The Parker Magnetostatic Theorem

We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibirum condition. The theorem then follows from the deduction that a continuous nonequilibrum field with a topology not in that subset must find a force-free state containing tangential discontinuities.Comment: 13 pages, no figur

An investigation of the plastic fracture of high strength steels

Three generally recognized stages of plastic fracture in high strength steels are considered in detail. These stages consist of void initiation, void growth, and void coalescence. A brief review of the existing literature on plastic fracture is included along with an outline of the experimental approach used in the investigation

Static current-sheet models of quiescent prominences

A particular class of theoretical models idealize the prominence to be a discrete flat electric-current sheet suspended vertically in a potential magnetic field. The weight of the prominence is supported by the Lorentz force in the current sheet. These models can be extended to have curved electric-current sheets and to vary three-dimensionally. The equation for force balance is 1 over 4 pi (del times B) times Bdel p- p9 z=zero. Using Cartesian coordinates we take, for simplicity, a uniform gravity with constant acceleration g in the direction -z. If we are interested not in the detailed internal structure of the prominence, but in the global magnetic configuration around the prominence, we may take prominence plasma to be cold. Consideration is given to how such equilibrium states can be constructed. To simplify the mathematical problem, suppose there is no electric current in the atmosphere except for the discrete currents in the cold prominence sheet. Let us take the plane z =0 to be the base of the atmosphere and restrict our attention to the domain z greater than 0. The task we have is to solve for a magnetic field which is everywhere potential except on some free surface S, subject to suit able to boundary conditions. The surface S is determined by requiring that it possesses a discrete electric current density such that the Lorentz force on it is everywhere vertically upward to balance the weight of the material m(S). Since the magnetic field is potential in the external atmosphere, the latter is decoupled from the magnetic field and its plane parallel hydrostatic pressure and density can be prescribed

Unraveling The Physics Behind Modified Higgs Couplings -- LHC vs. a Higgs Factory

Strongly modified Higgs-photon-photon and Higgs-gluon-gluon couplings indicate new electroweak and color mediators, respectively, with a light mass and a significant coupling to the Higgs boson. We point out the Higgs boson could have a significant decay width into the mediators and propose uncovering the hidden new physics through such exotic decays, which can probe the Higgs coupling with the mediators directly. Focusing on the electroweak mediators, we study a simplified model using as an example final states with tau leptons and neutrinos. Because one of the mediators is off-shell and its decay products are extremely soft, it is challenging to make a discovery at the Large Hadron Collider. A Higgs factory such as the International Linear Collider, however, could serve as a discovery machine for the EW mediators even in an early stage.Comment: 5 page

Toward a general theory of linking invariants

Let N_1, N_2, M be smooth manifolds with dim N_1 + dim N_2 +1 = dim M$ and let phi_i, for i=1,2, be smooth mappings of N_i to M with Im phi_1 and Im phi_2 disjoint. The classical linking number lk(phi_1,phi_2) is defined only when phi_1*[N_1] = phi_2*[N_2] = 0 in H_*(M). The affine linking invariant alk is a generalization of lk to the case where phi_1*[N_1] or phi_2*[N_2] are not zero-homologous. In arXiv:math.GT/0207219 we constructed the first examples of affine linking invariants of nonzero-homologous spheres in the spherical tangent bundle of a manifold, and showed that alk is intimately related to the causality relation of wave fronts on manifolds. In this paper we develop the general theory. The invariant alk appears to be a universal Vassiliev-Goussarov invariant of order < 2. In the case where phi_1*[N_1] and phi_2*[N_2] are 0 in homology it is a splitting of the classical linking number into a collection of independent invariants. To construct alk we introduce a new pairing mu on the bordism groups of spaces of mappings of N_1 and N_2 into M, not necessarily under the restriction dim N_1 + dim N_2 +1 = dim M. For the zero-dimensional bordism groups, mu can be related to the Hatcher-Quinn invariant. In the case N_1=N_2=S^1, it is related to the Chas-Sullivan string homology super Lie bracket, and to the Goldman Lie bracket of free loops on surfaces.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper42.abs.htm

New thermocouple-based microwave/millimeter-wave power sensor MMIC techniques in GaAs

We describe a new RF and microwave power sensor monolithic microwave integrated circuit design. The circuit incorporates a number of advances over existing designs. These include a III–V epitaxial structure optimized for sensitivity, the figure-of-merit applicable to the optimization, a mechanism for in-built detection of load ageing and damage to extend calibration intervals, and a novel symmetrical structure to linearize the high-power end of the scale

Three-dimensional magnetostatic models of the large-scale corona

A special class of magnetostatic equilibria is described, which are mathematically simple and yet sufficiently versatile so as to fit any arbitrary normal magnetic flux prescribed at the photosphere. With these solutions, the corona can be modeled with precisely the same mathematically simple procedure as has previously been done with potential fields. The magnetostatic model predicts, in addition to the coronal magnetic field, the three dimensional coronal density which can be compared with coronagraph observations

Towards a High Energy Theory for the Higgs Phase of Gravity

Spontaneous Lorentz violation due to a time-dependent expectation value for a massless scalar has been suggested as a method for dynamically generating dark energy. A natural candidate for the scalar is a Goldstone boson arising from the spontaneous breaking of a U(1) symmetry. We investigate the low-energy effective action for such a Goldstone boson in a general class of models involving only scalars, proving that if the scalars have standard kinetic terms then at the {\em classical} level the effective action does not have the required features for spontaneous Lorentz violation to occur asymptotically $(t \to \infty)$ in an expanding FRW universe. Then we study the large $N$ limit of a renormalizable field theory with a complex scalar coupled to massive fermions. In this model an effective action for the Goldstone boson with the properties required for spontaneous Lorentz violation can be generated. Although the model has shortcomings, we feel it represents progress towards finding a high energy completion for the Higgs phase of gravity.Comment: 20 pages, 5 figures;fixed typos and added reference

Performance related technique factors in Olympic sprint kayaking

A sprint kayaking specific deterministic model was used to identify key performance related technique factors using data from 12 international-level kayakers. There was large variability in the strength of the between-factor relationships across the group. The pull phase was split into 3 components with the 1st phase contributing the most to increases in boat velocity and the 3rd phase causing a decrease in velocity. The propulsive impulse had the largest influence on velocity, but the magnitude of the impact was moderated by blade slip. Large propulsive impulses in the 3rd phase of the pull were associated with larger decreases in velocity. The results show that the model can be used to identify key technique factors on an individual level, although the use of the model should be confirmed on additional kayakers before being used in an applied setting by practitioners