17,251 research outputs found
An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis
This paper outlines an energy-minimization finite-element approach to the
computational modeling of equilibrium configurations for nematic liquid
crystals under free elastic effects. The method targets minimization of the
system free energy based on the Frank-Oseen free-energy model. Solutions to the
intermediate discretized free elastic linearizations are shown to exist
generally and are unique under certain assumptions. This requires proving
continuity, coercivity, and weak coercivity for the accompanying appropriate
bilinear forms within a mixed finite-element framework. Error analysis
demonstrates that the method constitutes a convergent scheme. Numerical
experiments are performed for problems with a range of physical parameters as
well as simple and patterned boundary conditions. The resulting algorithm
accurately handles heterogeneous constant coefficients and effectively resolves
configurations resulting from complicated boundary conditions relevant in
ongoing research.Comment: 31 pages, 3 figures, 3 table
Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states
We define quaternionic Hermite polynomials by analogy with two families of
complex Hermite polynomials. As in the complex case, these polynomials
consatitute orthogonal families of vectors in ambient quaternionic
-spaces. Using these polynomials, we then define regular and anti-regular
subspaces of these -spaces, the associated reproducing kernels and the
ensuing quaternionic coherent states
The development of an autonomous rendezvous and docking simulation using rapid integration and prototyping technology
A generic planar 3 degree of freedom simulation was developed that supports hardware in the loop simulations, guidance and control analysis, and can directly generate flight software. This simulation was developed in a small amount of time utilizing rapid prototyping techniques. The approach taken to develop this simulation tool, the benefits seen using this approach to development, and on-going efforts to improve and extend this capability are described. The simulation is composed of 3 major elements: (1) Docker dynamics model, (2) Dockee dynamics model, and (3) Docker Control System. The docker and dockee models are based on simple planar orbital dynamics equations using a spherical earth gravity model. The docker control system is based on a phase plane approach to error correction
Topological characteristics of oil and gas reservoirs and their applications
We demonstrate applications of topological characteristics of oil and gas
reservoirs considered as three-dimensional bodies to geological modeling.Comment: 12 page
Min-oscillations in Escherichia coli induced by interactions of membrane-bound proteins
During division it is of primary importance for a cell to correctly determine
the site of cleavage. The bacterium Escherichia coli divides in the center,
producing two daughter cells of equal size. Selection of the center as the
correct division site is in part achieved by the Min-proteins. They oscillate
between the two cell poles and thereby prevent division at these locations.
Here, a phenomenological description for these oscillations is presented, where
lateral interactions between proteins on the cell membrane play a key role.
Solutions to the dynamic equations are compared to experimental findings. In
particular, the temporal period of the oscillations is measured as a function
of the cell length and found to be compatible with the theoretical prediction.Comment: 17 pages, 5 figures. Submitted to Physical Biolog
The Attractor and the Quantum States
The dissipative dynamics anticipated in the proof of 't Hooft's existence
theorem -- "For any quantum system there exists at least one deterministic
model that reproduces all its dynamics after prequantization" -- is constructed
here explicitly. We propose a generalization of Liouville's classical phase
space equation, incorporating dissipation and diffusion, and demonstrate that
it describes the emergence of quantum states and their dynamics in the
Schroedinger picture. Asymptotically, there is a stable ground state and two
decoupled sets of degrees of freedom, which transform into each other under the
energy-parity symmetry of Kaplan and Sundrum. They recover the familiar Hilbert
space and its dual. Expectations of observables are shown to agree with the
Born rule, which is not imposed a priori. This attractor mechanism is
applicable in the presence of interactions, to few-body or field theories in
particular.Comment: 14 pages; based on invited talk at 4th Workshop ad memoriam of Carlo
Novero "Advances in Foundations of Quantum Mechanics and Quantum Information
with Atoms and Photons", Torino, May 2008; submitted to Int J Qu Inf
Symmetry Breaking for Matter Coupled to Linearized Supergravity From the Perspective of the Current Supermultiplet
We consider a generic supersymmetric matter theory coupled to linearized
supergravity, and analyze scenarios for spontaneous symmetry breaking in terms
of vacuum expectation values of components of the current supermultiplet. When
the vacuum expectation of the energy momentum tensor is zero, but the scalar
current or pseudoscalar current gets an expectation, evaluation of the
gravitino self energy using the supersymmetry current algebra shows that there
is an induced gravitino mass term. The structure of this term generalizes the
supergravity action with cosmological constant to theories with CP violation.
When the vacuum expectation of the energy momentum tensor is nonzero,
supersymmetry is broken; requiring cancellation of the cosmological constant
gives the corresponding generalized gravitino mass formula.Comment: 11 page
An Error Estimator for Electrically Coupled Liquid Crystals
This paper extends an a posteriori error estimator for the elastic,
Frank-Oseen model of liquid crystals, derived in [9], to include electric and
flexoelectric effects. The problem involves a nonlinear coupled system of
equations with a local unit-length constraint imposed via a penalty method. The
proposed estimator is proven to be a reliable estimate of global approximation
error. The performance of the coupled error estimator as a guide for adaptive
refinement is shown in the numerical results, where the adapted grids
successfully yield substantial reductions in computational work and comparable
or better conformance to important physical laws.Comment: 10 Pages, 2 Figures, Conference: LSSC 2023. arXiv admin note:
substantial text overlap with arXiv:1806.0624
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