1,629 research outputs found
A locally quadratic Glimm functional and sharp convergence rate of the Glimm scheme for nonlinear hyperbolic systems
Consider the Cauchy problem for a strictly hyperbolic,
quasilinear system in one space dimension u_t+A(u) u_x=0,\qquad u(0,x)=\bar
u(x), \eqno (1) where is a smooth matrix-valued map, and
the initial data is assumed to have small total variation. We
investigate the rate of convergence of approximate solutions of (1) constructed
by the Glimm scheme, under the assumption that, letting ,
denote the -th eigenvalue and a corresponding eigenvector of
, respectively, for each -th characteristic family the linearly
degenerate manifold is either the whole space, or it is empty, or it consists of
a finite number of smooth, -dimensional, connected, manifolds that are
transversal to the characteristic vector field . We introduce a Glimm type
functional which is the sum of the cubic interaction potential defined in
\cite{sie}, and of a quadratic term that takes into account interactions of
waves of the same family with strength smaller than some fixed threshold
parameter. Relying on an adapted wave tracing method, and on the decrease
amount of such a functional, we obtain the same type of error estimates valid
for Glimm approximate solutions of hyperbolic systems satisfying the classical
Lax assumptions of genuine nonlinearity or linear degeneracy of the
characteristic families.Comment: To appear on Archive for Rational Mechanics and Analysi
Resonant Enhancement of Electronic Raman Scattering
We present an exact solution for electronic Raman scattering in a
single-band, strongly correlated material, including nonresonant, resonant and
mixed contributions. Results are derived for the spinless Falicov-Kimball
model, employing dynamical mean field theory; this system can be tuned through
a Mott metal-insulator transition.Comment: 4 pages, 3 figures, contribution to the SNS'2004 conferenc
Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities
The hydrodynamic limit for the Boltzmann equation is studied in the case when
the limit system, that is, the system of Euler equations contains contact
discontinuities. When suitable initial data is chosen to avoid the initial
layer, we prove that there exists a unique solution to the Boltzmann equation
globally in time for any given Knudsen number. And this family of solutions
converge to the local Maxwellian defined by the contact discontinuity of the
Euler equations uniformly away from the discontinuity as the Knudsen number
tends to zero. The proof is obtained by an appropriately chosen
scaling and the energy method through the micro-macro decomposition.Comment: 34 pages. submitte
Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations
In this paper, both structural and dynamical stabilities of steady transonic
shock solutions for one-dimensional Euler-Poission system are investigated.
First, a steady transonic shock solution with supersonic backgroumd charge is
shown to be structurally stable with respect to small perturbations of the
background charge, provided that the electric field is positive at the shock
location. Second, any steady transonic shock solution with the supersonic
background charge is proved to be dynamically and exponentially stable with
respect to small perturbation of the initial data, provided the electric field
is not too negative at the shock location. The proof of the first stability
result relies on a monotonicity argument for the shock position and the
downstream density, and a stability analysis for subsonic and supersonic
solutions. The dynamical stability of the steady transonic shock for the
Euler-Poisson equations can be transformed to the global well-posedness of a
free boundary problem for a quasilinear second order equation with nonlinear
boundary conditions. The analysis for the associated linearized problem plays
an essential role
Finite difference schemes for the symmetric Keyfitz-Kranzer system
We are concerned with the convergence of numerical schemes for the initial
value problem associated to the Keyfitz-Kranzer system of equations. This
system is a toy model for several important models such as in elasticity
theory, magnetohydrodynamics, and enhanced oil recovery. In this paper we prove
the convergence of three difference schemes. Two of these schemes is shown to
converge to the unique entropy solution. Finally, the convergence is
illustrated by several examples.Comment: 31 page
Laser powder bed fusion of high-strength and corrosion-resistant Inconel alloy 725
The development of additive manufacturing, or three-dimensional (3D) printing, technologies has produced breakthroughs in the design and manufacturing of products by enhancing design freedom and minimising manufacturing steps. In addition, the complex, unique microstructures imparted by the additive processes offer prospects of unprecedented advances to produce high-performance metal alloys for high-temperature and corrosive environments. Here, we present the first additive manufacturing of Inconel alloy 725, an advanced nickel-base superalloy that is the widely accepted gold standard material of choice for oil and gas, chemical, and marine applications. We explore the printability of Inconel alloy 725 and identify a wide processing space to build material with a crack- and near-pore-free microstructure. The conventionally heat-treated Inconel alloy 725 has an equiaxed, near-fully recrystallised microstructure containing copious twin boundaries and nano-precipitates. It also displays promising tensile properties and corrosion resistance compared to its wrought counterpart. Our work opens the door toward additive manufacturing of Inconel alloy 725 components with optimised microstructure and topology geometry for applications in harsh environments
Chain Length Dependence of the Photovoltaic Properties of Monodisperse Donor-Acceptor Oligomers as Model Compounds of Polydisperse Low Band Gap Polymers
Well-defined conjugated oligomers (Sn) containing from 1 to 8 units of a tricyclic building block involving a dioctyloxybenzothiadiazole unit with two thienyl side rings (S1) are synthesized by a bottom-up approach. UV–Vis absorption data of solutions show that chain extension produces a narrowing of the HOMO–LUMO gap (ΔE) to values slightly smaller than that of the parent polymer (P1). Plots of ΔE and of the band gap of films (E g) versus the reciprocal chain length show that ΔE and E g converge towards a limit corresponding to an effective conjugation length (ECL) of 7–8 S1 units. UV–Vis absorption and photoluminescence data of solutions and solid films show that chain extension enhances the propensity to inter-chain aggregation. This conclusion is confirmed by GIXD analyses which reveal that the edge-on orientation of short-chain systems evolves toward a face-on orientation as chain length increases while the π-stacking distance decreases beyond 7 units. The results obtained on solution-processed BHJ solar cells show a progressive improvement of power conversion efficiency (PCE) with chain extension; however, the convergence limit of PCE remains inferior to that obtained with the polymer. These results are discussed with regard to the role of mono/polydispersity and chain aggregation
Scheduling Analysis of Imprecise Mixed-Criticality Real-Time Tasks
In this paper, we study the scheduling problem of the imprecise mixed-criticality model (IMC) under earliest deadline first with virtual deadline (EDF-VD) scheduling upon uniprocessor systems. Two schedulability tests are presented. The first test is a concise utilization-based test which can be applied to the implicit deadline IMC task set. The suboptimality of the proposed utilization-based test is evaluated via a widely-used scheduling metric, speedup factors. The second test is a more effective test but with higher complexity which is based on the concept of demand bound function (DBF). The proposed DBF-based test is more generic and can apply to constrained deadline IMC task set. Moreover, in order to address the high time cost of the existing deadline tuning algorithm, we propose a novel algorithm which significantly improve the efficiency of the deadline tuning procedure. Experimental results show the effectiveness of our proposed schedulability tests, confirm the theoretical suboptimality results with respect to speedup factor, and demonstrate the efficiency of our proposed algorithm over the existing deadline tunning algorithm. In addition, issues related to the implementation of the IMC model under EDF-VD are discussed.Computer Systems, Imagery and Medi
Quantum Computing with Atomic Josephson Junction Arrays
We present a quantum computing scheme with atomic Josephson junction arrays.
The system consists of a small number of atoms with three internal states and
trapped in a far-off resonant optical lattice. Raman lasers provide the
"Josephson" tunneling, and the collision interaction between atoms represent
the "capacitive" couplings between the modes. The qubit states are collective
states of the atoms with opposite persistent currents. This system is closely
analogous to the superconducting flux qubit. Single qubit quantum logic gates
are performed by modulating the Raman couplings, while two-qubit gates result
from a tunnel coupling between neighboring wells. Readout is achieved by tuning
the Raman coupling adiabatically between the Josephson regime to the Rabi
regime, followed by a detection of atoms in internal electronic states.
Decoherence mechanisms are studied in detail promising a high ratio between the
decoherence time and the gate operation time.Comment: 7 figure
Magneto-transport in a quantum network: Evidence of a mesoscopic switch
We investigate magneto-transport properties of a shaped three-arm
mesoscopic ring where the upper and lower sub-rings are threaded by
Aharonov-Bohm fluxes and , respectively, within a
non-interacting electron picture. A discrete lattice model is used to describe
the quantum network in which two outer arms are subjected to binary alloy
lattices while the middle arm contains identical atomic sites. It is observed
that the presence of the middle arm provides localized states within the band
of extended regions and lead to the possibility of switching action from a high
conducting state to a low conducting one and vice versa. This behavior is
justified by studying persistent current in the network. Both the total current
and individual currents in three separate branches are computed by using
second-quantized formalism and our idea can be utilized to study magnetic
response in any complicated quantum network. The nature of localized
eigenstates are also investigated from probability amplitudes at different
sites of the quantum device.Comment: 7 pages, 9 figure
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