Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation

A reaction-diffusion problem with a Caputo time derivative of order = 2 (0; 1) is considered. The solution of such a problem is shown in general to have a weak singularity near the initial time t = 0, and sharp point wise bounds on certain derivatives of this solution are derived. A new analysis of a standard finite difference method for the problem is given, taking into account this initial singularity. This analysis encompasses both uniform meshes and meshes that are graded in time, and includes new stability and consistency bounds. The final convergence result shows clearly how the regularity of the solution and the grading of the mesh affect the order of convergence of the difference scheme, so one can choose an optimal mesh grading. Numerical results are presented that confirm the sharpness of the error analysis

Sensitivity of an image plate system in the XUV (60 eV < E < 900 eV)

Phosphor imaging plates (IPs) have been calibrated and proven useful for quantitative x-ray imaging in the 1 to over 1000 keV energy range. In this paper we report on calibration measurements made at XUV energies in the 60 to 900 eV energy range using beamline 6.3.2 at the Advanced Light Source at Lawrence Berkeley National Laboratory. We measured a sensitivity of ~25 plus or minus 15 counts/pJ over the stated energy range which is compatible with the sensitivity of Si photodiodes that are used for time-resolved measurements. Our measurements at 900 eV are consistent with the measurements made by Meadowcroft et al. at ~1 keV.Comment: 7 pages, 2 figure

Change of a Weibel-type to an Alfv\'enic shock in pair plasma by upstream waves

We examine with particle-in-cell (PIC) simulations how a parallel shock in pair plasma reacts to upstream waves, which are driven by escaping downstream particles. Initially, the shock is sustained in the two-dimensional simulation by a magnetic filamentation (beam-Weibel) instability. Escaping particles drive an electrostatic beam instability upstream. Modifications of the upstream plasma by these waves hardly affect the shock. In time, a decreasing density and increasing temperature of the escaping particles quench the beam instability. A larger thermal energy along than perpendicular to the magnetic field destabilizes the pair-Alfv\'en mode. In the rest frame of the upstream plasma, the group velocity of the growing pair-Alfv\'en waves is below that of the shock and the latter catches up with the waves. Accumulating pair-Alfv\'en waves gradually change the shock in the two-dimensional simulation from a Weibel-type shock into an Alfv\'enic shock with a Mach number that is about 6 for our initial conditions.Comment: 11 pages, 10 figures, accepted for publication in Physics of Plasma

Cord blood in regenerative medicine: do we need immune suppression?

Cord blood is currently used as an alternative to bone marrow as a source of stem cells for hematopoietic reconstitution after ablation. It is also under intense preclinical investigation for a variety of indications ranging from stroke, to limb ischemia, to myocardial regeneration. A major drawback in the current use of cord blood is that substantial morbidity and mortality are associated with pre-transplant ablation of the recipient hematopoietic system. Here we raise the possibility that due to unique immunological properties of both the stem cell and non-stem cell components of cord blood, it may be possible to utilize allogeneic cells for regenerative applications without needing to fully compromise the recipient immune system. Issues raised will include: graft versus host potential, the immunogeneicity of the cord blood graft, and the parallels between cord blood transplantation and fetal to maternal trafficking. The previous use of unmatched cord blood in absence of any immune ablation, as well as potential steps for widespread clinical implementation of allogeneic cord blood grafts will also be discussed

Therapeutic use of Aldara™ in chronic myeloid leukemia

The potent clinical responses seen in patients with chronic myeloid leukemia (CML) after administration of donor-specific lymphocytes, as well as the correlation between the presence of antigen specific T cells and prolonged remission in these patients, suggests a role for the immunological control of CML. Here we propose Aldara™, a clinically used formulation of imiquimod, as an agent for augmenting immune responses to CML antigens. Our proposition is based upon 3 tenets: 1) Endogenous dendritic cells (DC) of CML patients, which are known to be derived from the malignant clone, express and present various leukemic antigens; 2) CML-antigen reactive T cell clones exist in the patient but in many situations are ineffectively stimulated to cause significant hematological responses; and 3) Antigen presentation by mature, activated DC, which endogenously express CML-antigens may endow the pre-existing ineffective T cell responses with ability to control CML progression. The practical use of Aldara™ as a localized activator of DC in the context of present day leukemic therapeutics, as well as various properties of this unique immune modulator will be discussed

Design and development of a low temperature, inductance based high frequency ac susceptometer

We report on the development of an induction based low temperature high frequency ac susceptometer capable of measuring at frequencies up to 3.5 MHz and at temperatures between 2 K and 300 K. Careful balancing of the detection coils and calibration have allowed a sample magnetic moment resolution of $5\times10^{-10} Am^2$ at 1 MHz. We will discuss the design and characterization of the susceptometer, and explain the calibration process. We also include some example measurements on the spin ice material CdEr$_2$S$_4$ and iron oxide based nanoparticles to illustrate functionality

Statistical Properties of the Final State in One-dimensional Ballistic Aggregation

We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final `fan' state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Frechet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of N-body dissipative dynamics.Comment: 19 pages, 5 figures include

Emergence of pulled fronts in fermionic microscopic particle models

We study the emergence and dynamics of pulled fronts described by the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic reaction-diffusion process A + A A$ on the lattice when only a particle is allowed per site. To this end we identify the parameter that controls the strength of internal fluctuations in this model, namely, the number of particles per correlated volume. When internal fluctuations are suppressed, we explictly see the matching between the deterministic FKPP description and the microscopic particle model.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. E as a Rapid Communicatio

Risk, precaution and science: towards a more constructive policy debate. Talking point on the precautionary principle

Few issues in contemporary risk policy are as momentous or contentious as the precautionary principle. Since it first emerged in German environmental policy, it has been championed by environmentalists and consumer protection groups, and resisted by the industries they oppose (Raffensperger & Tickner, 1999). Various versions of the principle now proliferate across different national and international jurisdictions and policy areas (Fisher, 2002). From a guiding theme in European Commission (EC) environmental policy, it has become a general principle of EC law (CEC, 2000; Vos & Wendler, 2006). Its influence has extended from the regulation of environmental, technological and health risks to the wider governance of science, innovation and trade (O'Riordan & Cameron, 1994)