Framework Of Newtonian Mechanics Research Articles

Bloch oscillations probed quantum phases in HgTe quantum wells

The semiconductor quantum well based on mercury telluride is characterized by two distinct phases: conventional insulating phase and topological insulating phase with helical edge states. The system undergoes a topological quantum phase transition from one phase to the other, tuned by the critical geometric parameters of the quantum well. It is shown that the quantum states in each phase exhibit distinct flavors of Bloch oscillations, depending strongly on the geometric parameters and crystal momentum of the system. In particular, the group and Berry velocities and the real-space trajectories exhibit pronounced Bloch oscillations. Interestingly, the x- and y-components of the group velocity are interchanged by interchanging their corresponding components of the crystal momentum. In addition, a Gaussian wave packet undergoes distinct time evolution in each quantum phase of the HgTe quantum well. Moreover, the effects of applied in-plane electric and transverse magnetic fields are determined within the framework of Newtonian mechanics, leading to the geometric visualization of such an oscillatory motion. We find that in the presence of both applied in-plane electric and transverse magnetic fields simultaneously, the system undergoes a dynamic phase transition between confined and de-confined states, tuned by the relative strength of the fields. It is argued that the distinct Bloch oscillations originate from the peculiar band structure of HgTe quantum wells in each quantum phase. Furthermore, we find that the direct-current drift velocity in each quantum phase exhibits negative differential conductivity, a hallmark of the Bloch oscillation regime.

Equations of motion of masses of the Chelomey pendulum model

To verify the provisions stated by V.I. Bogomolov, B.I. Puzanov. and Linevich E.I. about the possibility of performing over-unit work by inertial forces, a closed mechanical system in the form of kinematically connected rotating masses is proposed for consideration. The research aimed, within the framework of Newtonian mechanics, to study the fulfillment of the laws of conservation of momentum, angular momentum and energy, to establish the possibility of performing work by inertial forces (centrifugal and Coriolis), to assess the change in kinetic parameters using the example of the Chelomey pendulum model. For the complex radial-circular motion of the masses of the Chelomey pendulum model, resolving equations are obtained. To verify the analytical calculations, algorithms for numerical solutions of the above problems have been developed and implemented in the MathCAD software package

Predicting high cycle fatigue life with unified mechanics theory

Fatigue life prediction of metals has been widely studied. However, most of the research is based on empirical models under the framework of Newtonian mechanics, that relies on experimental fatigue data for curve fitting a degradation evolution function. Unified mechanics theory (UMT), on the other hand, unifies the universal laws of motion of Newton by incorporating the second law of thermodynamics directly into the Newton's laws at the ab-initio level. UMT introduces an additional linearly independent axis called Thermodynamic State Index (TSI), which can have values between zero and one. Evolution along the TSI axis follows the Boltzmann's entropy formulation and the thermodynamic fundamental equation of the material. As a result, governing differential equations of any system automatically include energy dissipation, and degradation evolution. The fatigue model presented here is pure physics based and does not require an empirical evolution function obtained by curve fitting to fatigue test data. However, it does require deriving analytical thermodynamic fundamental equations of the material based on the principals of physics. Thermodynamic fundamental equation for high cycle metal fatigue is derived in this study.

Equations of motion of masses of the Chelomey pendulum model

Abstract. To verify the provisions stated by V.I. Bogomolov, B.I. Puzanov. and Linevich E.I. about the possibility of performing over-unit work by inertial forces, a closed mechanical system in the form of kinematically connected rotating masses is proposed for consideration. The research aimed, within the framework of Newtonian mechanics, to study the fulfillment of the laws of conservation of momentum, angular momentum and energy, to establish the possibility of performing work by inertial forces (centrifugal and Coriolis), to assess the change in kinetic parameters using the example of the Chelomey pendulum model. For the complex radial-circular motion of the masses of the Chelomey pendulum model, resolving equations are obtained. To verify the analytical calculations, algorithms for numerical solutions of the above problems have been developed and implemented in the MathCAD software package.

A Review of Damage, Void Evolution, and Fatigue Life Prediction Models

Degradation, damage evolution, and fatigue models in the literature for various engineering materials, mostly metals and composites, are reviewed. For empirical models established under the framework of Newtonian mechanics, Gurson–Tvergaard–Needleman (GTN) type model, Johnson-Cook (J-C) type damage model, microplasticity model, some other micro-mechanism based damage models, and models using irreversible entropy as a metric with an empirical evolution function are thoroughly discussed. For Physics-based models, the development and applications of unified mechanics theory is reviewed.

Some Results on Newtonian Gaseous Stars—Existence and Stability

This paper surveys some results on the existence and stability of solutions to some partial differential equations of gaseous stars in the framework of Newtonian mechanics, and presents some key ideas in the proofs.

Towards development of enhanced fully-Lagrangian mesh-free computational methods for fluid-structure interaction

Simulation of incompressible fluid flow-elastic structure interactions is targeted by using fully-Lagrangian mesh-free computational methods. A projection-based fluid model (moving particle semi-implicit (MPS)) is coupled with either a Newtonian or a Hamiltonian Lagrangian structure model (MPS or HMPS) in a mathematically-physically consistent manner. The fluid model is founded on the solution of Navier-Stokes and continuity equations. The structure models are configured either in the framework of Newtonian mechanics on the basis of conservation of linear and angular momenta, or Hamiltonian mechanics on the basis of variational principle for incompressible elastodynamics. A set of enhanced schemes are incorporated for projection-based fluid model (Enhanced MPS), thus, the developed coupled solvers for fluid structure interaction (FSI) are referred to as Enhanced MPS-MPS and Enhanced MPS-HMPS. Besides, two smoothed particle hydrodynamics (SPH)-based FSI solvers, being developed by the authors, are considered and their potential applicability and comparable performance are briefly discussed in comparison with MPS-based FSI solvers. The SPH-based FSI solvers are established through coupling of projection-based incompressible SPH (ISPH) fluid model and SPH-based Newtonian/Hamiltonian structure models, leading to Enhanced ISPH-SPH and Enhanced ISPH-HSPH. A comparative study is carried out on the performances of the FSI solvers through a set of benchmark tests, including hydrostatic water column on an elastic plate, high speed impact of an elastic aluminum beam, hydroelastic slamming of a marine panel and dam break with elastic gate.

How fast do living organisms move: Maximum speeds from bacteria to elephants and whales

Despite their variety and complexity, living organisms obey simple scaling laws due to the universality of the laws of physics. In the present paper, we study the scaling between maximum speed and size, from bacteria to the largest mammals. While the preferred speed has been widely studied in the framework of Newtonian mechanics, the maximum speed has rarely attracted the interest of physicists, despite its remarkable scaling property; it is roughly proportional to length throughout nearly the whole range of running and swimming organisms. We propose a simple order-of-magnitude interpretation of this ubiquitous relationship, based on physical properties shared by life forms of very different body structure and varying by more than 20 orders of magnitude in body mass.

The physics of bump drafting in car racing

The technique of bump drafting, also known as two-car drafting in motorsports, is analysed in the framework of Newtonian mechanics and simple aerodynamic drag forces. As an apparent unnatural effect that often pleases the enthusiasts of car racing, bump drafting provides a unique pedagogical opportunity for students to gain insights into the physics of drag in moving vehicles. In the context of a physics undergraduate course, it is shown that the dynamics of two moving cars in the same air slipstream on a straight line allows them to increase their speed up to a factor of . This conclusion is also extended to an arbitrary number of n identical moving cars, resulting in an increase of .

A Fundamental Reconsideration of the CRASH3 Damage Analysis Algorithm: The Case Against Uniform Ubiquitous Linearity Between BEV, Peak Collision Force Magnitude, and Residual Damage Depth

Objective: The objective of this study was a thorough reconsideration, within the framework of Newtonian mechanics and work–energy relationships, of the empirically interpreted relationships employed within the CRASH3 damage analysis algorithm in regards to linearity between barrier equivalent velocity (BEV) or peak collision force magnitude and residual damage depth. Methods: The CRASH3 damage analysis algorithm was considered, first in terms of the cases of collisions that produced no residual damage, in order to properly explain the damage onset speed and crush resistance terms. Under the modeling constraints of the collision partners representing a closed system and the a priori assumption of linearity between BEV or peak collision force magnitude and residual damage depth, the equations for the sole realistic model were derived. Results: Evaluation of the work–energy relationships for collisions at or below the elastic limit revealed that the BEV or peak collision force magnitude relationships are bifurcated based upon the residual damage depth. Rather than being additive terms from the linear curve fits employed in the CRASH3 damage analysis algorithm, the Campbell b 0 and CRASH3 AL terms represent the maximum values that can be ascribed to the BEV or peak collision force magnitude, respectively, for collisions that produce zero residual damage. Collisions resulting in the production of non-zero residual damage depth already account for the surpassing of the elastic limit during closure and therefore the secondary addition of the elastic limit terms represents a double accounting of the same. This evaluation shows that the current energy absorbed formulation utilized in the CRASH3 damage analysis algorithm extraneously includes terms associated with the A and G stiffness coefficients. This sole realistic model, however, is limited, secondary to reducing the coefficient of restitution to a constant value for all cases in which the residual damage depth is nonzero. Conclusion: Linearity between BEV or peak collision force magnitude and residual damage depth may be applicable for particular ranges of residual damage depth for any given region of any given vehicle. Within the modeling construct employed by the CRASH3 damage algorithm, the case of uniform and ubiquitous linearity cannot be supported. Considerations regarding the inclusion of internal work recovered and restitution for modeling the separation phase change in velocity magnitude should account for not only the effects present during the evaluation of a vehicle-to-vehicle collision of interest but also to the approach taken for modeling the force–deflection response for each collision partner. Supplemental materials are available for this article. Go to the publisher's online edition of Traffic Injury Prevention to view the supplemental file.

Newtonian–Machian analysis of the neo-Tychonian model of planetary motions

The calculation of the trajectories in the Sun–Earth–Mars system is performed using two different models, both in the framework of Newtonian mechanics. The first model is the well-known Copernican system, which assumes that the Sun is at rest and that all the planets orbit around it. The second is a less well-known model, developed by Tycho Brahe (1546–1601), according to which the Earth stands still, the Sun orbits around the Earth, and the other planets orbit around the Sun. The term ‘neo-Tychonian system’ refers to the assumption that orbits of distant masses around the Earth are synchronized with the Sun's orbit. It is the aim of this paper to show the kinematical and dynamical equivalence of these systems, under the assumption of Mach's principle.

Determination of total mechanical energy of the universe within the framework of Newtonian mechanics.

The recent astronomical observations indicate that the expanding universe having a finite particle horizon is homogeneous, isotropic and asymptotically flat. The Euclidean geometry of the universe enables to determine the total kinetic and gravitational energies of the universe within the framework of the Newtonian mechanics. It has been shown that almost the entire kinetic energy of the universe ensues from the cosmological expansion. Both, the total kinetic and gravitational energies of the universe have been determined in relation to an observer at arbitrary location. It is amazing that the modulus of the total gravitational energy differs from the total kinetic energy with a multiplier close to a unit. Thus, the total mechanical energy of the universe has been found close to zero. Both, the total kinetic energy and the modulus of total gravitational energy of the universe are estimated to 3/10 of its total rest energy Mc 2 .

Hydrodynamics and Thermodynamics of Newtonian Stars

We investigated spherically symmetric solution for nonrelativistic cosmological fluid equations and thermodynamic equation of state for Newtonian stars. It was shown that the assumption of a polytropic equation, , at the center of the star only suffices to integrate the equations explicitly. Our exact solution yields many fruitful results such as stellar stability, spherical oscillation and collapses of stars. Pressure, temperature, and density profiles inside stars were obtained. Central densities, pressures and temperatures of the Newtonian stars such as Sun, Jupiter and Saturn were also calculated. Collapse and expansion mechanism was explained by the heat transfer mechanism inside star. The upper bound value of white dwarf mass obtained by the Newtonian cosmological fluid equations turns out to be comparable to the static limit of Chandrasekhar one. Motion of the Universe was also discussed within the framework of Newtonian mechanics. Our calculation results without considering nuclear reactions inside stars may be applicable to the formation of protostars.

Gravitational instability of finite isothermal spheres in general relativity. Analogy with neutron stars

We investigate the effects of relativity on the gravitational instability of finite isothermal gaseous spheres. In the first part of the paper, we treat the gravitational field within the framework of Newtonian mechanics but we allow the speed of the particles to be close to the velocity of light so that special relativity must be taken into account. In the second part of the paper, we study the full general relativistic problem for a gas described by an equation of state such that the pressure is proportional to the energy density (“isothermal” distribution). For , this equation of state describes the core of neutron stars. The mass-density diagram displays some damped oscillations and there exists a critical value of mass-energy above which no equilibrium state is possible. We show analytically that the mass peaks are associated with new modes of instability. These results are strikingly similar to those obtained by Antonov (1962) and Lynden-Bell & Wood (1968) for a classical isothermal gas. Our study completes the analogy between isothermal spheres and neutron stars investigated by Yabushita (1974).

Classical decay of Coulomb charges.

In this paper we postulate and solve the following problem: Prove in the framework of Newtonian mechanics that three Coulomb charges (-1,Q,Q) for Q>4 will leave any initial volume in a finite time and estimate this time. We also discuss possible generalizations of the problem and its relation to stability of ions and molecules.

NEWTONIAN SUPERTASKS: A CRITICAL ANALYSIS

In two recent papers Perez Laraudogoitia has described a variety of supertasks involving elastic collisions in Newtonian systems containing a denumerably infinite set of particles. He maintains that these various supertasks give examples of systems in which energy is not conserved, particles at rest begin to move spontaneously, particles disappear from a system, and particles are created ex nihilo. An analysis of these supertasks suggests that they involve systems that do not satisfy the mathematical conditions required of Newtonian systems at the time the supertask is due to be completed, or else they rely on the application of the time-reversal transformation to states which are not well-defined. Consequently, it is unjustified to conclude that the paradoxical results are arising from within the framework of Newtonian mechanics. In the last part of this article, we discuss various aspects of the physics of these supertasks.

Rigorous Newtonian cosmology

It is generally believed that it is not possible to rigorously analyze a homogeneous and isotropic cosmological model in Newtonian mechanics. I show on the contrary that if Newtonian gravity theory is rewritten in geometrical language in the manner outlined in 1923–1924 by Élie Cartan [Ann. Ecole Norm. Sup. 40, 325–412 (1923); 41, 1–25 (1924)], then Newtonian cosmology is as rigorous as Friedmann cosmology. In particular, I show that the equation of geodesic deviation in Newtonian cosmology is exactly the same as equation of geodesic deviation in the Friedmann universe, and that this equation can be integrated to yield a constraint equation formally identical to the Friedmann equation. However, Newtonian cosmology is more general than Friedmann cosmology: Ever-expanding and recollapsing universes are allowed in any noncompact homogeneous and isotropic spatial topology. I shall give a brief history of attempts to do cosmology in the framework of Newtonian mechanics.

Computer simulation of a two-dimensional ideal gas: a simple molecular dynamics method for teaching purposes

A simple two-dimensional model of an ideal gas is described in order to study the time evolution of speed distribution in the framework of Newtonian mechanics. The results of a computer simulation of a system of 16 particles are shown. The approach to equilibrium is followed by observing changes in the experimentally obtained values of Boltzmann's H. An example of a possible way to use this simulation program in an introductory physics course is also given.

Orbital perturbations of a gravitationally bound two-body system with the passage of gravitational waves

view Abstract Citations References (1) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Perturbation of a satellite orbit by gravitational waves Kosbow, Michael ; Blome, Hans-Joachim Abstract The interaction of a weak monochromatic gravitational wave with a circular orbit of a satellite is studied. The Earth-spacecraft system (ME > > msat) is described within the framework of Newtonian mechanics. In our paper we elaborate some specific applications. The equations of motion are solved for the case of resonance and synchronism between the wave and the orbital frequency for first order perturbations. The case of synchronism leads to the strongest effect. If a satellite is used for detection of gravitational waves, a drag-free system should be considered to detach the detector from disturbances present in the Earth orbit. The oscillations which are caused by gravitational waves from binary systems will be calculated for ideal conditions. The range of detectable gravitational waves (approximately 10^-5 to 10^-4 Hz) depend on the orbit radius. Close binary systems like 44 iBoo should be considered for these form of detection due to necessary observation time of 10^7 sec and amplitude of 10^-7 mm. This method - to use a Earth-artificial satellite orbit as a gravitational wave detector - fits between the methods using pulsar timing observations (approximately 10^-8 to 10^-6 Hz) and Doppler tracking of interplanetary spacecraft (approximately 10^-5 to $10^-2 Hz). Publication: 55th International Astronautical Congress 2004 Pub Date: October 2004 DOI: 10.1086/159785 Bibcode: 2004iac..conf.2083K Keywords: gravitational waves; Binary systems full text sources Publisher |

Integral inequalities in the dynamics of a gravitating gas

In the framework of Newtonian mechanics, a study is made of the spherically symmetric problem of the adiabatic motion of a gravitating perfect gas in the presence of a shock wave produced by inhomogeneous gravitational collapse or a point explosion. The method of Golubyatnikov [1, 2] is used to construct a system of integro—differential inequalities that determine, in particular, the law of motion of the shock wave if the initial state of the gas is known. The investigated examples include some self-similar and nearly self-similar solutions to the problem of the gravitational contraction of dust with the formation of a strong shock wave, possibly with the release of energy; the self-similar problem of a point explosion in a gas at rest; and also the problem of the equilibrium of a gas sphere for γ=4/3 and arbitrary distribution of the entropy. In these cases, the inequalities reduce to algebraic relations and can be solved numerically.