Particle Physics Parameters Research Articles

Ultrahigh frequency primordial gravitational waves beyond the kHz: The case of cosmic strings

We investigate gravitational-wave backgrounds (GWBs) of primordial origin that would manifest only at ultrahigh frequencies, from kilohertz to 100 gigahertz, and leave no signal at LIGO, the Einstein Telescope, the Cosmic Explorer, LISA, or pulsar-timing arrays. We focus on GWBs produced by cosmic strings and make predictions for the GW spectra scanning over high-energy scale (beyond 1010 GeV) particle physics parameters. Signals from local string networks can easily be as large as the big bang nucleosynthesis/cosmic microwave background bounds, with a characteristic strain as high as 10−26 in the 10 kHz band, offering prospects to probe grand unification physics in the 1014–1017 GeV energy range. In comparison, GWB from axionic strings is suppressed (with maximal characteristic strain ∼10−31) due to the early matter era induced by the associated heavy axions. We estimate the needed reach of hypothetical futuristic GW detectors to probe such GWB and, therefore, the corresponding high-energy physics processes. Beyond the information of the symmetry-breaking scale, the high-frequency spectrum encodes the microscopic structure of the strings through the position of the UV cutoffs associated with cusps and kinks, as well as potential information about friction forces on the string. The IR slope, on the other hand, reflects the physics responsible for the decay of the string network. We discuss possible strategies for reconstructing the scalar potential, particularly the scalar self-coupling, from the measurement of the UV cutoff of the GW spectrum. Published by the American Physical Society 2024

Nanoparticle Isolation from Biological Media for Protein Corona Analysis: The Impact of Incubation and Recovery Protocols on Nanoparticle Properties

Nanoparticles are increasingly implemented in biomedical applications, including the diagnosis and treatment of disease. When exposed to complex biological media, nanoparticles spontaneously interact with their surrounding environment, leading to the surface-adsorption of small and bio- macromolecules- termed the “corona”. Corona composition is governed by nanoparticle properties and incubation parameters. While the focus of most studies is on the protein signature of the nanoparticle corona, the impact of experimental protocols on nanoparticle size in the presence of complex biological media, and the impact of nanoparticle recovery from biological media has not yet been reported. Here using a non-degradable robust model, we show how centrifugation-resuspension protocols used for the isolation of nanoparticles from incubation media, incubation duration and shear flow conditions alter nanoparticle parameters including particle size, zeta potential and total protein content.Our results show significant changes in nanoparticle size following exposure to media containing protein under different flow conditions, which also altered the composition of surface-adsorbed proteins profiled by SDS-PAGE. Our in situ analysis of nanoparticle size in media containing protein using particle tracking analysis highlights that centrifugation-resuspension is disruptive to agglomerates that are spontaneously formed in protein containing media, highlighting the need for in situ analytical methods that do not alter the intermediates formed following nanoparticle exposure to biological media.Nanomedicines are mostly intended for parenteral administration, and our findings show that parameters such as shear flow can significantly alter nanoparticle physicochemical parameters. Overall, we show that the centrifugation-resuspension isolation of nanoparticles from media significantly alters particle parameters in addition to the overall protein composition of surface-adsorbed proteins. We recommend that nanoparticle characterization pipelines studying bio-nano interactions during early nanomedicine development consider biologically-relevant shear flow conditions and media composition that can significantly alter particle physical parameters and subsequent conclusions from these studies.

Underestimating the uncertainty of aggregated results: the case of W-Boson mass

Estimates of uncertainty or variance in experimental means are central to physics. This is especially the case for ‘world averages’ of fundamental parameters in particle physics, which aggregate results from a number of experiments to express current knowledge about these parameters and where variances in these world averages reflect uncertainty in that knowledge. The standard aggregation method used in Particle Data Group reports to estimate such parameters is a form of fixed-effect meta-analysis. One problem with the fixed-effect approach is that it assumes no random variation between experiments (that is, no variation in experimental accuracy, which becomes increasingly important as experimental precision rises). This problem is well-known in the statistical literature, where the typical recommendation is to use random- rather than fixed-effect techniques. We illustrate this problem by applying random-effect meta-analysis to estimates of the W-Boson mass.

Mechanical grinding kinetics and particle packing novel characterization of iron ore tailings as inert filler for cement mortar

This study utilized image processing techniques to extract the morphological parameters of IOTs and established a grinding kinetic equation for particle morphology. The Divas-Aliavden equation and RRB model were applied to analyze the grinding kinetics of particle physical parameters. The Fuller and MAA particle packing models were employed to discuss the packing structure and density of particles in mortar. The relationship between particle physical parameters and compressive strength in the IOTs-cement system was explored through path analysis and grey correlation analysis. The results indicated that as the grinding process of IOTs progressed, the particle fineness decreased, the uniformity of particle size distribution and roundness increased, and using IOTs as inert fillers in mortar improved the particle packing structure and increased system density. Path analysis revealed the key influence of particle roundness on compressive strength, while the grey correlation analysis revealed that particles in the 2–60 μm range exerted a positive impact on the compressive strength of the composite binder system, with the most pronounced effect observed within the 8–16 μm range. Based on economic and technical considerations, the optimal mechanical grinding time for IOTs used as inert filler in cement mortar was determined to be 2.5 h.

Coupling Phenomenon Between Fugitive Dust and High-Temperature Tail Gas: A Thermal Infrared Signature Study

Abstract Fugitive dust, a physical factor commonly encountered in battle, would interact with the tail gas of armored vehicles during the diffusion process to affect infrared characteristics of tail gas and infrared detection probability of vehicles. However, limited information exists regarding the impacts of fugitive dust on infrared signature of tail gas. The gas-solid two-phase coupled flow and thermal infrared transport model was developed to comprehensively study the infrared characteristics of coupling phenomenon between dynamic dust and high-temperature tail gas, which considers the gas-solid coupled flow and heat transfer as well as the particle emission and scattering. The characteristics of coupled infrared caused by vehicle-induced dust were studied, along with the effects of particle physical parameters (i.e., particle size and concentration) on coupled infrared and the intrinsic mechanisms. Additionally, validation experiment was performed to validate the findings in the simulation results. The results show that (1) the coupling phenomenon can significantly enhance the infrared brightness and detection area of tail gas, especially in the 8–14 μm waveband; (2) the coupling phenomenon has different effects on the infrared signature of exhaust gas in different wavebands owing to the different proportions of particle radiation and gas radiation in the total radiation in different wavebands; and (3) the sensitivity of coupled infrared to particle size parameters and concentration parameters is also different, which is related to the spectral radiative physical parameters of dust particle components.

A solution for mixed elastohydrodynamic lubrication modeling considering effects of solid particles and surface roughness

To investigate the effects of solid particles on the point contact mixed lubrication, this paper aims to introduce solid particles into rough interfaces under mixed hydrodynamic lubrication. Statistical three-body micro-contact is utilized in modeling mixed EHL. The model is verified by comparing results without considering particles and roughness with those from classical EHL formula. Factors, such as particle physical parameters, surface roughness and operating condition acting on the system are discussed. The results show that the distribution of hydrodynamic pressure and oil film thickness on the point contact with particles still show typical characteristics of elastohydrodynamic lubrication. The physical parameters of particles and operating condition change the proportion of each part to the load carrying capacity, where an increase in particle size, concentration and surface orientation parameters increases the load ratio of particle and conversely an increase in surface roughness and sliding velocity decreases it. Both an increase in particle size and surface roughness result in an increase in the minimum oil film thickness, with the effect of surface roughness being more significant. In addition, the shear strength, size and concentration of the particles play an important role in the friction characteristics.

Characterization of particle sources and comparison of different particle metrics in an urban detached housing area, Finland

Particulate matter (PM) is emitted from various anthropogenic sources in urban areas affecting the local air quality. The aim of this study was to characterize the sources influencing air quality in detached house area in the Helsinki metropolitan area in Finland, and secondly, to explore the additional value of new particle physical properties to assess the impact of residential combustion on air quality. Measurements were conducted in an urban detached housing area between January and April 2019. Measured particle physical properties were particle number (PN), particle mass (PM1) and lung deposited surface area (LDSA) concentrations and number size distributions. In addition, particle chemical composition was measured using a soot particle aerosol mass spectrometer (SP-AMS; organic compounds, inorganic ions) and an aethalometer (black carbon (BC)). Concentrations of selected monosaccharide anhydrides and polycyclic aromatic hydrocarbons were analysed from the PM10 filter samples. The sources and characteristics of organic aerosol was investigated by applying positive matrix factorization to the mass spectra measured with the SP-AMS. Based on the variations in the measured particle physical parameters, chemical species and meteorology, the measurement period was divided into three sub periods dominated by urban background, wood burning and long-range transport (LRT) aerosols. Highest pollutant concentrations were measured during the wood burning and LRT periods. Wood burning increased the concentrations of all measured species, but the differences were most significant to levoglucosan, benzo(a)pyrene, BC and PM1 that had 12, 10, 6.4 and 3.6 times larger mean concentrations during the wood burning period compared to the urban background period, respectively. LRT affected significantly levoglucosan, PM1 and BC concentrations, since LRT pollutants partly originated from open biomass fires in Eastern Europe. The impact of local wood burning and LRT was quite small to particle number concentrations, whereas LDSA concentrations and size distributions were affected by traffic, wood combustion emissions and LRT. BC concentration correlated with the LDSA concentration during all periods suggesting a common origin. Particle number concentration was a good indicator of local combustion, especially traffic emissions, while the PM1 mass concentration together with secondary particle material was a good measure for the LRT pollutants. Benzo(a)pyrene was found to be a good indicator of local wood burning, but it was not detected in LRT biomass combustion particles.

Predicting Particle Separation and Sieve Blinding During Wheat Flour Sifting

HighlightsWheat flour cohesion was modeled using the Johnson-Kendall-Roberts (JKR) contact model.The size-based separation was highly influenced by particle size, particle roughness, cohesion, and sieve opening size.Sieve blinding happened at 15.25 and 10.32 s of sieving for hard red winter (HRW) and soft red winter (SRW) wheat flour particles, respectively.Abstract. Sifting or size-based separation of flour particles is an important operation in the wheat milling process. During the separation process, the flour particles often behave as imperfect solids with discontinuous flow and tend to form agglomerates due to interparticle cohesion. Interparticle cohesion in flours is highly dependent on the particle physical and chemical parameters and influences the sieving process. This study presents the development of a discrete element method (DEM) model to predict the size-based separation of wheat flours at 10% and 14% moisture contents (wet basis). DEM models of the size-based separation process were developed using the Hertz-Mindlin contact model. To account for the interparticle cohesion, the Johnson-Kendall-Roberts (JKR) model was coupled with the contact model. The size-based separation of hard red winter (HRW) and soft red winter (SRW) wheat flours was simulated and then validated using lab-scale experiments. Both the modeling and experimental approaches indicated that the percent particle separation was higher in the sieves with larger openings. Particle size, roughness, and cohesion affected the size-based separation in sieves with smaller openings. The model simulation results for the percent mass retained on the screens and the sieve blinding time were comparable with the experimental results. The standard error of prediction (SEP) ranged from 0.13 to 8.27, which indicates that this approach will be useful to predict the size-based separation of cohesive fine particles. The developed model will also be useful to estimate the sieve blinding time during sifting processes. Keywords: Cohesion, Johnson-Kendall-Roberts model, Sifting, Wheat milling.

Galactic condensates composed of multiple axion species

Ultralight scalar dark matter has been proposed to constitute a component of dark matter, though the minimal scenarios have increasingly become constrained. In this work, we analyze scenarios where the dark matter consists of more than one ultralight boson, each with different masses. This potentially leads to formation of gravitationally-bound Bose-Einstein condensates with structures that are very different from condensates composed of a single scalar field. By generalizing from the well-understood single-flavor case, we explore a large range of input parameters, subject to stability criteria, and determine the allowed parameter space for two-flavor condensates as a function of particle physics parameters, paying particular attention to cases where such condensates could compose galactic cores. We also analyze single-flavor condensates subject to external gravity from massive inner bodies and find that such systems may mimic the size of galactic cores as well.

BSM with cosmic strings: heavy, up to EeV mass, unstable particles

Unstable heavy particles well above the TeV scale are unaccessible experimentally. So far, Big-Bang Nucleosynthesis (BBN) provides the strongest limits on their mass and lifetime, the latter being shorter than 0.1 second. We show how these constraints could be potentially tremendously improved by the next generation of Gravitational-Wave (GW) interferometers, extending to lifetimes as short as 10−16 second. The key point is that these particles may have dominated the energy density of the universe and have triggered a period of matter domination at early times, until their decay before BBN . The resulting modified cosmological history compared to the usually-assumed single radiation era would imprint observable signatures in stochastic gravitational-wave backgrounds of primordial origin. In particular, we show how the detection of the GW spectrum produced by long-lasting sources such as cosmic strings would provide a unique probe of particle physics parameters. When applied to specific particle production mechanisms in the early universe, these GW spectra could be used to derive new constraints on many UV extensions of the Standard Model. We illustrate this on a few examples, such as supersymmetric models where the mass scale of scalar moduli and gravitino can be constrained up to 1010 GeV . Further bounds can be obtained on the reheating temperature of models with only-gravitationally-interacting particles as well as on the kinetic mixing of heavy dark photons at the level of 10−18.

Influence of Particle Shape and Contact Parameters on DEM-Simulated Bulk Density of Wheat

HighlightsDecreasing aspect ratio and improved geometrical smoothness of particles increased DEM-predicted bulk density of wheat.Among the three particle models, the 5-sphere ellipsoidal particle was the best option to represent wheat particles, as indicated by the simulated bulk densities that best agreed with the experiments.Among the contact parameters, the wheat-to-wheat coefficient of static friction and wheat-surface coefficient of rolling friction had the greatest influence on simulated bulk density.Abstract. The discrete element method (DEM) has been shown to be an effective tool for simulating the behavior of granular material. The accuracy of simulations depends highly on the contact models, particle physical parameters, and contact parameters used. The objectives of this study were to determine the influence of particle shape and contact parameters on simulated wheat bulk density and to develop an effective wheat particle model for DEM simulation of filling a container using EDEM software. Grain characteristics, including single-kernel weight, kernel density, kernel dimensions, aspect ratio, and bulk density, were determined for three size fractions of wheat used in the experiments. Three categories of particle models (5-sphere pseudo-ellipsoidal, 7-sphere pseudo-ellipsoidal, and ASG-generated) with varying aspect ratios and geometrical smoothness were tested in the simulations. Results showed that DEM-simulated bulk density of wheat increased with lower aspect ratio and greater geometrical smoothness of pseudo-ellipsoidal particles (7-sphere versus 5-sphere). Increasing the number of spheres to approximately 30 for better representation of wheat kernel shape, using ASG-generated particles, did not reproduce the trend of greater simulated bulk density seen in the experiments. Among the six contact parameters, the wheat-wheat coefficient of static friction and wheat-surface coefficient of rolling friction had the most significant effect on the simulated bulk density. Among the different sets of particle models, the 5-sphere pseudo-ellipsoidal particles, having aspect ratios close to that of wheat kernels in each size fraction, were found to be the most practical and appropriate particle model for use in DEM simulation of wheat bulk density. This study contributes to better understanding of the influence of particle shape and contact parameters on DEM-simulated bulk density and provides a calibrated particle model for use in simulating container filling operations. Keywords: Bulk density, Contact parameters, DEM, Particle shape, Wheat.

Fabrication and Evaluation of Weakly Cemented Three-dimensional Large-size Loose Sandstone Core

In order to realize the three-dimensional physical simulation experiment of loose sandstone reservoirs, one of the key points lies in how to obtain the three-dimensional large-size cores that can represent the actual reservoir conditions. However, due to the characteristics of small cementation strength, easy to loose, the large-scale cores drilling on site are difficult to achieve, so the preparation of weakly cemented three-dimensional large-scale loose sandstone cores is proposed. Through the design of the core mold, based on the particle size group and physical parameters of the target reservoir, and considering the macroscopic characteristics such as the actual reservoir thickness and the shale interlayer, weakly cemented three-dimensional large-scale core and saturated probe core are used. The physical properties of formed cores are evaluated and tested. The results show that compared with the actual reservoir, the porosity and permeability error of the core model is kept at about 10%, the precision is high, the homogeneity in the layer is good, the average cementation index of each layer is 1.6, which is a weak cementation category, and the degree of cementation consistent with the target reservoir. The prepared core can be done well in reducing the physical properties and macroscopic structure of the actual reservoir, and provides reliable core source support for the three-dimensional physical simulation experiment of the loose sandstone reservoir.

Numerical and experimental studies of corn particle properties on the forming of pile

Slope angle and porosity are two important parameters to describe granular stockpile which is related closely to some phenomena in nature and various industries. In order to study influence of particle physical parameters to the shape, slope angle and porosity of the pile, corn pile experiments and calculations were investigated. The results showed that once physical parameters are chosen properly, simulation results are in good agreement with experimental ones. Particle density, Young's modulus and Poisson's ratio have little influence on the shape, slope angle and the porosity of the pile. Coefficient of restitution has some effects on the slope angle and porosity, which both decreases with the increase of restitution coefficient. Furthermore coefficient of static and rolling friction have obviously effects on the shape, slope angle and porosity of the pile and all this properties are more sensitive to the former.

Particle Dark Matter constraints: the effect of Galactic uncertainties

Collider, space, and Earth based experiments are now able to probe several extensions of the Standard Model of particle physics which provide viable dark matter candidates. Direct and indirect dark matter searches rely on inputs of astrophysical nature, such as the local dark matter density or the shape of the dark matter density profile in the target in object. The determination of these quantities is highly affected by astrophysical uncertainties. The latter, especially those for our own Galaxy, are ill-known, and often not fully accounted for when analyzing the phenomenology of particle physics models. In this paper we present a systematic, quantitative estimate of how astrophysical uncertainties on Galactic quantities (such as the local galactocentric distance, circular velocity, or the morphology of the stellar disk and bulge) propagate to the determination of the phenomenology of particle physics models, thus eventually affecting the determination of new physics parameters. We present results in the context of two specific extensions of the Standard Model (the Singlet Scalar and the Inert Doublet) that we adopt as case studies for their simplicity in illustrating the magnitude and impact of such uncertainties on the parameter space of the particle physics model itself. Our findings point toward very relevant effects of current Galactic uncertainties on the determination of particle physics parameters, and urge a systematic estimate of such uncertainties in more complex scenarios, in order to achieve constraints on the determination of new physics that realistically include all known uncertainties.

The Relation between Fundamental Constants and Particle Physics Parameters

The observed constraints on the variability of the proton to electron mass ratio μ and the fine structure constant α are used to establish constraints on the variability of the Quantum Chromodynamic Scale and a combination of the Higgs Vacuum Expectation Value and the Yukawa couplings. Further model dependent assumptions provide constraints on the Higgs VEV and the Yukawa couplings separately. A primary conclusion is that limits on the variability of dimensionless fundamental constants such as μ and α provide important constraints on the parameter space of new physics and cosmologies.

What could we learn about high energy particle physics from cosmological observations at largest spatial scales ?

The very well known example of cosmology testing particle physics is the number of relativistic particles (photons and three active neutrinos within the Standard Model) at primordial nucleosynthesis. These days the earliest moment we can hope to probe with present cosmological data is the early time inflation. The particle physics conditions there and now are different because of different energy scales and different values of the scalar fields, that usually prohibits a reliable connection between the particle physics parameters at the two interesting epochs. The physics at the highest energy scales may be probed with observations at the largest spatial scales (just somewhat smaller than the size of the visible Universe). However, we are not (yet) ready to make the tests realistic, because of lack of a self-consistent theoretical description of the presently favorite cosmological models to be valid right after inflation.

Redshift-space distortions in massive neutrino and evolving dark energy cosmologies

Large-scale structure surveys in the coming years will measure the redshift-space power spectrum to unprecedented accuracy, allowing for powerful new tests of the LambdaCDM picture as well as measurements of particle physics parameters such as the neutrino masses. We extend the Time-RG perturbative framework to redshift space, computing the power spectrum P_s(k,mu) in massive neutrino cosmologies with time-dependent dark energy equations of state w(z). Time-RG is uniquely capable of incorporating scale-dependent growth into the P_s(k,mu) computation, which is important for massive neutrinos as well as modified gravity models. Although changes to w(z) and the neutrino mass fraction both affect the late-time scale-dependence of the non-linear power spectrum, we find that the two effects depend differently on the line-of-sight angle mu. Finally, we use the HACC N-body code to quantify errors in the perturbative calculations. For a LambdaCDM model at redshift z=1, our procedure predicts the monopole~(quadrupole) to 1% accuracy up to a wave number 0.19h/Mpc (0.28h/Mpc), compared to 0.08h/Mpc (0.07h/Mpc) for the Kaiser approximation and 0.19h/Mpc (0.16h/Mpc) for the current state-of-the-art perturbation scheme. Our calculation agrees with the simulated redshift-space power spectrum even for neutrino masses above the current bound, and for rapidly-evolving dark energy equations of state, |dw/dz| ~ 1. Along with this article, we make our redshift-space Time-RG implementation publicly available as the code redTime.

Scaling relations of halo cores for self-interacting dark matter

Using a simple analytic formalism, we demonstrate that significant dark matter self-interactions produce halo cores that obey scaling relations nearly independent of the underlying particle physics parameters such as the annihilation cross section and the mass of the dark matter particle. For dwarf galaxies, we predict that the core density ρc and the core radius rc should obey ρc rc ≈ 41 M⊙ pc−2 with a weak mass dependence ∼ M0.2. Remarkably, such a scaling relation has recently been empirically inferred. Scaling relations involving core mass, core radius, and core velocity dispersion are predicted and agree well with observational data. By calibrating against numerical simulations, we predict the scatter in these relations and find them to be in excellent agreement with existing data. Future observations can test our predictions for different halo masses and redshifts.

En-suite bathrooms in protected haematology wards: a source of filamentous fungal contamination?

In spite of 25 recently built high-risk haematology rooms with a protected environment and fitted with en-suite bathrooms in our university hospital centre in 2008, sporadic cases of hospital-acquired invasive aspergillosis remained in these wards. This study aimed to identify unsuspected environmental sources of filamentous fungal contamination in these rooms. Over two months, environmental fungal flora in the air (150 samples) as well as air particle counting and physical environmental parameters (airspeed, temperature, humidity, pressure) were prospectively monitored twice on the sampling day in all 25 protected rooms and en-suite bathrooms in use, and on bathroom surfaces (150 samples). In rooms under laminar airflow, in the presence of patients during sampling sessions, fungi were isolated in two samples (4%, 2/50) with a maximum value of 2cfu/500L (none was Aspergillus sp.). However, 88% of the air samples (44/50) in the bathroom were contaminated with a median range and maximum value of 2 and 16cfu/500L. Aspergillus spp. were involved in 24% of contaminated samples (12/44) and A.fumigatus in 6% (3/44). Bathroom surfaces were contaminated by filamentous fungi in 5% of samples (8/150). This study highlighted that en-suite bathrooms in protected wards are likely to be a source of fungi. Before considering specific treatment of air in bathrooms, technicians have first corrected the identified deficiencies: replacement of high-efficiency particulate air filters, improvement of air control automation, and restoration of initial technical specifications. Assessment of measure effectiveness is planned.

Particle limiting velocities from the bicubic equation derived from Einstein’s kinematics: PeV electron case

Here one reviews the particle limiting velocities derived from the Einstein’s kinematic generated bicubic equation: c1, the primary limiting velocity, c2, the obscure limiting velocity and c3, the normal limiting velocity. While c1 and c3 are real c2 is imaginary. Each of these limiting velocities depend on particle physics parameters of energy, E, mass, m, and ordinary velocity, v in such a way that c21 , c22 and c23 are all related to each other by simple transforms, leaving invariant the zero sum rule, c21 + c22+ c23= 0. As such, they form the bicubic particle kinematics. Now for the problem at hand, the limiting velocities are calculated specifically for the 0.5 MeV mass electron in the PeV energy region from the 2010 Crab Nebula Flare. Of the three solutions, c1; c2 and c3 one finds c1 to be very large and likely unphysical, similarly imaginary c2 with very large absolute value also likely unphysical and both of them Lorentz violating (LV), while the calculated normal limiting velocity c3 has acceptable values in this high energy case. With the electron energy in the PeV region, the electron mass has very little influence on c3. Even so one calculates miniscule subluminal and superluminal Lorentz violations, when respectively c3 ≾ c and c3 ≿ c, and the Lorentz invariance (LI) when the evaluation yields c3 = c. Qualitatively, because of miniscule masses, the calculated electron limiting velocity due to the Crab Nebula Flare PeV events shows great deal of similarities with the calculated neutrino limiting velocity from the OPERA neutrino velocity experiments. To get bigger mass effects on limiting velocities, one needs to go from the energy region E ≫ mc2 to the energy region E ≿ mc2 . With this, one would see whether in the lower energy region one has also c3 ≃ O(c) with LI and LV small portions. Also lower energy electron velocities, may even provide physical reasons for the existance or non-existance of c1 and c2.