Theorem on Magnet Fringe Field

Transverse particle motion in particle accelerators is governed almost totally by non-solenoidal magnets for which the body magnetic field can be expressed as a series expansion of the normal (b{sub n}) and skew (a{sub n}) multipoles, B{sub y} + iB{sub x} = {summation}(b{sub n} + ia{sub n})(x + iy){sup n}, where x, y, and z denote horizontal, vertical, and longitudinal (along the magnet) coordinates. Since the magnet length L is necessarily finite, deflections are actually proportional to ``field integrals`` such as {bar B}L {equivalent_to} {integral} B(x,y,z)dz where the integration range starts well before the magnet and ends well after it. For {bar a}{sub n}, {bar b}{sub n}, {bar B}{sub x}, and {bar B}{sub y} defined this way, the same expansion Eq. 1 is valid and the ``standard`` approximation is to neglect any deflections not described by this expansion, in spite of the fact that Maxwell`s equations demand the presence of longitudinal field components at the magnet ends. The purpose of this note is to provide a semi-quantitative estimate of the importance of {vert_bar}{Delta}p{sub {proportional_to}}{vert_bar}, the transverse deflection produced by the ion-gitudinal component of the fringe field at one magnet end relative to {vert_bar}{Delta}p{sub 0}{vert_bar}, the total deflection produced by passage through the whole magnet. To emphasize the generality and simplicity of the result it is given in the form of a theorem. The essence of the proof is an evaluation of the contribution of the longitudinal field B{sub x} from the vicinity of one magnet end since, along a path parallel to the magnet axis such as path BC

A Geometrical Method of Decoupling

The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries - like midplane symmetrie - are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as for instance the method of Teng and Edwards. In a preceeding paper it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all thinkable cases. Hence a systematic derivation of a more general treatment seemed advisable. In a second paper the author suggested the use of real Dirac matrices as basic tools to coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. It is shown that this algebraic decoupling is closely related to a geometric "decoupling" by the orthogonalization of the vectors $\vec E$, $\vec B$ and $\vec P$, that were introduced with the so-called "electromechanical equivalence". We present a structure-preserving block-diagonalization of symplectic or Hamiltonian matrices, respectively. When used iteratively, the decoupling algorithm can also be applied to n-dimensional systems and requires ${\cal O}(n^2)$ iterations to converge to a given precision.Comment: 13 pages, 1 figur

Analysis of OPM potentials for multiplet states of 3d transition metal atoms

We apply the optimized effective potential method (OPM) to the multiplet energies of the 3d$^n$ transition metal atoms, where the orbital dependence of the energy functional with respect to orbital wave function is the single-configuration HF form. We find that the calculated OPM exchange potential can be represented by the following two forms. Firstly, the difference between OPM exchange potentials of the multiplet states can be approximated by the linear combination of the potentials derived from the Slater integrals $F^2({\rm 3d,3d})$ and $F^4({\rm 3d,3d})$ for the average energy of the configuration. Secondly, the OPM exchange potential can be expressed as the linear combination of the OPM exchange potentials of the single determinants.Comment: 15 pages, 6 figures, to be published in J. Phys.

Deflections in Magnet Fringe Fields

A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of magnets whose end designs introduce no extraneous components, {\it i.e.} fields not required to be present by Maxwell's equations. Analytic evaluations of the deflections are obtained in various approximations. Mainly emphasized is a ``straight-line approximation'', in which particle orbits are treated as straight lines through the fringe field regions. This approximation leads to a readily-evaluated figure of merit, the ratio of r.m.s. end deflection to nominal body deflection, that can be used to determine whether or not a fringe field can be neglected. Deflections in ``critical'' cases (e.g. near intersection regions) are analysed in the same approximation.Comment: To be published in Physical Review

Wigner's DD-matrix elements for SU(3)SU(3) - A Generating Function Approach

A generating function for the Wigner's $D$-matrix elements of $SU(3)$ is derived. From this an explicit expression for the individual matrix elements is obtained in a closed form.Comment: RevTex 3.0, 22 pages, no figure

Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space

We present in this paper a fully covariant quantization of the minimally-coupled massless field on de Sitter space. We thus obtain a formalism free of any infrared (e.g logarithmic) divergence. Our method is based on a rigorous group theoretical approach combined with a suitable adaptation (Krein spaces) of the Wightman-G\"{a}rding axiomatic for massless fields (Gupta-Bleuler scheme). We make explicit the correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time. The minimally-coupled massless field is associated with a representation which is the lowest term of the discrete series of unitary representations of the de Sitter group. In spite of the presence of negative norm modes in the theory, no negative energy can be measured: expressions as \le n_{k_1}n_{k_2}...|T_{00}|n_{k_1}n_{k_2}...\re are always positive.Comment: 20 pages, appear in class. quantum gra

GATA4-targeted compound exhibits cardioprotective actions against doxorubicin-induced toxicity in vitro and in vivo : establishment of a chronic cardiotoxicity model using human iPSC-derived cardiomyocytes

Doxorubicin is a widely used anticancer drug that causes dose-related cardiotoxicity. The exact mechanisms of doxorubicin toxicity are still unclear, partly because most in vitro studies have evaluated the effects of short-term high-dose doxorubicin treatments. Here, we developed an in vitro model of long-term low-dose administration of doxorubicin utilizing human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs). Moreover, given that current strategies for prevention and management of doxorubicin-induced cardiotoxicity fail to prevent cancer patients developing heart failure, we also investigated whether the GATA4-targeted compound 3i-1000 has cardioprotective potential against doxorubicin toxicity both in vitro and in vivo. The final doxorubicin concentration used in the chronic toxicity model in vitro was chosen based on cell viability data evaluation. Exposure to doxorubicin at the concentrations of 1-3 mu M markedly reduced (60%) hiPSC-CM viability already within 48 h, while a 14-day treatment with 100 nM doxorubicin concentration induced only a modest 26% reduction in hiPCS-CM viability. Doxorubicin treatment also decreased DNA content in hiPSC-CMs. Interestingly, the compound 3i-1000 attenuated doxorubicin-induced increase in pro-B-type natriuretic peptide (proBNP) expression and caspase-3/7 activation in hiPSC-CMs. Moreover, treatment with 3i-1000 for 2 weeks (30 mg/kg/day, i.p.) inhibited doxorubicin cardiotoxicity by restoring left ventricular ejection fraction and fractional shortening in chronic in vivo rat model. In conclusion, the results demonstrate that long-term exposure of hiPSC-CMs can be utilized as an in vitro model of delayed doxorubicin-induced toxicity and provide in vitro and in vivo evidence that targeting GATA4 may be an effective strategy to counteract doxorubicin-induced cardiotoxicity.Peer reviewe

Variational perturbation approach to the Coulomb electron gas

The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the Coulomb interaction. The perturbation beyond a variational result can be carried out systematically by the modified Wick's theorem which defines a contraction rule about the renormalized perturbation. Utilizing the theorem, variational ring diagrams of the electron gas are summed up. As a result, the correlation energy is found to be much closer to the result of the Green's function Monte Carlo calculation than that of the conventional ring approximation is.Comment: 4 pages, 3 figure

Neuroprotection in a Novel Mouse Model of Multiple Sclerosis

The authors acknowledge the support of the Barts and the London Charity, the Multiple Sclerosis Society of Great Britain and Northern Ireland, the National Multiple Sclerosis Society, USA, notably the National Centre for the Replacement, Refinement & Reduction of Animals in Research, and the Wellcome Trust (grant no. 092539 to ZA). The siRNA was provided by Quark Pharmaceuticals. The funders and Quark Pharmaceuticals had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Parameterized optimized effective potential for atoms

The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both single configuration and multi configuration trial wave functions are implemented. Applications to several atomic systems are presented improving previous works. The results here obtained are very close to those calculated in either the Hartree-Fock and the multi configurational Hartree-Fock framework.Comment: 8 pages, 3 figure