Unphysical Artifacts Research Articles

Source-free converted-wave reverse time migration: Formulation and limitations

The source-free converted-wave (SFCW) reverse time migration is an alternative way to image the subsurface when the source information is missing or the overburden velocities are complex. However, it is challenging due to the lack of source-wavefield constraints. We have derived the SFCW imaging condition from the first gradients of waveform matching objective functions using a set of coupled P- and S-potential equations and small-perturbation approximations. We found that the images obtained from this SFCW imaging condition are second-order approximations to the shear-modulus perturbations. The images produced by the proposed imaging condition are free of the polarity reversal effects and have clear physical meanings. We also find that the acoustic wave equations can be used to back propagate the recorded P- and S-potentials, and the resulting images have the same kinematic accuracy and fewer unphysical mode-conversion artifacts than the SFCW images obtained by the elastic wave equations. Using multiple numerical examples, we determine the accuracy of our formulations, analyze the resolution and artifacts on the resulting images, and develop the limitations of the proposed method.

Fourth-order accurate finite-volume CWENO scheme for astrophysical MHD problems

In this work, a simple fourth-order accurate finite volume semi-discrete scheme is introduced to solve astrophysical magnetohydrodynamics (MHD) problems on Cartesian meshes. Hydrodynamic quantities like density, momentum and energy are discretised as volume averages. The magnetic field and electric field components are discretised as area and line averages respectively, so as to employ the constrained transport technique, which preserves the solenoidality of the magnetic field to machine precision. The present method makes use of a dimension-by-dimension approach employing a 1-D fourth-order accurate centrally weighted essentially non-oscillatory (1D-CWENO4) reconstruction polynomial. A fourth-order accurate, strong stability preserving (SSP) Runge-Kutta method is used to evolve the semi-discrete MHD equations in time. Higher-order accuracy of the scheme is confirmed in various linear and nonlinear multi-dimensional tests and the robustness of the method in avoiding unphysical numerical artifacts in the solution is demonstrated through several complex MHD problems.

Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability

A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is presented. We focus on k∥=0 universal (or entropy) modes driven by plasma gradients at small and large plasma β. These are small scale non-MHD instabilities with growth rates that typically peak near k⊥ρi∼1 and vanish in the long wavelength k⊥→0 limit. This work also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate γ=β/[2(1+β)]Cs/|Lp| with Cs2=p0/ρ0 for k⊥→0 and is universally unstable for 1/Lp≠0. We show that the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance p0+B02/(8π)=constant, which renders the assumption B0′=0 inconsistent if p0′≠0.

From plane waves to local Gaussians for the simulation of correlated periodic systems.

We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller-Plesset perturbation theory.

Determination of the large scale volume weighted halo velocity bias in simulations

A profound assumption in peculiar velocity cosmology is $b_v=1$ at sufficiently large scales, where $b_v$ is the volume weighted halo(galaxy) velocity bias with respect to the matter velocity field. However, this fundamental assumption has not been robustly verified in numerical simulations. Furthermore, it is challenged by structure formation theory (BBKS, 1986, ApJ; Desjacques and Sheth, 2010, PRD), which predicts the existence of velocity bias (at least for proto-halos) due to the fact that halos reside in special regions (local density peaks). The major obstacle to measure the volume weighted velocity from N-body simulations is an unphysical sampling artifact. It is entangled in the measured velocity statistics and becomes significant for sparse populations. With recently improved understanding of the sampling artifact (Zhang, Zheng and Jing, 2015, PRD; Zheng, Zhang and Jing, 2015, PRD), for the first time we are able to {\it appropriately correct this sampling artifact and then robustly measure the volume weighted halo velocity bias}. (1) We verify $b_v=1$ within $2\%$ model uncertainty at $k\lesssim 0.1h/$Mpc and $z=0$-$2$ for halos of mass $\sim 10^{12}$-$10^{13} h^{-1} M_\odot$, and, therefore, consolidates a foundation of the peculiar velocity cosmology. (2) We also find statistically significant signs of $b_v\neq 1$ at $k\gtrsim 0.1h/$Mpc. Unfortunately, whether this is real or caused by residual sampling artifact requires further investigation. Nevertheless, cosmology based on $k\gtrsim 0.1h/$Mpc velocity data shall be careful this potential velocity bias.

Modeling viscoelasticity through spring-dashpot models in intermittent-contact atomic force microscopy.

We examine different approaches to model viscoelasticity within atomic force microscopy (AFM) simulation. Our study ranges from very simple linear spring–dashpot models to more sophisticated nonlinear systems that are able to reproduce fundamental properties of viscoelastic surfaces, including creep, stress relaxation and the presence of multiple relaxation times. Some of the models examined have been previously used in AFM simulation, but their applicability to different situations has not yet been examined in detail. The behavior of each model is analyzed here in terms of force–distance curves, dissipated energy and any inherent unphysical artifacts. We focus in this paper on single-eigenmode tip–sample impacts, but the models and results can also be useful in the context of multifrequency AFM, in which the tip trajectories are very complex and there is a wider range of sample deformation frequencies (descriptions of tip–sample model behaviors in the context of multifrequency AFM require detailed studies and are beyond the scope of this work).

The Ionospheric Bubble Index deduced from magnetic field and plasma observations onboard Swarm

In the post-sunset tropical ionospheric F-region plasma density often exhibits depletions, which are usually called equatorial plasma bubbles (EPBs). In this paper we give an overview of the Swarm Level 2 Ionospheric Bubble Index (IBI), which is a standard scientific data of the Swarm mission. This product called L2-IBI is generated from magnetic field and plasma observations onboard Swarm, and gives information as to whether a Swarm magnetic field observation is affected by EPBs. We validate the performance of the L2-IBI product by using magnetic field and plasma measurements from the CHAMP satellite, which provided observations similar to those of the Swarm. The L2-IBI product is of interest not only for ionospheric studies, but also for geomagnetic field modeling; modelers can de-select magnetic data which are affected by EPBs or other unphysical artifacts.

The p(γ,K+)Λ reaction: Consistent high-spin interactions and Bayesian inference of its resonance content

A Bayesian analysis of the world's $p(\gamma,K^+)\Lambda$ data is presented. We adopt a Regge-plus-resonance framework featuring consistent interactions for nucleon resonances up to spin $J = 5/2$. The power of the momentum dependence of the consistent interaction structure rises with the spin of the resonance. This leads to unphysical structures in the energy dependence of the computed cross sections when the short-distance physics is cut off with standard hadronic form factors. A plausible, spin-dependent modification of the hadronic form factor is proposed which suppresses the unphysical artifacts. Next, we evaluate all possible combinations of 11 candidate resonances. The best model is selected from the 2048 model variants by calculating the Bayesian evidence values against the world's $p(\gamma,K^+)\Lambda$ data. From the proposed selection of 11 resonances, we find that the following nucleon resonances have the highest probability of contributing to the reaction: $S_{11}(1535)$, $S_{11}(1650)$, $F_{15}(1680)$, $P_{13}(1720)$, $D_{13}(1900)$, $P_{13}(1900)$, $P_{11}(1900)$, and $F_{15}(2000)$.

Vaporization and collision modeling of liquid fuel sprays in a co-axial fuel and air pre-mixer

Droplet collision occurs frequently in regions where the droplet number density is high. Even for Lean Premixed and Pre-vaporized (LPP) liquid sprays, the collision effects can be very high on the droplet size distributions, which will in turn affect the droplet vaporization process. Hence, in conjunction with vaporization modeling, collision modeling for such spray systems is also essential. The standard O’Rourke’s collision model, usually implemented in CFD codes, tends to generate unphysical numerical artifact when simulations are performed on Cartesian grid and the results are not grid independent. Thus, a new collision modeling approach based on no-time-counter method (NTC) proposed by Schmidt and Rutland is implemented to replace O’Rourke’s collision algorithm to solve a spray injection problem in a cylindrical coflow premixer. The so called “four-leaf clover” numerical artifacts are eliminated by the new collision algorithm and results from a diesel spray show very good grid independence. Next, the dispersion and vaporization processes for liquid fuel sprays are simulated in a coflow premixer. Two liquid fuels under investigation are jet-A and Rapeseed Methyl Esters (RME). Results show very good grid independence in terms of SMD distribution, droplet number distribution and fuel vapor mass flow rate. A baseline test is first established with a spray cone angle of 90° and injection velocity of 3m/s and jet-A achieves much better vaporization performance than RME due to its higher vapor pressure. To improve the vaporization performance for both fuels, a series of simulations have been done at several different combinations of spray cone angle and injection velocity. At relatively low spray cone angle and injection velocity, the collision effect on the average droplet size and the vaporization performance are very high due to relatively high coalescence rate induced by droplet collisions. Thus, at higher spray cone angle and injection velocity, the results expectedly show improvement in fuel vaporization performance since smaller droplet has a higher vaporization rate. The vaporization performance and the level of homogeneity of fuel–air mixture can be significantly improved when the dispersion level is high, which can be achieved by increasing the spray cone angle and injection velocity.

Pitfalls among the promises of mechanics-based restoration: Addressing implications of unphysical boundary conditions

Mechanics-based restoration has been seen by some in the structural geology community as a panacea – a new technology that melds the retrodeformational merits of kinematic balancing with principles of continuum mechanics. The method has been touted for its ability to simulate complex 3D systems without assumptions of plane strain, allowing for heterogeneous fault slip distributions and mechanical interaction of fault segments. It has been suggested as a means to predict distributions of geologic strain and associated small-scale structures; however, we demonstrate that the kinematics of restoration models may differ significantly from forward deformation. Restoration models are governed by boundary conditions that are different from the forces driving forward geologic deformation. Models may be improved by supplementing restoration boundary conditions with loads that attempt to reverse tectonic strain, but unphysical artifacts persist. Mechanics-based restoration may be an appropriate tool for traditional applications of kinematic models including validation of structural interpretation and modeling geometric evolution; however, more subtle features, particularly strain distribution, should be treated with skepticism. Restoration models may provide insights to the initial configuration of forward mechanical models with physically appropriate boundary conditions and non-linear material behavior. Forward models provide the best means for simulating deformation and predicting subsidiary structures.

Consistent interactions for high-spin fermion fields

We address the issue of consistent interactions for off-shell fermion fields of arbitrary spin. These interactions play a crucial role in the quantum hadrodynamical description of high-spin baryon resonances in hadronic processes. The Rarita-Schwinger (R-S) description of high-spin fermion fields involves unphysical degrees of freedom associated with their lower-spin content. These enter the interaction if not eliminated outright. The invariance condition of the interaction under the unconstrained R-S gauge removes the lower-spin content of the fermion propagator and leads to a consistent description of the interaction. We develop the most general consistent interaction structure for high-spin fermions. We find that the power of the momentum dependence of a consistent interaction rises with the spin of the fermion field. This leads to unphysical structures in the energy dependence of the computed tree-level cross sections when the short-distance physics is cut off with standard hadronic form factors. A spin-dependent hadronic form factor is proposed that suppresses the unphysical artifacts.

Effective constitutive parameters of plasmonic metamaterials: Homogenization by dual field interpolation

We introduce a general implementation of the recently proposed homogenization theory [Tsukerman, J. Opt. Soc. Am. B 28, 577 (2011)] allowing one to retrieve all 36 linear constitutive parameters of any 3D metamaterial with parallelepipedal unit cells. The effective parameters are defined directly as linear relations between pairs of coarse-grained fields, in contrast with methods where these parameters are obtained from reflection and transmission data or other indirect considerations. The method is applied to plasmonic metamaterials with spherical gold particles and split-ring resonators (SRR), respectively. In both cases, the expected physical behavior is reproduced almost perfectly, with no unphysical artifacts.

SHG simulations of plasmonic nanoparticles using curved elements

We demonstrate that simulating plasmonic nanostructures by means of curved elements (CEs) significantly increases the accuracy and computation speed not only in the linear but also in the nonlinear regime. We implemented CEs within the discontinuous Galerkin (DG) method and, as an example of a nonlinear effect, investigated second-harmonic generation (SHG) at a silver nanoparticle. The second-harmonic response of the material is simulated by an extended Lorentz model (ELM). In the linear regime the CEs are ≈ 9 times faster than ordinary elements for the same accuracy, provide a much better convergence and show fewer unphysical field artifacts. For DG-SHG calculations CEs are almost indispensable to obtain physically reasonable results at all. Additionally, their boundary approximation has to be of the same order as their polynomial degree to achieve artifact-free field distributions. In return, the use of such CEs with the DG method pays off more than evidently, since the additional computation time is only 1%.

Three roads to probe-brane superconductivity

We study a defect system of two parallel D5 probe branes in a large-N c D3 background. Using the non-abelian DBI action, we study three different fields that can give rise to a superconducting phase transition: A vector (p-wave), a scalar corresponding to a non-trivial “separation” of the branes in the (3 + 1) field theory directions and a scalar corresponding to a separation in the “internal” S 5 (both s-wave). Comparing these phases first in the α′2 expansion, we find that the internal scalar has the largest critical temperature and is always thermodynamically preferred. Further, there is an interesting attractor behavior. Taking a simplified version of the full DBI action that preserves its regularity and geometry, we find that the divergences of the α′2 expansion are resolved and some second order transitions turn into first order ones. In addition to some other changes of the phase diagram due to the structure of the DBI action, we observe that the ground state degeneracy of the unbroken theory is lifted. We also isolate the unphysical artifacts of our simplification.

Tempered wave functions: Schrödinger's equation within the light cone

The standard derivation of Schrödinger's equation from a Lorentz-invariant Feynman path integral consists in taking first the limit of infinite speed of light and then the limit of short time slice. In this order of limits the light cone of the path integral disappears, giving rise to an instantaneous spread of the wave function to the entire space. We ascribe the failure of the propagation in time according to Schrödinger's equation to retain the light cone of the path integral to the very nature of the limiting process: it is a regular expansion of a singular approximation problem, because the time-dependent boundary conditions of the path integral on the light cone are lost in this limit. We propose a distinguished limit of the time-sliced relativistic path integral, which produces Schrödinger's equation and preserves the zero boundary conditions on and outside the original light cone of the path integral. This produces an intermediate model between non-relativistic and relativistic mechanics of a single particle quantum particle. These boundary conditions relieve the solutions of Schrödinger's equation in the entire space of several annoying, seemingly unrelated unphysical artifacts, including non-analytic wave functions, spontaneous appearance of discontinuities, non-existence of moments when the initial wave function has a jump discontinuity (e.g., a collapsed wave function after a measurement), and so on. The practical implications of the present formulation are yet to be seen.

Phase diagram of two-color quark matter at nonzero baryon and isospin density

We investigate the properties of cold dense quark matter composed of two colors and two flavors of light quarks. In particular, we perform the first model calculation of the full phase diagram at nonzero baryon and isospin density, thus matching the model-independent predictions of chiral perturbation theory at low density to the conjectured phase structure at high density. We confirm the presence of the Fulde-Ferrell phase in the phase diagram and study its dependence on the tunable parameter in the Lagrangian that simulates the effects of the quantum axial anomaly. As a by-product, we clarify the calculation of the thermodynamic potential in the presence of the Fulde-Ferrell pairing, which was previously based on an ad hoc subtraction of an unphysical cutoff artifact. Furthermore, we argue that close to the diquark (or pion) Bose-Einstein condensation transition, the system behaves as a dilute Bose gas so that our simple fermionic model in the mean-field approximation is not quantitatively adequate. We suggest that including thermal fluctuations of the order parameter for Bose-Einstein condensation is crucial for understanding available lattice data.

N-dependence of electronic energies in atoms and molecules: Mulliken and exponential interpolations

The unphysical artifact of the Mulliken (parabolic) interpolation of the dependence of the electronic energy of atoms and molecules on the system average number of electrons N is identified. To remedy this shortcoming a smooth exponential interpolation between the energies of the neutral system, its cation and anion is suggested. The trends exhibited by the associated electronegativity and chemical hardness scales are examined.

Scalar meson spectroscopy with lattice staggered fermions

With sufficiently light up and down quarks the isovector (${a}_{0}$) and isosinglet (${f}_{0}$) scalar meson propagators are dominated at large distance by two-meson states. In the staggered-fermion formulation of lattice quantum chromodynamics, taste-symmetry breaking causes a proliferation of two-meson states that further complicates the analysis of these channels. Many of them are unphysical artifacts of the lattice approximation. They are expected to disappear in the continuum limit. The staggered-fermion fourth-root procedure has its purported counterpart in rooted staggered chiral perturbation theory ($\mathrm{rS}\ensuremath{\chi}\mathrm{PT}$). Fortunately, the rooted theory provides a strict framework that permits the analysis of scalar meson correlators in terms of only a small number of low-energy couplings. Thus the analysis of the point-to-point scalar meson correlators in this context gives a useful consistency check of the fourth-root procedure and its proposed chiral realization. Through numerical simulation we have measured correlators for both the ${a}_{0}$ and ${f}_{0}$ channels in the ``Asqtad'' improved staggered-fermion formulation in a lattice ensemble with lattice spacing $a=0.12\text{ }\text{ }\mathrm{fm}$. We analyze those correlators in the context of $\mathrm{rS}\ensuremath{\chi}\mathrm{PT}$ and obtain values of the low-energy chiral couplings that are reasonably consistent with previous determinations.

An efficient deterministic method for generating non-negative scattering cross-sections

In the conventional discrete ordinates approach, the scattering source is approximated as a truncated Legendre series. In case of highly anisotropic scattering problems (e.g., incident beam problems), the truncated Legendre scattering cross-sections give unphysical negative cross-sections in some values of μ (cosine of scattering angle). These unphysical artifacts cause negative scattering sources and negative angular fluxes. In addition to that, negative angular fluxes may cause wrong scalar flux as well. A new method to generate non-negative scattering cross-sections, which is very efficient and deterministic, is proposed in this paper. The main idea of this method is to make non-negative scattering cross-sections that produce equivalent scattering sources. This method does not have a practical limitation to generate non-negative scattering cross-sections because the calculations of the scattering sources are performed with the conventional truncated cross-section data provided from the standard processing codes. In the both neutron and the photon/electron coupled cases, an inadequate truncated Legendre order causes problems, e.g., inaccurate angular distribution of scattering for low order, oscillations of differential scattering cross-sections where cross-sections are small for high order expansions, and negative differential scattering cross-sections in some values of μ. In the neutron case, if the anisotropy is very high compared to the truncated Legendre order, inaccurate angular distributions of scattering occur especially in within-group scattering. Even if the truncated Legendre order is quite high to represent angular distribution of scattering in the photon/electron coupled case, it still causes oscillations where the cross-sections are small. The method in this paper achieves both an accurate angular distribution of scattering and non-negative scattering cross-sections for neutron and photon/electron coupled cases. The generated non-negative scattering cross-sections with the new method are compared to the conventional scattering cross-sections and tested in the transport calculations. The numerical results tested in the transport calculation give accurate results without unphysical negative angular fluxes.

Absorbing boundaries in numerical solutions of the time-dependent Schrödinger equation on a grid using exterior complex scaling

We study the suppression of reflections in the numerical simulation of the time-dependent Schr\"odinger equation for strong-field problems on a grid using exterior complex scaling (ECS) as an absorbing boundary condition. It is shown that the ECS method can be applied in both the length and the velocity gauge as long as appropriate approximations are applied in the ECS transformation of the electron-field coupling. It is found that the ECS method improves the suppression of reflection as compared to the conventional masking function technique in typical simulations of atoms exposed to an intense laser pulse. Finally, we demonstrate the advantage of the ECS technique to avoid unphysical artifacts in the evaluation of high harmonic spectra.