Explicit Density Dependence Research Articles

Macroscopic Behaviour in a Two-Species Exclusion Process Via the Method of Matched Asymptotics

We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for the two population densities in the dilute regime, namely a cross-diffusion system of partial differential equations for the two species’ densities. First, our result captures non-trivial interaction terms neglected in the mean-field approach, including a non-diagonal mobility matrix with explicit density dependence. Second, it generalises the rigorous hydrodynamic limit of Quastel (Commun Pure Appl Math 45(6):623–679, 1992), valid for species with equal jump rates and given in terms of a non-explicit self-diffusion coefficient, to the case of unequal rates in the dilute regime. In the equal-rates case, by combining matched asymptotic approximations in the low- and high-density limits, we obtain a cubic polynomial approximation of the self-diffusion coefficient that is numerically accurate for all densities. This cubic approximation agrees extremely well with numerical simulations. It also coincides with the Taylor expansion up to the second-order in the density of the self-diffusion coefficient obtained using a rigorous recursive method.

Relativistic Hartree Bogoliubov model with Density Dependent meson-nucleon couplings

A new improved relativistic mean-field effective interaction with explicit density dependence of the meson-nucleon couplings is proposed. The new effective interaction is called DD-ME2 and it is tested in Relativistic Hartree-Bogoliubov (RHB) and RPA calculations of nuclear ground-states and properties of excited states.

Superdeformation in Pb isotopes with large neutron excess

Covariant Density Functional theory (CDFT) is used to investigate superdeformation in Pb isotopes on the neutron rich side of the periodic table. Energy surfaces and deformation parameters in this region are calculated by solving the constrained Relativistic Hartree Bogoliubov (RHB) equations. We use the parameter set DDME2, which has an explicit density dependence as well in the isoscalar as in the isovector channel together with the finite range pairing force DIS of Gogny. With increasing neutron number we find a characteristic pattern for superdeformed minima in these nuclei.

Neighbourhood effects on plant reproduction: An experimental–analytical framework and its application to the invasive Senecio inaequidens

Abstract Density dependence is of fundamental importance for population and range dynamics. Density‐dependent reproduction of plants arises from competitive and facilitative plant–plant interactions that can be pollination independent or pollination mediated. In small and sparse populations, conspecific density dependence often turns from negative to positive and causes Allee effects. Reproduction may also increase with heterospecific density (community‐level Allee effect), but the underlying mechanisms are poorly understood and the consequences for community dynamics can be complex. Allee effects have crucial consequences for the conservation of declining species, but also the dynamics of range edge populations. In invasive species, Allee effects may slow or stop range expansion. Observational studies in natural plant communities cannot distinguish whether reproduction is limited by pollination‐mediated interactions among plants or by other neighbourhood effects (e.g. competition for abiotic resources). Even experimental pollen supply cannot distinguish whether variation in reproduction is caused by direct density effects or by plant traits correlated with density. Finally, it is unknown over which spatial scales pollination‐mediated interactions occur. To circumvent these problems, we introduce a comprehensive experimental and analytical framework which simultaneously (1) manipulates pollen availability and quality by hand pollination and pollinator exclusion, (2) manipulates neighbourhoods by transplanting target plants, and (3) analyses the effects of con‐ and heterospecific neighbourhoods on reproduction with spatially explicit trait‐based neighbourhood models. Applying this framework to Senecio inaequidens, one of Europe's fastest plant invaders, we found that the seed set was strongly pollen limited. Reproduction had increased by pollinator‐mediated facilitation by both con‐ and heterospecific neighbours which may lead to (community‐level) Allee effects. Pollination‐independent interactions, such as amelioration of abiotic conditions through neighbours, contributed to additional positive neighbour effects. However, these pollination‐independent interactions were weaker than the pollination‐mediated interactions and they occurred over smaller spatial scales. Finally, the strength and direction of neighbourhood effects depended on neighbour traits and thus changed with the trait composition of the neighbourhood. Synthesis. By manipulating both pollen availability and target plant locations within neighbourhoods, we can comprehensively analyse spatially explicit density dependence of plant reproduction. This experimental approach enhances our ability to understand the dynamics of sparse populations and of species geographical ranges.

Ab initio DFT – the seamless connection between WFT and DFT

Orbital-dependent exchange-correlation functionals and potentials play an increasingly important role in Density Functional Theory (DFT). Methods which use explicit orbital-dependent functionals can be viewed as a natural extension to the standard Kohn–Sham (KS) procedure in DFT, that traditionally have used functionals with explicit density-dependence but only implicit orbital-dependence. Ab initio DFT, invented at the Quantum Theory Project, is the method which could define rigorous orbital-dependent exchange-correlation functionals and potentials in the context of KS DFT theory. The local and multiplicative exchange-correlation potentials are derived from a general theoretical framework based on the density condition in KS theory and from coupled-cluster theory and many-body perturbation theory. Ab initio DFT guarantees to converge to the right answer in the correlation and basis set limit, just as does ab initio Wave Function Theory (WFT) and solves in a rigorous way most of the shortcomings of standard density-dependent KS DFT. It is also the route toward understanding the relationships between traditional ab initio WFT and DFT. The Optimized Effective Potential ‘journey’ on the borderline of WFT and DFT was inspired and possible only because of the Quantum Theory Project where we stayed as postdocs in 1999–2001. It seems to us then we were in the right place and at the right time, and certainly with the right people. The QTP scientific melting pot and Sanibel's meetings gave us an excellent possibility to work together, learn and hopefully solve many important scientific problems.

Annual routines of non‐migratory birds: optimal moult strategies

In a periodically changing environment it is important for animals to properly time the major events of their life in order to maximise their lifetime fitness. For a non‐migratory bird the timing of breeding and moult are thought to be the most crucial. We develop a state‐dependent optimal annual routine model that incorporates explicit density dependence in the food supply. In the model the birds’ decisions depend on the time of year, their energy reserves, breeding status, experience, and the quality of two types of feathers (outer and inner primaries). Our model predicts that, under a seasonal environment, feathers with large effects on flight ability, higher abrasion rate and lower energetic cost of moult should be moulted closer to the winter (i.e. later) than those with the opposite attributes. Therefore, we argue that the sequence of moult may be an adaptive response to the problem of optimal timing of moult of differing feathers within the same feather tract. The model also predicts that environmental seasonality greatly affects optimal annual routines. Under high seasonality birds breed first then immediately moult, whereas under low seasonality an alternation occurs between breeding and moulting some of the feathers in one year and having a complete moult but no breeding in the other year. Increasing food abundance has a similar effect.

Superdeformation in Pb isotopes with large neutron excess

Covariant density functional theory (CDFT) is used to investigate superdeformation in Pb isotopes on the neutron rich side of the periodic table. Energy surfaces and deformation parameters in this region are calculated by solving the constrained relativistic Hartree Bogoliubov (RHB) equations. We use the parameter set DD-ME2, which has an explicit density dependence as well in the isoscalar as in the isovector channel together with the finite range pairing force D1S of Gogny. With increasing neutron number, we find a characteristic pattern for superdeformed minima in these nuclei.

New relativistic mean-field interaction with density-dependent meson-nucleon couplings

We adjust a new improved relativistic mean-field effective interaction with explicit density dependence of the meson-nucleon couplings. The effective interaction DD-ME2 is tested in relativistic Hartree-Bogoliubov and quasiparticle random-phase approximation (QRPA) calculations of nuclear ground states and properties of excited states, in calculation of masses, and it is applied to the analysis of very recent data on superheavy nuclei.

Relativistic random-phase approximation with density-dependent meson-nucleon couplings

The matrix equations of the relativistic random-phase approximation (RRPA) are derived for an effective Lagrangian characterized by density-dependent meson-nucleon vertex functions. The explicit density dependence of the meson-nucleon couplings introduces rearrangement terms in the residual two-body interaction, that are essential for a quantitative description of excited states. Illustrative calculations of the isoscalar monopole, isovector dipole and isoscalar quadrupole response of $^{208}$Pb, are performed in the fully self-consistent RRPA framework, based on effective interactions with a phenomenological density dependence adjusted to nuclear matter and ground-state properties of spherical nuclei. The comparison of the RRPA results on multipole giant resonances with experimental data constrains the parameters that characterize the isoscalar and isovector channel of the density-dependent effective interactions.

Multifragmentation calculated with relativistic forces

A saturating hamiltonian is presented in a relativistically covariant formalism. The interaction is described by scalar and vector mesons, with coupling strengths adjusted to the nuclear matter. No explicit density depe ndence is assumed. The hamiltonian is applied in a QMD calculation to determine the fragment distribution in O + Br collision at different energies (50 -- 200 MeV/u) to test the applicability of the model at low energies. The results are compared with experiment and with previous non-relativistic calculations. PACS: 25.70Mn, 25.75.+r