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At least 289 records · Page 16

Explicitly correlated Gaussian calculations of the {sup 2}P{sup o} Rydberg spectrum of the lithium atom

Accurate quantum-mechanical nonrelativistic variational calculations are performed for the nine lowest members of the {sup 2}P{sup o} Rydberg series (1s{sup 2}np{sup 1}, n= 2, ..., 10) of the lithium atom. The effect of the finite nuclear mass is included in the calculations allowing for determining the isotopic shifts of the energy levels. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are variationally optimized with the aid of the analytical energy gradient determined with respect to those parameters. The calculated state energies are compared with the available experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Temperature dependent electrical transport characteristics of BaTiO{sub 3} modified lithium borate glasses

The glass samples with composition (70B{sub 2}O{sub 3}-29Li{sub 2}O-1Dy{sub 2}O{sub 3})-xBT; x = 0, 10 and 20 weight percent, have been prepared by conventional melt quench technique. The dielectric measurements as a function of temperature have been carried out on these samples in the frequency range 1 Hz-10 MHz. The dielectric relaxation characteristics of these samples have been studied by analyzing dielectric spectroscopy, dielectric loss, electric modulus formulation and electrical conductivity spectroscopy. It is found that the dielectric permittivity of the samples increases with an increase in the temperature and BT content. The frequency dependent ac conductivity has been analyzed using Jonscher’s universal power law whereas non exponential KWW function has been invoked to fit the experimental data of the imaginary part of the electric modulus. The values of the activation energy determined from the electric modulus and that from dc conductivity have been found to be quite close to each other suggesting that the same type of charge barriers are involved in the relaxation and the conduction mechanisms. The stretched exponent (β) and the power exponent (n) have been found to be temperature and composition dependent. The decrease in n with an increase in temperature further suggested that the ac conduction mechanism of the studied samples follows the correlated barrier hopping (CBH) model.

36 MATERIALS SCIENCE↗

Correlation function study for sea ice

For active and passive microwave remote sensing of sea ice, a correlation function of exponential form is extracted from the photograph of a horizontal thin section taken from a sample of artificially grown saline ice that closely resembled Arctic congelation sea ice. It is found that the extracted correlation lengths are consistent with the published average size of brine pockets. With the application of strong fluctuation theory and the bilocal approximation, the effective permittivity tensor is derived in the low-frequency limit for an unbounded uniaxial random medium with two-phase mixtures. Using the extracted correlation lengths, the effective permittivity tensor is computed as a function of fractional volume of brine inclusions and compared with in situ measurements at 4.8 and 9.5 GHz.

Lin, F. C.↗

On the high Mach number shock structure singularity caused by overreach of Maxwellian molecules

The high Mach number shock structure singularity arising in moment equations of the Boltzmann equation was investigated. The source of the singularity is shown to be the unbalanced treatment between two high order kinematic and dissipation terms caused by the overreach of Maxwellian molecule assumption. In compressive gaseous flow, the high order stress-strain coupling term of quadratic nature will grow far faster than the strain term, resulting in an imbalance with the linear dissipation term and eventually a blow-up singularity in high thermal nonequilibrium. On the other hand, the singularity arising from unbalanced treatment does not occur in the case of velocity shear and expansion flows, since the high order effects are cancelled under the constraint of the free-molecular asymptotic behavior. As an alternative method to achieve the balanced treatment, Eu's generalized hydrodynamics, consistent with the second law of thermodynamics, was revisited. After introducing the canonical distribution function in exponential form and applying the cumulant expansion to the explicit calculation of the dissipation term, a natural platform suitable for the balanced treatment was derived. The resulting constitutive equation with the nonlinear factor was then shown to be well-posed for all regimes, effectively removing the high Mach number shock structure singularity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spiking Neurons for Analysis of Patterns

Artificial neural networks comprising spiking neurons of a novel type have been conceived as improved pattern-analysis and pattern-recognition computational systems. These neurons are represented by a mathematical model denoted the state-variable model (SVM), which among other things, exploits a computational parallelism inherent in spiking-neuron geometry. Networks of SVM neurons offer advantages of speed and computational efficiency, relative to traditional artificial neural networks. The SVM also overcomes some of the limitations of prior spiking-neuron models. There are numerous potential pattern-recognition, tracking, and data-reduction (data preprocessing) applications for these SVM neural networks on Earth and in exploration of remote planets. Spiking neurons imitate biological neurons more closely than do the neurons of traditional artificial neural networks. A spiking neuron includes a central cell body (soma) surrounded by a tree-like interconnection network (dendrites). Spiking neurons are so named because they generate trains of output pulses (spikes) in response to inputs received from sensors or from other neurons. They gain their speed advantage over traditional neural networks by using the timing of individual spikes for computation, whereas traditional artificial neurons use averages of activity levels over time. Moreover, spiking neurons use the delays inherent in dendritic processing in order to efficiently encode the information content of incoming signals. Because traditional artificial neurons fail to capture this encoding, they have less processing capability, and so it is necessary to use more gates when implementing traditional artificial neurons in electronic circuitry. Such higher-order functions as dynamic tasking are effected by use of pools (collections) of spiking neurons interconnected by spike-transmitting fibers. The SVM includes adaptive thresholds and submodels of transport of ions (in imitation of such transport in biological neurons). These features enable the neurons to adapt their responses to high-rate inputs from sensors, and to adapt their firing thresholds to mitigate noise or effects of potential sensor failure. The mathematical derivation of the SVM starts from a prior model, known in the art as the point soma model, which captures all of the salient properties of neuronal response while keeping the computational cost low. The point-soma latency time is modified to be an exponentially decaying function of the strength of the applied potential. Choosing computational efficiency over biological fidelity, the dendrites surrounding a neuron are represented by simplified compartmental submodels and there are no dendritic spines. Updates to the dendritic potential, calcium-ion concentrations and conductances, and potassium-ion conductances are done by use of equations similar to those of the point soma. Diffusion processes in dendrites are modeled by averaging among nearest-neighbor compartments. Inputs to each of the dendritic compartments come from sensors. Alternatively or in addition, when an affected neuron is part of a pool, inputs can come from other spiking neurons. At present, SVM neural networks are implemented by computational simulation, using algorithms that encode the SVM and its submodels. However, it should be possible to implement these neural networks in hardware: The differential equations for the dendritic and cellular processes in the SVM model of spiking neurons map to equivalent circuits that can be implemented directly in analog very-large-scale integrated (VLSI) circuits.

Huntsberger, Terrance↗

The Area Coverage of Geophysical Fields as a Function of Sensor Field-of View

In many remote sensing studies of geophysical fields such as clouds, land cover, or sea ice characteristics, the fractional area coverage of the field in an image is estimated as the proportion of pixels that have the characteristic of interest (i.e., are part of the field) as determined by some thresholding operation. The effect of sensor field-of-view on this estimate is examined by modeling the unknown distribution of subpixel area fraction with the beta distribution, whose two parameters depend upon the true fractional area coverage, the pixel size, and the spatial structure of the geophysical field. Since it is often not possible to relate digital number, reflectance, or temperature to subpixel area fraction, the statistical models described are used to determine the effect of pixel size and thresholding operations on the estimate of area fraction for hypothetical geophysical fields. Examples are given for simulated cumuliform clouds and linear openings in sea ice, whose spatial structures are described by an exponential autocovariance function. It is shown that the rate and direction of change in total area fraction with changing pixel size depends on the true area fraction, the spatial structure, and the thresholding operation used.

Key, Jeffrey R.↗

Predator prey oscillations in a simple cascade model of drift wave turbulence

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separation for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dirichlet-type absorbing boundary conditions for peridynamic scalar waves in two-dimensional viscous media

Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave-type problems in viscous media. The proposed ABCs are constructed in the time and space domains and are of Dirichlet type. Consequently, their implementation is relatively simple, since no derivatives of the wave field are required. The proposed ABCs are derived at the continuum level, from a semi-analytical solution of the exterior domain using harmonic exponential basis functions in space and time (plane-wave modes). The numerical implementation is done using a meshfree collocation approach employed within a boundary layer adjacent to the interior domain boundary. The modes satisfy the peridynamic numerical dispersion relation, resulting in a compatible solution of the interior region (near-field) with that of the exterior region (far-field). The accuracy and stability of the proposed ABCs are demonstrated with several numerical examples in two-dimensional unbounded domains.

42 ENGINEERING↗

Efficiency and Risk of Investments in Nuclear Power

It is shown that together with the reduced cost of electricity it is also necessary to examine other efficiency criteria for investments in NPP – the internal profitability norm and the discounted payback time of investments – and their impact on the primary profitability criterion of an NPP project – the pure discounted income. The analytical interconnection of the pure discounted income, internal profitability norm of a project, and the discounted payback time of investments, which is obtained using an exponential discounting function for the expected cash flows, is shown. The requirements of the engineering and economic parameters of NPP that make NPP competitive on the world market are formulated from an analysis of the interrelation of investment efficiency criteria. The NPP investment risk evaluated by the Monte Carlo method with prescribed uncertainty of prediction of cash flows during construction and operation of NPP is presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Electrical cable utilization for wave energy converters

Here, this paper investigates the suitability of sizing the electrical export cable based on the rating of the contributing WECs within a farm. These investigations have produced a new methodology to evaluate the probabilities associated with peak power values on an annual basis. It has been shown that the peaks in pneumatic power production will follow an exponential probability function for a linear model. A methodology to combine all the individual probability functions into an annual view has been demonstrated on pneumatic power production by a Backward Bent Duct Buoy (BBDB). These investigations have also resulted in a highly simplified and perfunctory model of installed cable cost as a function of voltage and conductor cross-section. This work solidifies the need to determine electrical export cable rating based on expected energy delivery as opposed to device rating as small decreases in energy delivery can result in cost savings.

16 TIDAL AND WAVE POWER↗

Relativistic Lagrangians for the Lorentz–Dirac equation

We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An optical-input Maximum Likelihood Estimation feedback system demonstrated on tokamak horizontal equilibrium control

A readily parallelized Maximum Likelihood Estimation (MLE) algorithm with linear computational complexity is demonstrated in real time using only measurements from an extreme ultraviolet (EUV) diagnostic to control the horizontal position of a tokamak plasma. A set of trial emissivity profiles are parameterized by the control quantity of interest (R m ), and the MLE is identified from the profile which minimizes the signal reconstruction residual. The algorithm depends on an empirically determined likelihood function with exponential form. EUV emission (λ ≈ 15eV-1keV) is captured in a poloidal plane by four 16-channel AXUV diodes mounted at different poloidal angles with radial and angular resolution sufficient to discern plasma equilibrium evolution in HBT-EP. Calculations of the plasma major radius by the system are consistent within diagnostic uncertainty for the majority of the discharge with those of: a weighted average of vertical soft X-ray or EUV chords, magnetic sensors, and an equilibrium reconstruction. The feedback system corrects for a horizontal displacement of the major radius equal to 20% of the plasma minor radius by adjusting the vertical field produced from 40 in-vessel control coils in real time. The MLE calculation is performed on a GPU in a 15 μs cycle, with similar performance in this application to a simple weighted average of vertical chords. Finally, results demonstrate horizontal position control using magnetic actuators and an optical observer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Using SWMM for emergency response planning: A case study evaluating biological agent transport under various rainfall scenarios and urban surfaces

To assist in emergency preparedness for a biological agent terrorist attack or accidental pathogen release, potential contaminant levels and migration pathways of spores spread by urban stormwater were evaluated using a Storm Water Management Model (SWMM) of U.S. Coast Guard Base Elizabeth City, North Carolina. The high temporal-spatial resolution SWMM model was built using spore concentrations in stormwater runoff from asphalt, grass, and concrete collected from a point-scale field study. The subsequent modeled contamination scenarios included a notional plume release and point releases mimicking the field study under three rainfall conditions. The rainfall scenarios included a 6-hour natural rainfall event on Dec. 8, 2021 and two design storms (2-year and 100-year events). The observed spore concentrations from asphalt and concrete from the actual field experiment were applied to calibrate the washoff parameters in the SWMM model, using an exponential washoff function. The calibrated washoff coefficient (c 1 ) and exponent (c 2 ) were 0.01 and 1.00 for asphalt, 0.05 and 1.45 for grass, and 2.45 and 1.00 for concrete, respectively. The calibrated SWMM model simulated spore concentrations in runoff at times and magnitudes similar to the field study data. In the point release modeled scenario, the concrete surface generated 55.6% higher average spore concentrations than asphalt. Similarly, in the field experiment, a 175% (p < 0.05) higher average spore concentration in surface runoff was observed from concrete than from asphalt. Here, this study demonstrates how SWMM may be used to evaluate spore washoff from urban surfaces under different precipitation amounts, intensities, and durations, and how visualized spatial migration pathways in stormwater runoff may be used for emergency planning and remediation.

54 ENVIRONMENTAL SCIENCES↗

Measurement of free chlorine levels in water using potentiometric responses of biofilms and applications for monitoring and managing the quality of potable water

We report residual free chlorine is not monitored continuously at scale in drinking water distribution systems because existing real-time sensor technologies require frequent maintenance, cleaning, and calibration, which makes these products too costly to be used throughout a distribution system. As a result, current measurement approaches require manual sampling, which is not feasible for the consistent monitoring of free chlorine because chlorine concentrations vary significantly throughout pipeline distribution and over time and space. This research presents an alternative and cost-effective method of predicting free chlorine levels in drinking water using graphite electrodes coated with naturally grown microbial biofilms. This Microbial Potentiometric Sensor (MPS) array was installed in a Continuously Mixed Batch Reactor (CMBR), and drinking water containing variable free chlorine concentrations. The chlorine concentrations were introduced in a controlled manner, and the MPS signals were monitored over time. MPS signals were measured from the change in Open Circuit Potential (OCP) across the MPS array in real-time. An empirically derived relationship between the normalized change in OCP and free chlorine was established by fitting individual and average MPS data to a decaying exponential growth function in order to predict free chlorine levels. The results show that free chlorine can be predicted with reasonable accuracy, with model validation showing an average absolute error of ±0.09 ppm below 1.1 ppm and ±0.30 ppm between 1.1 and 2.7 ppm. However, the accuracy of predictions was reduced at higher free chlorine levels. The researchers conclude that MPS systems may benefit drinking water distribution systems by measuring free chlorine. These advantages of the MPS are especially pronounced in the developing world because this system is inexpensive and does not require routine maintenance or cleaning. The system relies on a naturally forming and regenerating biofilm and an inexpensive potentiometric meter to produce stable measurements.

54 ENVIRONMENTAL SCIENCES↗

Parameter estimation for models of ligninolytic and cellulolytic enzyme kinetics

While soil enzymes have been explicitly included in the soil organic carbon (SOC) decomposition models, there is a serious lack of suitable data for model parameterization. This study provides well-documented enzymatic parameters for application in enzyme-driven SOC decomposition models from a compilation and analysis of published measurements. In particular, we developed appropriate kinetic parameters for five typical ligninolytic and cellulolytic enzymes ( -glucosidase, cellobiohydrolase, endo-glucanase, peroxidase, and phenol oxidase). The kinetic parameters included the maximum specific enzyme activity (Vmax) and half-saturation constant (Km) in the Michaelis-Menten equation. The activation energy (Ea) and the pH optimum and sensitivity (pHopt and pHsen) were also analyzed. pHsen was estimated by fitting an exponential-quadratic function. The Vmax values, often presented in different units under various measurement conditions, were converted into the same units at a reference temperature (20 C) and pHopt. Major conclusions are: (i) Both Vmax and Km were log-normal distributed, with no significant difference in Vmax exhibited between enzymes originating from bacteria or fungi. (ii) No significant difference in Vmax was found between cellulases and ligninases; however, there was significant difference in Km between them. (iii) Ligninases had higher Ea values and lower pHopt than cellulases; average ratio of pHsen to pHopt ranged 0.3 0.4 for the five enzymes, which means that an increase or decrease of 1.1 1.7 pH units from pHopt would reduce Vmax by 50%. (iv) Our analysis indicated that the Vmax values from lab measurements with purified enzymes were 1 2 orders of magnitude higher than those for use in SOC decomposition models under field conditions.

54 ENVIRONMENTAL SCIENCES↗

Vapor-Phase Intercalation of Cesium into Black Phosphorous

Cesium vapors were charged into black phosphorous (BP) flakes at varied times and at a temperature gradient of 150 °C. The X-ray diffraction (XRD) measurements of these samples suggest a reduction in the strength of van der Waal interactions between BP layers leading to the loss of coherence of out-of-plane peaks. At the same time, the three main Raman modes of BP (A g 1 , B 2 g , and A g 2 ) steadily redshifted as exposure times were increased, with modes B 2 g and A g 2 shifting faster than A g 1 . After initial rapid downshifts of active BP phonon modes, this intercalation strategy showed its limits following prolonged exposure times. Saturation of BP flakes by Cs vapors ensued and the kinetics was fitted with an exponential decay function. Furthermore, the thermoelectric power (TEP) of cesiated BP exhibited an inversion in sign from positive to negative around 400 K, lending credence to the transformation of as-prepared BP which is a p-type semiconductor to an n-type equivalent due to Cs atom intercalation driven shifting of the Fermi level toward the conduction band of BP and the donation of electrons from Cs. Furthermore, density functional theory (DFT) calculations were used to delve deeper into understanding Cs intercalation on the structural evolution of BP.

36 MATERIALS SCIENCE↗

Forced Crowding of Colloids by Thermophoresis and Convection in a Custom Liquid Clusius–Dickel Microdevice

Here, we report a study demonstrating that simultaneous induction of a steady-state convection current and temperature gradient in a confined geometry can be an effective way to force crowding of dissolved particulates. To investigate this thermogravitationally driven concentration of particles in-situ, we developed a micro-device capable of sustaining controlled transverse temperature gradients within a 5 cm long, 0.1 mm inner diameter capillary that allowed visualization of particle movement with standard optical microscopy. Experiments were conducted on two material systems representative of nano-scale small molecules and micro-scale particles. With the small molecules (aromatic dyes, 530-790 g/mol, 1-1.5 nm) thermophoretic and gravitational effects in the micro-device resulted in an asymmetrical 2x concentration change along the capillary height over 3 days. In contrast, the concentration change under similar conditions for 40-micron diameter latex colloids is 50-fold in 30 minutes. This dramatic difference in separation times is consistent with simulations and models of thermophoresis where the thermophoretic effect scales with particle size. Induced crowding of particulates leads to formation of accumulation and depletion zones in at the bottom and top of the capillary respectively. Both the concentration of dye molecules over time in the depletion zone and spatial distribution of colloids over the entire capillary length were found to be good fits to simple first-order exponential decay functions. Furthermore, these results suggest potential applications of thermogravitational separation in developing new functional materials via thermophoretic and convective effects.

36 MATERIALS SCIENCE↗