Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in in the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize -using this extensive and exhaustive numerical study- the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.Comment: 7 pages, 4 figures, 2 tables, paper summary available at http://www.papercore.org/Kajantie2000. arXiv admin note: substantial text overlap with arXiv:1003.1591, arXiv:1005.5637, arXiv:1107.174

Large scale Gd-beta-diketonate based organic liquid scintillator production for antineutrino detection

Over the course of several decades, organic liquid scintillators have formed the basis for successful neutrino detectors. Gadolinium-loaded liquid scintillators provide efficient background suppression for electron antineutrino detection at nuclear reactor plants. In the Double Chooz reactor antineutrino experiment, a newly developed beta-diketonate gadolinium-loaded scintillator is utilized for the first time. Its large scale production and characterization are described. A new, light yield matched metal-free companion scintillator is presented. Both organic liquids comprise the target and "Gamma Catcher" of the Double Chooz detectors.Comment: 16 pages, 4 figures, 5 table

Large scale Gd-beta-diketonate based organic liquid scintillator production for antineutrino detection

Over the course of several decades, organic liquid scintillators have formed the basis for successful neutrino detectors. Gadolinium-loaded liquid scintillators provide efficient background suppression for electron antineutrino detection at nuclear reactor plants. In the Double Chooz reactor antineutrino experiment, a newly developed beta-diketonate gadolinium-loaded scintillator is utilized for the first time. Its large scale production and characterization are described. A new, light yield matched metal-free companion scintillator is presented. Both organic liquids comprise the target and "Gamma Catcher" of the Double Chooz detectors.Comment: 16 pages, 4 figures, 5 table

Large scale Gd-beta-diketonate based organic liquid scintillator production for antineutrino detection

Over the course of several decades, organic liquid scintillators have formed the basis for successful neutrino detectors. Gadolinium-loaded liquid scintillators provide efficient background suppression for electron antineutrino detection at nuclear reactor plants. In the Double Chooz reactor antineutrino experiment, a newly developed beta-diketonate gadolinium-loaded scintillator is utilized for the first time. Its large scale production and characterization are described. A new, light yield matched metal-free companion scintillator is presented. Both organic liquids comprise the target and "Gamma Catcher" of the Double Chooz detectors.Comment: 16 pages, 4 figures, 5 table

F-8C digital CCV flight control laws

A set of digital flight control laws were designed for the NASA F-8C digital fly-by-wire aircraft. The control laws emphasize Control Configured Vehicle (CCV) benefits. Specific pitch axis objectives were improved handling qualities, angle-of-attack limiting, gust alleviation, drag reduction in steady and maneuvering flight, and a capability to fly with reduced static stability. The lateral-directional design objectives were improved Dutch roll damping and turn coordination over a wide range in angle-of-attack. An overall program objective was to explore the use of modern control design methodilogy to achieve these specific CCV benefits. Tests for verifying system integrity, an experimental design for handling qualities evaluation, and recommended flight test investigations were specified

A new method for analyzing ground-state landscapes: ballistic search

A ``ballistic-search'' algorithm is presented which allows the identification of clusters (or funnels) of ground states in Ising spin glasses even for moderate system sizes. The clusters are defined to be sets of states, which are connected in state-space by chains of zero-energy flips of spins. The technique can also be used to estimate the sizes of such clusters. The performance of the method is tested with respect to different system sizes and choices of parameters. As an application the ground-state funnel structure of two-dimensional +or- J spin glasses of systems up to size L=20 is analyzed by calculating a huge number of ground states per realization. A T=0 entropy per spin of s_0=0.086(4)k_B is obtained.Comment: 10 pages, 11 figures, 35 references, revte

Effective dynamics using conditional expectations

The question of coarse-graining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarse-grained variable $\xi(x)$, where $x$ describes the configuration of the system in a high-dimensional space $\R^n$, and $\xi$ is a smooth function with value in $\R$ (typically a reaction coordinate). It is well known that, given a Boltzmann-Gibbs distribution on $x \in \R^n$, the equilibrium properties on $\xi(x)$ are completely determined by the free energy. On the other hand, the question of the effective dynamics on $\xi(x)$ is much more difficult to address. Starting from an overdamped Langevin equation on $x \in \R^n$, we propose an effective dynamics for $\xi(x) \in \R$ using conditional expectations. Using entropy methods, we give sufficient conditions for the time marginals of the effective dynamics to be close to the original ones. We check numerically on some toy examples that these sufficient conditions yield an effective dynamics which accurately reproduces the residence times in the potential energy wells. We also discuss the accuracy of the effective dynamics in a pathwise sense, and the relevance of the free energy to build a coarse-grained dynamics

A system of relational syllogistic incorporating full Boolean reasoning

We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related to all B; All A are R-related to some B; All A are R-related to all B. Such primitives formalize sentences from natural language like `All students read some textbooks'. Here A and B denote arbitrary sets (of objects), and R denotes an arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem.Comment: Available at http://link.springer.com/article/10.1007/s10849-012-9165-

Discrete energy landscapes and replica symmetry breaking at zero temperature

The order parameter P(q) for disordered systems with degenerate ground-states is reconsidered. We propose that entropy fluctuations lead to a trivial P(q) at zero temperature as in the non-degenerate case, even if there are zero-energy large-scale excitations (complex energy landscape). Such a situation should arise in the 3-dimensional +-J Ising spin glass and in MAX-SAT. Also, we argue that if the energy landscape is complex with a finite number of ground-state families, then replica symmetry breaking reappears at positive temperature.Comment: 7 pages; clarifications on valley definition

Optimal Vertex Cover for the Small-World Hanoi Networks

The vertex-cover problem on the Hanoi networks HN3 and HN5 is analyzed with an exact renormalization group and parallel-tempering Monte Carlo simulations. The grand canonical partition function of the equivalent hard-core repulsive lattice-gas problem is recast first as an Ising-like canonical partition function, which allows for a closed set of renormalization group equations. The flow of these equations is analyzed for the limit of infinite chemical potential, at which the vertex-cover problem is attained. The relevant fixed point and its neighborhood are analyzed, and non-trivial results are obtained both, for the coverage as well as for the ground state entropy density, which indicates the complex structure of the solution space. Using special hierarchy-dependent operators in the renormalization group and Monte-Carlo simulations, structural details of optimal configurations are revealed. These studies indicate that the optimal coverages (or packings) are not related by a simple symmetry. Using a clustering analysis of the solutions obtained in the Monte Carlo simulations, a complex solution space structure is revealed for each system size. Nevertheless, in the thermodynamic limit, the solution landscape is dominated by one huge set of very similar solutions.Comment: RevTex, 24 pages; many corrections in text and figures; final version; for related information, see http://www.physics.emory.edu/faculty/boettcher