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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,747 records · Page 97
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DOE OSTI2015

A multi-technique analysis of deuterium trapping and near-surface precipitate growth in plasma-exposed tungsten

In this work, we examine how deuterium becomes trapped in plasma-exposed tungsten and forms near-surface platelet-shaped precipitates. How these bubbles nucleate and grow, as well as the amount of deuterium trapped within, is crucial for interpreting the experimental database. Here, we use a combined experimental/theoretical approach to provide further insight into the underlying physics. With the Tritium Plasma Experiment, we exposed a series of ITER-grade tungsten samples to high flux D plasmas (up to 1.5 × 10{sup 22 }m{sup −2} s{sup −1}) at temperatures ranging between 103 and 554 °C. Retention of deuterium trapped in the bulk, assessed through thermal desorption spectrometry, reached a maximum at 230 °C and diminished rapidly thereafter for T > 300 °C. Post-mortem examination of the surfaces revealed non-uniform growth of bubbles ranging in diameter between 1 and 10 μm over the surface with a clear correlation with grain boundaries. Electron back-scattering diffraction maps over a large area of the surface confirmed this dependence; grains containing bubbles were aligned with a preferred slip vector along the <111> directions. Focused ion beam profiles suggest that these bubbles nucleated as platelets at depths of 200 nm–1 μm beneath the surface and grew as a result of expansion of sub-surface cracks. To estimate the amount of deuterium trapped in these defects relative to other sites within the material, we applied a continuum-scale treatment of hydrogen isotope precipitation. In addition, we propose a straightforward model of near-surface platelet expansion that reproduces bubble sizes consistent with our measurements. For the tungsten microstructure considered here, we find that bubbles would only weakly affect migration of D into the material, perhaps explaining why deep trapping was observed in prior studies with plasma-exposed neutron-irradiated specimens. We foresee no insurmountable issues that would prevent the theoretical framework developed here from being extended to a broader range of systems where precipitation of insoluble gases in ion beam or plasma-exposed metals is of interest.

36 MATERIALS SCIENCE↗
DOE OSTI2015

On sulfur core level binding energies in thiol self-assembly and alternative adsorption sites: An experimental and theoretical study

Characteristic core level binding energies (CLBEs) are regularly used to infer the modes of molecular adsorption: orientation, organization, and dissociation processes. Here, we focus on a largely debated situation regarding CLBEs in the case of chalcogen atom bearing molecules. For a thiol, this concerns the case when the CLBE of a thiolate sulfur at an adsorption site can be interpreted alternatively as due to atomic adsorption of a S atom, resulting from dissociation. Results of an investigation of the characteristics of thiol self-assembled monolayers (SAMs) obtained by vacuum evaporative adsorption are presented along with core level binding energy calculations. Thiol ended SAMs of 1,4-benzenedimethanethiol (BDMT) obtained by evaporation on Au display an unconventional CLBE structure at about 161.25 eV, which is close to a known CLBE of a S atom on Au. Adsorption and CLBE calculations for sulfur atoms and BDMT molecules are reported and allow delineating trends as a function of chemisorption on hollow, bridge, and atop sites and including the presence of adatoms. These calculations suggest that the 161.25 eV peak is due to an alternative adsorption site, which could be associated to an atop configuration. Therefore, this may be an alternative interpretation, different from the one involving the adsorption of atomic sulfur resulting from the dissociation process of the S–C bond. Calculated differences in S(2p) CLBEs for free BDMT molecules, SH group sulfur on top of the SAM, and disulfide are also reported to clarify possible errors in assignments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Hyper-Rayleigh scattering in centrosymmetric systems

Hyper-Rayleigh scattering (HRS) is an incoherent mechanism for optical second harmonic generation. The frequency-doubled light that emerges from this mechanism is not emitted in a laser-like manner, in the forward direction; it is scattered in all directions. The underlying theory for this effect involves terms that are quadratic in the incident field and involves an even-order optical susceptibility (for a molecule, its associated hyperpolarizability). In consequence, HRS is often regarded as formally forbidden in centrosymmetric media. However, for the fundamental three-photon interaction, theory based on the standard electric dipole approximation, representable as E1{sup 3}, does not account for all experimental observations. The relevant results emerge upon extending the theory to include E1{sup 2}M1 and E1{sup 2}E2 contributions, incorporating one magnetic dipolar or electric quadrupolar interaction, respectively, to a consistent level of multipolar expansion. Both additional interactions require the deployment of higher orders in the multipole expansion, with the E1{sup 2}E2 interaction analogous in rank and parity to a four-wave susceptibility. To elicit the correct form of response from fluid or disordered media invites a tensor representation which does not oversimplify the molecular components, yet which can produce results to facilitate the interpretation of experimental observations. The detailed derivation in this work leads to results which are summarized for the following: perpendicular detection of polarization components both parallel and perpendicular to the pump radiation, leading to distinct polarization ratio results, as well as a reversal ratio for forward scattered circular polarizations. The results provide a route to handling data with direct physical interpretation, to enable the more sophisticated design of molecules with sought nonlinear optical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Sustained magnetization oscillations in polyaniline-Fe{sub 3}O{sub 4} nanocomposites

We report experiments with polyaniline-Fe{sub 3}O{sub 4} (PANI-Fe{sub 3}O{sub 4}) nanocomposites synthesized under several different conditions. With a reaction carried out at room temperature and assisted by intense ultra-violet (UV) irradiation, we observe sustained oscillations in the magnetization with a period of about 25 min. The oscillations are interpreted as the result of an oscillatory chemical reaction in which part of the Fe{sup +2} ions of magnetite, Fe{sub 3}O{sub 4}, are oxidized by the UV irradiation to form Fe{sup +3} so that a fraction of the magnetite content transforms into maghemite, γ-Fe{sub 2}O{sub 3}. Then, Fe{sup +3} ions at the nanoparticle surfaces are reduced and transformed back into Fe{sup +2}, when acting as an oxidizing agent for polyaniline in the polymerization process. Since maghemite has smaller magnetization than magnetite, the oscillating chemical reaction results in the oscillatory magnetization. The observations are interpreted with the Lotka-Volterra nonlinear coupled equations with parameters that can be adjusted to fit very well the experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Mode specific dynamics of the H{sub 2} + CH{sub 3} → H + CH{sub 4} reaction studied using quasi-classical trajectory and eight-dimensional quantum dynamics methods

An eight-dimensional quantum dynamical model is proposed and applied to the title reaction. The reaction probabilities and integral cross sections have been determined for both the ground and excited vibrational states of the two reactants. The results indicate that the H{sub 2} stretching and CH{sub 3} umbrella modes, along with the translational energy, strongly promote the reactivity, while the CH{sub 3} symmetric stretching mode has a negligible effect. The observed mode specificity is confirmed by full-dimensional quasi-classical trajectory calculations. The mode specificity can be interpreted by the recently proposed sudden vector projection model, which attributes the enhancement effects of the reactant modes to their strong couplings with the reaction coordinate at the transition state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Direct-drive inertial confinement fusion: A review

In this study, the direct-drive, laser-based approach to inertial confinement fusion (ICF) is reviewed from its inception following the demonstration of the first laser to its implementation on the present generation of high-power lasers. The review focuses on the evolution of scientific understanding gained from target-physics experiments in many areas, identifying problems that were demonstrated and the solutions implemented. The review starts with the basic understanding of laser–plasma interactions that was obtained before the declassification of laser-induced compression in the early 1970s and continues with the compression experiments using infrared lasers in the late 1970s that produced thermonuclear neutrons. The problem of suprathermal electrons and the target preheat that they caused, associated with the infrared laser wavelength, led to lasers being built after 1980 to operate at shorter wavelengths, especially 0.35 um—the third harmonic of the Nd:glass laser—and 0.248 um (the KrF gas laser). The main physics areas relevant to direct drive are reviewed. The primary absorption mechanism at short wavelengths is classical inverse bremsstrahlung. Nonuniformities imprinted on the target by laser irradiation have been addressed by the development of a number of beam-smoothing techniques and imprint-mitigation strategies. The effects of hydrodynamic instabilities are mitigated by a combination of imprint reduction and target designs that minimize the instability growth rates. Several coronal plasma physics processes are reviewed. The two-plasmon–decay instability, stimulated Brillouin scattering (together with cross-beam energy transfer), and (possibly) stimulated Raman scattering are identified as potential concerns, placing constraints on the laser intensities used in target designs, while other processes (self-focusing and filamentation, the parametric decay instability, and magnetic fields), once considered important, are now of lesser concern for mainline direct-drive target concepts. Filamentation is largely suppressed by beam smoothing. Thermal transport modeling, important to the interpretation of experiments and to target design, has been found to be non-local in nature. Advances in shock timing and equation-of-state measurements relevant to direct-drive ICF are reported. Room-temperature implosions have provided an increased understanding of the importance of stability and uniformity. The evolution of cryogenic implosion capabilities, leading to an extensive series carried out on the 60-beam OMEGA laser [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)], is reviewed together with major advances in cryogenic target formation. A polar-drive concept has been developed that will enable direct-drive–ignition experiments to be performed on the National Ignition Facility [C. A. Haynam et al., Appl. Opt. 46 (16), 3276 (2007)]. The advantages offered by the alternative approaches of fast ignition and shock ignition and the issues associated with these concepts are described. The lessons learned from target-physics and implosion experiments are taken into account in ignition and high-gain target designs for laser wavelengths of 1/3 μm and 1/4 μm. Substantial advances in direct-drive inertial fusion reactor concepts are reviewed. Overall, the progress in scientific understanding over the past five decades has been enormous, to the point that inertial fusion energy using direct drive shows significant promise as a future environmentally attractive energy source.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

In this paper, a consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics

We derive a coarse-grained description of the dynamics of a nanoparticle immersed in an isothermal simple fluid by performing a systematic coarse graining of the underlying microscopic dynamics. As coarse-grained or relevant variables, we select the position of the nanoparticle and the total mass and momentum density field of the fluid, which are locally conserved slow variables because they are defined to include the contribution of the nanoparticle. The theory of coarse graining based on the Zwanzing projection operator leads us to a system of stochastic ordinary differential equations that are closed in the relevant variables. We demonstrate that our discrete coarse-grained equations are consistent with a Petrov-Galerkin finite-element discretization of a system of formal stochastic partial differential equations which resemble previously used phenomenological models based on fluctuating hydrodynamics. Key to this connection between our “bottom-up” and previous “top-down” approaches is the use of the same dual orthogonal set of linear basis functions familiar from finite element methods (FEMs), both as a way to coarse-grain the microscopic degrees of freedom and as a way to discretize the equations of fluctuating hydrodynamics. Another key ingredient is the use of a “linear for spiky” weak approximation which replaces microscopic “fields” with a linear FE interpolant inside expectation values. For the irreversible or dissipative dynamics, we approximate the constrained Green-Kubo expressions for the dissipation coefficients with their equilibrium averages. Under suitable approximations, we obtain closed approximations of the coarse-grained dynamics in a manner which gives them a clear physical interpretation and provides explicit microscopic expressions for all of the coefficients appearing in the closure. Our work leads to a model for dilute nanocolloidal suspensions that can be simulated effectively using feasibly short molecular dynamics simulations as input to a FEM fluctuating hydrodynamic solver.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Effects of aspect ratio and concentration on rheology of epoxy suspensions containing model plate-like nanoparticles

Hexagonal 2-dimensional α-zirconium phosphate crystals were prepared with lateral diameters ranging from 110 nm to 1.5 μm to investigate the effect of particle size on suspension rheology. The nanoplatelets were exfoliated to individual sheets with monodisperse thickness and dispersed in a Newtonian epoxy fluid. The steady shear response of dilute and semi-dilute suspensions was measured and compared to expressions obtained from theory for infinitely dilute suspensions. For suspensions containing the smaller nanoplatelets, aspect ratio ∼160, the low shear rate viscosity and transition to shear thinning behavior were well described by theory for loadings up to 0.5 vol. %. The agreement was improved by assuming a moderate polydispersity in lateral diameter, ∼30%–50%, which is consistent with experimental observation. For the higher aspect ratio nanoplatelets, good agreement between theory and experiment was observed only at high shear rates. At lower shear rate, theory consistently over-predicted viscosity, which was attributed to a progressive shift to non-isotropic initial conditions with increasing particle size. The results suggest that at a fixed Peclet number, there is an increasing tendency for the nanoplatelets to form transient, local stacks as particle size increases. The largest particles, aspect ratio ∼2200, showed unusual shear thinning and thickening behaviors that were attributed to particle flexibility. The findings demonstrate the surprising utility of theory for infinitely dilute suspensions to interpret, and in some cases quantitatively describe, the non-Newtonian viscosity of real suspensions containing high aspect ratio plate-like particles. A simple framework is proposed to interpret deviations from ideal behavior based on the local and collective behavior of the suspended nanoplatelets.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Analyzing and sense making of human factors in the Malaysian radiation and nuclear emergency planning framework

The evolution of current Radiation and Nuclear Emergency Planning Framework (RANEPF) simulator emphasizes on the human factors to be analyzed and interpreted according to the stakeholder’s tacit and explicit knowledge. These human factor criteria are analyzed and interpreted according to the “sense making theory” and Disaster Emergency Response Management Information System (DERMIS) design premises. These criteria are corroborated by the statistical criteria. In recent findings, there were no differences of distributions among the stakeholders according to gender and organizational expertise. These criteria are incrementally accepted and agreed the research elements indicated in the respective emergency planning frameworks and simulator (i.e. 78.18 to 84.32, p-value <0.05). This paper suggested these human factors criteria in the associated analyses and theoretical perspectives to be further acomodated in the future simulator development. This development is in conjunction with the proposed hypothesis building of the process factors and responses diagram. We proposed that future work which implies the additional functionality of the simulator, as strategized, condensed and concise, comprehensive public disaster preparedness and intervention guidelines, to be a useful and efficient computer simulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Modeling thermionic emission from laser-heated nanoparticles

An adjusted form of thermionic emission is applied to calculate emitted current from laser-heated nanoparticles and to interpret time-resolved laser-induced incandescence (TR-LII) signals. This adjusted form of thermionic emission predicts significantly lower values of emitted current compared to the commonly used Richardson-Dushman equation, since the buildup of positive charge in a laser-heated nanoparticle increases the energy barrier for further emission of electrons. Thermionic emission influences the particle's energy balance equation, which can influence TR-LII signals. Additionally, reports suggest that thermionic emission can induce disintegration of nanoparticle aggregates when the electrostatic Coulomb repulsion energy between two positively charged primary particles is greater than the van der Waals bond energy. Furthermore, since the presence and size of aggregates strongly influences the particle's energy balance equation, using an appropriate form of thermionic emission to calculate emitted current may improve interpretation of TR-LII signals.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2016

An improved quasi-diabatic representation of the 1, 2, 3 1 A coupled adiabatic potential energy surfaces of phenol in the full 33 internal coordinates

In a previous project we constructed a quasi-diabatic representation, H d , of the 1, 2, 3 1 A adiabatic states of phenol from high level multireference single and double excitation configuration interaction electronic structure data, energies, energy gradients, and derivative couplings. That H d accurately describes surface minima, saddle points, and also regions of strong nonadiabatic interactions, reproducing the locus of conical intersection seams and the coordinate dependence of the derivative couplings. The present work determines the accuracy of H d for describing phenol photodissociation. Additionally, we demonstrate that a modest energetic shift of two diabats yields a quantifiably more accurate H d compared with experimental energetics. The analysis shows that in favorable circumstances it is possible to use single point energies obtained from the most reliable electronic structure methods available, including methods for which the energy gradients and derivative couplings are not available, to improve the quality of a global representation of several coupled potential energy surfaces. Our data indicate an alternative interpretation of kinetic energy release measurements near λ phot ~ 248 nm.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Evidence for monoclinic distortion in the ground state phase of underdoped La{sub 1.95}Sr{sub 0.05}CuO{sub 4}: A single crystal neutron diffraction study

The existing controversy about the symmetry of the crystal structure of the ground state of the critical doped La{sub 1.95}Sr{sub 0.05}CuO{sub 4} has been resolved by analyzing the single crystal neutron diffraction data collected between 5 and 730 K. We observed small but significant intensities for “forbidden” reflections given by extinction rules of the orthorhombic Bmab space group at low temperatures. A careful investigation of neutron diffraction data reveals that the crystal structure of La{sub 1.95}Sr{sub 0.05}CuO{sub 4} at 5 K is monoclinic with B2/m (2/m 1 1) space group. The monoclinic structure emerges from the orthorhombic structure in a continuous way; however, the structure is stable below ∼120 K which agrees with other observed phenomena. Our results on symmetry changes are crucial for the interpretation of physical properties also in other high temperature superconductors with similar structures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Sub- and super-Maxwellian evaporation of simple gases from liquid water

Non-Maxwellian evaporation of light atoms and molecules (particles) such as He and H{sub 2} from liquids has been observed experimentally. In this work, we use simulations to study systematically the evaporation of Lennard-Jones particles from liquid water. We find instances of sub- and super-Maxwellian evaporation, depending on the mass of the particle and the particle-water interaction strength. The observed trends are in qualitative agreement with experiment. We interpret these trends in terms of the potential of mean force and the effectiveness and frequency of collisions during the evaporation process. The angular distribution of evaporating particles is also analyzed, and it is shown that trends in the energy from velocity components tangential and normal to the liquid surface must be understood separately in order to interpret properly the angular distributions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Deformation of nanotubes in peeling contact with flat substrate: An in situ electron microscopy nanomechanical study

Peeling of one-dimensional (1D) nanostructures from flat substrates is an essential technique in studying their adhesion properties. The mechanical deformation of the nanostructure in the peeling experiment is critical to the understanding of the peeling process and the interpretation of the peeling measurements, but it is challenging to measure directly and quantitatively at the nanoscale. Here, we investigate the peeling deformation of a bundled carbon nanotube (CNT) fiber by using an in situ scanning electron microscopy nanomechanical peeling technique. A pre-calibrated atomic force microscopy cantilever is utilized as the peeling force sensor, and its back surface acts as the peeling contact substrate. The nanomechanical peeling scheme enables a quantitative characterization of the deformational behaviors of the CNT fiber in both positive and negative peeling configurations with sub-10 nm spatial and sub-nN force resolutions. Nonlinear continuum mechanics models and finite element simulations are employed to interpret the peeling measurements. The measurements and analysis reveal that the structural imperfections in the CNT fiber may have a substantial influence on its peeling deformations and the corresponding peeling forces. The research findings reported in this work are useful to the study of mechanical and adhesion properties of 1D nanostructures by using nanomechanical peeling techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Near infrared laser annealing of CdTe and in-situ measurement of the evolution of structural and optical properties

The high performance of polycrystalline CdTe thin film solar cells is enabled by annealing in the presence of Cl. This process is typically carried out for tens of minutes resulting in reduction of defect states within the bandgap among other beneficial effects. In this work, we investigate laser annealing as a means of rapidly annealing CdTe using a continuous wave sub-bandgap 1064 nm laser. The partial transmission of the beam allows us to monitor the annealing process in-situ and in real time. We find that optoelectronic and structural changes occur through two distinct kinetic processes resulting in the removal of deep defects and twinned regions, respectively. A multilayer optical model including surface roughness is used to interpret both the in-situ transmission as well as ex-situ reflectivity measurements. These experiments demonstrate beneficial material changes resulting from sub-bandgap laser-driven CdCl{sub 2} treatment of CdTe in minutes, which is an important step towards accelerating the processing of the CdTe absorber layer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Chemical speciation of U, Fe, and Pu in melt glass from nuclear weapons testing

Nuclear weapons testing generates large volumes of glassy materials that influence the transport of dispersed actinides in the environment and may carry information on the composition of the detonated device. We determine the oxidation state of U and Fe (which is known to buffer the oxidation state of actinide elements and to affect the redox state of groundwater) in samples of melt glass collected from three U.S. nuclear weapons tests. For selected samples, we also determine the coordination geometry of U and Fe, and we report the oxidation state of Pu from one melt glass sample. We find significant variations among the melt glass samples and, in particular, find a clear deviation in one sample from the expected buffering effect of Fe(II)/Fe(III) on the oxidation state of uranium. In the first direct measurement of Pu oxidation state in a nuclear test melt glass, we obtain a result consistent with existing literature that proposes Pu is primarily present as Pu(IV) in post-detonation material. In addition, our measurements imply that highly mobile U(VI) may be produced in significant quantities when melt glass is quenched rapidly following a nuclear detonation, though these products may remain immobile in the vitrified matrices. The observed differences in chemical state among the three samples show that redox conditions can vary dramatically across different nuclear test conditions. The local soil composition, associated device materials, and the rate of quenching are all likely to affect the final redox state of the glass. The resulting variations in glass chemistry are significant for understanding and interpreting debris chemistry and the later environmental mobility of dispersed material.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices

In this paper we propose versions of the associative Yang-Baxter equation and higher order R-matrix identities which can be applied to quantum dynamical R-matrices. As is known quantum non-dynamical R-matrices of Baxter-Belavin type satisfy this equation. Together with unitarity condition and skew-symmetry it provides the quantum Yang-Baxter equation and a set of identities useful for different applications in integrable systems. The dynamical R-matrices satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation between the dynamical and non-dynamical cases is described by the IRF (interaction-round-a-face)-Vertex transformation. An alternative approach to quantum (semi-)dynamical R-matrices and related quantum algebras was suggested by Arutyunov, Chekhov, and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The purpose of this paper is twofold. First, we prove that the ACF elliptic R-matrix satisfies the associative Yang-Baxter equation with shifted spectral parameters. Second, we directly prove a simple relation of the IRF-Vertex type between the Baxter-Belavin and the ACF elliptic R-matrices predicted previously by Avan and Rollet. It provides the higher order R-matrix identities and an explanation of the obtained equations through those for non-dynamical R-matrices. As a by-product we also get an interpretation of the intertwining transformation as matrix extension of scalar theta function likewise R-matrix is interpreted as matrix extension of the Kronecker function. Relations to the Gervais-Neveu-Felder equation and identities for the Felder’s elliptic R-matrix are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗