Darwin Model Research Articles

Exterior problem of the Darwin model and its numerical computation

In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell's equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.

DERIVATION OF THE HYDRODYNAMIC EQUATIONS IN THE FRAMEWORK OF THE BOGOLIUBOV FUNCTIONAL HYPOTHESIS

We generalize the Bogoliubov functional hypothesis to the case of multiparticle interaction depending on both the coordinates and momenta of particles. We illustrate this with the examples of two weakly relativistic models: the Darwin model in the theory of charged particles and the Fock model in the general theory of relativity. For these models, based on the chain of the BBGKY equations, we calculate weakly relativistic corrections to the classical transport coefficients and find the conditions under which there is no bijective relation between the parameters of the local equilibrium distribution and the hydrodynamic variables.

Analytical and numerical studies of heavy ion beam transport in the fusion chamber

The propagation of a high-current finite-length ion charge bunch through a background plasma is of interest for many applications, including heavy ion fusion, plasma lenses, cosmic ray propagation, and so forth. Charge neutralization has been studied both analytically and numerically during ion beam entry, propagation, and exit from the plasma. A suite of codes has been developed for calculating the degree of charge and current neutralization of the ion beam pulse by the background plasma. The code suite consists of two different codes: a fully electromagnetic, relativistic particle-in-cell code, and a relativistic Darwin model for long beams. As a result of a number of simplifications, the second code is hundreds of times faster than the first one and can be used for most cases of practical interest, while the first code provides important benchmarking for the second. An analytical theory has been developed using the assumption of long charge bunches and conservation of generalized vorticity. The model predicts nearly complete charge neutralization during quasi-steady-state propagation provided the beam pulse duration τb is much longer than the inverse electron plasma frequency ωp−1, where ωp = (4πnpe2/me)1/2 and np is the background plasma density. In the opposite limit, the beam head excites large-amplitude plasma waves. Similarly, the beam current is well neutralized provided ωpτb >> 1 and the beam radius is much larger than plasma skin depth δp = c/ωp. Equivalently, the condition for current neutralization can be expressed in terms of the beam current as Ib >> 4.25Zb βb(nb /np)kA, where nb is the beam density, Zb is the ion charge, and Vb = βbc is the beam velocity; and the condition for charge neutralization can be expressed as Ib >> 4.25βb3(nb /np)(rb /lb)2kA, where lb and rb are the beam length and radius, respectively. For long charge bunches, the analytical results agree well with the results of numerical simulations. The visualization of the data obtained in the numerical simulations shows complex collective phenomena during beam entry into and exit from the plasma.

Pollinator-mediated selection on flower-tube length in a hawkmoth-pollinated Gladiolus (Iridaceae).

Darwin's mechanistic model whereby selection favours plants with flower tubes that exceed the tongue length of the primary pollinator, was tested using unmanipulated plants of the hawkmoth-pollinated South African iris, Gladiolus longicollis. The study population was characterized by exceptionally large phenotypic variation in flower-tube length (range 56-129 mm). Directional selection on tube length was revealed by a significant positive relationship between this trait and both fruit and seed set. Selection was attributed to the effect of tube length on pollen receipt, as supplemental hand pollinations showed fruit and seed set in the population to be pollen limited. Indirect selection on tube length may also occur through the correlation of this trait with inflorescence height, although direct selection on the latter trait was significant only for seed set. The main pollinators at the study site were individuals of the large hawkmoth Agrius convolvuli that had tongue lengths of 85-135 mm. Other hawkmoths had tongues that were much too short to reach the nectar in G. longicollis flowers and seldom carried pollen of G. longicollis. Flowers with tubes shorter than the tongues of A. convolvuli are apparently not effectively pollinated because stigmas do not contact the moth's head effectively. This study demonstrates that selection may occur among plants with natural phenotypic variation in flower-tube length, and supports Darwin's model of pollinator-mediated selection.

A modeling approach to teaching evolutionary biology in high schools*

AbstractThere are numerous empirical reports in the science education literature documenting the difficulty students have in understanding evolution, in particular natural selection. Unfortunately, because of the nature of empirical reports, much detail about the instruction that students in these studies received is seldom provided. In this article we describe the commitments and research that went into the design of a 9‐week high school course in evolutionary biology. This course was designed to bring students to an understanding of the practice of evolutionary biology by engaging them in developing, elaborating, and using one of the discipline's most important explanatory models—Darwin's model of natural selection. This article is not an empirical report on student understanding but is instead a description of our view of what constitutes understanding in evolution and of a curriculum designed from this perspective. Examples of student work are used to add richness to the description of the course as well as to illustrate the potential for sophisticated reasoning that exists when students are given the opportunity and conceptual tools to engage in realistic inquiry. © 2002 Wiley Periodicals, Inc. J Res Sci Teach 39: 185–204, 2002

Magneto-photoluminescence study of electronic transitions in InAs/GaAs quantum dot layers

Magneto-photoluminescence of single- and multi-layered self-organised MOCVD grown InAs quantum dots in GaAs has been investigated at 77 K in magnetic fields up to B=27 T in Faraday configuration. From one up to six peaks are resolved at B=0 T in the photoluminescence spectra when the excitation intensity increases from 10 mW up to 1 W (514.5 nm line of Ar + laser). Simple one particle Fock–Darwin model of two-dimensional electrons confined in a parabolic well describes satisfactorily the evolution of magneto-photoluminescence only for some peaks. The other peaks exhibit slight decrease in energy with increasing magnetic field (∼5 meV at 27 T).

Nonlinear perturbative electromagnetic (Darwin) particle simulation of high intensity beams

A multi-species perturbative nonlinear ( δf) electromagnetic particle simulation scheme has been developed for studying the propagation of intense charged particle beams in high-intensity accelerators and transport systems. The scheme is based on the Darwin approximation of Ampere's law, in which the transverse inductive electric field is neglected, resulting in the elimination of high-frequency transverse electromagnetic effects and, consequently, the associated numerical restrictions from the simulation. However, as noted previously, the presence of the time derivative of the vector potential in the equations of motion for the Darwin model can cause numerical instability. To circumvent this difficulty, we have adopted an approach by replacing the mechanical momentum, p z , in the direction of beam propagation, by the canonical momentum, P z = p z + qA z / c, as the phase-space variable. The resulting Ampere's law is then modified by the presence of an additional shielding term associated with the skin depth of the species. In order to minimize the numerical noise and to easily access both linear and nonlinear regimes for the physics of interest, we have also adopted the δf formalism for the Darwin model. The absence of unwanted high-frequency waves also enables us to use the adiabatic particle pushing scheme to compensate for the mass-ratio disparities for the various species of charge. The scheme is ideal for studying two-stream and filamentation instabilities, which may cause deterioration of the beam quality in the heavy ion fusion driver and fusion chamber.

Magneto-photoluminescence study of energy levels of self-organised InAs/GaAs quantum dots

Magneto-photoluminescence (MPL) of self-organised MOCVD epitaxially grown InAs dots embedded in GaAs has been investigated in order to identify the nature of the corresponding optical transitions and to determine the effective mass of confined electrons and holes. MPL was studied in the range of 0–28 T in Faraday and Voigt configurations. At zero field we have observed up to three PL peaks corresponding to a ground state transition (∼1 eV) and two excited state transitions (∼1.1 and ∼1.2 eV). The ground state transition showed a small diamagnetic shift, the first excited transition was split into two components and three split components were observed for the second excited transition as a function of magnetic field in the Faraday configuration. A simple one-particle Fock–Darwin model of two-dimensional electrons confined in a parabolic well seems to describe the PL behaviour in magnetic field.

Temperature-dependent X-ray dynamical diffraction: Darwin theory simulations.

Thermal vibrations destroy the perfect crystalline periodicity generally assumed by dynamical diffraction theories. This can lead to some difficulty in deriving the temperature dependence of X-ray reflectivity from otherwise perfect crystals. This difficulty is overcome here in numerical simulations based on the extended Darwin theory, which does not require periodicity. Using Si and Ge as model materials, it is shown how to map the lattice vibrations derived from measured phonon dispersion curves onto a suitable Darwin model. Good agreement is observed with the usual Debye-Waller behavior predicted by standard theories, except at high temperatures for high-order reflections. These deviations are discussed in terms of a possible breakdown of the ergodic hypothesis for X-ray diffraction.

Obliquity variations due to climate friction on Mars: Darwin versus layered models

In response to periodic variations in the obliquity, giant CO2 ice caps may form in the polar regions of Mars. The delayed response of the equatorial bulge of Mars to these periodic loads may introduce a secular term in the time evolution of the obliquity. Up to now, the variations in the flattening of Mars induced by the polar ice caps have been estimated using the Darwin model, which simply consists of a uniform sphere with Newtonian rheology. For Earth‐like viscosities of ∼3×1021 Pa s the Darwin model maximizes the friction and predicts a secular obliquity variation comparable to the currently observed value (∼24°). Our main purpose here is to address the role of two well‐recognized features of Mars (a thick lithosphere and a core) on the response of its equatorial bulge and thus on the secular changes of obliquity driven by climate friction. This is done using a layered model with Maxwell viscoelastic rheology. We show that for a wide range of admissible mantle viscosities the obliquity variation is sensibly smaller (by a factor of ∼2) than the one predicted by the Darwin model. On the basis of this finding, we can rule out the possibility that the present‐day obliquity of Mars totally results from climate friction.

Measurement of diffraction efficiencies relevant to crystal lens telescopes

The Toulouse/Argonne collaboration is working on a novel detector for gamma-ray astronomy based on a crystal lens that uses Bragg reflection of Ge crystals to concentrate photons onto a small detector in the image plane. The diffraction efficiency of the crystals is decisive for the energy bandpass, the field of view and the effective area of the crystal lens telescope. We have measured diffraction efficiencies of Ge crystals from 200 to 500 keV at the Advanced Photon Source synchrotron at Argonne National Laboratory in two experiments carried out at the sector 1 bending magnet beamline. The high brilliance and high particle energy of third-generation synchrotrons permit measurements at gamma-ray energies. The low angular divergence of synchrotron radiation is similar to that of an astronomical point source. The efficiencies ranged from 20% to 31% for diffraction of Ge (1 1 1) and (2 2 0) using crystals with a mosaic width of a few arc seconds. Neglecting absorption, the values ranged from 31% to 49%. The continuum flux diffracted in second-order diffraction (4 4 0) was a factor of 2.4–2.6 less than in first-order diffraction (2 2 0) . For third-order diffraction (the (3 3 3) and the (1 1 1) planes), the flux was reduced by a factor of 6.8. The peak efficiency and the rocking curve integral for mosaic widths ranging from a few arc seconds to 0.4° were measured. The results agree with the expectation of the Darwin model for mosaic crystals. This gives us confidence in the calculations of the crystal lens telescope performance, and allows an optimization of a balloon-borne and a satellite-based telescope configuration. Measurements were carried out with a wedged crystal, that was used to increase the diffraction efficiency of the lens crystals for a source at finite distance. The efficiency increase is due to both a bending and a straining of the crystal. We measured rocking curve widths of a crystal before and after etching to determine the effect of surface damage on the diffraction efficiency. The mean decrease in rocking curve width due to the etching was 1.7 arc sec in the center of the crystal and 6.9 arc sec at the crystal edge.

Origin of stone concentrations in loess-derived interfluve soils

Charles Darwin and Vasily Dokuchaev made early and important, but quite different, contributions to pedogenic theory. Their major contributions were both written as books — Darwin's, 1881 The Formation of Vegetable Mould, Through the Action of Worms, With Observation on Their Habits, and Dokuchaev's, 1883 Russian Chernozem. Although most soil scientists are familiar with Dokuchaev's legacy and lasting impact, far fewer know about or value equally Darwin's “worm book.”Dokuchaev's factorial approach to soil science, drawn from observations across the Eurasian steppe, helped map, classify, and place economic value on soils, while also providing key insight into their formation. This approach gained visibility in the 1930s and 1940s, when personnel at the U.S. Department of Agriculture, and some academic pedologists, recognized its utility for soil survey and for interpreting pedogenesis. Jenny's (1941) book, Factors of Soil Formation, helped the model to gain acceptance, and it eventually became entrenched as the core pedogenic model for North America, if not the world. Dokuchaev's legacy is tied to this model. Alternatively, Darwin's main contribution to the field was to shed light on soil processes, particularly faunal mixing (bioturbation) and the textural sorting it can produce. Although Darwin's findings fostered an array of multidisciplinary studies on pedogenic processes during the ensuing 50 years, his work languished in the broad shadow cast by Dokuchaev's model. In 1975, Darwin's ideas reappeared in Soil Taxonomy — associated with rudimentary biomantle concepts. Recently, empowered with new concepts and language, bioturbation concepts have gained considerable traction.We briefly summarize the backgrounds of Darwin and Dokuchaev, and compare their fundamentally different approaches to pedogenesis. But insofar as Dokuchaev's approach is more mainstream, we emphasize Darwin's, for balance. We show how Darwin's model, updated with current understandings of biomantle formation, is allowing new questions to be asked about pedogenesis and landscape evolution, and formerly intractable ones to be answered. We stress the profound role of conceptual models in guiding explanatory thought, and end by positing that both Darwin's and Dokuchaev's approaches, while different in their basic structure and goals, provide together a more complete view of pedogenesis than either can do singly.

A Decomposition of the Electromagnetic Field — Application to the Darwin Model

In many cases, the numerical resolution of Maxwell's equations is very expensive in terms of computational cost. The Darwin model, an approximation of Maxwell's equations obtained by neglecting the divergence free part of the displacement current, can be used to compute the solution more economically. However, this model requires the electric field to be decomposed into two parts for which no straightforward boundary conditions can be derived. In this paper, we consider the case of a computational domain which is not simply connected. With the help of a functional framework, a decomposition of the fields is derived. It is then used to characterize mathematically the solutions of the Darwin model on such a domain.

Finite element convergence for the Darwin model to Maxwell's equations

Dans des domaines polyhedriques tridimensionnels de frontiere Lipschitz continue, on calcule les formulations variationnelles dans H(rot ; Ω) et H(div, rot; Ω) du modele de Darwin qui est une approximation des equations de Maxwell. On prouve que les problemes variationnels sont bien poses, puis, une famille reguliere de triangulations (F h ) h etant donnee, on utilise les elements finis de type Nedelec et de type standard pour discretiser ces problemes. On demontre la convergence des methodes d'elements finis et des estimations d'erreur sont obtenues. En particulier, dans le cas ou l'on ne petit pas prouver l'equivalence des formes bilineaires symetriques des problemes variationnels et des normes usuelles independamment de h, on obtient ces resultats en utilisant une methode legerement modifiee de resolution des problemes de point-selle.

Low-frequency electromagnetic (Darwin) applications in plasma simulation

Plasma modelers have long sought to be free of the restrictive constraint on discretized time and space representations due to light waves. This constraint, commonly called the CFL condition, implies stability for explicit integration of Maxwell's hyperbolic partial differential equations as long as electromagnetic waves do not propagate more than the smallest grid spacing in a time step. The Darwin limit of Maxwell's equations eliminates these purely electromagnetic modes, making it an effective model for low-frequency phenomena because it retains fidelity for all physics resolved by the large time step that it permits. The early Darwin models suffered from numerical instabilities and non-intuitive boundary conditions. Nielson and Lewis first constructed numerically stable algorithms for the Darwin model but problems associated with vector decomposition remained. Decomposition is expensive and appears to be required in most facets of the electromagnetic calculation. Additionally, decompositions require boundary conditions that are beyond physical intuition. Over the last 15 years, both the physics model and the numerical problem have been significantly extended and restructured. These new formulations eliminate most, if not all, of the vector decomposition; the most demanding questions about boundary conditions do not arise. An overview is given of the most commonly used Darwin models, starting with a brief description of the underlying concept. Several variants of Darwin algorithms are presented; non-neutral and quasi-neutral finite-electron-mass, and quasi-neutral zero-electron-mass embodiments are included. Also discussed are new numerical methods that increase the range of parameters for which these models are practical. Finally a new Darwin variant is described that can follow the time dependence of surface and bulk currents in magnetically active materials (i.e. superconductors). Plasma need to be present-reflecting the new uses that are being found for traditional plasma algorithms.

Extension of the Streamlined Darwin Model to Quasineutral Plasmas

The finite electron mass streamlined Darwin field (SDF) model is derived for a quasineutral plasma and contrasted to the SDF model for a nonneutral plasma. Because the Darwin model is used, the Courant numerical stability condition c δt/δx < 1 is avoided. In a quasineutral plasma, the ω peδt < 2 stability condition and the δx/λ De < 1 accuracy condition are avoided by the use of a quasineutral Poisson equation. A fast coupled-elliptic solution technique, found to work extremely well with the nonneutral SDF model, also works well with the quasineutral SDF model. Because of the similarity of the field equations for a nonneutral and a quasineutral plasma, it may be possible to simulate a plasma with both nonneutral and quasineutral regions using a single SDF solver.

An analysis of the Darwin model of approximation to Maxwell’s equations

An analysis of the Darwin model of approximation to Maxwell’s equations

Boundary conditions for the Darwin model

The ambiguity in boundary conditions for the Darwin model is considered in depth. While no single boundary condition seems dictated by physical considerations alone, one set of boundary conditions is presented which has several desirable properties. These include a minimum error principle, numerical tractability, a well-behaved Poynting theorem, and a conservation law for the boundary charge density. The consequences of the boundary conditions are worked out for several simple geometries which are common in computational work.

Initial electron distributions for free electron lasers generated by injector and accelerator simulations

Early free electron laser (FEL) development was guided by simple performance criteria based on the number of undulator periods, electron beam quality, and current. The beam quality (emittance and energy spread) was used to characterize the initial distribution of axial electron velocities along the undulator axis. While the emittance and energy spread determine the overall width of the distribution, its detailed shape is also important. As new accelerators are designed specifically for FEL applications, it becomes important to obtain distribution shape information from simulations that include the electron gun, accelerator, and beam transport in addition to the usual electron/optical interaction in the undulator.The distribution at the entrance to the undulator can be calculated from numerical simulations of the cathode emission, acceleration, and transport of an electron beam. We have modeled the beam generation, from cathode emission up to the energy of the accelerator injector, using an axisymmetric, cylindrical geometry particle simulation (DPC). This code solves the relativistic force equation with fields obtained from Maxwell's equations in the Darwin model. The DPC calculation is run repeatedly varying parameters such as accelerating stress, electrode configuration, and axial magnetic field profile until a good match is obtained for the accelerator. The beam exiting from the injector can be accelerated and transported using the transfer matrix technique with a simple model for accelerating gaps and magnets. Alternatively, acceleration and transport can be simulated with a particle code that solves for the axisymmetric evolution of a slice of an electron beam including possible emittance growth.The phase space obtained from the accelerator can be evaluated for performance using either the simple FEL integral equation method or the more complete FRED simulation code.

Genetic determination of guarding and undertaking in honey-bee colonies

Darwin1 considered the dramatic differences in morphology and behaviour among sterile workers, the basis of colony division of labour in the social insects, to be a greater challenge to his theory of natural selection than the occurrence of worker sterility itself. Darwin's model for the evolution of these worker traits required: (1) heritable variation among workers within colonies; (2) variation in reproductive success among colonies due to different distributions of worker traits; and (3) changes in the distribution of worker traits within colonies due to colony-level selection. The role of genetics in this evolutionary process, unknown to Darwin, has still received little attention2,3. Calderone and Page4 recently demonstrated differences in the pollen-collecting behaviour of honey bees from two artificially selected strains5 co-fostered in wild-type colonies to be a consequence of genotypic differences between workers. These differences were caused by an artificial selection process analogous to that proposed by Darwin. Their study established a foundation for understanding genetic mechanisms underlying the evolution of division of labour but did not demonstrate a genetic basis for division of labour between related members of colonies, the essential element of the darwinian model. Here we report previously undescribed genetic differences in task specialization between related members of Apis mellifera colonies. These results, which support the first requirement of the darwinian model for the evolution of colony organisation, suggest that the genetic structure of an insect society plays a fundamental, and previously unrecognized, role in the division of labour.