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The calculation of the steady-state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem. Here we present the analytical derivation of the stationary joint and various marginal probability densities for a stochastic neuron model with adaptation current. Our approach assumes weak noise but is valid for arbitrary adaptation strength and time scale. The theory predicts several effects of adaptation on the statistics of the membrane potential of a tonically firing neuron: (i) a membrane potential distribution with a convex shape, (ii) a strongly increased probability of hyperpolarized membrane potentials induced by strong and fast adaptation, and (iii) a maximized variability associated with the adaptation current at a finite adaptation time scale. [ABSTRACT FROM AUTHOR]

The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different contexts may have different distributions, due to contextual biases in experimental design or physical interactions (signaling): a system of measurements has a maximally noncontextual description if they can be imposed a joint distribution on in which the measurements of any one property in different contexts are equal to each other with the maximal probability allowed by their different distributions. We derive necessary and sufficient conditions for the existence of such a description in a broad class of systems including Klyachko-Can-Binicioglu-Shumvosky-type (KCBS), EPR-Bell-type, and Leggett-Garg-type systems. Because these conditions allow for inconsistent connectedness, they are applicable to real experiments. We illustrate this by analyzing an experiment by Lapkiewicz and colleagues aimed at testing contextuality in a KCBS-type system. [ABSTRACT FROM AUTHOR]

The production cross sections of superheavy nuclei in hot fusion reactions are investigated systematically. In hot fusion reactions, the capture cross section can be obtained by calculating the weighted average of the transmission probability for different orientations of deformed colliding nuclei. An analytical formula for calculating the value of the fusion probability is proposed, which is suitable for both hot and cold fusion reactions. The orientation effects are considered empirically in calculating the fusion probability. The method proposed in the present work reproduces the measured evaporation residue (ER) cross sections in hot fusion reactions acceptably well. The formula also gives reasonable results for fusion probability in cold fusion reactions. Using this method the evaporation residue cross sections for synthesizing Z = 119 and 120 are predicted. It is found that for hot fusion reaction's larger maximal ER cross section of the 4n channel corresponds to lower optimal incident energy. [ABSTRACT FROM AUTHOR]

Neutron emission in the fusion process is investigated based on the Langevin equations coupled with the procedures describing the emission of neutron for the reaction systems 48Ca + 238U and 50Ti + 249Cf. The precompound neutron multiplicity npc, defined as the average number of neutron per fusion event, is obtained by means of those dynamic calculations. Influence of precompound neutron emission on the formation of superheavy elements is examined by means of the dynamic calculations using two different approaches, i.e., with and without taking the neutron emission into account in the fusion process. Our results show that the precompound neutron emission enhances the formation cross sections of superheavy nuclei. The origin responsible for the enhancement is that the precompound neutron emission increases the survival probability of the evaporation residue and hence increases the relevant cross sections. [ABSTRACT FROM AUTHOR]

Energies of the ground, ß and y bands as well as the associated B(E2) values are determined for each even-even isotope of the 180-196Pi chain by the exact solutions of some differential equations which approximate the generalized Bohr-Mottelson Hamiltonian. The emerging approaches are called the sextic and spheroidal approach (SSA), the sextic and Mathieu approach (SMA), the infinite square well and spheroidal approach (ISWSA), and the infinite square well and Mathieu approach (ISWMA). While the first three methods were formulated in some earlier papers, ISWMA is an unedited approach of this work. Numerical results are compared with those obtained with the so-called X(5) and Z(5) models. A contour plot for the probability density as function of the intrinsic dynamic deformations is given for a few states of the three considered bands with the aim of evidencing the shape evolution along the isotope chain and pointing out possible shape coexistence. [ABSTRACT FROM AUTHOR]

A phenomenological model of the β-delayed neutron-emission probability; based on a level density function, is presented. The effective level density systematics, empirically determined from the experimental dala, are found to be relatively flat, with discontinuities al the major shell closures. These systematics have been modeled and used to determine β-delayed neutron-emission probabilities. The present model is compared to other available models and is found to provide an improved description of the β-delayed neutron-emission probabilities across the entire mass surface. [ABSTRACT FROM AUTHOR]