Description Of Mechanisms Research Articles

Impact pressure coefficient and object mobilization length in mass flows

As the impact force of a flow overcomes the frictional resistance of an object, the object moves as long as the pressure exerted by the flow is greater than its shear resistance. With this concept, here, we develop simple analytical models for the mechanical description of the coefficient of impact pressure Cp0 and the mobilization length L when a mass flow impacts a movable object. We invented the obstacle mobilization number Cp0, a dimensionless number, which is expressed as the ratio of the obstacle shear resistance to the kinetic energy of the flow, per unit length. We also relate it to the obstacle Froude number Fr0. When the object moves through the length L against the basal friction, after consuming its kinetic energy, the object eventually stops. This balance between the kinetic energy and friction yields an analytical model for the mobilization length of the object. Equivalently, if the mobilization length is known, the impact velocity can be calculated. This is very important in estimating the flow velocity of any large-scale natural mass flows. Our model predicts that Cp0 decreases strongly to weakly non-linearly with the impact velocity, density ratio between the granular particle and the mobile object, and the area ratio between the grain covered area of the object and its base. Moreover, Cp0 increases linearly with the basal friction coefficient. However, the dynamic response of Cp0 to the shape of the object may vary immensely between objects of different shapes. Our model also predicts that the mobilization length L of the mobile object varies with the square of the impact velocity of flowing mass, but decreases with basal friction of the obstacle and the component of gravitational acceleration in the direction normal to the flow depth. We conduct several laboratory chute experiments with different native Nepalese complex fruit seeds and food grains to validate the physical significance and scope of Cp0 and L. Our simple analytical models very well describe the coefficient of impact pressure and the mobilization length of the mobile object impacted by the laboratory granular flows. We discuss the applicability of Cp0 and L to real flow situations in designing protective civil defense structures as well as mitigating from natural disasters, and industrial transports of complex granular flows.

A topological mechanism for robust and efficient global oscillations in biological networks

Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by underlying components. We propose a topological model that produces long oscillations around the network boundary, reducing the system dynamics to a lower-dimensional current in a robust manner. Using this to model KaiC, which regulates the circadian rhythm in cyanobacteria, we compare the coherence of oscillations to that in other KaiC models. Our topological model localizes currents on the system edge, with an efficient regime of simultaneously increased precision and decreased cost. Further, we introduce a new predictor of coherence from the analysis of spectral gaps, and show that our model saturates a global thermodynamic bound. Our work presents a new mechanism and parsimonious description for robust emergent oscillations in complex biological networks.

Neurological Disorders Induced by Drug Use: Effects of Adolescent and Embryonic Drug Exposure on Behavioral Neurodevelopment.

Clinical studies demonstrate that the risk of developing neurological disorders is increased by overconsumption of the commonly used drugs, alcohol, nicotine and cannabis. These drug-induced neurological disorders, which include substance use disorder (SUD) and its co-occurring emotional conditions such as anxiety and depression, are observed not only in adults but also with drug use during adolescence and after prenatal exposure to these drugs, and they are accompanied by long-lasting disturbances in brain development. This report provides overviews of clinical and preclinical studies, which confirm these adverse effects in adolescents and the offspring prenatally exposed to the drugs and include a more in-depth description of specific neuronal systems, their neurocircuitry and molecular mechanisms, affected by drug exposure and of specific techniques used to determine if these effects in the brain are causally related to the behavioral disturbances. With analysis of further studies, this review then addresses four specific questions that are important for fully understanding the impact that drug use in young individuals can have on future pregnancies and their offspring. Evidence demonstrates that the adverse effects on their brain and behavior can occur: (1) at low doses with short periods of drug exposure during pregnancy; (2) after pre-conception drug use by both females and males; (3) in subsequent generations following the initial drug exposure; and (4) in a sex-dependent manner, with drug use producing a greater risk in females than males of developing SUDs with emotional conditions and female offspring after prenatal drug exposure responding more adversely than male offspring. With the recent rise in drug use by adolescents and pregnant women that has occurred in association with the legalization of cannabis and increased availability of vaping tools, these conclusions from the clinical and preclinical literature are particularly alarming and underscore the urgent need to educate young women and men about the possible harmful effects of early drug use and to seek novel therapeutic strategies that might help to limit drug use in young individuals.

The theory of scaled electromechanics

A new scaling theory called finite similitude has appeared in the open literature for the scaling of physical systems. The theory is founded on the metaphysical concept of space scaling and consequently can in principle be applied to all physics. With regard to the application of the theory to multi-physics however, an obstacle is dissimilar mathematical formulations, that are preferred and applied in practice. This paper looks to combine electrical and mechanical physics under the rules of the scaling theory for the analysis of scaled electromechanical systems. To facilitate this the physics of electromechanics is described using transport equations on a projected space termed the scaling space. It is shown that this approach unifies the mechanical and electrical descriptions and allows the scaling theory to be applied and for scaling identities to be established. Additionally, on confirming that the scaling space possesses all the attributes of a real physical space (despite being a mere projection), mathematical modelling (to great advantage) is performed directly and integrated with the scaling theory. To showcase the concepts, mathematical models for previously researched electromechanical systems are directly analysed in the new scaling space. It is demonstrated how such models automatically account for scale dependencies in the electromechanical systems they represent. The huge potential of the new approach is revealed providing the means for formulating (for the first time) realistic representative scaled-mathematical models.

INTERPRETATION OF THE PHENOMENON OF SOCIAL CONTROL IN POSTMODERNISM AND METAMODERNISM

The paper presents a comparative analysis of the interpretation of the phenomenon of social control in postmodernism and metamodernism. The similarities and differences in the description of social control mechanisms are identified. The concepts of “society of the spectacle” (G.Debord), “society of surveillance” (M.Foucault) and “society of control” (J. Deleuze) are analyzed, which show the evolution of postmodernists’ views on social processes.. The concept of the “listening society” (G.Freinacht) as a metamodern alternative to the development of modern society is presented. Postmodernism focuses on criticizing society, drawing attention to its increasing fragmentation, the crisis of metanarratives, and the growing role of the media as a tool for social control. In contrast, metamodernism tries to balance modern and postmodern theories, recognizing the importance of centralized and decentralized forms of social control. This allows simultaneously taking into account the diversity of identities of a modern person and the possibility of his or her integration into society through the adoption of common norms and rules. Metamodernism seeks to reconstruct metanarratives that can contribute to new forms of social control based on cooperation and common interests. It emphasizes the importance of empathy in social control, whereas postmodernism rejects it as a false, simulated form of social relations. While postmodernism focuses more on critical analysis of existing structures, metamodernism aims to find hybrid and adaptive forms of control that combine traditional methods with the latest technologies. All these differences in the interpretation of the phenomenon of social control reflect the paradigm shift from postmodern deconstruction to synthesis and reconstruction within metamodernism.

Phenomenological model for unburned hydrocarbon emissions from spark-ignition, pre-chamber, and dual-fuel internal combustion engines

Considering the strict regulations on the transport sector emissions, predictive models for engine emissions are essential tools to optimize high-efficient low-emission internal combustion engines (ICE) for vehicles. This aspect is of major importance, especially for developing new combustion concepts (e.g. lean, pre-chamber) or using alternative fuels. Among the gaseous emissions from spark-ignition (SI) engines, unburned hydrocarbons (uHC) are the most challenging species to model due to the complexity of the formation mechanisms. Phenomenological models are successfully used in these cases to predict emissions with a reduced computational effort. In this work, uHC phenomenological model approaches by the authors are further developed to improve the model predictivity for multiple variations including engine design, engine operating parameters, as well as different fuels and ignition methods. The model accounts for uHC contributions from piston top-land crevice, wall flame quenching, oil film fuel adsorption/desorption and features a tabulated-chemistry approach to describe uHC post-oxidation. With the support of 3D-CFD simulations, multiple novel modelling assumptions are developed and verified. The model is validated against an extensive measurement database obtained with two small-bore single-cylinder engines (SCE) fuelled with gasoline-like fuel, one with SI and one with pre-chamber, as well as against data from two different ultra-lean large-bore engines fuelled with natural gas (one equipped with a pre-chamber and one dual-fuel with a diesel pilot). The model correctly predicts the trends and absolute values of uHC emissions for all the operating conditions and the engines with an accuracy on average of 11.4%. The results demonstrate the general applicability of the model to different engine designs, the correct description of the main mechanisms contributing to fuel partial oxidation, and the potential to be extended to predict unburned fuel emissions with other fuels.

Time-dependent surface-enhanced Raman scattering: A theoretical approach.

A new procedure for computing the time-dependent Raman scattering of molecules in the proximity of plasmonic nanoparticles (NPs) is proposed, drawing inspiration from the pioneering Lee and Heller's theory. This strategy is based on a preliminary simulation of the molecular vibronic wavefunction in the presence of a plasmonic nanostructure and an incident light pulse. Subsequently, the Raman signal is evaluated through an inverse Fourier Transform of the coefficients' dynamics. Employing a multiscale approach, the system is treated by coupling the quantum mechanical description of the molecule with the polarizable continuum model for the NP. This method offers a unique advantage by providing insights into the time evolution of the plasmon-enhanced Raman signal, tracking the dynamics of the incident electric field. It not only provides for the total Raman signal at the process's conclusion but also gives transient information. Importantly, the flexibility of this approach allows for the simulation of various incident electric field profiles, enabling a closer alignment with experimental setups. This adaptability ensures that the method is relevant and applicable to diverse real-world scenarios.

Employing Williams’ series for the identification of fracture mechanics parameters from phase-field simulations

Fracture mechanics and damage mechanics are two theories that describe the degradation of the bearing capacity of structures. Fracture mechanics is based on a discontinuous description of cracking, while damage mechanics proposes a continuous description of material degradation. These two approaches are often opposed in the literature, from both theoretical and numerical points of view. This work suggests correlating the two approaches by applying Williams’ series, usually dedicated to experimental results, to phase-field computations. Williams’ series are employed to extract equivalent fracture mechanics parameters as a post-processing step. The proposed analysis based on a fracture mechanics description excludes the fracture process zone. Typical fracture mechanics parameters such as energy release rate, stress intensity factors, fracture process zone size, and crack tip position are determined from the phase-field computations. The approach is illustrated on a two-dimensional structure representing a beam whose notch opening displacement is controlled. The dependence on the choice of the internal length of the phase-field model is studied. Similarities and differences between both modeling routes are discussed.

Quantum nature of spacetime near the black hole singularity

The concept of spacetime loses its usual interpretation at the essential singularity of a black hole. In consequence, all laws of physics must fail at this classical singularity. This unphysical behavior of spacetime at the singularity originates from general relativity. In order to have a consistent description of spacetime, this singularity must disappear in a quantum mechanical description of spacetime which is expected to be given by a quantum theory of gravity. In this paper, we therefore attempt to describe the quantum nature of spacetime in the vicinity of the (classical) singularity of a black hole. We take the Kantowsi–Sachs representation for the interior spacetime of a black hole and include inevitable vacuum fluctuations of matter field in the Klein–Gordon representation. Hence we obtain the Wheeler–DeWitt equation for the black hole interior and solve this equation exactly yielding a general expression for the interior wave function of the black hole. Admissible wave functions consistent with the DeWitt boundary condition implies that the Hilbert space has three nonoverlapping sectors distinguished by the relative character of the eigenvalues. Regular quantum black holes with admissible and well-behaved wave function having no singularity can exist only in two of those sectors. However, the remaining sector does not contain any regular quantum black hole.

Auditory localization: a comprehensive practical review.

Auditory localization is a fundamental ability that allows to perceive the spatial location of a sound source in the environment. The present work aims to provide a comprehensive overview of the mechanisms and acoustic cues used by the human perceptual system to achieve such accurate auditory localization. Acoustic cues are derived from the physical properties of sound waves, and many factors allow and influence auditory localization abilities. This review presents the monaural and binaural perceptual mechanisms involved in auditory localization in the three dimensions. Besides the main mechanisms of Interaural Time Difference, Interaural Level Difference and Head Related Transfer Function, secondary important elements such as reverberation and motion, are also analyzed. For each mechanism, the perceptual limits of localization abilities are presented. A section is specifically devoted to reference systems in space, and to the pointing methods used in experimental research. Finally, some cases of misperception and auditory illusion are described. More than a simple description of the perceptual mechanisms underlying localization, this paper is intended to provide also practical information available for experiments and work in the auditory field.

Harnessing ultrasound-derived hydroxyl radicals for the selective oxidation of aldehyde functions.

Ultrasonic irradiation holds potential for the selective oxidation of non-volatile organic substrates in the aqueous phase by harnessing hydroxyl radicals as chemical initiators. Here, a mechanistic description of hydroxyl radical-initiated glyoxal oxidation is constructed by gleaning insights from photolysis and radiation chemistry to explain the yields and kinetic trends for oxidation products. The mechanistic description and kinetic measurements reported herein reveal that increasing the formation rate of hydroxyl radicals by changing the ultrasound frequency increases both the rates of glyoxal consumption and the selectivity towards C2acid products over those from C-C cleavage. Glyoxal consumption also occurs more rapidly and with greater selectivity towards C2acids under acidic conditions, which favor the protonation of carboxylate intermediates into their less reactive acidic forms. Leveraging such pH and frequency effects is crucial to mitigating product degradation by secondary reactions with hydroxyl radicals and oxidation products (specifically hydrogen peroxide and superoxide). These findings demonstrate the potential of ultrasound as a driver forthe selective oxidation of aldehyde functions to carboxylic acids, offering a sustainable route for valorizing biomass-derived platform molecules.

Fuel pin failure modes in the UK's advanced gas cooled reactors

The current paper presents a review of key failure modes in AGR fuel, a description of failure mechanisms and the post failure effects that follow.The main failure modes of AGR fuel are found in the following proportions: ratchetting (axial clad straining and fuel-stacking with resulting fuel-stack gap formation and clad collapse) 3%; over pressure 4%; pellet clad mechanical interaction 7%; pin-brace interaction/rotating pins (fuel pin and support structure interaction, also known as fretting) 37%; clad restructuring/microstructural effects (including clad grain growth reducing ability of clad to withstand pellet clad interaction) 41%; other (including chipped pellets, endcap welds, and non-fuel component damage) 8%.A description of each failure mode is provided detailing the characteristics of the failure mode and a summary of the factors contributing to the failure mode.An overview of post-failure effects in AGR fuel is provided. Observations of failed fuel in hot-cells reveal a range of post-failure effects, in addition to the characteristics which contributed to the failure. Understanding post failure effects is important in order to isolate features which may have occurred prior to failure, and to inform on the behaviour of fuel between failure and discharge from reactor.

Insights and Challenges in Correcting Force Field Based Solvation Free Energies Using a Neural Network Potential.

We present a comprehensive study investigating the potential gain in accuracy for calculating absolute solvation free energies (ASFE) using a neural network potential to describe the intramolecular energy of the solute. We calculated the ASFE for most compounds from the FreeSolv database using the Open Force Field (OpenFF) and compared them to earlier results obtained with the CHARMM General Force Field (CGenFF). By applying a nonequilibrium (NEQ) switching approach between the molecular mechanics (MM) description (either OpenFF or CGenFF) and the neural net potential (NNP)/MM level of theory (using ANI-2x as the NNP potential), we attempted to improve the accuracy of the calculated ASFEs. The predictive performance of the results did not change when this approach was applied to all 589 small molecules in the FreeSolv database that ANI-2x can describe. When selecting a subset of 156 molecules, focusing on compounds where the force fields performed poorly, we saw a slight improvement in the root-mean-square error (RMSE) and mean absolute error (MAE). The majority of our calculations utilized unidirectional NEQ protocols based on Jarzynski's equation. Additionally, we conducted bidirectional NEQ switching for a subset of 156 solutes. Notably, only a small fraction (10 out of 156) exhibited statistically significant discrepancies between unidirectional and bidirectional NEQ switching free energy estimates.

Probing conformational dynamics of DNA binding by CO-sensing transcription factor, CooA

The transcription factor CooA is a CRP/FNR (cAMP receptor protein/ fumarate and nitrate reductase) superfamily protein that uses heme to sense carbon monoxide (CO). Allosteric activation of CooA in response to CO binding is currently described as a series of discrete structural changes, without much consideration for the potential role of protein dynamics in the process of DNA binding. This work uses site-directed spin-label electron paramagnetic resonance spectroscopy (SDSL-EPR) to probe slow timescale (μs-ms) conformational dynamics of CooA with a redox-stable nitroxide spin label, and IR spectroscopy to probe the environment at the CO-bound heme. A series of cysteine substitution variants were created to selectively label CooA in key functional regions, the heme-binding domain, the 4/5-loop, the hinge region, and the DNA binding domain. The EPR spectra of labeled CooA variants are compared across three functional states: Fe(III) “locked off”, Fe(II)-CO “on”, and Fe(II)-CO bound to DNA. We observe changes in the multicomponent EPR spectra at each location; most notably in the hinge region and DNA binding domain, broadening the description of the CooA allosteric mechanism to include the role of protein dynamics in DNA binding. DNA-dependent changes in IR vibrational frequency and band broadening further suggest that there is conformational heterogeneity in the active WT protein and that DNA binding alters the environment of the heme-bound CO.

Effects of nitric oxide inhalation on pulmonary arterial impedance: differences between normal and pulmonary hypertension male rats.

Nitric oxide (NO) inhalation improves pulmonary hemodynamics in participants with pulmonary arterial hypertension (PAH). Although it can reduce pulmonary vascular resistance (PVR) in PAH, its impact on the dynamic mechanics of pulmonary arteries and its potential difference between control and participants with PAH remain unclear. PA impedance provides a comprehensive description of PA mechanics. With an arterial model, PA impedance can be parameterized into peripheral pulmonary resistance (Rp), arterial compliance (Cp), characteristic impedance of the proximal arteries (Zc), and transmission time from the main PA to the reflection site. This study investigated the effects of inhaled NO on PA impedance and its associated parameters in control and monocrotaline-induced pulmonary arterial hypertension (MCT-PAH) male rats (6/group). Measurements were obtained at baseline and during NO inhalation at 40 and 80 ppm. In both groups, NO inhalation decreased PVR and increased the left atrial pressure. Notably, its impact on PA impedance was frequency dependent, as revealed by reduced PA impedance modulus in the low-frequency range below 10 Hz, with little effect on the high-frequency range. Furthermore, NO inhalation attenuated Rp, increased Cp, and prolonged transmission time without affecting Zc. It reduced Rp more pronouncedly in MCT-PAH rats, whereas it increased Cp and delayed transmission time more effectively in control rats. In conclusion, the therapeutic effects of inhaled NO on PA impedance were frequency dependent and may differ between the control and MCT-PAH groups, suggesting that the effect on the mechanics differs depending on the pathological state.NEW & NOTEWORTHY Nitric oxide inhalation decreased pulmonary arterial impedance in the low-frequency range (<10 Hz) with little impact on the high-frequency range. It reduced peripheral pulmonary resistance more pronouncedly in pulmonary hypertension rats, whereas it increased arterial compliance and transmission time in control rats. Its effect on the mechanics of the pulmonary arteries may differ depending on the pathological status.

Potential innovations from the application of beneficial soil microbes to promote sustainable crop production

Crop productivity may be significantly inhibited by factors, such as increased temperature, soil erosion, pathogen and pest attacks, and drought and salt stresses, mostly resulting from global climate change. However, microorganisms that are found in the rhizosphere can aid in the mobilization of essential soil nutrients, facilitate plant growth, and reduce abiotic and biotic stresses of plants. Soil microbes accomplish these beneficial functions via several mechanisms. Here, an elaborate description of the molecular mechanisms of plant growth-promotion by soil microbes and the potential of these organisms to be used as biofertilizers and biopesticides to improve plant health is provided. In addition, the possible revolution that could be realized by the synergism of these beneficial microbes with nanotechnology is discussed. While the use of biofertilizers to enhance plant growth has been demonstrated to be a beneficial phenomenon, this approach has often failed to yield the desired result in field applications. However, identifying microbial species with beneficial attributes and combining them with nanotechnology tools like nanoencapsulation and biosensors could lead to the formulation of important agriproducts (nanobiopesticides and nanobiofertilizers) that will ensure sustained delivery of the agriproducts and facilitate early detection and proper management of plant pests and diseases. It is anticipated that precision farming will improve agricultural sustainability by increasing crop production for the steadily increasing world population. Keywords: biofertilizers, secondary metabolites, nanoencapsulation, quorum sensing, volatile organic compounds, sustainable agriculture.

Reaction Mechanism in Standardized α-Cellulose Content Test: Study from Boehmeria nivea Fiber

In defense industry, α-cellulose is the main component of nitrocellulose propellant. However, a detailed description of the reaction mechanism of each treatment step in SNI 0444-2009 is still very scarce. This study addresses this gap by presenting the reaction mechanisms of each treatment and the symbols used in the SNI 0444-2009 procedure. The separation of lignin from α-cellulose occurred by breaking the C‒O bond linking them. This bond was broken by the ‒OH group of NaOH via a hydrolysis reaction. The reaction was initiated with the elimination of a hydrogen atom from the lignin structure by the hydroxyl ion (‒OH), and the C‒O bond was broken by a hydrolysis reaction. The breaking of this bond was indicated by the disappearance of the IR peaks at wavenumbers 1049 and 1190 cm–1 in the filtrate after extraction. The SNI 0444-2009 method for the α-cellulose content test was carried out by a redox back titration of Cr(VI) with Fe(II) from ferrous ammonium sulfate. This titration was conducted to calculate the amount of Cr(VI) ions in potassium dichromate or Cr(VI) that did not react with lignin or beta cellulose in the filtrate. Understanding the contribution and reaction mechanisms of each compound involved in the SNI 0444-2009 procedure contributed to obtaining accurate data on α-cellulose content. In this study, the calculated α-cellulose content of the flax fiber was 96.75%. Furthermore, the detailed mechanism of the redox reaction was discussed in detail in this paper.

An asymptotic description of a basic FcRn-regulated clearance mechanism and its implications for PBPK modelling of large antibodies.

A basic FcRn-regulated clearance mechanism is investigated using the method of matched asymptotic expansions. The broader aim of the work is to obtain further insight on the mechanism, thereby providing theoretical support for future pharmacologically-based pharmacokinetic modelling efforts. The corresponding governing equations are first non-dimensionalised and the order of magnitudes of the model parameters are assessed based on their values reported in the literature. Under the assumption of high FcRn-binding affinity, analytical approximations are derived that are valid over the characteristic phases of the problem. Additionally, relatively simple equations relating clearance and AUC to physiological model parameters are derived, which are valid over the longest characteristic time scale of the problem. For lower to moderate doses clearance is effectively linear, whereas for higher doses it is nonlinear. It is shown that for all doses sufficiently high the leading-order approximation for the IgG concentration in plasma, over the longest characteristic time scale, is independent of the initial dose. This is because IgG that is in 'excess' of FcRn is eliminated over a time scale much shorter than that of the terminal phase. In conclusion, analytical approximations of the basic FcRn mechanism have been derived using matched asymptotic expansions, leading to a simple equation relating clearance to FcRn binding affinity, the ratio of degradation and FcRn concentration, and the volumes of the system.

Unlocking the Potential: Semaglutide's Impact on Alzheimer's and Parkinson's Disease in Animal Models.

Semaglutide (SEM), a glucagon-like peptide-1 receptor agonist, has garnered increasing interest for its potential therapeutic effects in neurodegenerative disorders such as Alzheimer's disease (AD) and Parkinson's disease (PD). This review provides a comprehensive description of SEM's mechanism of action and its effects in preclinical studies of these debilitating conditions. In animal models of AD, SEM has proved beneficial effects on multiple pathological hallmarks of the disease. SEM administration has been associated with reductions in amyloid-beta plaque deposition and mitigation of neuroinflammation. Moreover, SEM treatment has been shown to ameliorate behavioral deficits related to anxiety and social interaction. SEM-treated animals exhibit improvements in spatial learning and memory retention tasks, as evidenced by enhanced performance in maze navigation tests and novel object recognition assays. Similarly, in animal models of PD, SEM has demonstrated promising neuroprotective effects through various mechanisms. These include modulation of neuroinflammation, enhancement of mitochondrial function, and promotion of neurogenesis. Additionally, SEM has been shown to improve motor function and ameliorate dopaminergic neuronal loss, offering the potential for disease-modifying treatment strategies. Overall, the accumulating evidence from preclinical studies suggests that SEM holds promise as a novel therapeutic approach for AD and PD. Further research is warranted to elucidate the underlying mechanisms of SEM's neuroprotective effects and to translate these findings into clinical applications for the treatment of these devastating neurodegenerative disorders.

The role of axial angular momentum in exact non-linear solutions of multipolar spherical and cylindrical vortices

The time-dependent acceleration of fluid particles in an arbitrary superposition of multipolar spherical and cylindrical vortices in presence of a background rotational rigid flow is the gradient of the difference between their kinetic energy and the product of their total axial angular momentum times the angular velocity of the background flow. If the potential energy is defined as the time-dependent field whose minus gradient equals the acceleration of the flow, then the total energy, defined as the sum of kinetic and potential energies, equals the total axial angular momentum times the angular velocity of the background flow. The total energy of a fluid particle has therefore a linear relationship with the azimuthal velocity field. The role of the axial angular momentum in these oscillating flows is explained also in the classical Lagrangian and Hamiltonian descriptions of motion. The linear relation between total energy and angular momentum makes possible that the free parameters of these flows may be obtained, in a way similar to that developed in the quantum mechanics description of motion, as the eigenvalues of linear operators acting on some components of the spherical modes. Beltrami flow solutions in prolate spheroidal geometry for axisymmetric flows are also discussed.