Potential Equation Research Articles

Wave excited motion of a body floating on water confined between a semi-infinite ice sheet and a side wall

In this paper, we investigate the diffraction and radiation coupling problem of a floating body confined between a fixed wall and a semi-infinite ice sheet under the action of incident waves. Based on the linear water wave theory and Kirchhoff Love elastic thin plate assumption, the ice sheet is considered as an elastic beam, and the boundary conditions of fluid boundaries covered by the ice sheet are obtained. Dividing flow domains with different upper surfaces, the eigenfunction expansion method was used to obtain the velocity potential expansion equations for each sub-domain. Then, through the matching conditions at the interface of sub-domains, a system of equations was constructed to solve the unknown coefficients of the expansion equations. The influence of the existence of the ice sheet on the diffraction and radiation motion of the floating body is analyzed. The effects of changes in the draft and open water width of the floating body on the wave excitation force and hydrodynamic coefficient of the floating body are discussed. The influence of the reflection effect of the ice sheet on the added mass and damping coefficient of the floating body has been discovered, especially the changes and oscillation rules of their extreme points. This research achievement provides theoretical support for the safety design of floating structures in frozen harbors.

Rossby waves with barotropic–baroclinic coherent structures and dynamics for the (2 + 1)-dimensional coupled cylindrical KP equations with variable coefficients

Starting from the classical quasi-geostrophic potential vorticity equation with equal depth two-layer fluid, the coupled cylindrical Kadomtsev–Petviashvili (KP) equations with variable coefficients for Rossby waves are studied. To be more general, the phase velocity is considered an indefinite integral about time and improves the analysis procedure. So the variable coefficients are obtained and some previous studies are reasonably explained. The cylindrical wave theory is therewith utilized to reduce the coupled cylindrical KP equations with variable coefficients, and based on the modified Hirota bilinear method, the lump solutions and interaction solutions are found. Through numerical simulations, the Rossby lump waves on both sides of the y axis move closer to the center, and their amplitude gradually decreases and tends to flatten with the generalized Rossby parameter growth. In the Rossby waves flow field, the dipole structures propagate to the east and lead to the appearance of the compress phenomenon during barotropic–baroclinic interaction. It is possibly useful for further theoretical research on atmospheric phenomena.

Effect of hills on wind turbine flow and power efficiency: A large-eddy simulation study

This study investigates the influence of topography on wind turbine flow and power efficiency. Specifically, a standalone wind turbine is positioned at the top of idealized two-dimensional hills, and the effects of hill geometry and turbine position are systematically investigated. Various parameters are studied, including hill slope, distance between the leeward side of the hill and the turbine, turbine hub height, and hill size. Overall, it is observed that the turbine wake is consistently stronger in the hill cases compared to the flat case. This is attributed to two characteristics of hill flows: (1) the negative streamwise velocity gradients on the leeward side of the hills and (2) the reduced turbulence above the hilltops and hill wake regions. In addition, it is observed that the turbine induction factor is consistently increased in the hill cases compared to the flat case, while the turbine power and thrust coefficients are reduced. In practice, this means that turbines on the hills produce less power output than those on flat terrain for an equivalent wind potential, with the potential decrease in power output reaching more than 20% for certain cases. Altogether, the results offer new insights into the effect of topography on turbine power efficiency. In addition, the study identifies clear relationships between the turbine power coefficient, the induction factor, the overall maximum deficit, and the base flow pressure gradient. These relationships could potentially be used to predict the change in power efficiency based on the wake flow or the base flow. Overall, the results show a clear connection between the turbine power efficiency and the turbine wake development.

An exact treatment of localization of electromagnetic plus separable potential

Equivalent local potential with energy-momentum dependence is developed for the combined interaction of Hulthén modified Yamaguchi potential by developing its exact Jost solution. The generated local potentials are applied to compute scattering phase parameters for (p-p) and (p-d) systems through the phase function method (PFM). The same are also calculated for the nonlocal potential from the expression of the Fredholm determinant. Our obtained data for both the energy-momentum dependent local and the pure nonlocal interactions are in reasonable agreement with the standard data. Reasonable correspondence between the results for the phase equivalent and the nonlocal potentials indicate that our equivalent local analysis is in proper order.

Performance of plant growth regulators in soybean cultivation under differente aplication methods

The utilization of biostimulants has emerged as a promising approach in agriculture, aiming to augment the physiological processes associated with germination and growth across diverse plant species, thereby leading to substantial and sustainable enhancements in agricultural productivity. Grounded in scientific insights, this study endeavored to juxtapose the efficacy of a biostimulant compound against conventional market-available products. The application methodologies encompassed seed treatment and foliar spraying at the V2 growth stage, with a primary focus on productivity augmentation. The investigation transpired at the Agricultural Technological Center of Paraguay (CETAPAR) in Colônia Iguazu, Paraguay, utilizing a randomized complete block design (RCBD) featuring 16 treatments replicated four times. Dosages were administered in adherence to label recommendations. Productivity data underwent rigorous statistical analyses, including the F-test and Dunnett's test, with a significance level set at 10%. Remarkably, foliar applications at the V2 phenological stage and seed treatments outperformed other modalities, yielding notable outputs of 4,431 kg.ha-1 and 4,419 kg.ha-1, respectively. Noteworthy is the observation that the tested biostimulant formulation exhibited equivalent or superior potential when juxtaposed with commercial counterparts. The findings underscore the viability of integrating biostimulants as a compelling strategy to optimize agricultural productivity, thereby furnishing farmers with an efficacious and sustainable alternative.

Accreting black holes in dark matter halos

We examine the thin accretion disk behaviors surrounding black holes embedded in cold dark matter halos and scalar field dark matter halos. We first calculate the event horizons and derive the equations of motion and effective potential in black hole geometries with different dark matter halos. We then compute the specific energy, specific angular momentum, and angular velocity of particles moving along circular orbits. We also derive the effective potentials to find the locations of the innermost stable circular orbit (ISCO) and compare them to the Schwarzschild and Kerr black holes without the dark matter halos. We also use the observed ISCO of the supermassive black hole at the Galactic Center of the Milky Way, Sagittarius A*, to constrain the dark matter halos. Published by the American Physical Society 2024

Symmetries of the Electromagnetic Turbulence in a Tokamak Edge

We construct the low-frequency formulation of the turbulence characterizing the plasma in a Tokamak edge. Under rather natural assumptions, we demonstrate that, even in the presence of poloidal magnetic fluctuations, it is possible to deal with a reduced model for turbulence dynamics. This model relies on a single equation for the electric potential from which all the physical turbulent properties can be calculated. The main result of the present analysis concerns the existence of a specific Fourier branch for the dynamics which demonstrate the attractive character of the two-dimensional turbulence with respect to non-axisymmetric fluctuations. The peculiar nature of this instability, affecting the non-axially symmetric modes, is discussed in some detail by recovering two different physical regimes.

Utilisation of the site assessment energy indices for aquaculture in exposed waters: biology, technology, operations and maintenance

When moving from a very sheltered aquaculture site to a very exposed oceanic aquaculture site, the energy increases proportionally in a continuum. Lojek et al. (in review) considered the primary influential parameters (water current, wave height, wave period, wavelength and water depth) which influence the species, structure, technology, methods, and operational aspects of any aquaculture endeavour and investigated six possible indices which cover these variables. Added to advanced computer modelling, assisted by detailed and constant environmental monitoring, it may be possible to refine site selection, structure selection and design, species selection, equipment and logistic requirements and health and safety requirements. This manuscript has selected two indicative indices: Specific Exposure Energy (SEE) index and Exposure Velocity (EV) index from the potential equations provided by Lojek et al. (in review) and compared them with known operational aquaculture sites highlighting present structural capability and limitations. The two indices are also utilized to reflect on their suitability for assessing sample sites with respect to biological, technological, operational or maintenance aspects of aquaculture activities. The indices have shown themselves to be useful tools in the general assessment of the energy that will influence the species and structure selection at potential aquaculture sites. This information can help prospective fish farmers characterize their sites concisely and accurately to consultants, regulators, equipment vendors, and insurance brokers.

Mechanism and experimental study of in situ metallization on the surface of silver ion conductive glass

AbstractIn situ metallization of Ag+ conductive glass was successfully achieved by applying electric and temperature fields to the glass to ensure the controlled migration of ions inside the glass. The transport and kinetic characteristics of Ag+ under the combined effect of electric field and temperature field were investigated by calculating and analyzing Ag+ diffusion coefficient. The correlations between ion transport and current were characterized with potential energy equations. The simulations and experiments of ion transport in the conducting glass were implemented, which revealed the mechanisms of ion transport and interfacial precipitation within the conducting glass. Further more, the existence of Ag+ deprivation layer was confirmed and it was clarified that the depth of the deprivation layer reached 30 µm under thermal polarization conditions of 60 V and 300°C. The microscopic morphology of in situ silver deposition layer was observed using SEM and TOF–SIMS. In addition, It was determined that the in situ metallization of conductive glass under the polarization condition of 60 V at 250°C was the best, and the thickness of deposited silver dendrites reached 1000 nm in the side of cathodically. This paper provides theoretical and experimental references for the optimization of the in situ metallization process for the ion conductive glass.

A comparison of intense rainfall characteristics and mechanisms between monsoon onset and retreat over the Yangtze River Basin

ABSTRACT The thermodynamic and convective characteristics of the seasonal progression of the monsoon over eastern China are examined, with the aim of understanding why regional heavy rainfall events (RHREs) over the Yangtze River Basin (YRB) are more frequent and intense during the monsoon progression from mid-June to mid-July than during the retreat from mid-August to mid-September. During the monsoon progression, the southerly monsoon flow at low and mid-levels intensifies and moves northward, while the Western Pacific subtropical high shifts northeastward. These changes result in enhanced moisture advection over eastern China. The stronger southerly flow brings warmer and moist air into the YRB, leading to a higher equivalent potential temperature (θE) and favouring convection. Conversely, during the monsoon retreat, the northerly flow becomes stronger and drier, causing lower θE air over the YRB. Additionally, as the Western Pacific subtropical anticyclone retreats, easterly prevailing winds prevail over eastern China, causing reduced specific humidity. The monsoon progression period exhibits higher convective available potential energy but also higher convective inhibition, which is overcome by the presence of the monsoon front providing sufficient dynamical uplift. Understanding the severity of RHREs, particularly over the YRB, is crucial for improving forecasting capabilities and reducing societal vulnerability.

Hydrodynamic Impact of Dusty Fluid-Suspended Solid Particles in a Single-Walled Corrugated Channel for Water-Curing Infrastructure Networks

Infrastructure engineering is impacted by solid particles in fluids, and engineering components are influenced by fluid flow methods. This work explores the effects of dusty fluids with suspended solid particles in a single-walled corrugated channel using electromagnetic hydrodynamics. Potential, continuity, and momentum equations were employed to study the periodic sinusoidal waves in the corrugations of two wavy walls using the perturbation method. We assessed the impact of corrugation on velocity for EMHD fluid flow using mathematical computation, concentrating on the analytical velocity solutions. The analysis of velocity profiles through graphs reveals that corrugation affects fluid and particle velocity behavior, with small amplitude reducing wave effects and dusty particles boosting velocity. The proposed model uses mathematical induction to solve engineering problems using corrugated wall conditions for fluid control during curing stages. It may be valuable for sanitation networks, rainwater drainage networks, and irrigation systems. In the end, a thorough examination of the obtained results and information from past papers demonstrated a high level of agreement. Additionally, its use in the curing of water will offer alternative methods of managing the flowing fluid than mechanical pressure.

On the calculation of irregular solutions of the Schrödinger equation for non-spherical potentials with applications to metallic alloys

The irregular solutions of the stationary Schrödinger equation are important for the fundamental formal development of scattering theory. They are also necessary for the analytical properties of the Green function, which in practice can greatly speed up calculations. Nevertheless, they are seldom considered in numerical treatments because of their divergent behavior at origin. This divergence demands high numerical precision that is difficult to achieve, particularly for non-spherical potentials which lead to different divergence rates in the coupled angular momentum channels. Based on an unconventional treatment of boundary conditions, an integral-equation method is here developed which is capable of dealing with this problem. The available precision is illustrated by electron-density calculations for NiTi in its monoclinic B19’ structure.

Compressible fluid limit for smooth solutions to the Landau equation

Although the compressible fluid limit of the Boltzmann equation with cutoff has been extensively investigated in Caflisch [Comm. Pure Appl. Math. 33 (1980), 651–666] and Guo, Jang, and Jiang [Comm. Pure Appl. Math. 63 (2010), 337–361], obtaining analogous results in the case of the angular non-cutoff or even in the grazing limit which gives the Landau equation, still remains largely open, essentially due to the velocity diffusion effect of the collision operator such that L^{\infty} estimates are hard to obtain without using Sobolev embeddings. In this paper, we are concerned with the compressible Euler and acoustic limits of the Landau equation for Coulomb potentials in the whole space. Specifically, over any finite time interval where the full compressible Euler system admits a smooth solution around constant states, we construct a unique solution in a high-order weighted Sobolev space for the Landau equation with suitable initial data and also show the uniform estimates independent of the small Knudsen number \varepsilon>0 , yielding the O(\varepsilon) convergence of the Landau solution to the local Maxwellian whose fluid quantities are the given Euler solution. Moreover, the acoustic limit for smooth solutions to the Landau equation in an optimal scaling is also established. For the proof, by using the macro-micro decomposition around local Maxwellians, together with techniques for viscous compressible fluid and properties of Burnett functions, we design an \varepsilon -dependent energy functional to capture the dissipation in the compressible fluid limit with the feature that only the highest-order derivatives are most singular.

Consistent and conservative lattice Boltzmann method for axisymmetric multiphase electrohydrodynamic flows

In this work, we first develop a consistent and conservative mathematical model to study multiphase electrohydrodynamic (EHD) flows, including the reduction-consistent and conservative Allen-Cahn equation for the multiphase field, the Laplace equation for the electric potential, and the consistent and conservative Navier–Stokes equations for the flow field. Owing to the reduction-consistent property, the present model can be used to handle a set of M (1≤M≤N) EHD fluids in N-phase system. Then a two-relaxation-time lattice Boltzmann (LB) method is proposed for axisymmetric multiphase EHD flows, which can correctly recover the axisymmetric governing equations through the direct Taylor expansion analysis. To test the capacity of the LB method, the deformations of a single two-phase droplet and a ternary-phase compound droplet under a uniform electric field are considered. It is found that different from a single droplet with two deformation modes, the compound droplet has four deformation modes, and additionally, the effects of the electric strength, the conductivity ratio and the permittivity ratio on the compound droplet are also investigated. Finally, the compound droplet in the quaternary-phase system is also explored, and there are eight deformation modes that have not been reported in the available literature.

Design and evaluation of a four-DoF upper limb exoskeleton with gravity compensation

Gravity compensation (GC) mechanisms are commonly employed to either support limb gravity in passive exoskeletons or decrease motor power for safe human-robot interaction in active exoskeletons. This paper proposes a four-degree-of-freedom (DoF) upper limb exoskeleton with a theoretically perfect GC system, incorporating three DoFs in the shoulder and one DoF in the elbow. Paired with the anthropomorphic structure, the compact and adjustable GC system housed within the exoskeleton's linkages, reduces limitations on the limb's motion range and facilitates the integration of actuators for an active system. First, the GC system is designed through the analysis of potential energy equations, employing five cable-pulley-spring based units interconnected by parallel and differential mechanisms. Subsequently, the mechanical structure of the exoskeleton is developed, and the theoretically perfect GC in the quasi-static state is verified through numerical calculations. Then, the prototype is fabricated, and its actual performance is evaluated through experiments. The experimental results demonstrate the effectiveness of the exoskeleton with GC. Finally, a potential solution for the integration of actuators is demonstrated, and the limitation of the proposed system is also well discussed.

Lagrangian multiform structure of discrete and semi-discrete KP systems

A variational structure for the potential AKP system is established using the novel formalism of a Lagrangian multiforms. The structure comprises not only the fully discrete equation on the 3D lattice, but also its semi-discrete variants including several differential-difference equations asssociated with, and compatible with, the partial difference equation. To this end, an overview is given of the various (discrete and semi-discrete) variants of the KP system, and their associated Lax representations, including a novel `generating PDE' for the KP hierarchy. The exterior derivative of the Lagrangian 3-form for the lattice potential KP equation is shown to exhibit a double-zero structure, which implies the corresponding generalised Euler-Lagrange equations. Alongside the 3-form structures, we develop a variational formulation of the corresponding Lax systems via the square eigenfunction representation arising from the relevant direct linearization scheme.

Delineating redox cooperativity in water-soluble and membrane multiheme cytochromes through protein design.

Nature has evolved diverse electron transport proteins and multiprotein assemblies essential to the generation and transduction of biological energy. However, substantially modifying or adapting these proteins for user-defined applications or to gain fundamental mechanistic insight can be hindered by their inherent complexity. De novo protein design offers an attractive route to stripping away this confounding complexity, enabling us to probe the fundamental workings of these bioenergetic proteins and systems, while providing robust, modular platforms for constructing completely artificial electron-conducting circuitry. Here, we use a set of de novo designed mono-heme and di-heme soluble and membrane proteins to delineate the contributions of electrostatic micro-environments and dielectric properties of the surrounding protein medium on the inter-heme redox cooperativity that we have previously reported. Experimentally, we find that the two heme sites in both the water-soluble and membrane constructs have broadly equivalent redox potentials in isolation, in agreement with Poisson-Boltzmann Continuum Electrostatics calculations. BioDC, a Python program for the estimation of electron transfer energetics and kinetics within multiheme cytochromes, also predicts equivalent heme sites, and reports that burial within the low dielectric environment of the membrane strengthens heme-heme electrostatic coupling. We conclude that redox cooperativity in our diheme cytochromes is largely driven by heme electrostatic coupling and confirm that this effect is greatly strengthened by burial in the membrane. These results demonstrate that while our de novo proteins present minimalist, new-to-nature constructs, they enable the dissection and microscopic examination of processes fundamental to the function of vital, yet complex, bioenergetic assemblies.

Physical quantity characteristics of severe aircraft turbulence near convective clouds over Australia

Using FY–2G satellite data, Aircraft Meteorological Data Relay (AMDAR) downlink data, and the fifth generation European Centre for Medium–Range Weather Forecasts (ECMWF) atmospheric reanalysis of the global climate (ERA5) dataset, we analyzed the circulation, thermal, and dynamic characteristics of the convective aircraft turbulence over Australia in the Southern Hemisphere. The results show that the near-convective clouds turbulence (NCCT) in the Southern Hemisphere mostly occurred in front of deep warm high–pressure ridges in mid–latitude regions and on the left side of the axis of the subtropical westerly jet stream. The isotherms in this area were relatively dense (i.e., large gradients), and the wind speed was high, with strong horizontal and/or vertical cyclonic wind shear. In addition, the NCCT usually occurred near the zero–divergence or zero–vorticity line and in areas with large vertical wind speed gradients. There were also strong vertical and horizontal wind shears in this area, which could easily trigger severe turbulence. Furthermore, the NCCT in the Southern Hemisphere mostly occurred at the intersection of cold and warm temperature advections (i.e., near the zero–temperature advection line), and the turbulence point was located near the high–altitude frontal zone where there was a strong gradient of cold and warm advections. There was temperature inversion with pseudo–equivalent potential temperatures in the middle and lower troposphere on the warmer side of the turbulence point. The unstable stratification of cold air at the top and warm air at the bottom was conducive to triggering convection from the ground, forming strong convective clouds, and causing severe turbulence.

Numerical Calculations of Liquid-Metal Magnetohydrodynamic Flows in Rectangular Ducts with Sudden Contractions

For the design of the liquid-metal blanket in a fusion reactor, numerical calculations have been carried out on liquid-metal magnetohydrodynamic flows in rectangular ducts with sudden contractions. Conservation equations of fluid mass and fluid momentum and the Poisson equation for electrical potential have been solved numerically. The numerical calculations have been conducted for a Hartmann number of ~10 000; a Reynolds number of ~10 000; and contraction ratios (CRs) of 2, 3, and 4. The pressure loss through the contraction has been estimated by the loss coefficient ζ divided by the interaction parameter N, i.e. ζ/N. The loss coefficient ζ/N through the contraction parallel to the magnetic field is much larger than that through the corresponding contraction perpendicular to the magnetic field. The loss coefficient ζ/N increases consistently with the CR and does not change very much with N. While ζ/N also does not change very much with the wall conductance ratio for the contraction parallel to the magnetic field, ζ/N increases gradually with the wall conductance ratio for the contraction perpendicular to the magnetic field.

What Is the Carbon Footprint of Adult Spinal Deformity Surgery?

Background/Objectives: While the economic cost of adult spinal deformity (ASD) surgery has been studied extensively, its environmental impact is unknown. The aim of this study is to determine the carbon footprint (CF) associated with ASD surgery. Methods: ASD patients who underwent > four levels of corrective surgery between 2017 and 2021 were included. The open group included a posterior-only, single-stage technique, while the minimally invasive surgery (MIS) group was defined as the use of lateral interbody fusion and percutaneous posterior screw fixation. The two groups were propensity-score matched to adjust for baseline demographic, surgical, and radiographic characteristics. Data on all disposables and reusable instruments, anesthetic gas, and non-gas medications used during surgery were collected from medical records. The CF of transporting, using, and disposing of each product and the footprint of energy use in operating rooms were calculated. The CF produced was evaluated using the carbon dioxide equivalent (CO2e), which is relative to the amount of CO2 with an equivalent global warming potential. Results: Of the 175 eligible patients, 15 pairs (65 ± 9 years, 47% female) were properly matched and analyzed for all variables. The average CF generated per case was 147.7 ± 37.3 kg-CO2e, of which 54% was attributable to energy used to sterilize reusable instruments, followed by anesthetic gas released into the environment (17%) and operating room air conditioning (15%). Conclusions: The CF generated during ASD surgery should be reduced using a multidisciplinary approach, taking into account that different surgical procedures have different impacts on carbon emission sources.