Presence Of Dissipative Forces Research Articles

Quantization in relativistic classical mechanics: the Stückelberg equation, neutrino oscillation and large-scale structure of the Universe

Based on the Chetaev theorem on stable dynamical trajectories in the presence of dissipative forces, we obtain the generalized condition for stability of relativistic classical Hamiltonian systems (with an invariant evolution parameter) in the form of the Stückelberg equation. As is known, this equation is the basis of a competing paradigm known as parametrized relativistic quantum mechanics (pRQM).It is shown that the energy of dissipative forces, which generate the Chetaev generalized condition of stability, coincides exactly with Bohmian relativistic quantum potential. Within the framework of Bohmian RQM supplemented by the generalized Chetaev theorem and on the basis of the principle of least action for dissipative forces, we show that the squared amplitude of a wave function in the Stückelberg equation is equivalent to the probability density function for the number of particle trajectories, relative to which the velocity and the position of the particle are not hidden parameters.The conditions for reasonableness of trajectory interpretation of pRQM are discussed. Based on analysis of a general formalism for vacuum-flavor mixing of neutrino within the context of the standard and pRQM models we show that the corresponding expressions for the probability of transition from one neutrino flavour to another differ appreciably, but they are experimentally testable: the estimations of absolute value for neutrino mass based on modern experimental data for solar and atmospheric neutrinos show that the pRQM results have a preference. It is noted that the selection criterion of mass solutions relies on proximity between the average size of condensed neutrino clouds, which is described by the Muraki formula (29th ICRC, 2005) and depends on the neutrino mass, and the average size of typical observed void structure (dark matter + hydrogen gas), which plays the role of characteristic dimension of large-scale structure of the Universe.

Quantization in classical mechanics and its relation to the Bohmian Ψ-field

Based on the Chetaev theorem on stable dynamical trajectories in the presence of dissipative forces, we obtain the generalized condition for stability of Hamilton systems in the form of the Schrödinger equation. It is shown that the energy of dissipative forces, which generate the Chetaev generalized condition of stability, coincides exactly with the Bohm “quantum” potential. Within the frame-work of Bohmian quantum mechanics supplemented by the generalized Chetaev theorem and on the basis of the principle of least action for dissipative forces, we show that the squared amplitude of a wave function in the Schrödinger equation is equivalent semantically and syntactically to the probability density function for the number of particle trajectories, relative to which the velocity and the position of the particle are not hidden parameters. The conditions for the correctness of trajectory interpretation of quantum mechanics are discussed.

Charmonium suppression in the presence of dissipative forces in a strongly-coupled quark–gluon plasma

We study the survival of charmonium states in a strongly-coupled quark–gluon plasma in the presence of dissipative forces. We consider first-order dissipative corrections to the plasma equation of motion in the Bjorken boost-invariant expansion with a strongly-coupled equation of state for QGP and study the survival of these states with the dissociation temperatures obtained by correcting the full Cornell potential not its Coulomb part alone with a dielectric function encoding the effects of deconfined medium. We further explore the sensitivity of prompt and sequential suppression of these states to the shear viscosity-to-entropy density ratio, η/s from perturbative QCD and AdS/CFT predictions. Our results show nice agreement with the recent experimental results at RHIC.

The stability and stabilization of non-linear, non-stationary mechanical systems

Mechanical systems acted upon by extremely non-linear positional forces are considered. The decomposition method is used to determine the sufficient conditions for asymptotic stability of an equilibrium. Problems of stabilizing the equilibrium of non-linear, non-stationary systems with specified potential forces by adding forces of different structure are studied. For systems with a non-stationary, homogeneous, positive-definite potential, the possibility of stabilization by linear dissipative forces, uncharacteristic of linear systems, is established. For systems with an even number of coordinates n ≥ 4, in the presence of dissipative forces with complete dissipation, the possibility of vibrational stabilization by adding circular and gyroscopic forces with coefficients fluctuating about zero is demonstrated.

An Energetic Control Methodology for Exploiting the Passive Dynamics of Pneumatically Actuated Hopping

This paper presents an energetically derived control methodology to specify and regulate the oscillatory motion of a pneumatic hopping robot. An ideal lossless pneumatic actuation system with an inertia is shown to represent an oscillator with a stiffness, and hence frequency, related to the equilibrium pressures in the actuator. Following from an analysis of the conservative energy storage elements in the system, a control methodology is derived to sustain a specified frequency of oscillation in the presence of energy dissipation. The basic control strategy is to control the pressure in the upper chamber of the pneumatic cylinder to specify the contact time of the piston, while controlling the total conservative energy stored in the system to specify the flight time and corresponding flight height of the cylinder. The control strategy takes advantage of the natural passive dynamics of the upper chamber to provide much of the required actuation forces and natural stiffness, while the remaining forces needed to overcome the energy dissipation present in a nonideal system with losses are provided by a nonlinear control law for the charging and discharging of the lower chamber of the cylinder. Efficient hopping motion, relative to a traditional nonconservative actuator, is achieved by allowing the energy storing capability of a pneumatic actuator to store and return energy to the system at a controlled specifiable frequency. The control methodology is demonstrated through simulation and experimental results to provide accurate and repeatable hopping motion for pneumatically actuated robots in the presence of dissipative forces.

Analysis of the interaction of inertial forces in a stability problem

Using the plane of characteristic indices we study the stability of an elastic filament with a distributed inertial load moving along it at constant speed. Taking account of the Coriolis inertial forces and assuming the presence of dissipative forces, we carry out a qualitative analysis of the results for different relations among the parameters of the system; this analysis is in agreement with the general stability theorems for elastic structures.

Finite amplitude Alfvén waves in a multi‐ion plasma: Propagation, acceleration, and heating

We derive an expression for the wave action flux of finite amplitude Alfvén waves in a multi‐ion plasma. The expression is valid in the presence of dissipative forces and allows an arbitrary angle between the average magnetic field and the wave vector. Applying the conservation of wave action and the first law of thermodynamics yields the following results for a multi‐ion plasma: (1) an expression for the spatial evolution of Alfvén wave amplitude in the absence of dissipation, (2) the relationship between the wave amplitude and the dissipative heating, and (3) an expression for the acceleration of an ion species by finite amplitude Alfvén waves. The acceleration consists of two terms: a nondissipative wave pressure that is identical to that derived previously under more restrictive conditions, and a new term giving the acceleration that must accompany dissipative heating. These results are discussed in the context of the observations of heavy ions in the solar wind.

Stochastic theory for classical and quantum mechanical systems

We formulate from first principles a theory of stochastic processes in configuration space. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schrodinger equation, which is derived here with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section.

Energy Relations of Atmospheric Tides and Their Significance to Approximate Methods of Solution for Tides with Dissipative Forces

Abstract The concepts of kinetic energy, potential energy and energy flux are clarified and quantified for atmospheric tides. An understanding of the tidal energy relations provides physical insight into the problem of dissipative effects an tidal structure. It is shown that mode coupling effects due to dissipative forces are related to the coupling of kinetic energy between different tidal modes, and the mode-coupling coefficients are computed for several tidal modes. A relation is derived linking energy density and variations of the eigenvalues of Laplace's tidal equation with frequency. A formalism of “analogous atmospheric oscillations” in a plane-parallel, uniformly rotating atmosphere is proposed to provide an approximate method of computing tidal structure in the presence of dissipative forces.

Oscillations of a capillary jet of infinite electrical conductivity in the presence of dissipative forces and a uniform axial magnetic field

The method of normal-mode analysis is applied to study the oscillations of a capillary jet for nonaxisymmetric perturbations in the presence of a uniform axial magnetic field when viscous forces are present. It is assumed that the liquid is infinitely conducting. It is found that the damping constants are smaller than those for the nonviscous case. In particular, the limiting case of high viscosity has been discussed and the damping constant form=1 has been calculated.

On the stability of motion of a horizontal gyrocompass in the presence of dissipative forces

On the stability of motion of a horizontal gyrocompass in the presence of dissipative forces