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A major part of the energy released upon the gravitational collapse of massive-star cores is carried away by neutrinos. Neutrinos play a crucial role in collapsing supernovae (SNe). At the present time, mathematical models of core-collapse SNe are based on multidimensional gas dynamics and thermonuclear reactions, whereas the neutrino transport is frequently treated in simplified way. An accurate analysis of neutrinos in a spherically symmetric gravitational collapse is performed on the basis of Boltzmann kinetic equations including all weak-interaction reactions with exact quantum-mechanical matrix elements. The role of multidimensional effects is studied bymeans of multidimensional gas dynamics allowing for the neutrino transport via diffusion treated by employing flux limiters. The possibility of largescale convection, which is of interest both from the point of view of explaining a type II supernova (SN) and from the point of view of implementing an experiment aimed at detecting possible energetic (≳10 MeV) neutrinos from an SN, is discussed. Thermonuclear burning leads to the explosion of a type I SN. A hot central region and the subsequent large-scale convection may also play an important role in the SN mechanism. If neutrinos and convection play a key role for a type II SN, then, in order to explain gamma radiation from product radioactive elements, convection is of importance in the case of SNe belonging to both types. In addition, convection may be important for bright type I SNe. Original methods are presented for multidimensional gas dynamics involving thermonuclear burning and for multitemperature gas dynamics involving radiative transfer.
Scientific research communities can be represented as heterogeneous or multidimensional networks encompassing multiple types of entities and relationships. These networks might include researchers, institutions, meetings, and publications, connected by relationships like authorship, employment, and attendance. We describe a method for efficiently and flexibly capturing, storing, and extracting information from multidimensional scientific networks using a graph database. The database structure is based on an ontology that captures allowable types of entities and relationships. This allows us to construct a variety of projections of the underlying multidimensional graph through database queries to answer specific research questions. We demonstrate this process through a study of the U.S. Biological Threat Reduction Program (BTRP), which seeks to develop Threat Reduction Networks to build and strengthen a sustainable international community of biosecurity, biosafety, and biosurveillance experts to address shared biological threat reduction challenges. Networks like these create connectional intelligence among researchers and institutions around the world, and are central to the concept of cooperative threat reduction. Our analysis focuses on a series of seven BTRP genome sequencing training workshops, showing how they created a growing network of participants and countries over time, which is also reflected in coauthorship relationships among attendees. By capturing concept and relationship hierarchies, our ontology-based approach allows us to pose general or specific questions about networks within the same framework. This approach can be applied to other research communities or multidimensional social networks to capture, analyze, and visualize different types of interactions and how they change over time.
We investigate core-collapse supernova (CCSN) nucleosynthesis with self-consistent, axisymmetric (2D) simulations performed using the neutrino hydrodynamics code Chimera. Computational costs have traditionally constrained the evolution of the nuclear composition within multidimensional CCSN models to, at best, a 14-species α-network capable of tracking only (α,γ) reactions from {sup 4}He to {sup 60}Zn. Such a simplified network limits the ability to accurately evolve detailed composition and neutronization or calculate the nuclear energy generation rate. Lagrangian tracer particles are commonly used to extend the nuclear network evolution by incorporating more realistic networks into post-processing nucleosynthesis calculations. However, limitations such as poor spatial resolution of the tracer particles; inconsistent thermodynamic evolution, including misestimation of expansion timescales; and uncertain determination of the multidimensional mass cut at the end of the simulation impose uncertainties inherent to this approach. We present a detailed analysis of the impact of such uncertainties for four self-consistent axisymmetric CCSN models initiated from solar-metallicity, nonrotating progenitors of 12, 15, 20, and 25 M{sub ⊙} and evolved with the smaller α-network to more than 1 s after the launch of an explosion.
Here, we explore the dimensionality of the U.S. Department of Agriculture’s household food security survey module among households with children. Using a novel methodological approach to measuring food security, we find that there is multidimensionality in the module for households with children that is associated with the overall household, adult, and child dimensions of food security. Additional analyses suggest official estimates of food security among households with children are robust to this multidimensionality. However, we also find that accounting for the multidimensionality of food security among these households provides new insights into the correlates of food security at the household, adult, and child levels of measurement.
The property of consistency with the point of symmetry is a natural requirement for an arbitrary estimate of the center (for the centrally symmetric distribution this follows from the affine equivariance of the estimate). Different notions of multidimensional symmetry and some of their properties are given in this paper. We establish that in the general case, the multidimensional simplicial Oja median identifies the point of symmetry, if it exists. By this criterion we compare the Oja median with the other best-known multidimensional medians.
Kelvin probe force microscopy (KPFM) has provided deep insights into the role local electronic, ionic and electrochemical processes play on the global functionality of materials and devices, even down to the atomic scale. Conventional KPFM utilizes heterodyne detection and bias feedback to measure the contact potential difference (CPD) between tip and sample. This measurement paradigm, however, permits only partial recovery of the information encoded in bias- and time-dependent electrostatic interactions between the tip and sample and effectively down-samples the cantilever response to a single measurement of CPD per pixel. This level of detail is insufficient for electroactive materials, devices, or solid-liquid interfaces, where non-linear dielectrics are present or spurious electrostatic events are possible. Here, we simulate and experimentally validate a novel approach for spatially resolved KPFM capable of a full information transfer of the dynamic electric processes occurring between tip and sample. General acquisition mode, or G-Mode, adopts a big data approach utilising high speed detection, compression, and storage of the raw cantilever deflection signal in its entirety at high sampling rates (> 4 MHz), providing a permanent record of the tip trajectory. We develop a range of methodologies for analysing the resultant large multidimensional datasets involving classical, physics-based and information-based approaches. Physics-based analysis of G-Mode KPFM data recovers the parabolic bias dependence of the electrostatic force for each cycle of the excitation voltage, leading to a multidimensional dataset containing spatial and temporal dependence of the CPD and capacitance channels. We use multivariate statistical methods to reduce data volume and separate the complex multidimensional data sets into statistically significant components that can then be mapped onto separate physical mechanisms. Overall, G-Mode KPFM offers a new paradigm to study dynamic electric phenomena in electroactive interfaces as well as offer a promising approach to extend KPFM to solid-liquid interfaces.
Expansion from coherent 2D spectroscopy to coherent 3D spectroscopy can provide significant advantages when studying molecules that have heavily perturbed energy levels. This paper illustrates such advantages by demonstrating how high resolution coherent 3D (HRC3D) spectroscopy can be used to study a portion of the visible spectrum of nitrogen dioxide. High resolution coherent 2D spectra usually contain rotational and vibrational patterns that are easy to analyze, but severe congestion and complexity preclude its effective use for many parts of the NO{sub 2} spectrum. HRC3D spectroscopy appears to be much more effective; multidimensional rotational and vibrational patterns produced by this new technique are easy to identify even in the presence of strong perturbations. A method for assigning peaks, which is based upon analyzing the resulting multidimensional patterns, has been developed. The higher level of multidimensionality is useful for reducing uncertainty in peak assignments, improving spectral resolution, providing simultaneous information on multiple levels and states, and predicting, verifying, and categorizing peaks.
Coherent multidimensional optical spectroscopy is an emerging technique for resolving structure and ultrafast dynamics of molecules, proteins, semiconductors, and other materials. A current challenge is the quality of kinetics that are examined as a function of waiting time. Inspired by noise-suppression methods of transient absorption, here we incorporate shot-by-shot acquisitions and balanced detection into coherent multidimensional optical spectroscopy. We demonstrate that implementing noise-suppression methods in two-dimensional electronic spectroscopy not only improves the quality of features in individual spectra but also increases the sensitivity to ultrafast time-dependent changes in the spectral features. Measurements on cresyl violet perchlorate are consistent with the vibronic pattern predicted by theoretical models of a highly displaced harmonic oscillator. The noise-suppression methods should benefit research into coherent electronic dynamics, and they can be adapted to multidimensional spectroscopies across the infrared and ultraviolet frequency ranges.
UPC++ is a Partitioned Global Address Space (PGAS) extension for C++, with three main objectives: 1) to provide an object-oriented PGAS programming model in the context of the popular C++ language; 2) to add useful parallel programming idioms unavailable in UPC, such as asynchronous remote function invocation and multidimensional arrays, to support complex scientific applications; 3) to offer an easy on-ramp to PGAS programming through interoperability with other existing parallel programming systems (e.g., MPI, OpenMP, CUDA). UPC++ includes two main features beyond UPC: 1) One of the major limitations of UPC in the context of DOE application is the relatively weak notion of multidimensional arrays, which it inherited from C. To remedy this problem in UPC++, we included a multidimensional domain and array library based on that of Titanium. Titanium's library is similar to Chapel's dense and strided domains, as both were inspired by the dense and strided regions and arrays in ZPL. 2) Another feature provided by UPC++ but not by UPC is remote function invocation, which is inspired by Phalanx, X10, Habanero-C, and C++11. The user may start an asynchronous remote function invocation with the following syntax: "async(place)(function, args...);". UPC++ provides two programming constructs for specifying dynamic dependencies among tasks: 1) event-driven execution as in Phalanx and Habanero-C; 2) finish-async as in X10. We implemented UPC++ with a "compiler-free" approach using C++ templates and runtime libraries. The UPC++ front-end consists of a set of C++ header files that enables the C++ compiler to "translate" UPC++ features in a user program to runtime library calls. In particular, we use templates and operator overloading to customize the behavior of UPC++ types. This software package has been replaced with UPCC++ V 1.0
A library for performing numerical computation with low-rank functions. The (C3) library enables performing continuous linear and multilinear algebra with multidimensional functions. Common tasks include taking "matrix" decompositions of vector- or matrix-valued functions, approximating multidimensional functions in low-rank format, adding or multiplying functions together, integrating multidimensional functions.
The 12 GeV upgrade of Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab will enable a new experimental program with substantial discovery potential in hadronic and nuclear physics. One of the flagship science programs is the study of multidimensional images of hadrons. A broad experimental program has been developed to map the nucleon's intrinsic correlated spin and momentum distribution through measurement of deeply exclusive and semi- inclusive processes. These multidimensional distributions open a new window on the elusive spin content of the nucleon through observables that are directly related to the orbital angular momentum of quarks and gluons. An overview of the 12 GeV upgrade with focus on the study of the multidimensional imaging of hadrons with the CLAS12 detector will be presented.
Coulombic interactions between charged species in pore water and at surface/solution interfaces are of pivotal importance for multicomponent reactive transport in porous media. In this study, we investigate the impact of domain dimensionality on electrostatically coupled dispersion and surface-solution reactions during transport of acidic plumes and major ions in porous media. Column and quasi two-dimensional flow-through experiments were performed, with identical silica porous media and under the same advection-dominated conditions. Equal mass fluxes of different electrolyte solutions (i.e., HCl - pH ~ 2.8, NaBr - 100 mM, HCl - pH ~ 2.8 plus NaBr - 100 mM) were continuously injected in the 1-D and 2-D experiments and breakthrough curves of pH and major ions were measured at the outlet of the domains. The presence of pronounced ionic strength gradients in the transverse direction in the 2-D setup caused distinct retardation and transport behaviors of protons and major ions which were not observed in the one-dimensional column experiments. Furthermore, in the cases of salt electrolytes injection, considerably enhanced release of H + (>61%) from the quartz surface was observed in the multidimensional system compared to the one-dimensional setup. Reactive transport modeling was performed to reproduce the experimental outcomes and to analyse the coupling between transport processes, based on the Nernst-Planck formulation of diffusive/dispersive fluxes and on surface complexation reactions at the solid-solution interface. Electrostatic interactions between Na + , B – , and H + , and deprotonation of the quartz surface upon the formation of sodium outer-sphere complexes, are the primary controllers of the spatial and temporal features displayed by the pH and major ions measurements. The reactive transport simulations allowed us to interpret the experimental observations, to visualize the distribution and spatio-temporal evolution of dissolved and solid species, to identify a spatially heterogeneous zonation of Coulombic interactions with distinct behavior at the fringe and core of the injected plumes in the multidimensional setup, and to quantify the different components of the Nerst-Planck fluxes of the charged solutes. This study demonstrates that the domain dimensionality directly affects electrostatic interactions between charged aqueous species in the pore water and surface complexation reactions at the solid-solution interface. The non-trivial effects of dimensionality on multicomponent ionic transport result in a significantly different behavior in 1-D and 2-D systems.
Modeling can provide physical insight to device operation, help distinguish important material properties from unimportant properties, predict trends, and help interpret experimental data. Numerical modeling is also useful to simulate different electro-optical experiments, in the presence of grain boundaries (GBs) and nonplanar junctions and geometries, and to help interpret data obtained in such experiments. This chapter presents methods for effective multidimensional modeling. The first step in creating a computational model is defining and providing discretization of a 2D area or a 3D volume. Two main approaches to the discretization have been used for studying solar cells: equivalent-circuit modeling and solving semiconductor equations. The chapter gives some examples of problems that were addressed with 2D or 3D modeling and the knowledge that was gained through them. Multidimensional modeling including GBs and other material variations is necessary to explain the device physics and experimental results present in diverse thin-film technologies.
Many energy conversion, sensing, and microelectronic applications based on ferroic materials are determined by the domain structure evolution under applied stimuli. New hyperspectral, multidimensional spectroscopic techniques now probe dynamic responses at relevant length and time scales to provide an understanding of how these nanoscale domain structures impact macroscopic properties. Such approaches, however, remain limited in use because of the difficulties that exist in extracting and visualizing scientific insights from these complex datasets. Using multidimensional band-excitation scanning probe spectroscopy and adapting tools from both computer vision and machine learning, an automated workflow is developed to featurize, detect, and classify signatures of ferroelectric/ferroelastic switching processes in complex ferroelectric domain structures. This approach enables the identification and nanoscale visualization of varied modes of response and a pathway to statistically meaningful quantification of the differences between those modes. Lastly, among other things, the importance of domain geometry is spatially visualized for enhancing nanoscale electromechanical energy conversion.
We develop a novel transformation that maps the linear, nonhomogeneous, multidimensional population balance equation (PBE) into an advection equation that is readily solved using the method of characteristics. The PBEs targeted by this transformation exclude aggregation, breakage, and time dependent birth and death rates. In addition, internal coordinates are assumed to grow independently of each other. The ensuing general formulation is then used to recover closed‐form analytical solutions for problems with monosurface and bulk‐diffusion growth‐rates as well as Gaussian‐type nucleation. For completeness, we derive the multidimensional Green's functions for our approach. This is followed by a brief discussion on how the proposed framework may be used for code verification of moment methods such as the quadrature method of moments and the direct quadrature method of moments. Finally, a sample Mathematica code is provided to derive analytical solutions for the single‐internal‐coordinate case given user‐specified growth, birth, and death rates. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1691–1698, 2015
Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented.
We have developed an open‐source, Python‐based software platform called ScopeFoundry for performing complex, multidimensional microscopy experiments that integrate diverse types of experimental hardware. ScopeFoundry streamlines experiment development by providing a modular environment where hardware controls and measurement schemes can be arranged and customized. Important software tasks such as data management and user interface generation are automated. Using this platform, we have implemented scanning Auger spectromicroscopy on a modified commercial surface analysis system. Spectromicroscopy produces multidimensional datasets with complete spectra at each image pixel, allowing for detailed analysis of material phases where Auger peaks may change in shape and position. Analysis of the surface phases of an advanced electron emission dispenser cathode is presented as an example. We describe the general ScopeFoundry platform, its application to Auger spectromicroscopy, and ways it can be applied to advance surface analysis and microscopy.