Energy Theorem Research Articles

On Cutter Deflection Profile Errors in End Milling: Modeling and Experimental Validation

In the present paper three dimensional cutter deflections and the corresponding profile errors during end milling are predicted by finite element and bond graph modeling approach. The deflections have been modeled considering the cutter as a cantilever beam fixed at the collet end. Rayleigh beam model is used for modeling to consider the shear force effect, and Castigliano's theorem of strain energy is used to predict the deflections due to radial, tangential, and axial cutting forces. The tool-workpiece contact region is sliced into small elements to apply the forces on the entire contact region and predict deflections more accurately. The predicted deflections at different parametric settings are compared with experimental measurements by measuring the geometric accuracy of the cut profiles. The depth of cut has the most significant influence on profile deviations, while feed and speed have marginal effects. The results reveal that the predictions by finite elements and the bond graph closely matches with the experimental results, and errors of the machined profile are significantly influenced by the radial and tangential deflections. The axial deflection is negligible and leads to insignificant deviation in depth of the cut profile. The proposed model shows that the bond graph simulation takes significantly less computational time and space as compared to the finite element technique.

Sedenion unified theory of gravi-electromagnetism

In this paper, we represent 16-component sedenions, the generalization of octonions, which is noncommutative space–time algebra. The sedenions is neither a composition algebra nor a division algebra because it has zero divisors. Here we have formulated the sedenionic unified potential equations, unified fields equations and unified current equations of dyons and gravito-dyons. We have developed the sedenionic unified theory of dyons and gravito-dyons in terms of two eight-potentials leading to the structural symmetry between generalized electromagnetic fields of dyons and generalized gravito-Heavisidian fields of gravito-dyons. Thus we have obtained the sedenionic form of generalized Dirac–Maxwell’s equations, unified work–energy theorem (Poynting theorem), generalized unified gravi-electromagnetic force and other quantum equations of dyons and gravito-dyons in simple, compact and consistent way incorporating the non-associativity and non-commutativity of sedenion variables.

Top partners and Higgs boson production

The Higgs boson is produced at the LHC through gluon fusion at roughly the Standard Model rate. New colored fermions, which can contribute to $gg\rightarrow h$, must have vector-like interactions in order not to be in conflict with the experimentally measured rate. We examine the size of the corrections to single and double Higgs production from heavy vector-like fermions in $SU(2)_L$ singlets and doublets and search for regions of parameter space where double Higgs production is enhanced relative to the Standard Model prediction. We compare production rates and distributions for double Higgs production from gluon fusion using an exact calculation, the low energy theorem (LET), where the top quark and the heavy vector-like fermions are taken to be infinitely massive, and an effective theory (EFT) where top mass effects are included exactly and the effects of the heavy fermions are included to ${\cal O}(1/M^2_X)$. Unlike the LET, the EFT gives an extremely accurate description of the kinematic distributions for double Higgs production.

Simultaneous Determination of Structures, Vibrations, and Frontier Orbital Energies from a Self-Consistent Range-Separated Hybrid Functional.

A self-consistent optimally tuned range-separated hybrid density functional (scOT-RSH) approach is developed. It can simultaneously predict accurate geometries, vibrational modes, and frontier orbital energies. This is achieved by optimizing the range-separation parameter, γ, to both satisfy the ionization energy theorem and minimize interatomic forces. We benchmark our approach against an established hybrid functional, B3LYP, using the G2 test set. scOT-RSH greatly improves the accuracy of occupied frontier orbital energies, with a mean absolute error (MAE) of only 0.2 eV relative to experimental ionization energies compared to 2.96 eV with B3LYP. Geometries do not change significantly compared to those obtained from B3LYP, with a bond length MAE of 0.012 Å compared to 0.008 Å for B3LYP, and a 6.5% MAE for zero-point energies, slightly larger than that of B3LYP (3.1%). scOT-RSH represents a new paradigm in which accurate geometries and ionization energies can be predicted simultaneously from a single functional approach.

Stiffness and Transfer Matrix Analysis in Global Coordinates of a 3D Curved Beam

This article presents the differential equation in the global coordinates governing the structural behavior of 3D curved beams existing in building structures and civil works. This differential equation presented is of the lower-triangular form, which allows us to obtain the transfer matrix, also of lower-triangular form and with unit diagonal, through simple integrals. The stiffness matrix is determined from the transfer matrix expression, only by reordering operations, without employing additional structural methods, energy theorems or other. This rearrangement can be more easily done under the global system, compared with the natural reference system, since the order of the matrices involved has been reduced. The examples presented show the process to apply this general procedure to derivation of the stiffness matrix of a member from its transfer expression, through reordering operations.

Holographic positive energy theorems in three-dimensional gravity

The covariant phase space of three-dimensional asymptotically flat and anti-de Sitter gravity is controlled by well-understood coadjoint orbits of the Virasoro group. Detailed knowledge on the behavior of the energy functional on these orbits can be used to discuss positive energy theorems.

Kähler non-collapsing, eigenvalues and the Calabi flow

We first prove a new compactness theorem of Kähler metrics, which confirms a prediction in [17]. Then we establish several eigenvalue estimates along the Calabi flow. Combining the compactness theorem and these eigenvalue estimates, we generalize the method developed for the Kähler–Ricci flow in [22] to obtain several new small energy theorems of the Calabi flow.

Prediction the Shear Strength for FRP Shear Strengthened RC Beams Based on Optimised Truss Models

This paper presents the analytical optimised truss model based on the principle of the minimum total strain energy theorem. The model was validated against 90 experimental data collected from the literature. The predicted shear strength in the analysis showed a very satisfactory correlation with the test results, with the average experimental/analytical failure load ratio of 1.09 and the coefficient of variation (C.O.V) of 14.1%. Furthermore, a comparison between the accuracy of the proposed model and the current design guidelines was also demonstrated in this study. It was observed that the optimised truss model led to be more viable than the standard 45-deg truss model in the design guidelines. A large dispersion of the results was found in ACI 440 with the C.O.V as far as 31.4%; whilst the TR 55 and fib 14 showed no significant difference with the C.O.V of 29.3% and 21.5%, respectively.

Matrix mechanics of the infinite square well and the equivalence proofs of Schrödinger and von Neumann

There are few simple examples of the formal equivalence of wave mechanics and matrix mechanics. The momentum matrix for a particle in an infinite square well is easy to calculate and rarely discussed in textbooks. We square this matrix to construct the energy levels and use the energy theorem of Fourier analysis to establish the wave-matrix connection. The key ingredients of the equivalence proofs of Schrödinger and von Neumann, such as the d/dx rule and the Riesz-Fischer theorem, find simple expression within the particle-in-a-box framework.

Stable bimetric theories

We prove that there are energetically stable bimetric theories. These theories satisfies a positive energy theorem. We construct a model example.

A Study on Effective Strains in Different FRP Shear Strengthening Schemes for Analytical Optimized Truss Models

This paper presents an optimized truss model based on the principle of minimum total energy theorem. Six most recent effective strain ɛfrp,e models including three design guidelines were selected for the analysis. Three reinforced concrete beams strengthened with different fiber reinforced polymer (FRP) schemes were chosen. Comparing with current design guidelines, the results of these three beams indicate that the optimized model is promising and encouraging.

Bulk viscosity of hot dense Quark matter in the PNJL model

Starting from the Kubo formula and the QCD low energy theorem, we study the the bulk viscosity of hot dense quark matter in the PNJL model from the equation of state. We show that the bulk viscosity has a sharp peak near the chiral phase transition, and that the ratio of bulk viscosity over entropy rises dramatically in the vicinity of the phase transition. These results agree with those from the lattice and other model calculations. In addition, we show that the increase of chemical potential raises the bulk viscosity.

Dynamic behaviors of a geared rotor system under time-periodic base angular motions

The dynamic behaviors of a geared rotor system under time-periodic base motions are studied in this paper. The equations of motion for a spur gear pair system are derived based on the energy theorem and Lagrange's principle. Three base angular motions, including the rolling, pitching and yawing motions, are assumed to be sinusoidal perturbations superimposed upon constant terms. Considering the time-varying base movements and gear meshing, the second order differential equations of the system will not only have time-periodic gyroscopic and stiffness coefficients, but also the multi-frequency external excitations. Numerical method is utilized to obtain the lateral and torsional responses of the geared system under transmission error and unbalanced mass excitations. The effects of various base angular motions on both frequency response and response spectra are discussed in detail. Compared with the other two types of periodic base motions, the rolling base motion has the greatest impact on the dynamic behaviors of the geared system. The transient response of the geared rotor system is always greatly enhanced no matter which type of base angular motion is in operation.

Pion properties at finite nuclear density based on in-medium chiral perturbation theory

The in-medium pion properties, {\it i.e.} the temporal pion decay constant $f_t$, the pion mass $m_\pi^*$ and the wave function renormalization, in symmetric nuclear matter are calculated in an in-medium chiral perturbation theory up to the next-to-leading order of the density expansion $O(k_F^4)$. The chiral Lagrangian for the pion-nucleon interaction is determined in vacuum, and the low energy constants are fixed by the experimental observables. We carefully define the in-medium state of the pion and find that the pion wave function plays an essential role for the in-medium pion properties. We show that the linear density correction is dominated and the next-leading corrections is not so large at the saturation density, while their contributions can be significant in higher densities. The main contribution of the next-leading order comes from the double scattering term. We also discuss whether the low energy theorems, the Gell-Mann--Oakes--Renner relation and the Glashow--Weinberg relation, are satisfied in nuclear medium beyond the linear density approximation. We find also that the wave function renormalization is enhanced as largely as $50\%$ at the saturation density including the next-leading contribution and the wave function renormalization could be measured in the in-medium $\pi^0\to \gamma\gamma$ decay.

R&D of a Foldable Obstacle-Striding Electromagnetic Coilgun

Electromagnetic coilgun and obstacle-striding mechanism are creatively integrated into the foldable obstacle-striding electromagnetic coilgun. According to the theorem of kinetic energy, permanent magnet NdFeB is used as a collisional armature to accelerate the projectile through a central collision. Meanwhile, structures such as shaft in shaft mechanism are designed. Both of the late-model mechanisms make the physical overall structure simple, compacted, and better capable of obstacle striding and operating performance. The testing results and operating performance of this late-model foldable obstacle-striding electromagnetic coilgun appear to be excellent through observing and analysing the results of experiments. It can successfully cross stairs, steps and other usual obstacles. If the stage and the number of turns of induction coil are increased, with safety protecting device, this equipment will be able to put into practice further in particular fields, for instance, military, anti-terrorism, tall building fire fighting and so on.

Two-dimensional analytical solution of elastic stresses for balanced single-lap joints—Variational method

A two-dimensional (2D) analytical method that is capable of providing an explicit closed-form solution is presented for the prediction of elastic stresses in balanced single-lap adhesive-bonded joints, assuming only a longitudinal normal stress linear distribution in the joint thickness direction. By selecting the four appropriate in-plane loading stress functions, the theory can predict the 2D stress distribution at any point, and the tensile force, shearing and bending moment at any cross section accurately, in both the adhesive and adherends. The method is based on 2D elasticity theory in conjunction with the variational theorem of complementary energy. Minimizing the energy functional leads to four coupled, fourth-order ordinary differential equations with constant coefficients for the determination of the stresses. All boundary conditions, including shear stress-free surfaces, are satisfied. The analytical method was verified by comparing with our previous 2D solutions, and the 2D geometrically nonlinear finite element analysis. It is indicated that the present solution can provide a good prediction for the stress and in-plane loading distributions in the adhesive and adherends.

Energy positivity, non-renormalization, and holomorphy in Lorentz-violating supersymmetric theories

This paper shows that the positive-energy and non-renormalization theorems of traditional supersymmetry survive the addition of Lorentz violating interactions. The Lorentz-violating coupling constants in theories using the construction of Berger and Kostelecky must obey certain constraints in order to preserve the positive energy theorem. Seiberg's holomorphic arguments are used to prove that the superpotential remains non-renormalized (perturbatively) in the presence of Lorentz-violating interactions of the Berger-Kostelecky type. We briefly comment on Lorentz-violating theories of the type constructed by Nibbelink and Pospelov to note that holomorphy arguments offer elegant proofs of many non-renormalization results, some known by other arguments, some new.

On fluid–shell coupling using an arbitrary Lagrangian–Eulerian fluid solver coupled to a positional Lagrangian shell solver

In this work, we develop a partitioned algorithm for three-dimensional geometric non-linear fluid–structure interaction analysis using the finite element method. The fluid solver is explicit and its time integration based on characteristics, which automatically introduces stabilising terms on stream direction. The Navier–Stokes equations are written using the arbitrary Lagrangian–Eulerian (ALE) description, in order to accept moving boundaries and coupling with Lagrangian shell elements. The structure is modelled using a novel finite element method formulation for geometric non-linear shell dynamics. Such shell formulation, so-called positional formulation, is based on the minimum potential energy theorem, written regarding nodal positions and generalised unconstrained vectors, not displacements and rotations. These characteristics avoid the use of large rotation approximations. The coupling between the two different meshes is done by mapping the fluid boundary nodes local positions over the shell elements and vice versa, avoiding the need for matching fluid and shell nodes. The fluid mesh is adapted using a simple approach based on shell positions and velocities. The efficiency and robustness of the proposed approach is demonstrated by examples.

OCTONION AND CONSERVATION LAWS FOR DYONS

Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the continuity equation and other wave equations of dyons in split octonions. Accordingly, we have investigated the work energy theorem or "Poynting Theorem," Maxwell stress tensor and Lorentz invariant for generalized fields of dyons in split octonion electrodynamics. Our theory of dyons in split octonion formulations is discussed in term of simple and compact notations. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.

Power Consumption Analysis of High-Speed Train’s Brake Discs

Apart from the aerodynamic drag produced by transitional motion of high-speed train, the rotational parts of the train, especially the ventilated discs mounted on axles, would also cause resistance torques due to air pumping effect, which consume traction power. In this paper the train running process is divided into traction, uniform running and braking three phases, then the power consumed by the brake discs as well as the proportion of which in total traction or braking power during the three periods is calculated based on kinetic energy theorem. The results indicate that, during traction and uniform running period, the power consumption of brake discs shares 2.84% and 12.87% of total traction power, and in brake stage, the proportion is 0.78%. What is more, in the uniform running phase, the proportion of brake discs power consumption caused by resistance torque can reach to 7.68%. If the air inlet of brake disc is blocked during traction and uniform running period to weaken air pumping effect, the useless power consumption can be effectively reduced and the traction efficiency can be improved.