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[en] When analyzing heavy qq- states with help of exponential moments we argue that a ratio of moments should be expanded rather than the moments themselves. Within a nonrelativistic approximation we show that the expanded ratio is totally independent on the quark mass definition, whereas the nonexpanded ratio of moments strongly depends on it. (Author)
[en] High-current beams must be matched to high order to minimize emittance growth and particle losses. For matching problems, the moment approach, in which the author describes the particle beam by the moments of its distributions, is particularly valuable. A variety of analytical results are available for linear motion. The moment approach is also the basis of the 3-D space-charge simulation code BEDLAM, in which the dynamical variables are the moments. Moment simulation codes are particularly useful for computing beams matched to nonlinear systems. This paper outlines what is known about the moment approach, describes work in progress on new space-charge models, and describes further potential applications of and improvements to moment-method simulations
[en] A method of moments is developed for the parametric form the solution of convolution equations of the first kind. Two models, the gamma model and the shifted gamma model, are studied in details and a non-parametric approach based on regularization is presented.
[en] We illustrate the use of the statistical method of moments for determining the position and momentum distributions of a quantum object from the statistics of a single measurement. The method is used for three different, though related, models: the sequential measurement model, the Arthurs-Kelly model, and the eight-port homodyne detection model. In each case, the method of moments gives the position and momentum distributions for a large class of initial states, the relevant condition being the exponential boundedness of the distributions.
[en] We study the exact controllability problem for a ring under stretching tension that varies in time. We are looking for a couple of forces, which drive the state solution to rest. We show that applying two forces is necessary for controllability and the ring is controllable in the time interval greater than the optical length of the string. We also explain why one force would not be enough to control the ring. We use the method of moments to reduce the controllability problem to a moment problem for the controlling forces. The solution of that problem is based on an auxiliary basis property result. Both method of moments and proof of the basis property are developed for the model with time-dependent parameters
[en] We continue our presentation of VINE. In this paper, we begin with a description of relevant architectural properties of the serial and shared memory parallel computers on which VINE is intended to run, and describe their influences on the design of the code itself. We continue with a detailed description of a number of optimizations made to the layout of the particle data in memory and to our implementation of a binary tree used to access that data for use in gravitational force calculations and searches for smoothed particle hydrodynamics (SPH) neighbor particles. We describe the modifications to the code necessary to obtain forces efficiently from special purpose 'GRAPE' hardware, the interfaces required to allow transparent substitution of those forces in the code instead of those obtained from the tree, and the modifications necessary to use both tree and GRAPE together as a fused GRAPE/tree combination. We conclude with an extensive series of performance tests, which demonstrate that the code can be run efficiently and without modification in serial on small workstations or in parallel using the OpenMP compiler directives on large-scale, shared memory parallel machines. We analyze the effects of the code optimizations and estimate that they improve its overall performance by more than an order of magnitude over that obtained by many other tree codes. Scaled parallel performance of the gravity and SPH calculations, together the most costly components of most simulations, is nearly linear up to at least 120 processors on moderate sized test problems using the Origin 3000 architecture, and to the maximum machine sizes available to us on several other architectures. At similar accuracy, performance of VINE, used in GRAPE-tree mode, is approximately a factor 2 slower than that of VINE, used in host-only mode. Further optimizations of the GRAPE/host communications could improve the speed by as much as a factor of 3, but have not yet been implemented in VINE. Finally, we find that although parallel performance on small problems may reach a plateau beyond which more processors bring no additional speedup, performance never decreases, a factor important for running large simulations on many processors with individual time steps, where only a small fraction of the total particles require updates at any given moment.
[en] In this paper, we measured plasma horizontal displacement using two experimental methods in the IR-T1 tokamak. First, two poloidal flux loops were designed and installed on the outer surface of the IR-T1 tokamak and were used to measure the Shafranov shift. Also, modified Rogowski and saddle sine coils based on the multipole moment method were designed, constructed and used. The results from these two methods are compared and are found to be in good agreement.
[en] The authors introduce a new approach for characteristic based Sn transport on arbitrary polygonal meshes in XY geometry. They approximate a general surface as an arbitrary polygon and rotate to a coordinate system aligned with the direction of particle travel. They use exact moment balance equations on whole cells and subregions called slices and close the system by analytically solving the characteristic equation. The authors assume spatial functions for boundary conditions and cell sources and formulate analogous functions for outgoing edge and cell angular fluxes which exactly preserve spatial moments of the analytic solution. In principle, their approach provides the framework to extend characteristic methods formulated on rectangular grids to arbitrary polygonal meshes. The authors derive schemes based on step and linear spatial approximations. Their step characteristic scheme is mathematically equivalent to the Extended Step Characteristic (ESC) method but their approach and scheme differ in the geometry rotation and in the solution form. Their solutions are simple and permit edge-based transport sweep ordering