Techniques in machine function integral calculations

This note is a summary of machine function integral expressions the author has accumulated in several years' work on accelerator physics. It is not of theoretical importance, but it can help much in practical calculation. Many accelerator physicists have noticed that to express such integrals by functions at some special points and parameters of the magnet in question has an advantage over step-by-step summation, owing to less time elapsed and better accuracy obtained. However, most of the formulae they present in papers or programs still have much room for simplification. To express the integrals as simply as possible saves time, and it can help set some parameters as function of goodness or fit function in searching for an ideal lattice configuration, though the parameters are usually considered too complicated

Decreased Fibroblast and Increased Osteoblast Functions on Ionic Plasma Deposited Nanostructured Ti Coatings

Bioactive coatings are in high demand to control cellular functions for numerous medical devices. The objective of this in vitro study was to characterize for the first time fibroblast (fibrous scar tissue forming cells) adhesion and proliferation on an important polymeric biomaterial (silicone) coated with titanium using a novel ionic plasma deposition (IPD) process. Fibroblasts are one of the first anchorage-dependent cells to arrive at an implant surface during the wound healing process. Persistent excessive functions of fibroblasts have been linked to detrimental fibrous tissue formation which may cause implant failure. The IPD process creates a surface-engineered nanostructure (with features usually below 100 nm) by first using a vacuum to remove all contaminants, then guiding charged metallic ions or plasma to the surface of a medical device at ambient temperature. Results demonstrated that compared to currently used titanium and uncoated silicone, silicone coated with titanium using IPD significantly decreased fibroblast adhesion and proliferation. Results also showed competitively increased osteoblast (bone-forming cells) over fibroblast adhesion on silicone coated with titanium; in contrast, osteoblast adhesion was not competitively increased over fibroblast adhesion on uncoated silicone or titanium controls. In this manner, this study strongly suggests that IPD should be further studied for biomaterial applications in which fibrous tissue encapsulation is undesirable (such as for orthopedic implants, cardiovascular components, etc.)

Extension to order β23\beta^{23} of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Using a renormalized linked-cluster-expansion method, we have extended to order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of $\chi$ and $\xi$. Our best estimates for the inverse critical temperatures are $\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. For the susceptibility exponent we get $\gamma=1.2375(6)$ and for the correlation length exponent we get $\nu=0.6302(4)$. The ratio of the critical amplitudes of $\chi$ above and below the critical temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for $\xi$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling amplitude ratio we obtain $a^+_{\xi}/a^+_{\chi}=0.87(6)$.Comment: Misprints corrected, 8 pages, latex, no figure

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice

25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining $\gamma=1.2373(2)$, $\nu=0.63012(16)$, $\alpha=0.1096(5)$, $\eta=0.03639(15)$, $\beta=0.32653(10)$, $\delta=4.7893(8)$. Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate $\Delta=0.52(3)$ for the exponent associated with the leading scaling corrections. By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.Comment: 40 pages, 15 figure

Contributions to the cross shock electric field at supercritical perpendicular shocks: Impact of the pickup ions

A particle-in-cell code is used to examine contributions of the pickup ions (PIs) and the solar wind ions (SWs) to the cross shock electric field at the supercritical, perpendicular shocks. The code treats the pickup ions self-consistently as a third component. Herein, two different runs with relative pickup ion density of 25% and 55% are presented in this paper. Present preliminary results show that: (1) in the low percentage (25%) pickup ion case, the shock front is nonstationary. During the evolution of this perpendicular shock, a nonstationary foot resulting from the reflected solar wind ions is formed in front of the old ramp, and its amplitude becomes larger and larger. At last, the nonstationary foot grows up into a new ramp and exceeds the old one. Such a nonstationary process can be formed periodically. hen the new ramp begins to be formed in front of the old ramp, the Hall term mainly contributed by the solar wind ions becomes more and more important. The electric field Ex is dominated by the Hall term when the new ramp exceeds the old one. Furthermore, an extended and stationary foot in pickup ion gyro-scale is located upstream of the nonstationary/self-reforming region within the shock front, and is always dominated by the Lorentz term contributed by the pickup ions; (2) in the high percentage (55%) pickup ion case, the amplitude of the stationary foot is increased as expected. One striking point is that the nonstationary region of the shock front evidenced by the self-reformation disappears. Instead, a stationary extended foot dominated by Lorentz term contributed by the pickup ions, and a tationary ramp dominated by Hall term contributed by the solar wind ions are clearly evidenced. The significance of the cross electric field on ion dynamics is also discussed.Comment: 11 pages, 6 figs and 1 table. This paper will be published in the journal: Astrophysics and Space Scienc

Edge Detection by Adaptive Splitting II. The Three-Dimensional Case

In Llanas and Lantarón, J. Sci. Comput. 46, 485–518 (2011) we proposed an algorithm (EDAS-d) to approximate the jump discontinuity set of functions defined on subsets of ℝ d . This procedure is based on adaptive splitting of the domain of the function guided by the value of an average integral. The above study was limited to the 1D and 2D versions of the algorithm. In this paper we address the three-dimensional problem. We prove an integral inequality (in the case d=3) which constitutes the basis of EDAS-3. We have performed detailed computational experiments demonstrating effective edge detection in 3D function models with different interface topologies. EDAS-1 and EDAS-2 appealing properties are extensible to the 3D cas

HighP–TNano-Mechanics of Polycrystalline Nickel

We have conducted highP–Tsynchrotron X-ray and time-of-flight neutron diffraction experiments as well as indentation measurements to study equation of state, constitutive properties, and hardness of nanocrystalline and bulk nickel. Our lattice volume–pressure data present a clear evidence of elastic softening in nanocrystalline Ni as compared with the bulk nickel. We show that the enhanced overall compressibility of nanocrystalline Ni is a consequence of the higher compressibility of the surface shell of Ni nanocrystals, which supports the results of molecular dynamics simulation and a generalized model of a nanocrystal with expanded surface layer. The analytical methods we developed based on the peak-profile of diffraction data allow us to identify “micro/local” yield due to high stress concentration at the grain-to-grain contacts and “macro/bulk” yield due to deviatoric stress over the entire sample. The graphic approach of our strain/stress analyses can also reveal the corresponding yield strength, grain crushing/growth, work hardening/softening, and thermal relaxation under highP–Tconditions, as well as the intrinsic residual/surface strains in the polycrystalline bulks. From micro-indentation measurements, we found that a low-temperature annealing (T < 0.4 Tm) hardens nanocrystalline Ni, leading to an inverse Hall–Petch relationship. We explain this abnormal Hall–Petch effect in terms of impurity segregation to the grain boundaries of the nanocrystalline Ni