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DOE OSTI2010

Half-lives and branchings for {beta}-delayed neutron emission for neutron-rich Co-Cu isotopes in the r-process

The {beta} decays of very neutron-rich nuclides in the Co-Zn region were studied experimentally at the National Superconducting Cyclotron Laboratory using the NSCL {beta}-counting station in conjunction with the neutron detector NERO. We measured the branchings for {beta}-delayed neutron emission (P{sub n} values) for {sup 74}Co (18{+-}15%) and {sup 75-77}Ni (10{+-}2.8%, 14{+-}3.6%, and 30{+-}24%, respectively) for the first time, and remeasured the P{sub n} values of {sup 77-79}Cu, {sup 79,81}Zn, and {sup 82}Ga. For {sup 77-79}Cu and for {sup 81}Zn we obtain significantly larger P{sub n} values compared to previous work. While the new half-lives for the Ni isotopes from this experiment had been reported before, we present here in addition the first half-life measurements of {sup 75}Co (30{+-}11 ms) and {sup 80}Cu (170{sub -50}{sup +110} ms). Our results are compared with theoretical predictions, and their impact on various types of models for the astrophysical rapid neutron-capture process (r-process) is explored. We find that with our new data, the classical r-process model is better able to reproduce the A=78-80 abundance pattern inferred from the solar abundances. The new data also influence r-process models based on the neutrino-driven high-entropy winds in core collapse supernovae.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2011

Z{sup '} model for the CDF dijet anomaly

We adopt a bottom-up approach to constructing a new physics model to explain the CDF excess seen in dijets with an associated lepton and missing transverse energy. We find that the 145 GeV broad feature seen by CDF in the dijet invariant mass distribution can be explained by a Z{sup '} boson with a mass of 145 GeV that couples only to first generation quarks. After dijet resonance constraints are considered, a sizeable region of the parameter space favored by the CDF anomaly remains viable.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Hund Physics Landscape of Two-Orbital Systems

Motivated by the recent discovery of superconductivity in infinite-layer nickelates RE 1–δ Sr δ NiO 2 (RE = Nd, Pr), we study the role of Hund coupling J in a quarter-filled two-orbital Hubbard model, which has been on the periphery of the attention. Here, a region of negative effective Coulomb interaction of this model is revealed to be differentiated from three- and five-orbital models in their typical Hund metal active fillings. We identify distinctive regimes including four different correlated metals, one of which stems from the proximity to a Mott insulator, while the other three, which we call “intermediate” metal, weak Hund metal, and valence-skipping metal, from the effect of J being away from Mottness. Defining criteria characterizing these metals is suggested, establishing the existence of Hund metallicity in two-orbital systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2000

Thermodynamics of Aqueous Organic Sulfur Compounds: A Key to the Organic Geochemistry of Hydrothermal Systems?

Hydrothermal environments are locations of varied geochemistry due to the disequilibrium between vent fluids and seawater. The disequilibrium geochemistry has been hypothesized to include reactions to synthesize organic compounds. Observations of the organic geochemistry of hydrothermal vent sites has received little attention. Experimental simulations of these environments, however, indicate that organic compounds may have difficulty forming in a purely aqueous environment. On the other hand, thiols. thioesters and disulfides have been implicated as reaction intermediates between CO or CO2 in experiments of carbon reduction in hydrothermal environments as well as in a variety of biological processes and other abiotic reactions (Wachtershauser, 1990, OLEB 20, 173; Heinen and Lauwers, 1996, OLEB 26, 13 1, Huber and Wachtershauser, 1997, Science 276, 245; Russell et al., 1998, in Thermophiles: The keys to molecular evolution and the origin of life?). The reduction of CO2 to thiols, for example, is observed using the FeS-H2S/FeS2 couple to provide the reducing power (see Schoonen et al., 1999, OLEB 29, 5). In addition, the enzyme involved in final stage of methanogenesis, coenzyme-M, is itself a thiol. Thus, organic sulfur compounds may hold the key to the organic chemistry leading to the origin of life at high temperatures. Understanding the biochemical processes of microorganisms that can live to temperatures at least as high as 113 C (Blochl et al., 1996, Extremophiles 1, 14) requires knowledge of the properties of the chemical reactions involved. In order to assess the role of aqueous organic sulfur compounds in hydrothermal organic geochemistry, we have been attempting to determine their thermodynamic properties. We have culled the literature to obtain the properties of organic sulfur compounds. We are able to calculate a number of essential properties, such as free energies of formation, from solubility data available in the literature together with standard properties of organic sulfur gases. However, a number of the properties for aqueous organic sulfur compounds have not been experimentally determined. Furthermore, most of thermodynamic data that are available are for 25 C and 1 bar. In order to determine reaction properties to temperatures and pressures appropriate to the hydrothermal conditions in which thermophilic organisms actually live, we use equations of state developed by Helgeson and co-workers (Helgeson et al., 1981, AJS 281, 1249). A key piece of information needed to go up in temperature is the partial molal heat capacity, which is one of the properties for which experimental data are unavailable for nearly all organic sulfur compounds. We have used correlation methods to determine the partial molal heat capacities and volumes of many organic solutes. These estimates allow us to asses the role of organic sulfur compounds during the reduction of carbon in hydrothermal settings. We will present these data, along with examples of the thermodynamic properties of reactions involving aqueous organic sulfur compounds.

Schulte, Mitchell↗

DOE OSTI2011

Crystallographic and Nuclear Magnetic Resonance Evaluation of the Impact of Peptide Binding to the Second PDZ Domain of Protein Tyrosine Phosphatase 1E

PDZ (PSD95/Discs large/ZO-1) domains are ubiquitous protein interaction motifs found in scaffolding proteins involved in signal transduction. Despite the fact that many PDZ domains show a limited tendency to undergo structural change, the PDZ family has been associated with long-range communication and allostery. One of the PDZ domains studied most in terms of structure and biophysical properties is the second PDZ ('PDZ2') domain from protein tyrosine phosphatase 1E (PTP1E, also known as PTPL1). Previously, we showed through NMR relaxation studies that binding of the RA-GEF2 C-terminal peptide substrate results in long-range propagation of side-chain dynamic changes in human PDZ2 [Fuentes, E. J., et al. (2004) J. Mol. Biol. 335, 1105-1115]. Here, we present the first X-ray crystal structures of PDZ2 in the absence and presence of RA-GEF2 ligand, determined to resolutions of 1.65 and 1.3 {angstrom}, respectively. These structures deviate somewhat from previously determined NMR structures and indicate that very minor structural changes in PDZ2 accompany peptide binding. NMR residual dipolar couplings confirm the crystal structures to be accurate models of the time-averaged atomic coordinates of PDZ2. The impact on side-chain dynamics was further tested with a C-terminal peptide from APC, which showed results nearly identical to those of RA-GEF2. Thus, allosteric transmission in PDZ2 induced by peptide binding is conveyed purely and robustly by dynamics. {sup 15}N relaxation dispersion measurements did not detect appreciable populations of a kinetic structural intermediate. Collectively, for ligand binding to PDZ2, these data support a lock-and-key binding model from a structural perspective and an allosteric model from a dynamical perspective, which together suggest a complex energy landscape for functional transitions within the ensemble.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

The Use of Macrophytes as Biosorbents in Radioactive Liquid Waste Treatment - 18039

An important stage of the management of radioactive liquid waste is the chemical treatment. In the last few years, bio-sorption has attracted attention as one alternative method to remove radionuclides in liquid LL/ILW due to its efficiency and low costs. There are many biomasses that can be applied for this purpose, as agricultural residues and Macrophytes. This study aims at studying Macrophytes (Pistia Stratiotes, Limnobium Laevigatum, Lemna sp and Azolla sp) ability to absorb uranium in liquid solutions. The bio-sorption capacity of uranium by the Macrophytes was experimentally determined. The experiments determine the metal uptake after the solution was in contact with each bio-sorbents by inductively coupled plasma optical emission spectrometry (ICP-OES). The results show that these materials are potentially applicable in the treatment of liquid radioactive waste. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2019

Model-Data Fusion Approaches for Retrospective and Predictive Assessment of the Pan-Arctic Scale Permafrost Carbon Feedback to Global Climate

Policy decisions regarding climate change mitigation and adaptation rely on having reliable projections of future climate change. Coupled climate-carbon models predict that the northern high latitudes will serve as a substantial land carbon sink during the 21stcentury, but these models lack many of the key processes governing high-latitude ecosystem processes. Arctic tundra and boreal forests are unique from other biomes particularly because of the presence of snow, ice and frozen ground, and it is important to understand the mechanisms that drive interconnected processes in these landscapes. Increasing our confidence in climate projections requires an integrated approach where existing, on-going and planned observational and experimental studies of high-latitude ecosystem processes are organized and analyzed in a framework designed to target improvements in understanding key ecosystem-climate feedbacks. For this project we designed an approach to improve our scientific understanding of the permafrost carbon feedback through broad-scale assessment of the drivers and responses of the Arctic system carbon cycle using data-driven models of simple-to-intermediate complexity. The made a valuable contribution to the first of its kind, data-driven quantitative assessment of the impact of permafrost thaw on pan-Arctic scale carbon cycle feedbacks to the global climate system. The approach drew on a conceptual framework for integrating the key system components and their underlying data within a “book-keeping” framework for assessment of the key processes driving the permafrost carbon feedback. The results provided quantitative model-data benchmarking to constrain future projections of carbon cycle responses to a warming Arctic. The framework used environmental proxy data sets examining recent-era geomorphologic land-form transitions and vegetation dynamics, through remotely-sensed data, to guide the extrapolation of site-based data on the key system components to larger regions. These products contribute to the development of finer-scale, more complex representation of permafrost carbon processes in terrestrial biogeochemistry models, to operate within coupled Earth system modeling frameworks.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Advances in rapid compression machine studies of low- and intermediate-temperature autoignition phenomena

Rapid compression machines (RCMs) are widely-used to acquire experimental insights into fuel autoignition and pollutant formation chemistry, especially at conditions relevant to current and future combustion technologies. RCM studies emphasize important experimental regimes, characterized by low- to intermediate-temperatures (600–1200 K) and moderate to high pressures (5–80 bar). At these conditions, which are directly relevant to modern combustion schemes including low temperature combustion (LTC) for internal combustion engines and dry low emissions (DLE) for gas turbine engines, combustion chemistry exhibits complex and experimentally challenging behaviors such as the chemistry attributed to cool flame behavior and the negative temperature coefficient regime. Challenges for studying this regime include that experimental observations can be more sensitive to coupled physical-chemical processes leading to phenomena such as mixed deflagrative/autoignitive combustion. Experimental strategies which leverage the strengths of RCMs have been developed in recent years to make RCMs particularly well suited for elucidating LTC and DLE chemistry, as well as convolved physical-chemical processes. Specifically, this work presents a review of experimental and computational efforts applying RCMs to study autoignition phenomena, and the insights gained through these efforts. A brief history of RCM development is presented towards the steady improvement in design, characterization, instrumentation and data analysis. Novel experimental approaches and measurement techniques, coordinated with computational methods are described which have expanded the utility of RCMs beyond empirical studies of explosion limits to increasingly detailed understanding of autoignition chemistry and the role of physical-chemical interactions. Fundamental insight into the autoignition chemistry of specific fuels is described, demonstrating the extent of knowledge of low-temperature chemistry derived from RCM studies, from simple hydrocarbons to multi-component blends and full-boiling range fuels. In conclusion, emerging needs and further opportunities are suggested, including investigations of under-explored fuels and the implementation of increasingly higher fidelity diagnostics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

The Influence of Hydrocarbon and CO2 on the Reversibility of Li-O2 Chemistry Using In Situ Ambient Pressure X-ray Photoelectron Spectroscopy

Identifying fundamental barriers that hinder reversible lithium oxygen (Li O2) redox reaction is essential for developing efficient and long lasting rechargeable Li O2 batteries. Addressing these challenges is being limited by parasitic reactions in the carbon based O2 electrode with aprotic electrolytes. Understanding the mechanisms of these parasitic reactions is hampered by the complexity that multiple and coupled parasitic reactions involving carbon, electrolytes, and Li O2 reaction intermediates/products can occur simultaneously. In this work, we employed solid state cells free of carbon and aprotic electrolytes to probe the influence of surface adventitious hydrocarbons and carbon dioxide (CO2) on the reversibility of the Li O2 redox chemistry using in situ synchrotron based ambient pressure X ray photoelectron spectroscopy. Direct evidence was provided, for the first time, that surface hydrocarbons and CO2 irreversibly react with Li O2 reaction intermediates/ products such as Li2O2 and Li2O, forming carboxylate and carbonate based species, which cannot be removed fully upon recharge. The slower Li2O2 oxidation kinetics was correlated with increasing coverage of surface carbonate/ carboxylate species. Our work critically points out that materials design that mitigates the reactivity between Li O2 reaction products and common impurities in the atmosphere is needed to achieve long cycle life Li O2 batteries.

Lu, Yi-chun↗

DOE OSTI2025

A Flat Analyzer Polycapillary Spectrometer for X-ray Absorption Spectroscopy of Dilute Transition Metals at X-ray-Free Electron Lasers

X-ray absorption spectroscopy (XAS) coupled with highly intense pulses from an X-ray-free electron laser (XFEL) can be used to track ultrafast chemical dynamics. Nonetheless, measurements for dilute samples (≤1 mM) have been exceptionally challenging, as scattering background signals dominate over the sample’s X-ray fluorescence. We show that femtosecond time-resolved XAS measurements of sub-millimolar transition metal solutions are now possible at the Linac Coherent Light Source (LCLS) using a high-throughput polycapillary XAS spectrometer, designed, developed, and commissioned at LCLS and the Stanford Synchrotron Radiation Lightsource (SSRL). The instrument integrates three polycapillary optics that collect and collimate X-ray fluorescence emitted from the interaction point with a high solid angle. X-ray collimated fluorescence is then selectively diffracted by coupled graphite analyzer crystals. As a result, the contribution of scattered photons is suppressed. Experiments at the Pt L 3 -edge on 0.1 mM aqueous K 2 PtCl 6 (delivered via a 100 μm liquid jet) were successfully performed in the laser pump X-ray probe configuration at the LCLS XCS and XPP instruments. We report the transient spectra of hexachloroplatinate within the first 10 ps after a 266 nm photoexcitation. We observed a short-lived reduced intermediate (≈2 ps). The polycapillary X-ray spectrometer at LCLS now enables the efficient study of the dynamics of ultradilute transition metals in solution. This capability opens the door to investigating plasmonic systems, photocatalysts, enzymes, and other scarce and dilute samples.

LCLS↗

DOE OSTI2016

Mononuclear ruthenium polypyridine complexes that catalyze water oxidation

Over the past decade, significant advances have been made in the development of molecular water oxidation catalysts (WOCs) in the context of developing a system that would accomplish artificial photosynthesis. Mononuclear ruthenium complexes with polypyridine ligands have drawn considerable attention in this regard, due to their high catalytic activity and relatively simple structure. In this perspective review, we will discuss mononuclear Ru polypyridine WOCs by organizing them into four groups according to their ligand environments. Each group will be discussed with regard to three fundamental questions: first, how does the catalyst initiate O–O bond formation? Second, which step in the catalytic cycle is rate-determining? Third, how efficient is the catalyst according to the specific descriptors such as turnover frequency? All discussion is based on the high-valent ruthenium intermediates that are proposed in the catalytic cycle according to experimental observation and theoretical simulation. Two fundamental mechanisms are set forth. An acid–base mechanism that involves the attack of a water molecule on the oxo of a high valent Ru=O species to form the O–O bond. Subsequent steps lead to dissociation of O 2 and rehydration of the metal center. A second mechanism involves the formation of a Ru–O˙ radical species, two of which then couple to form a Ru–O–O–Ru species that can release O 2 afterwards. The acid–base mechanism appears to be more common and mechanistic differences could result from variation directly related to polypyridine ligand structures. Thus, understanding how electronic, steric, and conformational properties can effect catalyst performance will lead to the rational design of more effective WOCs with not only ruthenium but also other transition metals.

14 SOLAR ENERGY↗

DOE OSTI2010

Multistate electron transfer dynamics in the condensed phase: Exact calculations from the reduced hierarchy equations of motion approach

Multiple displaced oscillators coupled to an Ohmic heat bath are used to describe electron transfer (ET) in a dissipative environment. By performing a canonical transformation, the model is reduced to a multilevel system coupled to a heat bath with the Brownian spectral distribution. A reduced hierarchy equations of motion approach is introduced for numerically rigorous simulation of the dynamics of the three-level system with various oscillator configurations, for different nonadiabatic coupling strengths and damping rates, and at different temperatures. The time evolution of the reduced density matrix elements illustrates the interplay of coherences between the electronic and vibrational states. The ET reaction rates, defined as a flux-flux correlation function, are calculated using the linear response of the system to an external perturbation as a function of activation energy. The results exhibit an asymmetric inverted parabolic profile in a small activation regime due to the presence of the intermediate state between the reactant and product states and a slowly decaying profile in a large activation energy regime, which arises from the quantum coherent transitions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators

We describe a general framework based on modal expansion for the study of optical-frequency combs generated with monolithic whispering-gallery-mode resonators. We obtain a set of time-domain rate equations describing the dynamics of each mode as a function of the main characteristics of the cavity, namely, Kerr nonlinearity, absorption, coupling losses, and cavity dispersion (geometrical and material). A stability analysis of the various side modes is performed, which finds analytically the threshold power needed for comb generation. We show that the various whispering gallery modes are excited in a nontrivial way, strongly dependent on the value of the overall cavity dispersion. We demonstrate that the combs are not simply generated through a direct transfer of energy from the pumped mode to all their neighbors but rather through complex intermediate interactions. Anomalous cavity dispersion is also demonstrated to be critical for these cascading processes, and comb generation is thereby unambiguously linked to modulational instability. This theory accurately describes the emergence of spectral modulation and free spectral-range tunability in the comb. It also enables a clear understanding of the various phenomena responsible for the spectral span limitation. Our theoretical predictions are in excellent agreement with the numerical simulations, and they successfully explain the internal mechanisms responsible for the generation of hundreds of Kerr modes in monolithic whispering-gallery-mode resonators.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Electromagnetic Response of Superconducting RF Cavities

Recently reported anomalies in frequency shift of order δƒ ~ 0.1–10 kHz for Niobium SRF cavities in a narrow temperature region near T c ≃ 9 K are sensitive to the surface preparation and Nitrogen doping. We developed methods for calculating the surface current response of Nb SRF cavities, as well as the resonant frequency shift and quality factor, as functions of temperature, frequency and disorder based on the Keldysh formulation of the theory for nonequilibrium superconductivity coupled with Maxwell’s theory and boundary conditions for the response functions and electromagnetic field. We show that the anomaly is sensitive to impurity disorder. Our results for the anomaly in the frequency shift are in good agreement with experimental results for Nb with an anisotropic gap on the Fermi surface and inhomogeneous non-magnetic disorder. We also show that the quality factor as a function of the impurity scattering rate is maximum for in SRF cavities with intermediate disorder, ℏ/τΔ~O(1) with the maximum $Q$ decreasing with increasing frequency.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2012

The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making use of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Secondary organic aerosol formation from ambient air in an oxidation flow reactor in central Amazonia

Abstract. Secondary organic aerosol (SOA) formation from ambient air was studied using an oxidation flow reactor (OFR) coupled to an aerosol mass spectrometer (AMS) during both the wet and dry seasons at the Observations and Modeling of the Green Ocean Amazon (GoAmazon2014/5) field campaign. Measurements were made at two sites downwind of the city of Manaus, Brazil. Ambient air was oxidized in the OFR using variable concentrations of either OH or O3, over ranges from hours to days (O3) or weeks (OH) of equivalent atmospheric aging. The amount of SOA formed in the OFR ranged from 0 to as much as 10 µg m−3, depending on the amount of SOA precursor gases in ambient air. Typically, more SOA was formed during nighttime than daytime, and more from OH than from O3 oxidation. SOA yields of individual organic precursors under OFR conditions were measured by standard addition into ambient air and were confirmed to be consistent with published environmental chamber-derived SOA yields. Positive matrix factorization of organic aerosol (OA) after OH oxidation showed formation of typical oxidized OA factors and a loss of primary OA factors as OH aging increased. After OH oxidation in the OFR, the hygroscopicity of the OA increased with increasing elemental O:C up to O:C∼1.0, and then decreased as O:C increased further. Possible reasons for this decrease are discussed. The measured SOA formation was compared to the amount predicted from the concentrations of measured ambient SOA precursors and their SOA yields. While measured ambient precursors were sufficient to explain the amount of SOA formed from O3, they could only explain 10–50 % of the SOA formed from OH. This is consistent with previous OFR studies, which showed that typically unmeasured semivolatile and intermediate volatility gases (that tend to lack C=C bonds) are present in ambient air and can explain such additional SOA formation. To investigate the sources of the unmeasured SOA-forming gases during this campaign, multilinear regression analysis was performed between measured SOA formation and the concentration of gas-phase tracers representing different precursor sources. The majority of SOA-forming gases present during both seasons were of biogenic origin. Urban sources also contributed substantially in both seasons, while biomass burning sources were more important during the dry season. This study enables a better understanding of SOA formation in environments with diverse emission sources.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2013

Effective field theory: A modern approach to anomalous couplings

We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons. -- Highlights: •We discuss the advantages of effective field theories compared to anomalous couplings. •We show that one need not be concerned with unitarity violation at high energy. •We discuss the application of effective field theory to weak boson physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2010

Controlling phase separation of binary Bose-Einstein condensates via mixed-spin-channel Feshbach resonance

We investigate controlled phase separation of a binary Bose-Einstein condensate in the proximity of a mixed-spin-channel Feshbach resonance in the |F=1,m{sub F}=+1> and |F=2,m{sub F}=-1> states of {sup 87}Rb at a magnetic field of 9.10 G. Phase separation occurs on the lower-magnetic-field side of the Feshbach resonance while the two components overlap on the higher-magnetic-field side. The Feshbach resonance curve of the scattering length is obtained from the shape of the atomic cloud by comparison with the numerical analysis of coupled Gross-Pitaevskii equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗