The unsatisfiability threshold revisited

The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. In this paper, we consider the problem of bounding the threshold value from above using methods that, we believe, are of interest on their own right. More specifically, we show how the method of local maximum satisfying truth assignments can be combined with results for the occupancy problem in schemes of random allocation of balls into bins in order to achieve an upper bound for the unsatisfiability threshold less than 4.571. In order to obtain this value, we establish a bound on the q-binomial coefficients (a generalization of the binomial coefficients). No such bound was previously known, despite the extensive literature on q-binomial coefficients. Finally, to prove our result we had to establish certain relations among the conditional probabilities of an event in various probabilistic models for random formulas. It turned out that these relations were considerably harder to prove than the corresponding ones for unconditional probabilities, which were previously known.     

Determination of the rate of rapid lipid transfer induced by poly(ethylene glycol) using the SLM Fourier transform phase and modulation spectrofluorometer

Rate constants were determined for the transfer of the fluorescent lipid probe 1-palmitoyl-2-[[2-[4-(6-phenyl-trans-1,3,5-hexatrienyl)phenyl]ethyl] oxy]carbonyl]-3-sn-phosphatidylcholine (DPHpPC) between large, unilamellar extrusion vesicles composed either of dipalmitoyl phosphatidylcholine (DPPC) or of DPPC mixed with a small amount (0.5 mol%) of lyso phosphatidylcholine (Lyso PC). Transfer of the lipid probe in the presence of varying concentrations of poly(ethylene glycol) (PEG) was monitored using the SLM 48000-MHF Multi-Harmonic Fourier Transform phase and modulation spectrofluorometer to collect multifrequency phase and modulation fluorescence data sets on a subsecond time scale. The unique ability of this instrument to yield accurate fluorescence lifetime data on this time scale allowed transfer to be detected in terms of a time-dependent change in the fluorescent lifetime distribution associated with the lipid-like DPHpPC probe. This probe demonstrates two short fluoresence decay times (ca. 1.1–1.4 and 4.3–4.8 ns) in a probe-rich environment but a single long lifetime (ca. 7 ns) in a probe-poor environment. A simple two-state model for initial lipid transfer was used to analyze the multifrequency data sets collected over a 4-s time frame to obtain the time rate of change of the concentrations of donor and acceptor probe populations following rapid mixing of vesicles with PEG. The ability to measure fluorescence lifetimes on this time scale has allowed us to show that the of rate of lipid transfer increased dramatically at 35% PEG in both fusing and nonfusing vesicle systems. These results are interpreted in terms of a distinct interbilayer structure associated with intimate bilayer contact induced by high and potentially fusogenic concentrations of PEG.     

Ab initio study on structure and phase transition of A- and B-type rare-earth sesquioxides Ln2O3 (Ln=La-Lu, Y, and Sc) based on density function theory

Ab initio energetic calculations based on the density functional theory (DFT) and projector augmented wave (PAW) pseudo-potentials method were performanced to determine the crystal structural parameters and phase transition data of the polymorphic rare-earth sesquioxides Ln₂O₃ (where Ln=La-Lu, Y, and Sc) with A-type (hexagonal) and B-type (monoclinic) configurations at ground state. The calculated results agree well with the limited experimental data and the critically assessed results. A set of systematic and self-consistent crystal structural parameters, energies and pressures of the phase transition were established for the whole series of the A- and B-type rare-earth sesquioxides Ln₂O₃. With the increase of the atomic number, the ionic radii of rare-earth elements Ln and the volumes of the sesquioxides Ln₂O₃ reflect the so-called “lanthanide contraction”. With the increase of the Ln³⁺-cation radius, the bulk modulus of Ln₂O₃ decreases and the polymorphic structures show a degenerative tendency.     

Standing waves, clustering, and phase waves in 1D simulations of kinetic relaxation oscillations in NO+NH3 on Pt(1 0 0) coupled by diffusion

The Lombardo–Imbihl–Fink (LFI) ODE model of the NO+NH₃ reaction on a Pt(1 0 0) surface shows stable relaxation oscillations with very sharp transitions for temperatures T between 404 and 433 K. Here we study numerically the effect of linear diffusive coupling of these oscillators in one spatial dimension. Depending on the parameters and initial conditions we find a rich variety of spatio-temporal patterns which we group into four main regimes: bulk oscillations (BOs), standing waves (SW), phase clusters (PC), and phase waves (PW). Two key ingredients for SW and PC are identified, namely the relaxation type of the ODE oscillations and a nonlocal (and nonglobal) coupling due to relatively fast diffusion of the kinetically slaved variables NH₃ and H. In particular, the latter replaces the global coupling through the gas phase used to obtain SW and PC in models of related surface reactions. The PW exist only under the assumption of (relatively) slow diffusion of NH₃ and H.     

光纤加速度传感器研究进展

光纤加速度传感器与传统加速度传感器相比，不但能抗电磁干扰，而且体小、质轻、动态范围宽、精度高、能在恶劣环境下工作，因此受到各先进国家军事与商业领域的极大重视，各种实用的光纤加速度传感器不断涌现。主要有光强调制型和相位调制型两大类。光强调制式有反射式、透射式和偏振式等等。相位调制式有Ｍａｃｈ－Ｚｅｎｄｅｒ干涉仪、Ｍｉｃｈｅｌｓｏｎ干涉仪和Ｆａｂｒｙ－Ｐｅｒｏｔ干涉仪。有一维的，也有二维的；有与水听器组合在一起的，也有与光纤陀螺仪组合的光纤加速度传感器。最小的已经做到２．５ｃｍ长，直径仅０．２５ｍｍ；测量精度已能达到１μｇ；共振频率可达到１０ｋＨｚ。为了克服温度不稳定性对测量精度的影响，人们采用了３×３耦合器解调法，双光路法，由单臂式改成推挽式等。一旦关键技术得以克服，光纤加速度传感器将会在惯性导航和其它领域发挥更重要的作用。本文将分别介绍目前各种类型光纤加速度传感器的结构、特点、走向实用化存在的问题。     

10.1007/s10955-006-9040-z

We derive hydrodynamic equations describing the evolution of a binary fluid segregated into two regions, each rich in one species,which are separated (on the macroscopic scale) by a sharp interface. Our starting point is a Vlasov-Boltzmann (VB) equation describing the evolution of the one particle position and velocity distributions, f_i (x, v, t), i = 1, 2. The solution of the VB equation is developed in a Hilbert expansion appropriate for this system. This yields incompressible Navier-Stokes equations for the velocity field u and a jump boundary condition for the pressure across the interface. The interface, in turn, moves with a velocity given by the normal component of u.     

Normalization and noise-reduction algorithm for fringe patterns

This paper presents a fringe pattern normalization and noise-reduction algorithm. Locally the background noise is suppressed, the modulation normalized and the noise smoothed. An expression to calculate the cosine-only term is formulated. It is related to the directional derivatives of the intensity fringes. Two-dimensional Fourier series are used to calculate the parameters needed for the algorithm. Experimental work is presented using diffraction and ESPI images. The programming is relatively simple and involves mainly local convolutions. The processing time using a 2 GHz computer to normalize an image of 256 × 256 pixels is approximately one second.     

Phase diagram of Na2S2O3 + ethanol + water at ambient pressure and temperature

In the present communication, we report the studies concerning liquid–liquid–solid equilibria for the ternary system sodium thiosulphate (Na₂S₂O₃) + ethanol + water at ambient pressure and at room temperature (303 ± 2 K). The solubility data of Na₂S₂O₃ are reported for solutions in water, ethanol and solutions of varying concentrations of ethanol in water. The phase diagram for the said system is developed, described and compared with similar system K₂CO₃ + methanol + water. These results have been explained in terms of structural properties of aqueous ethanol solutions and further discussed in terms of the effect of ions to cause phase separation.     

Topological order in the phase diagram for high-temperature superconductors with point defects

Applying a Lindemann like criterion obtained previously by Kierfeld et al. [J. Kierfeld, T. Nattermann, T. Hwa, Phys. Rev. B 55 (1997) 626], we estimate the magnetic field and temperature for a high-T_c superconductor, at which a topologically ordered vortex glass phase becomes unstable with respect to a disorder-induced formation of dislocations. The employed criterion is shown to be equivalent to a conventional phenomenological Lindemann criterion including the values for the numerical factors, i.e., for the Lindemann number. The positional correlation length of the topologically ordered vortex glass is calculated.     

Calculating Gibbs free energies of transfer from Gibbs ensemble Monte Carlo simulations

The partitioning of the ternary systems n-pentane/n-heptane/(helium or argon) at ambient conditions is investigated using configurational-bias Monte Carlo simulations in the Gibbs ensemble. The results demonstrate that this approach yields very precise partition constants and free energies of transfer. Simulations are carried out to study the dependence of the n-pentane partitioning with respect to the carrier gas, the system size, and the overall solute concentrations. None of the changes of variables, within the ranges used here, has a significant effect on the alkane partitioning. However, chemical potentials calculated via Widom's ghost particle insertions show a strong number dependence for phases containing relatively few molecules of a given type. This problem originates from the fact that the chemical potential is calculated for a concentration of real particles plus one ghost particle that is systematically larger than the equilibrium concentration. A simple correction term is suggested to account for this problem. Received: 13 May 1998 / Accepted: 18 June 1998 / Published online: 4 September 1998