SHARP: A Spatially Higher-order, Relativistic Particle-in-Cell Code

Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially higher-order accurate relativistic PIC algorithm in one spatial dimension, which conserves charge and momentum exactly. We utilize the smoothness implied by the usage of higher-order interpolation functions to achieve a spatially higher-order accurate algorithm (up to fifth order). We validate our algorithm against several test problems -- thermal stability of stationary plasma, stability of linear plasma waves, and two-stream instability in the relativistic and non-relativistic regimes. Comparing our simulations to exact solutions of the dispersion relations, we demonstrate that SHARP can quantitatively reproduce important kinetic features of the linear regime. Our simulations have a superior ability to control energy non-conservation and avoid numerical heating in comparison to common second-order schemes. We provide a natural definition for convergence of a general PIC algorithm: the complement of physical modes captured by the simulation, i.e., those that lie above the Poisson noise, must grow commensurately with the resolution. This implies that it is necessary to simultaneously increase the number of particles per cell and decrease the cell size. We demonstrate that traditional ways for testing for convergence fail, leading to plateauing of the energy error. This new PIC code enables us to faithfully study the long-term evolution of plasma problems that require absolute control of the energy and momentum conservation.Comment: 26 pages, 19 figures, discussion about performance is added, published in Ap

Spectroscopic Evidence for Multiple Order Parameter Components in the Heavy Fermion Superconductor CeCoIn_5

Point-contact spectroscopy was performed on single crystals of the heavy-fermion superconductor CeCoIn_5 between 150 mK and 2.5 K. A pulsed measurement technique ensured minimal Joule heating over a wide voltage range. The spectra show Andreev-reflection characteristics with multiple structures which depend on junction impedance. Spectral analysis using the generalized Blonder-Tinkham-Klapwijk formalism for d-wave pairing revealed two coexisting order parameter components, with amplitudes Delta_1 = 0.95 +/- 0.15 meV and Delta_2 = 2.4 +/- 0.3 meV, which evolve differently with temperature. Our observations indicate a highly unconventional pairing mechanism, possibly involving multiple bands.Comment: 4 pages, 3 figure

Multi-dimensional numerical simulations of type Ia supernova explosions

The major role type Ia supernovae play in many fields of astrophysics and in particular in cosmological distance determinations calls for self-consistent models of these events. Since their mechanism is believed to crucially depend on phenomena that are inherently three-dimensional, self-consistent numerical models of type Ia supernovae must be multi-dimensional. This field has recently seen a rapid development, which is reviewed in this article. The different modeling approaches are discussed and as an illustration a particular explosion model -- the deflagration model -- in a specific numerical implementation is presented in greater detail. On this exemplary case, the procedure of validating the model on the basis of comparison with observations is discussed as well as its application to study questions arising from type Ia supernova cosmology.Comment: 30 pages, 7 figures (Fig. 6 with reduced resolution

Surface Extraction from Neural Unsigned Distance Fields

We propose a method, named DualMesh-UDF, to extract a surface from unsigned distance functions (UDFs), encoded by neural networks, or neural UDFs. Neural UDFs are becoming increasingly popular for surface representation because of their versatility in presenting surfaces with arbitrary topologies, as opposed to the signed distance function that is limited to representing a closed surface. However, the applications of neural UDFs are hindered by the notorious difficulty in extracting the target surfaces they represent. Recent methods for surface extraction from a neural UDF suffer from significant geometric errors or topological artifacts due to two main difficulties: (1) A UDF does not exhibit sign changes; and (2) A neural UDF typically has substantial approximation errors. DualMesh-UDF addresses these two difficulties. Specifically, given a neural UDF encoding a target surface $\bar{S}$ to be recovered, we first estimate the tangent planes of $\bar{S}$ at a set of sample points close to $\bar{S}$. Next, we organize these sample points into local clusters, and for each local cluster, solve a linear least squares problem to determine a final surface point. These surface points are then connected to create the output mesh surface, which approximates the target surface. The robust estimation of the tangent planes of the target surface and the subsequent minimization problem constitute our core strategy, which contributes to the favorable performance of DualMesh-UDF over other competing methods. To efficiently implement this strategy, we employ an adaptive Octree. Within this framework, we estimate the location of a surface point in each of the octree cells identified as containing part of the target surface. Extensive experiments show that our method outperforms existing methods in terms of surface reconstruction quality while maintaining comparable computational efficiency.Comment: ICCV 202

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.Comment: 14 pages, 9 figure

Nonlinear diffusion & thermo-electric coupling in a two-variable model of cardiac action potential

This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10-degrees range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis

Assembly Bias and Splashback in Galaxy Clusters

We use publicly available data for the Millennium Simulation to explore the implications of the recent detection of assembly bias and splashback signatures in a large sample of galaxy clusters. These were identified in the SDSS/DR8 photometric data by the redMaPPer algorithm and split into high- and low-concentration subsamples based on the projected positions of cluster members. We use simplified versions of these procedures to build cluster samples of similar size from the simulation data. These match the observed samples quite well and show similar assembly bias and splashback signals. Previous theoretical work has found the logarithmic slope of halo density profiles to have a well-defined minimum whose depth decreases and whose radius increases with halo concentration. Projected profiles for the observed and simulated cluster samples show trends with concentration which are opposite to these predictions. In addition, for high-concentration clusters the minimum slope occurs at significantly smaller radius than predicted. We show that these discrepancies all reflect confusion between splashback features and features imposed on the profiles by the cluster identification and concentration estimation procedures. The strong apparent assembly bias is not reflected in the three-dimensional distribution of matter around clusters. Rather it is a consequence of the preferential contamination of low-concentration clusters by foreground or background groups.Comment: 17 pages, 16 figures, 3 tables, accepted versio

Elastic and inelastic diffraction of fast atoms,\linebreak Debye-Waller factor and M\"{o}ssbauer-Lamb-Dicke regime

The diffraction of fast atoms at crystal surfaces is ideal for a detailed investigation of the surface electronic density. However, instead of sharp diffraction spots, most experiments show elongated streaks characteristic of inelastic diffraction. This paper describes these inelastic profiles in terms of individual inelastic collisions with surface atoms taking place along the projectile trajectory and leading to vibrational excitation of the local Debye oscillator. A quasi-elastic regime where only one inelastic event contributes is identified as well as a mixed quantum-classical regime were several inelastic collision are involved. These regimes describe a smooth evolution of the scattering profiles from sharp spots to elongated streaks merging progressively into the classical diffusion regime