Particle Of Finite Mass Research Articles

An Investigation into the Behavior of Non-Isodense Particles in Chaotic Thermovibrational Flow

The ability to control the distribution of particles in a fluid is generally regarded as a factor of great importance in a variety of fields (manufacturing processes, biomedical applications, materials engineering and various particle separation processes, to cite a few). The present study considers the hitherto not yet addressed situation in which solid spherical particles are dispersed in a non-isothermal fluid undergoing turbulent vibrationally-induced convection (chaotic thermovibrational flow in a square cavity due to vibrations perpendicular to the imposed temperature difference). Although the possibility to use laminar thermovibrational flows (in microgravity) and turbulent flows of various types (in normal gravity conditions) to induce the accumulation of solid mass dispersed in a non-isodense fluid is already known, the interplay of finite-size finite-mass particles with chaotic flow in weightlessness conditions has never been considered. In the present study this subject is tackled through direct numerical solution of the fluid and particle tracking equations in the framework of a one-way coupling approach. Results are presented for relatively wide ranges of vibrational amplitude, particle size and density.

Damping of gravitational waves by matter

We develop a unified description, via the Boltzmann equation, of damping of gravitational waves by matter, incorporating collisions. We identify two physically distinct damping mechanisms -- collisional and Landau damping. We first consider damping in flat spacetime, and then generalize the results to allow for cosmological expansion. In the first regime, maximal collisional damping of a gravitational wave, independent of the details of the collisions in the matter is, as we show, significant only when its wavelength is comparable to the size of the horizon. Thus damping by intergalactic or interstellar matter for all but primordial gravitational radiation can be neglected. Although collisions in matter lead to a shear viscosity, they also act to erase anisotropic stresses, thus suppressing the damping of gravitational waves. Damping of primordial gravitational waves remains possible. We generalize Weinberg's calculation of gravitational wave damping, now including collisions and particles of finite mass, and interpret the collisionless limit in terms of Landau damping. While Landau damping of gravitational waves cannot occur in flat spacetime, the expansion of the universe allows such damping by spreading the frequency of a gravitational wave of given wavevector.

Towards a unified lattice kinetic scheme for relativistic hydrodynamics.

We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultrarelativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Jüttner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard tests and solvers in relativistic fluid dynamics such as Boltzmann approach multiparton scattering and previous relativistic lattice Boltzmann models. This work provides a significant step towards the formulation of a unified relativistic lattice kinetic scheme, covering both massive and near-massless particles regimes.

Dynamical mass reduction in the massive Yang-Mills spectrum in1+1dimensions

The (1+1)-dimensional SU}(N) Yang-Mills Lagrangian, with bare mass M, and gauge coupling e, naively describes gluons of mass M. In fact, renormalization forces M to infinity. The system is in a confined phase, instead of a Higgs phase. The spectrum of this diverging-bare-mass theory contains particles of finite mass. There are an infinite number of physical particles, which are confined hadron-like bound states of fundamental colored excitations. These particles transform under irreducible representations of the global subgroup of the explicitly-broken gauge symmetry. The fundamental excitations are those of the SU(N) X SU(N) principal chiral sigma model, with coupling e/M. We find the masses of meson-like bound states of two elementary excitations. This is done using the exact S matrix of the sigma model. We point out that the color-singlet spectrum coincides with that of the weakly-coupled anisotropic SU(N) gauge theory in 2+1 dimensions. We also briefly comment on how the spectrum behaves in the 't Hooft limit, with N approaching infinity.

Phase Space Reduction of the One-Dimensional Fokker-Planck (Kramers) Equation

A pointlike particle of finite mass m, moving in a one-dimensional viscous environment and biased by a spatially dependent force, is considered. We present a rigorous mapping of the Fokker-Planck equation, which determines evolution of the particle density in phase space, onto the spatial coordinate x. The result is the Smoluchowski equation, valid in the overdamped limit, m->0, with a series of corrections expanded in powers of m. They are determined unambiguously within the recurrence mapping procedure. The method and the results are interpreted on the simplest model with no field and on the damped harmonic oscillator.

Inertial Lévy Flight with Nonlinear Friction

Lévy flight with nonlinear friction is studied. Due to the occurrence of extremely long jumps Lévy flights often possess infinite variance and are physically problematic if describing the dynamics of a particle of finite mass. However, by introducing nonlinear friction, we show that the stochastic process subject to Lévy noise exhibits finite variance, leading to a well-defined kinetic energy. In the force-free field, normal diffusion behavior is observed and the diffusion coefficient decreases with Lévy index μ. Furthermore, we find a kinetic resonance of the particle in the harmonic potential to the external oscillating field in the generally underdamped region and the value of the linear friction γ0 determines whether resonance occurs or not.

A lagrangian scheme for the solution of the optimal mass transfer problem

A lagrangian method to numerically solve the L 2 optimal mass transfer problem is presented. The initial and final density distributions are approximated by finite mass particles having a gaussian kernel. Mass conservation and the Hamilton–Jacobi equation for the potential are identically satisfied by constant mass transport along straight lines. The scheme is described in the context of existing methods to solve the problem and a set of numerical examples including applications to medical imagery are presented.

Visualizing Particle/Flow Structure Interactions in the Small Bronchial Tubes

Particle deposition in the small bronchial tubes (generations six through twelve) is strongly influenced by the vortex-dominated secondary flows that are induced by axial curvature of the tubes. In this paper, we employ particle destination maps in conjunction with two-dimensional, finite-time Lyapunov exponent maps to illustrate how the trajectories of finite-mass particles are influenced by the presence of vortices. We consider two three-generation bronchial tube models: a planar, asymmetric geometry and a non-planar, asymmetric geometry. Our visualizations demonstrate that these techniques, coupled with judiciously seeded particle trajectories, are effective tools for studying particle/flow structure interactions.

Natural cutoff in Lévy flights caused by dissipative nonlinearity

Lévy flight models are often used to describe stochastic processes in complex systems. However, due to the occurrence of diverging position and/or velocity fluctuations Lévy flights are physically problematic if describing the dynamics of a particle of finite mass. Here we show that the velocity distribution of a random walker subject to Lévy noise can be regularized by nonlinear friction, leading to a natural cutoff in the velocity distribution and finite velocity variance.

Spatio-temporal history of decay

The decay process of a metastable excited state is studied in this Letter. We have modeled the system as a particle of finite mass coupled to a continuum of excitations and it is found that the excitations move instantaneously in space. We discuss our observations in connection with Fermi's two atom problem and Hegerfeldt's theorem. Our observations confirm Hegerfeldt's theorem for an exactly solvable and experimentally realizable model.

Binary collision model for quantum brownian motion

A binary collision model for phenomena of quantum dissipation is developed. Unlike the harmonic oscillator model, widely used for over thirty years, this model assumes nonlinear coupling between system and environment, and is applicable to both bosonic and fermionic baths. The system interacts with an ideal bath through binary collisions only. Solutions for the classical and quantum-mechanical problems in the case of free Brownian motion are presented, and the quantum-classical correspondence for nonequilibrium processes is established. It is shown that in the Brownian motion limit the two models lead to identical dynamical behavior, provided the coupling coefficients in the harmonic oscillator Hamiltonian are temperature dependent. For cases of bath particles of finite mass and number the two models lead to different results. Linear response theory for the model is developed, and the results are compared with those for the harmonic oscillator model. At the end, possible applications of the model are suggested.

Geodesics of bounded particles around a Kerr black hole

This paper reports on the physical properties of the geodesics followed by a particle of finite mass around a Kerr black hole (BH). Using numerical methods, the criteria for the existence of two kinds of particle in orbit is obtained. Example of trajectories for different constants of motion are given.

Theory of the Growth Resistance of Atomically Rough Surfaces of 4He Crystals

Two puzzling features of the growth resistance of atomically rough 4He crystals are explained by a theory in which rotons collide with “kinks” on the surface. The two kinds of kinks on each step or terrace form one-dimensional gases of particles of finite mass. Good agreement with experiment is obtained if the kinks have roughly the atomic mass and Boltzmann statistics.

R�S 3 special theory of relativity

A theory of relativity, along with its appropriate group of Lorentz-type transformations, is presented. The theory is developed on a metric withR×S3 topology as compared to ordinary relativity defined on the familiar Minkowskian metric. The proposed theory is neither the ordinary special theory of relativity (since it deals with noninertial coordinate systems) nor the general theory of relativity (since it is not a dynamical theory of gravitation). The theory predicts, among other things, that finite-mass particles in nature have maximum rotational velocities, a prediction highly supported by recent experiments on 14 nuclei, such as159Yb that survives fission with angular velocities of up to 0.9 of the predicted value but does not reach it.

The close-coupling equations for three-particle Coulomb system with finite masses

In scattering processes with three charged finite mass particles the close-coupling approximation equations are derived separating the angular part and transforming the exchange terms to the form without derivatives. General expressions are obtained to compute the potentials and exchange kernels between any bound two-particle Coulomb states at any masses, charges and total angular momentum.

Comment on "Failure of the connected-kernel method"

In a recent paper by Komarov et al., the claim is made that the coupled Faddeev-type equations for a system of two noninteracting particles in a fixed potential do not have a unique solution. It is shown here that the claim is not justified. Moreover, it is shown that the phenomenon on which the claim is based occurs even in a true three-body system of three finite-mass particles. Therefore, the property is not, as has been asserted, a consequence of the total Hamiltonian being the sum of commuting sub-Hamiltonians.

Fixed past and uncertain future: A single-time covariant quantum particle mechanics

A covariant quantum mechanics for systems of finite-mass particles at finite energy follows from interpreting as Wick-Yukawa fluctuations in particle number the quantum fluctuations which are needed by Phipps to understand measurement theory and by Gyftopoulos to understand the second law of thermodynamics. The dynamical one-variable equations require as input the (N − 1)-particle transition matrices and an N-N vertex or coupling constants at three-particle vertices.

Stimulated Emission from Nuclei

The feasibility of obtaining stimulated emission of both zero and finite mass particles from nuclei is considered, and the limitations imposed on the relevant nuclear parameters determined.

Optical Potential for Scattering from a System of Finite-Mass Particles

We consider a projectile scattering elastically from a system of finite-mass constituents via a separable microscopic interaction. In order to reduce the situation to a solvable problem, several standard assumptions are necessary. The validity of these assumptions can be checked in a given model problem. The optical potential is identified by comparing the multiple scattering series we obtain with that obtained in the equivalent one-body problem. The optical potential explicitly exhibits the effects of the Fermi motion and finite mass of the target particles and is a generalization of an optical potential obtained earlier. Our results are in a form suitable for application to intermediate energy projectile many-body target scattering.

On the Poincaré noninvariance of a recent alternative to the Dirac equation

Explicit construction of the infinitesimal generators of the Poincare group, demonstrating that the algebra of commutators closes only for the case of zero mass. Hence, the so-called Stigma equation proposed by Biedenharn et al. (1971) as an alternative to the Dirac equation (1928) for spin one-half, finite mass particles is not Poincare invariant except when the leptonic mass is zero.