772 research outputs found
General criteria for the stability of uniaxially ordered states of Incommensurate-Commensurate Systems
Reconsidering the variational procedure for uniaxial systems modeled by
continuous free energy functionals, we derive new general conditions for
thermodynamic extrema. The utility of these conditions is briefly illustrated
on the models for the classes I and II of incommensurate-commensurate systems.Comment: 5 pages, to be published in Phys. Rev. Let
Free energy functionals for efficient phase field crystal modeling of structural phase transformations
The phase field crystal (PFC) method has emerged as a promising technique for
modeling materials with atomistic resolution on mesoscopic time scales. The
approach is numerically much more efficient than classical density functional
theory (CDFT), but its single mode free energy functional only leads to
lattices with triangular (2D) or BCC (3D) symmetries. By returning to a closer
approximation of the CDFT free energy functional, we develop a systematic
construction of two-particle direct correlation functions that allow the study
of a broad class of crystalline structures. This construction examines planar
spacings, lattice symmetries, planar atomic densities and the atomic
vibrational amplitude in the unit cell of the lattice and also provides control
parameters for temperature and anisotropic surface energies. The power of this
new approach is demonstrated by two examples of structural phase
transformations.Comment: 4 pages, 4 figure
Thermal fluctuations in the lattice Boltzmann method for non-ideal fluids
We introduce thermal fluctuations in the lattice Boltzmann method for
non-ideal fluids. A fluctuation-dissipation theorem is derived within the
Langevin framework and applied to a specific lattice Boltzmann model that
approximates the linearized fluctuating Navier-Stokes equations for fluids
based on square-gradient free energy functionals. The obtained thermal noise is
shown to ensure equilibration of all degrees of freedom in a simulation to high
accuracy. Furthermore, we demonstrate that satisfactory results for most
practical applications of fluctuating hydrodynamics can already be achieved
using thermal noise derived in the long wavelength-limit.Comment: 15 pages, 5 figure
Unique Charactyerization of Materials With Memory
In general, materials with linear memory constitutive relations are characterized by a relaxation function. This leads to a situation where the free energy for most materials with memory is not unique. There is a convex set of free energy functionals with a minimum and a maximum element. An alternative procedure is proposed which characterizes a material by the kernel of the rate of dissipation functional. Using some recent results, we find that a unique free energy and relaxation function may then be deduced. An example is given for discrete spectrum materials. Also, the new results are used to show that a previously derived general representation of rate of dissipation and free energy functionals is not complete, in the sense that there are valid functionals which cannot be described by this general formula
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