arXiv subjects

R. M. Caplan

Publications and source records attributed to R. M. Caplan.

12 recordsLinked to original sources

arXiv2026

A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and its Application to the Nonlinear Schrödinger Equation

An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-square value of the solution at the boundaries and is defined as \[ \left.\dfrac{\partial Ψ}{\partial t}\right|_b \approx i\,\mbox{Im} \left[ \dfrac{1}{Ψ_{b-1}} \left.\dfrac{\partial Ψ}{\partial t}\right|_{b-1} \right]\,Ψ_b, \] where $Ψ$ is the complex field and the subscripts $b$ and $b-1$ refer to a boundary point and the closest interior point to the boundary respectively. Application of the MSD boundary condition to simulations of the nonlinear Schrödinger equation is shown, and numerical simulations are performed to demonstrate its usefulness and advantages over other simple boundary conditions.

math.NA↗

arXiv2026

Advancing Heliophysics and Space Weather Modeling through Open Science

We present a community-wide effort to develop a strategy and action plan to advance heliophysics and space weather modeling through open science. While open science has the potential to enhance the quality and pace of scientific discovery, its application to scientific modeling requires more careful consideration regarding open data and open software guidelines, as scientific models differ significantly from data analysis software. We gathered feedback from modeling teams worldwide through a living survey and discussion sessions at the 2024 Open Science Workshop in College Park, USA, and at the 2025 COSPAR ISWAT Working Meeting in Cape Canaveral, USA. We complement these findings with lessons learned from almost 25 years of experience at the Community Coordinated Modeling Center in enabling open use of models. We identify key roadblocks in current open science practices and guidelines and offer recommendations for future progress across four overlapping themes: open use of models and simulation results, open validation, open development, and open collaboration. An essential outcome of the discussion is the need for model developers and model users to speak with a united voice and promote the role of models in future open science efforts. We introduce a new cross-domain community initiative called the Heliophysics Open Modeling Environment (HOME), which will be integrated as an overarching activity within COSPAR ISWAT. HOME will serve as a platform for modelers and model users to work together, facilitate community modeling, improve the scientific return on modeling investment, and advance understanding, modeling, and forecasting in heliophysics and space weather.

physics.space-ph↗

arXiv2021

Optimization of Magnetic Flux Ropes Modeled with the RBSL method

The so-called regularized Biot-Savart laws (RBSLs) provide an efficient and flexible method for modeling pre-eruptive magnetic configurations of coronal mass ejections (CMEs) whose characteristics are constrained by observational images and magnetic-field data. This method allows one to calculate the field of magnetic flux ropes (MFRs) with small circular cross-sections and an arbitrary axis shape. The field of the whole configuration is constructed as a superposition of (1) such a flux-rope field and (2) an ambient potential field derived, for example, from an observed magnetogram. The RBSL kernels are determined from the requirement that the MFR field for a straight cylinder must be exactly force-free. For a curved MFR, however, the magnetic forces are generally unbalanced over the whole path of the MFR. To minimize these forces, we apply a modified Gauss-Newton method to find optimal MFR parameters. This is done by iteratively adjusting the MFR axis path and axial current. We then try to relax the resulting optimized configuration in a subsequent line-tied zero-beta magnetohydrodynamic simulation toward a force-free equilibrium. By considering two models of the sigmoidal pre-eruption configuration for the 2009 February 13 CME, we demonstrate how this approach works and what it is capable of. We show, in particular, that the building blocks of the core magnetic structure described by these models match to morphological features typically observed in such type of configurations. Our method will be useful for both the modeling of particular eruptive events and theoretical studies of idealized pre-eruptive MFR configurations.

astro-ph.SR↗

arXiv2021

Coronal Hole Detection and Open Magnetic Flux

Many scientists use coronal hole (CH) detections to infer open magnetic flux. Detection techniques differ in the areas that they assign as open, and may obtain different values for the open magnetic flux. We characterize the uncertainties of these methods, by applying six different detection methods to deduce the area and open flux of a near-disk center CH observed on 9/19/2010, and applying a single method to five different EUV filtergrams for this CH. Open flux was calculated using five different magnetic maps. The standard deviation (interpreted as the uncertainty) in the open flux estimate for this CH was about 26%. However, including the variability of different magnetic data sources, this uncertainty almost doubles to 45%. We use two of the methods to characterize the area and open flux for all CHs in this time period. We find that the open flux is greatly underestimated compared to values inferred from in-situ measurements (by 2.2-4 times). We also test our detection techniques on simulated emission images from a thermodynamic MHD model of the solar corona. We find that the methods overestimate the area and open flux in the simulated CH, but the average error in the flux is only about 7%. The full-Sun detections on the simulated corona underestimate the model open flux, but by factors well below what is needed to account for the missing flux in the observations. Under-detection of open flux in coronal holes likely contributes to the recognized deficit in solar open flux, but is unlikely to resolve it.

astro-ph.SR↗

arXiv2018

GPU Acceleration of an Established Solar MHD Code using OpenACC

GPU accelerators have had a notable impact on high-performance computing across many disciplines. They provide high performance with low cost/power, and therefore have become a primary compute resource on many of the largest supercomputers. Here, we implement multi-GPU acceleration into our Solar MHD code (MAS) using OpenACC in a fully portable, single-source manner. Our preliminary implementation is focused on MAS running in a reduced physics "zero-beta" mode. While valuable on its own, our main goal is to pave the way for a full physics, thermodynamic MHD implementation. We describe the OpenACC implementation methodology and challenges. "Time-to-solution" performance results of a production-level flux rope eruption simulation on multi-CPU and multi-GPU systems are shown. We find that the GPU-accelerated MAS code has the ability to run "zero-beta" simulations on a single multi-GPU server at speeds previously requiring multiple CPU server-nodes of a supercomputer.

physics.comp-ph↗

arXiv2017

The Open Flux Problem

The heliospheric magnetic field is of pivotal importance in solar and space physics. The field is rooted in the Sun's photosphere, where it has been observed for many years. Global maps of the solar magnetic field based on full disk magnetograms are commonly used as boundary conditions for coronal and solar wind models. Two primary observational constraints on the models are (1) the open field regions in the model should approximately correspond to coronal holes observed in emission, and (2) the magnitude of the open magnetic flux in the model should match that inferred from in situ spacecraft measurements. In this study, we calculate both MHD and PFSS solutions using fourteen different magnetic maps produced from five different types of observatory magnetograms, for the time period surrounding July, 2010. We have found that for all of the model/map combinations, models that have coronal hole areas close to observations underestimate the interplanetary magnetic flux, or, conversely, for models to match the interplanetary flux, the modeled open field regions are larger than coronal holes observed in EUV emission. In an alternative approach, we estimate the open magnetic flux entirely from solar observations by combining automatically detected coronal holes for Carrington rotation 2098 with observatory synoptic magnetic maps. This approach also underestimates the interplanetary magnetic flux. Our results imply that either typical observatory maps underestimate the Sun's magnetic flux, or a significant portion of the open magnetic flux is not rooted in regions that are obviously dark in EUV and X-ray emission.

astro-ph.SR↗

arXiv2016

Synchronic coronal hole mapping using multi-instrument EUV images: Data preparation and detection method

We describe a method for the automatic mapping of coronal holes (CH) using simultaneous multi-instrument EUV imaging data. Synchronized EUV images from STEREO/EUVI A&B 195A and SDO/AIA 193A are preprocessed, including PSF deconvolution and the application of data-derived intensity corrections that account for center-to-limb variations (limb brightening) and inter-instrument intensity normalization. We systematically derive a robust limb-brightening correction that takes advantage of unbiased long-term averages of data and respects the physical nature of the problem. The new preprocessing greatly assists in CH detection, allowing for the use of a simplified variable-connectivity two-threshold region growing image segmentation algorithm to obtain consistent detection results. We generate synchronic EUV and CH maps, and show a preliminary analysis of CH evolution. Several data and code products are made available to the community (www.predsci.com/chd): For the period of this study (06/10/2010 to 08/18/14) we provide synchronic EUV and coronal hole map data at 6-hour cadence, data-derived limb-brightening corrections for STEREO/EUVI A&B 195A and SDO/AIA 193A, and inter-instrument correction factors to equate their intensities. We also provide the coronal hole image segmentation code module (ezseg) implemented in both FORTRAN OpenMP and GPU-accelerated C-CUDA. A complete implementation of our coronal hole detection pipeline in the form of a ready-to-use MATLAB driver script euv2chm utilizing ezseg is also made available.

astro-ph.SR↗

arXiv2014

Scattering and leapfrogging of vortex rings in a superfluid

The dynamics of vortex ring pairs in the homogeneous nonlinear Schrödinger equation is studied. The generation of numerically-exact solutions of traveling vortex rings is described and their translational velocity compared to revised analytic approximations. The scattering behavior of co-axial vortex rings with opposite charge undergoing collision is numerically investigated for different scattering angles yielding a surprisingly simple result for its dependence as a function of the initial vortex ring parameters. We also study the leapfrogging behavior of co-axial rings with equal charge and compare it with the dynamics stemming from a modified version of the reduced equations of motion from a classical fluid model derived using the Biot-Savart law.

cond-mat.other↗

arXiv2013

A Two-Step High-Order Compact Scheme for the Laplacian Operator and its Implementation in an Explicit Method for Integrating the Nonlinear Schrödinger Equation

We describe and test an easy-to-implement two-step high-order compact (2SHOC) scheme for the Laplacian operator and its implementation into an explicit finite-difference scheme for simulating the nonlinear Schrödinger equation (NLSE). Our method relies on a compact `double-differencing' which is shown to be computationally equivalent to standard fourth-order non-compact schemes. Through numerical simulations of the NLSE using fourth-order Runge-Kutta, we confirm that our scheme shows the desired fourth-order accuracy. A computation and storage requirement comparison is made between the 2SHOC scheme and the non-compact equivalent scheme for both the Laplacian operator alone, as well as when implemented in the NLSE simulations. Stability bounds are also shown in order to get maximum efficiency out of the method. We conclude that the modest increase in storage and computation of the 2SHOC schemes are well worth the advantages of having the schemes compact, and their ease of implementation makes their use very useful for practical implementations.

math.NA↗

arXiv2012

NLSEmagic: Nonlinear Schrödinger Equation Multidimensional Matlab-based GPU-accelerated Integrators using Compact High-order Schemes

We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schrödinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their serial counterparts, and are much cheaper to run than on standard parallel clusters. The codes are developed with usability and portability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files.

cs.MS↗

arXiv2012

Existence, Stability, and Dynamics of Bright Vortices in the Cubic-Quintic Nonlinear Schrödinger Equation

We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the two-dimensional (2D) cubic-quintic nonlinear Schr{ö}dinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, and thus splitting the full 2D equation into radial and azimuthal 1D equations. A variational approach is used to predict the radial shape of the vortex soliton, using the radial equation, yielding results very close to those obtained from numerical solutions. Previously known existence bounds for the solitary vortices are recovered by means of this approach. The 1D azimuthal equation of motion is used to analyze the modulational instability of the vortex solitons. The semi-analytical predictions -- in particular, that for the critical intrinsic frequency of the vortex soliton at the instability border -- are compared to systematic 2D simulations. We also compare our findings to those reported in earlier works, which featured some discrepancies. We then perform a detailed computational study of collisions between stable vortices with different topological charges. Borders between elastic and destructive collisions are identified.

nlin.PS↗

arXiv2008

Azimuthal Modulational Instability of Vortices in the Nonlinear Schrödinger Equation

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schr{ö}dinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS. We briefly show how to extend the method to encompass nonlocal nonlinearities that tend to stabilize solutions.

nlin.PS↗