Boundary layers in weak solutions to hyperbolic conservation laws

This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the vanishing viscosity method and finite difference schemes (Lax-Friedrichs type schemes, Godunov scheme). We demonstrate that different regularization methods generate different boundary layers. Hence, the boundary condition can be formulated only if an approximation scheme is selected first. Assuming solely uniform L\infty bounds on the approximate solutions and so dealing with L\infty solutions, we derive several entropy inequalities satisfied by the boundary layer in each case under consideration. A Young measure is introduced to describe the boundary trace. When a uniform bound on the total variation is available, the boundary Young measure reduces to a Dirac mass. Form the above analysis, we deduce several formulations for the boundary condition which apply whether the boundary is characteristic or not. Each formulation is based a set of admissible boundary values, following Dubois and LeFloch's terminology in ``Boundary conditions for nonlinear hyperbolic systems of conservation laws'', J. Diff. Equa. 71 (1988), 93--122. The local structure of those sets and the well-posedness of the corresponding initial-boundary value problem are investigated. The results are illustrated with convex and nonconvex conservation laws and examples from continuum mechanics.Comment: 43 page

Historic Buildings and Rehabilitation Expenditures: A Panel Data Approach

This paper examines the relationship between the characteristics of buildings and their assessed value in a historic area in Winnipeg, Manitoba Canada. Using a unique panel data set, we use a hedonic model to examine the factors that have affected the market value assessments of a set of historic and non-historically designated buildings. Using a number of estimators, we find that controlling for a number of key characteristics of buildings, that the assessed value of a building is higher for some classes of historic buildings. In addition, we estimate a two stage Heckman sample selection model, to determine the factors that influence the rehabilitation decision, and the effect of those expenditures and other building characteristics on the change in assessed values of buildings. We find that the expenditures on renovations contribute significantly to the change in assessed values of buildings, although less than might be expected. We provide a rationale for this result and also discuss the factors that influence the probability of renovation of a building as well as the change in their assessed values. Apart from the above, a number of interesting empirical results are also reported which may be used as input into the design of cost effective rehabilitation strategies for historic preservation.

Forward Physics at the LHC: within and beyond the Standard Model

We review the detection capabilities in the forward direction of the various LHC experiments together with the associated physics programme. A selection of measurements accessible with near-beam instrumentation in various sectors (and extensions) of the Standard Model (SM) is outlined, including QCD (diffractive and elastic scattering, low-x parton dynamics, hadronic Monte Carlos for cosmic-rays), electroweak processes in gamma-gamma interactions, and Higgs physics (vector-boson-fusion and central exclusive production).Comment: 9 pages, 18 figs. Lectures given at the LAWHEP'07 School (Sao Miguel das Missoes, Brazil, 3-7 Dec 2007) to appear in Braz. J. Phys. Also presented in HLPW08 (Spa, Belgium, 6-8 Mar 2008) AIP Conf. Proceeds, to appear; and in HANUC European Grad. School (Jyvaskyla, Finland, 25-29 Aug. 2008

Drosophila as a model system to study nonautonomous mechanisms affecting tumour growth and cell death

The study of cancer has represented a central focus in medical research for over a century. The great complexity and constant evolution of the pathology require the use of multiple research model systems and interdisciplinary approaches. This is necessary in order to achieve a comprehensive understanding into the mechanisms driving disease initiation and progression, to aid the development of appropriate therapies. In recent decades, the fruit fly Drosophila melanogaster and its associated powerful genetic tools have become a very attractive model system to study tumour-intrinsic and non-tumour-derived processes that mediate tumour development in vivo. In this review, we will summarize recent work on Drosophila as a model system to study cancer biology. We will focus on the interactions between tumours and their microenvironment, including extrinsic mechanisms affecting tumour growth and how tumours impact systemic host physiology

A synthetic model of the gravitational wave background from evolving binary compact objects

Modeling the stochastic gravitational wave background from various astrophysical sources is a key objective in view of upcoming observations with ground- and space-based gravitational wave observatories such as Advanced LIGO, VIRGO, eLISA and PTA. We develop a synthetic model framework that follows the evolution of single and binary compact objects in an astrophysical context. We describe the formation and merger rates of binaries, the evolution of their orbital parameters with time and the spectrum of emitted gravitational waves at different stages of binary evolution. Our approach is modular and allows us to test and constrain different ingredients of the model, including stellar evolution, black hole formation scenarios and the properties of binary systems. We use this framework in the context of a particularly well-motivated astrophysical setup to calculate the gravitational wave background from several types of sources, including inspiraling stellar-mass binary black holes that have not merged during a Hubble time. We find that this signal, albeit weak, has a characteristic shape that can help constrain the properties of binary black holes in a way complementary to observations of the background from merger events. We discuss possible applications of our framework in the context of other gravitational wave sources, such as supermassive black holes.Comment: 13 pages, 6 figures. Accepted for publication in Phys. Rev. D. Revised to reflect final versio

The charge conjugation quantum number in multiquark systems

We discuss the charge conjugation quantum number for tetraquarks or meson-meson molecules, seen as possible interpretations of the newly found $XYZ$ charmonium-like resonances.Comment: 7 pages, 1 figure, based on a talk given at the Joint Meeting Heidelberg-Liege-Paris-Wroclaw (HLPW08): Three Days of Strong Interactions and Astrophysics, Spa, March 6-8, 2008, Eqs. (18)-(25) corrected, text slightly polished, conclusions unchange

Integral equation for gauge invariant quark Green's function

We consider gauge invariant quark two-point Green's functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the presence of an external gluon field, functional relations between Green's functions with different numbers of segments of the polygonal lines are established. An integral equation is obtained for the Green's function having a phase factor along a single straight line. The related kernels involve Wilson loops with skew-polygonal contours and with functional derivatives along the sides of the contours.Comment: 7 pages; talk given at the Joint Meeting Heidelberg-Liege-Paris-Wroclaw, Spa, 6-8 March 2008; to appear in the Proceedings (AIP