Results 1 - 10 of 4828
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[en] Space charge effect is ever of fundamental importance for low-energy parts of accelerators. Simple and robust estimations of the emittance degradation in various space charge affected beamlines were obtained analytically and numerically. Nonuniform longitudinal and transverse distribution of current, accelerating, and bunching were taken into account. The parameters of optimal beamlines for space charge affected beams were estimated
[en] The Monge-Kantorovich problem on finding a measure realizing the transportation of mass from R to R at minimum cost is considered. The initial and resulting distributions of mass are assumed to be the same and the cost of the transportation of the unit mass from a point x to y is expressed by an odd function f(x+y) that is strictly concave on R+. It is shown that under certain assumptions about the distribution of the mass the optimal measure belongs to a certain family of measures depending on countably many parameters. This family is explicitly described: it depends only on the distribution of the mass, but not on f. Under an additional constraint on the distribution of the mass the number of the parameters is finite and the problem reduces to the minimization of a function of several variables. Examples of various distributions of the mass are considered.
[en] A derivative of a functional with respect to matrices is defined. This definition is useful as a vehicle for obtaining a matrix that possesses a minimal norm. This minimization is required for determining the 'generalized bias operator'. The latter is used in calculations aimed at improving the agreement between the calculated and measured parameters of physical systems. (author)
[en] In [l] Brandt describes a general approach for algebraic coarsening. Given fine-grid equations and a prescribed relaxation method, an approach is presented for defining both the coarse-grid variables and the coarse-grid equations corresponding to these variables. Although, these two tasks are not necessarily related (and, indeed, are often performed independently and with distinct techniques) in the approaches of  both revolve around the same underlying observation. To determine whether a given set of coarse-grid variables is appropriate it is suggested that one should employ compatible relaxation. This is a generalization of so-called F-relaxation (e.g., ). Suppose that the coarse-grid variables are defined as a subset of the fine-grid variables. Then, F-relaxation simply means relaxing only the F-variables (i.e., fine-grid variables that do not correspond to coarse-grid variables), while leaving the remaining fine-grid variables (C-variables) unchanged. The generalization of compatible relaxation is in allowing the coarse-grid variables to be defined differently, say as linear combinations of fine-grid variables, or even nondeterministically (see examples in ). For the present summary it suffices to consider the simple case. The central observation regarding the set of coarse-grid variables is the following : Observation 1--A general measure for the quality of the set of coarse-grid variables is the convergence rate of compatible relaxation. The conclusion is that a necessary condition for efficient multigrid solution (e.g., with convergence rates independent of problem size) is that the compatible-relaxation convergence be bounded away from 1, independently of the number of variables. This is often a sufficient condition, provided that the coarse-grid equations are sufficiently accurate. Therefore, it is suggested in  that the convergence rate of compatible relaxation should be used as a criterion for choosing and evaluating the set of coarse-grid variables. Once a coarse grid is chosen for which compatible relaxation converges fast, it follows that the dependence of the coarse-grid variables on each other decays exponentially or faster with the distance between them, measured in mesh-sizes. This implies that highly accurate coarse-grid equations can be constructed locally. A method for doing this by solving local constrained minimization problems is described in . It is also shown how this approach can be applied to devise prolongation operators, which can be used for Galerkin coarsening in the usual way. In the present research we studied and developed methods based, in part, on these ideas. We developed and implemented an AMG approach which employs compatible relaxation to define the prolongation operator (hut is otherwise similar in its structure to classical AMG); we introduced a novel method for direct (i.e., non-Galerkin) algebraic coarsening, which is in the spirit of the approach originally proposed by Brandt in , hut is more efficient and well-defined; we investigated an approach for treating systems of equations and other problems where there is no unambiguous correspondence between equations and unknowns
[en] FOCal Underdetermined System Solver (FOCUSS) is a useful method through reweighted ℓ_2 minimization for sparse recovery. In this paper, we introduce an improved FOCUSS by enhancing sparsity with two reweighted ℓ_2 minimization. The reweighted FOCUSS method has higher mission success rate and better accuracy than FOCUSS. The simulation results illustrate the advantage of reweighted FOCUSS
[en] The printing quality delivered by a drop-on-demand inkjet printhead is severely affected by the residual oscillations in an ink channel and the cross-talk between neighboring ink channels. For a single ink channel, our earlier contribution shows that the actuation pulse can be designed, using a physical model, to effectively damp the residual oscillations. It is not always possible to obtain a good physical model for a single ink channel. A physical model for a multi-input multi-output (MIMO) inkjet printhead is made even more sophisticated by the presence of the cross-talk effect. This paper proposes a system identification-based approach to build a MIMO model for an inkjet printhead. Additionally, the identified MIMO model is used to design new actuation pulses to effectively minimize the residual oscillations and the cross-talk. Using simulation and experimental results, we demonstrate the efficacy of the proposed method. (paper)
[en] A particular engineering aspect of distributed sensor networks that has not received adequate attention is the system level hardware architecture of the individual nodes of the network. A novel hardware architecture based on an idea of task specific modular computing is proposed to provide for both the high flexibility and low power consumption required for distributed sensing solutions. The power consumption of the architecture is mathematically analyzed against a traditional approach, and guidelines are developed for application scenarios that would benefit from using this new design. Furthermore a method of decentralized control for the modular system is developed and analyzed. Finally, a few policies for power minimization in the decentralized system are proposed and analyzed.
[en] We consider the problem of reconstructing an N-dimensional continuous vector x from P constraints which are generated from its linear transformation under the assumption that the number of non-zero elements of x is typically limited to ρN (0≤ρ≤1). Problems of this type can be solved by minimizing a cost function with respect to the Lp-norm ||x||p= lim ε→+0Σi=1N |xi|p+ε, subject to the constraints under an appropriate condition. For several values of p, we assess a typical case limit αc(ρ), which represents a critical relation between α = P/N and ρ for successfully reconstructing the original vector by the minimization for typical situations in the limit N,P→∞ while keeping α finite, utilizing the replica method. For p = 1, αc(ρ) is considerably smaller than its worst case counterpart, which has been rigorously derived in the existing literature on information theory. (letter)
[en] We study metric properties of ring Q-homeomorphisms with respect to the p-modulus, p > 2, in the complex plane and establish lower bounds for the areas of disks. An extremal problem concerning minimization of the area functional is also solved.
[en] In this report we study space-mapping and manifold-mapping, two multi-level optimization techniques that aim at accelerating expensive optimization procedures with the aid of simple auxiliary models. Manifold-mapping improves in accuracy the solution given by space-mapping. In this report, the two mentioned techniques are basically described and then applied in the solving of two minimization problems. Several coarse models are tried, both from a two and a three level perspective. The results with these simple tests confirm the speed-up expected for the multi-level approach