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At least 631 records · Page 35

A new method to search for high-redshift clusters using photometric redshifts

We describe a new method (Poisson probability method, PPM) to search for high-redshift galaxy clusters and groups by using photometric redshift information and galaxy number counts. The method relies on Poisson statistics and is primarily introduced to search for megaparsec-scale environments around a specific beacon. The PPM is tailored to both the properties of the FR I radio galaxies in the Chiaberge et al. sample, which are selected within the COSMOS survey, and to the specific data set used. We test the efficiency of our method of searching for cluster candidates against simulations. Two different approaches are adopted. (1) We use two z ∼ 1 X-ray detected cluster candidates found in the COSMOS survey and we shift them to higher redshift up to z = 2. We find that the PPM detects the cluster candidates up to z = 1.5, and it correctly estimates both the redshift and size of the two clusters. (2) We simulate spherically symmetric clusters of different size and richness, and we locate them at different redshifts (i.e., z = 1.0, 1.5, and 2.0) in the COSMOS field. We find that the PPM detects the simulated clusters within the considered redshift range with a statistical 1σ redshift accuracy of ∼0.05. The PPM is an efficient alternative method for high-redshift cluster searches that may also be applied to both present and future wide field surveys such as SDSS Stripe 82, LSST, and Euclid. Accurate photometric redshifts and a survey depth similar or better than that of COSMOS (e.g., I < 25) are required.

79 ASTRONOMY AND ASTROPHYSICS↗

Effective description of higher-order scalar-tensor theories

Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Spectroscopy of Multielectrode Tunnel Barriers

Despite their ubiquity in nanoscale electronic devices, the physics of tunnel barriers has not been developed to the extent necessary for the engineering of devices in the few-electron regime. This problem is of urgent interest, as this is the specific regime into which current extreme-scale electronics fall. Here, we propose theoretically and validate experimentally a compact model for multielectrode tunnel barriers, suitable for design-rules-based engineering of tunnel junctions in quantum devices. We perform transport spectroscopy at approximately T = 4 K, extracting effective barrier heights and widths for a wide range of biases, using an efficient Landauer-Büttiker tunneling model to perform the analysis. We find that the barrier height shows several regimes of voltage dependence, either linear or approximately exponential. Effects on threshold, such as metal-insulator transition and lateral confinement, are included because they influence parameters that determine barrier height and width (e.g., the Fermi energy and local electric fields). We compare these results to semiclassical solutions of Poisson’s equation and find them to agree qualitatively. Finally, this characterization technique is applied to an efficient lateral tunnel barrier design that does not require an electrode directly above the barrier region in order to estimate barrier heights and widths.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Trap-Assisted Dopant Compensation Prevents Shunting in poly-Si Passivating Interdigitated Back Contact Silicon Solar Cells

Interdigitated back contact (IBC) solar cells achieve the highest efficiencies of single-junction architectures, but complicated patterning of the rear fingers and spreading of dopants during processing inhibit their mainstream adoption due to concerns of shunting between the IBC fingers. One method of simplifying patterning at the rear is by using contact masks combined with plasma-enhanced chemical vapor deposition (PECVD) or ion implantation. However, the intrinsic isolation region becomes contaminated during high-temperature annealing by lateral diffusion of dopants and during masked PECVD by spreading of dopant radicals through region between the mask and the substrate. Despite this contamination, we show through scanning spreading resistance microscopy and Kelvin probe force microscopy that a ~20 µm wide compensating region exists with high enough resistivity to prevent shunting. We model this p-i-n poly-Si system using two simulation models: a simple resistor model considering only the capture of charge carriers by trap defects in poly-Si to reduce the conductivity, and a more refined 1-dimensional finite element model using Poisson’s equation, drift-diffusion equations, and recombination of carriers. Using this model, we show that high defect density significantly decreases the current across the region between the p- and n-type fingers, preventing shunting.

atom probe↗

Dynamically accumulated dose and 4D accumulated dose for moving tumors

Purpose: The purpose of this work was to investigate the relationship between dynamically accumulated dose (dynamic dose) and 4D accumulated dose (4D dose) for irradiation of moving tumors, and to quantify the dose uncertainty induced by tumor motion. Methods: The authors established that regardless of treatment modality and delivery properties, the dynamic dose will converge to the 4D dose, instead of the 3D static dose, after multiple deliveries. The bounds of dynamic dose, or the maximum estimation error using 4D or static dose, were established for the 4D and static doses, respectively. Numerical simulations were performed (1) to prove the principle that for each phase, after multiple deliveries, the average number of deliveries for any given time converges to the total number of fractions (K) over the number of phases (N); (2) to investigate the dose difference between the 4D and dynamic doses as a function of the number of deliveries for deliveries of a 'pulsed beam'; and (3) to investigate the dose difference between 4D dose and dynamic doses as a function of delivery time for deliveries of a 'continuous beam.' A Poisson model was developed to estimate the mean dose error as a function of number of deliveries or delivered time for both pulsed beam and continuous beam. Results: The numerical simulations confirmed that the number of deliveries for each phase converges to K/N, assuming a random starting phase. Simulations for the pulsed beam and continuous beam also suggested that the dose error is a strong function of the number of deliveries and/or total deliver time and could be a function of the breathing cycle, depending on the mode of delivery. The Poisson model agrees well with the simulation. Conclusions: Dynamically accumulated dose will converge to the 4D accumulated dose after multiple deliveries, regardless of treatment modality. Bounds of the dynamic dose could be determined using quantities derived from 4D doses, and the mean dose difference between the dynamic dose and 4D dose as a function of number of deliveries and/or total deliver time was also established.

60 APPLIED LIFE SCIENCES↗

Oscillatory growth behavior of multistream instabilities

Multistream instabilities in the one-dimensional Vlasov−Poisson system are studied numerically by using plasmas with multi-humped electron distributions. The evolution of the total wave energy of the plasma oscillations excited by (numerical) noise consists of transient, growth, and nonlinear saturation stages. It is found that, in the growth stage, the total wave energy oscillates for odd number of streams, but it does not oscillate for even number of streams. It is also found that different spectral (Fourier) modes can dominate different stages of the “linear” growth and nonlinear saturation stages.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisons with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.

97 MATHEMATICS AND COMPUTING↗

Comparative Study of Finite Element Methods Using the Time-Accuracy-Size(TAS) Spectrum Analysis

We present a performance analysis appropriate for comparing algorithms using different numerical discretizations. By taking into account the total time-to-solution, numerical accuracy with respect to an error norm, and the computation rate, a cost-benefit analysis can be performed to determine which algorithm and discretization are particularly suited for an application. This work extends the performance spectrum model in for interpretation of hardware and algorithmic tradeoffs in numerical PDE simulation. As a proof-of-concept, popular finite element software packages are used to illustrate this analysis for Poisson’s equation.

97 MATHEMATICS AND COMPUTING↗

Lattice Green’s Functions for High-Order Finite Difference Stencils

Lattice Green's Functions (LGFs) are fundamental solutions to discretized linear operators, and as such they are a useful tool for solving discretized elliptic PDEs on domains that are unbounded in one or more directions. The majority of existing numerical solvers that make use of LGFs rely on a second-order discretization and operate on domains with free-space boundary conditions in all directions. Under these conditions, fast expansion methods are available that enable precomputation of 2D or 3D LGFs in linear time, avoiding the need for brute-force multi-dimensional quadrature of numerically unstable integrals. Here we focus on higher-order discretizations of the Laplace operator on domains with more general boundary conditions, by (1) providing an algorithm for fast and accurate evaluation of the LGFs associated with high-order dimension-split centered finite differences on unbounded domains, and (2) deriving closed-form expressions for the LGFs associated with both dimension-split and Mehrstellen discretizations on domains with one unbounded dimension. Through numerical experiments we demonstrate that these techniques provide LGF evaluations with near machine-precision accuracy, and that the resulting LGFs allow for numerically consistent solutions to high-order discretizations of the Poisson's equation on fully or partially unbounded 3D domains.

97 MATHEMATICS AND COMPUTING↗

Ion Distributions at Electrified Water-Organic Interfaces: PB-PMF Calculations and Impedance Spectroscopy Measurements

The interface between two immiscible electrolyte solutions consisting of alkali chlorides in water and the organic electrolyte BTPPATPFB in 1,2-dichloroethane is characterized with X-ray reflectivity, interfacial tension and impedance spectroscopy measurements over a range of applied voltage between the bulk solutions. X-ray reflectivity probes the interfacial ion distribution on the sub-nanometer length scale, whereas interfacial tension and impedance spectroscopy characterize quantities such as interfacial excess charge and differential capacitance that represent integrations over the interfacial ion distribution. Predictions of interfacial ion distributions by the recently introduced PB-PMF method, which combines Poisson's equation with ion potentials of mean force, provide excellent agreement, within one to two experimental standard deviations, with both X-ray reflectivity and interfacial tension measurements. However, the agreement with the differential capacitance measured by impedance spectroscopy, and modeled by the Randles equivalent circuit, is not as good. Values of measured and calculated differential capacitance can deviate by as much as 20% for applied electric potential differences larger than approximately ±100 mV. These comparisons indicate that our understanding of the ion distributions that underlie these measurements is adequate, but that further understanding of the modeling of impedance spectroscopy data is required for quantitative agreement at larger applied electric potential differences.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On Space Charge and Spatial Distribution of Defects in Yttria-Stabilized Zirconia

Space charge in 8YSZ is examined theoretically. The Poisson-Boltzmann equation is solved by free energy minimization. The Helmholtz free energy of a crystal containing various defects is minimized subject to two constraints: The total dopant concentration is fixed and the maximum amount of surface charge is limited by site density. Large dopant concentration leads to defect concentrations which deviate from Boltzmann distribution. When free energy isminimized assuming all defects attain their equilibrium distributions, the corresponding electrochemical potentials are equilibrated through the crystal. These calculations correspond to long annealing times. Calculations are also conducted for a case in which only oxygen vacancies are allowed to equilibrate at lower temperature after a high temperature anneal. At lower temperatures, cations are frozen corresponding to high temperature anneal. In this case, only the electrochemical potential of oxygen vacancies equilibrates. In all cases Y segregates to grain boundaries/free surfaces lowering the corresponding oxygen vacancy concentration, consistent with reported effect of space charge on grain boundary conductivity. The results show a significant concentration of oxygen vacancies form defect complexes with Y dopant. Thus, free oxygen vacancy concentration is considerably lower than the usually assumed electroneutrality condition based on total dopant concentration.

36 MATERIALS SCIENCE↗

Modeling the Environment-Dependent Kinetics of Oxygen Reduction Reaction – a Continuum Model for Electric Double Layer

Here, for proton-exchange-membrane fuel cells (PEMFCs) to achieve broad commercialization, improved energy-conversion efficiency with minimal Pt-based electrocatalyst is required. Because the sluggish rate of oxygen reduction reaction (ORR) limits the efficiency of PEMFCs, the efficiency improvement requires a better understanding of ORR kinetics and mechanism to design better catalyst. To understand the ORR mechanism, theoretical and experimental analyses have been conducted. While previous studies reasonably explained the catalyst-dependent activity on single crystal catalysts in 0.1 M perchloric acid solution, the explicit effect of electrolyte and related microenvironments is not thoroughly understood. The change in the electrolyte alters the electric-double-layer (EDL) structure and thus the local microenvironment at the electrode/electrolyte interface. Thus, the structure of the EDL should be carefully analyzed to uncover the electrolyte-dependent reaction kinetics. In this talk, we propose a multiscale continuum model to predict the EDL structure and examine the effect of perchloric acid concentration on ORR activity on Pt (111). The model includes Density Potential Functional Theory (DPFT) for electron density and Modified Poisson Boltzmann equation for species’ density and electric potential. Also, the interaction between adsorbents and electric field is taken into account by minimizing the grand potential. After model validation with experimentally measured double-layer capacity data as a function of applied potential and concentration, the effect of the perchloric acid concentration (0.02 M – 0.2 M) on ORR activity is analyzed and discussed. It is shown that the model reproduces the specific activity obtained in the experiments when assuming the oxygen adsorption is limiting the rate, which can be attributed to the large energetic barrier for solvent reorganization. Then, extension of the model to PEMFC ionomer electrolytes will be introduced. Overall, the model framework and findings provide insights into the ORR mechanism and guidance on how to tailor catalyst materials for increased PEMFC performance.

30 DIRECT ENERGY CONVERSION↗

Monotonicity conditions in the nodal mimetic finite difference method for diffusion problems on quadrilateral meshes

A set of sufficient and necessary conditions for the local stiffness matrix of the nodal mimetic finite difference method on quadrilaterals is derived under which such matrix is a singular M-matrix. These conditions are directly related to the shape of the quadrilaterals and to the value of the off-diagonal elements and they are illustrated by the new concept, here introduced, of monotonicity region. When such conditions are satisfied, the global matrix for the Poisson problem with Dirichlet boundary conditions is a singular M-matrix. After setting the boundary condition, yields a monotone matrix operator and we prove that the final discretization possesses a Discrete Maximum Principle.

97 MATHEMATICS AND COMPUTING↗

Simulation of primary fuel atomization processes at subcritical pressures.

This report documents results from an LDRD project for the first-principles simulation of the early stages of spray formation (primary atomization). The first part describes a Cartesian embedded-wall method for the calculation of flow internal to a real injector in a fully coupled primary calculation. The second part describes the extension to an all-velocity formulation by introducing a momentum-conservative semi-Lagrangian advection and by adding a compressible term in the Poisson s equation. Accompanying the description of the new algorithms are verification tests for simple two-phase problems in the presence of a solid interface; a validation study for a scaled-up multi-hole Diesel injector; and demonstration calculations for the closing and opening transients of a single-hole injector and for the high-pressure injection of liquid fuel at supersonic velocity.

Arienti, Marco↗

Radiochemistry and the Study of Chemisorption

The triple layer model would benefit from a three dimensional solution to the Poisson-Boltzman equation. In general, the inner-sphere complex of metal ions appear to be proportional to the first hydrolysis constant of the metal ion. Different metal oxide surfaces can be treated as Lewis bases. The strength of the base is proportional to the second hydrolysis constant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Crystallization and Thermoelectric Transport in Semiconductor Micro- and Nanostructures Under Extreme Conditions

This project focused on thermoelectric transport in semiconductor micro and nanostructures where moderate and typical operating voltages and currents lead to extreme thermal gradients and current densities. Models that describe behavior of semiconducting materials typically assume an equilibrium condition or slight deviations from it. In these cases the generation-recombination processes are assumed to have reached a local equilibrium for a given temperature. Hence, free carrier concentrations and their mobilities, band-gap, thermal conductivity, thermoelectric properties, mobility of atoms and mechanical properties of the material, can be described as a function of temperature. In the case of PN junctions under electrical bias, carrier concentrations can change up to ~ 1020 cm-3 and a drift-diffusion approximation is typically used to obtain the carrier concentrations while assuming that the material properties do not change. In non-equilibrium conditions, the assumption that the material properties remain the same may not be valid. While the increased conduction-band electron concentration may not have a drastic effect on the material, large hole concentration is expected to soften the material as ‘a hole’ comes into existence as a broken bond in the lattice. As the hole density approaches 1022 cm-3, the number of bonds holding the lattice together is significantly reduced, making it easier to break additional bonds, reduce band-gap and inhibit phonon transport. As these holes move away from where they were generated, local properties are expected to deviate significantly from the equilibrium case. Hence, temperature alone is not sufficient to describe the behavior of the material. The behavior of the solid material close to a molten region (liquid-solid interfaces) is also expected to deviate from the equilibrium case as a function of hole injection rate, which can be drastically increased or decreased in the presence of an electric field. In the past years we have investigated the possible thermoelectric explanation of asymmetric melting of self-heated Si micro-structures using equilibrium materials’ properties that exist in the literature. We have analyzed the contribution of the electrons and the holes and identified the generation-transport-recombination of minority carriers (GTR) as the reason for an extreme change in the thermal profile in presence of strong generation and electric field. A more complete analysis required construction of models that capture the individual generation and recombination processes to understand the thermal profile as well as the possibility of electronic softening and non-equilibrium melting of the structure below melting temperature. The possibility of melting a material at a lower temperature breaks the correlation between the atomic mobility and the kinetic energy in the system for a given temperature and may allow alternative growth processes. This may also be the mechanism behind ‘amorphization-without-melting in layered structures heated with laser pulses’ that has been reported earlier. The conventional models for semiconductors are constructed for low temperature operation and their projections to higher temperatures do not yield reasonable carrier concentrations. Using these models, the free hole concentrations are calculated to be on the order of 1019 cm-3 at melting, which also do not correlate well with the latent heat of fusion. The melt is expected to correspond to broken bond concentrations on the order of the atomic density (~5x1022 cm-3 for Silicon). Hence, using conventional models the thermoelectric contribution expected from the GTR process is estimated to be much smaller than it likely is. Our work focused on improving the computational models and electrical characterization of materials and devices to better understand thermoelectric trabsport under extremen thermal gradients and current densities. Specifically, during this project, we have - Expanded our computational models to include self-consistent solution of Poisson charge equation (together with current and heat equations currently solved) for improved accuracy of role of bipolar conduction, - Developed a crystallization model incorporating experimentally determined nucleation rates and growth velocities to enable simulation of grain growth, growth-from-melt, filament formation and retention, - Performed high-temperature characterization of relevant materials (including metal contacts, interfacial and insulation layers); electrical and thermal conductivities, Seebeck coefficient, carrier mobility and concentration, - Performed High-speed device-level characterization of metastable amorphous and crystalline phases, crystallization and amorphization dynamics, melting and crystalline growth-from-melt, - Observed and characterized formation of microplasmas in electrically stressed ZnO nanoforests.

36 MATERIALS SCIENCE↗

On the fractional Laplacian of variable order

We present a novel definition of variable-order fractional Laplacian on R n based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n/2). We then discuss some properties of the fractional Poisson’s equation involving this operator and we compute the corresponding Green’s function, for which we provide some instructive examples for specific problems.

97 MATHEMATICS AND COMPUTING↗

Non-conformal interface-cohesive modeling with the shifted boundary method

The accurate simulation of boundary- and interface-dominated problems on complex geometries remains challenging when boundary- or interface-fitted meshes are difficult to generate, particularly for curved boundaries, polycrystalline microstructures, and dense interface networks. The Shifted Boundary Method (SBM) alleviates this meshing burden by shifting the enforcement of boundary conditions from the true boundary to a nearby surrogate boundary and recovering the effect of the true boundary through geometric correction terms, thereby enabling standard finite element spaces on non-boundary-fitted meshes. In this report, we develop a general shiftedboundary and shifted-interface framework within the open-source MOOSE framework. We first present a general SBM implementation for complex geometries on non-boundary-fitted meshes. We then adopt the Shifted Interface Method (SIM) for internal interfaces and develop a unified shifted-interface treatment in which the interface law is enforced on a surrogate interface and the effect of the true interface is recovered through shifted jumps, fluxes, and tractions. This perspective brings scalar thermal-contact and vector-valued cohesive-zone mechanics into a single framework, the latter realized as the Shifted Cohesive Zone Method (SCZM) and coupled with history-dependent constitutive models from NEML2. We further extend the MOOSE mesh infrastructure to support cohesive-zone calculations on distributed meshes. The framework is verified and demonstrated through three progressive studies: Poisson’s equation on a smoothed starshaped domain, a manufactured thermal-contact problem on a non-interface-fitted mesh, and a two-dimensional polycrystalline representative volume element combining crystal plasticity with cohesive grain-boundary interfaces. Across these studies, the shifted formulations reproduce boundary- and interface-fitted reference solutions with high fidelity, indicating that the proposed framework provides an accurate and efficient route to boundary- and interface-dominated simulations on arbitrary geometries without requiring fitted meshes.

Yang, Cheng-Hau↗