Total Particle Density Research Articles

Energy distribution of massless particles on black hole backgrounds with generalized uncertainty principle

We derive new formulas for the spectral energy density and total energy density of massless particles in a general spherically symmetric static metric from a generalized uncertainty principle. Compared with blackbody radiation, the spectral energy density is strongly damped at high frequencies. For large values of $r$, the spectral energy density diminishes when $r$ grows, but at the event horizon, the spectral energy density vanishes and therefore thermodynamic quantities near a black hole, calculated via the generalized uncertainty principle, do not require any cutoff parameter. We find that the total energy density can be expressed in terms of Hurwitz zeta functions. It should be noted that at large $r$ (low local temperature), the difference between the total energy density and the Stefan-Boltzmann law is too small to be observed. However, as $r$ approaches an event horizon, the effect of the generalized uncertainty principle becomes more and more important, which may be observable. As examples, the spectral energy densities in the background metric of a Schwarzschild black hole and of a Schwarzschild black hole plus quintessence are discussed. It is interesting to note that the maximum of the distribution shifts to higher frequencies when the quintessence equation of state parameter $w$ decreases.

The effect of dust size distribution on envelope wave packet in magnetized two-temperature-ion dusty plasma

The effect of arbitrary dust size distribution on a nonlinear envelope wave packet in a magnetized two-temperature-ion dusty plasma has been studied in this paper. By using the reductive perturbation method, the dispersion relation and a (3+1)-dimensional nonlinear Schrödinger equation (NLSE) have been obtained. It is found that the frequency, the group velocity, and the propagation behavior of the envelope waves have been significantly influenced by different dust size distributions. It is also found that the frequency increases as the total number density of dust particles increases. Moreover, it seems that the frequency for usual dusty plasma is smaller than that of the unusual case. On the other hand, the modulational instability of envelope waves has also been discussed by analyzing the solution of the NLSE. It is shown that the conditions of modulational instability for envelope waves are different for various cases.

Exhaustion of nucleation in a closed system

We determine the distribution of cluster sizes that emerges from an initial phase of homogeneous aggregation with conserved total particle density. The physical ingredients behind the predictions are essentially classical: Supercritical nuclei are created at the Zeldovich rate, and before the depletion of monomers is significant, the characteristic cluster size is so large that the clusters undergo diffusion-limited growth. Mathematically, the distribution of cluster sizes satisfies an advection partial differential equation (PDE) in "size space." During this creation phase, clusters are nucleated and then grow much larger than the critical size, so nucleation of supercritical clusters at the Zeldovich rate is represented by an effective boundary condition at zero size. The advection PDE subject to the effective boundary condition constitutes a "creation signaling problem" for the evolving distribution of cluster sizes during the creation era. Dominant balance arguments applied to the advection signaling problem show that the characteristic time and cluster size of the creation era are exponentially large in the initial free-energy barrier against nucleation, G*. Specifically, the characteristic time is proportional to e(2/5)G*/kBT} and the characteristic number of monomers in a cluster is proportional to e(3/5)G*/kBT. The exponentially large characteristic time and cluster size give a posteriori validation of the mathematical signaling problem. In a short note, Marchenko [JETP Lett. 64, 66 (1996)] obtained these exponentials and the numerical prefactors 2/5 and 3/5. Our work adds the actual solution of the kinetic model implied by these scalings, and the basis for connection to subsequent stages of the aggregation process after the creation era.

Antiferromagnetic order of strongly interacting fermions in a trap: real-space dynamical mean-field analysis

We apply dynamical mean-field theory to strongly interacting fermions in an inhomogeneous environment. With the help of this real-space dynamical mean-field theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting fermions with spin- in a harmonic potential. Within R-DMFT, antiferromagnetic order is found to be stable in spatial regions with total particle density close to one, but persists also in parts of the system where the local density significantly deviates from half filling. In systems with spin imbalance, we find that antiferromagnetism is gradually suppressed and phase separation emerges beyond a critical value of the spin imbalance.

Evaluation of the Performance of a Three-Phase Fluidized Bed Reactor with Immobilized Yeast Cells for the Biotechnological Production of Xylitol

This work deals with the evaluation of the hydrodynamic characteristics and fermentation parameters of a bench-scale three-phase fluidized bed reactor (FBR) with cells of the yeast Candida guilliermondii immobilized calcium alginate beads for xylitol production. The effects of the following hydrodynamic variables on cell immobilization were evaluated: total particle density, terminal velocity, particles drag force, minimum fluidization velocity and bed porosity (?). According to the results obtained, the reactor was shown to operate similar to a fixed-bed bioreactor at ? < 0.5 and a fluidized bed bioreactor at ? > 0.5, respectively. The maximum flowrate needed to obtain maximum bed fluidization in the reactor was equal to the terminal velocity of the immobilized cell particles. As for the fermentation parameters, the effects of the aeration rate and fermentation time on the process productivity and yield were analyzed. The maximum xylitol concentration of 28.9 g xylitol/l was obtained at a high aeration rate of 600ml/min after 70h of fermentation, indicating that the use of a high aeration rate in this system is favored for better oxygen transfer into the immobilized cells. The specific xylitol productivity and the xylitol yield were of 0.41 g xylitol/l.h and 0.582 g xylitol/g xylose respectively. After 90h of fermentation xylitol productivity and yield decreased to 0.256 g xylitol/l.h and 0.47 g xylitol/g xylose respectively, indicating the beginning of xylitol consumption by the yeast.

Effect of various parameters on the solid circulation rate in a liquid–solid circulating fluidized bed

AbstractA liquid–solid circulating fluidized bed (LSCFB) is operated at high liquid velocity, where particle entrainment is highly significant, and between the conventional liquid fluidized bed and the dilute‐phase liquid transport regimes. In the present work, systematic experiments were carried out in a 0.094 m i.d. and 2.4 m height laboratory‐scale LSCFB apparatus by using various solid particles and tap water as fluidizing medium to study the hydrodynamics. The effects of operating parameters, i.e. primary liquid flow rate in the riser (jf), auxiliary liquid flow rate (ja), total liquid flow rate (jl), particle density (ρs), particle diameter (dp) and solid feed pipe diameter (do) on the solid circulation rate were analyzed from the experimental data. Finally, a correlation was developed from the experimental data to estimate solid velocity (solid circulation rate), and was compared with the present experimental and available data in the literature. They agree well with a maximum root mean‐square (RMS) deviation of 12%. Copyright © 2008 Curtin University of Technology and John Wiley & Sons, Ltd.

Evaluation of hydrodynamic parameters of a fluidized‐bed reactor with immobilized yeast

AbstractThe fluidized bed reactor has successfully been used to perform biotechnological processes addressed to the production of high added value. The present work evaluates hydrodynamic parameters of a bench‐scale fluidized bed reactor with cells of the yeast Candida guilliermondii immobilized either in calcium alginate beads or in polyvinyl alcohol (PVA). The effects of the following variables on cell immobilization were evaluated at 30 °C and feeding a synthetic medium containing 50 g L−1 xylose: total particle density (cells plus support), terminal velocity, particle drag force, minimum fluidization velocity and bed porosity. According to the results obtained, the reactor was shown to operate like a fixed‐bed bioreactor at ξ < 0.5 and a fluidized bed bioreactor at ξ > 0.5. The maximum flow rate needed to obtain maximum bed fluidization in the reactor was equal to the terminal velocity of the immobilized cell particles. Particles of cells immobilized within these supports showed values of drag coefficient lower than those reported for other high‐density supports. The evaluation of these hydrodynamic characteristics lead to an adequate bed fluidization inside the reactor, thus improving oxygen transference and availability in the fermentation medium, making the process more viable for future scale‐up. Copyright © 2008 Society of Chemical Industry

Phase transition in a three-states reaction–diffusion system

A one-dimensional reaction–diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and annihilation of particles. It has been shown that the model undergoes a continuous phase transition from a phase where the currents of different species of particles are equal to another phase in which they are different. The total density of particles and also their currents in each phase are calculated exactly.

Diffusive epidemic process: theory and simulation

We study the continuous absorbing-state phase transition in the one-dimensional diffusiveepidemic process via mean-field theory and Monte Carlo simulation. In this model,particles of two species (A and B) hop on a lattice and undergo reactions and ; the total particle number is conserved. We formulate the model as a continuous-timeMarkov process described by a master equation. A phase transition between the(absorbing) B-free state and an active state is observed as the parameters (reaction anddiffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising,nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles.A computational realization of the process that is faithful to the transition rates definingthe model is devised, allowing for direct comparison with theory. Using the quasi-stationarysimulation method we determine the order parameter and the survival time in systems ofup to 4000 sites. Due to strong finite-size effects, the results converge only for large systemsizes. We find no evidence for a discontinuous transition. Our results are consistentwith the existence of three distinct universality classes, depending on whether Aparticles diffusive more rapidly, less rapidly or at the same rate as B particles. Wealso perform quasi-stationary simulations of the triplet creation model, whichyield results consistent with a discontinuous transition at high diffusion rates.

Tests of the hydrodynamic equivalence of direct-drive implosions with different D2 and He3 mixtures

Direct drive implosions of targets filled with different mixtures of D2 and He3 gas on the OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] have shown an unexpected scaling of experimental nuclear yields. At temperatures above a few electron volts, D2 and He3 gases are fully ionized, and hydrodynamically equivalent fuels with different ratios of D2 and He3 can be chosen to have the same mass density, total particle density, and equation of state. Implosions with a 50/50 mixture of D:He3 by atom consistently result in measured nuclear yields half of that anticipated by scaling from measured yields of implosions with pure D2 and nearly pure He3. This observation is seen over a wide range of experimental configurations, including targets with a variety of shell thicknesses and fill pressures, simultaneously for two different nuclear yields (DD and DHe3), and for shock and compression yields. A number of possible mechanisms to cause the scaling are considered, but no dominant mechanism has been identified.

Observations of meteoric material and implications for aerosol nucleation in the winter Arctic lower stratosphere derived from in situ particle measurements

Abstract. Number concentrations of total and non-volatile aerosol particles with size diameters >0.01 μm as well as particle size distributions (0.4–23 μm diameter) were measured in situ in the Arctic lower stratosphere (10–20.5 km altitude). The measurements were obtained during the campaigns European Polar Stratospheric Cloud and Lee Wave Experiment (EUPLEX) and Envisat-Arctic-Validation (EAV). The campaigns were based in Kiruna, Sweden, and took place from January to March 2003. Measurements were conducted onboard the Russian high-altitude research aircraft Geophysica using the low-pressure Condensation Nucleus Counter COPAS (COndensation PArticle Counter System) and a modified FSSP 300 (Forward Scattering Spectrometer Probe). Around 18–20 km altitude typical total particle number concentrations nt range at 10–20 cm−3 (ambient conditions). Correlations with the trace gases nitrous oxide (N2O) and trichlorofluoromethane (CFC-11) are discussed. Inside the polar vortex the total number of particles >0.01 μm increases with potential temperature while N2O is decreasing which indicates a source of particles in the above polar stratosphere or mesosphere. A separate channel of the COPAS instrument measures the fraction of aerosol particles non-volatile at 250°C. Inside the polar vortex a much higher fraction of particles contained non-volatile residues than outside the vortex (~67% inside vortex, ~24% outside vortex). This is most likely due to a strongly increased fraction of meteoric material in the particles which is transported downward from the mesosphere inside the polar vortex. The high fraction of non-volatile residual particles gives therefore experimental evidence for downward transport of mesospheric air inside the polar vortex. It is also shown that the fraction of non-volatile residual particles serves directly as a suitable experimental vortex tracer. Nanometer-sized meteoric smoke particles may also serve as nuclei for the condensation of gaseous sulfuric acid and water in the polar vortex and these additional particles may be responsible for the increase in the observed particle concentration at low N2O. The number concentrations of particles >0.4 μm measured with the FSSP decrease markedly inside the polar vortex with increasing potential temperature, also a consequence of subsidence of air from higher altitudes inside the vortex. Another focus of the analysis was put on the particle measurements in the lowermost stratosphere. For the total particle density relatively high number concentrations of several hundred particles per cm3 at altitudes below ~14 km were observed in several flights. To investigate the origin of these high number concentrations we conducted air mass trajectory calculations and compared the particle measurements with other trace gas observations. The high number concentrations of total particles in the lowermost stratosphere are probably caused by transport of originally tropospheric air from lower latitudes and are potentially influenced by recent particle nucleation.

Dissipation of Atrazine and Two N‐Dealkylated Metabolites in Soils of Sugarcane Plantations Under Field Conditions in Barbados

The widespread use of atrazine (AT) as a preemergent herbicide has raised concerns about its persistence in soils of sugarcane plantations in Barbados. Reported are results of field studies to measure the dissipation of AT and two primary metabolites at two sites in sugarcane plantations in Barbados. The investigation was intended to provide values of the half‐lives for dissipation of the herbicide at various depths in the soil profile. Field studies indicated that there is significant potential for AT to leach from Barbados soils to vulnerable groundwater. Residues of the parent and the two metabolites persisted and leached to all profiles of the soil throughout the study period. AT dissipation occurred at all soil depths, was described by first‐order kinetics, and proceeded with half‐life values of 15–28 days. In Profile 1 at the Henley study site, AT concentration decreased exponentially by 72% from 1.16 µg/g on the application day of the herbicide to 0.084 µg/g at the end of day 84 of the study period. A similar decrease occurred in soils from a second site, Edgecumbe; from 2.84 g/g to 0.077 g/g. At deeper depths, the concentration of AT appeared to decrease at a slower rate than near‐surface soils. Dissipation of AT concentration in both fields was generally accompanied by increases in the concentration of the dealkylated metabolites: deethylatrazine (DEAT) and deisopropylatrazine (DIAT). For example, 14% and 7% conversion of AT to DEAT and DIAT occurred by day 14 of the application, respectively. Generally, the deethylated metabolite was present at a higher concentration than the deisopropylated metabolite. By day 274, the day before the second application of AT, the concentration was 0.01 µg/g, typically only 0.3–0.9% of the AT applied. In general, dissipation of AT appeared to be independent of localized factors, such as soil type (silt, clay, and sand), organic matter content, pH, cation exchange capacity, total pore size, bulk density, particle density, and saturated hydraulic conductivity.

Exact solution of a reaction-diffusion model with particle-number conservation

We analytically investigate a one-dimensional branching-coalescing model with reflecting boundaries in a canonical ensemble where the total number of particles on the chain is conserved. Exact analytical calculations show that the model has two different phases which are separated by a second-order phase transition. The thermodynamic behavior of the canonical partition function of the model has been calculated exactly in each phase. Density profiles of particles have also been obtained explicitly. It is shown that the exponential part of the density profiles decays on three different length scales which depend on the total density of particles.

Symmetry and species segregation in diffusion-limited pair annihilation

We consider a system of q diffusing particle species A1, A2, ..., Aq that are all equivalent under a symmetry operation. Pairs of particles may annihilateaccording to Ai + Aj → 0 with reaction rates kij that respect the symmetry, and without self-annihilation(kii = 0). For spatialdimension d > 2 mean-field theory predicts that the total particle density decays as ρ(t) ~ t -1, provided that the system remains spatially uniform. We determine the conditions on the matrixk under which there exists a critical segregation dimensiondseg below which this uniformity condition is violated; the symmetry between the species is thenlocally broken. We argue that in those cases the density decay slows down to ρ(t) ~ t -d/dseg for 2<d < dseg. We showthat when dseg exists, its value can be expressed in terms of the ratio of the smallest to the largest eigenvalue ofk. The existence of a conservation law (as in the special two-species annihilation A + B → 0), although sufficient for segregation, is shown not to be a necessary condition for thisphenomenon to occur. We work out specific examples and present Monte Carlo simulationscompatible with our analytical results.

Segregation in diffusion-limited multispecies pair annihilation

The kinetics of the q species pair annihilation reaction (A_i + A_j -> 0 for 1 <= i < j <= q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as rho(t) ~ t^{- alpha}. For d = 1 the system segregates into single species domains, yielding a different value of alpha for each q; for a simplified version of the model in one dimension we derive alpha(q) = (q-1) / (2q). Within mean-field theory, applicable in d >= 2, segregation occurs only for q < 1 + (4/d). The only physical realisation of this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed by an extra local conservation law. For d >= 2 and q >= 1 + (4/d) the system remains disordered and its density is shown to decay universally with the mean-field power law (alpha = 1) that also characterises the single-species annihilation process A + A -> 0.

On the Structure of the Superfluid State and Quasiparticle Spectrum in a Bose Liquid with a Suppressed Bose–Einstein Condensate

A self-consistent model of the superfluid (SF) state of a Bose liquid with strong interaction between bosons and a weak single-particle Bose–Einstein condensate (BEC) is considered. The ratio of the BEC density n 0 to the total particle density n of the Bose liquid is used as a small parameter of the model, n 0/n≪1, unlike in the Bogolyubov theory of a quasi-ideal Bose gas, in which the small parameter is the ratio of the number of supracondensate excitations to the number of particles in an intensive BEC, (n−n 0)/n 0≪1. A closed system of nonlinear integral equations for the normal ~Σ11(p, ω) and anomalous ~Σ12(p, ω) self-energy parts is obtained with account for terms of first order in the BEC density. A renormalized perturbation theory is used, which is built on combined hydrodynamic (at p→0) and field (at p≠0) variables with analytic functions ~Σ ij (p, e) at pe0 and e→0 and a nonzero SF order parameter ~Σ12(0, 0)≠0, proportional to the density ρ s of the SF component. Various pair interaction potentials U(r) with inflection points in the radial dependence and with an oscillating sign-changing momentum dependence of the Fourier component V(p) are considered. Collective many-body effects of renormalization (“screening”) of the initial interaction, which are described by the bosonic polarization operator Π(p, ω), lead to a suppression of the repulsion [V(p)<0] and an enhancement of the effective attraction [V(p)<0] in the respective domains of nonzero momentum transfer, due to the negative sign of the real part of Π(p, ω) on the “mass shell” ω=E(p). In the framework of the “soft spheres” model with the single fitting parameter—the value of the repulsion potential at r=0—the quasiparticle spectrum E(p) is calculated, which is in good accordance with the experimental spectrum E exp(p) of elementary excitations in superfluid 4He. It is shown that the roton minimum in the quasiparticle spectrum is directly associated with the first negative minimum of the Fourier component of the renormalized (“screened”) potential of pair interaction between bosons.

Non-LTE and optical depth effects to be considered in quantitative spectroscopy of cold and dense plasmas

This paper describes a collisional radiative steady state model for spatially homogeneous plasmas including an arbitrary number of levels of the ion to be considered. Non-equilibrium situations are taken into account as well as optical depth effects. Total particle density and temperature are used as independent parameters while the optical source thickness is obtained from the corresponding absorption coefficients. No particular case is assumed for the transitions considered and line intensities ratios can be obtained for any pair of allowed dipolar transitions. Temperature, particle and the derived electron densities ranges are considered which are of fundamental interest in quantitative spectroscopy (e.g. laser induced breakdown spectroscopy). Some well established results for simple cases are reproduced by the model and other results are presented for complex ions.

Path integral calculation of superfluid [formula omitted] vortex core structure

A structure of a superfluid 4 He vortex core is studied with a path integral Monte Carlo method. The distribution of superfluid and normal fluid densities around the vortex core is obtained. The total particle density decreases in the vortex core region. The radius of the core is nearly equal to the particle diameter. The vortex core is filled with normal fluid in the temperature region T≃ T λ . In the low temperature region, the normal fluid component of a vortex core decreases remarkably. Consequently the number of particle density of a vortex core region becomes extremely small.

Binding energies of nuclei and their density distributions in a nonlocal extended Thomas-Fermi approximation

Basic properties of the ground states of spherical nuclei are investigated in a nonlocal extended Thomas-Fermi approximation under the assumption of Skyrme forces. It is shown that, for nuclei occurring near the β-stability line, the binding energies, the root-mean-square radii, and the density distributions found on this basis agree well with experimental data. Binding energies, root-mean-square radii, and density distributions are also calculated for the ground states of nuclei lying far off the β-stability line and for superheavy elements. For the proton, the neutron, and the total particle density, the thickness of the diffuse layer is investigated as a function of the number of neutrons in tin isotopes.

Inclusion of Radiation Effects in Plasma-Neutral Codes

Experiments on Alcator C-Mod have demonstrated edge plasma conditions with optically thick hydrogenic Lyman lines [1, 2]. In these high opacity plasma regions, the total neutral particle density and excited-state populations depend on the radiation field. Current edge plasma-neutral fluid codes ignore this dependence in their atomic physics models. For instance, collisional-radiative models are commonly used to define effective ionization, recombination and energy loss rates exclusively as functions of the local electron density and electron temperature [3]. To include radiation effects in plasma-neutral codes, we are working towards two goals: (1) extending the local atomic physics model to account for a spatially varying radiation field; and (2) driving the extended model with results from a non-local thermodynamic equilibrium atomic kinetics and radiation transfer code.