Analytical Estimation of the Beam-Beam Interaction Limited Dynamic Apertures and Lifetimes in e^+e^- Circular Colliders

Physically speaking, the delta function like beam-beam nonlinear forces at interaction points (IPs) act as a sum of delta function nonlinear multipoles. By applying the general theory established in ref. 1, in this paper we investigate analytically the beam-beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between the beam-beam limited beam lifetimes and the beam-beam tune shifts are established, which show clearly why experimentally one has always a maximum beam-beam tune shift, \xi_{y, max}, around 0.045 for e-^+e$^- circular colliders, and why one can use round beams to double this value approximately. Comparisons with some machine parameters are given. Finally, we discuss the mechanism of the luminosity reduction due to a definite collision crossing angle.Comment: 25 page

An Analysis of Phase Transition in NK Landscapes

In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the uniform probability model, we prove that the phase transition is easy in the sense that there is a polynomial algorithm that can solve a random instance of the problem with the probability asymptotic to 1 as the problem size tends to infinity. For the fixed ratio model, we establish several upper bounds for the solubility threshold, and prove that random instances with parameters above these upper bounds can be solved polynomially. This, together with our empirical study for random instances generated below and in the phase transition region, suggests that the phase transition of the fixed ratio model is also easy

Gravitational Lensing and Anisotropies of CBR on the Small Angular Scales

We investigate the effect of gravitational lensing, produced by linear density perturbations, for anisotropies of the Cosmic Background Radiation (CBR) on scales of arcminutes. In calculations, a flat universe ($\Omega=1$) and the Harrison-Zel'dovich spectrum ($n=1$) are assumed. The numerical results show that on scales of a few arcminutes, gravitational lensing produces only negligible anisotropies in the temperature of the CBR. Our conclusion disagrees with that of Cay\'{o}n {\it et al.} who argue that the amplification of $\Delta T/T$ on scales $\le 3'$ may even be larger than 100\%.Comment: Accepted by MNRAS. 16 pages, 2 figures, tarred, compressed and uuencoded Postscript file

Design Studies for a High Current Bunching System for CLIC Test Facility (CTF3) Drive Beam

A bunching system is proposed for the initial stage of CTF3 which consists of one (two) 3 GHz prebunchers and one 3 GHz travelling wave (TW) buncher with variable phase velocities. The electron beam is emitted from a 140 KV DC gun. Since the macropulse beam current (3.5 A) at the exit of the TW buncher is rather high, inside the TW buncher one has to take the beam loading effect into consideration. By using PARMELA, it is shown numerically that the bunching system can provide the bunches whose properties satisfy the design requirement of CTF3. The 0.8 m long TW buncher working at 2pi/3 mode has two phase velocities, 0.75 and 1. The dimensions of the caities in the two phase velocity regions are proposed considering the beam loading effect. The transient beam loading effect and the multibunch transverse instabilities are studied numerically, and it is concluded that higher order mode couplers should be installed in the TW buncher with the loaded quality factor of the dipole mode lower than 80.Comment: 5 figures, presented at the Linear Accelerator Conference 2000, August 2000, US

Next-to-leading order QCD predictions for graviton and photon associated production in the Large Extra Dimensions model at the LHC

We present the calculations of the complete next-to-leading order(NLO) QCD corrections to the inclusive total cross sections for the Kaluza-Klein(KK) graviton and photon associated production process $pp \to \gamma G_{KK} + X$ in the large extra dimensions(LED) model at the LHC. We show that the NLO QCD corrections in general enhance the total cross sections and reduce the dependence of the total cross sections on the factorization and renormalization scales. When jet veto is considered, the NLO corrections reduce the total cross sections. We also calculate some important differential cross sections for this process at NLO: the missing transverse momentum distribution, the transverse momentum distribution and the pseudorapidity distribution of photon.Comment: 28 pages, 14 figures; minor changes, version published in Phys.Rev.

On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297