147 research outputs found
A finite element method for fully nonlinear elliptic problems
We present a continuous finite element method for some examples of fully
nonlinear elliptic equation. A key tool is the discretisation proposed in
Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of
a linear PDE. An added benefit to making use of this discretisation method is
that a recovered (finite element) Hessian is a biproduct of the solution
process. We build on the linear basis and ultimately construct two different
methodologies for the solution of second order fully nonlinear PDEs. Benchmark
numerical results illustrate the convergence properties of the scheme for some
test problems including the Monge-Amp\`ere equation and Pucci's equation.Comment: 22 pages, 31 figure
Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates
The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q)
for the numerical solution of initial value problems for ordinary differential
equations are based on piecewise polynomial approximation of degree q on
partitions in time with time steps which may vary for different components of
the computed solution. In this paper, we prove general order a priori error
estimates for the mcG(q) and mdG(q) methods. To prove the error estimates, we
represent the error in terms of a discrete dual solution and the residual of an
interpolant of the exact solution. The estimates then follow from interpolation
estimates, together with stability estimates for the discrete dual solution
Computational Modeling of Dynamical Systems
In this short note, we discuss the basic approach to computational modeling
of dynamical systems. If a dynamical system contains multiple time scales,
ranging from very fast to slow, computational solution of the dynamical system
can be very costly. By resolving the fast time scales in a short time
simulation, a model for the effect of the small time scale variation on large
time scales can be determined, making solution possible on a long time
interval. This process of computational modeling can be completely automated.
Two examples are presented, including a simple model problem oscillating at a
time scale of 1e-9 computed over the time interval [0,100], and a lattice
consisting of large and small point masses
Pressure-induced and Composition-induced Structural Quantum Phase Transition in the Cubic Superconductor (Sr/Ca)_3Ir_4Sn_{13}
We show that the quasi-skutterudite superconductor Sr_3Ir_4Sn_{13} undergoes
a structural transition from a simple cubic parent structure, the I-phase, to a
superlattice variant, the I'-phase, which has a lattice parameter twice that of
the high temperature phase. We argue that the superlattice distortion is
associated with a charge density wave transition of the conduction electron
system and demonstrate that the superlattice transition temperature T* can be
suppressed to zero by combining chemical and physical pressure. This enables
the first comprehensive investigation of a superlattice quantum phase
transition and its interplay with superconductivity in a cubic charge density
wave system.Comment: 4 figures, 5 pages (excluding supplementary material). To be
published in Phys. Rev. Let
A computational model of open-irrigated radiofrequency catheter ablation accounting for mechanical properties of the cardiac tissue
Radiofrequency catheter ablation (RFCA) is an effective treatment for cardiac arrhythmias. Although generally safe, it is not completely exempt from the risk of complications. The great flexibility of computational models can be a major asset in optimizing interventional strategies, if they can produce sufficiently precise estimations of the generated lesion for a given ablation protocol. This requires an accurate description of the catheter tip and the cardiac tissue. In particular, the deformation of the tissue under the catheter pressure during the ablation is an important aspect that is overlooked in the existing literature, that resorts to a sharp insertion of the catheter into an undeformed geometry. As the lesion size depends on the power dissipated in the tissue, and the latter depends on the percentage of the electrode surface in contact with the tissue itself, the sharp insertion geometry has the tendency to overestimate the lesion obtained, especially when a larger force is applied to the catheter. In this paper we introduce a full 3D computational model that takes into account the tissue elasticity, and is able to capture the tissue deformation and realistic power dissipation in the tissue. Numerical results in FEniCS-HPC are provided to validate the model against experimental data, and to compare the lesions obtained with the new model and with the classical ones featuring a sharp electrode insertion in the tissue.La Caixa 2016 PhD grant to M. Leoni, and Abbott non-conditional grant to J.M. Guerra Ramo
Automated derivation of the adjoint of high-level transient finite element programs
In this paper we demonstrate a new technique for deriving discrete adjoint
and tangent linear models of finite element models. The technique is
significantly more efficient and automatic than standard algorithmic
differentiation techniques. The approach relies on a high-level symbolic
representation of the forward problem. In contrast to developing a model
directly in Fortran or C++, high-level systems allow the developer to express
the variational problems to be solved in near-mathematical notation. As such,
these systems have a key advantage: since the mathematical structure of the
problem is preserved, they are more amenable to automated analysis and
manipulation. The framework introduced here is implemented in a freely
available software package named dolfin-adjoint, based on the FEniCS Project.
Our approach to automated adjoint derivation relies on run-time annotation of
the temporal structure of the model, and employs the FEniCS finite element form
compiler to automatically generate the low-level code for the derived models.
The approach requires only trivial changes to a large class of forward models,
including complicated time-dependent nonlinear models. The adjoint model
automatically employs optimal checkpointing schemes to mitigate storage
requirements for nonlinear models, without any user management or intervention.
Furthermore, both the tangent linear and adjoint models naturally work in
parallel, without any need to differentiate through calls to MPI or to parse
OpenMP directives. The generality, applicability and efficiency of the approach
are demonstrated with examples from a wide range of scientific applications
Dynamics of skyrmionic states in confined helimagnetic nanostructures
In confined helimagnetic nanostructures, skyrmionic states in the form of incomplete and isolated skyrmion states can emerge as the ground state in absence of both external magnetic field and magnetocrystalline anisotropy. In this work, we study the dynamic properties (resonance frequencies and corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples. We employ two different methods in finite-element based micromagnetic simulation: eigenvalue and ringdown method. The eigenvalue method allows us to identify all resonance frequencies and corresponding eigenmodes that can exist in the simulated system. However, using a particular experimentally feasible excitation can excite only a limited set of eigenmodes. Because of that, we perform ringdown simulations that resemble the experimental setup using both in-plane and out-of-plane excitations. In addition, we report the nonlinear dependence of resonance frequencies on the external magnetic bias field and disk sample diameter and discuss the possible reversal mode of skyrmionic states. We compare the power spectral densities of incomplete skyrmion and isolated skyrmion states and observe several key differences that can contribute to the experimental identification of the state present in the sample. We measure the FeGe Gilbert damping, and using its value we determine what eigenmodes can be expected to be observed in experiments. Finally, we show that neglecting the demagnetization energy contribution or ignoring the magnetization variation in the out-of-film direction—although not changing the eigenmode's magnetization dynamics significantly—changes their resonance frequencies substantially. Apart from contributing to the understanding of skyrmionic states physics, this systematic work can be used as a guide for the experimental identification of skyrmionic states in confined helimagnetic nanostructures
The receptors for gibbon ape leukemia virus and amphotropic murine leukemia virus are not downregulated in productively infected cells
<p>Abstract</p> <p>Background</p> <p>Over the last several decades it has been noted, using a variety of different methods, that cells infected by a specific gammaretrovirus are resistant to infection by other retroviruses that employ the same receptor; a phenomenon termed receptor interference. Receptor masking is thought to provide an earlier means of blocking superinfection, whereas receptor down regulation is generally considered to occur in chronically infected cells.</p> <p>Results</p> <p>We used replication-competent GFP-expressing viruses containing either an amphotropic murine leukemia virus (A-MLV) or the gibbon ape leukemia virus (GALV) envelope. We also constructed similar viruses containing fluorescence-labeled Gag proteins for the detection of viral particles. Using this repertoire of reagents together with a wide range of antibodies, we were able to determine the presence and availability of viral receptors, and detect viral envelope proteins and particles presence on the cell surface of chronically infected cells.</p> <p>Conclusions</p> <p>A-MLV or GALV receptors remain on the surface of chronically infected cells and are detectable by respective antibodies, indicating that these receptors are not downregulated in these infected cells as previously proposed. We were also able to detect viral envelope proteins on the infected cell surface and infected cells are unable to bind soluble A-MLV or GALV envelopes indicating that receptor binding sites are masked by endogenously expressed A-MLV or GALV viral envelope. However, receptor masking does not completely prevent A-MLV or GALV superinfection.</p
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