5,082 research outputs found
An efficient BEM for numerical solution of the biharmonic boundary value problem
This paper presents an efficient BEM for solving biharmonic equations. All boundary values including geometries are approximated by the universal high order radial basis function networks (RBFNs) rather than the usual low order interpolations. Numerical results show that the proposed BEM is considerably superior to the linear/quadratic-BEM in terms of both accuracy and convergence rate
Solving high-order partial differential equations with indirect radial basis function networks
This paper reports a new numerical method based on radial basis function networks (RBFNs) for solving high-order partial differential equations (PDEs). The variables and their derivatives in the governing equations are represented by integrated RBFNs. The use of integration in constructing neural networks allows the straightforward implementation of multiple boundary conditions and the accurate approximation of high-order derivatives. The proposed RBFN method is verified successfully through the solution of thin-plate bending and viscous flow problems which are governed by biharmonic equations. For thermally driven cavity flows, the solutions are obtained up to a high Rayleigh number
Comparative studies of some simple viscoelastic theories
Comparative studies of some simple viscoelastic theorie
Inductively coupled plasma mass spectrometer with axial field in a quadrupole reaction cell
AbstractA novel reaction cell for ICP-MS with an electric field provided inside the quadrupole along its axis is described. The field is implemented via a DC bias applied to additional auxiliary electrodes inserted between the rods of the quadrupole. The field reduces the settling time of the pressurized quadrupole when its mass bandpass is dynamically tuned. It also improves the transmission of analyte ions. It is shown that for the pressurized cell with the field activated, the recovery time for a change in quadrupole operating parameters is reduced to <4 ms, which allows fast tuning of the mass bandpass in concert with and at the speed of the analyzing quadrupole. When the cell is operated with ammonia, the field reduces ion-ammonia cluster formation, further enhancing the transmission of atomic ions that have a high cluster formation rate. NiĀ·(NH3)n+ cluster formation in a cell operated with a wide bandpass (i.e., Ni+ precursors are stable in the cell) is shown to be dependent on the axial field strength. Clusters at n = 2ā4 can be suppressed by 9, 1200, and >610 times, respectively. The use of a retarding axial field for in-situ energy discrimination against cluster and polyatomic ions is shown. When the cell is pressurized with O2 for suppression of 129Xe+, the formation of 127IH2+ by reactions with gas impurities limits the detection of 129I to isotopic abundance of ā¼10ā6. In-cell energy discrimination against 127IH2+ utilizing a retarding axial field is shown to reduce the abundance of the background at m/z = 129 to ca. 3 Ć 10ā8 of the 127I+ signal. In-cell energy discrimination against 127IH2+ is shown to cause less I+ loss than a post-cell potential energy barrier for the same degree of 127IH2+ suppression
Random Unitaries Give Quantum Expanders
We show that randomly choosing the matrices in a completely positive map from
the unitary group gives a quantum expander. We consider Hermitian and
non-Hermitian cases, and we provide asymptotically tight bounds in the
Hermitian case on the typical value of the second largest eigenvalue. The key
idea is the use of Schwinger-Dyson equations from lattice gauge theory to
efficiently compute averages over the unitary group.Comment: 14 pages, 1 figur
Stability properties of the collective stationary motion of self-propelling particles with conservative kinematic constraints
In our previous papers we proposed a continuum model for the dynamics of the
systems of self-propelling particles with conservative kinematic constraints on
the velocities. We have determined a class of stationary solutions of this
hydrodynamic model and have shown that two types of stationary flow, linear and
radially symmetric (vortical) flow, are possible. In this paper we consider the
stability properties of these stationary flows. We show, using a linear
stability analysis, that the linear solutions are neutrally stable with respect
to the imposed velocity and density perturbations. A similar analysis of the
stability of the vortical solution is found to be not conclusive.Comment: 13 pages, 3 figure
In-situ measurements of the optical absorption of dioxythiophene-based conjugated polymers
Conjugated polymers can be reversibly doped by electrochemical means. This
doping introduces new sub-bandgap optical absorption bands in the polymer while
decreasing the bandgap absorption. To study this behavior, we have prepared an
electrochemical cell allowing measurements of the optical properties of the
polymer. The cell consists of a thin polymer film deposited on gold-coated
Mylar behind which is another polymer that serves as a counterelectrode. An
infrared transparent window protects the upper polymer from ambient air. By
adding a gel electrolyte and making electrical connections to the
polymer-on-gold films, one may study electrochromism in a wide spectral range.
As the cell voltage (the potential difference between the two electrodes)
changes, the doping level of the conjugated polymer films is changed
reversibly. Our experiments address electrochromism in
poly(3,4-ethylene-dioxy-thiophene) (PEDOT) and
poly(3,4-dimethyl-propylene-dioxy-thiophene) (PProDOT-Me). This closed
electrochemical cell allows the study of the doping induced sub-bandgap
features (polaronic and bipolaronic modes) in these easily oxidized and highly
redox switchable polymers. We also study the changes in cell spectra as a
function of polymer thickness and investigate strategies to obtain cleaner
spectra, minimizing the contributions of water and gel electrolyte features
Tweed in Martensites: A Potential New Spin Glass
We've been studying the ``tweed'' precursors above the martensitic transition
in shape--memory alloys. These characteristic cross--hatched modulations occur
for hundreds of degrees above the first--order shape--changing transition. Our
two--dimensional model for this transition, in the limit of infinite elastic
anisotropy, can be mapped onto a spin--glass Hamiltonian in a random field. We
suggest that the tweed precursors are a direct analogy of the spin--glass
phase. The tweed is intermediate between the high--temperature cubic phase and
the low--temperature martensitic phase in the same way as the spin--glass phase
can be intermediate between ferromagnet and antiferromagnet.Comment: 18 pages and four figures (included
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