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

Palynological, geochemical, and mineralogical characteristics of the Early Jurassic Liasidium Event in the Cleveland Basin, Yorkshire, UK

A previously proposed hyperthermal episode in the Early Jurassic (mid-Sinemurian) is investigated from the shallow marine succession at Robin Hood’s Bay, Cleveland Basin, Yorkshire, UK. Palynological study confirms that the stratigraphical extent of the distinctive dinoflagellate cyst Liasidium variabile corresponds very closely to the oxynotum Zone. The range of Liasidium variabile also corresponds to an overall negative excursion in carbon-isotopes measured in bulk organic matter, which here exhibits a double spike in the middle oxynotum Zone. Additionally, Liasidium variabile abundances track overall transgressive-regressive facies trends with peak abundance of dinoflagellate cysts corresponding to deepest water facies and maximum flooding. Lithological cycles (parasequences), defined by visual description and hand-held X-ray fluorescence analysis of powdered samples, match previously suggested short eccentricity cycles, and allow a total duration for the event of at least one million years to be suggested. Changes in clay mineralogy throughout the section determined by whole rock X-ray diffraction and scanning electron microscopy are shown to be largely related to authigenic processes, and neither support nor refute the proposition of coeval palaeoclimate changes. The combined characteristics of the Liasidium Event described from Robin Hood’s Bay are similar to, but much less extreme than, the Early Jurassic Toarcian Oceanic Anoxic Event albeit, at this locality, there is no evidence for the development of significant bottom water deoxygenation

Generalized-ensemble Monte carlo method for systems with rough energy landscape

We present a novel Monte Carlo algorithm which enhances equilibrization of low-temperature simulations and allows sampling of configurations over a large range of energies. The method is based on a non-Boltzmann probability weight factor and is another version of the so-called generalized-ensemble techniques. The effectiveness of the new approach is demonstrated for the system of a small peptide, an example of the frustrated system with a rugged energy landscape.Comment: Latex; ps-files include

A comparison of extremal optimization with flat-histogram dynamics for finding spin-glass ground states

We compare the performance of extremal optimization (EO), flat-histogram and equal-hit algorithms for finding spin-glass ground states. The first-passage-times to a ground state are computed. At optimal parameter of tau=1.15, EO outperforms other methods for small system sizes, but equal-hit algorithm is competitive to EO, particularly for large systems. Flat-histogram and equal-hit algorithms offer additional advantage that they can be used for equilibrium thermodynamic calculations. We also propose a method to turn EO into a useful algorithm for equilibrium calculations. Keywords: extremal optimization. flat-histogram algorithm, equal-hit algorithm, spin-glass model, ground state.Comment: 10 LaTeX pages, 2 figure

Transition Matrix Monte Carlo Reweighting and Dynamics

We study an induced dynamics in the space of energy of single-spin-flip Monte Carlo algorithm. The method gives an efficient reweighting technique. This dynamics is shown to have relaxation times proportional to the specific heat. Thus, it is plausible for a logarithmic factor in the correlation time of the standard 2D Ising local dynamics.Comment: RevTeX, 5 pages, 3 figure

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

Evolution of the Toarcian (Early Jurassic) carbon-cycle and global climatic controls on local sedimentary processes (Cardigan Bay Basin, UK)

The late Early Jurassic Toarcian Stage represents the warmest interval of the Jurassic Period, with an abrupt rise in global temperatures of up to ∼7 °C in mid-latitudes at the onset of the early Toarcian Oceanic Anoxic Event (T-OAE; ∼183 Ma). The T-OAE, which has been extensively studied in marine and continental successions from both hemispheres, was marked by the widespread expansion of anoxic and euxinic waters, geographically extensive deposition of organic-rich black shales, and climatic and environmental perturbations. Climatic and environmental processes following the T-OAE are, however, poorly known, largely due to a lack of study of stratigraphically well-constrained and complete sedimentary archives. Here, we present integrated geochemical and physical proxy data (high-resolution carbon-isotope data (δ13C), bulk and molecular organic geochemistry, inorganic petrology, mineral characterisation, and major- and trace-element concentrations) from the biostratigraphically complete and expanded entire Toarcian succession in the Llanbedr (Mochras Farm) Borehole, Cardigan Bay Basin, Wales, UK. With these data, we (1) construct the first high-resolution biostratigraphically calibrated chemostratigraphic reference record for nearly the complete Toarcian Stage, (2) establish palaeoceanographic and depositional conditions in the Cardigan Bay Basin, (3) show that the T-OAE in the hemipelagic Cardigan Bay Basin was marked by the occurrence of gravity-flow deposits that were likely linked to globally enhanced sediment fluxes to continental margins and deeper marine (shelf) basins, and (4) explore how early Toarcian (tenuicostatum and serpentinum zones) siderite formation in the Cardigan Bay Basin may have been linked to low global oceanic sulphate concentrations and elevated supply of iron (Fe) from the hinterland, in response to climatically induced changes in hydrological cycling, global weathering rates and large-scale sulphide and evaporite deposition

Orbital pacing and secular evolution of the Early Jurassic carbon cycle

Cyclic variations in Earth’s orbit drive periodic changes in the ocean–atmosphere system at a time scale of tens to hundreds of thousands of years. The Mochras δ13CTOC record illustrates the continued impact of long-eccentricity (405-ky) orbital forcing on the carbon cycle over at least ∼18 My of Early Jurassic time and emphasizes orbital forcing as a driving mechanism behind medium-amplitude δ13C fluctuations superimposed on larger-scale trends that are driven by other variables such as tectonically determined paleogeography and eruption of large igneous provinces. The dataset provides a framework for distinguishing between internal Earth processes and solar-system dynamics as the driving mechanism for Early Jurassic δ13C fluctuations and provides an astronomical time scale for the Sinemurian Stage

Astronomical constraints on the duration of the Early Jurassic Pliensbachian Stage and global climatic fluctuations

The Early Jurassic was marked by multiple periods of major global climatic and palaeoceanographic change, biotic turnover and perturbed global geochemical cycles, commonly linked to large igneous province volcanism. This epoch was also characterised by the initial break-up of the super-continent Pangaea and the opening and formation of shallow-marine basins and ocean gateways, the timing of which are poorly constrained. Here, we show that the Pliensbachian Stage and the Sinemurian–Pliensbachian global carbon-cycle perturbation (marked by a negative shift in δ13Cδ13C of 2–4‰2–4‰), have respective durations of ∼8.7 and ∼2 Myr. We astronomically tune the floating Pliensbachian time scale to the 405 Kyr eccentricity solution (La2010d), and propose a revised Early Jurassic time scale with a significantly shortened Sinemurian Stage duration of 6.9±0.4 Myr6.9±0.4 Myr. When calibrated against the new time scale, the existing Pliensbachian seawater 87Sr/86Sr record shows relatively stable values during the first ∼2 Myr of the Pliensbachian, superimposed on the long-term Early Jurassic decline in 87Sr/86Sr. This plateau in 87Sr/86Sr values coincides with the Sinemurian–Pliensbachian boundary carbon-cycle perturbation. It is possibly linked to a late phase of Central Atlantic Magmatic Province (CAMP) volcanism that induced enhanced global weathering of continental crustal materials, leading to an elevated radiogenic strontium flux to the global ocean