17,854 research outputs found
Nanovoid nucleation by vacancy aggregation and vacancy-cluster coarsening in high-purity metallic single crystals
A numerical model to estimate critical times required for nanovoid nucleation in high-purity aluminum single crystals subjected to shock loading is presented. We regard a nanovoid to be nucleated when it attains a size sufficient for subsequent growth by dislocation-mediated plasticity. Nucleation is assumed to proceed by means of diffusion-mediated vacancy aggregation and subsequent vacancy cluster coarsening. Nucleation times are computed by a combination of lattice kinetic Monte Carlo simulations and simple estimates of nanovoid cavitation pressures and vacancy concentrations. The domain of validity of the model is established by considering rate-limiting physical processes and theoretical strength limits. The computed nucleation times are compared to experiments suggesting that vacancy aggregation and cluster coarsening are feasible mechanisms of nanovoid nucleation in a specific subdomain of the pressure-strain rate-temperature space
Symplectic-energy-momentum preserving variational integrators
The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving. To do this, a spaceātime view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy. Criteria for the solvability of the time steps and some numerical examples are given
Stripes, topological order, and deconfinement in a planar t-Jz model
We determine the quantum phase diagram of a two-dimensional bosonic t-Jz
model as a function of the lattice anisotropy gamma, using a quantum Monte
Carlo loop algorithm. We show analytically that the low-energy sectors of the
bosonic and the fermionic t-Jz models become equivalent in the limit of small
gamma. In this limit, the ground state represents a static stripe phase
characterized by a non-zero value of a topological order parameter. This phase
remains up to intermediate values of gamma, where there is a quantum phase
transition to a phase-segregated state or a homogeneous superfluid with dynamic
stripe fluctuations depending on the ratio Jz/t.Comment: 4 pages, 5 figures (2 in color). Final versio
Frictional Collisions Off Sharp Objects
This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact
geometries for which neither normals nor gap functions can be defined. Such situations arise
in the early stage of fragmentation when a number of angular fragments undergo complex collision
sequences before eventually scattering. Such situations precludes the application of most contact
algorithms proposed to date
Variational integrators, the Newmark scheme, and dissipative systems
Variational methods are a class of symplectic-momentum integrators for ODEs. Using
these schemes, it is shown that the classical Newmark algorithm is structure preserving in a
non-obvious way, thus explaining the observed numerical behavior. Modifications to variational
methods to include forcing and dissipation are also proposed, extending the advantages
of structure preserving integrators to non-conservative systems
Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
Motivated by the prospect of attaining Majorana modes at the ends of
nanowires, we analyze interacting Majorana systems on general networks and
lattices in an arbitrary number of dimensions, and derive various universal
spin duals. Such general complex Majorana architectures (other than those of
simple square or other crystalline arrangements) might be of empirical
relevance. As these systems display low-dimensional symmetries, they are
candidates for realizing topological quantum order. We prove that (a) these
Majorana systems, (b) quantum Ising gauge theories, and (c) transverse-field
Ising models with annealed bimodal disorder are all dual to one another on
general graphs. As any Dirac fermion (including electronic) operator can be
expressed as a linear combination of two Majorana fermion operators, our
results further lead to dualities between interacting Dirac fermionic systems.
The spin duals allow us to predict the feasibility of various standard
transitions as well as spin-glass type behavior in {\it interacting} Majorana
fermion or electronic systems. Several new systems that can be simulated by
arrays of Majorana wires are further introduced and investigated: (1) the {\it
XXZ honeycomb compass} model (intermediate between the classical Ising model on
the honeycomb lattice and Kitaev's honeycomb model), (2) a checkerboard lattice
realization of the model of Xu and Moore for superconducting arrays,
and a (3) compass type two-flavor Hubbard model with both pairing and hopping
terms. By the use of dualities, we show that all of these systems lie in the 3D
Ising universality class. We discuss how the existence of topological orders
and bounds on autocorrelation times can be inferred by the use of symmetries
and also propose to engineer {\it quantum simulators} out of these Majorana
networks.Comment: v3,19 pages, 18 figures, submitted to Physical Review B. 11 new
figures, new section on simulating the Hubbard model with nanowire systems,
and two new appendice
Nonsmooth Lagrangian mechanics and variational collision integrators
Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem.
Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated
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