Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

Dynamics and constraints of the massive graviton dark matter flat cosmologies

We discuss the dynamics of the Universe within the framework of the massive graviton cold dark matter scenario (MGCDM) in which gravitons are geometrically treated as massive particles. In this modified gravity theory, the main effect of the gravitons is to alter the density evolution of the cold dark matter component in such a way that the Universe evolves to an accelerating expanding regime, as presently observed. Tight constraints on the main cosmological parameters of the MGCDM model are derived by performing a joint likelihood analysis involving the recent supernovae type Ia data, the cosmic microwave background shift parameter, and the baryonic acoustic oscillations as traced by the Sloan Digital Sky Survey red luminous galaxies. The linear evolution of small density fluctuations is also analyzed in detail. It is found that the growth factor of the MGCDM model is slightly different (similar to 1-4%) from the one provided by the conventional flat Lambda CDM cosmology. The growth rate of clustering predicted by MGCDM and Lambda CDM models are confronted to the observations and the corresponding best fit values of the growth index (gamma) are also determined. By using the expectations of realistic future x-ray and Sunyaev-Zeldovich cluster surveys we derive the dark matter halo mass function and the corresponding redshift distribution of cluster-size halos for the MGCDM model. Finally, we also show that the Hubble flow differences between the MGCDM and the Lambda CDM models provide a halo redshift distribution departing significantly from the those predicted by other dark energy models. These results suggest that the MGCDM model can observationally be distinguished from Lambda CDM and also from a large number of dark energy models recently proposed in the literature.

Dynamic polarizability, Cauchy moments, and the optical absorption spectrum of liquid water: A sequential molecular dynamics/quantum mechanical approach

The dynamic polarizability and optical absorption spectrum of liquid water in the 6-15 eV energy range are investigated by a sequential molecular dynamics (MD)/quantum mechanical approach. The MD simulations are based on a polarizable model for liquid water. Calculation of electronic properties relies on time-dependent density functional and equation-of-motion coupled-cluster theories. Results for the dynamic polarizability, Cauchy moments, S(-2), S(-4), S(-6), and dielectric properties of liquid water are reported. The theoretical predictions for the optical absorption spectrum of liquid water are in good agreement with experimental information.

Signature of the interaction between dark energy and dark matter in observations

We investigate the effect of an interaction between dark energy and dark matter upon the dynamics of galaxy clusters. This effect is computed through the Layser-Irvine equation, which describes how an astrophysical system reaches virial equilibrium and was modified to include the dark interactions. Using observational data from almost 100 purportedly relaxed galaxy clusters we put constraints on the strength of the couplings in the dark sector. We compare our results with those from other observations and find that a positive (in the sense of energy flow from dark energy to dark matter) nonvanishing interaction is consistent with the data within several standard deviations.

Field theory model for dark matter and dark energy in interaction

We propose a field theory model for dark energy and dark matter in interaction. Comparing the classical solutions of the field equations with the observations of the CMB shift parameter, baryonic acoustic oscillations, lookback time, and the Gold supernovae sample, we observe a possible interaction between dark sectors with energy decay from dark energy into dark matter. The observed interaction provides an alleviation to the coincidence problem.

Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei

We evaluate the coincidence spectra in the nonmesonic weak decay (NMWD) Lambda N -> nN of Lambda hypernuclei (4)(Lambda)He, (5)(Lambda)He, (12)(Lambda)C, (16)(Lambda)O, and (28)(Lambda)Si, as a function of the sum of kinetic energies E(nN)=E(n)+E(N) for N=n,p. The strangeness-changing transition potential is described by the one-meson-exchange model, with commonly used parametrization. Two versions of the independent-particle shell model (IPSM) are employed to account for the nuclear structure of the final residual nuclei. They are as follows: (a) IPSM-a, where no correlation, except for the Pauli principle, is taken into account and (b) IPSM-b, where the highly excited hole states are considered to be quasistationary and are described by Breit-Wigner distributions, whose widths are estimated from the experimental data. All np and nn spectra exhibit a series of peaks in the energy interval 110 MeV < E(nN)< 170 MeV, one for each occupied shell-model state. Within the IPSM-a, and because of the recoil effect, each peak covers an energy interval proportional to A(-1) , going from congruent to 4 MeV for (28)(Lambda)Si to congruent to 40 MeV for (4)(Lambda)He. Such a description could be pretty fair for the light (4)(Lambda)He and (5)(Lambda)He hypernuclei. For the remaining, heavier, hypernuclei it is very important, however, to consider as well the spreading in strength of the deep-hole states and bring into play the IPSM-b approach. Notwithstanding the nuclear model that is employed the results depend only very weakly on the details of the dynamics involved in the decay process proper. We propose that the IPSM is the appropriate lowest-order approximation for the theoretical calculations of the of kinetic energy sum spectra in the NMWD. It is in comparison to this picture that one should appraise the effects of the final-state interactions and of the two-nucleon-induced decay mode.

Spin dynamics of NiCl(2)-4SC(NH(2))(2) in the field-induced ordered phase

NiCl(2)-4SC(NH(2))(2) (known as DTN) is a spin-1 material with a strong single-ion anisotropy that is regarded as a new candidate for Bose-Einstein condensation (BEC) of spin degrees of freedom. We present a systematic study of the low-energy excitation spectrum of DTN in the field-induced magnetically ordered phase by means of high-field electron spin resonance measurements at temperatures down to 0.45 K. We argue that two gapped modes observed in the experiment can be consistently interpreted within a four-sublattice antiferromagnet model with a finite interaction between two tetragonal subsystems and unbroken axial symmetry. The latter is crucial for the interpretation of the field-induced ordering in DTN in terms of BEC.

Energy gain induced by boundary crisis

We consider a nonlinear system and show the unexpected and surprising result that, even for high dissipation, the mean energy of a particle can attain higher values than when there is no dissipation in the system. We reconsider the time-dependent annular billiard in the presence of inelastic collisions with the boundaries. For some magnitudes of dissipation, we observe the phenomenon of boundary crisis, which drives the particles to an asymptotic attractive fixed point located at a value of energy that is higher than the mean energy of the nondissipative case and so much higher than the mean energy just before the crisis. We should emphasize that the unexpected results presented here reveal the importance of a nonlinear dynamics analysis to explain the paradoxical strategy of introducing dissipation in the system in order to gain energy.

A quasiclassical trajectory study of the OH plus SO reaction: The role of rotational energy

A full dimensional quasiclassical trajectory study of the OH+SO reaction is presented with the aim of investigating the role of the reactants rotational energy in the reactivity. Different energetic combinations with one and both reactants rotationally excited are studied. A passive method is used to correct zero-point-energy leakage in the classical calculations. The reactive cross sections, for each combination, are calculated and fitted to a capturelike model combined with a factor accounting for recrossing effects. Reactivity decreases as rotational energy is increased in any of both reactants. This fact provides a theoretical support for the experimental dependence of the rate constant on temperature.

Ultra-high-energy cosmic rays from centaurus A: jet interaction with gaseous shells

Ultra-high-energy cosmic rays (UHECRs), with energies above similar to 6 x 10(19) eV, seem to show a weak correlation with the distribution of matter relatively near to us in the universe. It has earlier been proposed that UHECRs could be accelerated in either the nucleus or the outer lobes of the nearby radio galaxy Cen A. We show that UHECR production at a spatially intermediate location about 15 kpc northeast from the nucleus, where the jet emerging from the nucleus is observed to strike a large star-forming shell of gas, is a plausible alternative. A relativistic jet is capable of accelerating lower energy heavy seed cosmic rays (CRs) to UHECRs on timescales comparable to the time it takes the jet to pierce the large gaseous cloud. In this model, many CRs arising from a starburst, with a composition enhanced in heavy elements near the knee region around PeV, are boosted to ultra-high energies by the relativistic shock of a newly oriented jet. This model matches the overall spectrum shown by the Auger data and also makes a prediction for the chemical composition as a function of particle energy. We thus predict an observable anisotropy in the composition at high energy in the sense that lighter nuclei should preferentially be seen toward the general direction of Cen A. Taking into consideration the magnetic field models for the Galactic disk and a Galactic magnetic wind, this scenario may resolve the discrepancy between HiRes and Auger results concerning the chemical composition of UHECRs.

Evolutionary dynamics on rugged fitness landscapes: Exact dynamics and information theoretical aspects

The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the random energy model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.

Density functional theory and ab initio molecular dynamics study of NO adsorption on Pd(111) and Pt(111) surfaces

The origin of the unique geometry for nitric oxide (NO) adsorption on Pd(111) and Pt(111) surfaces as well as the effect of temperature were studied by density functional theory calculations and ab initio molecular dynamics at finite temperature. We found that at low coverage, the adsorption geometry is determined by electronic interactions, depending sensitively on the adsorption sites and coverages, and the effect of temperature on geometries is significant. At coverage of 0.25 monolayer (ML), adsorbed NO at hollow sites prefer an upright configuration, while NO adsorbed at top sites prefer a tilting configuration. With increase in the coverage up to 0.50 ML, the enhanced steric repulsion lead to the tilting of hollow NO. We found that the tilting was enhanced by the thermal effects. At coverage of 0.75 ML with p(2 x 2)-3NO(fcc+hcp+top) structure, we found that there was no preferential orientation for tilted top NO. The interplay of the orbital hybridization, thermal effects, steric repulsion, and their effects on the adsorption geometries were highlighted at the end.

Dissipation as a mechanism of energy gain

Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 2: shells

Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods

A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.