Unexpected patterns of plastic energy allocation in stochastic environments

When environmental conditions vary stochastically, individuals accrue fitness benefits by exhibiting phenotypic plasticity. Such benefits may be counterbalanced by costs of plasticity that increase with the exhibited degree of plasticity. Here we introduce and analyze a general dynamic- programming model describing an individuals optimal energy allocation in a stochastic environment. After maturation, individuals decide repeatedly how to allocate incoming energy between reproduction and maintenance. We investigate the optimal fraction of energy invested into reproduction and the resultant degree of plasticity in dependence on the variability and predictability of the environment. Our analyses reveal unexpected patterns of optimal energy allocation. In environments with very low energy availability, all energy is allocated to reproduction, although this implies that individuals will not survive after reproduction. Above a certain threshold of energy availability, the optimal reproductive investment rapidly decreases to a minimum, and even vanishes entirely when the environment is highly variable. With further improvement of energy availability, optimal reproductive investment gradually increases again, until almost all energy is allocated to reproduction. Costs of plasticity affect this allocation pattern only quantitatively. Our results show that optimal reproductive investment does not increase monotonically with growing energy availability and that small changes in energy availability can lead to major variations in optimal energy allocation. Our results help to unify two apparently opposing predictions from life-history theory, that organisms should increase reproductive investment both with improved environmental conditions and when conditions deteriorate ('terminal investment')

Compact magneto-optical sources of slow atoms

Three different configurations of compact magneto-optical sources of slow Rb atoms(LVIS, 2D(+)-MOT and 2D-MOT) were compared with each other at fixed geometry of cooling laser beams. A precise control of the intensity balances between the four separate transverse cooling laser beams provided a total continuous flux of cold atoms from the LVIS and 2D(+)-MOT sources about 8x10^9 atoms/s at total laser power of 60 mW. The flux was measured directly from the loading rate of a 3D-MOT, placed 34 cm downstream from the sources. Average velocities of the cooled atomic beam for the LVIS and 2D(+)-MOT sources were about 8.5 m/s and 11 m/s respectively. An essential advantage of the compact magneto-optical sources is that their background flux of thermal atoms is two to three orders of the magnitude smaller than the flux of slow atoms.Comment: 12 pages, 10 figures. to be published in Optics Communication

How large can the electron to proton mass ratio be in Particle-In-Cell simulations of unstable systems?

Particle-in-cell (PIC) simulations are widely used as a tool to investigate instabilities that develop between a collisionless plasma and beams of charged particles. However, even on contemporary supercomputers, it is not always possible to resolve the ion dynamics in more than one spatial dimension with such simulations. The ion mass is thus reduced below 1836 electron masses, which can affect the plasma dynamics during the initial exponential growth phase of the instability and during the subsequent nonlinear saturation. The goal of this article is to assess how far the electron to ion mass ratio can be increased, without changing qualitatively the physics. It is first demonstrated that there can be no exact similarity law, which balances a change of the mass ratio with that of another plasma parameter, leaving the physics unchanged. Restricting then the analysis to the linear phase, a criterion allowing to define a maximum ratio is explicated in terms of the hierarchy of the linear unstable modes. The criterion is applied to the case of a relativistic electron beam crossing an unmagnetized electron-ion plasma.Comment: To appear in Physics of Plasma

Intermediate landscape disturbance maximizes metapopulation density

The viability of metapopulations in fragmented landscapes has become a central theme in conservation biology. Landscape fragmentation is increasingly recognized as a dynamical process: in many situations, the quality of local habitats must be expected to undergo continual changes. Here we assess the implications of such recurrent local disturbances for the equilibrium density of metapopulations. Using a spatially explicit lattice model in which the considered metapopulation as well as the underlying landscape pattern change dynamically, we show that equilibrium metapopulation density is maximized at intermediate frequencies of local landscape disturbance. On both sides around this maximum, the metapopulation may go extinct. We show how the position and shape of the intermediate viability maximum is responding to changes in the landscape's overall habitat quality and the population's propensity for local extinction. We interpret our findings in terms of a dual effect of intensified landscape disturbances, which on the one hand exterminate local population and on the other hand enhance a metapopulation's capacity for spreading between habitat clusters

Adaptive dynamics with interaction structure

Evolutionary dynamics depend critically on a population's interaction structure - the pattern of which individuals interact with which others, depending on the state of the population and the environment. Previous research has shown, for example, that cooperative behaviors disfavored in well-mixed populations can be favored when interactions occur only between spatial neighbors or group members. Combining the adaptive dynamics approach with recent advances in evolutionary game theory, we here introduce a general mathematical framework for analyzing the long-term evolution of continuous game strategies for a broad class of evolutionary models, encompassing many varieties of interaction structure. Our main result, the "canonical equation of adaptive dynamics with interaction structure", characterizes expected evolutionary trajectories resulting from any such model, thereby generalizing a central tool of adaptive dynamics theory. Interestingly, the effects of different interaction structures and update rules on evolutionary trajectories are fully captured by just two real numbers associated with each model, which are independent of the considered game. The first, a structure coefficient, quantifies the effects on selection pressures, and thus on the shapes of expected evolutionary trajectories. The second, an effective population size, quantifies the effects on selection responses, and thus on the expected rates of adaptation. Applying our results to two social dilemmas, we show how the range of evolutionarily stable cooperative behaviors systematically varies with a model's structure coefficient

Instability and dynamics of two nonlinearly coupled laser beams in a plasma

We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations.Comment: 18 pages, 8 figure

The evolution of age-dependent plasticity

When organisms encounter environments that are heterogeneous in time, phenotypic plasticity is often favored by selection. The degree of such plasticity can vary during an organism's lifetime, but the factors promoting differential plastic responses at different ages or life stages remain poorly understood. Here we develop and analyze an evolutionary model to investigate how environmental information is optimally collected and translated into phenotypic adjustments at different ages. We demonstrate that plasticity must often be expected to vary with age in a nonmonotonic fashion. Early in life, it is generally optimal to delay phenotypic adjustments until sufficient information has been collected about the state of the environment to warrant a costly phenotypic adjustment. Toward the end of life, phenotypic adjustments are disfavored as well because their beneficial effects can no longer be fully reaped before death. Our analysis clarifies how patterns of age-dependent plasticity are shaped by the interplay of environmental uncertainty, the accuracy of perceived information, and the costs of phenotypic adjustments with life-history determinants such as the relative strengths of fecundity and viability selection experienced by the organism over its lifetime. We conclude by comparing our results with expectations for alternative mechanisms, including developmental constraints, that promote age-dependent plasticity

Contrast Interferometry Using Bose-Einstein Condensates to Measure h/m and the Fine Structure Constant

The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency using an interferometric technique called ``contrast interferometry''. Optical standing wave pulses were used as atom-optical elements to create a symmetric three-path interferometer with a Bose-Einstein condensate. The recoil phase accumulated in different paths was measured using a single-shot detection technique. The scheme allows for additional photon recoils within the interferometer and its symmetry suppresses several random and systematic errors including those from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to $7$ppm precision, using a simple realization of this scheme. Plausible extensions should yield a sufficient precision to bring within reach a ppb-level determination of $h/m$ and the fine structure constant $\alpha$

A Zeeman Slower based on magnetic dipoles

A transverse Zeeman slower composed of an array of compact discrete neodymium magnets is considered. A simple and precise model of such a slower based on magnetic dipoles is developed. The theory of a general Zeeman slower is modified to include spatial nonuniformity of the slowing laser beam intensity due to its convergence and absorption by slowed atoms. The slower needs no high currents or water cooling and the spatial distribution of its magnetic field can be adjusted. In addition the slower provides a possibility to cool the slowed atoms transversally along the whole length of the slower. Such a slower would be ideal for transportable optical atomic clocks and their future applications in space physics.Comment: 17 pages, 9 figure

Engpassmanagement im Europäischen Strommarkt

Funktionierender Wettbewerb auf Strommärkten wird im entscheidenden Maße vom freien Netzzugang bestimmt. Dies gilt sowohl auf nationaler Ebene, vor dem Hintergrund eines europäischen Strombinnenmarktes aber auch für grenzüberschreitende Übertragungsleitungen. Deren Kapazität allerdings ist beschränkt, so dass es einer effizienten Zuteilung bedarf, die auch international für eine Stromversorgung durch die günstigsten Kraftwerke sorgt. Die Arbeit überprüft nun, inwieweit die in der europäischen Stromhandelsverordnung vorgesehenen Allokationsmechanismen geeignet sind, dieses zu erreichen und identifiziert sowohl qualitativ als auch quantitativ anhand eines optionstheoretischen Ansatzes mögliche Gründe für eine Zielverfehlung