56,319 research outputs found
Collective Coordinate Control of Density Distributions
Real collective density variables [c.f.
Eq.\ref{Equation3})] in many-particle systems arise from non-linear
transformations of particle positions, and determine the structure factor
, where denotes the wave vector. Our objective is to
prescribe and then to find many-particle configurations
that correspond to such a target using a numerical optimization
technique. Numerical results reported here extend earlier one- and
two-dimensional studies to include three dimensions. In addition, they
demonstrate the capacity to control in the neighborhood of
0. The optimization method employed generates
multi-particle configurations for which , , and 1, 2, 4,
6, 8, and 10. The case 1 is relevant for the Harrison-Zeldovich
model of the early universe, for superfluid , and for jammed
amorphous sphere packings. The analysis also provides specific examples of
interaction potentials whose classical ground state are configurationally
degenerate and disordered.Comment: 26 pages, 8 figure
Augmented Lagrangian Method for Constrained Nuclear Density Functional Theory
The augmented Lagrangiam method (ALM), widely used in quantum chemistry
constrained optimization problems, is applied in the context of the nuclear
Density Functional Theory (DFT) in the self-consistent constrained Skyrme
Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of
multidimensional energy surfaces in the space of collective coordinates that
are needed to, e.g., determine fission pathways and saddle points; it improves
accuracy of computed derivatives with respect to collective variables that are
used to determine collective inertia; and is well adapted to supercomputer
applications.Comment: 6 pages, 3 figures; to appear in Eur. Phys. J.
A Constrained Sequential-Lamination Algorithm for the Simulation of Sub-Grid Microstructure in Martensitic Materials
We present a practical algorithm for partially relaxing multiwell energy
densities such as pertain to materials undergoing martensitic phase
transitions. The algorithm is based on sequential lamination, but the evolution
of the microstructure during a deformation process is required to satisfy a
continuity constraint, in the sense that the new microstructure should be
reachable from the preceding one by a combination of branching and pruning
operations. All microstructures generated by the algorithm are in static and
configurational equilibrium. Owing to the continuity constrained imposed upon
the microstructural evolution, the predicted material behavior may be
path-dependent and exhibit hysteresis. In cases in which there is a strict
separation of micro and macrostructural lengthscales, the proposed relaxation
algorithm may effectively be integrated into macroscopic finite-element
calculations at the subgrid level. We demonstrate this aspect of the algorithm
by means of a numerical example concerned with the indentation of an Cu-Al-Ni
shape memory alloy by a spherical indenter.Comment: 27 pages with 9 figures. To appear in: Computer Methods in Applied
Mechanics and Engineering. New version incorporates minor revisions from
revie
Existence of Dyons in Minimally Gauged Skyrme Model via Constrained Minimization
We prove the existence of electrically and magnetically charged particlelike
static solutions, known as dyons, in the minimally gauged Skyrme model
developed by Brihaye, Hartmann, and Tchrakian. The solutions are spherically
symmetric, depend on two continuous parameters, and carry unit monopole and
magnetic charges but continuous Skyrme charge and non-quantized electric charge
induced from the 't Hooft electromagnetism. The problem amounts to obtaining a
finite-energy critical point of an indefinite action functional, arising from
the presence of electricity and the Minkowski spacetime signature. The
difficulty with the absence of the Higgs field is overcome by achieving
suitable strong convergence and obtaining uniform decay estimates at singular
boundary points so that the negative sector of the action functional becomes
tractable.Comment: 24 page
Free energies, vacancy concentrations and density distribution anisotropies in hard--sphere crystals: A combined density functional and simulation study
We perform a comparative study of the free energies and the density
distributions in hard sphere crystals using Monte Carlo simulations and density
functional theory (employing Fundamental Measure functionals). Using a recently
introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009))
we obtain crystal free energies to a high precision. The free energies from
Fundamental Measure theory are in good agreement with the simulation results
and demonstrate the applicability of these functionals to the treatment of
other problems involving crystallization. The agreement between FMT and
simulations on the level of the free energies is also reflected in the density
distributions around single lattice sites. Overall, the peak widths and
anisotropy signs for different lattice directions agree, however, it is found
that Fundamental Measure theory gives slightly narrower peaks with more
anisotropy than seen in the simulations. Among the three types of Fundamental
Measure functionals studied, only the White Bear II functional (Hansen-Goos and
Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for
the equilibrium vacancy concentration and a physical behavior of the chemical
potential in crystals constrained by a fixed vacancy concentration.Comment: 17 pages, submitted to Phys. Rev.
An Exactly Solvable Phase-Field Theory of Dislocation Dynamics, Strain Hardening and Hysteresis in Ductile Single Crystals
An exactly solvable phase-field theory of dislocation dynamics, strain
hardening and hysteresis in ductile single crystals is developed. The theory
accounts for: an arbitrary number and arrangement of dislocation lines over a
slip plane; the long-range elastic interactions between dislocation lines; the
core structure of the dislocations resulting from a piecewise quadratic Peierls
potential; the interaction between the dislocations and an applied resolved
shear stress field; and the irreversible interactions with short-range
obstacles and lattice friction, resulting in hardening, path dependency and
hysteresis. A chief advantage of the present theory is that it is analytically
tractable, in the sense that the complexity of the calculations may be reduced,
with the aid of closed form analytical solutions, to the determination of the
value of the phase field at point-obstacle sites. In particular, no numerical
grid is required in calculations. The phase-field representation enables
complex geometrical and topological transitions in the dislocation ensemble,
including dislocation loop nucleation, bow-out, pinching, and the formation of
Orowan loops. The theory also permits the consideration of obstacles of varying
strengths and dislocation line-energy anisotropy. The theory predicts a range
of behaviors which are in qualitative agreement with observation, including:
hardening and dislocation multiplication in single slip under monotonic
loading; the Bauschinger effect under reverse loading; the fading memory
effect, whereby reverse yielding gradually eliminates the influence of previous
loading; the evolution of the dislocation density under cycling loading,
leading to characteristic `butterfly' curves; and others
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