We consider the satisfiability problem (SAT) for Boolean formulas given in conjunctive normal form with the restriction that each clause contains three literals (3-CNF). Generation of random formulas ...with a fixed clause length is widely used in empirical studies. An interesting phenomenon of this method is the repeatedly confirmed linear dependence of the number of clauses in the formula on the number of Boolean variables at the point of the “phase transition” from satisfiable to unsatisfiable formulas (when the fraction of unsatisfiable formulas becomes prevailing). We propose and study a method for generating random formulas that has a smaller coefficient (3.49) of proportionality between the number of clauses and the number of variables at the point of the “phase transition” (for the previously known generation method this coefficient is 4.23).
The first searches for axions and axionlike particles with the Large Underground Xenon experiment are presented. Under the assumption of an axioelectric interaction in xenon, the coupling constant ...between axions and electrons g_{Ae} is tested using data collected in 2013 with an exposure totaling 95 live days ×118 kg. A double-sided, profile likelihood ratio statistic test excludes g_{Ae} larger than 3.5×10^{-12} (90% C.L.) for solar axions. Assuming the Dine-Fischler-Srednicki-Zhitnitsky theoretical description, the upper limit in coupling corresponds to an upper limit on axion mass of 0.12 eV/c^{2}, while for the Kim-Shifman-Vainshtein-Zhakharov description masses above 36.6 eV/c^{2} are excluded. For galactic axionlike particles, values of g_{Ae} larger than 4.2×10^{-13} are excluded for particle masses in the range 1-16 keV/c^{2}. These are the most stringent constraints to date for these interactions.
A comprehensive model for explaining scintillation yield in liquid xenon is introduced. We unify various definitions of work function which abound in the literature and incorporateall available data ...on electron recoil scintillation yield. This results in a better understanding of electronrecoil, and facilitates an improved description of nuclear recoil. An incident gamma energyrange of O(1 keV) to O(1 MeV) and electric fields between 0 and O(10 kV/cm) are incorporatedinto this heuristic model. We show results from a Geant4 implementation, but because the modelhas a few free parameters, implementation in any simulation package should be simple. We usea quasi-empirical approach with an objective of improving detector calibrations and performanceverification. The model will aid in the design and optimization of future detectors. This model isalso easy to extend to other noble elements. In this paper we lay the foundation for an exhaustivesimulation code which we call NEST (Noble Element Simulation Technique).
A mathematical model of a solid body with mesoscopic defects is presented and validated. The constitutive relations proposed earlier allow describing the deformation behavior of typical ...elastic-viscoplastic materials (metals and alloys) in a wide range of strain rates, temperatures, and stresses. Methods for identifying unknown parameters of the model by solving a number of independent optimization problems using data from independent experiments are developed and implemented. For identification we use both the results of a literature review and experimental data. The experimental study on high-speed collision of a cylindrical specimen with an obstacle in the form of a bar (Taylor–Hopkinson test) is carried out by recording the temperature field in the course of deformation. The data are used to verify the model. For comparison the calculations are performed in the three-dimensional statement and in the axisymmetric statement. The formulated boundary value problems are solved numerically by the finite element method. The results of numerical calculations are in good agreement with the experimental data: the shape of the specimen after collision and the measured temperature (mechanical energy dissipation during inelastic deformation) coincide. This confirms the adequacy of the developed mathematical model and indicates that it can be used to solve both fundamental and applied problems of solid mechanics. The analysis of parallelism efficiency shows that the use of eight cores yields a five-fold acceleration and, as the number of cores increases further, this trend presumably continues.
The self-similarity of characteristic stages of damage-failure transition has been studied both theoretically and experimentally, with the damage localization kinetics analyzed according to the ...nonlinearity of free energy release of solids with defects: Free energy in the generalized Ginzburg–Landau form reflecting the specific criticality of solids with defects, and the structural-scaling transition in the presence of two critical points separating qualitatively different material responses corresponds to the types of collective modes of defects. These collective modes have the nature of the self-similar solutions of the damage evolution equation. The final damage stage is associated with the singular self-similar blow-up solutions localized on a set of spatial scales. The presence of two singularities (the stress field at the crack tip and the blow-up damage modes) allows the interpretation of self-similarity of damage localization kinetics to be construed as a criticality sign of damage-failure transition and has been illustrated by the original experimental statements: transition from the steady state to branching crack dynamics, dynamic fragmentation statistics, resonance regimes of failure in shocked materials.
We present experimental constraints on the spin-dependent WIMP-nucleon elastic cross sections from the total 129.5 kg yr exposure acquired by the Large Underground Xenon experiment (LUX), operating ...at the Sanford Underground Research Facility in Lead, South Dakota (USA). A profile likelihood ratio analysis allows 90% C.L. upper limits to be set on the WIMP-neutron (WIMP-proton) cross section of σ_{n}=1.6×10^{-41} cm^{2} (σ_{p}=5×10^{-40} cm^{2}) at 35 GeV c^{-2}, almost a sixfold improvement over the previous LUX spin-dependent results. The spin-dependent WIMP-neutron limit is the most sensitive constraint to date.
In the process of modeling multilayer semiconductor nanostructures, an important role is played by the rapid acquisition of accurate values of the characteristics of the structure under ...consideration. One of these characteristics is the value of the interaction energy of atoms within the structure. The energy value is also important for obtaining other quantities, such as the bulk modulus of elasticity of the structure and the shear modulus. The paper discusses a method for obtaining the energy of the interaction between two atoms, based on machine learning methods. A model built based on the Gaussian Approximation Potential (GAP) is trained on a previously prepared sample and allows predicting the energy values of pairs of atoms for the test data. The values of the coordinates of interacting atoms, the distance between the atoms, the value of the lattice constant of the structure, an indication of the type of interacting atoms, and a value describing the environment of the atoms are used as attributes. The computational experiment is carried out with the participation of one-component compounds, such as Si, Ge, and C. The rate of obtaining the energy of interacting atoms and the accuracy of the obtained value are estimated. The speed and accuracy characteristics are compared with the values obtained using the multiparticle interatomic potential, the Tersoff potential.
The dualism of the regularities of transition from the dispersion accumulation of damages to macroscopic failure, which is presented in two-parameter criteria of fracture, is tied to two types of ...singular solutions in solid bodies with defects: self-similar intermediate-asymptotic distribution of stresses in the vicinity of the crack tip and self-similar kinetics of localization of the damage. In addition to the value of the coefficient of stress intensity, two extra parameters (cohesive strength and cohesion length) are determined by kinetic conditions for the formation of fracture zones on the characteristic spatial scale when the critical values are attained by the stresses in the zones of local damage. These parameters are associated with the nonlinear self-similar kinetics of damage localization, and the existence of two self-similar solutions determines different stages of fracture, including the initiation and propagation of cracks and the fracture of specimens in the presence of concentrators. The stages of development of fracture in the presence of two types of self-similar solutions is investigated experimentally from the data on the kinetics of crack extension in PMMA and DIC data during the deformation of a composite specimen with a circular concentrator, and also demonstrates the analogous dynamics of stages of fracture, which confirms the possibility of using two-parameter criteria to describe the stages of fracture.