Oscillations and potentials of mesons and baryons

In the following, the oscillations and potentials of mesons and baryons are examined and analyzed in detail. The oscillations result from a simple formula that describes the resonance energy at which the corresponding particle can absorb energy and thus appear. The potentials describe three mechanisms that describe the fine splitting of the masses of the elementary particles. These potentials can be read off and derived from the experimentally determined masses of the elementary particles as coefficients. The three mechanisms are internal mass charge binding energy, external mass charge binding energy, and Coulomb interaction.

Pythagorean numbers and the calculation of the masses of the elementary particles

We attempt here to calculate the particle masses for all known elementary particles starting from the Rydberg equation and from the Sommerfeld fine structure constant. Remarkably, this is possible. Next, we try to explain why this is possible and what the meaning of the approach seems to be. Thereby, we find some interesting connections. In addition, we realize that there are two different kinds of mass-charge binding energies in an elementary particle: The internal mass-charge binding energy and the external mass-charge binding energy. These two kinds of mass-charge binding energies can explain the higher masses of the highly charged brother particles in some of the heavier particle triplets (such as the charmed sigma particles).

Discrete scattering and meta-arrest of locally resonant elastic wave metamaterials with a semi-infinite crack

Previous investigations on wave scattering and crack propagation in the discrete periodic structure are concentrated on the conditional mass–spring model, in which the internal mass is not included. In this work, elastic wave metamaterials with local resonators are studied to show the scattering of elastic waves by a semi-infinite crack and the arrest behaviour. The influences of internal mass–spring structure are analysed and the discrete Wiener–Hopf method is used to obtain the displacement solution. Numerical calculations are performed to show that the dynamic negative effective mass and band gaps can be observed owing to the local resonance of the internal mass. Therefore, the scattering of an elastic wave with a specific frequency by a semi-infinite crack can be avoided by tuning the structural parameters. Moreover, the energy release ratio which characterizes the splitting resistance is presented and the meta-arrest performance is found. It is expected that this study will increase understanding of how to control the scattering characteristics of elastic waves by a semi-infinite crack in locally resonant metamaterials and also help to improve their fracture resistance.

Reconstruction of the mass and geometry of snowfall particles frommulti angle snowflake camera (MASC) images

This paper presents a method named 3D-GAN, based on a generative adversarial network (GAN), to retrieve the total mass, 3D structure and the internal mass distribution of snowflakes. The method uses as input a triplet of binary silhouettes of particles, corresponding to the triplet of stereoscopic images of snowflakes in free fall captured by a Multi-Angle Snowflake Camera (MASC). 3D-GAN is trained on simulated snowflakes of known characteristics whose silhouettes are statistically similar to real MASC observations and it is evaluated by means of snowflake replicas printed in 3D at 1 : 1 scale. The estimation of mass obtained by 3D-GAN has a normalized RMSE (NRMSE) of 40 %, a mean normalized bias (MNB) of 8 % and largely outperforms standard relationships based on maximum size and compactness. The volume of the convex hull of the particles is retrieved with MNRSE of 35 % and MNB of +19 %. In order to illustrate the potential of 3D-GAN to study snowfall microphysics and highlight its complementarity with existing retrieval algorithms, some application examples and ideas are provided, using as showcases the large available datasets of MASC images collected worldwide during various field campaigns. The combination of mass estimates (from 3D-GAN) and hydrometeor classification or riming degree estimation (from independent methods) allows for example to obtain mass-to-size power law parameters stratified on hydrometeor type or riming degree. The parameters obtained in this way are consistent with previous findings, with exponents overall around 2 and increasing with the degree of riming.

Investigating the effects of substrate morphology and experimental conditions on the enzymatic hydrolysis of lignocellulosic biomass through modeling

Background Understanding how the digestibility of lignocellulosic biomass is affected by its morphology is essential to design efficient processes for biomass deconstruction. In this study, we used a model based on a set of partial differential equations describing the evolution of the substrate morphology to investigate the interplay between experimental conditions and the physical characteristics of biomass particles as the reaction proceeds. Our model carefully considers the overall quantity of cellulase present in the hydrolysis mixture and explores its interplay with the available accessible cellulose surface. Results Exploring the effect of various experimental and structural parameters highlighted the significant role of internal mass transfer as the substrate size increases and/or the enzyme loading decreases. In such cases, diffusion of cellulases to the available cellulose surface limits the rate of glucose release. We notably see that increasing biomass loading, while keeping enzyme loading constant should be favored for both small- (R < 300 $$\mu m$$ μ m ) and middle-ranged (300 < R < 1000 $$\mu m$$ μ m ) substrates to enhance enzyme diffusion while minimizing the use of enzymes. In such cases, working at enzyme loadings exceeding the full coverage of the cellulose surface (i.e. eI>1) does not bring a significant benefit. For larger particles (R > 1000 $$\mu m$$ μ m ), increases in biomass loading do not offset the significant internal mass transfer limitations, but high enzyme loadings improve enzyme penetration by maintaining a high concentration gradient within the particle. We also confirm the well-known importance of cellulose accessibility, which increases with pretreatment. Conclusions Based on the developed model, we are able to propose several design criteria for deconstruction process. Importantly, we highlight the crucial role of adjusting the enzyme and biomass loading to the wood particle size and accessible cellulose surface to maintain a strong concentration gradient, while avoiding unnecessary excess in cellulase loading. Theory-based approaches that explicitly consider the entire lignocellulose particle structure can be used to clearly identify the relative importance of bottlenecks during the biomass deconstruction process, and serve as a framework to build on more detailed cellulase mechanisms.

A mobile Mathieu oscillator model for vibrational locomotion of a bristlebot

Terrestrial locomotion that is produced by creating and exploiting frictional anisotropy is common amongst animals such as snakes, gastropods, limbless lizards. In this paper we present a model of a bristle bot that locomotes by generating frictional anisotropy due to the oscillatory motion of an internal mass and show that this is equivalent to a stick-slip Mathieu oscillator. Such vibrational robots have been available as toys and theoretical curiosities and have seen some applications such as the well known kilobot and in pipe line inspection, but much remains unknown about this type of terrestrial locomotion. In this paper, motivated by a toy model of a bristle bot made from a toothbrush, we derive a theoretical model for its dynamics and show that its dynamics can be classified into four modes of motion : purely stick (no locomotion), slip, stick-slip and hopping. In the stick mode, the dynamics of the system are those of a nonlinear Mathieu oscillator and large amplitude resonance oscillations lead to the slip mode of motion. The mode of motion depends on the amplitude and frequency of the periodic forcing. We compute a phase diagram that captures this behavior, that is reminiscent of the tongues of instability seen in a Mathieu oscillator. The broader result that emerges in this paper is that mobile limbless continuum or soft robots can exploit high frequency parametric oscillations to generate fast and efficient terrestrial motion.

Heterogeneous mass distribution of the rubble-pile asteroid (101955) Bennu

The gravity field of a small body provides insight into its internal mass distribution. We used two approaches to measure the gravity field of the rubble-pile asteroid (101955) Bennu: (i) tracking and modeling the spacecraft in orbit about the asteroid and (ii) tracking and modeling pebble-sized particles naturally ejected from Bennu’s surface into sustained orbits. These approaches yield statistically consistent results up to degree and order 3, with the particle-based field being statistically significant up to degree and order 9. Comparisons with a constant-density shape model show that Bennu has a heterogeneous mass distribution. These deviations can be modeled with lower densities at Bennu’s equatorial bulge and center. The lower-density equator is consistent with recent migration and redistribution of material. The lower-density center is consistent with a past period of rapid rotation, either from a previous Yarkovsky-O’Keefe-Radzievskii-Paddack cycle or arising during Bennu’s accretion following the disruption of its parent body.