Effects of projectile parameters on the momentum transfer and projectile melting during hypervelocity impact

The effects of projectile/target impedance matching and projectile shape on energy,momentum transfer and projectile melting during collisions are investigated by numerical simulation.By comparing the computation results with the experimental results,the correctness of the calculation and the statistical method of momentum transfer coefficient is verified.Different shapes of aluminum,copper and heavy tungsten alloy projectiles striking aluminum,basalt,and pumice target for impacts up to 10 km/s are simulated.The influence mechanism of the shape of the projectile and projectile/target density on the momentum transfer was obtained.With an increase in projectile density and length-diameter ratio,the energy transfer time between the projectile and targets is prolonged.The projectile decelerates slowly,resulting in a larger cratering depth.The energy consumed by the projectile in the excavation stage increased,resulting in lower mass-velocity of ejecta and momentum transfer coefficient.The numerical simulation results demonstrated that for different projectile/target combinations,the higher the wave impedance of the projectile,the higher the initial phase transition velocity and the smaller the mass of phase transition.The results can provide theoretical guidance for kinetic impactor design and material selection.

A Dark Energy Hypothesis I

The cosmological constant, Λ, represents dark energy. The dark energy hypothesis (DEH) replaces Λ with a variable quantity, the cosmological parameter: Λ=1a2η2In this formula, “a” is the scale factor and η the conformal time: adη = cdt. A companion paper (DEH II) develops and explores a cosmological model with this variable parameter. This paper portrays the origin of the cosmological parameter in the uncoupling of time and space in the early universe from a prior state in which the comoving coordinates x0 = η and x1 = χ, the cosmic latitude, are coupled. In this hypothesis dark matter is a co-product of the decoupling, but its nature remains mysterious.

A Locally Conservative Energy-Momentum Tensor in the General Relativity Based on a Cosmological Model without Singularity

According to the conventional theory it is difficult to define the energy-momentum tensor which is locally conservative. The energy-momentum tensor of the gravitational field is defined. Based on a cosmological model without singularity, the total energy-momentum tensor is defined which is locally conservative in the general relativity. The tensor of the gravitational mass is different from the energy-momentum tensor, and it satisfies the gravitational field equation and its covariant derivative is zero.

Steering the energy sharing of electrons in nonsequential double ionization with orthogonally polarized two-color field

Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.

Absorbing Charged Rotating Metric in de Sitter Space in Advanced Time Coordinates and the Related Energy-Momentum Tensor

Absorbing charged rotating(ACR)metric in de Sitter space and related energy-momentum tensor are derived.The ACR metric is very simple in advanced time coordinates.The ACR metric involves 8 independent parameters which are divided into two c the mass M,charge Q,angular momentum per unit mass a,and cosmological constant A;(2)■M/■v,■^(2)M/■v^(2),■q/■V,and ■^(2)Q/■v^(2).The non-stationary part of the energy-momentum tensor is positive definite everywhere.

Energy momentum pseudo-tensor of high frequency gravitational waves and their dynamical back-reaction

To describe properties of the high frequency gravitational wave （HFGW） propagating through the vacuum gravitational field in Robertson-Walker background space-time, we calculated its energy momentum pseudo-tensor （EMPT） in the limit of short wavelengths by taking the Brill-Hartle average on the second order perturbation of the Einstein tensor over several wavelengths. By rewriting the EMPT as a form of perfect fluid, the dynamical back-reaction of HIFGW on the background spacetime was discussed. The result shows that the energy density of HFGW, which is in the gauge we chose, is positive definite. The HFGW serves as a source for curving the background space-time and affects the dynamical evolution and time evolution of the scale factor of the Robertson-Walker metric.

The Strange Relationship between the Momentum of a Photon Emitted from an Electron and the Momentum Acquired by the Electron

In quantum mechanics, the energy of a hydrogen atom is minimized when the principal quantum number n is 1. However, the author has previously pointed out that the hydrogen atom has a state where n=0. An electron in the state where n=0has zero rest mass energy. However, a hydrogen atom has an energy level even lower than the n=0state. This is hard to accept from the standpoint of common sense. Thus, the author has previously pointed out that an electron at the energy level where n=0has zero energy because the positive energy mec2and negative energy −mec2cancel each other out. This paper elucidates the strange relationship between the momentum of a photon emitted when a hydrogen atom is formed by an electron with such characteristics, and the momentum acquired by the electron.

Fourth Rank Energy-Momentum Tensor

In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.

Bias Momentum Attitude Control System Using Energy/Momentum Wheels

The integrated power and attitude control for a bias momentum attitudecontrol system is investigated. A pair of counter-spinning wheels is used to provide the biasangular momentum and store/ discharge energy for power requirement of the devices on the spacecraft.The roll/yaw motion is controlled by pitch magnetic dipole moment. The torque-based control law ofthe wheels is designed, so that the desired pitch control torque is provided and the operation ofcharging/discharging energy is carried out based on the given power. System singularity in thecontrol law of wheels is fully avoided by keeping the wheels counter-spinning. A power managementscheme using kinetic energy feedback is proposed to keep energy balance, which can avoid wheelsaturation caused by superfluous energy. The minimum moment of inertia of the wheels is limited bythe maximum bias angular momentum and the minimum energy, such constrains are analyzed incombination with the geometrical method. Numerical simulation results are presented to demonstratethe effectiveness of the control scheme.

Contributions of optimized tensor interactions on the binding energies of nuclei

The tensor parts of Skyrme interactions are constrained from the collective charge-exchange spin-dipole and Gamow-Teller excitation energies in 90Zr and 208Pb,together with the isotopic dependence of energy splitting between proton h11=2 and g7=2 single-particle orbits along the Z=50 isotopes.With the optimized tensor interactions,the binding energies of spherical or weakly deformed nuclei with A=54-228 are studied systematically.The present results show that the global effect of tensor interaction is attractive and systematically increases the binding energies of all these nuclei and makes the nuclei more bound.The root mean squared deviation of the calculated binding energies from the experimental values is significantly improved by the optimized tensor interactions,and the contribution of the tensor interaction to the binding energy is estimated.

Cosmic Dark Energy Density from Classical Mechanics and Seemingly Redundant Riemannian Finitely Many Tensor Components of Einstein’s General Relativity

We determine the limit of the ratio formed by the independent components of the Riemann tensor to the non-zero component as space dimensionality tends to infinity and find it to be 12. Subsequently we use this result in conjunction with Newtonian classical mechanics to show that the ordinary measurable cosmic energy density is given by while the dark energy density is obviously the Legendre transformation dual energy E(D) = 1 -?E(O). The result is in complete agreement with the COBE, WMAP and type 1a supernova measurements.

Energy and Momentum Considerations in an Ideal Solenoid

The electromagnetic linear momentum and the energy balance in an infinite solenoid with a time-dependant current are examined. We show that the electromagnetic linear momentum density and its associated force density are balanced by the hidden momentum density and its associated hidden force density respectively. We also show that exactly half the energy delivered by the power supply appears as stored magnetic energy inside the solenoid. The other half is lost against the induced electromotive force that appears in the windings of the solenoid during the time through which the current is building up towards its final value. This energy loss, which is found in other analogue situations, is necessary to transfer the system from an initial non-equilibrium state to a final equilibrium one.

Energy,momentum and angular momentum in the dyadosphere of a charged spacetime in teleparallel equivalent of general relativity

We apply the energy momentum and angular momentum tensor to a tetrad field, with two unknown functions of radial coordinate, in the framework of a teleparallel equivalent of general relativity （TEGR）. The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-NordstrSm black hole. We also calculate the spatial momentum and angular momentum.

Gedanken Experiment for Fluctuation of Mass of a Graviton, Based on the Trace of GR Stress Energy Tensor-Pre Planckian Conditions that Lead to Gaining of Graviton Mass, and Planckian Conditions That Lead to Graviton Mass Shrinking to 10-62 Grams

We will be looking at the energy of a graviton, based upon the Stress energy tensor, and from there ascertaining how fluctuations in early universe conditions impact the mass of a graviton. Physically the mass of the graviton would be shrinking right after Planck time and presumably it would be going to its equilibrium value of about 10-62 grams, for its present day value. It, graviton mass, would increase up to the Plank time of about 10-44 seconds. Note that the result that graviton mass shrinks to 10-62 grams for its present day value works only for relic gravitons.

Five-dimensional teleparallel theory equivalent to general relativity,the axially symmetric solution,energy and spatial momentum

A theory of （4＋1）-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity. The fundamental gravitational field variables are the five-dimensional vector fields （pentad）, defined globally on a manifold M, and gravity is attributed to the torsion. The Lagrangian density is quadratic in the torsion tensor. We then give the exact five-dimensional solution. The solution is a generalization of the familiar Schwarzschild and Kerr solutions of the four-dimensional teleparallel equivalent of general relativity. We also use the definition of the gravitational energy to calculate the energy and the spatial momentum.

Effect of Short-Range and Tensor Force Correlations on High-Density Behavior of Symmetry Energy

The effect of short-range and tensor correlations on nuclear symmetry energy is investigated by using realistic nuclear momentum distribution n(k).For finite nuclei,the n(k)is discussed in detail within an analytical model that allows inclusion of both short-range and tensor correlation effects in a physically very transparent way.The equation of state of symmetric nuclear matter is calculated by using realistic n(k)parameterization.The tensor-force induced short-range correlations are shown to have a significant impact on the behavior of symmetry energy.

An Adaptive Momentum CMA Blind Equalization Based on Error Energy

To solve the problem of large steady state residual error of momentum constant modulus algorithm (CMA) blind equalization, a momentum CMA blind equalization controlled by energy steady state was proposed. The energy of the equalizer weights is estimated during the updating process. According to the adaptive filtering theory, the energy of the equalizer weights reaches to the steady state after the algorithm is converged, and then the momentum can be set to 0 when the energy change rate is less than the threshold, which can avoid the additional gradient noise caused by momentum and further improve the convergence precision of the algorithm. The proposed algorithm takes advantage of momentum to quicken the convergence rate and to avoid the local minimum in the cost function to some extent;meanwhile, it has the same convergence precision with CMA. Computer simulation results show that, compared with CMA, momentum CMA (MCMA) and adaptive momentum CMA (AMCMA) blind equalization, the proposed algorithm has the fastest convergence rate and the same steady state residual error with CMA.

Conservation laws for energy and momentum in curved spaces

In arbitrary Riemannian 4-spaces, continuity equations are constructed which could be interpreted as conservation laws for the energy and momentum of the gravitational field. Special attention is given to general relativity to obtain, of natural manner, the pseudotensors of Einstein, Landau-Lifshitz, Moeller, Goldberg and Stachel, and also the conservation equations of Komar, Trautman, DuPlessis and Moss.

Interaction Energy Prediction of Organic Molecules using Deep Tensor Neural Network

The interaction energy of two molecules system plays a critical role in analyzing the interacting effect in molecular dynamic simulation.Since the limitation of quantum mechanics calculating resources,the interaction energy based on quantum mechanics can not be merged into molecular dynamic simulation for a long time scale.A deep learning framework,deep tensor neural network,is applied to predict the interaction energy of three organic related systems within the quantum mechanics level of accuracy.The geometric structure and atomic types of molecular conformation,as the data descriptors,are applied as the network inputs to predict the interaction energy in the system.The neural network is trained with the hierarchically generated conformations data set.The complex tensor hidden layers are simplified and trained in the optimization process.The predicted results of different molecular sys tems indica te that deep t ensor neural net work is capable to predic t the interaction energy with 1 kcal/mol of the mean absolute error in a relatively short time.The prediction highly improves the efficiency of interaction energy calculation.The whole proposed framework provides new insights to introducing deep learning technology into the interaction energy calculation.

Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors,energy,momentum and angular momentum

The energy--momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space--time their energies are different. Therefore, a regularized expression of the gravitational energy--momentum tensor of the teleparallel equivalent of general relativity （TEGR）, is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy--momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space--times are calculated. In spite of using a static space--time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space--times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.