Statistics of trajectories in two-state master equations

We derive a simple expression for the probability of trajectories of a master equation. The expression is particularly useful when the number of states is small and permits the calculation of observables that can be defined as functionals of whole trajectories. We illustrate the method with a two-state master equation, for which we calculate the distribution of the time spent in one state and the distribution of the number of transitions, each in a given time interval. These two expressions are obtained analytically in terms of modified Bessel functions.Comment: 4 pages, 3 figure

The evolution of a magnetic field subject to Taylor′s constraint using a projection operator

In the rapidly rotating, low-viscosity limit of the magnetohydrodynamic equations as relevant to the conditions in planetary cores, any generated magnetic field likely evolves while simultaneously satisfying a particular continuous family of invariants, termed Taylor′s constraint. It is known that, analytically, any magnetic field will evolve subject to these constraints through the action of a time-dependent coaxially cylindrical geostrophic flow. However, severe numerical problems limit the accuracy of this procedure, leading to rapid violation of the constraints. By judicious choice of a certain truncated Galerkin representation of the magnetic field, Taylor′s constraint reduces to a finite set of conditions of size O(N), significantly less than the O(N3) degrees of freedom, where N denotes the spectral truncation in both solid angle and radius. Each constraint is homogeneous and quadratic in the magnetic field and, taken together, the constraints define the finite-dimensional Taylor manifolδ whose tangent plane can be evaluated. The key result of this paper is a description of a stable numerical method in which the evolution of a magnetic field in a spherical geometry is constrained to the manifold by projecting its rate of change onto the local tangent hyperplane. The tangent plane is evaluated by contracting the vector of spectral coefficients with the Taylor tensor, a large but very sparse 3-D array that we define. We demonstrate by example the numerical difficulties in finding the geostrophic flow numerically and how the projection method can correct for inaccuracies. Further, we show that, in a simplified system using projection, the normalized measure of Taylorization, t, may be maintained smaller than O(10-10) (where t= 0 is an exact Taylor state) over 1/10 of a dipole decay time, eight orders of magnitude smaller than analogous measures applied to recent low Ekman-number geodynamo model

Measuring Burstiness in Data Center Applications

Buffer sizing is a tricky task --- it depends on a large number of variables, ranging from congestion control to traffic engineering. Still, the most unpredictable contributors are the workloads running in the network. The link utilization and burstiness of these workloads dictate the buffer depth needed by a switch. But what is a burst? Do traditional definitions still apply in the age in which switches transfer terabits of data and billions of packets every second? Unless we assess bursts correctly, we are unlikely to size buffers appropriately. In this work, we present a measurement-led evaluation of the burstiness of different data center applications. We address the question of ``what is a burst?'' and assert that common techniques cannot answer this question in modern data centers. We quantify the change in burstiness of the studied applications across multiple vectors, including latency and network perspective, and generalize our results to the common case. Our observations can inform future buffer sizing efforts and guide switch configurations. Our dataset is openly available for the benefit of the community.Leverhulme Trust Isaac Newton Trus

The Roll of the Burgh Courts of Aberdeen, August-October 1317

Publisher PD

Do Spinors Frame-Drag?

We investigate the effect of the intrinsic spin of a fundamental spinor field on the surrounding spacetime geometry. We show that despite the lack of a rotating stress-energy source (and despite claims to the contrary) the intrinsic spin of a spin-half fermion gives rise to a frame-dragging effect analogous to that of orbital angular momentum, even in Einstein-Hilbert gravity where torsion is constrained to be zero. This resolves a paradox regarding the counter-force needed to restore Newton's third law in the well known spin-orbit interaction. In addition, the frame-dragging effect gives rise to a {\it long-range} gravitationally mediated spin-spin dipole interaction coupling the {\it internal} spins of two sources. We argue that despite the weakness of the interaction, the spin-spin interaction will dominate over the ordinary inverse square Newtonian interaction in any process of sufficiently high-energy for quantum field theoretical effects to be non-negligible.Comment: V2: published version, mostly minor clarifications from V

Heat shock factor 1 regulates lifespan as distinct from disease onset in prion disease

Prion diseases are fatal, transmissible, neurodegenerative diseases caused by the misfolding of the prion protein (PrP). At present, the molecular pathways underlying prion-mediated neurotoxicity are largely unknown. We hypothesized that the transcriptional regulator of the stress response, heat shock factor 1 (HSF1), would play an important role in prion disease. Uninoculated HSF1 knockout (KO) mice used in our study do not show signs of neurodegeneration as assessed by survival, motor performance, or histopathology. When inoculated with Rocky Mountain Laboratory (RML) prions HSF1 KO mice had a dramatically shortened lifespan, succumbing to disease ≈20% faster than controls. Surprisingly, both the onset of home-cage behavioral symptoms and pathological alterations occurred at a similar time in HSF1 KO and control mice. The accumulation of proteinase K (PK)-resistant PrP also occurred with similar kinetics and prion infectivity accrued at an equal or slower rate. Thus, HSF1 provides an important protective function that is specifically manifest after the onset of behavioral symptoms of prion disease

An experimental and computational study of tip clearance effects on a transonic turbine stage

This paper describes an experimental and computational investigation into the influence of tip clearance on the blade tip heat load of a high-pressure (HP) turbine stage. Experiments were performed in the Oxford Rotor facility which is a 1½ stage, shroudless, transonic, high pressure turbine. The experiments were conducted at an engine representative Mach number and Reynolds number. Rotating frame instrumentation was used to capture both aerodynamic and heat flux data within the rotor blade row. Two rotor blade tip clearances were tested (1.5% and 1.0% of blade span). The experiments were compared with computational fluid dynamics (CFD) predictions made using a steady Reynolds-averaged Navier–Stokes (RANS) solver. The experiments and computational predictions were in good agreement. The blade tip heat transfer was observed to increase with reduced tip gap in both the CFD and the experiment. The augmentation of tip heat load at smaller clearances was found to be due to the ingestion of high relative total temperature fluid near the casing, generated through casing shear.This work was sponsored by Rolls-Royce plc and the Isle of Man Government.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.ijheatfluidflow.2015.09.00

Design and characterization of optical-THz phase-matched traveling-wave photomixers

Design and characterization of optical-THz phase-matched traveling-wave photomixers for difference-frequency generation of THz waves are presented. A de-biased coplanar stripline fabricated on low-temperature-grown GaAs is illuminated by two non-collinear laser beams which generate moving interference fringes that are accompanied by THz waves. By tuning the offset angle between the two laser beams, the velocity of the interference fringe can be matched to the phase velocity of the THz wave in the coplanar stripline. The generated THz waves are radiated into free space by the antenna at the termination of the stripline. Enhancement of the output power was clearly observed when the phase-matching condition was satisfied. The output power spectrum has a 3-dB bandwidth of 2 THz and rolls off as ~9 dB/Oct which is determined by the frequency dependent attenuation in the stripline, while the bandwidth of conventional photomixer design has the limitation by the RC time constant due to the electrode capacitance. The device can handle the laser power of over 380 mW, which is 5 times higher than the maximum power handring capability of conventional small area devices. The results show that the traveling-wave photomixers have the potential to surpass small area designs, especially at higher frequencies over I THz, owing to their great thermal dissipation capability and capacitance-free wide bandwidth