Unified Equation of Fundamental Forces’ Coupling Values, and the Existence of Subsequent, Fifth and Other, Forces

This paper provides an equation to entangle all known fundamental forces by employing their coupling constants, i.e., strong (αs), electromagnetic (α), weak (αw), and gravitational (αg) interaction coupling values. The constant coupling formulation is further indicative of many other fundamental forces with significantly weaker coupling values. As an example, the fifth fundamental force, Kashi’s Force, is found to have a coupling constant of 10-1446, which is significantly smaller than the smallest known fundamental force, gravitational force, with an approximate coupling constant value of 10-38. Additionally, the paper finds the sum of all fundamental forces based on the equation proposed is equal to 0.118065, which is within the range of effective world value of the strong coupling constant αs(M2z).

Inverse-time Backup Protection Based on Unified Characteristic Equation for Distribution Networks with High Proportion of Distributed Generations

The setting work of backup protection using steady-state current is tedious,and mismatches occasionally occur due to the increased proportion of distributed generations(DGs)connected to the power grid.Thus,there is a practical need to study a backup protection technology that does not require step-by-step setting and can be adaptively coordinated.This paper proposes an action sequence adaptive to fault positions that uses only positive sequence fault component(PSFC)voltage.Considering the influence of DGs,the unified time dial setting can be obtained by selecting specific points.The protection performance is improved by using the adjacent upstream and downstream protections to meet the coordination time interval in the case of metallic faults at the near-and far-ends of the line.Finally,the expression and implementation scheme for inverse-time backup protection(ITBP)based on the unified characteristic equation is given.Simulation results show that this scheme can adapt to DG penetration scenarios and can realize the adaptive coordination of multi-level relays.

Statistical deduction and experimental verification on kinetic equations for the curing reactions of epoxy resins/amines

Based on three typical mechanisms (second-order, third-order and competitive mechanisms) for the curing reactions of the epoxy resins with amines, a pair of the kinetic equations (for primary and secondary aminations) was presented to explain the uniformity and relationship among the three different kinetic mechanisms of the reactions. The presented macro-equations were deduced from the kinetic micro-equations by the statistics method. And the constitutive equations were verified by experimental data at different reaction times and temperatures (95°C, 60°C and 39°C), taking diglycidyl ether of bisphenol A (DGEBA) /ethyleneamine (EA) as a model.

Direct modeling for computational fluid dynamics

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes （NS） equations. The current computational fluid dynamics （CFD） focuses on the numerical solution of partial differential equations （PDEs）, and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numer- ical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require fur- ther expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional dis- tinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of con- structing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm develop- ment. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be mod- eled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of dis- crete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydro- dynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

Thermo-hydro-mechanical-air coupling finite element method and its application to multi-phase problems

In this paper, a finite element method （FEM）-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air （THMA） behavior of geomaterial and using finite element-finite difference （FE-FD） scheme for so/l-water-air three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste （HLRW）, are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. （2007）, is simulated in the framework of soil-water-air three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz （2006） is simulated in the same framework under the conditions of variable temperature hut constant air pressure.

Acceleration Workspace of Cooperating Multi-Finger Robot Systems

We present a mathematical method for acceleration workspace analysis of cooperating multi-finger robot systems using a model of point-contact with friction. A new unified formulation from dynamic equations of cooperating multi-finger robots is derived considering the force and acceleration relationships between the fingers and the object to be handled. From the dynamic equation, maximum translational and rotational acceleration bounds of an object are calculated under given constraints of contact conditions, configurations of fingers, and bounds on the torques of joint actuators for each finger. Here, the rotational acceleration bounds can be applied as an important manipulability index when the multi-finger robot grasps an object. To verify the proposed method, we used a set of case studies with a simple multi-finger mechanism system. The achievable acceleration boundary in task space can be obtained successfully with the proposed method and the acceleration boundary depends on the configurations of fingers.

A Unified Momentum Equation Approach for Computing Flow-Induced Stresses in Structures with Arbitrarily-Shaped Stationary Boundaries

This article presents a novel monolithic numerical method for computing flow-induced stresses for problems involving arbitrarily-shaped stationary boundaries.A unified momentum equation for a continuum consisting of both fluids and solids is derived in terms of velocity by hybridizing the momentum equations of incompressible fluids and linear elastic solids.Discontinuities at the interface are smeared over a finite thickness around the interface using the signed distance function,and the resulting momentum equation implicitly takes care of the interfacial conditions without using a body-fitted grid.A finite volume approach is employed to discretize the obtained governing equations on a Cartesian grid.For validation purposes,this method has been applied to three examples,lid-driven cavity flow in a square cavity,lid-driven cavity flow in a circular cavity,and flow over a cylinder,where velocity and stress fields are simultaneously obtained for both fluids and structures.The simulation results agree well with the results found in the literature and the results obtained by COMSOL Multiphysicsr.

THE ASYMPTOTIC PRESERVING UNIFIED GAS KINETIC SCHEME FOR GRAY RADIATIVE TRANSFER EQUATIONS ON DISTORTED QUADRILATERAL MESHES

In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285（2015）,265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme（UGKS）,we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30（2008）,1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.

New physical structures and patterns to the optical solutions of the nonlinear Schrödinger equation with a higher dimension

It is commonly recognized that,despite current analytical approaches,many physical aspects of nonlinear models remain unknown.It is critical to build more efficient integration methods to design and construct numerous other unknown solutions and physical attributes for the nonlinear models,as well as for the benefit of the largest audience feasible.To achieve this goal,we propose a new extended unified auxiliary equation technique,a brand-new analytical method for solving nonlinear partial differential equations.The proposed method is applied to the nonlinear Schrödinger equation with a higher dimension in the anomalous dispersion.Many interesting solutions have been obtained.Moreover,to shed more light on the features of the obtained solutions,the figures for some obtained solutions are graphed.The propagation characteristics of the generated solutions are shown.The results show that the proper physical quantities and nonlinear wave qualities are connected to the parameter values.It is worth noting that the new method is very effective and efficient,and it may be applied in the realisation of novel solutions.