Description Of Particle Motion Research Articles

Development of the quantum theory of T-odd asymmetries for prescission and evaporated third particles in ternary nuclear fission induced by cold polarized neutrons

A comparative analysis of the results obtained by experimentally and theoretically studying T-odd asymmetries for various third particles in the true and delayed ternary nuclear fission induced by cold polarized neutrons was performed. It was confirmed that the appearance of these asymmetries was associated with the effect of rotation of a polarized system undergoing fission on the angular distributions of prescission and evaporated third particles with respect to the direction along which the emerging fission fragments flew apart, this effect being determined by the Coriolis interaction of the rotational and the internalmotion of the fissioning system. A quantum-mechanical description of particle motion in a rotating coordinate system was generalized to the case where gamma-ray emission was present. It was shown that the separation of the motions of an axially symmetric fissile system into a rotational and an internal motion was valid in the external region as well, where ternary-fission products had already been formed, if it was considered that the motion of fission fragments was tightly connected with the system symmetry axis, which rotated in the laboratory frame. It was found that the dependence of the fissile-system moment of inertia appearing in the Coriolis interaction Hamiltonian on the distance between the fission fragments flying apart generated an additional phase in the amplitude of the radial distribution of fission fragments. It was shown that this phase might change sizably the contribution of the interference between fission amplitudes of neutron resonances excited in a fissile compound nucleus to the absolute values of T -odd asymmetries, especially for third particles such as neutrons and photons, which interacted only slightly with fission fragments.

Active teaching of diffusion through history of science, computer animation and role playing

We developed and tested a lesson plan for active teaching of diffusion in secondary schools (grades 10–13), which stimulates understanding of the thermal (Brownian) motion of particles as the principle underlying diffusion. During the lesson, students actively explore the Brownian motion through microscope observations of irregularly moving small particles, a computer animation showing events at the molecular level and a role play simulating diffusion. The lesson plan follows the history of scientific discoveries, from Robert Brown's description of particle motion to Albert Einstein's explanation of the phenomenon at the molecular level. Students are encouraged to learn towards conceptual change and to critically evaluate scientific models. Both secondary school teachers and students perceived the lesson as interesting and easy to understand. The lesson plan was developed through a universityschool partnership project.

Fractional advection‐dispersion equations for modeling transport at the Earth surface

Characterizing the collective behavior of particle transport on the Earth surface is a key ingredient in describing landscape evolution. We seek equations that capture essential features of transport of an ensemble of particles on hillslopes, valleys, river channels, or river networks, such as mass conservation, superdiffusive spreading in flow fields with large velocity variation, or retardation due to particle trapping. Development of stochastic partial differential equations such as the advection‐dispersion equation (ADE) begins with assumptions about the random behavior of a single particle: possible velocities it may experience in a flow field and the length of time it may be immobilized. When assumptions underlying the ADE are relaxed, a fractional ADE (fADE) can arise, with a non‐integer‐order derivative on time or space terms. Fractional ADEs are nonlocal; they describe transport affected by hydraulic conditions at a distance. Space fractional ADEs arise when velocity variations are heavy tailed and describe particle motion that accounts for variation in the flow field over the entire system. Time fractional ADEs arise as a result of power law particle residence time distributions and describe particle motion with memory in time. Here we present a phenomenological discussion of how particle transport behavior may be parsimoniously described by a fADE, consistent with evidence of superdiffusive and subdiffusive behavior in natural and experimental systems.

Newton equation for canonical, Lie-algebraic, and quadratic deformation of classical space

The Newton equation describing particle motion in a constant external field force on canonical, Lie-algebraic, and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of the particle is generated. We also indicate that in the case of spatial coordinates commuting in a Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces.

A Lévy flight for light

A random walk is a stochastic process in which particles or waves travel along random trajectories. The first application of a random walk was in the description of particle motion in a fluid (brownian motion); now it is a central concept in statistical physics, describing transport phenomena such as heat, sound and light diffusion. Lévy flights are a particular class of generalized random walk in which the step lengths during the walk are described by a 'heavy-tailed' probability distribution. They can describe all stochastic processes that are scale invariant. Lévy flights have accordingly turned out to be applicable to a diverse range of fields, describing animal foraging patterns, the distribution of human travel and even some aspects of earthquake behaviour. Transport based on Lévy flights has been extensively studied numerically, but experimental work has been limited and, to date, it has not seemed possible to observe and study Lévy transport in actual materials. For example, experimental work on heat, sound, and light diffusion is generally limited to normal, brownian, diffusion. Here we show that it is possible to engineer an optical material in which light waves perform a Lévy flight. The key parameters that determine the transport behaviour can be easily tuned, making this an ideal experimental system in which to study Lévy flights in a controlled way. The development of a material in which the diffusive transport of light is governed by Lévy statistics might even permit the development of new optical functionalities that go beyond normal light diffusion.

Slowly varying envelope kinetic simulations of pulse amplification by Raman backscattering

A numerical code based on an eikonal formalism has been developed to simulate laser-plasma interactions, specifically Raman backscatter (RBS). In this code, the dominant laser modes are described by their wave envelopes, avoiding the need to resolve the laser frequency; appropriately time-averaged equations describe particle motion. The code is fully kinetic, and thus includes critical physics such as particle trapping and Landau damping which are beyond the scope of the commonly used fluid three-wave equations. The dominant forces on the particles are included: the ponderomotive force resulting from the beat wave of the forward and backscattered laser fields and the self-consistent plasma electric field. The code agrees well, in the appropriate regimes, with the results from three-wave equations and particle-in-cell simulations. The effects of plasma temperature on RBS amplification are studied. It is found that increasing the plasma temperature results in modification to particle trapping and the saturation of RBS, even before the onset of Landau damping of the plasma wave. This results in a reduction in the coupling efficiency compared to predictions based on the three-wave equations.

Catalytic Wheel as a Brownian Motor

A system is considered in which transitions between two states occur through two reaction channels. Because of coupling with an external process which consists of cyclic switching between two regimes (each characterized by a certain fixed set of rate constants), the net circulation flux arises in the system even in the absence of an external generalized force. Such a mechanism underlying a catalytic wheel of many biological processes is considered as a Brownian motor. The basic operational motor characteristics are calculated for the regular and random inter-regime switching, being better in the former case and reaching the optimum at equal relaxation-to-lifetime ratios for the two regimes. The general Brownian motor formalism is exemplified by two particular realizations, the electroconformational-coupling model and the flashing-potential model. The former concerns enzymatically catalyzed ligand pumping through a membrane, and the latter describes particle motion under two sets of potential wells and barriers. Because of a unified thread between the two models, their parameters are interrelated, and all of the relevant conclusions are valid for either of them. In the tight coupling limit, the optimal conditions are analyzed, and they imply that a catalytic wheel operated by the Brownian motor works with the maximum output energy (useful work) or with the maximum efficiency tending to unity under certain conditions.

Particle path correlations in a phonon bath

The path integral formalism is applied to derive the full partition function of ageneralized Su–Schrieffer–Heeger Hamiltonian describing particle motion in a bathof oscillators. The electronic correlations are computed versus temperature forsome choices of oscillator energies. We study the perturbing effect of atime-averaged particle path on the phonon subsystem, deriving the relevanttemperature-dependent cumulant corrections to the harmonic partition functionand free energy. The method has been applied to compute the total heat capacityup to room temperature: a low temperature upturn in the heat capacityover temperature ratio points to a glassy-like behaviour ascribable to atime-dependent electronic hopping with variable range in the linear chain.

A new look at the derivation of the Schrödinger equation from Newtonian mechanics

We present a modified version of Nelson's seminal paper on the derivation of the time-dependent Schrodinger equation which draws on the equation of motion of a particle that moves under the influence of a classical force field and additional stochastic forces. The emphasis of our elaboration is focused on the implication of allowing stochastic forces to occur, viz. that the energy E of the particle is no longer conserved on its trajectory in a conservative force field. We correlate this departure Δ E from its classical energy with the energy/time uncertainty relation where Δ t is the average time for Δ E to persist. The stability of atoms, the zero-point energy of oscillators, the tunneling effect and the diffraction at slits are shown to be directly connected with the occurrence of such energy fluctuations. We discuss and rederive Nelson's theory entirely from this point of view and generalize his approach to systems of N particles which interact via pair forces. Achieving reversibility in a description of particle motion that is akin to Brownian motion, represents a salient point of the derivation. We demonstrate that certain objections raised against Nelson's theory are without substance. We also try to put the particular worldview of this version of stochastic quantum mechanics into perspective with regard to the established Copenhagen interpretation.

A new look at the derivation of the Schrödinger equation from Newtonian mechanics

AbstractWe present a modified version of Nelson's seminal paper on the derivation of the time‐dependent Schrödinger equation which draws on the equation of motion of a particle that moves under the influence of a classical force field and additional stochastic forces. The emphasis of our elaboration is focused on the implication of allowing stochastic forces to occur, viz. that the energy E of the particle is no longer conserved on its trajectory in a conservative force field. We correlate this departure Δ E from its classical energy with the energy/time uncertainty relation where Δ t is the average time for Δ E to persist. The stability of atoms, the zero‐point energy of oscillators, the tunneling effect and the diffraction at slits are shown to be directly connected with the occurrence of such energy fluctuations. We discuss and rederive Nelson's theory entirely from this point of view and generalize his approach to systems of N particles which interact via pair forces. Achieving reversibility in a description of particle motion that is akin to Brownian motion, represents a salient point of the derivation. We demonstrate that certain objections raised against Nelson's theory are without substance. We also try to put the particular worldview of this version of stochastic quantum mechanics into perspective with regard to the established Copenhagen interpretation.

Limitations due to the spontaneous emission of low-frequency photons on the applicability of the Newtonian description of particle motion in a gas

It is shown that the spontaneous emission of low-frequency photons in collision of atoms and molecules in a gas is very rapidly, in several free-transit intervals, radically changes the trajectories and the order of the collisions of the particles as compared with the predictions of the equations of classical mechanics.

Kinetic theory of plasma adiabatic major radius compression in tokamaks

In order to understand the individual charged particle behavior as well as plasma macroparameters (temperature, density, etc.) during the adiabatic major radius compression (R-compression) in a tokamak, a kinetic approach is used. The perpendicular electric field from the Ohm’s law at zero resistivity is made use of in order to describe particle motion during the R-compression. Expressions for both passing and trapped particle energy and pitch angle change are derived for a plasma with high aspect ratio and circular magnetic surfaces. The particle behavior near the passing trapped boundary during the compression is studied to simulate the compression-induced collisional losses of alpha particles. Qualitative agreement is obtained with the alphas loss measurements in deuterium-tritium (D-T) experiments in the Tokamak Fusion Test Reactor (TFTR) [World Survey of Activities in Controlled Fusion Research [Nucl. Fusion special supplement (1991)] (International Atomic Energy Agency, Vienna, 1991)]. The plasma macroparameters evolution at the R-compression is calculated by solving the gyroaveraged drift kinetic equation.

Hamiltonian formalism for space charge dominated beams in a uniform focusing channel.

We employ the Kapchinskij-Vladimirskij envelope Hamiltonian [I. M. Kapchinskij and V. V. Vladimirskij, in 2 The Proceedings of the 9th International Conference on High Energy Accelerators, edited by L. Kowarski (CERN, Geneva, 1959), p. 274] to describe the envelope evolution and the particle Hamiltonian to describe particle motion in a space charge dominated beam. Properties of the envelope function in a mismatched uniform focusing channel are studied. Parametric resonances of the particle Hamiltonian due to envelope oscillations of a mismatched beam are studied. We find that the Hamiltonian dynamics depends only on a single effective space charge parameter, the ratio of the space charge perveance to the focusing strength. The onset of global chaos exhibits a first order phase-transition-like behavior when the amplitude of envelope oscillations for a mismatched beam is larger than a critical value. This global chaos can greatly enhance the halo formation. The relation between the critical envelope mismatch for the halo formation and the effective space charge parameter is numerically obtained. Possible experiments are suggested.

Airway Surface Irregularities Promote Particle Diffusion in the Human Lung

Current NCRP and ICRP particle deposition models employed in risk assessment analyses treat the airways of the human lung as smooth-walled tubes. However, the upper airways of the tracheobronchial (TB) tree are lined with cartilaginous rings. Recent supercomputer simulations of in vivo conditions (cited herein), where cartilaginous ring morphologies were based upon fibre-optic bronchscope examinations, have clearly demonstrated their profound effects upon fluid dynamics. Since inhaled radionuclides of health effects concern such as randon progeny are entrained and transported by airstreams, their trajectories and deposition probabilities will be influenced by the character (i.e. laminar or turbulent) of air motion and its loca velocity profiles. A physiologically based analytical model of fluid dynamics is presented, focusing upon applications to particle diffusion within the TB tree. The new model is the first to describe particle motion while simulaneously simulating effects of wall irregularities, entrace conditions and tube curvatures. The results show that particle dose to the large bronchi may be underestimated by up to 35% if cartilaginous rings are not considered. The work has fundamental implications for modelling concepts and health effects applications. The findings indicate that caution must be exercised when extrapolating heat and/or mass transfer correlations derived from standard thermodynamic-hydrodynamic engineering problems to biological issues, and that human subject activity levels have pronounced effects on particle diffusion in the lung. For instance, the submicron particle deposition efficiency differences between a sedentary condition (i.e. office worker) and light activity (i.e. manual labourer) approach 40%. This study may explain the enhanced deposition by particle diffusion detected in replica case experiments and have salient implications for the clinically observed preferential distributions of bronchogenic carcinomas associated with inhaled radionuclides

Particle dynamics in chirped-frequency fluctations.

Hamiltonian systems describing particle motion in a wave with time-dependent (chirped) frequency are studied. The wave is found to form a single-node separatrix (bucket) moving in the phase space at a rate proportional to that of the frequency change. Particles trapped inside the bucket undergo convection, while untrapped particles colliding with the bucket get a resonant kick, in phase space. In toroidal systems, these effects can result in a large radial convective flux roughly proportional to the size of the bucket and the frequency chirping. Possible applications of this novel mechanism to tokamak plasmas are discussed.

PHASE-SPACE DIFFUSION EQUATIONS FOR SINGLE BROWNIAN PARTICLE MOTION NEAR SURFACES

In numerous physical processes involving the motion of micron and submicron sized particles near surfaces, such as the filtration of hydrosols and aerosols, the particle motion is the net result of the combined effects of fluid convection, external forces, particle inertia, Brownian particle motion, and particle-surface fluid dynamic interactions. The most general method of describing particle motion under the combined action of these effects is through the so-called Fokker-Planck equation. In the absence of particle-surface fluid dynamic interactions, the Fokker-Planck equation is well-known, and it has been applied in a general way to problems involving the adsorption or deposition of Brownian particles onto surfaces through a solution technique known as the Brownian dynamics simulation method. In this study, the Fokker-Planck equation for Brownian particle motion near surfaces is generalized to include particle-surface fluid dynamic interactions. The Fokker-Planck equation is shown to follow from the L...

Neutral line chaos and phase space structure

Numerical surface of section techniques and analytic methods are used to study phase space structure and chaos near a neutral line. We find that, for −(2h)1/2 ≤ Py ≤ (2h)1/2, the ratio of fields, bn, rather than κ, is the appropriate chaos parameter, where Py and h are the normalized canonical momentum and energy. We find that the action integral adiabatic constant is approximately conserved and can be used to describe particle motion as long as bn ≪ 1 or bn ≫ 1.

Test Particle Calculations for the Texas Experimental Tokamak with Resonant Magnetic Fields

A simple test particle model that attempts to describe particle motion in the presence of intrinsic electrostatic fluctuations in a prescribed tokamak magnetic field is presented. In particular, magnetic field configurations that include externally produced magnetic islands and stochastic regions are considered. The resulting test particle transport is compared with the predictions of analytic models and with the experimentally measured electron heat and particle transport on the Texas Experimental Tokamak (TEXT). Agreement between the test particle results and applicable analytic theories is found. However, there is only partial agreement with the experimental results, and possible reasons for the discrepancies are explored. Good agreement is found between predicted and measured spatially asymmetric particle distributions. The particle collection efficiency of an apertured limiter inside a magnetic island (an intra-island pump limiter) is discussed.

A model for bubble-induced erosion in fluidized-bed combustors and comparison with experiment

A simple model is developed for the erosion of surfaces in a fluidized-bed combustor as a result of particle motion induced by bubbles. Davidson's bubble model, used to describe particle motion in a fluidized bed, and Finnie's erosion model, which describes erosion due to the particle motion, are combined to give an expression for the erosion of a surface by the passage of a bubble. This erosion model predicts a strong dependence on bubble size and the distance between the bubble and the eroding surface: erosion increases for larger bubbles and smaller distances. The model is compared with two experimental studies, and agreement of better than an order of magnitude is obtained.

Channeling and the periodic Lorentz gas

Properties of the periodic Lorentz gas, which describes particle motion in a lattice of hard spheres, are related to experiments on channeling in crystals. Extensive theoretical knowledge of the Lorentz gas can be applied to make predictions about diffusion and radiation in channeling experiments.