Modified conjugated gradient method for diagonalising large matrices

We present an iterative method to diagonalise large matrices. The basic idea is the same as the conjugated gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroduce errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trail vectors, play a similar role of the conjugated gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitably for first principle calculations.Comment: 6 Pages, 2EPS figures. (To appear in Phys. Rev. E

Two-dimensional negative donors in magnetic fields

A finite-difference solution of the Schroedinger equation for negative donor centers D^- in two dimensions is presented. Our approach is of exact nature and allows us to resolve a discrepancy in the literature on the ground state of a negative donor. Detailed calculations of the energies for a number of states show that for field strengths less than \gamma=0.117 a.u. the donor possesses one bound state, for 0.117<\gamma<1.68 a.u. there exist two bound states and for field strengths \gamma>1.68 a.u. the system possesses three bound states. Further relevant characteristics of negative donors in magnetic fields are provided.Comment: 7 pages, 1 figur

How Many Topics? Stability Analysis for Topic Models

Topic modeling refers to the task of discovering the underlying thematic structure in a text corpus, where the output is commonly presented as a report of the top terms appearing in each topic. Despite the diversity of topic modeling algorithms that have been proposed, a common challenge in successfully applying these techniques is the selection of an appropriate number of topics for a given corpus. Choosing too few topics will produce results that are overly broad, while choosing too many will result in the "over-clustering" of a corpus into many small, highly-similar topics. In this paper, we propose a term-centric stability analysis strategy to address this issue, the idea being that a model with an appropriate number of topics will be more robust to perturbations in the data. Using a topic modeling approach based on matrix factorization, evaluations performed on a range of corpora show that this strategy can successfully guide the model selection process.Comment: Improve readability of plots. Add minor clarification

Quantum Phase Transition of Spin-2 Cold Bosons in an Optical Lattice

The Bose-Hubbard Hamiltonian of spin-2 cold bosons with repulsive interaction in an optical lattice is proposed. After neglecting the hopping term, the site-independent Hamiltonian and its energy eigenvalues and eigenstates are obtained. We consider the hopping term as a perturbation to do the calculations in second order and draw the phase diagrams for different cases. The phase diagrams show that there is a phase transition from Mott insulator with integer number bosons to superfluid when the ratio $c_0/t$ ($c_0$ is the spin-independent on-site interaction and $t$ the hopping matrix element between adjacent lattice sites) is decreased to a critical value and that there is different phase boundary between superfluid and Mott insulator phase for different Zeeman level component in some ground states. We find that the position of phase boundary for different Zeeman level component is related to its average population in the Mott ground state.Comment: 16 pages, 6 figure

Comparison between unipolar and bipolar single phase grid-connected inverters for PV applications

An inverter is essential for the interfacing of photovoltaic panels with the AC network. There are many possible inverter topologies and inverter switching schemes and each one will have its own relative advantages and disadvantages. Efficiency and output current distortion are two important factors governing the choice of inverter system. In this paper, it is argued that current controlled inverters offer significant advantages from the point of view of minimisation of current distortion. Two inverter switching strategies are explored in detail. These are the unipolar current controlled inverter and the bipolar current controlled inverter. With respect to low frequency distortion, previously published works provide theoretical arguments in favour of bipolar switching. On the other hand it has also been argued that the unipolar switched inverter offers reduced switching losses and generates less EMI. On efficiency grounds, it appears that the unipolar switched inverter has an advantage. However, experimental results presented in this paper show that the level of low frequency current distortion in the unipolar switched inverter is such that it can only comply with Australian Standard 4777.2 above a minimum output current. On the other hand it is shown that at the same current levels bipolar switching results in reduced low frequency harmonics

High-Energy Aspects of Solar Flares: Overview of the Volume

In this introductory chapter, we provide a brief summary of the successes and remaining challenges in understanding the solar flare phenomenon and its attendant implications for particle acceleration mechanisms in astrophysical plasmas. We also provide a brief overview of the contents of the other chapters in this volume, with particular reference to the well-observed flare of 2002 July 23Comment: This is the introductory article for a monograph on the physics of solar flares, inspired by RHESSI observations. The individual articles are to appear in Space Science Reviews (2011

Black Hole Production from High Energy Scattering in AdS/CFT

In this article we show how to set up initial states in ${\cal N} =4$ SYM theory that correspond to high energy graviton collisions, leading to black hole formation in $AdS_5\times S^5$. For this purpose, we study states in the gauge theory that are dual to graviton wavepackets localized at the center of $AdS_5$, and carrying large angular momentum along the $S^5$. These states are created by exciting only the s-wave mode of one of the complex adjoint scalars of SYM. For a single graviton, the state is 1/2 BPS and one can show that it is dual to a linearized 1/2 BPS geometry in the bulk. Exploiting this dictionary, we show how to localize the particle's wavefunciton so that the dual linearized metric has the form of a Aichelburg-Sexl shock wave. One can then put two such shock waves into a head-on collision, which is known to produce a trapped surface. Finally, we discuss the prospect of studying graviton scattering directly at strong coupling in the gauge theory using a reduced model of matrix quantum mechanics.Comment: 11 pages, revtex format, no figure

Constitutive behavior of as-cast A356

The constitutive behavior of aluminum alloy A356 in the as-cast condition has been characterized using compression tests performed over a wide range of deformation temperatures (30-500{\deg}C) and strain rates (\approx0.1-10 /s). This work is intended to support the development of process models for a wide range of conditions including those relevant to casting, forging and machining. The flow stress behavior as a function of temperature and strain rate has been fit to a modified Johnson-Cook and extended Ludwik-Hollomon expression. The data has also been assessed with both the strain-independent Kocks-Mecking and Zener-Hollomon frameworks. The predicted plastic flow stress for each expression are compared. The results indicate that the extended Ludwik-Hollomon is best suited to describe small strain conditions (stage III hardening), while the Kocks-Mecking is best employed for large strain (stage IV). At elevated temperatures, it was found that the Zener-Hollomon model provides the best prediction of flow stress.Comment: 34 pages, 12 figure

Donor Centers and Absorption Spectra in Quantum Dots

We have studied the electronic properties and optical absorption spectra of three different cases of donor centers, D^{0}, D^{-} and D^{2-}, which are subjected to a perpendicular magnetic field, using the exact diagonalization method. The energies of the lowest lying states are obtained as function of the applied magnetic field strength B and the distance zeta between the positive ion and the confinement xy-plane. Our calculations indicate that the positive ion induces transitions in the ground-state, which can be observed clearly in the absorption spectra, but as zeta goes to 0 the strength of the applied magnetic field needed for a transition to occur tends to infinity.Comment: 5 pages, 4 figures, REVTeX 4, gzipped tar fil

Superconducting and pseudogap phases from scaling near a Van Hove singularity

We study the quantum corrections to the Fermi energy of a two-dimensional electron system, showing that it is attracted towards the Van Hove singularity for a certain range of doping levels. The scaling of the Fermi level allows to cure the infrared singularities left in the BCS channel after renormalization of the leading logarithm near the divergent density of states. A phase of d-wave superconductivity arises beyond the point of optimal doping corresponding to the peak of the superconducting instability. For lower doping levels, the condensation of particle-hole pairs due to the nesting of the saddle points takes over, leading to the opening of a gap for quasiparticles in the neighborhood of the singular points.Comment: 4 pages, 6 Postscript figures, the physical discussion of the results has been clarifie