A similarity law for stressing rapidly heated thin-walled cylinders

When a thin cylindrical shell of uniform thickness is very rapidly heated by hot high-pressure gas flowing inside the shell, the temperature of material decreases steeply from a high temperature at the inside surface to ambient temperatures at the outside surface. Young's modulus of material thus varies. The purpose of the present paper is to reduce the problem of stress analysis of such a cylinder to an equivalent problem in conventional cylindrical shell without temperature gradient in the wall. The equivalence concept is expressed as a series of relations between the quantities for the hot cylinder and the quantities for the cold cylinder. These relations give the similarity law whereby strains for the hot cylinder can be simply deduced from measured strains on the cold cylinder and thus greatly simplify the problem of experimental stress analysis

A computer solution for the dynamic load, lubricant film thickness and surface temperatures in spiral bevel gears

A complete analysis of spiral bevel gear sets is presented. The gear profile is described by the movements of the cutting tools. The contact patterns of the rigid body gears are investigated. The tooth dynamic force is studied by combining the effects of variable teeth meshing stiffness, speed, damping, and bearing stiffness. The lubrication performance is also accomplished by including the effects of the lubricant viscosity, ambient temperature, and gear speed. A set of numerical results is also presented

Solvability and regularity for an elliptic system prescribing the curl, divergence, and partial trace of a vector field on Sobolev-class domains

We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field are prescribed in an open, bounded, Sobolev-class domain, and either the normal component or the tangential components of the vector field are prescribed on the boundary. The proof is based on a regularity theory for vector elliptic equations set on Sobolev-class domains and with Sobolev-class coefficients.Comment: 49 Pages, improved exposition and corrected typo

Collective Quartics and Dangerous Singlets in Little Higgs

Any extension of the standard model that aims to describe TeV-scale physics without fine-tuning must have a radiatively-stable Higgs potential. In little Higgs theories, radiative stability is achieved through so-called collective symmetry breaking. In this letter, we focus on the necessary conditions for a little Higgs to have a collective Higgs quartic coupling. In one-Higgs doublet models, a collective quartic requires an electroweak triplet scalar. In two-Higgs doublet models, a collective quartic requires a triplet or singlet scalar. As a corollary of this study, we show that some little Higgs theories have dangerous singlets, a pathology where collective symmetry breaking does not suppress quadratically-divergent corrections to the Higgs mass.Comment: 4 pages; v2: clarified the existing literature; v3: version to appear in JHE

Copying equations to assess mathematical competence: An evaluation of pause measures using graphical protocol analysis

Can mathematical competence be measured by analyzing the patterns of pauses between written elements in the freehand copying of mathematical equations? Twenty participants of varying levels of mathematical competence copied sets of equations and sequences of numbers on a graphics tablet. The third quartile of pauses is an effective measure, because it re- flects the greater number of chunks and the longer time spent per chunk by novices as they processed the equations. To compensate for individual differences in speeds of elementary operations and skill in writing basic mathematical symbols, variants on the measure were devised and tested

Dynamic response and stability of a gas-lubricated Rayleigh-step pad

The quasi-static, pressure characteristics of a gas-lubricated thrust bearing with shrouded, Rayleigh-step pads are determined for a time-varying film thickness. The axial response of the thrust bearing to an axial forcing function or an axial rotor disturbance is investigated by treating the gas film as a spring having nonlinear restoring and damping forces. These forces are related to the film thickness by a power relation. The nonlinear equation of motion in the axial mode is solved by the Ritz-Galerkin method as well as the direct, numerical integration. Results of the nonlinear response by both methods are compared with the response based on the linearized equation. Further, the gas-film instability of an infinitely wide Rayleigh step thrust pad is determined by solving the transient Reynolds equation coupled with the equation of the motion of the pad. Results show that the Rayleigh-step geometry is very stable for bearing number A up to 50. The stability threshold is shown to exist only for ultrahigh values of Lambda equal to or greater than 100, where the stability can be achieved by making the mass heavier than the critical mass

The Universal Real Projective Plane: LHC phenomenology at one Loop

The Real Projective Plane is the lowest dimensional orbifold which, when combined with the usual Minkowski space-time, gives rise to a unique model in six flat dimensions possessing an exact Kaluza Klein (KK) parity as a relic symmetry of the broken six dimensional Lorentz group. As a consequence of this property, any model formulated on this background will include a stable Dark Matter candidate. Loop corrections play a crucial role because they remove mass degeneracy in the tiers of KK modes and induce new couplings which mediate decays. We study the full one loop structure of the corrections by means of counter-terms localised on the two singular points. As an application, the phenomenology of the (2,0) and (0,2) tiers is discussed at the LHC. We identify promising signatures with single and di-lepton, top antitop and 4 tops: in the dilepton channel, present data from CMS and ATLAS may already exclude KK masses up to 250 GeV, while by next year they may cover the whole mass range preferred by WMAP data.Comment: 45 pages, 3 figure

Possibly New Charmed Baryon States from Bˉ0→ppˉD0\bar B^0\to p\bar p D^{0} Decay

We examine the invariant mass spectrum of $D^{0}p$ in $\bar B^0\to p\bar p D^{0}$ decay measured by BABAR and find that through the 2-step processes of $\bar B^0\to {\bf B_c^+}(\to D^{0} p)\bar p$, where ${\bf B_c}$ denotes a charmed baryon state, some of the peaks can be identified with the established $\Sigma_c(2800)^+$, $\Lambda_c(2880)^+$ and $\Lambda_c(2940)^+$. Moreover, in order to account for the measured spectrum, it is necessary to introduce a new charmed baryon resonance with $(m,\,\Gamma)=(3212\pm 20,\,167\pm 34)$ MeV.Comment: 8 pages, 1 figure, title changed and discussions updated, version accepted for publication in Phys. Rev.

Learning Points and Routes to Recommend Trajectories

The problem of recommending tours to travellers is an important and broadly studied area. Suggested solutions include various approaches of points-of-interest (POI) recommendation and route planning. We consider the task of recommending a sequence of POIs, that simultaneously uses information about POIs and routes. Our approach unifies the treatment of various sources of information by representing them as features in machine learning algorithms, enabling us to learn from past behaviour. Information about POIs are used to learn a POI ranking model that accounts for the start and end points of tours. Data about previous trajectories are used for learning transition patterns between POIs that enable us to recommend probable routes. In addition, a probabilistic model is proposed to combine the results of POI ranking and the POI to POI transitions. We propose a new F$_1$ score on pairs of POIs that capture the order of visits. Empirical results show that our approach improves on recent methods, and demonstrate that combining points and routes enables better trajectory recommendations