionalization in strongly interacting electron systems using a $Z_2$ gauge theory formulation. Here we discuss the connection with the earlier U(1) gauge theory approaches based on the slave boson mean field theory. In particular, we identify the relationship between the holons and Spinons of the slave-boson theory and the true physical excitations of the fractionalized phases that are readily described in the $Z_2$ approach.Comment: 4 page

Confinement of Slave-Particles in U(1) Gauge Theories of Strongly-Interacting Electrons

We show that slave particles are always confined in U(1) gauge theories of interacting electron systems. Consequently, the low-lying degrees of freedom are different from the slave particles. This is done by constructing a dual formulation of the slave-particle representation in which the no-double occupany constraint becomes linear and, hence, soluble. Spin-charge separation, if it occurs, is due to the existence of solitons with fractional quantum numbers

Extending the Globular Cluster System-Halo Mass Relation to the Lowest Galaxy Masses

High mass galaxies, with halo masses $M_{200} \ge 10^{10} M_{\odot}$, reveal a remarkable near-linear relation between their globular cluster (GC) system mass and their host galaxy halo mass. Extending this relation to the mass range of dwarf galaxies has been problematic due to the difficulty in measuring independent halo masses. Here we derive new halo masses based on stellar and HI gas kinematics for a sample of nearby dwarf galaxies with GC systems. We find that the GC system mass--halo mass relation for galaxies populated by GCs holds from halo masses of $M_{200} \sim 10^{14} M_{\odot}$ down to below $M_{200}$ $\sim 10^9 M_{\odot}$, although there is a substantial increase in scatter towards low masses. In particular, three well-studied ultra diffuse galaxies, with dwarf-like stellar masses, reveal a wide range in their GC-to-halo mass ratios. We compare our GC system--halo mass relation to the recent model of El Badry et al., finding that their fiducial model does not reproduce our data in the low mass regime. This may suggest that GC formation needs to be more efficient than assumed in their model, or it may be due to the onset of stochastic GC occupation in low mass halos. Finally, we briefly discuss the stellar mass-halo mass relation for our low mass galaxies with GCs, and we suggest some nearby dwarf galaxies for which searches for GCs may be fruitful.Comment: 16 pages, 5 figures, accepted for publication in MNRA

On the Current Carried by `Neutral' Quasiparticles

The current should be proportional to the momentum in a Galilean-invariant system of particles of fixed charge-to-mass ratio, such as an electron liquid in jellium. However, strongly-interacting electron systems can have phases characterized by broken symmetry or fractionalization. Such phases can have neutral excitations which can presumably carry momentum but not current. In this paper, we show that there is no contradiction: `neutral' excitations {\em do} carry current in a Galilean-invariant system of particles of fixed charge-to-mass ratio. This is explicitly demonstrated in the context of spin waves, the Bogoliubov-de Gennes quasiparticles of a superconductor, the one-dimensional electron gas, and spin-charge separated systems in 2+1 dimensions. We discuss the implications for more realistic systems, which are not Galilean-invariant

Possible realization of an ideal quantum computer in Josephson junction array

We introduce a new class of Josephson arrays which have non-trivial topology and exhibit a novel state at low temperatures. This state is characterized by long range order in a two Cooper pair condensate and by a discrete topological order parameter. These arrays have degenerate ground states with this degeneracy 'protected' from the external perturbations (and noise) by the topological order parameter. We show that in ideal conditions the low order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built in error correction and show that even a small array exhibits interesting physical properties such as superconductivity with double charge, 4e, and extremely long decoherence times.Comment: RexTeX4, 8 pages, 3 EPS figures. Significantly longer version with more detailed estimates of decoherence times and many new relevant reference

A Monte Carlo study of O(3) antiferromagnetic models in three dimensions

We study three antiferromagnetic formulations of the O(3) spin model in three dimensions by means of Monte Carlo simulations: 1. a two parameter $\sigma$ model with nearest and next to nearest neighbors couplings in a cubic lattice; 2. a face centered cubic lattice with nearest neighbors interaction; 3. a cubic lattice with a set of fully frustrating couplings. We discuss in all cases the vacua properties and analyze the phase transitions. Using Finite Size Scaling analysis we conclude that all phase transitions found are of first order.Comment: 24 pages, uuencoded gzipped postscript file. 13 figures include

An RVB phase in the triangular lattice quantum dimer model

We study the quantum dimer model on the triangular lattice, which is expected to describe the singlet dynamics of frustrated Heisenberg models in phases where valence bond configurations dominate their physics. We find, in contrast to the square lattice, that there is a truly short ranged resonating valence bond (RVB) phase with no gapless collective excitations and with deconfined, gapped, spinons for a {\it finite} range of parameters. We also establish the presence of three crystalline phases in this system.Comment: 4 pages, 2 figures, Revtex 3.