Implicit and Implicit-Explicit Strong Stability Preserving Runge-Kutta Methods with High Linear Order

When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity properties satisfied by the spatial discretization when coupled with the first order forward Euler, under a certain time-step restriction. While the allowable time-step depends on both the spatial and temporal discretizations, the contribution of the temporal discretization can be isolated by taking the ratio of the allowable time-step of the high order method to the forward Euler time-step. This ratio is called the strong stability coefficient. The search for high order strong stability time-stepping methods with high order and large allowable time-step had been an active area of research. It is known that implicit SSP Runge-Kutta methods exist only up to sixth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and we can find implicit SSP Runge-Kutta methods of any linear order. In the current work we aim to find very high linear order implicit SSP Runge-Kutta methods that are optimal in terms of allowable time-step. Next, we formulate an optimization problem for implicit-explicit (IMEX) SSP Runge-Kutta methods and find implicit methods with large linear stability regions that pair with known explicit SSP Runge-Kutta methods of orders plin=3,4,6 as well as optimized IMEX SSP Runge-Kutta pairs that have high linear order and nonlinear orders p=2,3,4. These methods are then tested on sample problems to verify order of convergence and to demonstrate the sharpness of the SSP coefficient and the typical behavior of these methods on test problems

Collapse of an Instanton

We construct a two parameter family of collapsing solutions to the 4+1 Yang-Mills equations and derive the dynamical law of the collapse. Our arguments indicate that this family of solutions is stable. The latter fact is also supported by numerical simulations.Comment: 17 pages, 1 figur

Non-radially symmetric solutions to the Ginzburg-Landau equation

We study an atom with finitely many energy levels in contact with a heat bath consisting of photons (black body radiation) at a temperature $T >0$. The dynamics of this system is described by a Liouville operator, or thermal Hamiltonian, which is the sum of an atomic Liouville operator, of a Liouville operator describing the dynamics of a free, massless Bose field, and a local operator describing the interactions between the atom and the heat bath. We show that an arbitrary initial state which is normal with respect to the equilibrium state of the uncoupled system at temperature $T$ converges to an equilibrium state of the coupled system at the same temperature, as time tends to $+ \infty

On collapse of wave maps

We derive the universal collapse law of degree 1 equivariant wave maps (solutions of the sigma-model) from the 2+1 Minkowski space-time,to the 2-sphere. To this end we introduce a nonlinear transformation from original variables to blowup ones. Our formal derivations are confirmed by numerical simulations.Comment: 1 figur

Expression of phosphorylcholine-specific B cells during murine development

The TEPC 15 (T15) clonotype, a putatively germline antibody specificity, does not appear in the neonatal B-cell repertoire until approximately 1 wk of age. This report extends this observation by the demonstration that (a) the T15 clonotype follows similar kinetics of appearance in germfree as well as conventionally-reared mice; (b) maternal influences and genetic background play a minor role in the development of the T15 clonotype since CBFI neonates raised by C57BL/6 or BALB/c mothers acquire the T15 clonotype at the same time in ontogeny as BALB/c neonates; (c) the lack of phosphorylcholine (PC)-specific B cells shortly after birth is reflected in a dearth of PC-binding cells in the neonate as well; and (d) no PC-specifc B cells are found in 19-day fetal liver or in bone marrow until 7 days of life, coincident with their appearance in the spleen. These findings, along with a previous report that PC-specific splenic B cells are tolerizable as late as day 10 after birth, confirm the invariant, late occurrence of the T15 clonotype and support a highly- ordered, rigorously predetermined mechanism for the acquisition of the B- cell repertoire. The results are discussed in light of other studies on the ontogeny of B-cell specificity, and in terms of the implications on the mechanism by which antibody diversity is generated

Completeness of the Coulomb scattering wave functions

Completeness of the eigenfunctions of a self-adjoint Hamiltonian, which is the basic ingredient of quantum mechanics, plays an important role in nuclear reaction and nuclear structure theory. However, until now, there was no a formal proof of the completeness of the eigenfunctions of the two-body Hamiltonian with the Coulomb interaction. Here we present the first formal proof of the completeness of the two-body Coulomb scattering wave functions for repulsive unscreened Coulomb potential. To prove the completeness we use the Newton's method [R. Newton, J. Math Phys., 1, 319 (1960)]. The proof allows us to claim that the eigenfunctions of the two-body Hamiltonian with the potential given by the sum of the repulsive Coulomb plus short-range (nuclear) potentials also form a complete set. It also allows one to extend the Berggren's approach of modification of the complete set of the eigenfunctions by including the resonances for charged particles. We also demonstrate that the resonant Gamow functions with the Coulomb tail can be regularized using Zel'dovich's regularization method.Comment: 12 pages and 1 figur

THE ACCUSED IS ENTERING THE COURTROOM: THE LIVE-TWEETING OF A MURDER TRIAL.

© 2017 Informa UK Limited, trading as Taylor & Francis GroupThe use of social media is now widely accepted within journalism as an outlet for news information. Live tweeting of unfolding events is standard practice. In March 2014, Oscar Pistorius went on trial in the Gauteng High Court for murder. Hundreds of journalists present began live-tweeting coverage, an unprecedented combination of international interest, permission to use technology and access which resulted in massive streams of consciousness reports of events as they unfolded. Based on a corpus of Twitter feeds of twenty-four journalists covering the trial, this study analyses the content and strategies of these feeds in order to present an understanding of how microblogging is used as a live reporting tool. This study shows the development of standardised language and strategies in reporting on Twitter, concluding that journalists adopt a narrow range of approaches, with no significant variation in terms of gender, location, or medium. This is in contrast to earlier studies in the field (Awad, 2006, Hedman, 2015; Kothari, 2010; Lariscy, Avery, Sweetser, & Howes, 2009 Lasorsa, 2012; Lasorsa, Lewis, & Holton, 2011; Sigal, 1999, Vis, 2013).Peer reviewe

Biomarkers of Tuberculosis Severity and Treatment Effect: A Directed Screen of 70 Host Markers in a Randomized Clinical Trial.

More efficacious treatment regimens are needed for tuberculosis, however, drug development is impeded by a lack of reliable biomarkers of disease severity and of treatment effect. We conducted a directed screen of host biomarkers in participants enrolled in a tuberculosis clinical trial to address this need. Serum samples from 319 protocol-correct, culture-confirmed pulmonary tuberculosis patients treated under direct observation as part of an international, phase 2 trial were screened for 70 markers of infection, inflammation, and metabolism. Biomarker assays were specifically developed for this study and quantified using a novel, multiplexed electrochemiluminescence assay. We evaluated the association of biomarkers with baseline characteristics, as well as with detailed microbiologic data, using Bonferroni-adjusted, linear regression models. Across numerous analyses, seven proteins, SAA1, PCT, IL-1β, IL-6, CRP, PTX-3 and MMP-8, showed recurring strong associations with markers of baseline disease severity, smear grade and cavitation; were strongly modulated by tuberculosis treatment; and had responses that were greater for patients who culture-converted at 8weeks. With treatment, all proteins decreased, except for osteocalcin, MCP-1 and MCP-4, which significantly increased. Several previously reported putative tuberculosis-associated biomarkers (HOMX1, neopterin, and cathelicidin) were not significantly associated with treatment response. In conclusion, across a geographically diverse and large population of tuberculosis patients enrolled in a clinical trial, several previously reported putative biomarkers were not significantly associated with treatment response, however, seven proteins had recurring strong associations with baseline radiographic and microbiologic measures of disease severity, as well as with early treatment response, deserving additional study