Narrow Results

The minimum energy and size of doubly muonic D₃ molecule, which two of the electrons are replaced by the much heavier muons, are calculated by the well-known variational method. The calculations show that the system possesses two minimum positions, one at typically muonic distance and the second at the atomic distance. It is shown that at the muonic distance, the effective charge, z_eff is 2.9. We assumed a symmetric planar vibrational model between two minima and an oscillation potential energy is approximated in this region.

We examine the application of the Variational Monte Carlo (VMC) method to a cluster model for halo nuclei. Particular attention is paid to the error estimate in the presence of correlations in the underlying random walk. We analyze the required steps for a reliable application of the VMC in the case of a complicated many-body problem, such as the direct solution of the nuclear Hamiltonian with realistic interactions. We also examine the possibility of variance reduction through the "zero variance principle", paying particular attention to the complexity of the many-body problem.

A variational approach using new wave functions to and muonic symmetric molecular ions is proposed. The present method is based on the calculations of the photodecay widths of muonically excited molecular states and their comparison with recent precise data. The numerical calculations were done with a short computation time. Our results are close to the report.

The decay process of meta-stable muonic molecules produced in hydrogen isotopes is investigated. J and ν are ro-vibrational quantum numbers. This muonic molecular ion is formed in collisions of excited pμ(2s) atoms with H₂ molecules. Decay of the opens a path for the muon from pμ(2s) to pμ(1s). A scattering-theoretical model, employing a new wave function, is introduced for this process. Variational numerical calculation for decay widths of three low states of is performed using adiabatic representation method.

A variational approach using a new wave function to ttμ muonic antisymmetric molecular ion is proposed. This approach requires two terms in the total three-body wave function. The formation and fusion take place by the reason of the existence of the both Coulomb potential and nuclear absorption as the Wood–Saxon shape. The nuclear fusion rates for such levels below tμ(1s)+t threshold are calculated with a high accuracy and a short computation time.

Using the LAMP model for nuclear quark structure, we calculate the binding energy and quark structure of a B meson merging with a D meson. Our variational calculation shows that a molecular, deuteron-like state structure changes rather abruptly, as the separation between the two mesons decreases, and at a separation of about 0.14 fm, the hadronic system transforms into a four-quark bound state, although one maintaining an internal structure rather than that of a four-quark "bag." Unlike the deuteron, pion exchange does not provide any contribution to the ≈ 150 MeV binding.

A variational approach is given which can be applied to functionals of a general form to determine a corresponding Euler–Lagrange or shape equation. It is the intention to formulate the theory in detail based on a moving frame approach. It is then applied to a functional of a general form which depends on both the mean and Gaussian curvatures as well as the area and volume elements of the manifold. Only the case of a two-dimensional closed manifold is considered. The first variation of the functional is calculated in terms of the variations of the basic variables of the manifold. The results of the first variation allow for the second variation of the functional to be evaluated.

A smooth surface is considered which has a curved boundary. A system of exterior differential forms is introduced which describes the surface and boundary curves completely in the moving frame approach. A total free energy functional is defined based on these forms for which an equilibrium equation and boundary conditions of the surface are derived by calculating the variation of the total free energy. These results can be applied to a surface with several freely exposed edges.

This paper summarizes our recent attempts to integrate action and perception within a single optimization framework. We start with a statistical formulation of Helmholtz's ideas about neural energy to furnish a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring the causes of our sensory inputs and learning regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain's organization and responses. We will demonstrate the brain-like dynamics that this scheme entails by using models of birdsongs that are based on chaotic attractors with autonomous dynamics. This provides a nice example of how non-linear dynamics can be exploited by the brain to represent and predict dynamics in the environment.