Total Momentum Conservation Law Research Articles

Effective Interaction Force between an Electric Charge and a Magnetic Dipole and Locality (or Nonlocality) in Quantum Effects of the Aharonov–Bohm TypeSupported partially by the CDCHT (ULA, Mérida, Venezuela).

Classical electrodynamics foresees that the effective interaction force between a moving charge and a magnetic dipole is modified by the time-varying total momentum of the interaction fields. We derive the equations of motion of the particles from the total stress-energy tensor, assuming the validity of Maxwell’s equations and the total momentum conservation law. Applications to the effects of Aharonov–Bohm type show that the observed phase shift may be due to the relative lag between interfering particles caused by the effective local force.

Modeling wavefields in saturated elastic porous media based on thermodynamically compatible system theory for two-phase solid-fluid mixtures

A two-phase model and its application to wavefields numerical simulation are discussed in the context of modeling of compressible fluid flows in elastic porous media. The derivation of the model is based on a theory of thermodynamically compatible systems and on a model of nonlinear elastoplasticity combined with a two-phase compressible fluid flow model. The governing equations of the model include phase mass conservation laws, a total momentum conservation law, an equation for the relative velocities of the phases, an equation for mixture distortion, and a balance equation for porosity. They form a hyperbolic system of conservation equations that satisfy the fundamental laws of thermodynamics. Two types of phase interaction are introduced in the model: phase pressure relaxation to a common value and interfacial friction. Inelastic deformations also can be accounted for by source terms in the equation for distortion. The thus formulated model can be used for studying general compressible fluid flows in a deformable elastoplastic porous medium, and for modeling wave propagation in a saturated porous medium. Governing equations for small-amplitude wave propagation in a uniform porous medium saturated with a single fluid are derived. They form a first-order hyperbolic PDE system written in terms of stress and velocities and, like in Biot’s model, predict three type of waves existing in real fluid-saturated porous media: fast and slow longitudinal waves and shear waves. For the numerical solution of these equations, an efficient numerical method based on a staggered-grid finite difference scheme is used. The results of solving some numerical test problems are presented and discussed.

The accelerated removal of kidney stones by concomitant use of camel thorn distillate and Rowatinex drug: A case report

The coupled magnetic and mechanical motion of a ferromagnetic nanoparticle in a viscous fluid is considered within the dynamical approach. The equation based on the total momentum conservation law is used for the description of the mechanical rotation, while the modified Landau-Lifshitz-Gilbert equation is utilized for the description of the internal magnetic dynamics. The exact expressions for the particles trajectories and the power loss are obtained in the linear approximation. The comparison with the results of other widespread approaches, such as the model of fixed particle and the model of rigid dipole, is performed. It is established that in the small oscillations mode the damping precession of the nanoparticle magnetic moment is the main channel of energy dissipation, but the motion of the nanoparticle easy axis can significantly influence the value of the resulting power loss.

Power loss for a periodically driven ferromagnetic nanoparticle in a viscous fluid: The finite anisotropy aspects

The coupled magnetic and mechanical motion of a ferromagnetic nanoparticle in a viscous fluid is considered within the dynamical approach. The equation based on the total momentum conservation law is used for the description of the mechanical rotation, while the modified Landau-Lifshitz-Gilbert equation is utilized for the description of the internal magnetic dynamics. The exact expressions for the particles trajectories and the power loss are obtained in the linear approximation. The comparison with the results of other widespread approaches, such as the model of fixed particle and the model of rigid dipole, is performed. It is established that in the small oscillations mode the damping precession of the nanoparticle magnetic moment is the main channel of energy dissipation, but the motion of the nanoparticle easy axis can significantly influence the value of the resulting power loss.

A general, rotating, hard sphere model applied to the transport properties of a low density gas.

A general, spherical, rigid model is introduced for describing rotating and translating particles. The model contains a parameter, which we label γ, that smoothly interpolates between the smooth hard sphere (γ = 0) and rough hard sphere (γ = 1) limits. Analytic expressions for transport coefficients are determined for the general model in the low density limit and compared with those for the smooth and rough hard sphere cases. While the diffusion constant decreases monotonically on moving from the smooth to the rough sphere limits, both the viscosity and thermal conductivity first decrease and then increase, thereby producing a minimum between the two limits. This qualitative change in behaviour is new and suggests translational-rotational coupling acts to decrease the values of the transport coefficients (in contrast to the prediction from the rough sphere model). Although the model still has the (known) deficiencies of rigid models, it is more flexible than either the smooth or rough sphere model and should find use in better representing molecular behaviour. The general model provides a consistent representation of the transport coefficients because it has proper, microscopic collision dynamics obeying conservation laws for total momentum, total angular momentum, and total energy.

The semi-classical limit of the Aharonov-Bohm effect: The actualized approach

We suggest an approach, which formally allows us to describe the Aharonov-Bohm (AB) effect in the semi-classical language. In the framework of this approach, we keep the classical concepts of electromagnetic field and force. At the same time, instead of point-like classical charges, we introduce a finite-size elementary charge distribution, modelling the wave-like packet, associated with the motion of a given electron. In this case we derive the force on the wave-like packet on behalf of the solenoid via the minimization of action defined through the Lagrangian density (instead of the Lagrangian used in common classical electrodynamics of point-like charges). We show that this force due to the solenoid, being dependent on the vector potential, yields the common expression for the magnetic AB phase, when the original wave packet is splitted into a superposition of two packets encirling the solenoid. We also analyze in the classical language the implementation of total momentum conservation law for the isolated system “moving electrons plus elongated solenoid” and determine the properties of finite-size charge distribution, when this law is fulfilled. The results obtained are discussed.

Modified shallow water equations which admit the propagation of discontinuous waves over a dry bed

A method for modeling the propagation of discontinuous waves over a dry bed using the first approximation of shallow water theory is proposed. The method is based on a modified conservation law of total momentum that takes into account the concentrated momentum losses due to the formation of local turbulent vortex structures in the fluid surface layer at a discontinuous-wave front. A quantitative estimate of these losses is obtained by deriving the shallow water equations from the Navier-Stokes equations with allowance for viscosity, which has a rapidly increasing effect in the turbulent flow regions described by discontinuous waves. The stability of the discontinuous waves admitted by the modified system of conservation laws of shallow water theory is examined. As an example, a comparative analysis is performed of the solutions of the dam-break problem obtained for the classical and modified shallow water models.

Numerical simulation of discontinuous waves propagating over a dry bed

A numerical algorithm is proposed for simulating the propagation of discontinuous waves over a dry bed governed by the shallow water equations in the first approximation. The algorithm is based on a modified conservation law of total momentum that takes into account the concentrated momentum loss associated with the formation of local eddy structures within the framework of the long-wave approximation. The modified conservation law involves a heuristic parameter that is chosen so as to agree with laboratory experiments. Numerical results are presented for the formation, propagation, and transformation of a discontinuous wave arising in a complete or partial (in the planned case) collapse of a dam over a bed with a horizontal or sloping bottom or a bottom with a local obstacle in the tailwater area.

Dynamics of charge density fluctuations in two-component hydrogen plasma

A systematic study is made of the dynamical properties of the charge density fluctuations in strongly coupled two-component plasmas. The time-correlation function of the partial density fluctuations is described with the use of the memory function formalism. A second-order memory function is approximately expressed in terms of its self-part by taking into account the total momentum conservation law. After assuming a Gaussian time-dependence for the self-part, the excitation spectrum of the charge density fluctuation is calculated for the semi-classical hydrogen plasma, and is in fairly good agreement with the molecular dynamics calculation due to Hansen & McDonald. It is found that the collisional effects play an important role in the strongly coupled system.

Active mass in relativistic gravity - Theoretical interpretation of the Kreuzer experiment

A 1966 experiment performed by Kreuzer set an upper limit of 5 parts in 10/sup 5/ on the difference in the ratio of active to passive mass between fluorine and bromine. (Active mass of a body is the mass that generates gravity, while passive mass is the mass that responds to gravity.) A parametrized post-Newtonian formalism is introduced for the spacetime metric of a system of charged point particles using parameters (..gamma..,..beta.., ..cap alpha../sub 1/, ..cap alpha../sub 2/, ..cap alpha../sub 3/, zeta/sub 1/, zeta/sub 2/, zeta/subW/, epsilon/sub 1/, epsilon/sub 2/, epsilon/sub 3/) whose values vary from gravitation theory to gravitation theory. The prediction of this formalism for the active gravitational masses of fluorine and bromine nuclei is compared with the results of the Kreuzer experiment and place an upper limit on a combination of these PPN parameters. By making a detailed comparison of the point-mass formalism with the standard perfect-fluid PPN formalism, it is shown that for the theories of gravitation whose perfect-fluid equations are blind to the different forms of internal energy and pressure in the fluid, the perfect-fluid PPN parameters must satisfy the constraint zeta/sub 3/+2zeta/sub 4/-..cap alpha../sub 3/-2/3zeta/sub 1/ =0. For such theories it is demonstrated thatmore » the Kreuzer experiment imposes the limit vertical-barzeta/sub 3/vertical-bar<0.06. Any theory of gravity that possesses post-Newtonian integral conservation laws for total momentum automatically agrees with the Kreuzer experiment. (AIP)« less