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We discuss the failure of the Markov approximation in the description of atom-surface fluctuation-induced interactions, both in equilibrium (Casimir-Polder forces) and out of equilibrium (quantum friction). Using general theoretical arguments, we show that the Markov approximation can lead to erroneous predictions of such phenomena with regard to both strength and functional dependencies on system parameters. In particular, we show that the long-time power-law tails of two-time dipole correlations and their corresponding low-frequency behavior, neglected in the Markovian limit, affect the prediction of the force. Our findings highlight the importance of non-Markovian effects in dispersion interactions.
We present an optically induced remanent photostriction in BiFeO3, resulting from the photovoltaic effect, which is used to modify the ferromagnetism of Ni film in a hybrid BiFeO3/Ni structure. The 75% change in coercivity in the Ni film is achieved via optical and nonvolatile control. This photoferromagnetic effect can be reversed by static or ac electric depolarization of BiFeO3. Hence, the strain dependent changes in magnetic properties are written optically, and erased electrically. Light-mediated straintronics is therefore a possible approach for low-power multistate control of magnetic elements relevant for memory and spintronic applications.
Context. Quasi-stellar objects (quasars) located behind nearby galaxies provide an excellent absolute reference system for astrometric studies, but they are difficult to identify because of fore-and background contamination. Deep wide-field, high angular resolution surveys spanning the entire area of nearby galaxies are needed to obtain a complete census of such quasars. Aims. We embarked on a program to expand the quasar reference system behind the Large and the Small Magellanic Clouds, the Magellanic Bridge, and the Magellanic Stream that connects the Clouds with the Milky Way. Methods. Hundreds of quasar candidates were selected based on their near-infrared colors and variability properties from the ongoing public ESO VISTA Magellanic Clouds survey. A subset of 49 objects was followed up with optical spectroscopy. Results. We confirmed the quasar nature of 37 objects (34 new identifications): four are low redshift objects, three are probably stars, and the remaining three lack prominent spectral features for a secure classification. The bona fide quasars, identified from their broad emisison lines, are located as follows: 10 behind the LMC, 13 behind the SMC, and 14 behind the Bridge. The quasars span a redshift range from z similar to 0.5 to z similar to 4.1. Conclusions. Upon completion the VMC survey is expected to yield a total of similar to 1500 quasars with Y < 19.32 mag, J < 19.09 mag, and K-s < 18.04 mag.
We investigate the role of interatomic interactions when a Bose gas, in a double-well potential with a finite tunneling probability (a 'Bose–Josephson junction'), is exposed to external noise. We examine the rate of decoherence of a system initially in its ground state with equal probability amplitudes in both sites. The noise may induce two kinds of effects: firstly, random shifts in the relative phase or number difference between the two wells and secondly, loss of atoms from the trap. The effects of induced phase fluctuations are mitigated by atom–atom interactions and tunneling, such that the dephasing rate may be suppressed by half its single-atom value. Random fluctuations may also be induced in the population difference between the wells, in which case atom–atom interactions considerably enhance the decoherence rate. A similar scenario is predicted for the case of atom loss, even if the loss rates from the two sites are equal. We find that if the initial state is number-squeezed due to interactions, then the loss process induces population fluctuations that reduce the coherence across the junction. We examine the parameters relevant for these effects in a typical atom chip device, using a simple model of the trapping potential, experimental data, and the theory of magnetic field fluctuations near metallic conductors. These results provide a framework for mapping the dynamical range of barriers engineered for specific applications and set the stage for more complex atom circuits ('atomtronics').
Biomembranes are exceptionally crowded with proteins with typical protein-to-lipid ratios being around 1:50 - 1:100. Protein crowding has a decisive role in lateral membrane dynamics as shown by recent experimental and computational studies that have reported anomalous lateral diffusion of phospholipids and membrane proteins in crowded lipid membranes. Based on extensive simulations and stochastic modeling of the simulated trajectories, we here investigate in detail how increasing crowding by membrane proteins reshapes the stochastic characteristics of the anomalous lateral diffusion in lipid membranes. We observe that correlated Gaussian processes of the fractional Langevin equation type, identified as the stochastic mechanism behind lipid motion in noncrowded bilayer, no longer adequately describe the lipid and protein motion in crowded but otherwise identical membranes. It turns out that protein crowding gives rise to a multifractal, non-Gaussian, and spatiotemporally heterogeneous anomalous lateral diffusion on time scales from nanoseconds to, at least, tens of microseconds. Our investigation strongly suggests that the macromolecular complexity and spatiotemporal membrane heterogeneity in cellular membranes play critical roles in determining the stochastic nature of the lateral diffusion and, consequently, the associated dynamic phenomena within membranes. Clarifying the exact stochastic mechanism for various kinds of biological membranes is an important step towards a quantitative understanding of numerous intramembrane dynamic phenomena.
We present a detailed analysis of the kinematics of the Galactic globular cluster NGC 6397 based on more than similar to 18 000 spectra obtained with the novel integral field spectrograph MUSE. While NGC 6397 is often considered a core collapse cluster, our analysis suggests a flattening of the surface brightness profile at the smallest radii. Although it is among the nearest globular clusters, the low velocity dispersion of NGC 6397 of < 5 km s(-1) imposes heavy demands on the quality of the kinematical data. We show that despite its limited spectral resolution, MUSE reaches an accuracy of 1 km s(-1) in the analysis of stellar spectra. We find slight evidence for a rotational component in the cluster and the velocity dispersion profile that we obtain shows a mild central cusp. To investigate the nature of this feature, we calculate spherical Jeans models and compare these models to our kinematical data. This comparison shows that if a constant mass-to-light ratio is assumed, the addition of an intermediate-mass black hole with a mass of 600 M-circle dot brings the model predictions into agreement with our data, and therefore could be at the origin of the velocity dispersion profile. We further investigate cases with varying mass-to-light ratios and find that a compact dark stellar component can also explain our observations. However, such a component would closely resemble the black hole from the constant mass-to-light ratio models as this component must be confined to the central similar to 5 ' of the cluster and must have a similar mass. Independent constraints on the distribution of stellar remnants in the cluster or kinematic measurements at the highest possible spatial resolution should be able to distinguish the two alternatives.
Renormalized emissivity maps of Themis Regio at the three surface windows are determined from 64 measurement repetitions. Retrieval errors are estimated by a statistical evaluation of maps derived from various disjoint selections of spectra and using different assumptions on the interfering parameters. Double standard deviation errors for the three surface windows amount to 3%, 8%, and 4%, respectively, allowing geologic interpretation. A comparison to results from an earlier error analysis based on synthetic spectra shows that unconsidered time variations of interfering atmospheric parameters are a major error source. Spatial variations of the 1.02 mu m surface emissivity of 20% that correspond to the difference between unweathered granitic and basaltic rocks would be easily detectable, but such variations are ruled out for the studied target area. Emissivity anomalies of up to 8% are detected at both 1.02 and 1.18 mu m. At present sensitivity, no anomalies are identified at 1.10 mu m, but anomalies exceeding the determined error level can be excluded. With single standard deviation significance, all three maps show interesting spatial emissivity variations. (C) 2015 Elsevier Inc. All rights reserved.
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
During the July 2000 geomagnetic storm, known as the Bastille Day storm, Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX)/Heavy Ion Large Telescope (HILT) observed a strong injection of similar to 1MeV electrons into the slot region (L similar to 2.5) during the storm main phase. Then, during the following month, electrons were clearly seen diffusing inward down to L=2 and forming a pronounced split structure encompassing a narrow, newly formed slot region around L=3. SAMPEX observations are first compared with electron and proton observations on HEO-3 and NOAA-15 to validate that the observed unusual dynamics was not caused by proton contamination of the SAMPEX instrument. The time-dependent 3-D Versatile Electron Radiation Belt (VERB) simulation of 1MeV electron flux evolution is compared with the SAMPEX/HILT observations. The results show that the VERB code predicts overall time evolution of the observed split structure. The simulated split structure is produced by pitch angle scattering into the Earth atmosphere of similar to 1MeV electrons by plasmaspheric hiss.
This paper describes a strategy for preparing photosensitive polymeric grafts on flat solid surfaces by loading diblock-copolymer or homopolymer brushes with cationic azobenzene-containing surfactants. In contrast to previous work, we utilize photosensitive surfactants that bear positively-charged polyamine head groups whose charge varies between 1(+) and 3(+). Poly(methylmethacrylate-b-methacrylic acid) (PMMA-b-PMAA) brushes were prepared by employing atom transfer radical polymerization, where the bottom poly(methyl methacrylate) block was grown first followed by the synthesis of t-butyl methacrylate block that after de-protection yielded poly(methacrylic acid). We used PMMA-b-PMAA brushes with constant grafting density and length of the PMMA block, and three different lengths of the PMAA block. The azobenzene-based surfactants attached only to the PMAA block. The degree of binding (i.e., the number of surfactant molecules per binding site on the brush backbone) of the surfactants to the brush depends strongly on the valence of the surfactant head-group; within the brushes the concentration of the surfactant carrying unit charge is larger than that of multivalent surfactants. We detect pronounced response of the brush topography on irradiation with UV interference pattern even at very low degree of binding (as small as 0.08) of multi-valence surfactant. Areas on the sample that receive the highest UV dose exhibit chain scission. By removing the ruptured chains from the substrate via good solvent, one uncovers a surface topographical relief grating, whose spatial arrangement follows the intensity distribution of the UV light on the sample during irradiation. Due to strong coupling of the multi-valence surfactants to the polymer brush, it was possible in some cases to completely remove the polyelectrolyte block from the PMMA layer. The application of multi-valence azobenzene surfactants for triggering brush photosensitive has important advantage over usage of surfactant with unit charge because relative to single-valence surfactants much lower concentrations of the multivalent surfactant are needed to achieve comparable response upon UV irradiation. (C) 2016 Elsevier Ltd. All rights reserved.
We investigate light-induced changes in thickness and roughness of photosensitive polymer brushes containing azobenzene cationic surfactants by atomic force microscopy (AFM) in real time during light irradiation. Because the cis-state of azobenzene unit requires more free volume than its trans counterpart, the UV light-induced expansion of polymer thin films associated with the trans-to-cis isomerism of azobenzene groups is expected to occur. This phenomenon is well documented in physisorbed polymer films containing azobenzene groups. In contrast, photosensitive polymer brushes show a decrease in thickness under UV irradiation. We have found that the azobenzene surfactants in their trans-state form aggregates within the brush. Under irradiation, the surfactants undergo photoisomerization to the cis-state, which is more hydrophilic. As a consequence, the aggregates within the brush are disrupted, and the polymer brush contracts. When subsequently irradiated with blue light the polymer brush thickness returns back to its initial value. This behavior is related to isomerization of the surfactant to the more hydrophobic trans-state and subsequent formation of surfactant aggregates within the polymer brush. The photomechanical function of the dry polymer brush, i.e., contraction and expansion, was found to be reversible with repeated irradiation cycles and requires only a few seconds for switching. In addition to the thickness change, the roughness of the brush also changes reversibly between a few Angstroms (blue light) and several nanometers (UV light). Photosensitive polymer brushes represent smart films with light responsive thickness and roughness that could be used for generating dynamic fluctuating surfaces, the function of which can be turned on and off in a controllable manner on a nanometer length scale.
Using Causal Effect Networks to Analyze Different Arctic Drivers of Midlatitude Winter Circulation
(2016)
In recent years, the Northern Hemisphere midlatitudes have suffered from severe winters like the extreme 2012/13 winter in the eastern United States. These cold spells were linked to a meandering upper-tropospheric jet stream pattern and a negative Arctic Oscillation index (AO). However, the nature of the drivers behind these circulation patterns remains controversial. Various studies have proposed different mechanisms related to changes in the Arctic, most of them related to a reduction in sea ice concentrations or increasing Eurasian snow cover. Here, a novel type of time series analysis, called causal effect networks (CEN), based on graphical models is introduced to assess causal relationships and their time delays between different processes. The effect of different Arctic actors on winter circulation on weekly to monthly time scales is studied, and robust network patterns are found. Barents and Kara sea ice concentrations are detected to be important external drivers of the midlatitude circulation, influencing winter AO via tropospheric mechanisms and through processes involving the stratosphere. Eurasia snow cover is also detected to have a causal effect on sea level pressure in Asia, but its exact role on AO remains unclear. The CEN approach presented in this study overcomes some difficulties in interpreting correlation analyses, complements model experiments for testing hypotheses involving teleconnections, and can be used to assess their validity. The findings confirm that sea ice concentrations in autumn in the Barents and Kara Seas are an important driver of winter circulation in the midlatitudes.
X-ray free electron lasers (XFELs) enable unprecedented new ways to study the electronic structure and dynamics of transition metal systems. L-edge absorption spectroscopy is a powerful technique for such studies and the feasibility of this method at XFELs for solutions and solids has been demonstrated. However, the required x-ray bandwidth is an order of magnitude narrower than that of self-amplified spontaneous emission (SASE), and additional monochromatization is needed. Here we compare L-edge x-ray absorption spectroscopy (XAS) of a prototypical transition metal system based on monochromatizing the SASE radiation of the linac coherent light source (LCLS) with a new technique based on self-seeding of LCLS. We demonstrate how L-edge XAS can be performed using the self-seeding scheme without the need of an additional beam line monochromator. We show how the spectral shape and pulse energy depend on the undulator setup and how this affects the x-ray spectroscopy measurements. (C) 2016 Optical Society of America
Since more than 15 years, the Cluster mission passes through Earth's radiation belts at least once every 2 days for several hours, measuring the electron intensity at energies from 30 to 400 keV. These data have previously been considered not usable due to contamination caused by penetrating energetic particles (protons at >100 keV and electrons at >400 keV). In this study, we assess the level of distortion of energetic electron spectra from the Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector, determining the efficiency of its shielding. We base our assessment on the analysis of experimental data and a radiation transport code (Geant4). In simulations, we use the incident particle energy distribution of the AE9/AP9 radiation belt models. We identify the Roederer L values, L⋆, and energy channels that should be used with caution: at 3≤L⋆≤4, all energy channels (40–400 keV) are contaminated by protons (≃230 to 630 keV and >600 MeV); at L⋆≃1 and 4–6, the energy channels at 95–400 keV are contaminated by high-energy electrons (>400 keV). Comparison of the data with electron and proton observations from RBSP/MagEIS indicates that the subtraction of proton fluxes at energies ≃ 230–630 keV from the IES electron data adequately removes the proton contamination. We demonstrate the usefulness of the corrected data for scientific applications.
We study the properties of ageing Scher-Montroll transport in terms of a biased subdiffusive continuous time random walk in which the waiting times between consecutive jumps of the charge carriers are distributed according to the power law probability with . As we show, the dynamical properties of the Scher-Montroll transport depend on the ageing time span between the initial preparation of the system and the start of the observation. The Scher-Montroll transport theory was originally shown to describe the photocurrent in amorphous solids in the presence of an external electric field, but it has since been used in many other fields of physical sciences, in particular also in the geophysical context for the description of the transport of tracer particles in subsurface aquifers. In the absence of ageing () the photocurrent of the classical Scher-Montroll model or the breakthrough curves in the groundwater context exhibit a crossover between two power law regimes in time with the scaling exponents and . In the presence of ageing a new power law regime and an initial plateau regime of the current emerge. We derive the different power law regimes and crossover times of the ageing Scher-Montroll transport and show excellent agreement with simulations of the process. Experimental data of ageing Scher-Montroll transport in polymeric semiconductors are shown to agree well with the predictions of our theory.
In the first part of my work I have investigated the ageing properties of the first passage time distributions in a one-dimensional subdiffusive continuous time random walk with power law distributed waiting times of the form $\psi(\tau) \sim \tau^{-1-\alpha}$ with $0<\alpha<1$ and $1<\alpha<2$. The age or ageing time $t_a$ is the time span from the start of the stochastic process to the start of the observation of this process (at $t=0$). I have calculated the results for a single target and two targets, also including the biased case, where the walker is driven towards the boundary by a constant force. I have furthermore refined the previously derived results for the non-ageing case and investigated the changes that occur when the walk is performed in a discrete quenched energy landscape, where the waiting times are fixed for every site. The results include the exact Laplace space densities and infinite (converging) series as exact results in the time space. The main results are the dominating long time power law behavior regimes, which depend on the ageing time. For the case of unbiased subdiffusion ($\alpha < 1$) in the presence of one target, I find three different dominant terms for ranges of $t$ separated by $t_a$ and another crossover time $t^{\star}$, which depends on $t_a$ as well as on the anomalous exponent $\alpha$ and the anomalous diffusion coefficient $K_{\alpha}$. In all three regimes ($t \ll t_a$, $t_a \ll t \ll t^{\star}$, $t \gg t^{\star}$) one finds power law decay with exponents depending on $\alpha$. The middle regime only exists for $t_a \ll t^{\star}$. The dominant terms in the first two regimes (ageing regimes) come from the probability distribution of the forward waiting time, the time one has to wait for the stochastic process to make the first step during the observation. When the observation time is larger than the second crossover time $t^{\star}$, the first passage time density does not show ageing and the non-ageing first passage time dominates. The power law exponents in the respective regimes are $-\alpha$ for strong ageing, $-1-\alpha$ in the intermediate regime, and $-1-\alpha/2$ in the final non-ageing regime. A similar split into three regimes can be found for $1<\alpha<2$, only with a different second crossover time $t^*$. In this regime the diffusion is normal but also age-dependent. For the diffusion in quenched energy landscapes one cannot detect ageing. The first passage time density shows a quenched power law $^\sim t^{-(1+2\alpha)/(1+\alpha)}$. For diffusion between two target sites and the biased diffusion towards a target only two scaling regimes emerge, separated by the ageing time. In the ageing case $t \ll t_a$ the forward waiting time is again dominant with power law exponent $-\alpha$, while the non-ageing power law $-1-\alpha$ is found for all times $t \gg t_a$. An intermediate regime does not exist. The bias and the confinement have similar effects on the first passage time density. For quenched diffusion, the biased case is interesting, as the bias reduces correlations due to revisiting of the same waiting time. As a result, CTRW like behavior is observed, including ageing. Extensive computer simulations support my findings.
The second part of my research was done on the subject of ageing Scher-Montroll transport, which is in parts closely related to the first passage densities. It explains the electrical current in an amorphous material. I have investigated the effect of the width of a given initial distribution of charge carriers on the transport coefficients as well as the ageing effect on the emerging power law regimes and a constant initial regime. While a spread out initial distribution has only little impact on the Scher-Montroll current, ageing alters the behavior drastically. Instead of the two classical power laws one finds four current regimes, up to three of which can appear in a single experiment. The dominant power laws differ for $t \ll t_a, t_c$, $t_a \ll t \ll t_c$, $t_c \ll t \ll t_a$, and $t \gg t_a,t_c$. Here, $t_c$ is the crossover time of the non-aged Scher-Montroll current. For strongly aged systems one can observe a constant current in the first regime while the others are dominated by decaying power laws with exponents $\alpha -1$, $-\alpha$, and $-1-\alpha$. The ageing regimes are the 1st and 3rd one, while the classical regimes are the 2nd and the 4th. I have verified the theory using numerical integration of the exact integrals and applied the new results to experimental data.
In the third part I considered a single file of subdiffusing particles in an energy landscape. Every occupied site of the landscape acts as a boundary, from which a particle is immediately reflected to its previous site, if it tries to jump there. I have analysed the effects single-file diffusion a quenched landscape compared to an annealed landscape and I have related these results to the number of steps and related quantities. The diffusion changes from ultraslow logarithmic diffusion in the annealed or CTRW case to subdiffusion with an anomalous exponent $\alpha/(1+\alpha)$ in the quenched landscape. The behavior is caused by the forward waiting time, which changes drastically from the quenched to the annealed case. Single-file effects in the quenched landscape are even more complicated to consider in the ensemble average, since the diffusion in individual landscapes shows extremely diverse behavior. Extensive simulations support my theoretical arguments, which consider mainly the long time evolution of the mean square displacement of a bulk particle.
Air pollution is the number one environmental cause of premature deaths in Europe. Despite extensive regulations, air pollution remains a challenge, especially in urban areas. For studying summertime air quality in the Berlin–Brandenburg region of Germany, the Weather Research and Forecasting Model with Chemistry (WRF-Chem) is set up and evaluated against meteorological and air quality observations from monitoring stations as well as from a field campaign conducted in 2014. The objective is to assess which resolution and level of detail in the input data is needed for simulating urban background air pollutant concentrations and their spatial distribution in the Berlin–Brandenburg area. The model setup includes three nested domains with horizontal resolutions of 15, 3 and 1 km and anthropogenic emissions from the TNO-MACC III inventory. We use RADM2 chemistry and the MADE/SORGAM aerosol scheme. Three sensitivity simulations are conducted updating input parameters to the single-layer urban canopy model based on structural data for Berlin, specifying land use classes on a sub-grid scale (mosaic option) and downscaling the original emissions to a resolution of ca. 1 km × 1 km for Berlin based on proxy data including traffic density and population density. The results show that the model simulates meteorology well, though urban 2 m temperature and urban wind speeds are biased high and nighttime mixing layer height is biased low in the base run with the settings described above. We show that the simulation of urban meteorology can be improved when specifying the input parameters to the urban model, and to a lesser extent when using the mosaic option. On average, ozone is simulated reasonably well, but maximum daily 8 h mean concentrations are underestimated, which is consistent with the results from previous modelling studies using the RADM2 chemical mechanism. Particulate matter is underestimated, which is partly due to an underestimation of secondary organic aerosols. NOx (NO + NO2) concentrations are simulated reasonably well on average, but nighttime concentrations are overestimated due to the model's underestimation of the mixing layer height, and urban daytime concentrations are underestimated. The daytime underestimation is improved when using downscaled, and thus locally higher emissions, suggesting that part of this bias is due to deficiencies in the emission input data and their resolution. The results further demonstrate that a horizontal resolution of 3 km improves the results and spatial representativeness of the model compared to a horizontal resolution of 15 km. With the input data (land use classes, emissions) at the level of detail of the base run of this study, we find that a horizontal resolution of 1 km does not improve the results compared to a resolution of 3 km. However, our results suggest that a 1 km horizontal model resolution could enable a detailed simulation of local pollution patterns in the Berlin–Brandenburg region if the urban land use classes, together with the respective input parameters to the urban canopy model, are specified with a higher level of detail and if urban emissions of higher spatial resolution are used.
The electric-field noise above a layered structure composed of a planar metal electrode covered by a thin dielectric is evaluated and it is found that the dielectric film considerably increases the noise level, in proportion to its thickness. Importantly, even a thin (mono) layer of a low-loss dielectric can enhance the noise level by several orders of magnitude compared to the noise above a bare metal. Close to this layered surface, the power spectral density of the electric field varies with the inverse fourth power of the distance to the surface, rather than with the inverse square, as it would above a bare metal surface. Furthermore, compared to a clean metal, where the noise spectrum does not vary with frequency (in the radio-wave and microwave bands), the dielectric layer can generate electricfield noise which scales in inverse proportion to the frequency. For various realistic scenarios, the noise levels predicted from this model are comparable to those observed in trapped-ion experiments. Thus, these findings are of particular importance for the understanding and mitigation of unwanted heating and decoherence in miniaturized ion traps.
Anti-Stokes resonant x-ray Raman scattering for atom specific and excited state selective dynamics
(2016)
Ultrafast electronic and structural dynamics of matter govern rate and selectivity of chemical reactions, as well as phase transitions and efficient switching in functional materials. Since x-rays determine electronic and structural properties with elemental, chemical, orbital and magnetic selectivity, short pulse x-ray sources have become central enablers of ultrafast science. Despite of these strengths, ultrafast x-rays have been poor at picking up excited state moieties from the unexcited ones. With time-resolved anti-Stokes resonant x-ray Raman scattering (AS-RXRS) performed at the LCLS, and ab initio theory we establish background free excited state selectivity in addition to the elemental, chemical, orbital and magnetic selectivity of x-rays. This unparalleled selectivity extracts low concentration excited state species along the pathway of photo induced ligand exchange of Fe(CO)(5) in ethanol. Conceptually a full theoretical treatment of all accessible insights to excited state dynamics with AS-RXRS with transform-limited x-ray pulses is given-which will be covered experimentally by upcoming transform-limited x-ray sources.