Monte Carlo simulation and global optimization without parameters

We propose a new ensemble for Monte Carlo simulations, in which each state is assigned a statistical weight $1/k$, where $k$ is the number of states with smaller or equal energy. This ensemble has robust ergodicity properties and gives significant weight to the ground state, making it effective for hard optimization problems. It can be used to find free energies at all temperatures and picks up aspects of critical behaviour (if present) without any parameter tuning. We test it on the travelling salesperson problem, the Edwards-Anderson spin glass and the triangular antiferromagnet.Comment: 10 pages with 3 Postscript figures, to appear in Phys. Rev. Lett

Multicanonical Recursions

The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded Z-compressed .tar file created by uufiles), figure file corrected

Monte Carlo simulations of the screening potential of the Yukawa one-component plasma

A Monte Carlo scheme to sample the screening potential H(r) of Yukawa plasmas notably at short distances is presented. This scheme is based on an importance sampling technique. Comparisons with former results for the Coulombic one-component plasma are given. Our Monte Carlo simulations yield an accurate estimate of H(r) as well for short range and long range interparticle distances.Comment: to be published in Journal of Physics A: Mathematical and Genera

Multicanonical Hybrid Monte Carlo: Boosting Simulations of Compact QED

We demonstrate that substantial progress can be achieved in the study of the phase structure of 4-dimensional compact QED by a joint use of hybrid Monte Carlo and multicanonical algorithms, through an efficient parallel implementation. This is borne out by the observation of considerable speedup of tunnelling between the metastable states, close to the phase transition, on the Wilson line. We estimate that the creation of adequate samples (with order 100 flip-flops) becomes a matter of half a year's runtime at 2 Gflops sustained performance for lattices of size up to 24^4.Comment: 15 pages, 8 figure

The structure of fluid trifluoromethane and methylfluoride

We present hard X-ray and neutron diffraction measurements on the polar fluorocarbons HCF3 and H3CF under supercritical conditions and for a range of molecular densities spanning about a factor of ten. The Levesque-Weiss-Reatto inversion scheme has been used to deduce the site-site potentials underlying the measured partial pair distribution functions. The orientational correlations between adjacent fluorocarbon molecules -- which are characterized by quite large dipole moments but no tendency to form hydrogen bonds -- are small compared to a highly polar system like fluid hydrogen chloride. In fact, the orientational correlations in HCF3 and H3CF are found to be nearly as small as those of fluid CF4, a fluorocarbon with no dipole moment.Comment: 11 pages, 9 figure

Inelastic neutron scattering studies of methyl chloride synthesis over alumina

Not only is alumina the most widely used catalyst support material in the world, it is also an important catalyst in its own right. One major chemical process that uses alumina in this respect is the industrial production of methyl chloride. This is a large scale process (650 000 metric tons in 2010 in the United States), and a key feedstock in the production of silicones that are widely used as household sealants. In this Account, we show how, in partnership with conventional spectroscopic and reaction testing methods, inelastic neutron scattering (INS) spectroscopy can provide additional insight into the active sites present on the catalyst, as well as the intermediates present on the catalyst surface.<p></p> INS spectroscopy is a form of vibrational spectroscopy, where the spectral features are dominated by modes involving hydrogen. Because of this, most materials including alumina are largely transparent to neutrons. Advantageously, in this technique, the entire “mid-infrared”, 0–4000 cm<sup>–1</sup>, range is accessible; there is no cut-off at 1400 cm<sup>–1</sup> as in infrared spectroscopy. It is also straightforward to distinguish fundamental modes from overtones and combinations. <p></p> A key parameter in the catalyst’s activity is the surface acidity. In infrared spectroscopy of adsorbed pyridine, the shifts in the ring stretching modes are dependent on the strength of the acid site. However, there is a very limited spectral range available. We discuss how we can observe the low energy ring deformation modes of adsorbed pyridine by INS spectroscopy. These modes can undergo shifts that are as large as those seen with infrared inspectroscopy, potentially enabling finer discrimination between acid sites. <p></p> Surface hydroxyls play a key role in alumina catalysis, but in infrared spectroscopy, the presence of electrical anharmonicity complicates the interpretation of the O–H stretch region. In addition, the deformations lie below the infrared cut-off. Both of these limitations are irrelevant to INS spectroscopy, and all the modes are readily observable. When we add HCl to the catalyst surface, the acid causes changes in the spectra. We can then deduce both that the surface chlorination leads to enhanced Lewis acidity and that the hydroxyl group must be threefold coordinated. <p></p> When we react η-alumina with methanol, the catalyst forms a chemisorbed methoxy species. Infrared spectroscopy clearly shows its presence but also indicates the possible coexistence of a second species. Because of INS spectroscopy’s ability to discriminate between fundamental modes and combinations, we were able to unambiguously show that there is a single intermediate present on the surface of the active catalyst. This work represents a clear example where an understanding of the chemistry at the molecular level can help rationalize improvements in a large scale industrial process with both financial and environmental benefits. <p></p&gt

A Method to Study Relaxation of Metastable Phases: Macroscopic Mean-Field Dynamics

We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter $m$ through the restricted free energy $F(m)$ and are designed to give the correct equilibrium distribution for $m$. The connection between macroscopic dynamics and the underlying microscopic dynamic are considered in the context of a projection- operator formalism. Application to the square-lattice nearest-neighbor Ising ferromagnet gives good agreement with droplet theory and Monte Carlo simulations of the underlying microscopic dynamic. This includes quantitative agreement for the exponential dependence of the lifetime on the inverse of the applied field $H$, and the observation of distinct field regions in which the derivative of the lifetime with respect to $1/H$ depends differently on $H$. In addition, at very low temperatures we observe oscillatory behavior of this derivative with respect to $H$, due to the discreteness of the lattice and in agreement with rigorous results. Similarities and differences between this work and earlier works on finite Ising models in the fixed-magnetization ensemble are discussed.Comment: 44 pages RevTeX3, 11 uuencoded Postscript figs. in separate file

Seismic isolation and suspension systems for Advanced LIGO

To meet the overall isolation and alignment requirements for the optics in Advanced LIGO, the planned upgrade to LIGO, the US laser interferometric gravitational wave observatory, we are developing three sub-systems: a hydraulic external pre-isolator for low frequency alignment and control, a two-stage active isolation platform designed to give a factor of ~1000 attenuation at 10 Hz, and a multiple pendulum suspension system that provides passive isolation above a few hertz. The hydraulic stage uses laminar-flow quiet hydraulic actuators with millimeter range, and provides isolation and alignment for the optics payload below 10 Hz, including correction for measured Earth tides and the microseism. This stage supports the in-vacuum two-stage active isolation platform, which reduces vibration using force feedback from inertial sensor signals in six degrees of freedom. The platform provides a quiet, controlled structure to mount the suspension system. This latter system has been developed from the triple pendulum suspension used in GEO 600, the German/UK gravitational wave detector. To meet the more stringent noise levels required in Advanced LIGO, the baseline design for the most sensitive optics calls for a quadruple pendulum, whose final stage consists of a 40 kg sapphire mirror suspended on fused silica ribbons to reduce suspension thermal noise

Grundstate Properties of the 3D Ising Spin Glass

We study zero--temperature properties of the 3d Edwards--Anderson Ising spin glass on finite lattices up to size $12^3$. Using multicanonical sampling we generate large numbers of groundstate configurations in thermal equilibrium. Finite size scaling with a zero--temperature scaling exponent $y = 0.74 \pm 0.12$ describes the data well. Alternatively, a descriptions in terms of Parisi mean field behaviour is still possible. The two scenarios give significantly different predictions on lattices of size $\ge 12^3$.Comment: LATEX 9pages,figures upon request ,SCRI-9

Multi-Overlap Simulations for Transitions between Reference Configurations

We introduce a new procedure to construct weight factors, which flatten the probability density of the overlap with respect to some pre-defined reference configuration. This allows one to overcome free energy barriers in the overlap variable. Subsequently, we generalize the approach to deal with the overlaps with respect to two reference configurations so that transitions between them are induced. We illustrate our approach by simulations of the brainpeptide Met-enkephalin with the ECEPP/2 energy function using the global-energy-minimum and the second lowest-energy states as reference configurations. The free energy is obtained as functions of the dihedral and the root-mean-square distances from these two configurations. The latter allows one to identify the transition state and to estimate its associated free energy barrier.Comment: 12 pages, (RevTeX), 14 figures, Phys. Rev. E, submitte