Force Approximation Research Articles

Mooring systems with submerged buoys: influence of buoy geometry and modelling fidelity

Mooring systems often make use of submerged buoys (SBs) in order to make the moorings compliant. In this paper we present the dynamic effects of changing the buoy geometry or the buoy model fidelity on the mooring system response. Three cylindrical SBs with increasing slenderness (height/diameter) are studied for a mooring leg with two polyester ropes and a SB. The results show a large impact of SB geometry on the mooring dynamics. A larger height/diameter ratio (with preserved mass and buoyancy) is shown to be beneficial as it gives both smaller tension force magnitudes and, more importantly, avoids slack-snap occurrence in the upper cable. We further present a comparison between four numerical methods for SB dynamics: (i) a high-fidelity model using computational fluid dynamics (CFD); (ii) the Morison equation with slender body drag force approximation using numerical quadrature; (iii) the Morison equation with an independent evaluation of the fluid drag due to translation and rotation; and (iv) a translating Morison model which simulates a vertical cylinder in three degrees of freedom with no rotation. All methods are used together with a high-order finite element mooring dynamics solver. The results show that the translating method is inadequate to model this mooring configuration. The remaining three methods agree moderately well, but the Morison formulations give larger motions and higher tensions compared to the CFD results. We show that the quadrature drag model is better suited to model the drag moment on SBs than the independent model, and that the improvement increases with increasing slenderness of the buoy. The uncertainty, sensitivity and importance of the hydrodynamic coefficients of the buoy are discussed and examined by a regression analysis from the CFD data.

Supercritical CO2 extraction of pelletized oilseeds: Representation using a linear driving force model with a nonlinear sorption isotherm

This work develops a general, predictive model for the SuperCritical (SC) CO2 extraction of pelletized oilseeds. Cumulative SC-CO2 extraction curves of small (S, dp = 2.5 mm) and large (L, dp = 4.0 mm) cylindrical evening primrose seed pellets were modeled simultaneously using a Linear Driving Force (LDF) approximation modified to consider the nonlinear oil partition between CO2 and the substrate and extrapolated using the actual solubility of oil in CO2 at extraction conditions (40 °C and 45 MPa). Model best-fitting parameter was a single interparticle porosity (εp) of pellets considering equilibrium conditions after static extraction, and mass transfer kinetics during dynamic extraction. The adaptation of general model to bisized mixtures containing 25–75% S-pellets, predicted experimental results better than a monosized version (same Sauter mean diameters) because of the negative impact on overall cumulative extraction curves of slow-extracting L-pellets. Finally, a simplified version of the general model was developed that neglected the intraparticle porosity (εp = 0) and used a microstructural factor (FM∝(εp)−2) in the general model as the best-fitting parameter. This simplified model saved 33% of computational time at the expense of overestimating extraction rates, particularly at the beginning of the diffusion-controlled period, which diminished as εp decreased and FM increased.

Plane-wave approach to the exact van der Waals interaction between colloid particles.

The numerically exact evaluation of the van der Waals interaction, also known as Casimir interaction when including retardation effects, constitutes a challenging task. We present a new approach based on the plane-wave basis and demonstrate that it possesses advantages over the more commonly used multipole basis. The rotational symmetry of the plane-sphere and sphere-sphere geometries can be exploited by means of a discrete Fourier transform. The new technique is applied to a study of the interaction between a colloid particle made of polystyrene or mercury and another polystyrene sphere or a polystyrene wall in an aqueous solution. Special attention is paid to the influence of screening caused by a variable salt concentration in the medium. It is found that, in particular for low salt concentrations, the error implied by the proximity force approximation is larger than usually assumed. For a mercury droplet, a repulsive interaction is found for sufficiently large distances, provided that screening is negligible. We emphasize that the effective Hamaker parameter depends significantly on the scattering geometry on which it is based.

Classical symmetron force in Casimir experiments

The symmetron is a typical example of screened modified gravity, wherein the symmetron force is dynamically suppressed in dense environments. This allows it to hide in traditional tests of gravity. However, the past decade has seen great experimental progress toward measuring screened forces in the laboratory or in space. Screening relies on nonlinearities in the equation of motion, which significantly complicates the theoretical analysis of such forces. Here, we present a calculation of the symmetron force between a dense plate and sphere surrounded by vacuum. This is done via semianalytical approaches in two limiting cases, based on the size of the sphere: large spheres are analyzed via the proximity force approximation, whilst small spheres are treated as screened test particles. In the intermediate regime we solve the problem numerically. Our results allow us to make contact with Casimir force experiments, which often employ a plate and sphere configuration for practical reasons, and may therefore be used to constrain symmetrons. We use our results to forecast constraints on the symmetron's parameters for a hypothetical Casimir experiment that is based on the current state of the art. The forecasts compare favorably to other leading laboratory tests of gravity, particularly atom interferometry and bouncing neutrons. We thus conclude that near-future Casimir experiments will be capable of placing tight new bounds on symmetrons. Our results for the symmetron force are derived in a scale-invariant way, such that although we here focus on Casimir experiments, they may be applied to any other plate-sphere system, ranging from microscopic to astrophysical scales.

3D simulations of solidification with liquid phase flow

The work discusses issues related to 3D coagulation simulations including liquid phase flow. The approach chosen by the authors is based on the numerical solution of the enthalpy solidification formula and the Navier-Stokes equation, in which the buoyancy force approximation was added. Both of these equations are discretized in space using Finite Element Method, and in both cases time integration utilizes the Theta scheme, which is a generalized form of Euler Backward approach. The presence of the Navier-Stokes equation in the model forces the use of special techniques to ensure the convergence of the solution. From a number of available methods, the method of adding stabilizing elements in the FEM formulation was chosen, i.e. the stabilization formulas PSPG/SUPG (Pressure Stabilized Petrov Galerkin/Streamline Upwind Stabilized Petrov Galerkin). The occurrence of large temperature gradients, however, made it necessary to use the so-called lumped mass matrix in the energy equation. The work presents the results obtained using a model implemented by the authors in the form of a computer program written in C++ programming language. The use of this language and appropriate libraries made it possible to obtain sufficient performance to perform 3D solidification simulations.

Finite line contact stiffness under elastohydrodynamic lubrication considering linear and nonlinear force models

The aim of this study is to analyze the stiffness of finite line contact under elastohydrodynamic lubrication (EHL) with linear and nonlinear force approximations. The numerical solution of the finite line contact is compared with experimental results of optical interferometry. Four types of profiles are evaluated: non-profiled roller, crowned roller, dub-off profile and logarithmic profile. For each type of roller, the geometry values vary in order to identify the behavior of the reduced contact force parameters. The results of the force model showed good correspondence with the numerical solution of the EHL contact.

Force approximation of the human hand in contact with a climbing wall handle

Force approximation of the human hand in contact with a climbing wall handle

Enhanced solvation force extrapolation for speeding up molecular dynamics simulations of complex biochemical liquids.

We propose an enhanced approach to the extrapolation of mean potential forces acting on atoms of solute macromolecules due to their interactions with solvent atoms in complex biochemical liquids. It improves and extends our previous extrapolation schemes by additionally including new techniques such as an exponential scaling transformation of coordinate space with weights complemented by an automatically adjusted balancing between the least square minimization of force deviations and the norm of expansion coefficients in the approximation. The expensive mean potential forces are treated in terms of the three-dimensional reference interaction site model with Kovalenko-Hirata closure molecular theory of solvation. During the dynamics, they are calculated only after every long (outer) time interval, i.e., quite rarely to reduce the computational costs. At much shorter (inner) time steps, these forces are extrapolated on the basis of their outer values. The equations of motion are then solved using a multiple time step integration within an optimized isokinetic Nosé-Hoover chain thermostat. The new approach is applied to molecular dynamics simulations of various systems consisting of solvated organic and biomolecules of different complexity. For example, we consider hydrated alanine dipeptide, asphaltene in toluene solvent, miniprotein 1L2Y, and protein G in aqueous solution. It is shown that in all these cases, the enhanced extrapolation provides much better accuracy of the solvation force approximation than the existing approaches. As a result, it can be used with much larger outer time steps, leading to a significant speedup of the simulations.

Non-Causal Linear Optimal Control of Wave Energy Converters With Enhanced Robustness by Sliding Mode Control

Sea wave energy converter control is a non-causal optimal control problem, and the control performance relies on the accuracy of wave prediction information. However, the existing wave prediction methods, such as Auto-Regressive (AR) method, extended Kalman Filter (EKF), Artificial neural network and deterministic sea wave prediction (DSWP), inevitably introduce prediction errors. This paper presents a robust non-causal linear optimal control of wave energy converters to explicitly cope with the prediction error of sea wave prediction and simultaneously compensate the modelling uncertainty caused by wave force approximations. This is achieved by designing a non-causal linear optimal control (LOC) to maximize the energy output and a sliding mode control (SMC) to compensate unmodeled WEC dynamics and wave prediction error. The parameters of both SMC and non-causal LOC are calculated off-line, which significantly enhances the real-time implementation of the proposed controller with reasonably low computational load. Simulation results demonstrate the efficacy of the proposed control strategy.

Understanding Hydrogen Bonding in Terms of the Theory of Generalized Charges

New expressions for the energy and the length of interatomic bonds depending on atomic number, bond order, and angular momentum are derived within the theory of generalized charges, which is an asymptotic approximation for interatomic forces in the quantum-statistical model of a multicomponent electron gas. In particular, expressions for bond energies and bond lengths in hydrides are derived as functions of atomic numbers. As a consequence of the developed theory, hydrogen bonding is viewed as a one-electron covalent bonding, which is used to derive corresponding quantitative relations. The energy of hydrogen bonding cannot be lower than some specific value determined by the charge of the bonded atom. The region of existence of hydrogen bonding is established. The boundaries of the region are determined by the classes of substances distinguished by their ability to form hydrogen bonding. Quantitative estimations are used to explain the ability or inability of substances containing electronegative atoms to dissolve in water.

How drag force evolves in global common envelope simulations

ABSTRACT We compute the forces, torque, and rate of work on the companion-core binary due to drag in global simulations of common envelope (CE) evolution for three different companion masses. Our simulations help to delineate regimes when conventional analytic drag force approximations are applicable. During and just prior to the first periastron passage of the in-spiral phase, the drag force is reasonably approximated by conventional analytic theory and peaks at values proportional to the companion mass. Good agreement between global and local 3D ‘wind tunnel’ simulations, including similar net drag force and flow pattern, is obtained for comparable regions of parameter space. However, subsequent to the first periastron passage, the drag force is up to an order of magnitude smaller than theoretical predictions, quasi-steady, and depends only weakly on companion mass. The discrepancy is exacerbated for larger companion mass and when the inter-particle separation reduces to the Bondi–Hoyle–Lyttleton accretion radius, creating a turbulent thermalized region. Greater flow symmetry during this phase leads to near balance of opposing gravitational forces in front of and behind the companion, hence a small net drag. The reduced drag force at late times helps explain why companion-core separations necessary for envelope ejection are not reached by the end of limited duration CE simulations.

Selective copper extraction by multi-modified mesoporous silica material, SBA-15

Selective copper (Cu) recovery from wastewater mitigates environmental pollution and is economically valuable. Mesoporous silica adsorbents, SBA-15, with amine-grafting (SBA-15-NH2) and manganese loading along with amine-grafting (Mn-SBA-15-NH2) were fabricated using KMnO4 and 3-aminopropyltriethoxysilane. The characteristics of the synthesized adsorbents were evaluated in detail in terms of its crystal structure peaks, surface area and pore size distribution, transmission electron microscope and X-ray photoelectron spectroscopy. The results established the 2.08mmol/g of Cu adsorption capacity on Mn-SBA-15-NH2. Furthermore, in a mixed heavy metal solution, high selective Cu adsorption capacity on Mn-SBA-15-NH2 (2.01mmol/g) was achieved while maintaining 96% adsorption amount as that of a single Cu solution. Comparatively, Cu adsorption on SBA-15-NH2 decreased by half due to high competition with other heavy metals. Optimal Cu adsorption occurred at pH5. This pH condition enabled grafted amine group in Mn-SBA-15-NH2 to form strong chelating bonds with Cu, avoiding protonation of amine group (below pH5) as well as precipitation (above pH5). The adsorption equilibrium well fitted to Langmuir and Freundlich isotherm models, while kinetic results were represented by models of linear driving force approximation (LDFA) and pore diffusion model (PDM). High regeneration and reuse capacity of Mn-SBA-15-NH2 were well established by its capacity to maintain 90% adsorption capacity in a multiple adsorption-desorption cycle. Cu was selectively extracted from Mn-SBA-15-NH2 with an acid solution.

Linear Driving Force Approximations as Predictive Models for Reactive Sorption

Herein, the utilization of linear driving‐force approximations as predictive models for hydrogen sulfide removal on a commercial copper‐based sorbent is assessed. Sorption experiments are carried out in a fixed‐bed reactor at different flow conditions, temperatures, total pressures, and inlet hydrogen sulfide concentrations. For large pellet sizes (≥800 μm), quasi‐chemical linear driving‐force approximations, that are first order in both bulk gas‐phase concentration and solid‐phase capacity, effectively model contaminant breakthrough curves. Experimentally determined rate parameters (10.7 ± 0.7 s−1 and 6.5 ± 0.5 s−1 for 800 and 1000 μm‐sized particles, respectively) reflect those determined from pore diffusion within pellets. For small pellet sizes (≤212 μm), linear driving‐force approximations, that are zero order in bulk gas‐phase concentration but first order in solid‐phase capacity, model contaminant breakthrough curves; and rate parameters reflect reaction and diffusion at reactive interfaces rather than bulk or pore diffusion. These studies demonstrate that linear driving‐force approximations can model experimentally determined trace hydrogen sulfide removal parameters. Alternatively, under conditions where bulk and/or pore diffusions are limiting, the rate parameters can be calculated from known engineering theories (e.g., the Chapman–Enskog relation or the Wilke–Chang correlation).

Examining the Casimir puzzle with an upgraded AFM-based technique and advanced surface cleaning

We performed measurements of the gradient of the Casimir force between Au-coated surfaces of a sphere and a plate by means of significantly upgraded dynamic atomic force microscope (AFM) based technique. By introducing combined cleaning procedure of interior surfaces of the vacuum chamber and the test bodies by means of UV light and Ar ions, we reached higher vacuum and eliminated the role of electrostatic patches. Furthermore, the use of much softer cantilever allowed a sixfold decrease of the systematic error in measuring the force gradient. The experimental data are compared with theoretical predictions of the Lifshitz theory taking into account corrections due to the inaccuracy of the proximity force approximation and that due to surface roughness. It is shown that the theoretical approach accounting for the relaxation properties of free electrons is excluded by the data up to a larger than previous sphere-plate separation of 820~nm, whereas an alternative approach is found in a very good agreement with the data. Importance of these results in connection with the foundations of quantum statistical physics is discussed.

Nuclear multipole excitations in the framework of self-consistent Hartree–Fock random phase approximation for Skyrme forces

In this study, the fully self-consistent Hartree–Fock (HF)-based random phase approximation (RPA) calculations were done for the $$^{40}\hbox {Ca}$$ and $$^{48}\hbox {Ca}$$ nuclei using 20 Skyrme-type interactions: KDE0, KDE0v1, SLy4, SLy5, SLy6, SK255, SKI2, SKI3, SKI5, SKM, SKMP, SKP, LNS, SGII, RAPT, SV-bas, SV-m56-O, SV-m64-O, SV-min and T6. Having a large number of Skyrme-force parameterisations requires a continuous search for the best for describing the experimental data. To examine our results, we compared the strength functions S(E), the charge density distribution and centroid energies $$E_{\mathrm{CEN}}$$ of the isoscalar giant monopole resonance (ISGMR), $$J^{\pi } = 0^{+}$$ , $$T = 0$$ , the isovector giant dipole resonance (IVGDR), $$J^{\pi } = 1^{-}$$ , $$T = 1$$ , and isoscalar giant quadrupole resonance (ISGQR), $$J^{\pi } = 2^{+}$$ , $$T = 0$$ with the available experimental data. Moreover, we discussed the sensitivities of the centroid energy $$m_{1}/m_{0}$$ and moment $$m_{1}$$ of the S(E) to the bulk properties of nuclear matter (NM), such as $$K_\mathrm{NM}$$ , the effective mass m* / m and the enhancement factor $$\kappa $$ .

Electrostatic Force and Moment Approximations of Coulomb Charged Spacecraft Based on Center of Charge

A novel analytical formula is developed for the second order approximation of the potential function of a pair of charged spacecraft assuming either particle-body or body-body interactions. These approximations use the center of charge (CoCh) as the center of expansions provided that the charge distribution is known. The generated formulas for the potential function are then used to analytically find Coulomb force and corresponding moment about the center of mass (CoM) of the interacting bodies. The resulting expressions are presented in terms of the entire charge and the quadrupole charge tensor (QCT) of each individual body about the corresponding CoCh, as well as the relative distance between the centers of charge of the two charged spacecraft. Because of using expansions about the CoCh, dipole moments of each individual spacecraft do not explicitly appear in the resulting equations. Closed-form approximations of the force and moment are also obtained from the potential function using the CoM expansions. As it is shown, the CoCh expansions are generally more accurate when the distance between the CoCh and the CoM is a significant fraction of the separation distance.

Convergence analysis of inertial lift force estimates using the finite element method

We conduct a convergence analysis for the estimation of inertial lift force on a spherical particle suspended in flow through a straight square duct using the finite element method. Specifically, we consider the convergence of an inertial lift force approximation with respect to a range of factors including the truncation of the domain, the resolution of the tetrahedral mesh and the boundary conditions imposed at the (truncated) ends of the domain. Additionally, we compare estimates obtained via the Lorentz reciprocal theorem with those obtained via a direct integration of fluid stress over the particle surface. 
 
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Analytical results of the extensible freely jointed chain model

Based on classical statistical mechanics, we calculate analytically the length extension and the fluctuations, under a pulling force, of a polymer modeled as a freely jointed chain with extensible bonds, the latter considered as harmonic springs. We obtain an analytical formula for the partition function, and derive both the extension curve of the chain and the fluctuations as a function of the force. An independent high force approximation has been also evaluated. The analytical formulas have been validated by analyzing the exactness of their fit on data obtained from Langevin simulations, and compared with the phenomenological expressions largely used in the past literature.

CO2 capture on activated carbon from PET (polyethylene terephthalate) waste: Kinetics and modeling studies

CO2 emissions from flue gases can be restricted via a promising post-combustion capture technique, namely, adsorption. In the present work, behavior of adsorbents, prepared from PET (polyethylene terephthalate) waste, for CO2 capture studies was investigated to understand the fixed bed adsorption dynamics. The effect of activation on textural properties, surface functional groups and elemental composition was studied through nitrogen adsorption/desorption, XPS, FTIR, and EDX analysis. Thermal stability of adsorbent samples was also evaluated. The kinetics of the adsorption process was studied using Lagergren’s pseudo-first-order model, pseudo-second, fractional order, Elovich, and Avrami models. Freundlich isotherm fit confirmed the heterogeneous nature of adsorbent’s surface. Adsorption column breakthrough profiles were modeled using linear driving force (LDF) approximation for mass transfer. Model equations were solved using the Method of lines in MATLAB environment. Results show that the model closely approximated the column breakthrough curves for different CO2 concentrations (5–12.5%) and different adsorption temperatures (30–100 °C).

A model for transient diffusion in bidisperse pore structures

A bidisperse model for transient diffusion and adsorption processes in porous materials is presented in this paper. The mathematical model is solved by numerical methods based on finite elements combined with the linear driving force approximation. A criterion based on the model to identify the diffusion controlling mechanism (macropore diffusion, micropore diffusion, or both) is proposed. The effects of different adsorption isotherms (linear, Freundlich, or Langmuir) on the concentration profiles and on curves of fractional uptake versus time are investigated. In addition, the influences of model parameters concerning the pore networks on the fractional uptake are studied as well.