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At least 19 records

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm

A new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is base upon a generalization of de Veubeke's complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and thg resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a complete separation of the boundary value problem (for stress rate and velocity) and the initial value problem (for total stress and deformation); hence, their numerical treatments are essentially independent. After a fairly comprehensive discussion of the numerical treatment of the boundary value problem, we launch into a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.

Reed, K. W.↗

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm - Applications

A new hybrid-stress finite element algorithm suitable for analyzing large quasistatic deformations of inelastic solids is presented and its feasibility and performance are demonstrated with examples. The algorithm provides extremely accurate bifurcation analysis which is stable with respect to variation in the finite element mesh, so long as the same type of element is used in every mesh. When the mesh element is varied, the result changes in a predictable manner. The method does not necessarily lead to an upper or lower bound for the critical load. An explicit forward gradient scheme is used to improve stability and is shown to be useful also for elongation-dominated deformations. The application of the method to the onset of necking in plane extension and to deformation and stress in plane extension of an elasticoviscous fluid with an array of cylindrical voids is given in detail.

Reed, K. W.↗

Atom-atom inelastic collisions and three-body atomic recombination in weakly ionized argon plasmas

A stationary collisional-radiative model including both inelastic electron-atom and atom-atom collisions is used to examine nonequilibrium weakly ionized argon plasmas with atomic densities 10 to the 16th to 10 to the 20th/cu cm, temperatures below 6000 K, and with different degrees of radiation trapping. It is shown that three-body atomic recombination becomes important at high particle densities. Comparison is made between the present approach and Thomson's theory for atomic recombination.

Braun, C. G.↗

Second quantization techniques in the scattering of nonidentical composite bodies

Second quantization techniques for describing elastic and inelastic interactions between nonidentical composite bodies are presented and are applied to nucleus-nucleus collisions involving ground-state and one-particle-one-hole excitations. Evaluations of the resultant collision matrix elements are made through use of Wick's theorem.

Norbury, J. W.↗

Inelastic strain analogy for piecewise linear computation of creep residues in built-up structures

An analogy between inelastic strains caused by temperature and those caused by creep is presented in terms of isotropic elasticity. It is shown how the theoretical aspects can be blended with existing finite-element computer programs to exact a piecewise linear solution. The creep effect is determined by using the thermal stress computational approach, if appropriate alterations are made to the thermal expansion of the individual elements. The overall transient solution is achieved by consecutive piecewise linear iterations. The total residue caused by creep is obtained by accumulating creep residues for each iteration and then resubmitting the total residues for each element as an equivalent input. A typical creep law is tested for incremental time convergence. The results indicate that the approach is practical, with a valid indication of the extent of creep after approximately 20 hr of incremental time. The general analogy between body forces and inelastic strain gradients is discussed with respect to how an inelastic problem can be worked as an elastic problem.

Jenkins, Jerald M.↗

Prediction and observation of intermodulation sidebands from anharmonic phonons in NaBr

A quantum Langevin model, like models from optomechanics, was developed for phonons. It predicts intermodulation phonon sidebands (IPSs) in anharmonic crystals. Ab initio calculations of anharmonic phonons in rock-salt NaBr showed these spectral features as many-body effects. Modern inelastic neutron scattering measurements on a crystal of NaBr at 300 K revealed diffuse intensity at high phonon energy from a predicted upper IPS. The transverse optical (TO) part of the new features originates from phonon intermodulation between the transverse acoustic (TA) and TO phonons. The longitudinal optical spectral features originate from three-phonon coupling between the TA modes and the TO lattice modes. The partner lower IPS proves to be an intrinsic localized mode. Interactions with the thermal bath broaden and redistribute the spectral weight of the IPS pair. These sidebands are a probe of the anharmonicity and quantum noise of phonons in NaBr and suggest novel interactions between photons and phonons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Body frame close coupling wave packet approach to gas phase atom-rigid rotor inelastic collisions

The close coupling wave packet (CCWP) method is formulated in a body-fixed representation for atom-rigid rotor inelastic scattering. For J greater than j-max (where J is the total angular momentum and j is the rotational quantum number), the computational cost of propagating the coupled channel wave packets in the body frame is shown to scale approximately as N exp 3/2, where N is the total number of channels. For large numbers of channels, this will be much more efficient than the space frame CCWP method previously developed which scales approximately as N-squared under the same conditions.

Sun, Y.↗

Theoretical studies of molecular collisions

The following subject areas are covered: (1) total integral reactive cross sections and vibrationally resolved reaction probabilities for F + H2 = HF + H; (2) a theoretical study of inelastic O + N2 collisions; (3) body frame close coupling wave packet approach to gas phase atom-rigit rotor inelastic collisions; (4) wave packet study of gas phase atom-rigit motor scattering; (5) the application of optical potentials for reactive scattering; (6) time dependent, three dimensional body frame quantal wave packet treatment of the H + H2 exchange reaction; (7) a time dependent wave packet approach to atom-diatom reactive collision probabilities; (8) time dependent wave packet for the complete determination of s-matrix elements for reactive molecular collisions in three dimensions; (9) a comparison of three time dependent wave packet methods for calculating electron-atom elastic scattering cross sections; and (10) a numerically exact full wave packet approach to molecule-surface scattering.

Kouri, Donald J.↗

Impact of the MARATHON data on F 2⁢n⁡ /F 2⁢p and off-shell effects in light nuclei

The neutron structure function, F 2⁢n⁡ , has historically been extracted from measurements of the deuteron structure function, which is limited by our understanding of the nuclear effects on the bound proton and neutron. The MARATHON Collaboration recently extracted F 2⁢n⁡ from the comparison of 3 H and 3 He targets, where the nuclear effects are larger but nearly identical, yielding a precise extraction of F 2⁢n⁡ /F 2⁢p . Here, to ensure that this comparison is not biased by the specific model of nuclear effects used by MARATHON, we examine a range of models of the nuclear effects to obtain a more conservative, but more model-independent, extraction of F 2⁢n⁡ /F 2⁢p for comparison with deuteron extractions. Even with this approach, the results are precise enough to compare to deuteron extractions, providing new constraints on the nuclear effects in the deuteron and indicating the need for larger nuclear corrections than those included in most models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Colloquium : Planckian dissipation in metals

The appearance of the Planckian time $\tau$ Pl = ℏ/k B T is reviewed in both conventional and unconventional metals. A pedagogical discussion of the various different timescales (quasiparticle, transport, many-body) that characterize metals is given, with an emphasis on conditions under which these times are the same or different. Further, the possibility of a Planckian bound on dissipation is discussed from both a quasiparticle and a many-body perspective. Planckian quasiparticles can arise naturally from a combination of inelastic scattering and mass renormalization. Many-body dynamics, on the other hand, is constrained by the basic timescales and length scales of local thermalization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Evolution of planetesimal velocities

A self-consistent set of equations for the velocity evolution of a general planetesimal population is presented. The equations are given in a form convenient for calculations of the early stages of planetary accumulation when it is necessary to model the planetesimal swarm by methods of gas dynamics, rather than follow the orbital evolution of individual bodies. Steady state velocities of a simple planetesimal population consisting of two different sizes of bodies are calculated. Dynamical friction is found to be an important mechanism for transferring kinetic energy from the larger planetesimals to the smaller ones. When the small planetesimals are relatively abundant, gas drag and inelastic collisions among the smaller bodies are of comparable importance for dissipating energy from the population.

Stewart, Glen R.↗

Confinement of many-body Bethe strings

Based on the Bethe ansatz approach and inelastic neutron scattering experiments, we reveal the evolution of confinement of many-body Bethe strings in ordered regions of the quasi-one-dimensional antiferromagnet YbAlO 3 . In the antiferromagnetic phase, the spin dynamics is dominated by confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Finally, our results establish a unified picture based on a Bethe string for the spin dynamics in different magnetic phases of YbAlO 3 , and thus provide profound insight into many-body quantum magnetism.

1-dimensional spin chains↗

On the early scattering processes of the outer planets

The gradual scattering of small bodies by the Jovian planets in the late stage of their accretion is simulated by Monte Carlo calculation. The effects of collisional interaction of the scattered planetesimals with the inner planets and asteroidal belt are estimated. The total mass influx injected into the terrestrial zones from the outer planetary zone could be appreciable; however, if the damping effects due to the mutual inelastic or catastrophic collisions among the small bodies were significant, the total mass influx would be greatly reduced. The origin of the cometary Oort cloud in relation to these scattering processes is also discussed. The calculation indicates that, in addition to Jupiter, Uranus and Neptune were likely to be the major contributors to the population of long-period comets if they originated from such scattering processes.

Ip, W. H.↗