A new approach to nonlinear constrained Tikhonov regularization

We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rates results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented.Comment: 21 pages, to appear in Inverse Problem

A Two-stage Method for Inverse Medium Scattering

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with mixed regularization. The first step is strictly direct and of sampling type, and faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer sizes as well as intensities. The model is efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the approach is accurate, computationally efficient, and robust with respect to data noise.Comment: 18 pages, 5 figure

Spectral and Polarization Properties of Photospheric Emission From Stratified Jets

We explore the spectral and polarization properties of photospheric emissions from stratified jets in which multiple components, separated by a sharp velocity shear regions, are distributed in lateral direction. Propagation of thermal photons injected at high optical depth region are calculated until they escape from the photosphere. It is found that presence of the lateral structure within the jet leads to non-thermal feature of the spectra and significant polarization signal in the resulting emission. The deviation from thermal spectra as well as the polarization degree tends to be enhanced as the velocity gradient in the shear region increases. In particular, we show that emissions from multi-component jet can reproduce the typical observed spectra of gamma-ray bursts (GRBs) irrespective to the position of the observer when a velocity shear region is closely spaced in various lateral ($\theta$) positions. The degree of polarization associated in the emission is significant (> few%) at wide range of observer angles and can be higher than 30%.Comment: 21 pages, 12 figures, accepted for publication in Ap

Gradient-based estimation of Manning's friction coefficient from noisy data

We study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional model are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory.Comment: 19 pages, 3 figure

Massively parallel quantum computer simulator, eleven years later

A revised version of the massively parallel simulator of a universal quantum computer, described in this journal eleven years ago, is used to benchmark various gate-based quantum algorithms on some of the most powerful supercomputers that exist today. Adaptive encoding of the wave function reduces the memory requirement by a factor of eight, making it possible to simulate universal quantum computers with up to 48 qubits on the Sunway TaihuLight and on the K computer. The simulator exhibits close-to-ideal weak-scaling behavior on the Sunway TaihuLight,on the K computer, on an IBM Blue Gene/Q, and on Intel Xeon based clusters, implying that the combination of parallelization and hardware can track the exponential scaling due to the increasing number of qubits. Results of executing simple quantum circuits and Shor's factorization algorithm on quantum computers containing up to 48 qubits are presented.Comment: Substantially rewritten + new data. Published in Computer Physics Communicatio