Scaling Properties of Paths on Graphs

Let $G$ be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on $G$. Fix vertices $u$ and $v$ and consider the set of paths that start at $u$ and end at $v$, self-intersecting in any number of places along the way. For each path, sum the weights of its edges, and then list the path weights in increasing order. The asymptotic behaviour of this sequence is described, in terms of the structure and type of strongly connected components on the graph. As a special case, for a Markov chain the asymptotic probability of paths obeys either a power law scaling or a weaker type of scaling, depending on the structure of the transition matrix. This generalizes previous work by Mandelbrot and others, who established asymptotic power law scaling for special classes of Markov chains.Comment: 23 pages, 2 figure

Strength of the DTM RapidSteel 1.0 Material

This paper reports the results of a study into the strength of the DTM RapidSteel 1.0 material. Elastic modulus and strength of the metal/copper composite material was investigated as a function of the distance from the point of copper infiltration, the furnace cycle duration, and the furnace type. The microstructure of the RapidSteel material was also examined in an attempt to understand the science behind the infiltration process. The results have implications for the design of tools to be made using the RapidTool process in situations where the tool will be used as a production tool, rather than a prototype tool.Mechanical Engineerin

A modified method of integral relations approach to the blunt-body equilibrium air flow field, including comparisons with inverse solutions

Numerical calculation of inviscid adiabatic flow field around blunt bodies at hypersonic speed

The role of spatial and temporal radiation deposition in inertial fusion chambers: the case of HiPER¿

The first wall armour for the reactor chamber of HiPER will have to face short energy pulses of 5 to 20 MJ mostly in the form of x-rays and charged particles at a repetition rate of 5–10 Hz. Armour material and chamber dimensions have to be chosen to avoid/minimize damage to the chamber, ensuring the proper functioning of the facility during its planned lifetime. The maximum energy fluence that the armour can withstand without risk of failure, is determined by temporal and spatial deposition of the radiation energy inside the material. In this paper, simulations on the thermal effect of the radiation–armour interaction are carried out with an increasing definition of the temporal and spatial deposition of energy to prove their influence on the final results. These calculations will lead us to present the first values of the thermo-mechanical behaviour of the tungsten armour designed for the HiPER project under a shock ignition target of 48 MJ. The results will show that only the crossing of the plasticity limit in the first few micrometres might be a threat after thousands of shots for the survivability of the armour

The Fluctuations of the Quark Number and of the Chiral Condensate

The distributions of the quark number and chiral condensate over the gauge fields are computed for QCD in Euclidean space at nonzero quark chemical potential. As both operators are non-hermitian the distributions are in the complex plane. Moreover, because of the sign problem, the distributions are not real and positive. The computations are carried out within leading order chiral perturbation theory and give a direct insight into the delicate cancellations that take place in contributions to the total baryon number and the chiral condensate.Comment: 19 pages, 2 figure

Mapping the dynamic interactions between vortex species in highly anisotropic superconductors

Here we use highly sensitive magnetisation measurements performed using a Hall probe sensor on single crystals of highly anisotropic high temperature superconductors $Bi_{2}Sr_{2}CaCu_{2}O_{8}$ to study the dynamic interactions between the two species of vortices that exist in such superconductors. We observe a remarkable and clearly delineated high temperature regime that mirrors the underlying vortex phase diagram. Our results map out the parameter space over which these dynamic interaction processes can be used to create vortex ratchets, pumps and other fluxonic devices.Comment: 7 pages, 3 figures, to be published in Supercond. Sci. Techno

Critical Collapse of an Ultrarelativistic Fluid in the Γ→1\Gamma\to 1 Limit

In this paper we investigate the critical collapse of an ultrarelativistic perfect fluid with the equation of state $P=(\Gamma-1)\rho$ in the limit of $\Gamma\to 1$. We calculate the limiting continuously self similar (CSS) solution and the limiting scaling exponent by exploiting self-similarity of the solution. We also solve the complete set of equations governing the gravitational collapse numerically for $(\Gamma-1) = 10^{-2},...,10^{-6}$ and compare them with the CSS solutions. We also investigate the supercritical regime and discuss the hypothesis of naked singularity formation in a generic gravitational collapse. The numerical calculations make use of advanced methods such as high resolution shock capturing evolution scheme for the matter evolution, adaptive mesh refinement, and quadruple precision arithmetic. The treatment of vacuum is also non standard. We were able to tune the critical parameter up to 30 significant digits and to calculate the scaling exponents accurately. The numerical results agree very well with those calculated using the CSS ansatz. The analysis of the collapse in the supercritical regime supports the hypothesis of the existence of naked singularities formed during a generic gravitational collapse.Comment: 23 pages, 16 figures, revised version, added new results of investigation of a supercritical collapse and the existence of naked singularities in generic gravitational collaps

HAMSTRING CONTRACTILE TIMING IN ANTERIOR CRUCIATE LIGAMENT DEFICIENT PATIENTS

The purpose of this research is to examine contractile timing of the hamstrings in patients with anterior cruciate ligament (ACL) deficient knees. Ten patients were tested for hamstring contractile timing using Electromyographic (EMG) recordings during gait speeds of 3km/h and 5km/h on both a level and ten degree incline. An ANOVA analysis was used to demonstrate timing onset differences between the deficient and normal leg for each test condition and muscle onset timing was related to the Lysholm scale for perceived knee function. Significant interaction differences were found for legs and speed variations plus a negative correlation between functional scores and hamstring timing onset

Single polymer dynamics: coil-stretch transition in a random flow

By quantitative studies of statistics of polymer stretching in a random flow and of a flow field we demonstrate that the stretching of polymer molecules in a 3D random flow occurs rather sharply via the coil-stretch transition at the value of the criterion close to theoretically predicted.Comment: 4 pages, 5 figure