Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.

Novel Motor-Kinetic-Energy-Based Power Pulsation Buffer Concept for Single-Phase-Input Electrolytic-Capacitor-Less Motor-Integrated Inverter System

The motor integration of singe-phase-supplied Variable-Speed Drives (VSDs) is prevented by the significant volume, short lifetime, and operating temperature limit of the electrolytic capacitors required to buffer the pulsating power grid. The DC-link energy storage requirement is eliminated by using the kinetic energy of the motor as a buffer. The proposed concept is called the Motor-Integrated Power Pulsation Buffer (MPPB), and a control technique and structure are detailed that meet the requirements for nominal and faulted operation with a simple reconfiguration of existing controller blocks. A 7.5 KW, motor-integrated hardware demonstrator validated the proposed MPPB concept and loss models for a scroll compressor drive used in auxiliary railway applications. The MPPB drive with a front-end CISPR 11/Class A EMI filter, PFC rectifier stage, and output-side inverter stage achieved a power density of 0.91 KW L−1 (15 W in−3). The grid-to-motor-shaft efficiency exceeded 90% for all loads over 5 kW or 66% of nominal load, with a worst-case loss penalty over a conventional system of only 17%.

Possible mechanisms related to internal dynamics for anomalously high rainfall during August 2020 of Indian Summer Monsoon

In the present study, an investigation is made to understand the physical mechanism behind the anomalous high rainfall during August 2020 over the Indian subcontinent using both observation and GFS T1534 weather forecast model. According to India Meteorological Department (IMD), the country receives 27% excess rainfall in the month of August 2020. The excess rainfall is mainly contributed by the 5 well marked low pressure systems which formed over Bay of Bengal and moved west-northwestwards across central India up to Western Madhya Pradesh and Rajasthan. The analysis reveals that the observed anomalous rainfall is distributed over central India region extending from coastal Orissa to central part of Chhattisgarh, Madhya Pradesh and western coast of Gujarat region. It is also found that the August-2020 heavy rainfall is mainly contributed by the synoptic (2-10 days) component of the total rainfall whereas the contribution of the large-scale intraseasonal oscillation (ISO) component (10-90 days) is quite less. Although the present operational Global Forecast System (GFS) T1534 (GFS T1534) is able to predict the anomalous high rainfall with day-1 lead time, it underestimates the magnitude of the synoptic variance. Further, the large-scale dynamical and thermodynamical parameters show anomalous behaviour in terms of strong low level (850 hPa) jet, vertical velocity and associated moisture convergence in the lower level. The GFS T1534 is able to forecast the above large-scale features reasonably well even with day-5 lead time. From energetics analysis, it is found that the mean kinetic energy (MKE) is stronger for August 2020 as compared to climatological value and the strong MKE efficiently transfers the energy to the synoptic scale, and hence the synoptic eddy kinetic energy is higher. Along with that, the ISO scale kinetic energy for August 2020 is less compared to the August climatological value. GFS T1534 model has some fidelity in capturing the energy conversion processes, but it has some difficulty in capturing the magnitude with increased lead time.

Two Notes on the Theoretical Physics of ATP Synthase

ATP Synthase is an essential molecule in cell and molecular biology. It is responsible for the production of ATP during cellular respiration, a molecule that provides the energy required to drive a number of cellular processes. In this paper, I explore the rotational physics of ATP Synthase’s rotor, a part of the protein that spins during the production of ATP. Firstly, I discuss some elementary rotational kinematics of the rotor. I then derive two alternate formulations for the total linear acceleration of the rotor. Finally, I derive formulas for the moment of inertia, angular momentum, net torque, and kinetic energy of the rotor. Through this, I hope to provide a theoretical and mathematical insight into the mechanics of ATP Synthase during the production of ATP.

Two Notes on the Theoretical Physics of ATP Synthase

ATP Synthase is an essential molecule in cell and molecular biology. It is responsible for the production of ATP during cellular respiration, a molecule that provides the energy required to drive a number of cellular processes. In this paper, I explore the rotational physics of ATP Synthase’s rotor, a part of the protein that spins during the production of ATP. Firstly, I discuss some elementary rotational kinematics of the rotor. I then derive two alternate formulations for the total linear acceleration of the rotor. Finally, I derive formulas for the moment of inertia, angular momentum, net torque, and kinetic energy of the rotor. Through this, I hope to provide a theoretical and mathematical insight into the mechanics of ATP Synthase during the production of ATP.

Inherent anharmonicity of harmonic solids

Atomic vibrations, in the form of phonons, are foundational in describing the thermal behavior of materials. The possible frequencies of phonons in materials are governed by the complex bonding between atoms, which is physically represented by a spring-mass model that can account for interactions (spring forces) between the atoms (masses). The lowest order, harmonic, approximation only considers linear forces between atoms and is thought incapable of explaining phenomena like thermal expansion and thermal conductivity, which are attributed to non-linear, anharmonic, interactions. Here we show that the kinetic energy of atoms in a solid produces a pressure much like the kinetic energy of atoms in a gas does. This vibrational or phonon pressure naturally increases with temperature, as it does in a gas, and therefore results in a thermal expansion. Because thermal expansion thermodynamically defines a Grüneisen parameter, which is a typical metric of anharmonicity, we show that even a harmonic solid will necessarily have some anharmonicity. A consequence of this phonon pressure model is a harmonic estimation of the Grüneisen parameter from the ratio of the transverse and longitudinal speeds of sound. We demonstrate the immediate utility of this model by developing a high-throughput harmonic estimate of lattice thermal conductivity that is comparable to other state-of-the-art estimations. By linking harmonic and anharmonic properties explicitly, this study provokes new ideas about the fundamental nature of anharmonicity, while also providing a basis for new materials engineering design metrics.

Turbulence parameters measured by the Beijing Mesosphere–Stratosphere–Troposphere radar in the troposphere/lower stratosphere with three models: Comparison and analyses

Based on the quality-controlled observational spectral width data of the Beijing Mesosphere–Stratosphere–Troposphere (MST) radar in the altitudinal range of 3–19.8 km from 2012 to 2014, this paper analyzes the relationship between the proportion of negative turbulent kinetic energy (N-TKE) and the horizontal wind speed/horizontal wind vertical shear domain, and gives the distributional characteristics of atmospheric turbulence parameters obtained by using different calculation models. Three calculation models of the spectral width method were used in this study—namely, the H model (Hocking, 1985), N-2D model (Nastrom, 1997) and D-H model (Dehghan and Hocking, 2011). The results showed that the proportion of N-TKE in the H model increases with the horizontal wind speed and/or the vertical shear of horizontal wind speed, up to 80 %. When the horizontal wind speed is greater than 40 m·s−1, the proportion of N-TKE in the H model is greater than 60 %, and thus the H model is not applicable. When the horizontal wind speed is greater than 20 m s−1, the proportion of N-TKE in the N-2D model and D-H model increases with the horizontal wind speed, independent of the vertical shear of the horizontal wind speed, and the maximum values are 2 % and 4 %, respectively. However, it is still necessary to consider the applicability of the N-2D model and D-H model in some weather processes with strong winds. The distributional characteristics with height of the turbulent kinetic energy dissipation rate 𝜀 and the vertical eddy diffusion coefficient Kz derived by the three models are consistent with previous studies. Still, there are differences in the values of turbulence parameters. Also, the range resolution of the radar has little effect on the differences in the range of turbulence parameters' values. The median values of 𝜀 in the H model, N-2D model and D-H model are 10−3.2–10−2.8 m2 s−3, 10−2.8–10−2.4 m2 s−3 and 10−3.0–10−2.5 m2 s−3, respectively. The median values of Kz in these three models are 100.18–100.67 m2 s−1, 100.57–100.90 m2 s−1 and 100.44–100.74 m2 s−1.

Numerical simulation of reynolds number effect of a free incompressible isothermal turbulent coaxial jet

This paper studies the effect of Reynolds number on a two-dimensional free incompressible isothermal coaxial turbulent jet over a range of high Reynolds numbers. This is necessary because of its application in noise control and mixing. The Reynolds numbers at the nozzle exit were 9824, 19648, 29472, 39296 and 49120. The models were designed in ANSYS Design Modeler and the numerical simulation was done using a finite volume based Computational Fluid Dynamics (CFD) in ANSYS FLUENT using the two-dimensional Realizable turbulence model. The Governing equations were discretized using the finite volume method with the solution based on the PISO algorithm. The decay of centerline velocity, turbulent kinetic energy profile, the radial profile of axial velocity and similarity profile were investigated along the flow direction. Contour plot indicates that the velocity is high at the jet exit and decreases downstream due to the rapid mixing of the inner and outer jet and the surrounding fluid. It is found generally that Reynolds number plays significant role especially before self-similarity region. The result shows that increasing the Reynolds number give rise to more turbulence which in turn decreases the potential core length, turbulent kinetic energy and enhances the mixing of the fluid. However, at the jet exit, the flow with the lowest Reynolds number has the highest turbulent kinetic energy because it suffers the greater shear. The spreading of the jet was more or less independent of the Reynolds number beyond the self-similarity region. It is also found that the velocity profile is brought to congruence at about z/D=25 for the Reynolds numbers considered

The bifunctional formalism: an alternative treatment of density functionals

The bifunctional formalism presents an alternative how to obtain the functional value from its functional derivative by exploiting homogeneous density scaling. In the bifunctional formalism the density dependence of the functional derivative is suppressed. Consequently, those derivatives have to be treated as formal functional derivatives. For a pointwise correspondence between the true and the formal functional derivative, the bifunctional expression yields the same value as the density functional. Within the bifunctional formalism the functional value can directly be obtained from its derivative (while the functional itself remains unknown). Since functional derivatives are up to a constant uniquely defined, this approach allows for a pointwise comparison between approximate potentials and reference potentials. This aspect is especially important in the field of orbital-free density functional theory, where the burden is to approximate the kinetic energy. Since in the bifunctional approach the potential is approximated directly, full control is given over the latter, and consequently over the final electron densities obtained from variational procedure. Besides the bifunctional formalism itself another concept is introduced, dividing the total non-interacting kinetic energy into a known functional part and a remainder, called Pauli kinetic energy. Only the remainder requires further approximations. For practical purposes sufficiently accurate Pauli potentials for application on atoms, molecular and solid-state systems are presented.