Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction

Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.Comment: 4 pages, 3 figure

A mathematical model of the effect of a predator on species diversity

Mathematical model determines reaction between new predator and microbe competitor when the competitor is the predator's sole nutrient resource. The model utilizes differential equations to describe the interactions with the specific growth rates, and analyzes these growth rates as they are affected by population density and nutrient concentration

Solvable Lattice Gas Models with Three Phases

Phase boundaries in p-T and p-V diagrams are essential in material science researches. Exact analytic knowledge about such phase boundaries are known so far only in two-dimensional (2D) Ising-like models, and only for cases with two phases. In the present paper we present several lattice gas models, some with three phases. The phase boundaries are either analytically calculated or exactly evaluated.Comment: 5 pages, 6 figure

Xenon fluorides show potential as fluorinating agents

Xenon fluorides permit the controlled addition of fluorine across an olefinic double bond. They provide a series of fluorinating agents that permit ready separation from the product at a high purity. The reactions may be carried out in the vapor phase

Quantum phase transition and engineering in two-component BEC in optical lattices

In this paper we review recent progress in studying quantum phase transitions in one- and two-component Bose-Einstein condensates (BEC) in optical lattices. These phase transitions involve the emergence and disappearance of quantum coherence over whole optical lattice and of linear superposition of macroscopic quantum states. The latter may provide new means to engineer and to manipulate novel macroscopic quantum states and novel coherent atomic beams for quantum information processing, quantum computing etc.Comment: Format: LaTex2e. 7 pages, no figure. Talk at the Yang Symposium (in honor of C.N. Yang's 80th birthday), Beijing, China, June 2002. To appear in the Proceeding

GAPS IN THE HEISENBERG-ISING MODEL

We report on the closing of gaps in the ground state of the critical Heisenberg-Ising chain at momentum $\pi$. For half-filling, the gap closes at special values of the anisotropy $\Delta= \cos(\pi/Q)$, $Q$ integer. We explain this behavior with the help of the Bethe Ansatz and show that the gap scales as a power of the system size with variable exponent depending on $\Delta$. We use a finite-size analysis to calculate this exponent in the critical region, supplemented by perturbation theory at $\Delta\sim 0$. For rational $1/r$ fillings, the gap is shown to be closed for {\em all} values of $\Delta$ and the corresponding perturbation expansion in $\Delta$ shows a remarkable cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques

Design and analysis of a wire-driven flexible manipulator for bronchoscopic interventions

Bronchoscopic interventions are widely performed for the diagnosis and treatment of lung diseases. However, for most endobronchial devices, the lack of a bendable tip restricts their access ability to get into distal bronchi with complex bifurcations. This paper presents the design of a new wire-driven continuum manipulator to help guide these devices. The proposed manipulator is built by assembling miniaturized blocks that are featured with interlocking circular joints. It has the capability of maintaining its integrity when the lengths of actuation wires change due to the shaft flex. It allows the existence of a relatively large central cavity to pass through other instruments and enables two rotational degrees of freedom. All these features make it suitable for procedures where tubular anatomies are involved and the flexible shafts have to be considerably bent in usage, just like bronchoscopic interventions. A kinematic model is built to estimate the relationship between the translations of actuation wires and the manipulator tip position. A scale-up model is produced for evaluation experiments and the results validate the performance of the proposed mechanism

Fractional Energy Loss and Centrality Scaling

The phenomenon of centrality scaling in the high-\pt spectra of $\pi^0$ produced in Au-Au collisions at $\sqrt s=200$ GeV is examined in the framework of relating fractional energy loss to fractional centrality increase. A new scaling behavior is found where the scaling variable is given a power-law dependence on $N_{\rm part}$. The exponent $\gamma$ specifies the fractional proportionality relationship between energy loss and centrality, and is a phenomenologically determined number that characterizes the nuclear suppression effect. The implication on the parton energy loss in the context of recombination is discussed.Comment: 4 pages in RevTe

Nanodroplets on rough hydrophilic and hydrophobic surfaces

We present results of Molecular Dynamics (MD) calculations on the behavior of liquid nanodroplets on rough hydrophobic and hydrophilic solid surfaces. On hydrophobic surfaces, the contact angle for nanodroplets depends strongly on the root mean square roughness amplitude, but it is nearly independent of the fractal dimension of the surface. Since increasing the fractal dimension increases the short-wavelength roughness, while the long-wavelength roughness is almost unchanged, we conclude that for hydrophobic interactions the short-wavelength (atomistic) roughness is not very important. We show that the nanodroplet is in a Cassie-like state. For rough hydrophobic surfaces, there is no contact angle hysteresis due to strong thermal fluctuations, which occur at the liquid-solid interface on the nanoscale. On hydrophilic surfaces, however, there is strong contact angle hysteresis due to higher energy barrier. These findings may be very important for the development of artificially biomimetic superhydrophobic surfaces.Comment: 15 pages, 25 figures. Minimal changes with respect to the previous one. A few small improvements, references updated, added the reference to the published paper. Previous work on the same subject: arXiv:cond-mat/060405