Small Inhomogeneities Research Articles

Are small-scale substructures a universal property of galaxy haloes? The case of the giant elliptical NGC 5128★

We present an analysis of the spatial and chemical substructures in a remote halo field in the nearby giant elliptical galaxy Centaurus A (NGC 5128), situated ∼38 kpc from the centre of the galaxy. The observations were taken with the Advanced Camera for Surveys instrument onboard the Hubble Space Telescope, and reach down to the horizontal branch. In this relatively small 3.8 x 3.8 kpc 2 field, after correcting for Poisson noise, we do not find any statistically strong evidence for the presence of small-scale substructures in the stellar spatial distribution on scales ≳ 100 pc. However, we do detect the presence of significant small spatial-scale inhomogeneities in the stellar median metallicity over the surveyed field. We argue that these localized chemical substructures could be associated with not fully mixed debris from the disruption of low-mass systems. NGC 5128 joins the ranks of the late-type spiral galaxies the Milky Way, for which the stellar halo appears to be dominated by small-scale spatial substructures, and NGC 891, where localized metallicity variations have been detected in the inner extraplanar regions. This suggests that the presence of small-scale substructures may be a generic property of stellar haloes of large galaxies.

Double-Kasner spacetime: Peculiar velocities and cosmic jets

In dynamic spacetimes in which asymmetric gravitational collapse/expansion is taking place, the timelike geodesic equation appears to exhibit an interesting property: Relative to the collapsing configuration, free test particles undergo gravitational ``acceleration'' and form a double-jet configuration parallel to the axis of collapse. We illustrate this aspect of peculiar motion in simple spatially homogeneous cosmological models such as the Kasner spacetime. To estimate the effect of spatial inhomogeneities on cosmic jets, timelike geodesics in the Ricci-flat double-Kasner spacetime are studied in detail. While spatial inhomogeneities can significantly modify the structure of cosmic jets, we find that under favorable conditions the double-jet pattern can initially persist over a finite period of time for sufficiently small inhomogeneities.

Homogenising time series: beliefs, dogmas and facts

Abstract. In the recent decades various homogenisation methods have been developed, but the real effects of their application on time series are still not known sufficiently. The ongoing COST action HOME (COST ES0601) is devoted to reveal the real impacts of homogenisation methods more detailed and with higher confidence than earlier. As a part of the COST activity, a benchmark dataset was built whose characteristics approach well the characteristics of real networks of observed time series. This dataset offers much better opportunity than ever before to test the wide variety of homogenisation methods, and analyse the real effects of selected theoretical recommendations. Empirical results show that real observed time series usually include several inhomogeneities of different sizes. Small inhomogeneities often have similar statistical characteristics than natural changes caused by climatic variability, thus the pure application of the classic theory that change-points of observed time series can be found and corrected one-by-one is impossible. However, after homogenisation the linear trends, seasonal changes and long-term fluctuations of time series are usually much closer to the reality than in raw time series. Some problems around detecting multiple structures of inhomogeneities, as well as that of time series comparisons within homogenisation procedures are discussed briefly in the study.

Signal detectability in diffusive media using phased arrays in conjunction with detector arrays

We investigate Hotelling observer performance (i.e., signal detectability) of a phased array system for tasks of detecting small inhomogeneities and distinguishing adjacent abnormalities in uniform diffusive media. Unlike conventional phased array systems where a single detector is located on the interface between two sources, we consider a detector array, such as a CCD, on a phantom exit surface for calculating the Hotelling observer detectability. The signal detectability for adjacent small abnormalities (2 mm displacement) for the CCD-based phased array is related to the resolution of reconstructed images. Simulations show that acquiring high-dimensional data from a detector array in a phased array system dramatically improves the detectability for both tasks when compared to conventional single detector measurements, especially at low modulation frequencies. It is also observed in all studied cases that there exists the modulation frequency optimizing CCD-based phased array systems, where detectability for both tasks is consistently high. These results imply that the CCD-based phased array has the potential to achieve high resolution and signal detectability in tomographic diffusive imaging while operating at a very low modulation frequency. The effect of other configuration parameters, such as a detector pixel size, on the observer performance is also discussed.

Concentric Slitting of a Ring-Shaped Bulk Superconductor for a Reduction in Circumferential Inhomogeneity of the Trapped Magnetic Field

Magnetic field trapped in a superconducting bulk magnet has non-negligible inhomogeneity resulting from nonuniform superconducting properties. Counteracting the inhomogeneity is one of the challenging problems in applications of bulk magnets to NMR and MRI. In this study, we fabricated a bulk magnet with concentric slits for trapping a field with reduced circumferential inhomogeneity. A GdBaCuO superconductor, 60 mm in outer diameter, was sliced with a thickness of 2 mm. Three equally-spaced concentric slits were formed using a sandblasting technique. The magnets were cooled with liquid nitrogen in an external field of 600 mT. The z-component of trapped field was measured along circular trajectories. The magnet with slits exhibited smaller inhomogeneities of fields compared with an equal-sized one without slit. On a trajectory 30 mm in diameter, the field inhomogeneities of magnets with and without slits were 7% and 11%, respectively. On a 13-mm trajectory, the slits resulted in the reduction of inhomogeneity from 0.9% to 0.3%.

The importance of tissue segmentation for dose calculations for kilovoltage radiation therapy

The aim of this work was to evaluate the effect of tissue segmentation on the accuracy of Monte Carlo (MC) dose calculations for kilovoltage radiation therapy, which are commonly used in preclinical radiotherapy studies and are also being revisited as a clinical treatment modality. The feasibility of tissue segmentation routinely done on the basis of differences in tissue mass densities was studied and a new segmentation scheme based on differences in effective atomic numbers was developed. MC dose calculations in a cylindrical mouse phantom with small cylindrical inhomogeneities consisting of 34 ICRU-44 tissues were performed using the EGSnrc/BEAMnrc and DOSXYZnrc codes. The dose to tissue was calculated for five different kilovoltage beams currently used in small animal radiotherapy: a microCT 120 kV beam, two 225 kV beams filtered with either 4 mm of Al or 0.5 mm of Cu, a heavily filtered 320 kV beam, and a 192Ir beam. The mean doses to the 34 ICRU-44 tissues as a function of tissue mass density and effective atomic number and beam energy were studied. A treatment plan for an orthotopic lung tumor model was created, and the dose distribution was calculated for three tissue segmentation schemes using 4, 8, and 39 tissue bins to assess the significance of the simulation results for kilovoltage radiotherapy. In our model, incorrect assignment of adipose tissue to muscle caused dose calculation differences of 27%, 13%, and 7% for the 120 kV beam and the 225 kV beams filtered with 4 mm Al and 0.5 mm Cu, respectively. For the heavily filtered 320 kV beam and a 192Ir source, potential dose calculation differences due to tissue mis-assignment were below 4%. There was no clear relationship between the dose to tissue and its mass density for x-ray beams generated by tube potentials equal or less than 225 kV. A second order polynomial fit approximated well the absorbed dose to tissue as a function of effective atomic number for these beams. In the mouse study, the 120 kV beam dose to bone was overestimated by 100% and underestimated by 10% for the 4 and 8-tissue segmentation schemes compared to the 39-tissue segmentation scheme, respectively. Dose to adipose tissue was overestimated by 30% and underestimated by 10%, respectively. In general, organ at risk (OAR) doses were overestimated in the 4-tissue and the 8-tissue segmentation schemes compared to the 39-tissue segmentation. Tissue segmentation was shown to be a key parameter for dose calculations with kilovoltage beams used in small animal radiotherapy when an x-ray tube with a potential < or = 225 kV is used as a source. A new tissue segmentation scheme with 39 tissues based on effective number differences derived from mass density differences has been implemented.

Dosimetric impact of density variations in Solid Water 457 water‐equivalent slabs

The purpose of this study was to determine the dosimetric impact of density variations observed in water‐equivalent solid slabs. Measurements were performed using two 30 cm×30 cm water‐equivalent slabs, one being 4 cm think and the other 5 cm thick. The location and extent of density variations were determined by computed tomography (CT) scans. Additional imaging measurements were made with an amorphous silicon megavoltage portal imaging device and an ultrasound unit. Dosimetric measurements were conducted with a 2D ion chamber array, and a scanned diode in water. Additional measurements and calculations were made of small rectilinear void inhomogeneities formed with water‐equivalent slabs, using a 2D ion chamber array and the convolution superposition algorithm. Two general types of density variation features were observed on CT images: 1) regions of many centimeters across, but typically only a few millimeters thick, with electron densities a few percent lower than the bulk material, and 2) cylindrical regions roughly 0.2 cm in diameter and up to 20 cm long with electron densities up to 5% lower than the surrounding material. The density variations were not visible on kilovoltage, megavoltage or ultrasound images. The dosimetric impact of the density variations were not detectable to within 0.1% using the 2D ion chamber array or the scanning photon diode at distances 0.4 cm to 2 cm beyond the features. High‐resolution dosimetric calculations using the convolution–superposition algorithm with density corrections enabled on CT‐based datasets showed no discernable dosimetric impact. Calculations and measurements on simulated voids place the upper limit on possible dosimetric variations from observed density variations at much less than 0.6%. CT imaging of water‐equivalent slabs may reveal density variations which are otherwise unobserved with kV, MV, or ultrasound imaging. No dosimetric impact from these features was measureable with an ion chamber array or scanned photon diode. Consequently, they were determined to be acceptable for all clinical use.PACS numbers: 87.55.km, 87.55.Qr

New framework for analyzing the effects of small scale inhomogeneities in cosmology

We develop a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our approach is an adaptation of Burnett's formulation of the shortwave approximation, which we generalize to analyze the effects of matter inhomogeneities as well as gravitational radiation. Our framework requires the metric to be close to a background metric, but allows arbitrarily large stress-energy fluctuations on small scales. We prove that, within our framework, if the matter stress-energy tensor satisfies the weak energy condition (i.e., positivity of energy density in all frames), then the only effect that small-scale inhomogeneities can have on the dynamics of the background metric is to provide an effective stress-energy tensor that is traceless and has positive energy density---corresponding to the presence of gravitational radiation. In particular, nonlinear effects produced by small-scale inhomogeneities cannot mimic the effects of dark energy. We also develop perturbation theory off of the background metric. We derive an equation for the long-wavelength part of the leading order deviation of the metric from the background metric, which contains the usual terms occurring in linearized perturbation theory plus additional contributions from the small-scale inhomogeneities. Under various assumptions concerning the absence of gravitational radiation and the nonrelativistic behavior of the matter, we argue that the short-wavelength deviations of the metric from the background metric near a point $x$ should be accurately described by Newtonian gravity, taking into account only the matter lying within a homogeneity length scale of $x$. Finally, we argue that our framework should provide an accurate description of the actual universe.

Lamb-Dip Laser-Induced Fluorescence Spectroscopy for Measuring Magnetic Field in a Plasma

We have developed a Lamb-dip laser-induced fluorescence (LIF) system to precisely measure the local magnetic field strength in a plasma. Utilizing the hole burning effect, we made sharp dips on the LIF spectrum as the frequency markers and accurately determined the Zeeman splitting by reading the frequency interval of the dips. The method is valid even in the conditions where the Doppler broadening of the LIF spectrum is larger than the Zeeman shift. The newly developed LIF system is capable of determining a magnetic field strength on the order of 10-4 T. It has been demonstrated that the Lamb-dip LIF system can successfully reproduce a very small field inhomogeneity in the HYPER-I linear device.

Wave scattering by small bodies and creating materials with a desired refraction coefficient

In this paper the author’s invited plenary talk at the 7-th PACOM (Pan African Congress of Mathematicians), is presented. Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small inhomogeneities, whose physical properties are described by their refraction coefficients. Equations for the effective field in the limiting medium are derived. The limit is considered as the size a of the particles or inhomogeneities tends to zero while their number M(a) tends to infinity. These results are applied to the problem of creating materials with a desired refraction coefficient. For example, the refraction coefficient may have wave-focusing property, or it may have negative refraction, i.e., the group velocity may be directed opposite to the phase velocity. This paper is a review of the author’s results presented in MR2442305 (2009g:78016), MR2354140 (2008g:82123), MR2317263 (2008a:35040), MR2362884 (2008j:78010), and contains new results.

The realistic QCD equation of state in relativistic heavy-ion collisions and the early Universe

The realistic equation of state of strongly interacting matter, that has been successfully applied in the recent hydrodynamic studies of hadron production in relativistic heavy-ion collisions at RHIC, is used in the Friedmann equation to determine the precise time evolution of thermodynamic parameters in the early Universe. A comparison with the results obtained with simple ideal-gas equations of state is made. The realistic equation of state describes a crossover rather than the first-order phase transition between the quark–gluon plasma and hadronic matter. Our numerical calculations show that small inhomogeneities of strongly interacting matter in the early Universe are moderately damped during such crossover.

Gibbs elasticity effect in foam shear flows: a non quasi-static 2D numerical simulation

The origin of the dissipation in liquid foams is not fully understood, especially in the large deformation, large velocity regime. Numerical simulations, now very accurate in the quasi static regime, are still sparse in the dissipative regime, and are all based on restrictive assumptions or very small bubble numbers. Here we present the results obtained with 2D numerical simulations involving 500 bubbles under simple shear, in a non-quasi static regime. The bubble description is kept as simple as possible and the dissipation is assumed to arise from surface tension variations induced by film area variations. This model leads to a steady state stress under simple shear that is well fitted by a Herschel–Bulkley law with an exponent 0.6. We show that small tension dynamical inhomogeneities induce foam structure modifications responsible for the largest part of the stress increase.

Dynamic current localization during turn-off of high-power microgate bipolar switches

The turn-off process of semiconductor switches with distributed microgates in the presence of small embedded technological inhomogeneities of their structure parameters is considered. The process dynamics is studied based on the analytical model of residual plasma displacement and the space charge region dynamics in the base, taking into account ionization in high electric fields. A spatially inhomogeneous switch structure is modeled by two groups of controlled cells with different parameters, i.e., emitter injection efficiencies or carrier lifetimes in n-type bases. Voltage coupling of all cells is complemented by the device interaction with the external circuit. The detrimental effect of current localization at the turn-off stage, which occurs even at a relatively small parameter variance, was studied within the proposed model. The results obtained allow quantitative characterization of the effect of technological inhomogeneities on safe operating area of high-power microgate bipolar switches.

Thermal activation of current in an inhomogeneous Schottky diode with a Gaussian distribution of barrier height

This paper investigates the thermal activation behaviour of current in an inhomogeneous Schottky diode with a Gaussian distribution of barrier height by numerical simulation. The analytical Gaussian distribution model predicted that the I-V-T curves may intersect with the possibility of the negative thermal activation of current, but may be contradictory to the thermionic emission mechanism in a Schottky diode. It shows that the cause of the unphysical phenomenon is related to the incorrect calculation of current across very low barriers. It proposes that junction voltage Vj, excluding the voltage drop across series resistance from the external bias, is a crucial parameter for correct calculation of the current across very low barriers. For correctly employing the thermionic emission model, Vj needs to be smaller than the barrier height ø. With proper scheme of series resistance connection where the condition of Vj > ø is guaranteed, I-V-T curves of an inhomogeneous Schottky diode with a Gaussian distribution of barrier height have been simulated, which demonstrate normal thermal activation. Although the calculated results exclude the intersecting possibility of I-V-T curves with an assumption of temperature-independent series resistance, it shows that the intersecting is possible when the series resistance has a positive temperature coefficient. Finally, the comparison of our numerical and analytical results indicates that the analytical Gaussian distribution model is valid and accurate in analysing I-V-T curves only for small barrier height inhomogeneity.

Emergence of variability in isogenic Escherichia coli populations infected by a filamentous virus.

The spread of epidemics not only depends on the average number of parasites produced per host, but also on the existence of highly infectious individuals. It is widely accepted that infectiousness depends on genetic and environmental determinants. However, even in clonal populations of host and viruses growing in homogeneous conditions, high variability can exist. Here we show that Escherichia coli cells commonly display high differentials in viral burst size, and address the kinetics of emergence of such variability with the non-lytic filamentous virus M13. By single-cell imaging of a virally-encoded fluorescent reporter, we monitor the viral charge distribution in infected bacterial populations at different time following infection. A mathematical model assuming autocatalytic virus replication and inheritance of bacterial growth rates quantitatively reproduces the experimental distributions, demonstrating that deterministic amplification of small host inhomogeneities is a mechanism sufficient to explain large and highly skewed distributions. This mechanism of amplification is general and may occur whenever a parasite has an initial phase of exponential growth within its host. Moreover, it naturally reproduces the shift towards higher virulence when the host is experimenting poor conditions, as observed commonly in host-parasite systems.

Deterministic inhomogeneous inertia ratchets

We study the deterministic dynamics of a periodically driven particle in the underdamped case in a spatially symmetric periodic potential. The system is subjected to a space-dependent friction coefficient, which is similarly periodic as the potential but with a phase difference. We observe that frictional inhomogeneity in a symmetric periodic potential mimics most of the qualitative features of deterministic dynamics in a homogeneous system with an asymmetric periodic potential. We point out the need of averaging over the initial phase of the external drive at small frictional inhomogeneity parameter values or analogously low potential asymmetry regimes in obtaining ratchet current. We also show that at low amplitudes of the drive, where ratchet current is not possible in the deterministic case, noise plays a significant role in realizing ratchet current.

Growth of Aligned MWNT Arrays Using a Micrometer Scale Local-Heater at Low Ambient Temperature

Ambient room temperature growth of aligned multi-walled carbon nanotube arrays on micrometer scale local heaters is demonstrated. High growth rates of up to 8.8 microm per second have been achieved and the growth has been monitored in situ using optical microscopy. The growth starts and ends abruptly over the length of the local heater. The terminal length of the nanotubes shows a clear dependence on growth temperature and small inhomogeneities in temperature across the heater are seen to lead to interesting microstructure of the arrays. The activation energy for growth was seen to be consistent with earlier reports for acetylene growth of nanotubes on iron catalysts.

The effect of a small background inhomogeneity on the asymptotic properties of linear perturbations

General regularities in the evolution of one-dimensional unstable linear perturbations on a weakly inhomogeneous background are studied when, at the initial instant, the perturbations are concentrated in the δ-neighbourhood of a certain point. Times are considered when these perturbations do not fall outside the limits of a certain domain of size l such that δ ≪ l ≪ L, where L is the large characteristic size of the background inhomogeneity. With contain assumptions, the effect of the background inhomogeneity on the asymptotic behaviour of the perturbations at long times is taken into account in a general form. The first corrections to the well known asymptotic relation for the evolution of perturbations on a homogeneous background, that arise because of background inhomogeneity, are obtained using Hamilton's method. An example of the use of the proposed approximate method is considered and the error in the approximation is estimated.

Characterization of inclined GaSb nanopillars by angle resolved Mueller polarimetry

Color in living organisms is primarily generated by two mechanisms: selective absorption by pigments and structural coloration, or a combination of both. In this study, we investigated the coloration of cuticle from the wings (elytra) of the two ground beetle species Carabus auronitens and Carabus auratus. The greenish iridescent color of both species is created by a multilayer structure consisting of periodically alternating layers with different thicknesses and composition which is located in the 1-2 µm thick outermost layer of the cuticle (epicuticle). Illuminated with white light, reflectance spectra in both linear polarisation show an angle-dependent characteristic peak in the blue/green region of the spectrum. Furthermore, the reflected light is polarised linearly. Scattering experiments with laser illumination at 532 nm show diffuse scattering over a larger angular range. The polarisation dependence of the scattered light is consistent with the interpretation of small inhomogeneities as scattering centres in the elytra.

Spectral and angular distribution of light scattered from the elytra of two carabid beetle species

Color in living organisms is primarily generated by two mechanisms: selective absorption by pigments and structural coloration, or a combination of both. In this study, we investigated the coloration of cuticle from the wings (elytra) of the two ground beetle species Carabus auronitens and Carabus auratus. The greenish iridescent color of both species is created by a multilayer structure consisting of periodically alternating layers with different thicknesses and composition which is located in the 1-2 µm thick outermost layer of the cuticle (epicuticle). Illuminated with white light, reflectance spectra in both linear polarisation show an angle-dependent characteristic peak in the blue/green region of the spectrum. Furthermore, the reflected light is polarised linearly. Scattering experiments with laser illumination at 532 nm show diffuse scattering over a larger angular range. The polarisation dependence of the scattered light is consistent with the interpretation of small inhomogeneities as scattering centres in the elytra.