3,250 research outputs found
Solving the incompressible surface Navier-Stokes equation by surface finite elements
We consider a numerical approach for the incompressible surface Navier-Stokes
equation on surfaces with arbitrary genus . The approach is
based on a reformulation of the equation in Cartesian coordinates of the
embedding , penalization of the normal component, a Chorin
projection method and discretization in space by surface finite elements for
each component. The approach thus requires only standard ingredients which most
finite element implementations can offer. We compare computational results with
discrete exterior calculus (DEC) simulations on a torus and demonstrate the
interplay of the flow field with the topology by showing realizations of the
Poincar\'e-Hopf theorem on -tori
Some comments on quasi-birth-and-death processes and matrix measures
In this paper we explore the relation between matrix measures and Quasi-Birth-and-Death processes. We derive an integral representation of the transition function in terms of a matrix valued spectral measure and corresponding orthogonal matrix polynomials. We characterize several stochastic properties of Quasi-Birth-and-Death processes by means of this matrix measure and illustrate the theoretical results by several examples. --Block tridiagonal infinitesimal generator,Quasi-Birth-and-Death processes,spectral measure,matrix measure,canonical moments
Hydrodynamic interactions in polar liquid crystals on evolving surfaces
We consider the derivation and numerical solution of the flow of passive and
active polar liquid crystals, whose molecular orientation is subjected to a
tangential anchoring on an evolving curved surface. The underlying passive
model is a simplified surface Ericksen-Leslie model, which is derived as a
thin-film limit of the corresponding three-dimensional equations with
appropriate boundary conditions. A finite element discretization is considered
and the effect of hydrodynamics on the interplay of topology, geometric
properties and defect dynamics is studied for this model on various stationary
and evolving surfaces. Additionally, we consider an active model. We propose a
surface formulation for an active polar viscous gel and exemplarily demonstrate
the effect of the underlying curvature on the location of topological defects
on a torus
Magnetic order and paramagnetic phases in the quantum J1-J2-J3 honeycomb model
Recent work shows that a quantum spin liquid can arise in realistic fermionic
models on a honeycomb lattice. We study the quantum spin-1/2 Heisenberg
honeycomb model, considering couplings J1, J2, and J3 up to third nearest
neighbors. We use an unbiased pseudofermion functional renormalization group
method to compute the magnetic susceptibility and determine the ordered and
disordered states of the model. Aside from antiferromagnetic, collinear, and
spiral order domains, we find a large paramagnetic region at intermediate J2
coupling. For larger J2 within this domain, we find a strong tendency to
staggered dimer ordering, while the remaining paramagnetic regime for low J2
shows only weak plaquet and staggered dimer response. We suggest this regime to
be a promising region to look for quantum spin liquid states when charge
fluctuations would be included.Comment: 4 pages, 3 figure
Spiral order in the honeycomb iridate Li2IrO3
The honeycomb iridates A2IrO3 (A=Na, Li) constitute promising candidate
materials to realize the Heisenberg-Kitaev model (HKM) in nature, hosting
unconventional magnetic as well as spin liquid phases. Recent experiments
suggest, however, that Li2IrO3 exhibits a magnetically ordered state of
incommensurate spiral type which has not been identified in the HKM. We show
that these findings can be understood in the context of an extended
Heisenberg-Kitaev scenario satisfying all tentative experimental evidence: (i)
the maximum of the magnetic susceptibility is located inside the first
Brillouin zone, (ii) the Curie-Weiss temperature is negative relating to
dominant antiferromagnetic fluctuations, and (iii) significant second-neighbor
spin-exchange is involved.Comment: 5 pages, 5 figures, selected as an Editors' suggestio
Finite-temperature phase diagram of the Heisenberg-Kitaev model
We discuss the finite-temperature phase diagram of the Heisenberg-Kitaev
model on the hexagonal lattice, which has been suggested to describe the
spin-orbital exchange of the effective spin-1/2 momenta in the Mott insulating
Iridate Na2IrO3. At zero-temperature this model exhibits magnetically ordered
states well beyond the isotropic Heisenberg limit as well as an extended
gapless spin liquid phase around the highly anisotropic Kitaev limit. Using a
pseudofermion functional renormalization group (RG) approach, we extract both
the Curie-Weiss scale and the critical ordering scale (for the magnetically
ordered states) from the RG flow of the magnetic susceptibility. The
Curie-Weiss scale switches sign -- indicating a transition of the dominant
exchange from antiferromagnetic to ferromagnetic -- deep in the magnetically
ordered regime. For the latter we find no significant frustration, i.e. a
substantial suppression of the ordering scale with regard to the Curie-Weiss
scale. We discuss our results in light of recent experimental susceptibility
measurements for Na2IrO3.Comment: 4+e pages, 5 figure
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