1,172 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
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
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
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
Change of decoherence scenario and appearance of localization due to reservoir anharmonicity
Although coupling to a super-Ohmic bosonic reservoir leads only to partial
dephasing on short time scales, exponential decay of coherence appears in the
Markovian limit (for long times) if anharmonicity of the reservoir is taken
into account. This effect not only qualitatively changes the decoherence
scenario but also leads to localization processes in which superpositions of
spatially separated states dephase with a rate that depends on the distance
between the localized states. As an example of the latter process, we study the
decay of coherence of an electron state delocalized over two semiconductor
quantum dots due to anharmonicity of phonon modes.Comment: 4 pages, 1 figure; moderate changes; auxiliary material added; to
appear in Phys. Rev. Let
Many--Particle Correlations in Relativistic Nuclear Collisions
Many--particle correlations due to Bose-Einstein interference are studied in
ultrarelativistic heavy--ion collisions. We calculate the higher order
correlation functions from the 2--particle correlation function by assuming
that the source is emitting particles incoherently. In particular
parametrizations of and relations between longitudinal, sidewards, outwards and
invariant radii and corresponding momenta are discussed. The results are
especially useful in low statistics measurements of higher order correlation
functions. We evaluate the three--pion correlation function recently measured
by NA44 and predict the 2--pion--2--kaon correlation function. Finally, many
particle Coulomb corrections are discussed.Comment: 5 corrected misprints, 14 pages, revtex, epsfig, 6 figures included,
manuscript also available at http://www.nbi.dk/~vischer/publications.htm
A forward-backward splitting algorithm for the minimization of non-smooth convex functionals in Banach space
We consider the task of computing an approximate minimizer of the sum of a
smooth and non-smooth convex functional, respectively, in Banach space.
Motivated by the classical forward-backward splitting method for the
subgradients in Hilbert space, we propose a generalization which involves the
iterative solution of simpler subproblems. Descent and convergence properties
of this new algorithm are studied. Furthermore, the results are applied to the
minimization of Tikhonov-functionals associated with linear inverse problems
and semi-norm penalization in Banach spaces. With the help of
Bregman-Taylor-distance estimates, rates of convergence for the
forward-backward splitting procedure are obtained. Examples which demonstrate
the applicability are given, in particular, a generalization of the iterative
soft-thresholding method by Daubechies, Defrise and De Mol to Banach spaces as
well as total-variation based image restoration in higher dimensions are
presented
Entanglement in SO(3)-invariant bipartite quantum systems
The structure of the state spaces of bipartite (N tensor N) quantum systems
which are invariant under product representations of the group SO(3) of
three-dimensional proper rotations is analyzed. The subsystems represent
particles of arbitrary spin j which transform according to an irreducible
representation of the rotation group. A positive map theta is introduced which
describes the time reversal symmetry of the local states and which is unitarily
equivalent to the transposition of matrices. It is shown that the partial time
reversal transformation theta_2 = (I tensor theta) acting on the composite
system can be expressed in terms of the invariant 6-j symbols introduced by
Wigner into the quantum theory of angular momentum. This fact enables a
complete geometrical construction of the manifold of states with positive
partial transposition and of the sets of separable and entangled states of (4
tensor 4) systems. The separable states are shown to form a three-dimensional
prism and a three-dimensional manifold of bound entangled states is identified.
A positive maps is obtained which yields, together with the time reversal, a
necessary and sufficient condition for the separability of states of (4 tensor
4) systems. The relations to the reduction criterion and to the recently
proposed cross norm criterion for separability are discussed.Comment: 15 pages, 3 figure
Preparation of Knill-Laflamme-Milburn states using tunable controlled phase gate
A specific class of partially entangled states known as
Knill-Laflamme-Milburn states (or KLM states) has been proved to be useful in
relation to quantum information processing [Knill et al., Nature 409, 46
(2001)]. Although the usage of such states is widely investigated, considerably
less effort has been invested into experimentally accessible preparation
schemes. This paper discusses the possibility to employ a tunable controlled
phase gate to generate an arbitrary Knill-Laflamme-Milburn state. In the first
part, the idea of using the controlled phase gate is explained on the case of
two-qubit KLM states. Optimization of the proposed scheme is then discussed for
the framework of linear optics. Subsequent generalization of the scheme to
arbitrary n-qubit KLM state is derived in the second part of this paper.Comment: 5 pages, 4 figures, accepted in Journal of Physics
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