A BOUNDARY ELEMENT APPROXIMATION OF A SIGNORINI PROBLEM WITH FRICTION OBEYING COULOMB LAW

In this work, a Signorini problem with Coulomb friction in two dimensional elasticity is considered. Based on a new representation of the derivative of the double-layer potential, the original problem is reduced to a system of variational inequalities on the boundary of the given domain. The existence and uniqueess of this system are established for a small frictional coefficient. The boundary element approximation of this system is presented and an error estimate is given.

Q-Theory: A Connection between Newton’s Law and Coulomb’s Law?

Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, qpl, was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, , where ζ(3) equals Apery’s constant, 1.202 …, and, n+(0)=n_(0), is the relaxed, i.e., , number density of the positive and negative mass planckions. In the present epoch, we estimate that, n+(0) equals, 7.848E54 m-3, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, l+(0)=l_(0)=5.032E-19 meters. These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, , due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E-48 meters, within the vacuum made up of these particles. On the surface of the earth, where, g=9.81m/s2, the displacement amounts to, 7.824E-38 meters. All of these displacements are due to increased gravitational pressure within the vacuum, which in turn is caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure.

Social Distancing via Coulomb’s Law

This research effort addresses the social-distancing problem. As the COVID-19 pandemic continues, we’ve learned the importance of keeping proper distance, so as to avoid (or minimize) the spread of infection. For this paper, individuals are represented as positively-charged particles, behaving in accordance with Coulomb’s Law. Additionally, negatively-charged stationary (non-moving) particles are positioned such that their attraction to the positively-charged particles guides the movement of the positively-charged particles in a desirable fashion. During a simulation process, Coulomb’s Law guides particle behavior such that the positively-charged particles arrange themselves in a way such that their spacing is essentially optimal. Of course, these positively charged particles can be thought of as a surrogate for individuals, resulting in the optimal spacing of individuals.

One Method to Derivate Coulomb’s Law between Two Charges

In electromagnetics, Coulomb’s law is a very classic formula. Almost all textbooks give this formula, but none of them give a detailed corresponding theoretical derivation. In order for beginners of physics to better understand the physical meaning of this formula, we explored the source, the physical model and mechanism of this formula. Based on the principle that the interaction between two different fields can generate energy density, which is equal to the pressure, we analyzed the distribution of the electric field energy density as well as the corresponding pressure on the charged surface. Through the rigorous mathematical derivation, we give the theoretical derivation of this formula.

Moderated PEF from Transitioning between the Micro and Macroscopic Usage of Coulomb’s Law

The dielectric constant in Coulomb’s Law, D, can quantify an empirical reduction of force. It can also quantify a reduction of electrostatic field as seen in classical electrostatic theory where the induced charge layer is assumed to be infinitely thin. The two approaches exemplify two traditions that have been used in parallel for decades. They produce Potential Energy Functions (PEFs) that differ by a factor of the permittivity, εr. The classical electrostatic theory result can be incorporated into force field models with an effective dielectric function, Deff, which spans the induced charge layer and accommodates both traditions. The Deff function increases the magnitude of local terms as compared with cumulative long distance terms. It is shown that the Deff function reduces distance dependence of the radial PEF within the induced charge layer and improves computational stability for some systems including substrate in dilute salt solution. End use applications include pharmaceutical development (e.g. protein calculations with docking), materials development, solvation energy calculations and QM/MM calculations.

An Analysis of the Origin of the Interaction Force between Electric Charges, including Justification of the ln<i>r</i>Term in the Completed Coulomb’s Law, in HM16 Ether

In this study, we demonstrate the correctness of our 2010 hypothesis regarding the need to complete Coulomb’s FC law with the term lnr, resulting in the completed FCC force. For this purpose, we consider the electrical interactions between charged microparticles (MPs), which develop as fundamental vibrations (FVs) in ether, producing the vibrational strains &epsilon;and &gamma;and the resulting stresses &sigma;and &tau;, as percussions of ether cells (ECs) upon the MP surface. The stresses &sigma;?and?&tau;produce a resultant force FP, due to the percussions which constitute the real electric force FCC. The spatial effect of ether on FP is demonstrated by an analytical method, considering the electrical interaction between MPs through various equidistant spatial paths li of FVs, modelled on the basis of the Huygens principle for waves. For this issue, we utilized a numerical calculation, which could be generalized. But this spatial effect of the ether leads at a very slow decreasing of the FP forces ratio rF when doubling the distance l, in contrast to Coulomb’s FC forces whose ratio rF?decreases accentuate with doubling l. Accordingly, the necessity of including the term ln r in the FCC force, which is limited to 1.0 for doubling l, at long distances, was justified.

Motion State Modification of Coulomb’s Law and Dynamic Gravitation

As we know, Coulomb’s law describes the interaction between static charges. In this paper, the modified formula of Coulomb’s law in the state of charge motion is given. Based on this formula, Ampere’s law and Lorentz’s law of force are derived by pure mathematics. According to the similarity between the formula of universal gravitation and Coulomb’s law, the correction of the formula of universal gravitation under the state of motion is assumed boldly, and some inferences are made on the motion law of celestial bodies.

纤维拔出时Coulomb摩擦界面应力传递

假设纤维/基体界面分离区域内的摩擦剪切应力遵循Coulomb摩擦律,包括泊松效应的影响,建立了纤维拔出时的摩擦界面应力传递模型,获得了包含摩擦滑移和由纤维/基体热失配引起的法向残余热应力效应的纤维轴向应力和界面剪切应力的表达式.对纤维增强复合材料SCS-6/Ti-6Al-4V作参数化的数值计算,且和有限元结果进行比较.结果表明,随纤维轴向位置的增加,纤维轴向应力和界面剪切应力均减小;法向残余热应力、高纤维体积分数和短纤维延缓纤维失效.

Potential Simplification of Charge and the Coulomb Force without Affecting Predictions

We are taking a deeper look at charge and the Coulomb force and other electric properties. There is an embedded 10-7 in the Coulomb constant that we will claim is “only” needed to cancel out an embedded 107 in the charge squared. We suggest three alternatives to redefine the charge and the Coulomb constant that give considerable simplification. The Coulomb constant is not needed as a separate constant as, in the new suggested framework, it can be replaced with simply the speed of light without affecting predicted output values. We also point out potential issues with the 2019 redefinition of the Coulomb constant and elementary charge. This is not meant conclusive but to open up for further discussion on how one potential can simplify parts of physics.

Coulomb材料中滑移线性质的研究

对Ｃｏｕｌｏｍｂ材料中滑移线的性质进行了研究，结论是沿β（α）滑移线移动，则α（β）滑移线曲率半径的变化等于沿β（α）线滑移的距离与ｃｏｓφ的乘积．

数值模拟静态应力扰动下的断层失稳:结果分析兼与Dieterich模型和Coulomb模型的对比

基于大量岩石力学实验,Dieterich和其他研究者(Dieterich,1978;Ruina,1983)首先提出了描述岩石摩擦过程的速率-状态摩擦定律(R-S摩擦定律).如今R-S摩擦定律已成为研究地震成核等地震演化机制的有效手段.Dieterich(1992,1994)最早提出了描述受静态剪应力扰动后断层失稳时间提前或推后的余震触发机制的解析模型.现在Dieterich模型已经成为解释余震随时间衰减规律的Omori定律等地震观测现象的有力工具.与之相对应,广泛使用的Coulomb应力失稳模型也可以给出断层受到静态剪应力扰动后,断层失稳时间的提前和推后量.Dieterich模型和Coulomb应力失稳模型基于不同的物理方法,所以在进行地震危险性评估时,二者均有各自的局限性.本文利用R-S摩擦定律控制的1-D弹簧-滑块模型,模拟计算了理论地震循环以及在不同静态剪切应力扰动下,失稳时间的提前和推后量的变化情况,然后将计算得到的时间提前和推后量分别与Dieterich模型和Coulomb模型的相应计算结果进行了定量化对比和差异性分析,并给出了相应的解释.数值模拟结果显示,对于R-S摩擦定律在参数不变的条件下,断层模型失稳时间的提前和推后量的大小强烈依赖于静态剪应力扰动的大小和作用时间,而且绝对值相同的正、负向静态剪应力扰动造成的失稳时间的提前和推后量的变化情况并不完全一致.在震后松弛/滑移阶段和闭锁阶段,时间提前和推后量是常数,且随静态剪应力扰动绝对值的增大而增大,两者的比值接近于1.0,这与Dieterich模型和Coulomb模型的结果是一致的,相应的差值小于两模型结果的10%.而在自加速阶段,模拟计算结果则存在与Dieterich模型和Coulomb模型结果不同的特征.首先,在自加速阶段模拟计算结果均偏离Coulomb模型,而且时间提前和推后量的比值小于1.0,相异于Coulomb模型的论断.不过当受到正向静态剪应力扰动后,Dieterich模型的结果和模拟计算结果是一致的,最大相差量不超过Dieterich模型结果的7%,可接近0.对于负向静态剪应力扰动,当其绝对值较小时,Dieterich模型的结果很接近模拟计算结果,相差量不超过该结果的14%.但对于绝对值较大的情况,模拟计算结果远大于Dieterich模型的结果,最大可达Dieterich模型结果的35倍,这是由于负向静态剪应力扰动后使得Ω=δ·θ/dc1的条件不再成立,进而使得Dieterich模型不再成立.总的来说,与模拟计算相比Dieterich模型可以很好地描述1-D断层受扰后失稳时间提前和推后量的变化情况,并且可以体现出正、负静态剪切应力扰动后失稳时间提前量和推后量变化的差异性,而Coulomb模型则不能完整地给出受到静态剪应力扰动后断层失稳时间提前或推后的估计值.

Analysis of Electrical Dipoles Interaction Forces as a Function of the Distance and of the Form of Electrical Force Law

Here, we initially introduced and demonstrated two principles: orientation OR principle and attraction AT principle of electrical dipoles. The OR principle stipulates that any two electrical dipoles P1A, P1B, from two bodies A and B, at any distance in the free state each, will be reciprocally oriented parallel and in the same sense if the electrical interaction forces F between them are of decreasing type with distance r. If the electrical interaction forces F are of increasing type with distance, the two dipoles will be reciprocally oriented parallel but on the opposite sense. The AT principle stipulate that any two electrical dipoles P1A, P1B, at any distance in the free state each, will present always a reciprocal force of attraction FD in both cases of orientation accordingly to OR principle in case of any type of electrical force F decreasing or increasing with distance. These findings may complete our previous work where we found that FD force, between two electrical dipoles P1A, P1B considered at atomic and nuclear level, is in fact the actual gravitation Newton force FN. The paper must be considered together with this work for more consistency.

Coulomb Force, Charge, and Electric Properties under Collision Space-Time

We have recently published a series of papers on a theory we call collision space-time, that seems to unify gravity and quantum mechanics. In this theory, mass and energy are redefined. We have not so far demonstrated how to make it compatible with electric properties such as charge and the Coulomb force. The aim of this paper is to show how electric properties can be reformulated to make it consistent with collision space-time. It is shown that we need to incorporate the Planck scale into the electric constants to do so. This is also fully possible from a practical point of view, as it has recently been shown how to measure the Planck length independent of other constants and without the need for dimensional analysis.

Calculating Newton’s Gravity (Big G) from Coulomb, Lorentz and Centripetal Force

The velocity of the Earth around the Sun and its corresponding mass are used in a standard centripetal force equation to match what Isaac Newton calculated with the Universal Law of Gravitation in 1687. Electromagnetic calculations are used to prove that electromagnetic forces are an insignificant contributor to the centripetal force or gravity, but do provide the bending force for the planets to maintain a circular orbit around the Sun. It is thus proven using classical physics that the force of gravity is a simple centripetal force with a very small electromagnetic force contribution.

Adapted Metrics for a Modified Coulomb/Newton’s Potential

Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.

Relativized Quantum Physics Generating <i>N</i>-Valued Coulomb Force and Atomic Hydrogen Energy Spectrum

Though not well-known, Einstein endeavored much of his life to general-relativize quantum mechanics, (rather than quantizing gravity). Albeit he did not succeed, his legacy lives on. In this paper, we begin with the general relativistic field equations describing flat spacetime, but stimulated by vacuum energy fluctuations. In our precursor paper, after straightforward general relativistic calculations, the resulting covariant and contravariant energy-momentum tensors were identified as n-valued operators describing graviton excitation. From these two operators, we were able to generate all three boson masses (including the Higgs mass) in precise agreement as reported in the 2010 CODATA (NIST);moreover local, as-well-as large-scale, accelerated spacetimes were shown to naturally occur from this general relativized quantum physics approach (RQP). In this paper, applying the same approach, we produce an n-valued Coulombs Force Law leading to the energy spectrum for atomic hydrogen, without assuming quantized atomic radii, velocity and momentum, as Bohr did.

盐城滨海湿地芦苇群落和互花米草群落对碱蓬群落挤压的时空变化特征

碱蓬是盐城滨海湿地土著物种,在生态功能维持中具有重要的意义。以盐城国家级自然保护区核心区为研究案例,以1983—2021年12期遥感影像为数据源,引入物理学库仑定律,分析芦苇群落和互花米草群落对碱蓬群落挤压的时空变化特征,结果如下:(1)芦苇、互花米草群落面积随时间呈线性增加,碱蓬群落面积呈先增加后减少的趋势。(2)芦苇群落对碱蓬群落的挤压力(F_(lj))呈线性增加,并以1992年和2002年为节点分为3个阶段;作用点轨迹以向东为主,移动了约4700 m。互花米草群落对碱蓬群落的挤压力(F_(mj))先增加后降低,同样表现出3阶段特征;轨迹点向西移动了约700 m,向北移动了约270 m。芦苇群落和互花米草群落对碱蓬群落综合挤压力(F_(合))呈线性增加,作用力方向2002年之前,在NNE向的左侧,2002年之后,在NE向的右侧;轨迹点向东北方向移动,以向东移动为主。(3)RDA排序能够反映碱蓬群落面积与F_(lj)、F_(mj)、F合的关系,12个时期的碱蓬群落面积变量被F合按照“三二一四”顺时针分布在4个象限;被变量F_(lj)、F_(mj)按照“三四一二”的顺序分布在4个象限,阶段性特征明显。(4)多元回归结果显示,F_(lj)对碱蓬群落面积的影响总体上大于F_(mj);景观格局指数ED、LSI、SHDI、AI与F_(lj)、F_(mj)、F合表现出较高的相关性。研究结果可为盐城滨海湿地生态恢复和世界自然遗产地的可持续建设提供参考。

广义破裂活动准则

岩石破裂及其后续活动是最基本的构造变形方式,然而,经典的破裂准则(Coulomb-Mohr准则、Griffith准则和以Byerlee律为代表的滑动摩擦律)在实际应用中存在不同方面的局限。文章在经典破裂准则的基础上,从产生破裂(扩张破裂和剪切破裂)的物理本质出发,结合广义剪切活动准则和长期的研究实践,通过理论分析,提出了“广义破裂活动准则”。该准则用统一的无量纲因子(破裂活动趋势因子)来表达扩张破裂活动和剪切破裂活动,可以用来定量判断任意介质、在任意三轴应力状态下、任意方位界面(包括先存薄弱面和非薄弱面)发生破裂活动的可能性以及破裂的类型,把Coulomb-Mohr准则、Byerlee律和Griffith准则统一起来,将破裂(fracturing)扩展到破裂活动(fracturing activity)。该准则在与破裂活动相关的资源勘探开发(如页岩气、干热岩等)、灾害(如地震与滑坡等)预测和防治中具有广阔的应用前景。

基于物理学史的“库仑定律”教学设计

库仑定律在静电学中的地位与万有引力定律在力学中的地位相当,学习库仑定律发现的历史,领会库仑等科学家在探索过程中所展现出来的科学态度、科学精神,对培养学生的物理核心素养意义重大。文章基于库仑定律发现的物理史实进行了教学设计,以期对物理教师讲授库仑定律,运用物理学史提供借鉴作用。

基于库仑摩擦定律的机床导轨润滑研究

机械结构磨损的本质就是有相对摩擦,减小摩擦就能降低磨损,而机床减小摩擦的方式便是有足够的润滑。润滑是机床设计和使用中特别重要的一个环节,机床的结构中包含了很多机械传动形式及各式各样的摩擦副,润滑方式的选择是其设计中的要点,也是判断其性能优劣的一个重要指标。导轨是机床实际应用中最容易、最常见的磨损机构。本文以库伦摩擦定律为理论基础,以机床导轨的润滑为例,提出了相应的设计方法和理念,期望本文能够给机床生产厂和机床使用厂家提供设计参考,将更加高效可靠的润滑方式进行推广,推动中国制造更好的向前发展。