Initial Density Distribution Research Articles

Duality in Phase Space and Complex Dynamics of an Integrated Pest Management Network Model

Fragmented habitat patches between which plants and animals can disperse can be modeled as networks with varying degrees of connectivity. A predator–prey model with network structures is proposed for integrated pest management (IPM) with impulsive control actions. The model was analyzed using numerical methods to investigate how factors such as the impulsive period, the releasing constant of natural enemies and the mode of connections between the patches affect pest outbreak patterns and the success or failure of pest control. The concept of the cluster as defined by Holland and Hastings is used to describe variations in results ranging from global synchrony when all patches have identical fluctuations to n-cluster solutions with all patches having different dynamics. Heterogeneity in the initial densities of either pest or natural enemy generally resulted in a variety of cluster oscillations. Surprisingly, if n > 1, the clusters fall into two groups one with low amplitude fluctuations and the other with high amplitude fluctuations (i.e. duality in phase space), implying that control actions radically alter the system's characteristics by inducing duality and more complex dynamics. When the impulsive period is small enough, i.e. the control strategy is undertaken frequently, the pest can be eradicated. As the period increases, the pest's dynamics shift from a steady state to become chaotic with periodic windows and more multicluster oscillations arise for heterogenous initial density distributions. Period-doubling bifurcation and periodic halving cascades occur as the releasing constant of the natural enemy increases. For the same ecological system with five differently connected networks, as the randomness of the connectedness increases, the transient duration becomes smaller and the probability of multicluster oscillations appearing becomes higher.

Suppression of Rayleigh-Taylor instabilities in Z-pinches

Experiments on studying the stability of Z-pinch compression were carried out at a current of 450 kA with a build-up time of 450 ns. The plasma shell of the pinches was formed by evaporating the electrode material in the process of vacuum arc burning. The Rayleigh–Taylor (RT) instabilities were suppressed using the regime of arc combustion on the surface of one of the electrodes in the high-voltage gap in which the pinch was positioned. As a result of free plasma discharge, the radial density distribution was formed such that the plasma concentration increased from the outer boundary to the shell axis. The experiments demonstrated that such an initial radial density distribution almost completely suppresses of the RT instability.

Sensitivity analysis and optimization of eigenmode localization in continuum systems

A model problem arising from optical design of photonic bandgap structure is investigated. That is, the optimization problem is to find the material inhomogeneity in a domain so that a particular eigenmode governed by the scalar Helmholtz equation is localized. The continuum sensitivity analysis of the objective function including the eigenmode is carried out. The derivative of the objective function with respect to the density function is obtained by the sensitivity problem and the adjoint problem in continuum systems. When the multiplicity of eigenmode happens, our strategy is to select the closest eigenmode to the current eigenmode. Four numerical examples in a square domain are studied, with different weight functions and initial density distributions. The numerical results illustrate the validity of the algorithm based on the continuum sensitivity analysis.

Initialization of hydrodynamics in relativistic heavy ion collisions with an energy-momentum transport model

A key ingredient of hydrodynamical modeling of relativistic heavy ion collisions is thermal initial conditions, an input that is the consequence of a pre-thermal dynamics which is not completely understood yet. In the paper we employ a recently developed energy-momentum transport model of the pre-thermal stage to study influence of the alternative initial states in nucleus-nucleus collisions on flow and energy density distributions of the matter at the starting time of hydrodynamics. In particular, the dependence of the results on isotropic and anisotropic initial states is analyzed. It is found that at the thermalization time the transverse flow is larger and the maximal energy density is higher for the longitudinally squeezed initial momentum distributions. The results are also sensitive to the relaxation time parameter, equation of state at the thermalization time, and transverse profile of initial energy density distribution: Gaussian approximation, Glauber Monte Carlo profiles, etc. Also, test results ensure that the numerical code based on the energy-momentum transport model is capable of providing both averaged and fluctuating initial conditions for the hydrodynamic simulations of relativistic nuclear collisions.

The Effect of Metallicity on the Dynamical Evolution of A Globular Cluster1,2

The dynamical process and stellar evolution, as well as their mutual interaction will make important influences on the evolution of a globular cluster. As the matallicity may affect the track of stellar evolution, the associated variation of stellar mass loss rate will make influence on the dynamical process of the globular cluster as well. A series of N-body simulations are performed to study the effects of matallicity on the mass loss rate and radius of a globular cluster, and the reasons are analyzed. At the same time, the effects of large-mass stars and the cluster's initial number density distribution are also studied. In the simulations, the adopted initial number of member stars in the globular cluster model is N =50000, they move in the Galaxy-like gravitational potential, and their evolutions are also taken into consideration. The results indicate that because the low-matallicity stars have a faster evolutionary timescale, so in the early period the metal-poor globular cluster will have a higher mass loss, but at the same time its core collapse will be obviously delayed in time, hence after the core collapse its mass loss will be overtaken by the metal-rich globular cluster. In addition, as the evolution of large-mass star causes a larger mass loss, hence the existence of large-mass stars will make the matallicity even significantly influence on the early period expansion of the globular cluster, and the succeeding process of core collapse, besides, the influence of the cluster's initial number density distribution is also not negligible.

Fast ignition when heating the central part of an inertial confinement fusion target by an ion beam

We investigate the ignition and burning of a precompressed laser fusion target when it is rapidly heated by an ion beam with the formation of a temperature peak in the central part of the target. We present the results of our comprehensive numerical simulations of the problem that include the following components: (1) the target compression under the action of a profiled laser pulse, (2) the heating of the compressed target with spatially nonuniform density and temperature distributions by a beam of high-energy ions, and (3) the burning of the target with the initial spatial density distribution formed at the instant of maximum target compression and the initial spatial temperature distribution formed as a result of the compressed-target heating by an ion beam. The dependences of the threshold energies of the igniting ion beam and the thermonuclear gain on the width of the Gaussian beam ion energy spectrum have been established. The peculiarities of fast ignition by an ion beam related to the spatial distribution of parameters for the target precompressed by a laser pulse are discussed.

The effect of ponderomotive force on the density in the interaction of two superposing fundamental modes with plasma in an elliptical waveguide

The interaction of high power microwaves and plasma is studied through the propagation of two fundamental TE11 modes in a plasma-filled elliptical waveguide, when their fields have a phase difference and they superpose at a small angle. Here we derive two nonlinear differential equations for the amplitude of the electric field in a plasma-filled elliptical waveguide. These equations are solved numerically using the fourth order Runge–Kutta method for the field amplitude of the microwave in the waveguide considering the waveguide to be made up of a perfect conductor and to be filled by plasma with a homogeneous initial density distribution. The effects of electron temperature, the microwave field and its frequency are studied on the perturbed density in relation to the ponderomotive force exerted by the resultant mode. It is shown that the field of the microwave is altered and that the density profile can be controlled by the angle of superposition, the phase difference between the fields of the two modes, the microwave frequency and the microwave field amplitude.

Adiabatic contraction revisited: Implications for primordial black holes

We simulate the adiabatic contraction of a dark matter (DM) distribution during the process of the star formation, paying particular attention to the phase space distribution of the DM particles after the contraction. Assuming the initial uniform density and Maxwellian distribution of DM velocities, we find that the number $n(r)$ of DM particles within the radius $r$ scales like $n(r) \propto r^{1.5}$, leading to the DM density profile $\rho\propto r^{-1.5}$, in agreement with the Liouville theorem and previous numerical studies. At the same time, the number of DM particles $\nu(r)$ with periastra smaller than $r$ is parametrically larger, $\nu(r) \propto r$, implying that many particles contributing at any given moment into the density $\rho(r)$ at small $r$ have very elongated orbits and spend most of their time at distances larger than $r$. This has implications for the capture of DM by stars in the process of their formation. As a concrete example we consider the case of primordial black holes (PBH). We show that accounting for very eccentric orbits boosts the amount of captured PBH by a factor of up to $2\times 10^3$ depending on the PBH mass, improving correspondingly the previously derived constraints on the PBH abundance.

Thermal photon v3 at LHC from fluctuating initial conditions

We calculate the triangular flow parameter $v_3$ of thermal photons for 0--40\% central collisions of Pb nuclei at LHC using an event-by-event hydrodynamic model with fluctuating initial conditions. Thermal photon $v_3$ with respect to the the participant plane angle is found to be positive and significant compared to the elliptic flow parameter $v_2$ of thermal photons. In addition, photon $v_3$ as a function of $p_T$ shows similar qualitative nature to photon $v_2$ in the region $1< p_T <6$ GeV/$c$. We argue that while $v_3$ originates from $\epsilon_3$ deformations of the initial state density distribution, fast buildup of radial flow due to fluctuations is the main driving mechanism for the observed large value.

Modification of density profile at interaction of three superposing fundamental modes with plasma in a cylindrical waveguide

The interaction of high-power microwave and plasma is studied through the propagation of three fundamental modes in a plasma-filled cylindrical waveguide, when their fields have a phase difference and they superpose at a small angle. Furthermore, a modification of the electron density distribution of the plasma by the ponderomotive force of the microwave propagating into the configuration is studied. Here, we derive two coupled equations obtained using the wave and Maxwell’s equations for the resultant mode along with the contribution of plasma cylindrical waveguide. These equations are solved numerically using fourth order Runge–Kutta method for the field amplitude of the microwave in the waveguide considering the waveguide to be made up of a perfect conductor and filled by plasma with homogeneous initial density distribution. It is graphically shown that the field of the microwave gets altered and also the density profile can be controlled by the angle of superposition, phase difference between the fields of the three modes, microwave frequency, electron temperature and microwave field amplitude.

Study of the stability of Z-pinch implosions with different initial density profiles

Stability of metal-puff Z pinches was studied experimentally. Experiments were carried out on a facility producing a load current up to 450 kA with a rise time of 450 ns. In a metal-puff Z pinch, the plasma shell is produced due to evaporation of the electrode material during the operation of a vacuum arc. In the experiment to be reported, a single-shell and a shell-on-jet pinch load with magnesium electrodes were used. Two-dimensional, 3 ns gated, visible-light images were taken at different times during the implosion. When the shell was formed from a collimated plasma flow with small radial divergence, Rayleigh–Taylor (RT) instability typical of gas-puff implosions was recorded. The RT instability was completely suppressed in a mode where the initial density distribution of the shell approached a tailored density profile [A. L. Velikovich et al., Phys. Rev. Lett. 77, 853 (1996)].

A simulation study of the propagation of whistler-mode chorus in the Earth’s inner magnetosphere

We study the propagation of whistler-mode chorus in the magnetosphere by a spatially two-dimensional simulation code in the dipole coordinates. We set the simulation system so as to assume the outside of the plasmapause, corresponding to the radial distance from 3.9 to 4.1 RE in the equatorial plane and the latitudinal range from −15° to +15°, where RE is the Earth’s radius. We assume a model chorus element propagating northward from the magnetic equator of the field line at L=4 with a rising tone from 0.2 to 0.7 Ωe 0 in the time scale of 5,000 , where Ωe 0 is the electron gyrofrequency at the magnetic equator. For the initial density distribution of cold electrons, we assume three types of initial conditions in the outside of the plasmapause: without a duct (run 1), a density enhancement duct (run 2), and a density decrease duct (run 3). In run 1, the simulation result reveals that whistler-mode waves of the different wave frequencies propagate in the different ray path in the region away from the magnetic equator. In runs 2 and 3, the model chorus element propagates inside the assumed duct with changing wave normal angle. The simulation results show the different propagation properties of the chorus element in runs 2 and 3 and reveal that resultant wave spectra observed along the field line are different between the density enhancement and density decrease duct cases. The spectral modification of chorus by the propagation effect should play a significant role in the interactions between chorus and energetic electrons in the magnetosphere, particularly in the region away from the equator. The present study clarifies that the variation of propagation properties of chorus should be taken into account for the thorough understanding of resonant interactions of chorus with energetic electrons in the inner magnetosphere.

Inclusion of initial powder distribution in FEM modelling of near net shape PM hot isostatic pressed components

The final shape of powder metallurgy hot isostatic pressing (HIP) components is determined by many factors, including the shape and size of the capsule, the initial density distribution of the powder before HIP, and HIP process parameters. Current HIP simulation, which usually assumes that the powder inside the capsule is homogeneous, cannot predict non-uniform shrinkage. Therefore, the purpose of this work is to develop a methodology to quantitatively determine the initial powder density distribution inside HIP capsules, which were precompacted by different techniques. The relative density distribution obtained from experimental work is used as the initial condition for numerical simulations. The final shapes of the capsules produced by HIP are compared to simulation results. The paper shows the sensitivity of the final shape on the initial powder density distribution and illustrates the need to implement the initial powder distribution into the finite element model to improve the quality of the near net shape HIP simulation.

Occurrence of Naked Singularities in Higher Dimensional Dust Collapse

We consider here the gravitational collapse of a inhomogeneous dust cloud described by Tolmanbondi models. We find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of initial density distribution. Collapse ends into a black hole if the dimensionless quantity ψ is greater than −22.18033 and ends into a naked singularity if ψ ≤ −22.18033. We find the occurrence of naked singularity in higher dimensional case. We proposed the concept of ‘trapped range’ of initial data in the different higher dimensional space-times. We show that ‘trapped range’ of initial data increases with the increase in dimensions of the space-times.

Geostrophic adjustment in a closed basin with islands

AbstractWe consider the geostrophic adjustment of a density-stratified fluid in a basin of constant depth on an $f$-plane in the context of linearized theory. For a single vertical mode, the equations are equivalent to those for a linearized shallow-water theory for a homogeneous fluid. Associated with any initial state there is a unique steady geostrophically adjusted component of the flow compatible with the initial conditions. This steady component gives the time average of the flow and is analogous to the adjusted flow in an unbounded domain without islands. The remainder of the response consists of superinertial Poincaré and subinertial Kelvin wave modes and expressions for the energy partition between the modes in arbitrary basins again follow directly from the initial conditions. The solution for an arbitrary initial density distribution released from rest in a circular domain is found in closed form. When the Rossby radius is much smaller than the basin radius, appropriate for the baroclinic modes, the interior adjusted solution is close to that of the initial state, except for small-amplitude trapped Poincaré waves, while Kelvin waves propagate around the boundaries, carrying, without change of form, the deviation of the initial height field from its average.

A Three‐Dimensional Structure and Process Model for Integrated Hydro‐Geo‐Pedologic Analysis of a Constructed Hydrological Catchment

A structure model describes the boundary geometries and the three‐dimensional solid phase distributions of the catchment. In contrast to an established ecosystem, feedback relations can be assumed for an initial geosystem between the development of spatial structures and the water and element fluxes. The objective was to develop a hydrological catchment model as a three‐dimensional spatial database of the solid phase that allows an integrative analysis, a periodical mass balance, and the generation of distributed model parameters for the developing system. Data were from the constructed catchment “Chicken Creek.” The initial texture and bulk density distributions were generated by imitating sediment dumping, segregation, and compaction. Boundary geometries and changes in surface topography due to erosion and sedimentation processes were quantified on the basis of digital elevation models (DEMs) derived from aerial photographs. The catchment was visualized with the three‐dimensional software GoCad; the “emergence” of the water table and other structures (e.g., soil horizons, root zone) could be spatially assigned and quantified to identify regions with specific processes. A combination of three‐dimensional catchment with time‐dependent two‐dimensional surface models allowed generating the development of spatially distributed erosion–deposition patterns that formed new initial surfaces. The three‐dimensional distributed solid phase structure of the catchment allowed for a more direct comparison with observations using minimal invasive methods. The mass balance of the solids could be related with pedologic development and transfer to other geopedologic systems achieved by adapting sediment transport and deposition in the descriptions of the model. This model may help improve the integrative analysis of hydrological catchments.

Elliptic flow of thermal photons from an event-by-event hydrodynamic model

Elliptic flow of direct photons in relativistic heavy ion collisions is believed to be dominated by contribution from thermal radiation of quark gluon plasma up to $p_T$ $\sim 5$ GeV/$c$, although other sources start outshining the thermal contribution at already smaller values of $p_T$ in the direct photon spectrum. The elliptic flow of thermal photons from ideal hydrodynamics considering a smooth initial density distribution under-predicts the PHENIX direct photon data from 200A GeV Au+Au collisions at RHIC by a large margin in the range $1 < p_T < 5$ GeV/$c$. However, a significant enhancement of thermal photon production due to fluctuations in the initial QCD matter density distributions is expected. We show that such fluctuations result in substantially larger photon elliptic flow for $p_T > 2.5 $ GeV/$c$ compared to a smooth initial-state-averaged density profile. The results from event-by-event hydrodynamics are found to be sensitive to the fluctuation size parameter. However, the effects of initial state fluctuations are insufficient to account for the discrepancy to the PHENIX data for direct photon elliptic flow. Furthermore, the photon $v_2$ is reduced even more when we include the NLO pQCD prompt photon component. We also calculate the spectra and elliptic flow of thermal photons for 2.76A TeV Pb+Pb collisions at LHC and for the 0--40% centrality bin. Thermal photons from event-by-event hydrodynamics along with prompt photons from NLO pQCD calculations explain the ALICE preliminary direct photon data well in the region $p_T \ge 2.5$ GeV/c. Similar to RHIC, the elliptic flow results at LHC are again found to be much smaller than the ALICE preliminary $v_2$ data.

Exact solution in the form of a shock wave for the Maxwell and gravitomagnetism equations

Over the last halfcentury , much attention in vari� ous fields of mathematical and theoretical physics (1-3) and in applied mathematics (4-7) has been given to approaches providing mathematically rigor� ous results, namely, to the search for exactly solvable models and to rigorous formulations of the original equations of such models as based on fundamental principles. In this work, the method of characteristics is used to construct exact solutions of model problems described by the Maxwell and gravitomagnetism equa� tions for the evolution of the charge or mass density function in spherical or infinite cylindrical domains. The initial charge or mass density distribution in such a domain is radially symmetric, i.e., depends only the radius . In the case of an inhomogeneous initial charge or mass density distribution, we show the existence of a shock wave solution ( Ψ�effect).

EFFECTS OF INITIAL INHOMOGENEOUS DENSITY DISTRIBUTION AND VOID SHAPE ON POWDER FORGING OF POROUS METAL

The deformation behavior during axisymmetric upsetting of sintered metals has been studied based on the finite-element method. The investigation on the effects of the initial density distribution, void shape and die friction on the density distribution and punch force during deformation have been conducted. It was found that under low-friction conditions, the initial density distribution affects the deformation geometry and the density distribution. However, the effect of the initial density distribution was found to be negligible under high-friction conditions. The initial density distribution did not affect the punch force or the average density, regardless of the friction conditions. When the force is perpendicular to semi-major axis of elliptical void, it is not only good for densification but also decrease the punch force in forging of porous metal.

Density modification by two superposing TE10 modes in a plasma filled rectangular waveguide

Microwave and plasma interaction is examined via two fundamental TE10 modes propagating in a plasma filled rectangular waveguide after superposing at a smaller angle. The propagation of the resultant mode realized from these two modes is governed by a wave equation obtained using the Maxwell's equations. This equation is solved numerically using fourth order Runge-Kutta method for the field amplitude of the microwave in the waveguide considering the waveguide to be made up of a perfect conductor and filled with different types of initial plasma density distributions, viz. homogeneous density, linear density with gradient in the propagation direction, and the density with Gaussian profile along the waveguide width. A phenomenon similar to the duct formation by high power microwaves is found to take place, where the plasma density attains interesting profiles. These profiles can be controlled by the angle of superposition, phase difference between the fields of the two modes, microwave frequency and microwave field amplitude.