Feed-down effect in dipole alignment

The field of strong super conducting magnets contains substantial multipole errors. An upper limit of their value is specified on the reference closed orbit. When the dipole is installed in a real machine, its axis cannot be exactly on the reference orbit, and "feed-down multipoles" are introduced. This paper describes an analytical approach to the alignment specification associated with this effect with an example from the LHC at CERN

Symplectic integrators for index one constraints

We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity constraints nondegenerate in the velocities, such as those arising in sub-Riemannian geometry and control theory.Comment: 13 pages, accepted in SIAM J Sci Compu

Moment Analysis of Magnetic Resonance Signals

A relation is given between the moments of a generalized convolution transform of a function, and the moments of the function itself. This relation is applied to the signal obtained with a field‐modulated EPR spectrometer, a consequence being that the integrated intensity of an absorption line may be obtained from first moment measurements at any modulation amplitude, regardless of line shape or various instrumental nonidealities. This result has been verified experimentally to within a few percent with a Varian EPR spectrometer. Extension to measurement of higher moments is discussed

Infantile de novo primary antiphospholipid syndrome revealed by neonatal stroke

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Sound and light from fractures in scintillators

Prompted by intriguing events observed in certain particle-physics searches for rare events, we study light and acoustic emission simultaneously in some inorganic scintillators subject to mechanical stress. We observe mechanoluminescence in ${Bi}_4{Ge}_{3}{O}_{12}$, ${CdWO}_{4}$ and ${ZnWO}_{4}$, in various mechanical configurations at room temperature and ambient pressure. We analyze how the light emission is correlated to acoustic emission during fracture. For ${Bi}_4{Ge}_{3}{O}_{12}$, we set a lower bound on the energy of the emitted light, and deduce that the fraction of elastic energy converted to light is at least $3 \times 10^{-5}$

Interface relaxation in electrophoretic deposition of polymer chains: Effects of segmental dynamics, molecular weight, and field

Using different segmental dynamics and relaxation, characteristics of the interface growth is examined in an electrophoretic deposition of polymer chains on a three (2+1) dimensional discrete lattice with a Monte Carlo simulation. Incorporation of faster modes such as crankshaft and reptation movements along with the relatively slow kink-jump dynamics seems crucial in relaxing the interface width. As the continuously released polymer chains are driven (via segmental movements) and deposited, the interface width $W$ grows with the number of time steps $t$, $W \propto t^{\beta},$ ($\beta \sim 0.4$--$0.8)$, which is followed by its saturation to a steady-state value $W_s$. Stopping the release of additional chains after saturation while continuing the segmental movements relaxes the saturated width to an equilibrium value ($W_s \to W_r$). Scaling of the relaxed interface width $W_r$ with the driving field $E$, $W_r \propto E^{-1/2}$ remains similar to that of the steady-state $W_s$ width. In contrast to monotonic increase of the steady-state width $W_s$, the relaxed interface width $W_r$ is found to decay (possibly as a stretched exponential) with the molecular weight.Comment: 5 pages, 7 figure

Corporate Hierarchies and the Size of Nations: Theory and Evidence

Corporate organization varies within a country and across countries with country size. The paper starts by establishing some facts about corporate organization based on unique data of 660 Austrian and German corporations. The larger country (Germany) has larger firms with flatter more decentral corporate hierarchies compared to the smaller country (Austria). Firms in the larger country change their organization less fast than firms in the smaller country. Over time firms have been introducing less hierarchical organizations by delegating power to lower levels of the corporation. We develop a theory which explains these facts and which links these features to the trade environment that countries and firms face. We introduce firms with internal hierarchies in a Krugman (1980) model of trade. We show that international trade and the toughness of competition in international markets induce a power struggle in firms which eventually leads to decentralized corporate hierarchies. We offer econometric evidence which is consistent with the models predictions

Geometric Generalisations of SHAKE and RATTLE

A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In addition, the geometric insight naturally generalises Shake and Rattle to allow for a strictly larger class of constrained Hamiltonian systems than in the classical setting. In order for Shake and Rattle to be well defined, two basic assumptions are needed. First, a nondegeneracy assumption, which is a condition on the Hamiltonian, i.e., on the dynamics of the system. Second, a coisotropy assumption, which is a condition on the geometry of the constrained phase space. Non-trivial examples of systems fulfilling, and failing to fulfill, these assumptions are given