Effective Low-Energy Model for f-Electron Delocalization

We consider a Periodic Anderson Model (PAM) with a momentum-dependent inter-band hybridization that is strongly suppressed near the Fermi level. Under these conditions, we reduce the PAM to an effective low-energy Hamiltonian, $H_{\rm eff}$, by expanding in the small parameter $V_0/t$ ( $V_0$ is the maximum inter-band hybridization amplitude and $t$ is the hopping integral of the broad band). The resulting model consists of a t-J f-band coupled via the Kondo exchange to the electrons in the broad band. $H_{\rm eff}$ allows for studying the f-electron delocalization transition. The result is a doping-induced Mott transition for the f-electron delocalization, which we demonstrate by density-matrix renormalization group (DMRG) calculations

The temperature dependence of the local tunnelling conductance in cuprate superconductors with competing AF order

Based on the $t-t'-U-V$ model with proper chosen parameters for describing the cuprate superconductors, it is found that near the optimal doping at low temperature ($T$), only the pure d-wave superconductivity ($d$SC) prevails and the antiferromagnetic (AF) order is completely suppressed. At higher $T$, the AF order with stripe modulation and the accompanying charge order may emerge, and they could exist above the $d$SC transition temperature. We calculate the local differential tunnelling conductance (LDTC) from the local density of states (LDOS) and show that their energy variations are rather different from each other as $T$ increases. Although the calculated modulation periodicity in the LDTC/LDOS and bias energy dependence of the Fourier amplitude of LDTC in the "pseudogap" region are in good agreement with the recent STM experiment [Vershinin $et al.$, Science {\bf 303}, 1995 (2004)], we point out that some of the energy dependent features in the LDTC do not represent the intrinsic characteristics of the sample

Fermi gas in harmonic oscillator potentials

Assuming the validity of grand canonical statistics, we study the properties of a spin-polarized Fermi gas in harmonic traps. Universal forms of Fermi temperature $T_F$, internal energy $U$ and the specific heat per particle of the trapped Fermi gas are calculated as a {\it function} of particle number, and the results compared with those of infinite number particles.Comment: 8 pages, 1 figure, LATE

Interacting Individuals Leading to Zipf's Law

We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statisticsComment: 4 pages 2 figure

Bilateral symmetry of object silhouettes under perspective projection

Symmetry is an important property of objects and is exhibited in different forms e.g., bilateral, rotational, etc. This paper presents an algorithm for computing the bilateral symmetry of silhouettes of shallow objects under perspective distortion, exploiting the invariance of the cross ratio to projective transformations. The basic idea is to use the cross ratio to compute a number of midpoints of cross sections and then fit a straight line through them. The goodness-of-fit determines the likelihood of the line to be the axis of symmetry. We analytically estimate the midpoint’s location as a function of the vanishing point for a given object silhouette. Hence finding the symmetry axis amounts to a 2D search in the space of vanishing points. We present experiments on two datasets as well as internet images of symmetric objects that validate our approach. under perspectivities, we analytically compute a set of midpoints of the object as a function of the vanishing point. Then, we fit a straight line passing through the midpoints. The goodness-of-fit defines the likelihood of this line to be a symmetry axis. Using the proposed method, searching for the symmetry axis is reduced to searching for a vanishing point. Our approach is global in the sense that we consider the whole silhouette of the object rather than small parts of it. The results show that the method presented here is capable of finding axes of symmetry of considerably distorted perspective images. 2 Related Work

On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the electromagnetic PIC algorithm to analyze the origin of these instabilities. We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm, and then specialize to the Yee FDTD scheme. In particular, we account for the manner in which the PIC algorithm updates and samples the fields and distribution function. Temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme are also explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical 1D modes admitted in the system and their aliases. The most significant interaction is due critically to the correct represenation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction.Comment: 25 pages, 6 figure

Chemical evolution of star clusters

I discuss the chemical evolution of star clusters, with emphasis on old globular clusters, in relation to their formation histories. Globular clusters clearly formed in a complex fashion, under markedly different conditions from any younger clusters presently known. Those special conditions must be linked to the early formation epoch of the Galaxy and must not have occurred since. While a link to the formation of globular clusters in dwarf galaxies has been suggested, present-day dwarf galaxies are not representative of the gravitational potential wells within which the globular clusters formed. Instead, a formation deep within the proto-Galaxy or within dark-matter minihaloes might be favoured. Not all globular clusters may have formed and evolved similarly. In particular, we may need to distinguish Galactic halo from Galactic bulge clusters.Comment: 27 pages, 2 figures. To appear as invited review article in a special issue of the Phil. Trans. Royal Soc. A: Ch. 6 "Star clusters as tracers of galactic star-formation histories" (ed. R. de Grijs). Fully peer reviewed. LaTeX, requires rspublic.cls style fil

Mass and energy of erupting solar plasma observed with the X-Ray Telescope on Hinode

We investigate seven eruptive plasma observations by Hinode/XRT. Their corresponding EUV and/or white light CME features are visible in some events. Five events are observed in several passbands in X-rays, which allows the determination of the eruptive plasma temperature using a filter ratio method. We find that the isothermal temperatures vary from 1.6 to 10 MK. These temperatures are an average weighted toward higher temperature plasma. We determine the mass constraints of eruptive plasmas by assuming simplified geometrical structures of the plasma with isothermal plasma temperatures. This method provides an upper limit to the masses of the observed eruptive plasmas in X-ray passbands since any clumping causes the overestimation of the mass. For the other two events, we assume the temperatures are at the maximum temperature of the XRT temperature response function, which gives a lower limit of the masses. We find that the masses in XRT, ~3x10 13 - 5x10 14 g, are smaller in their upper limit than total masses obtained by LASCO, ~1x10 15 g. In addition, we estimate the radiative loss, thermal conduction, thermal, and kinetic energies of the eruptive plasma in X-rays. For four events, we find that the thermal conduction time scales are much shorter than the duration of eruption. This result implies that additional heating during the eruption may be required to explain the plasma observations in X-rays for the four events