Difference Methods for Boundary Value Problems in Ordinary Differential Equations

A general theory of difference methods for problems of the form Ny ≡ y' - f(t,y) = O, a ≦ t ≦ b, g(y(a),y(b))= 0, is developed. On nonuniform nets, t_0 = a, t_j = t_(j-1) + h_j, 1 ≦ j ≦ J, t_J = b, schemes of the form N_(h)u_j = G_j(u_0,•••,u_J) = 0, 1 ≦ j ≦ J, g(u_0,u_J) = 0 are considered. For linear problems with unique solutions, it is shown that the difference scheme is stable and consistent for the boundary value problem if and only if, upon replacing the boundary conditions by an initial condition, the resulting scheme is stable and consistent for the initial value problem. For isolated solutions of the nonlinear problem, it is shown that the difference scheme has a unique solution converging to the exact solution if (i) the linearized difference equations are stable and consistent for the linearized initial value problem, (ii) the linearized difference operator is Lipschitz continuous, (iii) the nonlinear difference equations are consistent with the nonlinear differential equation. Newton’s method is shown to be valid, with quadratic convergence, for computing the numerical solution

Transcriptional repression by ApiAP2 factors is central to chronic toxoplasmosis

Tachyzoite to bradyzoite development in Toxoplasma is marked by major changes in gene expression resulting in a parasite that expresses a new repertoire of surface antigens hidden inside a modified parasitophorous vacuole called the tissue cyst. The factors that control this important life cycle transition are not well understood. Here we describe an important transcriptional repressor mechanism controlling bradyzoite differentiation that operates in the tachyzoite stage. The ApiAP2 factor, AP2IV-4, is a nuclear factor dynamically expressed in late S phase through mitosis/cytokinesis of the tachyzoite cell cycle. Remarkably, deletion of the AP2IV-4 locus resulted in the expression of a subset of bradyzoite-specific proteins in replicating tachyzoites that included tissue cyst wall components BPK1, MCP4, CST1 and the surface antigen SRS9. In the murine animal model, the mis-timing of bradyzoite antigens in tachyzoites lacking AP2IV-4 caused a potent inflammatory monocyte immune response that effectively eliminated this parasite and prevented tissue cyst formation in mouse brain tissue. Altogether, these results indicate that suppression of bradyzoite antigens by AP2IV-4 during acute infection is required for Toxoplasma to successfully establish a chronic infection in the immune-competent host

A Constrained Path Monte Carlo Method for Fermion Ground States

We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an over-complete basis of Slater determinants. By constraining the determinants according to a trial wave function $|\psi_T\rangle$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|\psi_T\rangle$ is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to $16\times 16$ and for various electron fillings and interaction strengths. Besides highly accurate estimates of the ground-state energy, we find that the method also yields reliable estimates of other ground-state observables, such as superconducting pairing correlation functions. We conclude by discussing possible extensions of the algorithm.Comment: 29 pages, RevTex, 3 figures included; submitted to Phys. Rev.

Surface dissipation in nanoelectromechanical systems: Unified description with the standard tunneling model and effects of metallic electrodes

By modifying and extending recent ideas [C. Seoanez et al., Europhys. Lett. 78, 60002 (2007)], a theoretical framework to describe dissipation processes in the surfaces of vibrating micro- and nanoelectromechanical devices, thought to be the main source of friction at low temperatures, is presented. Quality factors as well as frequency shifts of flexural and torsional modes in doubly clamped beams and cantilevers are given, showing the scaling with dimensions, temperature, and other relevant parameters of these systems. Full agreement with experimental observations is not obtained, leading to a discussion of limitations and possible modifications of the scheme to reach a quantitative fitting to experiments. For nanoelectromechanical systems covered with metallic electrodes, the friction due to electrostatic interaction between the flowing electrons and static charges in the device and substrate is also studied.Comment: 17 pages, 7 figure

Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach

We have applied the momentum space version of the Density Matrix Renormalization Group method ($k$-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in the new context. We have shown numerically that it is possible to determine the desired accuracy of the method in advance of the calculations by dynamically controlling the truncation error and the number of block states using a novel protocol which we dubbed Dynamical Block State Selection (DBSS). The relationship between the real error and truncation error has been studied as a function of the number of orbitals and the fraction of filled orbitals. We have calculated the ground state of the molecules CH$_2$, H$_2$O, and F$_2$ as well as the first excited state of CH$_2$. Our largest calculations were carried out with 57 orbitals, the largest number of block states was 1500--2000, and the largest dimensions of the Hilbert space of the superblock configuration was 800.000--1.200.000.Comment: 12 page

Magnetic field diagnostics and spatio-temporal variability of the solar transition region

Magnetic field diagnostics of the transition region from the chromosphere to the corona faces us with the problem that one has to apply extreme UV spectro-polarimetry. While for coronal diagnostic techniques already exist through infrared coronagraphy above the limb and radio observations on the disk, for the transition region one has to investigate extreme UV observations. However, so far the success of such observations has been limited, but there are various projects to get spectro-polarimetric data in the extreme UV in the near future. Therefore it is timely to study the polarimetric signals we can expect for such observations through realistic forward modeling. We employ a 3D MHD forward model of the solar corona and synthesize the Stokes I and Stokes V profiles of C IV 1548 A. A signal well above 0.001 in Stokes V can be expected, even when integrating for several minutes in order to reach the required signal-to-noise ratio, despite the fact that the intensity in the model is rapidly changing (just as in observations). Often this variability of the intensity is used as an argument against transition region magnetic diagnostics which requires exposure times of minutes. However, the magnetic field is evolving much slower than the intensity, and thus when integrating in time the degree of (circular) polarization remains rather constant. Our study shows the feasibility to measure the transition region magnetic field, if a polarimetric accuracy on the order of 0.001 can be reached, which we can expect from planned instrumentation.Comment: Accepted for publication in Solar Physics (4.Mar.2013), 19 pages, 9 figure

Observations of the 8 December 1987 occultation of AG+40 deg 0783 by 324 Bamberga

The occultation of AG+40 deg 0783 by 324 Bamberga on 8 December 1987 was observed at 13 sites in the United States, Japan, and China. At four sites the event was observed photoelectrically; the other observations were visual. A least-squares fit of a circular limb profile to the data gives a diameter of 227.6 + or - 1.9 km. However, this solution is inconsistent with a negative visual observation near the northern edge of the ground track. The inconsistency cannot be removed by assuming an elliptical profile. The data suggest that Bamberga, despite its low-amplitude lightcurve, may depart significantly from a spherical or ellipsoidal shape. The asteroid also appears to be at least 10 percent smaller than indicated by infrared radiometry

1942: Abilene Christian College Bible Lectures - Full Text

Delivered in the Auditorium of Abilene Christian College, February, 1942 Abilene, Texas Published September, 1942 Price: $1.00. FIRM FOUNDATION PUBLISHING HOUSE Austin, Texa

The preemptive repeat hybrid server interruption model

We analyze a discrete-time queueing system with server interruptions and a hybrid preemptive repeat interruption discipline. Such a discipline encapsulates both the preemptive repeat identical and the preemptive repeat different disciplines. By the introduction and analysis of so-called service completion times, we significantly reduce the complexity of the analysis. Our results include a.o. the probability generating functions and moments of queue content and delay. Finally, by means of some numerical examples, we assess how performance measures are affected by the specifics of the interruption discipline

Individual Rights, Economic Transactions, and Recognition: A Legal Approach to Social Economics

Modernity brought the idea of individual property rights as a com- plex phenomenon. However, economics adopted a simplistic view of property as a fundamental institution, understating the complex interaction of different rights and obligations that frame the legal environment of economic processes with an insufficiently elaborated tool. Here, a more elaborate view of legal elements will be propose