Coulomb's Law Research Articles

A new class of history-dependent quasi variational–hemivariational inequalities with constraints

In this paper we consider an abstract class of time-dependent quasi variational–hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of solution by using a recent result for elliptic variational–hemivariational inequalities in reflexive Banach spaces combined with a fixed-point principle for history-dependent operators. Then, we apply the abstract result to show the unique weak solvability to a quasistatic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity and the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated slip.

Investigation of the dynamic structural factor of binary ionic mixtures

The method of moments is used to investigate and analyze the dynamic characteristics of dense systems consisting of ions of two types with different masses and charges, and the number of screening electrons corresponding to the charges of the ions.In this paper, we discuss the characteristics of a binary ionic mixture whose component masses differ by a factor of two. Within the framework of the developed self-consistent method of moments, the dynamic structure factors (DSF) of such a plasma are calculated for various thermodynamic parameters. In this case, the calculation algorithm is based on the use, on the one hand, of the static structural factor of the system, which is determined from the solution of the Ornstein-Zernike equation, and on the other hand, the so-called Nevanlinna parameter function (NPF), which is included in the calculated relations. The calculations were carried out within the framework of the classical system of charged particles interacting according to the Coulomb law. The paper analyzes the data obtained using various methods for calculating the NPF. The results obtained in this work qualitatively and quantitatively agree with the data of theoretical calculations and numerical experiments of the authors of other studies of the dynamic properties of a dense multicomponent plasma.

An improved artificial electric field algorithm and its application in neural network optimization

Artificial electric field (AEF) algorithm is a newly developed meta-heuristic optimization technique inspired by the Coulomb's law of electrostatic force. As so far, AEF algorithm has been successfully applied in some scientific research and engineering fields, but it still has the defects of premature convergence and poor search ability in handling complex optimization problems. To address such issues, a novel Coulomb's constant generation scheme is explored to calculate the electrostatic force, and then an improved AEF (IAEF) algorithm is developed to strengthen the global exploration capability. Subsequently, 18 popular test functions with different dimensions are selected as benchmarks for performance evaluation. Furthermore, two nonlinear problems of neural network optimization are employed to further investigate the effectiveness and superiority of IAEF algorithm. Experimental results demonstrate that the proposed IAEF is efficient and effective optimization method in comparison with the conventional AEF and several famous evolutionary algorithms.

“Touch‐aware” contact model for peridynamics modeling of granular systems

AbstractThis article presents an innovative “touch‐aware” frictional contact model for peridynamics to efficiently simulate the contact behavior between irregularly shaped particles. Conventional short‐range force contact model formulates the contact force field in such a way that leaves a large gap between particles, leading to a softer stiffness of contact and inaccurate simulation of densely packed granular materials. The developed “touch‐aware” contact model initiates the contact force calculation when contacting bodies are in touch, which leaves no gap between contacting bodies and provides a stiffer contact in an accurate and efficient way. It simulates frictional contact behaviors and damping between contacting bodies with irregular shapes. Different examples are given to verify the touch‐aware contact model with theoretical solutions such as Hertz theory of contact, Hertz theory of impact, Coulomb's law and damping formulation. The model is also compared with conventional peridynamics contact model and the discrete element method. Finally, the touch‐aware contact model is used to simulate condensation of an aggregate of irregularly shaped particles. These examples demonstrate excellent capacity of the “touch‐aware” model in simulating packed granular systems.

Algorithm for controlling an inertioid robot with a flywheel and an unbalance in conditions of restrictions on the angular acceleration of the unbalance

The plane-parallel motion of a vibrating robot containing one unbalanced rotor and one flywheel is considered. The robot body is supported by two points on a rough supporting plane. The friction is modeled with Coulomb's law. The motion is controlled by the angular acceleration of the unbalanced rotor and the flywheel. The control strategy implies the alternation of two modes. In one mode, the unbalanced rotor gains the required angular momentum using the friction of the body against the surface. In the second mode, the body is lifted off the surface and moved in the desired direction. The first integrals of the unbalanced rotor rotation equations are found for both modes. It is shown that if no restrictions are imposed on the angular acceleration of the rotor then the angular velocity of the rotor tends to infinity. An algorithm for controlling the motion of the robot's body in a given direction is proposed that takes into account the constraint on the angular acceleration of the unbalanced rotor. Motion modes are added with constant control and control stabilizing the angular velocity of the unbalanced rotor. The numerical simulation of the robot motion with the proposed control was performed in a wide range of values of the friction coefficient. It is shown that, in some cases, several revolutions of the unbalanced rotor are required in order to gain the required angular momentum.

Exploring the inner workings of the clove hitch knot

We perform a combined experimental and computational investigation of the clove hitch knot. We develop a physical model for the clove hitch by tying an elastic rod onto a rigid cylinder. In the experiments, we characterize the mechanical performance, geometry, and stability conditions of the knot. X-ray tomography allows us to characterize the 3D geometry of the rod centerline. These results also serve to validate our finite element modeling (FEM), which we use to quantify the tension profile, not accessible experimentally, along the knotted rod. We find that the clove hitch comprises alternating segments with two types of contact regions: one where the rod is in single frictional contact with the cylinder, and another with rod self-contact (where a rod segment pinches another against the cylinder). In the first region, the internal tension decays exponentially (akin to the capstan configuration), whereas, in the second, the pinch (nip) regions lead to discontinuous tension drops. We analyze these nip regions with an even simpler model system where an elastic rod is pinched between two rigid cylinders. Despite the complex contact geometry of this pinching experiment, we find that the frictional behavior of our model systems still obeys the classic Amontons–Coulomb law. Ultimately, we can regard the clove hitch knot, if tied correctly, as a functional structure enabling to drop high tension at one extremity of a filament secured onto a rigid post, all the way to zero at the other extremity.

Stability, aggregation, and sedimentation behaviors of typical nano metal oxide particles in aqueous environment

The wide use of nano metal oxide particles (NMOPs) brings about their inevitable release into the water environment, affecting the environment and human health. Therefore, the stability, aggregation, and sedimentation process of four typical NMOPs (ZnO NPs, CeO2 NPs, TiO2 NPs, and CuO NPs) were investigated in artificial water and real municipal sewage to reveal their complicated behavior. Results showed that NMOPs aggregated at the pH of zero-charge point, and their hydrodynamic diameters and aggregation rates could reach the maximum values. The hydrodynamic diameters and aggregation rates of ZnO NPs, CeO2 NPs, TiO2 NPs, and CuO NPs at the zero-charge point were 617, 1760, 870, 1502 nm, and 31.7, 1158.1, 48.3, 115.7 nm/min, respectively. In addition, the dissolution of NMOPs led to the sedimentation rates under acidic conditions being much lower than those under neutral and alkaline conditions. The aggregation and sedimentation performance of NMOPs were affected by not only pH but also ionic strength (IS) and species. The aggregation rates of NMOPs increased with the increase of IS (0–10 mM), and the maximum aggregation rate of CeO2 NPs was 470.1 nm/min (pH = 7 and CaCl2 = 10 mM). According to Coulomb's law, divalent cations (Mg2+, Ca2+) were more competitively adsorbed on the surface of NMOPs than monovalent cations (K+, Na+), which increased the zeta potential and aggregation rate of NMOPs. Furthermore, the NMOPs were easier to aggregate in municipal sewage because of the homogeneous aggregation between nanoparticles and heterogeneous aggregation with natural colloids. The total interaction energy between NMOPs was calculated by the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theoretical formula, which was consistent with the experimental results.

Fullerenes Materials Contribute to Ordered Interfacial Cell Water Improving Cellular Electrodynamics and Oxidative Stress Management

The role of water in living systems is complex and a primary mediator of localized and long‐range biological effects in the cell. Of the approximately 70% of cell water, 20‐30% forms a structured semi‐crystalline gel state of water layers, where it also hydrates surfaces of biomolecules and cell structures and is essential for life. Decreases in ordered interfacial water are associated with cellular dysfunction and disease. This interfacial water behaves quantumly. The customary Coulomb Law of electrostatics does not apply, allowing the accumulation of tissues composed of negatively charged cell bodies. Interfacial water is responsible for the thermodynamics of proton and electron transfer and long‐range quantum electrodynamic coherence coordinating quantum criticality of the cellular machinery and systemic integration necessary of complex organisms. We propose that fullerene material increases interfacial water ordering, beneficially altering its electromagnetic properties. Fullerene materials can bind with cellular structures and protein secondary structures not typically available for water interaction, through weak van der Waals forces or pi‐pi stacking arrangements containing aromatic rings with dense pi electron clouds and hydrophobic functional groups. Modulating partial charges, dipoles, and quadrupoles in fullerene materials that result from coherent microtubule‐generated electromagnetic fields helps enhance and extend long‐range ordered water layers and electrostatics between hydrophobic molecules thought necessary for the self‐assembly of bio‐macromolecules. We propose that fullerenes short and long‐range enhancement of structured interfacial water contributes to many of the observed effects of fullerenes in vivo, including a non‐stoichiometric redox mechanism for the well‐established antioxidant activity of fullerene materials.

Numerical modeling of defect formation in friction stir welding

This study presents an investigation of welding defect formation in joining AZ61 magnesium alloy with friction stir welding by means of a 3D finite element model. The numerical model was created and analyzed in the ABAQUS software. This numerical model uses coupled Eulerian Lagrangian formulation, modified Coulomb's friction law, Johnson-Cook material law, mass scaling technique, and temperature dependent friction coefficient values. The numerical model was validated with experimental results in terms of heat input, temperature distribution, plastic deformation type-amount, and weld defect formation in the weld zone. In friction stir welding, the heat input with a certain tool simply changes directly proportional to the ratio of tool rotation speed to tool feed rate for constant tool compressive force. In the numerical model, as in the experimental study, when the ratio of tool rotational speed to tool feed rate is 2, low heat input results in insufficient plastic deformation, leading to the formation of weld defects in the form of void. When the ratio of tool rotational speed to tool feed rate is 3, however, it was observed that sufficient heat input is provided, and no welding defects occur. The generated numerical model enables the determination of the welding defects that occur in the form of voids in the friction stir welding in a very short processing time. Besides, weld seam geometry can be predicted quite accurately with this model.

Shielding the electrostatic attraction by design of zwitterionic single ion conducting polymer electrolyte with high dielectric constant

According to Coulomb's law, besides the design of bulky anion, increase in dielectric constant can also reduce the electrostatic attraction force, both of which are benefit for ion dissociation. Here, we report a zwitterionic single ion conducting polymer electrolyte by chemically grafting two propanesulfonyl(trifluoromethanesulfonyl)imide groups to the nitrogen of poly(biphenyl piperidium) (PBP-g-Li(PSI)2). One of side-chain groups burdens negative charge to counterbalance the positive charge of quaternary ammonium of main chain, and the other one provides lithium ion to conduct charge. Poly(biphenyl piperidinium) grafted with one lithium propanesulfonyl(trifluoromethanesulfonyl)imide (PBP-g-LiPSI) is synthesized for contrast. It is discovered that the dielectric constant of PBP-g-Li(PSI)2 is 22.3 at 2 MHz which is 3.5 times that of PBP-g-LiPSI, and the ionic conductivity of PBP-g-Li(PSI)2 gel polymer electrolyte membrane is 2.41 × 10−4 S cm−1 at 25 °C, nearly twice that of PBP-g-LiPSI gel polymer electrolyte membrane. The dipole structure of bonded bis(sulfonyl)imide anion and quaternary ammonium cation can shield the electrostatic attraction between lithium cation and immobilized anion as confirmed by Li 1s XPS and 7Li NMR. Zwitterionic polymer electrolyte not only withstands galvanostatic cycling in lithium symmetric cell at ±0.5 mA cm−2@2 mAh cm−2 for 2000 h, but also performs stably in lithium metal secondary battery.

Podolsky's Electrodynamics Via First Principles

A theory of electromagnetism with higher order derivatives, which attained by generalizing the laws of electrostatics, laws that follow from the generalized Coulomb's law and the superposition principle, so that they are consistent with special relativity.

A bed pressure correction of the friction term for depth-averaged granular flow models

Depth-averaged models, such as the Savage-Hutter model with Coulomb or Pouliquen friction laws, do not in some cases preserve the physical threshold of motion. In particular, the simulated granular mass can start to flow (or stay at rest) even if the slope angle of its free surface is lower (or higher) than the repose angle of the granular material involved. The problem is related to the hydrostatic pressure assumption, associated with the direction of integration, which is orthogonal to a reference plane or a reference bottom. We propose here an initial method to correct this misleading behavior. Firstly, we define a correction of the friction term that accounts for the Jacobian of a change of coordinates, making it possible to reproduce the physical threshold of motion and thus the solutions at rest. Secondly, we observe that the 3D model presented in [F. Bouchut, I. Ionescu, and A. Mangeney. An analytic approach for the evolution of the static-flowing interface in viscoplastic granular flows. Commun, Math. Sci., 14(8):2101–2126, 2016] verifies the physical thresholds of motion because it is based on a second order correction of the pressure valid for slow granular flows. The correction proposed here ensures that the model preserves, up to the second order, the physical threshold of motion defined by the repose angle of the material. Several numerical tests are presented to illustrate certain problems related to classical depth averaged models and the remedial effect of the proposed correction, in particular through comparisons with experimental data. We finally show that this correction is not exact far from the starting and stopping phases of the granular avalanche and should be improved by adding other second order terms in the pressure approximation.

Study on test set-ups for determining the failure characterisation in masonry components

This paper presents experimental studies and detailed micro-modelling on test set-ups to determine the strength and failure mechanism of brick masonry components. Experimental studies include compressive strength tests of masonry units, red clay brick masonry triplet tests and Z-shaped flexural bond tests. Failure mechanisms for masonry relates not only to mortar and brick material properties, but also to the bond strength between the brick and mortar. A contact law based on the cohesive zone model and Coulomb's law was used to describe the fracture behaviour of mortar joints. Numerical studies are based on the interface cohesive model for mixed modes I and II. Tests were evaluated numerically using the Benzeggagh–Kenane mixed mode criterion. The results obtained from finite-element (FE) simulation showed the reliability of computational modelling approaches for masonry bed joint behaviour. Finally, a parametric study on masonry triplet under various compression stresses was carried out by using the FE simulation. The results indicate that an increase in normal compression stress leads to an increase in shear bond strength of masonry.

A unilateral constraint contact problem for viscoelastic materials with wear

The aim of this work is to investigate a mathematical model that describes the frictional contact between viscoelastic materials with a long memory and a moving foundation. The contact condition is modeled with a version of normal compliance condition with unilateral constraint in which wear of foundation is considered. Friction contact condition follows a sliding version of Coulomb's law of dry friction. We derive a variational formulation of the problem, which couples a variational inequality and an integral equation. Then, we obtain the unique weak solvability of the contact problem by virtue of a fixed point theorem. By using the penalization method, we discuss the convergence of the contact problem. Further, we obtain the unique solution of the penalized problem and this solution converges to the solution of the original contact model as the penalization parameter converges to zero.

Molecular electrostatic potential analysis: A powerful tool to interpret and predict chemical reactivity

AbstractThe molecular electrostatic potential (MESP) V(r) data derived from a reliable quantum chemical method has been widely used for the interpretation and prediction of various aspects of chemical reactivity. A rigorous mapping of the MESP topology is achieved by computing both ∇V(r) data and the elements of the Hessian matrix at the critical points where ∇V(r) = 0. In the MESP topology, intra‐ and inter‐molecular bonded regions show the characteristic (3, −1) bond critical points (BCPs) while the electron‐rich regions such as lone pair and π‐bonds show (3, +3) minimum (Vmin) CPs. The Vmin analysis provides a simple and powerful technique to characterize the electron‐rich region in a molecular system as it corresponds to the condensed information of the wave function at this point due to the nuclei and electronic distribution through the Coulomb's law. The Vmin analysis has been successfully applied to explain the phenomena related to chemical reactivity such as π‐conjugation, aromaticity, substituent effect, ligand electronic effects, trans‐influence, redox potential, activation energy, cooperativity, noncovalent interactions, and so on. The MESP parameters ∆Vmin and ∆Vn, derived for arene systems have been used as powerful measures of substituent effects while Vmin at the lone pair region of ligands has been used as a reliable electronic parameter to assess their σ‐donating ability to metal centers. Furthermore, strong predictions on the intermolecular interactive behavior of molecular systems can be made from MESP topology studies. This review summarizes the chemical reactivity applications offered by MESP topology analysis for a large variety of organic, organometallic, and inorganic molecular systems.This article is categorized under: Molecular and Statistical Mechanics > Molecular Interactions Structure and Mechanism > Reaction Mechanisms and Catalysis Structure and Mechanism > Molecular Structures

Derivation of the Coefficients in the Coulomb Constant Shear Friction Law from Experimental Data on the Extrusion of a Material into V-Shaped Channels with Different Convergence Angles: New Method and Algorithm

The combined Coulomb constant shear friction law is widely used in commercial and research software for the finite-element analysis (FEA) of metalworking and is naturally more flexible and hence, more relevant to real-life manufacturing than the individual Coulomb and constant shear friction laws. In this work, a new mathematical model of coefficients in the Coulomb constant shear friction law for extruding a metal through narrow V-shaped channels with small convergence angles has been developed and evaluated and compared with laboratory measurements. The extrusion of the model material (lead) through narrow V-shaped channels with small convergence angles varying from 0 to 3.5 degrees has been studied. The Coulomb friction coefficient µ and the constant friction factor m appear to be independent of the dimension ratio and are influenced mostly by roughness and range from µ = 0.363 (with lubricant) to µ = 0.488 (without lubricant) and from m = 0.726 (with lubricant) to 0.99 (without lubricant). The relative length dominated by the Coulomb friction law is less than 1%, and the Coulomb’s coefficient of friction can be approximated as ½ the constant shear friction factor for all tested cases. The developed method and algorithm can be used in both FEA of manufacturing processes and efficiency tests for lubricants used in metalworking.

Numerical model of interation of package of open shells with a weakly compressible filler in a friction shock absorber

The problems of protecting equipment, structures and operators from the harmful effects of vibrations are among the most painful topics of modern mechanical engineering. In this research an original design of a friction shock absorber is presented in which the principle of operation is based on the contact interaction of a package of open shells with weakly compressible deformable filler. The proposed design is simple and technologically advanced, suitable for operation under high dynamic loads and at the same time has a compact transverse dimension. Such shock absorbers are projected to be used in the mining and oil and gas industries. A finite element model of a friction shock absorber with two contact pairs has been constructed: the first contact pair is "filler - package of open shells"; the second contact pair is "inner shell of the package - outer shell". The contacting bodies were presented as separate arrays of finite elements and the conditions of frictional interaction on the contact surfaces were set in the form of Coulomb's law. We considered the behavior of such a structurally nonlinear system under the action of a monotonic and nonmonotonic load. In the course of the study, the main operational characteristics of the shock absorber including the strength, rigidity, hysteresis characteristics and natural frequencies were determined. The possibility of adjusting the rigidity and shock-absorbing characteristics of the proposed device is discussed.

A High-dimensional Outlier Detection Approach Based on Local Coulomb Force

Traditional outlier detections are inadequate for high-dimensional data analysis due to the interference of distance tending to be concentrated (curse of dimensionality). Inspired by the Coulombs law, we propose a new high-dimensional data similarity measure vector, which consists of outlier Coulomb force and outlier Coulomb resultant force. Outlier Coulomb force not only effectively gauges similarity measures among data objects, but also fully reflects differences among dimensions of data objects by vector projection in each dimension. More importantly, Coulomb resultant force can effectively measure deviations of data objects from a data center, making detection results interpretable. We introduce a new neighborhood outlier factor, which drives the development of a high-dimensional outlier detection algorithm. In our approach, attribute values with a high deviation degree is treated as interpretable information of outlier data. Finally, we implement and evaluate our algorithm using the UCI and synthetic datasets. Our experimental results show that the algorithm effectively alleviates the interference of Curse of Dimensionality. The findings confirm that high-dimensional outlier data originated by the algorithm are interpretable.

A Realistic Interpretation of Quantum Wavefunctions as Temperature Dependent Vacuum Polarization Waves

We discuss in this paper a novel interpretation of Born rule as an approximated thermodynamic law which emerges from the interaction of a quantum system with a non-stationary thermal bath associated to vacuum fluctuations induced by external environment radiation. In particular we assume that vacuum polarization is a real non relativistic phenomena caused by hidden vacuum charge oscillations which diffuses heat energy in a dispersive and dissipative dielectric medium with a temperature dependent speed of propagation. We propose a model which couples vacuum wavefunctions to vacuum charge fluctuations and we deduce a temperature dependent running fine structure constant function proportional, at first approximation, to the squared of the effective electron charge and compatible with known experimental data. We interpret the vacuum symmetry breaking energy fluctuations induced in scattering experiments of particle physics and in laser assisted nuclear reactions as thermal quasi-monochromatic beams produced by the decay of hidden non equilibrium massive photons propagating with a variable light speed. We suggest, exploiting an old analogy between plasmons and pseudo Goldstone bosons, to interpret heat diffusion of this non relativistic polarized vacuum as a real De Broglie electromagnetic scalar wave associated to the radiation emitted by the hidden massive photons with acceleration proportional to vacuum Unruh like temperature. We predict a temperature dependent deviation from Coulomb law and a generalized dispersive law of these hidden unstable photons that could be revealed as not stationary coloured noise in experiments on anomalous heat diffusions associated to the decay of unstable accelerated pairs produced in nuclear physics experiments. We discuss then how our proposal of a temperature dependent non relativistic vacuum polarization might be applied to deduce a dynamic generalization of Born rule based on a realistic interpretation of quantum wavefunctions as averaged electromagnetic waves of hidden massive photons. Finally we suggest to test our time asymmetric model looking for very fast oscillating polarization thermal waves emitted during the not instantaneous wavefunction collapse and revealed as not stationary bulk heating effects in experiments on accelerated conductors and nanoconductors.

Numerical measurement of flow fluctuations to quantify cohesion in granular materials.

The flow of cohesive granular materials in a two-dimensional rotating drum is investigated using discrete element method simulations. Contacts between particles are modeled based on the widely used model of the spring-dashpot and Coulomb's friction law. A simplified model of intermediate range attraction between grains (i.e., cohesion) has been used in order to reproduce the flow of electrostatic or wet granular materials. Granular flow is generated by means of a rotating drum and the effect of the rotation speed, the friction between the grains, and the cohesion are studied. Significantly different flow behaviors are observed when cohesion is added. Plug flow appears in the rotating drum for a wide range of rotation speeds when cohesion becomes sufficiently strong. We propose a measurement of surface flow fluctuations to quantify the strength of cohesion, inspired by the previous observation of plug flow. Then, we make use of the results to include the effect of cohesion into a theoretical flow model. A good agreement is obtained between theory and numerical measurements of the granular bed's dynamic angle of repose, which allows us to propose a method for estimating the microscopic cohesion between grains based on the measurement of surface fluctuations.