Implications of Color Gauge Symmetry For Nucleon Spin Structure

We study the chromodynamical gauge symmetry in relation to the internal spin structure of the nucleon. We show that 1) even in the helicity eigenstates the gauge-dependent spin and orbital angular momentum operators do not have gauge-independent matrix element; 2) the evolution equations for the gluon spin take very different forms in the Feynman and axial gauges, but yield the same leading behavior in the asymptotic limit; 3) the complete evolution of the gauge-dependent orbital angular momenta appears intractable in the light-cone gauge. We define a new gluon orbital angular momentum distribution $L_g(x)$ which {\it is} an experimental observable and has a simple scale evolution. However, its physical interpretation makes sense only in the light-cone gauge just like the gluon helicity distribution $\Delta g(x)$y.Comment: Minor corrections are made in the tex

Characterization of Metastatic Tumor Formation by the Colony Size Distribution

Knowledge regarding the kinetics of metastatic tumor formation, as related to the growth of the primary tumor, represents a fundamental issue in cancer biology. Using an in vivo mammalian model, we show here that one can obtain useful information from the frequency distribution of the sizes of metastatic colonies in distant organs after serial sectioning and image reconstruction. To explain the experimental findings, we constructed a biophysical model based on the respective growth patterns of the primary tumor and metastases and a stochastic process of metastatic colony formation. Heterogeneous distributions of various biological parameters were considered. We found that the elementary assumption of exponential forms of growth for the primary tumor and metastatic colonies predicts a linear relation on a log-log plot of a metastatic colony size distribution, which was consistent with the experimental results. Furthermore, the slope of the curve signifies the ratio of growth rates of the primary and the metastases. Non-exponential (Gompertzian and logistic) tumor growth patterns were also incorporated into the theory to explain possible deviation from the log-log linear relation. The observed metastasis-free probability also supported the assumption of a time-dependent Poisson process. With this approach, we determined the mechanistic parameters governing the process of metastatogenesis in the lungs for two murine tumor cell lines (KHT and MCaK). Since biological parameters specified in the model could be obtained in the laboratory, a workable metastatic "assay" may be established for various malignancies and in turn contribute in formulating rational treatment regimens for subclinical metastases.Comment: 14 pages, 6 figure

Reciprocatory magnetic reconnection in a coronal bright point

Coronal bright points (CBPs) are small-scale and long-duration brightenings in the lower solar corona. They are often explained in terms of magnetic reconnection. We aim to study the sub-structures of a CBP and clarify the relationship among the brightenings of different patches inside the CBP. The event was observed by the X-ray Telescope (XRT) aboard the Hinode spacecraft on 2009 August 22$-$23. The CBP showed repetitive brightenings (or CBP flashes). During each of the two successive CBP flashes, i.e., weak and strong flashes which are separated by $\sim$2 hr, the XRT images revealed that the CBP was composed of two chambers, i.e., patches A and B. During the weak flash, patch A brightened first, and patch B brightened $\sim$2 min later. During the transition, the right leg of a large-scale coronal loop drifted from the right side of the CBP to the left side. During the strong flash, patch B brightened first, and patch A brightened $\sim$2 min later. During the transition, the right leg of the large-scale coronal loop drifted from the left side of the CBP to the right side. In each flash, the rapid change of the connectivity of the large-scale coronal loop is strongly suggestive of the interchange reconnection. For the first time we found reciprocatory reconnection in the CBP, i.e., reconnected loops in the outflow region of the first reconnection process serve as the inflow of the second reconnection process.Comment: 13 pages, 8 figure

Quark Orbital-Angular-Momentum Distribution in the Nucleon

We introduce gauge-invariant quark and gluon angular momentum distributions after making a generalization of the angular momentum density operators. From the quark angular momentum distribution, we define the gauge-invariant and leading-twist quark {\it orbital} angular momentum distribution $L_q(x)$. The latter can be extracted from data on the polarized and unpolarized quark distributions and the off-forward distribution $E(x)$ in the forward limit. We comment upon the evolution equations obeyed by this as well as other orbital distributions considered in the literature.Comment: 8 pages, latex, no figures, minor corrections mad

Parametric survey of longitudinal prominence oscillation simulations

It is found that both microflare-sized impulsive heating at one leg of the loop and a suddenly imposed velocity perturbation can propel the prominence to oscillate along the magnetic dip. An extensive parameter survey results in a scaling law, showing that the period of the oscillation, which weakly depends on the length and height of the prominence, and the amplitude of the perturbations, scales with $\sqrt{R/g_\odot}$, where $R$ represents the curvature radius of the dip, and $g_\odot$ is the gravitational acceleration of the Sun. This is consistent with the linear theory of a pendulum, which implies that the field-aligned component of gravity is the main restoring force for the prominence longitudinal oscillations, as confirmed by the force analysis. However, the gas pressure gradient becomes non-negligible for short prominences. The oscillation damps with time in the presence of non-adiabatic processes. Compared to heat conduction, the radiative cooling is the dominant factor leading to the damping. A scaling law for the damping timescale is derived, i.e., $\tau\sim l^{1.63} D^{0.66}w^{-1.21}v_{0}^{-0.30}$, showing strong dependence on the prominence length $l$, the geometry of the magnetic dip (characterized by the depth $D$ and the width $w$), and the velocity perturbation amplitude $v_0$. The larger the amplitude, the faster the oscillation damps. It is also found that mass drainage significantly reduces the damping timescale when the perturbation is too strong.Comment: 17 PAGES, 8FIGURE

Heisenberg-picture approach to the evolution of the scalar fields in an expanding universe

We present the Heisenberg-picture approach to the quantum evolution of the scalar fields in an expanding FRW universe which incorporates relatively simply the initial quantum conditions such as the vacuum state, the thermal equilibrium state, and the coherent state. We calculate the Wightman function, two-point function, and correlation function of a massive scalar field. We find the quantum evolution of fluctuations of a self-interacting field perturbatively and discuss the renormalization of field equations.Comment: 15 pages, RevTeX, no figure

Spin-lattice order in frustrated ZnCr2O4

Using synchrotron X-rays and neutron diffraction we disentangle spin-lattice order in highly frustrated ZnCr$_2$O$_4$ where magnetic chromium ions occupy the vertices of regular tetrahedra. Upon cooling below 12.5 K the quandary of anti-aligning spins surrounding the triangular faces of tetrahedra is resolved by establishing weak interactions on each triangle through an intricate lattice distortion. The resulting spin order is however, not simply a N\'{e}el state on strong bonds. A complex co-planar spin structure indicates that antisymmetric and/or further neighbor exchange interactions also play a role as ZnCr$_2$O$_4$ resolves conflicting magnetic interactions