4,897 research outputs found
Local stability and a renormalized Newton Method for equilibrium liquid crystal director modeling
We consider the nonlinear systems of equations that result from discretizations of a prototype variational model for the equilibrium director field characterizing the orientational properties of a liquid crystal material. In the presence of pointwise unit-vector constraints and coupled electric fields, the numerical solution of such equations by Lagrange-Newton methods leads to problems with a double saddle-point form, for which we have previously proposed a preconditioned nullspace method as an effective solver [A. Ramage and E. C. Gartland, Jr., submitted]. The characterization of local stability of solutions is complicated by the double saddle-point structure, and here we develop efficiently computable criteria in terms of minimum eigenvalues of certain projected Schur complements. We also propose a modified outer iteration (“Renormalized Newton Method”) in which the orientation variables are normalized onto the constraint manifold at each iterative step. This scheme takes advantage of the special structure of these problems, and we prove that it is locally quadratically convergent. The Renormalized Newton Method bears some resemblance to the Truncated Newton Method of computational micromagnetics, and we compare and contrast the two
Calculation of Densities of States and Spectral Functions by Chebyshev Recursion and Maximum Entropy
We present an efficient algorithm for calculating spectral properties of
large sparse Hamiltonian matrices such as densities of states and spectral
functions. The combination of Chebyshev recursion and maximum entropy achieves
high energy resolution without significant roundoff error, machine precision or
numerical instability limitations. If controlled statistical or systematic
errors are acceptable, cpu and memory requirements scale linearly in the number
of states. The inference of spectral properties from moments is much better
conditioned for Chebyshev moments than for power moments. We adapt concepts
from the kernel polynomial approximation, a linear Chebyshev approximation with
optimized Gibbs damping, to control the accuracy of Fourier integrals of
positive non-analytic functions. We compare the performance of kernel
polynomial and maximum entropy algorithms for an electronic structure example.Comment: 8 pages RevTex, 3 postscript figure
A method for molecular dynamics on curved surfaces
Dynamics simulations of constrained particles can greatly aid in
understanding the temporal and spatial evolution of biological processes such
as lateral transport along membranes and self-assembly of viruses. Most
theoretical efforts in the field of diffusive transport have focussed on
solving the diffusion equation on curved surfaces, for which it is not
tractable to incorporate particle interactions even though these play a crucial
role in crowded systems. We show here that it is possible to combine standard
constraint algorithms with the classical velocity Verlet scheme to perform
molecular dynamics simulations of particles constrained to an arbitrarily
curved surface, in which such interactions can be taken into account.
Furthermore, unlike Brownian dynamics schemes in local coordinates, our method
is based on Cartesian coordinates allowing for the reuse of many other standard
tools without modifications, including parallelisation through domain
decomposition. We show that by applying the schemes to the Langevin equation
for various surfaces, confined Brownian motion is obtained, which has direct
applications to many biological and physical problems. Finally we present two
practical examples that highlight the applicability of the method: (i) the
influence of crowding and shape on the lateral diffusion of proteins in curved
membranes and (ii) the self-assembly of a coarse-grained virus capsid protein
model.Comment: 30 pages, 5 figure
Implementation of Input Oriented Dynamic Voltage and Frequency Scaling for Multiplier on FPGA
This paper presents an Implementation of Dynamic voltage and frequency scaling according to input data. In the conventional method the power supply is fixed and independent on workload, so, voltage and area will be consumed unnecessary .Paper proposes the approach which focuses on making system dynamic for low power digital multiplier on reconfigurable device FPGA (Spartan III). For making system Dynamic input workload should be known and scanning is used to detect range of input so system can adjust voltage and frequency. Control signal generated from scanning which can dynamically change voltage and frequency for low power consumption according to input data
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