1,721 research outputs found
An alternative to the Allen-Cahn phase field model for interfaces in solids - numerical efficiency
The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the
Clausius-Duhem inequality. This is not a derivation in the strict sense of the
word, since other phase field equations can be fomulated satisfying this
inequality. Motivated by the form of sharp interface problems, we formulate
such an alternative equation and compare the properties of the models for the
evolution of phase interfaces in solids, which consist of the elasticity
equations and the Allen-Cahn equation or the alternative equation. We find that
numerical simulations of phase interfaces with small interface energy based on
the alternative model are more effective then simulations based on the
Allen-Cahn model.Comment: arXiv admin note: text overlap with arXiv:1505.0544
Non-Markovian generalization of the Lindblad theory of open quantum systems
A systematic approach to the non-Markovian quantum dynamics of open systems
is given by the projection operator techniques of nonequilibrium statistical
mechanics. Combining these methods with concepts from quantum information
theory and from the theory of positive maps, we derive a class of correlated
projection superoperators that take into account in an efficient way
statistical correlations between the open system and its environment. The
result is used to develop a generalization of the Lindblad theory to the regime
of highly non-Markovian quantum processes in structured environments.Comment: 10 pages, 1 figure, replaced by published versio
Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians
The algebraic-geometric approach is extended to study solutions of
N-component systems associated with the energy dependent Schrodinger operators
having potentials with poles in the spectral parameter, in connection with
Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems
under study include the shallow water equation and Dym type equation. The
classes of solutions are described in terms of theta-functions and their
singular limits by using new parameterizations. A qualitative description of
real valued solutions is provided
Interface motion by interface diffusion driven by bulk energy: Justification of a diffusive interface model
We construct an asymptotic solution of a system consisting of the partial differential equations of linear elasticity theory coupled with a degenerate parabolic equation, and show that when a regularity parameter tends to zero, this solution converges to a solution of a sharp interface model, which describes the phase interface in an elastically deformable solid moving by interface diffusion. Therefore, the coupled system can be used as diffusive interface model. Differently from diffusive interface models based on the Cahn-Hilliard equation, the interface diffusion is solely driven by the bulk energy, hence the Laplacian of the curvature is not part of the driving force. Also, no rescaling of the parabolic equation is necessary. Since the asymptotic solution does not solve the system exactly, the proof is formal
Solutions to a model with Neumann boundary conditions for phase transitions driven by configurational forces
We study an initial boundary value problem of a model describing the evolution in time of diffusive phase interfaces in solid materials, in which martensitic phase transformations driven by configurational forces take place. The model was proposed earlier by the authors and consists of the partial differential equations of linear elasticity coupled to a nonlinear, degenerate parabolic equation of second order for an order parameter. In a previous paper global existence of weak solutions in one space dimension was proved under Dirichlet boundary conditions for the order parameter. Here we show that global solutions also exist for Neumann boundary conditions. Again, the method of proof is only valid in one space dimension
Class of PPT bound entangled states associated to almost any set of pure entangled states
We analyze a class of entangled states for bipartite systems,
with non-prime. The entanglement of such states is revealed by the
construction of canonically associated entanglement witnesses. The structure of
the states is very simple and similar to the one of isotropic states: they are
a mixture of a separable and a pure entangled state whose supports are
orthogonal. Despite such simple structure, in an opportune interval of the
mixing parameter their entanglement is not revealed by partial transposition
nor by the realignment criterion, i.e. by any permutational criterion in the
bipartite setting. In the range in which the states are Positive under Partial
Transposition (PPT), they are not distillable; on the other hand, the states in
the considered class are provably distillable as soon as they are Nonpositive
under Partial Transposition (NPT). The states are associated to any set of more
than two pure states. The analysis is extended to the multipartite setting. By
an opportune selection of the set of multipartite pure states, it is possible
to construct mixed states which are PPT with respect to any choice of bipartite
cuts and nevertheless exhibit genuine multipartite entanglement. Finally, we
show that every -positive but not completely positive map is associated to a
family of nondecomposable maps.Comment: 12 pages, 3 figures. To appear in Phys. Rev.
Continuous macroscopic limit of a discrete stochastic model for interaction of living cells
In the development of multiscale biological models it is crucial to establish
a connection between discrete microscopic or mesoscopic stochastic models and
macroscopic continuous descriptions based on cellular density. In this paper a
continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded
volume is derived, describing cells moving in a medium and reacting to each
other through both direct contact and long range chemotaxis. The continuous
macroscopic model is obtained as a Fokker-Planck equation describing evolution
of the cell probability density function. All coefficients of the general
macroscopic model are derived from parameters of the CPM and a very good
agreement is demonstrated between CPM Monte Carlo simulations and numerical
solution of the macroscopic model. It is also shown that in the absence of
contact cell-cell interactions, the obtained model reduces to the classical
macroscopic Keller-Segel model. General multiscale approach is demonstrated by
simulating spongy bone formation from loosely packed mesenchyme via the
intramembranous route suggesting that self-organizing physical mechanisms can
account for this developmental process.Comment: 4 pages, 3 figure
Entanglement quantification through local observable correlations
We present a significantly improved scheme of entanglement detection inspired
by local uncertainty relations for a system consisting of two qubits.
Developing the underlying idea of local uncertainty relations, namely
correlations, we demonstrate that it's possible to define a measure which is
invariant under local unitary transformations and which is based only on local
measurements. It is quite simple to implement experimentally and it allows
entanglement quantification in a certain range for mixed states and exactly for
pure states, without first obtaining full knowledge (e.g. through tomography)
of the state.Comment: 5 pages, 3 figures, revised version with new proof and replaced
figure
Thermal analysis of hadron multiplicities from relativistic quantum molecular dynamics
Some questions arising in the application of the thermal model to hadron
production in heavy ion collisions are studied. We do so by applying the
thermal model of hadron production to particle yields calculated by the
microscopic transport model RQMD(v2.3). We study the bias of incomplete
information about the final hadronic state on the extraction of thermal
parameters.It is found that the subset of particles measured typically in the
experiments looks more thermal than the complete set of stable particles. The
hadrons which show the largest deviations from thermal behaviour in RQMD(v2.3)
are the multistrange baryons and antibaryons. We also looked at the influence
of rapidity cuts on the extraction of thermal parameters and found that they
lead to different thermal parameters and larger disagreement between the RQMD
yields and the thermal model.Comment: 12 pages, 2 figures, uses REVTEX, only misprint and stylistic
corrections, to appear in Physical Review
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