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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

The deuterium fractionation timescale in dense cloud cores: A parameter space exploration

The deuterium fraction, [N{sub 2}D{sup +}]/[N{sub 2}H{sup +}], may provide information about the ages of dense, cold gas structures, which are important for comparing dynamical models of cloud core formation and evolution. Here we introduce a complete chemical network with species containing up to three atoms, with the exception of the oxygen chemistry, where reactions involving H{sub 3}O{sup +} and its deuterated forms have been added, significantly improving the consistency with comprehensive chemical networks. Deuterium chemistry and spin states of H{sub 2} and H{sub 3}{sup +} isotopologues are included in this primarily gas-phase chemical model. We investigate the dependence of deuterium chemistry on these model parameters: density (n{sub H}), temperature, cosmic ray ionization rate, and gas-phase depletion factor of heavy elements (f{sub D}). We also explore the effects of time-dependent freeze-out of gas-phase species and the dynamical evolution of density at various rates relative to free-fall collapse. For a broad range of model parameters, the timescales to reach large values of D{sub frac}{sup N{sub 2}H{sup +}}≳0.1, observed in some low- and high-mass starless cores, are relatively long compared to the local free-fall timescale. These conclusions are unaffected by introducing time-dependent freeze-out and considering models with evolving density, unless the initial f{sub D} ≳ 10. For fiducial model parameters, achieving D{sub frac}{sup N{sub 2}H{sup +}}≳0.1 requires collapse to be proceeding at rates at least several times slower than that of free-fall collapse, perhaps indicating a dynamically important role for magnetic fields in supporting starless cores and thus the regulation of star formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Cooling, AGN feedback, and star formation in simulated cool-core galaxy clusters

Numerical simulations of active galactic nuclei (AGNs) feedback in cool-core galaxy clusters have successfully avoided classical cooling flows, but often produce too much cold gas. We perform adaptive mesh simulations that include momentum-driven AGN feedback, self-gravity, star formation, and stellar feedback, focusing on the interplay between cooling, AGN heating, and star formation in an isolated cool-core cluster. Cold clumps triggered by AGN jets and turbulence form filamentary structures tens of kpc long. This cold gas feeds both star formation and the supermassive black hole (SMBH), triggering an AGN outburst that increases the entropy of the intracluster medium (ICM) and reduces its cooling rate. Within 1–2 Gyr, star formation completely consumes the cold gas, leading to a brief shutoff of the AGN. The ICM quickly cools and redevelops multiphase gas, followed by another cycle of star formation/AGN outburst. Within 6.5 Gyr, we observe three such cycles. There is good agreement between our simulated cluster and the observations of cool-core clusters. ICM cooling is dynamically balanced by AGN heating, and a cool-core appearance is preserved. The minimum cooling time to free-fall time ratio typically varies between a few and ≳20. The star formation rate (SFR) covers a wide range, from 0 to a few hundred M{sub ⊙} yr{sup −1}, with an average of ∼40 M{sub ⊙} yr{sup −1}. The instantaneous SMBH accretion rate shows large variations on short timescales, but the average value correlates well with the SFR. Simulations without stellar feedback or self-gravity produce qualitatively similar results, but a lower SMBH feedback efficiency (0.1% compared to 1%) results in too many stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Sub-Chandrasekhar-mass White Dwarf Detonations Revisited

The detonation of a sub-Chandrasekhar-mass white dwarf (WD) has emerged as one of the most promising Type Ia supernova (SN Ia) progenitor scenarios. Recent studies have suggested that the rapid transfer of a very small amount of helium from one WD to another is sufficient to ignite a helium shell detonation that subsequently triggers a carbon core detonation, yielding a "dynamically driven double-degenerate double-detonation" SN Ia. Because the helium shell that surrounds the core explosion is so minimal, this scenario approaches the limiting case of a bare C/O WD detonation. Motivated by discrepancies in previous literature and by a recent need for detailed nucleosynthetic data, we revisit simulations of naked C/O WD detonations in this paper. We disagree to some extent with the nucleosynthetic results of previous work on sub-Chandrasekhar-mass bare C/O WD detonations; for example, we find that a median-brightness SN Ia is produced by the detonation of a 1.0 ${M}_{\odot }$ WD instead of a more massive and rarer 1.1 ${M}_{\odot }$ WD. The neutron-rich nucleosynthesis in our simulations agrees broadly with some observational constraints, although tensions remain with others. There are also discrepancies related to the velocities of the outer ejecta and light curve shapes, but overall our synthetic light curves and spectra are roughly consistent with observations. We are hopeful that future multidimensional simulations will resolve these issues and further bolster the dynamically driven double-degenerate double-detonation scenario's potential to explain most SNe Ia.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Influence of core size on the upconversion luminescence properties of spherical Gd{sub 2}O{sub 3}:Yb{sup 3+}/Er{sup 3+}@SiO{sub 2} particles with core-shell structures

Spherical SiO{sub 2} particles with different sizes (30, 80, 120, and 180 nm) have been coated with Gd{sub 2}O{sub 3}:Yb{sup 3+}/Er{sup 3+} layers by a heterogeneous precipitation method, leading to the formation of core-shell structural Gd{sub 2}O{sub 3}:Yb{sup 3+}/Er{sup 3+}@SiO{sub 2} particles. The samples were characterized by using X-ray diffraction, field emission scanning electron microscopy, transmission electron microscopy, upconversion (UC) emission spectra, and fluorescent dynamical analysis. The obtained core-shell particles have perfect spherical shape with narrow size distribution. Under the excitation of 980 nm diode laser, the core-shell samples showed size-dependent upconversion luminescence (UCL) properties. The inner SiO{sub 2} cores in core-shell samples were proved to have limited effect on the total UCL intensities of Er{sup 3+} ions. The UCL intensities of core-shell particles were demonstrated much higher than the values obtained in pure Gd{sub 2}O{sub 3}:Yb{sup 3+}/Er{sup 3+} with the same phosphor volume. The dependence of the specific area of a UCL shell on the size of its inner SiO{sub 2} particle was calculated and analyzed for the first time. It was confirmed that the surface effect came from the outer surfaces of emitting shells is dominant in influencing the UCL property in the core-shell samples. Three-photon UC processes for the green emissions were observed in the samples with small sizes of SiO{sub 2} cores. The results of dynamical analysis illustrated that more nonradiative relaxation occurred in the core-shell samples with smaller SiO{sub 2} core sizes.

36 MATERIALS SCIENCE↗
NASA NTRS2011

Effect of Cross-Correlation on Geomagnetic Forecast Accuracies

Surface geomagnetic observation can determine up to degree L = 14 time-varying spherical harmonic coefficients of the poloidal magnetic field. Assimilation of these coefficients to numerical dynamo simulation could help us understand better the dynamical processes in the Earth's outer core, and to provide more accurate forecast of geomagnetic secular variations (SV). In our previous assimilation studies, only the poloidal magnetic field in the core is corrected by the observations in the analysis. Unobservable core state variables (the toroidal magnetic field and the core velocity field) are corrected via the dynamical equations of the geodynamo. Our assimilation experiments show that the assimilated core state converges near the CMB, implying that the dynamo state is strongly constrained by surface geomagnetic observations, and is pulled closer to the truth by the data. We are now carrying out an ensemble of assimilation runs with 1000 years of geomagnetic and archeo/paleo magnetic record. In these runs the cross correlation between the toroidal and the poloidal magnetic fields is incorporated into the analysis. This correlation is derived from the physical boundary conditions of the toroidal field at the core-mantle boundary (CMB). The assimilation results are then compared with those of the ensemble runs without the cross-correlation, aiming at understanding two fundamental issues: the effect of the crosscorrelation on (1) the convergence of the core state, and (2) the SV prediction accuracies. The constrained dynamo solutions will provide valuable insights on interpreting the observed SV, e.g. the near-equator magnetic flux patches, the core-mantle interactions, and possibly other geodynamic observables.

Kuang, Weijia↗
NASA NTRS2015

Acoustic Database for Turbofan Engine Core-Noise Sources: Volume - I

In this program, a database of dynamic temperature and dynamic pressure measurements were acquired inside the core of a TECH977 turbofan engine to support investigations of indirect combustion noise. Dynamic temperature and pressure measurements were recorded for engine gas dynamics up to temperatures of 3100 degrees Fahrenheit and transient responses as high as 1000 hertz. These measurements were made at the entrance of the high pressure turbine (HPT) and at the entrance and exit of the low pressure turbine (LPT). Measurements were made at two circumferential clocking positions. In the combustor and inter-turbine duct (ITD), measurements were made at two axial locations to enable the exploration of time delays. The dynamic temperature measurements were made using dual thin-wire thermocouple probes. The dynamic pressure measurements were made using semi-infinite probes. Prior to the engine test, a series of bench, oven, and combustor rig tests were conducted to characterize the performance of the dual wire temperature probes and to define and characterize the data acquisition systems. A measurement solution for acquiring dynamic temperature and pressure data on the engine was defined. A suite of hardware modifications were designed to incorporate the dynamic temperature and pressure instrumentation into the TECH977 engine. In particular, a probe actuation system was developed to protect the delicate temperature probes during engine startup and transients in order to maximize sensor life. A set of temperature probes was procured and the TECH977 engine was assembled with the suite of new and modified hardware. The engine was tested at four steady state operating speeds, with repeats. Dynamic pressure and temperature data were acquired at each condition for at least one minute. At the two highest power settings, temperature data could not be obtained at the forward probe locations since the mean temperatures exceeded the capability of the probes. The temperature data were processed using software that accounts for the effects of convective and conductive heat transfer. The software was developed under previous NASA sponsored programs. Compensated temperature spectra and compensated time histories corresponding to the dynamic temperature of the gas stream were generated. Auto-spectral and cross-spectral analyses of the data were performed to investigate spectral features, acoustic circumferential mode content, signal coherence, and time delays. The dynamic temperature data exhibit a wideband and fairly flat spectral content. The temperature spectra do not change substantially with operating speed. The pressure spectra in the combustor and ITD exhibit generally similar shapes and amplitudes, making it difficult to identify any features that suggest the presence of indirect combustion noise. Cross-spectral analysis reveal a strong correlation between pressure and temperature fluctuations in the ITD, but little correlation between temperature fluctuations at the entrance of the HPT and pressure fluctuations downstream of it. Temperature fluctuations at the entrance of the low pressure turbine were an order of magnitude smaller than those at the entrance to the high pressure turbine. Time delay analysis of the temperature fluctuations in the combustor was inconclusive, perhaps due to the substantial mixing that occurs between the upstream and downstream locations. Time delay analysis of the temperature fluctuations in the ITD indicate that they convect at the mean flow speed. Analysis of the data did not reveal any convincing indications of the presence of indirect combustion noise. However, this analysis has been preliminary and additional exploration of the data is recommended including the use of more sophisticated signal processing to explore subtle issues that have been revealed but which are not yet fully understood or explained.

Aeroacoustics↗
NASA NTRS2001

Geodynamo Modeling of Core-Mantle Interactions

Angular momentum exchange between the Earth's mantle and core influences the Earth's rotation on time scales of decades and longer, in particular in the length of day (LOD) which have been measured with progressively increasing accuracy for the last two centuries. There are four possible coupling mechanisms for transferring the axial angular momentum across the core-mantle boundary (CMB): viscous, magnetic, topography, and gravitational torques. Here we use our scalable, modularized, fully dynamic geodynamo model for the core to assess the importance of these torques. This numerical model, as an extension of the Kuang-Bloxham model that has successfully simulated the generation of the Earth's magnetic field, is used to obtain numerical results in various physical conditions in terms of specific parameterization consistent with the dynamical processes in the fluid outer core. The results show that depending on the electrical conductivity of the lower mantle and the amplitude of the boundary topography at CMB, both magnetic and topographic couplings can contribute significantly to the angular momentum exchange. This implies that the core-mantle interactions are far more complex than has been assumed and that there is unlikely a single dominant coupling mechanism for the observed decadal LOD variation.

Kuang, Wei-Jia↗
DOE OSTI2015

Core structures analyses of (a+c)-edge dislocations in wurtzite GaN through atomistic simulations and Peierls–Nabarro model

The core structures and slip characteristics of (a+c)-edge dislocations on pyramidal planes in wurtzite GaN were investigated employing molecular dynamics simulations. Multiple stable core configurations are identified for dislocations along the glide and shuffle planes. The corresponding generalized-stacking-fault energy (GSFE) curves for the glide and shuffle slips are calculated. The GSFE curves, combined with the Peierls–Nabarro model, demonstrate that the shuffle slip is favored over the glide slip given the markedly lower Peierls energy and stress of the shuffle slip. Our findings also indicate that in general slip motions for (a+c)-edge dislocations are only possible at elevated temperature, and the necessity of further studies of thermally activated processes to better understand the dynamics of (a+c) dislocations in GaN.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2003

CHAMP Magnetic Anomalies of the Antarctic Crust

Regional magnetic signals of the crust are strongly masked by the core field and its secular variations components and hence difficult to isolate in the satellite measurements. In particular, the un-modeled effects of the strong auroral external fields and the complicated- behavior of the core field near the geomagnetic poles conspire to greatly reduce the crustal magnetic signal-to-noise ratio in the polar regions relative to the rest of the Earth. We can, however, use spectral correlation theory to filter the static lithospheric and core field components from the dynamic external field effects. To help isolate regional lithospheric from core field components, the correlations between CHAMP magnetic anomalies and the pseudo magnetic effects inferred from gravity-derived crustal thickness variations can also be exploited.. Employing these procedures, we processed the CHAMP magnetic observations for an improved magnetic anomaly map of the Antarctic crust. Relative to the much higher altitude Orsted and noisier Magsat observations, the CHAMP magnetic anomalies at 400 km altitude reveal new details on the effects of intracrustal magnetic features and crustal thickness variations of the Antarctic.

Kim, Hyung Rae↗
DOE OSTI2019

Ab initio investigation of Br-3d core-excited states in HBr and HBr + toward XUV probing of photochemical dynamics

Ultrafast X-ray/XUV transient absorption spectroscopy is a powerful tool for real-time probing of chemical dynamics. Interpretation of the transient absorption spectra requires knowledge of core-excited potentials, which necessitates assistance from high-level electronic-structure computations. In this study, we investigate Br-3d core-excited electronic structures of hydrogen bromide (HBr) using spin-orbit general multiconfigurational quasidegenerate perturbation theory (SO-GMC-QDPT). Potential energy curves and transition dipole moments are calculated from the Franck-Condon region to the asymptotic limit and used to construct core-to-valence absorption strengths for five electronic states of HBr ( 1 Σ 0 +, 3 Π 1 , 1 Π 1 , 3 Π 0 +, 3 Σ 1 ) and two electronic states of HBr+ ( 2 Π 3/2 , 2 Σ 1/2 ). The results illustrate the capabilities of Br-3d edge probing to capture transitions of the electronic-state symmetry as well as nonadiabatic dissociation processes that evolve across avoided crossings. Furthermore, core-to-valence absorption spectra are simulated from the neutral 1 Σ 0 + state and the ionic 2 Π 1/2,3/2 states by numerically solving the time-dependent Schrödinger equation and exhibit excellent agreement with the experimental spectrum. The comprehensive and quantitative picture of the core-excited states obtained in this work allows for transparent analysis of the core-to-valence absorption signals, filling gaps in the theoretical understanding of the Br-3d transient absorption spectra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Prompt core confinement improvement across the L–H transition in DIII-D: Profile stiffness, turbulence dynamics, and isotope effect

Here, we elaborate on the nature of the prompt core confinement improvement observed at the L–H transition in DIII-D, which is a long-standing issue unsolved for more than two decades and can impact future fusion reactor performance. Dynamic transport analysis suggests the essential role of the profile stiffness for understanding the mechanism of the prompt core confinement improvement. Beam emission spectroscopy shows that transport reduction at the core cannot be explained only by the ion scale turbulence density fluctuation suppression. Properties of nonlocal confinement improvement across the L–H transition are experimentally assessed in hydrogen (H) and deuterium (D) plasmas. Prompt core confinement improvement is found to be more rapid in the lighter hydrogen isotope.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Report of the panel on earth rotation and reference frames, section 7

Objectives and requirements for Earth rotation and reference frame studies in the 1990s are discussed. The objectives are to observe and understand interactions of air and water with the rotational dynamics of the Earth, the effects of the Earth's crust and mantle on the dynamics and excitation of Earth rotation variations over time scales of hours to centuries, and the effects of the Earth's core on the rotational dynamics and the excitation of Earth rotation variations over time scales of a year or longer. Another objective is to establish, refine and maintain terrestrial and celestrial reference frames. Requirements include improvements in observations and analysis, improvements in celestial and terrestrial reference frames and reference frame connections, and improved observations of crustal motion and mass redistribution on the Earth.

Dickey, Jean O.↗
DOE OSTI2017

Electronic structure study of screw dislocation core energetics in Aluminum and core energetics informed forces in a dislocation aggregate

Here we use a real-space formulation of orbital-free DFT to study the core energetics and core structure of an isolated screw dislocation in Aluminum. Using a direct energetics based approach, we estimate the core size of a perfect screw dislocation to be ≈ 7 |b|, which is considerably larger than previous estimates of 1–3 |b| based on displacement fields. The perfect screw upon structural relaxation dissociates into two Shockley partials with partial separation distances of 8.2 Å and 6.6 Å measured from the screw and edge component differential displacement plots, respectively. Similar to a previous electronic structure study on edge dislocation, we find that the core energy of the relaxed screw dislocation is not a constant, but strongly dependent on macroscopic deformations. Next, we use the edge and screw dislocation core energetics data with physically reasonable assumptions to develop a continuum energetics model for an aggregate of dislocations that accounts for the core energy dependence on macroscopic deformations. Further, we use this energetics model in a discrete dislocation network, and from the variations of the core energy with respect to the nodal positions of the network, we obtain the nodal core force which can directly be incorporated into discrete dislocation dynamics frameworks. We analyze and classify the nodal core force into three different contributions based on their decay behavior. Two of these contributions to the core force, both arising from the core energy dependence on macroscopic deformations, are not accounted for in currently used discrete dislocation dynamics models which assume the core energy to be a constant excepting for its dependence on the dislocation line orientation. Using case studies involving simple dislocation structures, we demonstrate that the contribution to the core force from the core energy dependence on macroscopic deformations can be significant in comparison to the elastic Peach–Koehler force even up to distances of 10–15 nm between dislocation structures. Thus, these core effects, whose origins are in the electronic structure of the dislocation core, can play an important role in influencing dislocation-dislocation interactions to much larger distances than considered heretofore.

36 MATERIALS SCIENCE↗
DOE OSTI2013

RELAP-7 Simulation Resolving an SBO Scenario on a Simplified Geometry of a BWR

The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). RELAP-7 will become the main reactor systems toolkit for the Risk-Informed Safety Margin Characterization Pathway of the Light Water Reactor Sustainability Program and the next generation tool in the RELAP reactor safety/systems analysis application series (i.e., the replacement for RELAP5). The code is being developed based on Idaho National Laboratory’s modern scientific software development framework – MOOSE (the Multi-Physics Object-Oriented Simulation Environment). During Fiscal Year 2013, a number of physical components with two-phase flow capability have been developed to support the simplified boiling water reactor (BWR) station blackout analyses. The case selected for demonstration calculation is built from the specifications documented in an Organization for Economic Cooperation and Development benchmark problem for BWR turbine trip analysis. The reference design for the benchmark problem was from the Peach Bottom-2 nuclear station, which is a General Electric BWR-4 design. The demonstration case includes the major components for the primary system of a BWR, as well as the safety system components for reactor core isolation cooling (RCIC) and the wet well of a BWR containment. The case was initially run to steady-state with RELAP-7. The station blackout transient simulations were subsequently initiated by using the INL-developed RAVEN code. Two scenarios for the station blackout simulations have been considered. Scenario I represents an extreme station blackout accident with no safety injection functioning. The reactor core could experience dry out fairly quickly with this scenario. Scenario II represents a more probable station blackout accident progression with the RCIC system functioning. In this scenario, the RCIC system is fully coupled with the reactor primary system and the safety injection to provide makeup cooling water to the reactor core from the suppression pool is dynamically simulated. With the RCIC system functioning, the core dry out is significantly postponed when compared to the results from Scenario I. This fully coupled RCIC system simulation capability represents the first-of-a-kind simulation capability. Sensitivity studies have also been carried out to study the effect of RCIC control strategy with varying core makeup cooling water mass flow rates. The next stage of development will be to demonstrate more refined BWR station blackout analyses with more realistic geometries, to be reported in the next demonstration simulation report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1993

Ultraviolet properties of individual hot stars in globular cluster cores. I - NGC 1904 (M79)

As part of an observing program using the IUE satellite to investigate the properties of stars within the cores of Galactic globular clusters, we have obtained three spectra of the cluster NGC 1904 (M79). All three were long-integration-time, short-wavelength (SWP) spectra obtained at the so-called 'center-of-light', and all three showed evidence of multiple sources within the IUE large aperture. We describe the analysis of these spectra and present evidence that the UV sources represent individual hot stars in the post-horizontal-branch stage of evolution. We see more UV-bright objects in the core of this cluster than expected from surveys of similar objects discovered in the outer regions of other globulars, leading us to conclude that dynamical effects in the core may significantly alter the path of evolution off the horizontal branch. The spectra also appear to be fitted more closely by models using Population I metal abundances than by Population II abundance models.

Altner, B.↗
NASA NTRS1996

Evolutionary status of the pre-protostellar core L1498

L1498 is a classic example of a dense cold pre-protostellar core. To study the evolutionary status, the structure, dynamics, and chemical properties of this core we have obtained high spatial and high spectral resolution observations of molecules tracing densities of 10(3)-10(5) cm-3. We observed CCS, NH3, C3H2, and HC7N with NASA's DSN 70 m antennas. We also present large-scale maps of C18O and 13CO observed with the AT&T 7 m antenna. For the high spatial resolution maps of selected regions within the core we used the VLA for CCS at 22 GHz, and the Owens Valley Radio Observatory (OVRO) MMA for CCS at 94 GHz and CS (2-1). The 22 GHz CCS emission marks a high-density [n(H2) > 10(4) cm -3] core, which is elongated with a major axis along the SE-NW direction. NH3 and C3H2 emissions are located inside the boundary of the CCS emission. C18O emission traces a lower density gas extending beyond the CCS boundary. Along the major axis of the dense core, CCS, NH3 and C3H2 emission show evidence of limb brightening. The observations are consistent with a chemically differentiated onion-shell structure for the L1498 core, with NH3 in the inner and CCS in the outer parts of the core. The high angular resolution (9"-12") spectral line maps obtained by combining NASA Goldstone 70 m and VLA data resolve the CCS 22 GHz emission in the southeast and northwest boundaries into arclike enhancements, supporting the picture that CCS emission originates in a shell outside the NH3 emitting region. Interferometric maps of CCS at 94 GHz and CS at 98 GHz show that their emitting regions contain several small-scale dense condensations. We suggest that the differences between the CCS, CS, C3H2, and NH3 emission are caused by a time-dependent effect as the core evolves slowly. We interpret the chemical and physical properties of L1498 in terms of a quasi-static (or slowly contracting) dense core in which the outer envelope is still growing. The growth rate of the core is determined by the density increase in the CCS shell resulting from the accretion of the outer low-density gas traced by C18O. We conclude that L1498 could become unstable to rapid collapse to form a protostar in less than 5 x 10(6) yr.

NASA Discipline Exobiology↗
DOE OSTI2013

Cascaded spin motive force driven by the dynamics of the skyrmion lattice

We numerically investigate the spin motive force (SMF) driven by the dynamics of a Skyrmion lattice. The rotating mode of the Skyrmion core excited by the AC magnetic field induces the large spin-dependent electric field near the core. Due to the collective dynamics of Skyrmion lattice, the measurable voltage is enhanced by the cascade effect of the SMF. The amplitude of the AC voltage is estimated to 30 μV in a macroscopic sample, where 100 Skyrmions exist between two probes. We also investigate the SMF due to the dynamics of the helical magnetic state, where the enhancement of the SMF does not occur.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗