Quadratic momentum dependence in the nucleon-nucleon interaction

We investigate different choices for the quadratic momentum dependence required in nucleon-nucleon potentials to fit phase shifts in high partial-waves. In the Argonne v18 potential L**2 and (L.S)**2 operators are used to represent this dependence. The v18 potential is simple to use in many-body calculations since it has no quadratic momentum-dependent terms in S-waves. However, p**2 rather than L**2 dependence occurs naturally in meson-exchange models of nuclear forces. We construct an alternate version of the Argonne potential, designated Argonne v18pq, in which the L**2 and (L.S)**2 operators are replaced by p**2 and Qij operators, respectively. The quadratic momentum-dependent terms are smaller in the v18pq than in the v18 interaction. Results for the ground state binding energies of 3H, 3He, and 4He, obtained with the variational Monte Carlo method, are presented for both the models with and without three-nucleon interactions. We find that the nuclear wave functions obtained with the v18pq are slightly larger than those with v18 at interparticle distances < 1 fm. The two models provide essentially the same binding in the light nuclei, although the v18pq gains less attraction when a fixed three-nucleon potential is added.Comment: v.2 important corrections in tables and minor revisions in text; reference for web-posted subroutine adde

Fast Neural Network Predictions from Constrained Aerodynamics Datasets

Incorporating computational fluid dynamics in the design process of jets, spacecraft, or gas turbine engines is often challenged by the required computational resources and simulation time, which depend on the chosen physics-based computational models and grid resolutions. An ongoing problem in the field is how to simulate these systems faster but with sufficient accuracy. While many approaches involve simplified models of the underlying physics, others are model-free and make predictions based only on existing simulation data. We present a novel model-free approach in which we reformulate the simulation problem to effectively increase the size of constrained pre-computed datasets and introduce a novel neural network architecture (called a cluster network) with an inductive bias well-suited to highly nonlinear computational fluid dynamics solutions. Compared to the state-of-the-art in model-based approximations, we show that our approach is nearly as accurate, an order of magnitude faster, and easier to apply. Furthermore, we show that our method outperforms other model-free approaches

Variational Monte Carlo Calculations of 3^3H and 4^4He with a relativistic Hamiltonian - II

In relativistic Hamiltonians the two-nucleon interaction is expressed as a sum of $\tilde{v}_{ij}$, the interaction in the ${\bf P}_{ij}=0$ rest frame, and the ``boost interaction'' $\delta v({\bf P}_{ij})$ which depends upon the total momentum ${\bf P}_{ij}$ and vanishes in the rest frame. The $\delta v$ can be regarded as a sum of four terms: $\delta v_{RE}$, $\delta v_{LC}$, $\delta v_{TP}$ and $\delta v_{QM}$; the first three originate from the relativistic energy-momentum relation, Lorentz contraction and Thomas precession, while the last is purely quantum. The contributions of $\delta v_{RE}$ and $\delta v_{LC}$ have been previously calculated with the variational Monte Carlo method for $^3$H and $^4$He. In this brief note we report the results of similar calculations for the contributions of $\delta v_{TP}$ and $\delta v_{QM}$. These are found to be rather small.Comment: 7 pages, P-94-09-07

Spin-Isospin Structure and Pion Condensation in Nucleon Matter

We report variational calculations of symmetric nuclear matter and pure neutron matter, using the new Argonne v18 two-nucleon and Urbana IX three-nucleon interactions. At the equilibrium density of 0.16 fm^-3 the two-nucleon densities in symmetric nuclear matter are found to exhibit a short-range spin-isospin structure similar to that found in light nuclei. We also find that both symmetric nuclear matter and pure neutron matter undergo transitions to phases with pion condensation at densities of 0.32 fm^-3 and 0.2 fm^-3, respectively. Neither transtion occurs with the Urbana v14 two-nucleon interaction, while only the transition in neutron matter occurs with the Argonne v14 two-nucleon interaction. The three-nucleon interaction is required for the transition to occur in symmetric nuclear matter, whereas the the transition in pure neutron matter occurs even in its absence. The behavior of the isovector spin-longitudinal response and the pion excess in the vicinity of the transition, and the model dependence of the transition are discussed.Comment: 44 pages RevTeX, 15 postscript figures. Minor modifications to original postin

EU support for biofuels and bioenergy, environmental sustainability criteria, and trade policy

This paper presents physics-based surrogate modeling algorithms for systems governed by parameterized partial differential equations (PDEs) commonly encountered in design optimization and uncertainty analysis. We first outline unsupervised learning approaches that leverage advances in the machine learning literature for a meshfree solution of PDEs. Subsequently, we propose continuum and discrete formulations for systems governed by parameterized steady-state PDEs. We consider the case of both deterministically and randomly parameterized systems. The basic idea is to embody the design variables or uncertain parameters in additional dimensions of the governing PDEs along with the spatial coordinates. We show that the undetermined parameters of the surrogate model can be estimated by minimizing a physics-based objective function derived using a multidimensional least-squares collocation or the Bubnov-Galerkin scheme. This potentially allows us to construct surrogate models without using data from computer experiments on a deterministic analysis code. Finally, we also outline an extension of the present approach to directly approximate the density function of random algebraic equations

Spin-orbit interaction in Hartree-Fock calculations

The contribution of the spin-orbit interaction in Hartree-Fock calculations for closed shell nuclei is studied. We obtain explicit expressions for the finite range spin-orbit force. New terms with respect to the traditional spin-orbit expressions are found. The importance of the finite-range is analyzed. Results obtained with spin-orbit terms taken from realistic interactions are presented. The effect of the spin-orbit isospin dependent terms is evaluated.Comment: To be published on Nuovo Cimento

Photostatistics Reconstruction via Loop Detector Signatures

Photon-number resolving detectors are a fundamental building-block of optical quantum information processing protocols. A loop detector, combined with appropriate statistical processing, can be used to convert a binary on/off photon counter into a photon-number-resolving detector. Here we describe the idea of a signature of photon-counts, which may be used to more robustly reconstruct the photon number distribution of a quantum state. The methodology is applied experimentally in a 9-port loop detector operating at a telecommunications wavelength and compared directly to the approach whereby only the number of photon-counts is used to reconstruct the input distribution. The signature approach is shown to be more robust against calibration errors, exhibit reduced statistical uncertainty, and reduced reliance on a-priori assumptions about the input state.Comment: 13 pages, 12 figure

Mixed quark-nucleon phase in neutron stars and nuclear symmetry energy

The influence of the nuclear symmetry energy on the formation of a mixed quark-nucleon phase in neutron star cores is studied. We use simple parametrizations of the nuclear matter equation of state, and the bag model for the quark phase. The behavior of nucleon matter isobars, which is responsible for the existence of the mixed phase, is investigated. The role of the nuclear symmetry energy changes with the value of the bag constant B. For lower values of B the properties of the mixed phase do not depend strongly on the symmetry energy. For larger B we find that a critical pressure for the first quark droplets to form is strongly dependent on the nuclear symmetry energy, but the pressure at which last nucleons disappear is independent of it.Comment: 12 pages, 16 figures, Phys. Rev. C in pres

Ground State Correlations in 16O and 40Ca

We study the ground state properties of doubly closed shell nuclei $^{16}$O and $^{40}$Ca in the framework of Correlated Basis Function theory using state dependent correlations, with central and tensor components. The realistic Argonne $v_{14}$ and $v'_{8}$ two-nucleon potentials and three-nucleon potentials of the Urbana class have been adopted. By means of the Fermi Hypernetted Chain integral equations, in conjunction with the Single Operator Chain approximation, we evaluate the ground state energy, one- and two-body densities and electromagnetic and spin static responses for both nuclei. In $^{16}$O we compare our results with the available Monte Carlo and Coupled Cluster ones and find a satisfying agreement. As in the nuclear matter case with similar interactions and wave functions, the nuclei result under-bound by 2--3 MeV/A.Comment: 33 RevTeX pages + 8 figures, to appear in Phys.Rev.

Microscopic calculation of the equation of state of nuclear matter and neutron star structure

We present results for neutron star models constructed with a new equation of state for nuclear matter at zero temperature. The ground state is computed using the Auxiliary Field Diffusion Monte Carlo (AFDMC) technique, with nucleons interacting via a semi-phenomenological Hamiltonian including a realistic two-body interaction. The effect of many-body forces is included by means of additional density-dependent terms in the Hamiltonian. In this letter we compare the properties of the resulting neutron-star models with those obtained using other nuclear Hamiltonians, focusing on the relations between mass and radius, and between the gravitational mass and the baryon number.Comment: modified version with a slightly different Hamiltonian and parametrization of the EO