On graphs with a large chromatic number containing no small odd cycles

In this paper, we present the lower bounds for the number of vertices in a graph with a large chromatic number containing no small odd cycles

High Radiation Resistant DC-DC Converter Regulators for use in Magnetic fields for LHC High Luminosity Silicon Trackers

For more efficient power transport to the electronics embedded inside large colliding beam detectors, we explore the feasibility of supplying higher DC voltage and using local DC-DC conversion to 1.3 V (or lower, depending upon on the lithography of the embedded electronics) using switch mode regulators located very close to the front end electronics. These devices will be exposed to high radiation and high magnetic fields, 10 – 100 Mrads and 2 - 4 Tesla at the SLHC

An Improved Bound for First-Fit on Posets Without Two Long Incomparable Chains

It is known that the First-Fit algorithm for partitioning a poset P into chains uses relatively few chains when P does not have two incomparable chains each of size k. In particular, if P has width w then Bosek, Krawczyk, and Szczypka (SIAM J. Discrete Math., 23(4):1992--1999, 2010) proved an upper bound of ckw^{2} on the number of chains used by First-Fit for some constant c, while Joret and Milans (Order, 28(3):455--464, 2011) gave one of ck^{2}w. In this paper we prove an upper bound of the form ckw. This is best possible up to the value of c.Comment: v3: referees' comments incorporate

An Improved Upper Bound for the Ring Loading Problem

The Ring Loading Problem emerged in the 1990s to model an important special case of telecommunication networks (SONET rings) which gained attention from practitioners and theorists alike. Given an undirected cycle on $n$ nodes together with non-negative demands between any pair of nodes, the Ring Loading Problem asks for an unsplittable routing of the demands such that the maximum cumulated demand on any edge is minimized. Let $L$ be the value of such a solution. In the relaxed version of the problem, each demand can be split into two parts where the first part is routed clockwise while the second part is routed counter-clockwise. Denote with $L^*$ the maximum load of a minimum split routing solution. In a landmark paper, Schrijver, Seymour and Winkler [SSW98] showed that $L \leq L^* + 1.5D$, where $D$ is the maximum demand value. They also found (implicitly) an instance of the Ring Loading Problem with $L = L^* + 1.01D$. Recently, Skutella [Sku16] improved these bounds by showing that $L \leq L^* + \frac{19}{14}D$, and there exists an instance with $L = L^* + 1.1D$. We contribute to this line of research by showing that $L \leq L^* + 1.3D$. We also take a first step towards lower and upper bounds for small instances

Bounding biomass in the Fisher equation

The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.Comment: 32 Pages, 13 Figure

A study on the radiation hardness of lead tungstate crystals

This report presents recent progress of a study on the radiation damage in lead tungstate (PbWO_4) crystals. The dose rate dependence of radiation damage in PbWO_4 has been observed, confirming our early prediction based upon a kinetic model of color centers. An optimization of the oxygen compensation through post-growth thermal annealing, carried out in Shanghai Institute of Ceramics, has led to PbWO_4 crystals with significantly improved radiation hardness. A comparison between front versus uniform irradiations revealed that the later caused a factor of 2 to 6 times more severe damage. A measurement of a preliminary batch of lanthanum doped PbWO_4 crystals indicates that the La doping seems not a determine factor for PbWO_4 radiation hardness improvement. Finally, a TEM/EDS analysis confirmed our previous conjecture that the radiation damage in PbWO_4 crystals is caused by oxygen vacancies

A study of the optical and radiation damage properties of lead tungstate crystals

A study has been made of the optical and radiation damage properties of undoped and niobium doped lead tungstate crystals. Data were obtained on the optical absorbance, the intensity and decay time of the scintillation light output, and the radioluminescence and photoluminescence emission spectra. Radiation damage was studied in several undoped and niobium doped samples using ^(60)Co gamma ray irradiation. The change in optical absorption and observed scintillation light output was measured as a function of dose up to total cumulative doses on the order of 800 krad. The radiation induced phosphorescence and thermoluminescence was also measured, as well as recovery from damage by optical bleaching and thermal annealing. An investigation was also made to determine trace element impurities in several samples