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

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

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

Discovery of a new supernova remnant G150.3+4.5

Large-scale radio continuum surveys have good potential for discovering new Galactic supernova remnants (SNRs). Surveys of the Galactic plane are often limited in the Galactic latitude of |b| ~ 5 degree. SNRs at high latitudes, such as the Cygnus Loop or CTA~1, cannot be detected by surveys in such limited latitudes. Using the available Urumqi 6 cm Galactic plane survey data, together with the maps from the extended ongoing 6 cm medium latitude survey, we wish to discover new SNRs in a large sky area. We searched for shell-like structures and calculated radio spectra using the Urumqi 6 cm, Effelsberg 11 cm, and 21 cm survey data. Radio polarized emission and evidence in other wavelengths are also examined for the characteristics of SNRs. We discover an enclosed oval-shaped object G150.3+4.5 in the 6 cm survey map. It is about 2.5 degree wide and 3 degree high. Parts of the shell structures can be identified well in the 11 cm, 21 cm, and 73.5 cm observations. The Effelsberg 21 cm total intensity image resembles most of the structures of G150.3+4.5 seen at 6 cm, but the loop is not closed in the northwest. High resolution images at 21 cm and 73.5 cm from the Canadian Galactic Plane Survey confirm the extended emission from the eastern and western shells of G150.3+4.5. We calculated the radio continuum spectral indices of the eastern and western shells, which are $\beta \sim -2.4$ and $\beta \sim -2.7$ between 6 cm and 21 cm, respectively. The shell-like structures and their non-thermal nature strongly suggest that G150.3+4.5 is a shell-type SNR. For other objects in the field of view, G151.4+3.0 and G151.2+2.6, we confirm that the shell-like structure G151.4+3.0 very likely has a SNR origin, while the circular-shaped G151.2+2.6 is an HII region with a flat radio spectrum, associated with optical filamentary structure, H$\alpha$, and infrared emission.Comment: 5 pages, 3 figures, accepted for publication of Astronomy and Astrophysic

Structure of polydisperse inverse ferrofluids: Theory and computer simulation

By using theoretical analysis and molecular dynamics simulations, we investigate the structure of colloidal crystals formed by nonmagnetic microparticles (or magnetic holes) suspended in ferrofluids (called inverse ferrofluids), by taking into account the effect of polydispersity in size of the nonmagnetic microparticles. Such polydispersity often exists in real situations. We obtain an analytical expression for the interaction energy of monodisperse, bidisperse, and polydisperse inverse ferrofluids. Body-centered tetragonal (bct) lattices are shown to possess the lowest energy when compared with other sorts of lattices and thus serve as the ground state of the systems. Also, the effect of microparticle size distributions (namely, polydispersity in size) plays an important role in the formation of various kinds of structural configurations. Thus, it seems possible to fabricate colloidal crystals by choosing appropriate polydispersity in size.Comment: 22 pages, 8 figure

Magnetophoresis of nonmagnetic particles in ferrofluids

Ferrofluids containing nonmagnetic particles are called inverse ferrofluids. On the basis of the Ewald-Kornfeld formulation and the Maxwell-Garnett theory, we theoretically investigate the magnetophoretic force exerting on the nonmagnetic particles in inverse ferrofluids due to the presence of a nonuniform magnetic field, by taking into account the structural transition and long-range interaction. We numerically demonstrate that the force can be adjusted by choosing appropriate lattices, volume fractions, geometric shapes, and conductivities of the nonmagnetic particles, as well as frequencies of external magnetic fields.Comment: 24 pages, 7 figure