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At least 649 records · Page 36

Multi-frequency klystron designed for high efficiency

A multi-frequency klystron has an electron gun which generates a beam, a circuit of bunch-align-collect (BAC) tuned cavities that bunch the beam and amplify an RF signal, a collector where the beam is collected and dumped, and a standard output cavity and waveguide coupled to a window to output RF power at a fundamental mode to an external load. In addition, the klystron has additional bunch-align-collect (BAC) cavities tuned to a higher harmonic frequency, and a harmonic output cavity and waveguide coupled via a window to an additional external load.

47 OTHER INSTRUMENTATION↗

Measurements of the E-mode polarization and temperature-E-mode correlation of the CMB from SPT-3G 2018 data

We present measurements of the E -mode ( E E ) polarization power spectrum and temperature- E -mode ( T E ) cross-power spectrum of the cosmic microwave background using data collected by SPT-3G, the latest instrument installed on the South Pole Telescope. This analysis uses observations of a 1500 deg 2 region at 95, 150, and 220 GHz taken over a four-month period in 2018. We report binned values of the E E and T E power spectra over the angular multipole range 300 ≤ ℓ < 3000 , using the multifrequency data to construct six semi-independent estimates of each power spectrum and their minimum-variance combination. These measurements improve upon the previous results of SPTpol across the multipole ranges 300 ≤ ℓ ≤ 1400 for E E and 300 ≤ ℓ ≤ 1700 for T E , resulting in constraints on cosmological parameters comparable to those from other current leading ground-based experiments. We find that the SPT-3G data set is well fit by a Λ CDM cosmological model with parameter constraints consistent with those from Planck and SPTpol data. From SPT-3G data alone, we find H 0 = 68.8 ± 1.5 km s - 1 Mpc - 1 and σ 8 = 0.789 ± 0.016 , with a gravitational lensing amplitude consistent with the Λ CDM prediction ( A L = 0.98 ± 0.12 ). We combine the SPT-3G and the Planck data sets and obtain joint constraints on the Λ CDM model. The volume of the 68% confidence region in six-dimensional Λ CDM parameter space is reduced by a factor of 1.5 compared to Planck-only constraints, with no significant shifts in central values. We note that the results presented here are obtained from data collected during just half of a typical observing season with only part of the focal plane operable, and that the active detector count has since nearly doubled for observations made with SPT-3G after 2018.

79 ASTRONOMY AND ASTROPHYSICS↗

Ionization Collection in Detectors of the Cryogenic Dark Matter Search

Determining the composition of dark matter is at the forefront of modern scientific research. There is compelling evidence for the existence of vast quantities of dark matter throughout the universe, however it has so-far eluded all direct detection efforts and its identity remains a mystery. Weakly interacting massive particles (WIMPs) are a favored dark matter candidate and have been the primary focus of direct detection for several decades. The Cryogenic Dark Matter Search (CDMS) has developed the Z-dependent Ionization and Phonon (ZIP) detector to search for such particles. Typically made from germanium, these detectors are capable of distinguishing between electromagnetic background and a putative WIMP signal through the simultaneous measurement of ionization and phonons produced by scattering events. CDMS has operated several arrays of these detectors at the Soudan Underground Laboratory (Soudan, MN, USA) resulting in many competitive (often world-leading) WIMP exclusion limits. This dissertation focuses on ionization collection in these detectors under the sub-Kelvin, low electric field, and high crystal purity conditions unique to CDMS. The design and performance of a fully cryogenic HEMT-based amplifier capable of achieving the SuperCDMS SNOLAB ionization energy resolution goal of 100 eVee is presented. The experimental apparatus which has been used to record electron and hole properties under CDMS conditions is described. Measurements of charge transport, trapping, and impact ionization as a function of electric field in two CDMS detectors are shown, and the ionization collection efficiency is determined. The data is used to predict the error in the nuclear recoil energy scale under both CDMSlite and iZIP operating modes. A two species, two state model is developed to describe how ionization collection and space charge generation in CDMS detectors are controlled by the presence of “overcharged” D- donor and A+ acceptor impurity states. The thermal stability of these states is exclusive to sub-Kelvin operation, explaining why ionization collection in CDMS detectors differs from similar semiconductor detectors operating at higher temperature. This work represents a solid foundation for the understanding ionization collection in CDMS detectors.

79 ASTRONOMY AND ASTROPHYSICS↗

On the structure of the two-stream instability–complex G-Hamiltonian structure and Krein collisions between positive- and negative-action modes

The two-stream instability is probably the most important elementary example of collective instabilities in plasma physics and beam-plasma systems. For a warm plasma with two charged particle species, the instability diagram of the two-stream instability based on a 1D warm-fluid model exhibits an interesting band structure that has not been explained. We show that the band structure for this instability is the consequence of the Hamiltonian nature of the warm two-fluid system. Interestingly, the Hamiltonian nature manifests as a complex G-Hamiltonian structure in wave-number space, which directly determines the instability diagram. Specifically, it is shown that the boundaries between the stable and unstable regions are locations for Krein collisions between eigenmodes with different Krein signatures. In terms of physics, this rigorously implies that the system is destabilized when a positive-action mode resonates with a negative-action mode, and that this is the only mechanism by which the system can be destabilized. It is anticipated that this physical mechanism of destabilization is valid for other collective instabilities in conservative systems in plasma physics, accelerator physics, and fluid dynamics systems, which admit infinite-dimensional Hamiltonian structures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Green Principles for Vehicle Lightweighting

A large portion of life cycle transportation impacts happen during vehicle operation, and key improvement strategies include increasing powertrain efficiency, vehicle electrification, and lightweighting vehicles by reducing their mass. The probable energy benefits of vehicle lightweighting are large, given that 29.5 EJ was used in all modes of U.S. transportation in 2016, and roughly half of the energy spent in wheeled transportation and the majority of energy spent in aircraft is used to move vehicle mass. We collect and review previous work on lightweighting, identify key parameters affecting vehicle environmental performance (e.g., vehicle mode, fuel type, material type, and recyclability), and propose a set of 10 principles, with examples, to guide environmental improvement of vehicle systems through lightweighting. These principles, based on a life cycle perspective and taken as a set, allow a wide range of stakeholders (designers, policy-makers, and vehicle manufacturers and their material and component suppliers) to evaluate the trade-offs inherent in these complex systems. This set of principles can be used to evaluate trade-offs between impact categories and to help avoid shifting of burdens to other life cycle phases in the process of improving use-phase environmental performance.A large portion of life cycle transportation impacts occur during vehicle operation, and key improvement strategies include increasing powertrain efficiency, vehicle electrification, and lightweighting vehicles by reducing their mass. The potential energy benefits of vehicle lightweighting are large, given that 29.5 EJ was used in all modes of U.S. transportation in 2016, and roughly half of the energy spent in wheeled transportation and the majority of energy spent in aircraft is used to move vehicle mass. We collect and review previous work on lightweighting, identify key parameters affecting vehicle environmental performance (e.g., vehicle mode, fuel type, material type, and recyclability), and propose a set of 10 principles, with examples, to guide environmental improvement of vehicle systems through lightweighting. These principles, based on a life cycle perspective and taken as a set, enable a wide range of stakeholders (designers, policy-makers, and vehicle manufacturers and their material and component suppliers) to evaluate the trade-offs inherent in these complex systems. This set of principles can be used to evaluate trade-offs between impact categories and to help avoid shifting of burdens to other life cycle phases in the process of improving use-phase environmental performance.

54 ENVIRONMENTAL SCIENCES↗

An adaptive quantization method for burst mode synthetic aperture radar data

Synthetic aperture radar (SAR) has high data rate because it collects and processes the data coherently. The data rate limitation of the system has to be satisfied while maintaining good image quality. Thus, a quantizer with minimum data rate and high SNR should be employed. An adaptive quantization method is proposed for the burst mode SAR. This adaptive quantizer uses uniformly quantized data to select a subset of bits which is equivalent to changing the step size of the uniform quantizer. A simple implementation which uses the previous burst data to compute the local statistics for the bit selection is presented. The use of previous burst simplifies the implementation because it does not require storage or delay; however, an abrupt change in the terrain could result in incorrect bit selection. An error analysis of this implementation and comparison of two burst mode SAR images formed using the uniformly quantized and adaptively quantized data is presented.

Joo, T. H.↗

Nanosecond Lipid Dynamics in Membranes Containing Cholesterol

Lipid dynamics in the cholesterol-rich (40 mol%) liquid-ordered (lo) phase of dimyristoylphosphatidylcholine membranes were studied using neutron spin-echo and neutron backscattering. Recent theoretical and experimental evidence supports the notion of the liquid-ordered phase in phospholipid membranes as a locally structured liquid, with small ordered domains of a highly dynamic nature in equilibrium with a disordered matrix [S. Meinhardt, R. L. C. Vink and F. Schmid, Proc. Natl. Acad. Sci. U. S. A., 2013, 110(12), 4476 4481, C. L. Armstrong et al., PLoS One, 2013, 8(6), e66162]. This local structure was found to have a pronounced impact on the membranes' dynamical properties. We found that the long-wavelength dynamics in the liquid-ordered phase, associated with the elastic properties of the membranes, were faster by two orders of magnitude as compared to the liquid disordered phase. At the same time, collective nanoscale diffusion was significantly slower. The presence of a soft-mode (a slowing down) in the longwavelength dispersion relationship suggests an upper size limit for the ordered lipid domain of ~220 A. Moreover, from the relaxation rate of the collective lipid diffusion of lipid lipid distances, the lifetime of these domains was estimated to be about 100 nanoseconds.

Armstrong, Clare L↗

Inclusive and exclusive measurements of B decays to χ c 1 and χ c 2 at Belle

We report inclusive and exclusive measurements for χ c1 and χ c2 production in B decays. We measure B(B→ χc1 X) = (3.03 ± 0.05(stat) ± 0.24(syst)) × 10 –3 and B(B→χ c2 X) = (0.70 ± 0.06(stat) ± 0.10(syst)) × 10 –3 . For the first time, χ c2 production in exclusive B decays in the modes B 0 →χ c2 π – K + and B + →χ c2 π + π – K + has been observed, along with first evidence for the B + →χ c2 π + K$^{0}_{S}$ decay mode. For χ c1 production, we report the first observation in the B + →χ c1 π + π – K + , B 0 →χ c1 π + π – K$^{0}_{S}$ and B 0 →χ c1 π 0 π – K + decay modes. Using these decay modes, we observe a difference in the production mechanism of χ c2 in comparison to χ c1 in B decays. In addition, we report searches for X(3872) and χ c1 (2P) in the B + →(χ c1 π + π – )K + decay mode. In conclusion, the reported results use 772 × 10 6 BB¯ events collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e + e – collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Leaching Behavior of Rare Earth Elements in Fort Union Lignite Coals of North America

Rare earth elements are crucial materials in an incredible array of consumer goods, energy system components and military defense applications. However, the global production and entire value chain for rare earth elements is dominated by China, with the U.S. currently 100% import reliant for these critical materials. Traditional mineral ores including those previously mined in the U.S., however, have several challenges. Chief among these is that the content of the most critical and valuable of the rare earths are deficient, making mining uneconomical. Further, the supply of these most critical rare earths is nearly 100% produced in China from a single resource that is only projected to last another 10 to 20 years. The U.S. currently considers the rare earths market an issue of national security. It is imperative that alternative domestic sources of rare earths be identified and methods developed to produce them. Recently, coal and coal byproducts have been identified as one of these promising alternative resources. This paper details the results of a study on characterization of North Dakota lignite and lignite-related feedstocks as an assessment of their feasibility for rare earth element recovery. The abundance, distribution and modes of occurrence of the rare earth elements in the samples collected were determined in this initial study to inform the selection of appropriate extraction and concentration methods to recover the rare earth elements. Materials investigated include the lignite coals, clay-rich sediments associated with the coal seams, and materials associated with a lignite beneficiation system and power plant. The results show that high rare earth element levels exist both in lignite coals and associated sediments. The form of the rare earth elements in the clay materials is primarily as ultra-fine mineral grains. In the lignite coals, approximately 80-95% of the rare earths content is organically associated, primarily as coordination complexes.

Laudal, Daniel A.↗

Dynamic localization and shear-induced hopping of particles: A way to understand the rheology of dense colloidal dispersions

For decades, attempts have been made to understand the formation of colloidal glasses and gels by linking suspension mechanics to particle properties where details of size, shape, and spatial dependencies of pair potentials present a bewildering array of variables that can be manipulated to achieve observed properties. Despite the range of variables that control suspension properties, one consistent observation is the remarkably similarity of flow properties observed as particle properties are varied. Understanding the underlying origins of the commonality in those behaviors (e.g., shear-thinning with increasing stress, diverging zero shear rate viscosity with increasing volume fraction, development of a dynamic yield stress plateau with increases in volume faction or strength of attraction, development of two characteristic relaxation times probed in linear viscoelasticity, the creation of a rubbery plateau modulus at high strain frequencies, and shear-thickening) remains a challenge. Recently, naïve mode coupling and dynamic localization theories have been developed to capture collective behavior giving rise to formation of colloidal glasses and gels. This approach characterizes suspension mechanics of strongly interacting particles in terms of sluggish long-range particle diffusion modulated by varying particle interactions and volume fraction. These theories capture the scaling of the modulus with the volume fraction and strength of interparticle attraction, the frequency dependence of the moduli at the onset of the gel/glass transition, together with the divergence of the zero shear rate viscosity and cessation of diffusivity for hard sphere systems as close packing is approached. In this study, we explore the generality of the predictions of dynamic localization theory for systems of particles composed of bimodal particle size distributions experiencing weak interactions. We find that the mechanical properties of these suspensions are well captured within the framework of dynamic localization theory and that suspension mechanics can be understood in terms of a dynamical potential barrier, the magnitude of which governs the zero shear rate viscosity, and onset of a dynamic yield stress plateau as volume fraction or strength of interaction is raised.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evaluating the Interplay between Trajectory Segmentation and Mode Inference Error

Travel behavior changes are essential to transportation decarbonization. Travel diaries, consisting of sequences of trips between places, are typically used to instrument human travel behavior. However, these diaries are only as accurate as the underlying methods used to construct them. Travel diary algorithms have been a popular research topic since the advent of Global Positioning System tracking surveys. These algorithms have typically been validated using prompted recall of presegmented trips, thus disregarding the continuity of mode inference. Phone operating systems have adopted battery-conserving techniques, but the resulting data collection errors have not been studied extensively. We introduce a framework to evaluate the accuracy of trip length computations and mode inference by analyzing continuous mode-segmented trajectories for groups of trips. We then use the framework to identify the input data quality and the impact of postprocessing. Our primary inputs to this evaluation are MobilityNet, a public dataset containing information from three artificial timelines covering 15 different travel modes, and sample open-source travel diary creation algorithms from the OpenPATH project. Our framework concretely shows that the variance of the distance error drops from (0.217, 0.0848) to (o.011, 0.0407) (Android, iOS) after postprocessing. Similarly, the weighted F-scores for mode inference increase from (0.25, 0.29) to (0.60, 0.74) (iOS, Android) between random forest and geographic information system-based models. We hope that this standardized method will be adapted to evaluate other, potentially proprietary, travel diary algorithms. Finally, the results can be used to understand and improve the state of the art in the travel diary creation field.

33 ADVANCED PROPULSION SYSTEMS↗

Fuzzy logic, neural networks, and soft computing

The past few years have witnessed a rapid growth of interest in a cluster of modes of modeling and computation which may be described collectively as soft computing. The distinguishing characteristic of soft computing is that its primary aims are to achieve tractability, robustness, low cost, and high MIQ (machine intelligence quotient) through an exploitation of the tolerance for imprecision and uncertainty. Thus, in soft computing what is usually sought is an approximate solution to a precisely formulated problem or, more typically, an approximate solution to an imprecisely formulated problem. A simple case in point is the problem of parking a car. Generally, humans can park a car rather easily because the final position of the car is not specified exactly. If it were specified to within, say, a few millimeters and a fraction of a degree, it would take hours or days of maneuvering and precise measurements of distance and angular position to solve the problem. What this simple example points to is the fact that, in general, high precision carries a high cost. The challenge, then, is to exploit the tolerance for imprecision by devising methods of computation which lead to an acceptable solution at low cost. By its nature, soft computing is much closer to human reasoning than the traditional modes of computation. At this juncture, the major components of soft computing are fuzzy logic (FL), neural network theory (NN), and probabilistic reasoning techniques (PR), including genetic algorithms, chaos theory, and part of learning theory. Increasingly, these techniques are used in combination to achieve significant improvement in performance and adaptability. Among the important application areas for soft computing are control systems, expert systems, data compression techniques, image processing, and decision support systems. It may be argued that it is soft computing, rather than the traditional hard computing, that should be viewed as the foundation for artificial intelligence. In the years ahead, this may well become a widely held position.

Zadeh, Lofti A.↗

Observing Mode Attitude Controller for the Lunar Reconnaissance Orbiter

The Lunar Reconnaissance Orbiter (LRO) mission is the first of a series of lunar robotic spacecraft scheduled for launch in Fall 2008. LRO will spend at least one year in a low altitude polar orbit around the Moon, collecting lunar environment science and mapping data to enable future human exploration. The LRO employs a 3-axis stabilized attitude control system (ACS) whose primary control mode, the "Observing mode", provides Lunar Nadir, off-Nadir, and Inertial fine pointing for the science data collection and instrument calibration. The controller combines the capability of fine pointing with that of on-demand large angle full-sky attitude reorientation into a single ACS mode, providing simplicity of spacecraft operation as well as maximum flexibility for science data collection. A conventional suite of ACS components is employed in this mode to meet the pointing and control objectives. This paper describes the design and analysis of the primary LRO fine pointing and attitude re-orientation controller function, known as the "Observing mode" of the ACS subsystem. The control design utilizes quaternion feedback, augmented with a unique algorithm that ensures accurate Nadir tracking during large angle yaw maneuvers in the presence of high system momentum and/or maneuver rates. Results of system stability analysis and Monte Carlo simulations demonstrate that the observing mode controller can meet fine pointing and maneuver performance requirements.

Calhourn, Philip C.↗

Observing Mode Attitude Controller for the Lunar Reconnaissance Orbiter

The Lunar Reconnaissance Orbiter (LRO) mission is the first of a series of lunar robotic spacecraft scheduled for launch in Fall 2008. LRO will spend at least one year in a low altitude polar orbit around the Moon, collecting lunar environment science and mapping data to enable future human exploration. The LRO employs a 3-axis stabilized attitude control system (ACS) whose primary control mode, the "Observing mode", provides Lunar Nadir, off-Nadir, and Inertial fine pointing for the science data collection and instrument calibration. The controller combines the capability of fine pointing with that of on-demand large angle full-sky attitude reorientation into a single ACS mode, providing simplicity of spacecraft operation as well as maximum flexibility for science data collection. A conventional suite of ACS components is employed in this mode to meet the pointing and control objectives. This paper describes the design and analysis of the primary LRO fine pointing and attitude re-orientation controller function, known as the "Observing mode" of the ACS subsystem. The control design utilizes quaternion feedback, augmented with a unique algorithm that ensures accurate Nadir tracking during large angle yaw maneuvers in the presence of high system momentum and/or maneuver rates. Results of system stability analysis and Monte Carlo simulations demonstrate that the observing mode controller can meet fine pointing and maneuver performance requirements.

Calhoun, Philip C.↗

Potential seal bypass and caprock storage produced by deformation-band-to-opening-mode-fracture transition at the reservoir/caprock interface

Here, we examined the potential impact on CO 2 transport of zones of deformation bands in reservoir rock that transition to opening-mode fractures within overlying caprock. Sedimentological and petrophysical measurements were collected along an approximately 5 m × 5 m outcrop of the Slick Rock and Earthy Members of the Entrada Sandstone on the eastern flank of the San Rafael Swell, Utah, USA. Measured deformation band permeability (2 mD) within the reservoir facies is about three orders of magnitude lower than the host sandstone. Average permeability of the caprock facies (0.0005 mD) is about seven orders of magnitude lower than the host sandstone. Aperture-based permeability estimates of the opening-mode caprock fractures are high (3.3 × 10 7 mD). High-resolution CO 2 –H 2 O transport models incorporate these permeability data at the millimeter scale. We then varied fault properties at the reservoir/caprock interface between open fractures and deformation bands as part of a sensitivity study. Numerical modeling results suggest that zones of deformation bands within the reservoir strongly compartmentalize reservoir pressures largely blocking lateral, cross-fault flow of supercritical CO 2 . Significant vertical CO 2 transport into the caprock occurred in some scenarios along opening-mode fractures. The magnitude of this vertical CO 2 transport depends on the small-scale geometry of the contact between the opening-mode fracture and the zone of deformation bands, as well as the degree to which fractures penetrate caprock. Finally, the presence of relatively permeable units within the caprock allows storage of significant volumes of CO 2 , particularly when the fracture network does not extend all the way through the caprock.

58 GEOSCIENCES↗

STARBASE: Database software for the automated plate scanner

The Automated Plate Scanner (APS) of the University of Minnesota, a unique high speed 'flying spot' laser scanner, is currently being used to scan and digitize the 936 O and E plate pairs of the first epoch Palomar Sky Survey. The resultant database will be used to produce a catalog of approximately a billion stars and several million galaxies. The authors describe the ongoing development of a dedicated APS database management system which will be made available to the astronomical community via INTERNET. A specialized DBMS called STARBASE has been written to provide fast access to the hundreds of millions of images collected by the APS. This system provides an initial reduction mode for parameterizing APS images and classifying image types using a novel set of neural network image classifiers. A second analysis mode, which will be that commonly used by the general user, provides for searches of the database which may be constrained by any combination of physical and positional parameters. Through the use of pointer hash trees, the system has been optimized for extremely fast positional searches using either right ascension and declination on the sky or linear X and Y positions on the POSS field. In addition to fast data retrieval, the system provides a graphical interface for displaying scatter plots or histograms of the collected data. In addition, a specialized image display system is being developed to allow the user to view densitometric data for all objects classified as extended by the neural network system. Finally, STARBASE has a flexible programmable interface which allows other programs to access information in the database. This allows users to write applications suited to their particular needs to process APS data.

Odewahn, S. C.↗

Recent Progress in the Structure Determination of GPCRs, a Membrane Protein Family with High Potential as Pharmaceutical Targets

G protein-coupled receptors (GPCRs) constitute a highly diverse and ubiquitous family of integral membrane proteins, transmitting signals inside the cells in response to an assortment of disparate extra-cellular stimuli. Their strategic location on the cell surface and their involvement in crucial cellular and physiological processes turn these receptors into highly important pharmaceutical targets. Recent technological developments aimed at stabilization and crystallization of these receptors have led to significant breakthroughs in GPCR structure determination efforts. One of the successful approaches involved receptor stabilization with the help of a fusion partner combined with crystallization in lipidic cubic phase (LCP). The success of using an LCP matrix for crystallization is generally attributed to the creation of a more native, membrane-like stabilizing environment for GPCRs just prior to nucleation and to the formation of type I crystal lattices, thus generating highly ordered and strongly diffracting crystals. Here they describe protocols for reconstituting purified GPCRs in LCP, performing pre-crystallization assays, setting up crystallization trials in manual mode, detecting crystallization hits, optimizing crystallization conditions, harvesting, and collecting crystallographic data. The protocols provide a sensible framework for approaching crystallization of stabilized GPCRs in LCP, however, as in any crystallization experiment, extensive screening and optimization of crystallization conditions as well as optimization of protein construct and purification steps are required. The process remains risky and these protocols do not necessarily guarantee success.

Cherezov, Vadim↗

Kink dynamics in a parametric Φ 6 system: a model with controllably many internal modes

We explore a variant of the Φ 6 model originally proposed in Phys. Rev.D 12 (1975) 1606 as a prototypical, so-called, “bag” model in which domain walls play the role of quarks within hadrons. We examine the steady state of the model, namely an apparent bound state of two kink structures. We explore its linearization, and we find that, as a function of a parameter controlling the curvature of the potential, an effectively arbitrary number of internal modes may arise in the point spectrum of the linearization about the domain wall profile. We explore some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, and how they depend on the principal parameter of the model. We find that the critical velocity exhibits a non-monotonic dependence on the parameter controlling the curvature of the potential. For the multi-bounce windows, we find that their range and complexity decrease as the relevant parameter decreases (and as the number of internal modes in the model increases). We use a modified collective coordinates method [in the spirit of recent works such as Phys. Rev.D 94 (2016) 085008] in order to capture the relevant phenomenology in a semi-analytical manner.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗