Analysis of Dynamic Heterogeneity in a Glass Former from the Spatial Correlations of Mobility

The growth of characteristic length scales associated with dynamic heterogeneity in glass-forming liquids is investigated in an extensive computational study of a four-point, time-dependent structure factor defined from spatial correlations of mobility, for a model liquid for system sizes extending up to 351 232 particles, in constant-energy and constant-temperature ensembles. Our estimates for dynamic correlation lengths and susceptibilities are consistent with previous results from finite size scaling. We find scaling exponents that are inconsistent with predictions from inhomogeneous mode coupling theory and a recent simulation confirmation of these predictions.

Spatial survival probability for one-dimensional fluctuating interfaces in the steady state

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the "sampling interval" used in the measurement for both "steady-state" and "finite" initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A "deterministic approximation" is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.

Markov random fields and spatial smoothing in improving of forest inventory estimates

Markov random fields (MRF) are popular in image processing applications to describe spatial dependencies between image units. Here, we take a look at the theory and the models of MRFs with an application to improve forest inventory estimates. Typically, autocorrelation between study units is a nuisance in statistical inference, but we take an advantage of the dependencies to smooth noisy measurements by borrowing information from the neighbouring units. We build a stochastic spatial model, which we estimate with a Markov chain Monte Carlo simulation method. The smooth values are validated against another data set increasing our confidence that the estimates are more accurate than the originals.

Role of spatial coherence on the rotation sensitivity of Lau fringes: an experimental study

A simple technique involving the use of a rotating and a stationary diffuser has been developed to vary the spatial coherence of light from a He-Ne laser. Using this technique an experimental investigation of the dependence of rotation sensitivity of Lau fringes on the spatial coherence of the illuminating wavefield has been carried out. It is observed that (i) the rotation sensitivity of Lau fringes varies in a well-defined manner as a function of the spatial coherence of the light used; (ii) the extremely good rotation sensitivity of Lau fringes can be used to great advantage (compared to the conventional double slit method) in the measurement of the spatial coherence of a wavefield; (iii) Lau fringes are formed at various levels of spatial coherence and as such it appears that the Lau effect need not be associated with an incoherent optical field

Microsite occupancy and spatial structure of regeneration in three late-successional Norway spruce forests in northern Europe

A comparison of microsite occupancy and the spatial structure of regeneration in three areas of late-successional Norway spruce dominated forest. Pallas-Ylläs is understood to have been influenced only by small-scale disturbance; Dvina-Pinega has had sporadic larger-scale disturbances; Kazkim has been affected by fire. All spruce and birch trees with diameter at breast height (DBH) ?10 cm were mapped in five stands on 40 m x 400 m transects, and those with DBH < 10 cm on 2 or 4 m x 400 m subplots. Microsite type was inventoried at 1m intervals along the centre line and for each tree with DBH < 10 cm. At all study areas small seedlings (h < 0.3 m, DBH < 10 cm) preferentially occupied disturbed microsites. In contrast, spruce saplings (h ? 1.3 m, DBH <10 cm) at all study areas showed less, or no, preference. At Pallas-Ylläs spruce seedlings (h < 1.3 m, DBH < 10 cm) and saplings (h ? 1.3 m, DBH < 10 cm) exhibited spatial correlation at scales from 32-52 m. At Dvina-Pinega saplings of both spruce and birch exhibited spatial correlation at scales from 32-81 m. At Kazkim spatial correlation of seedlings and saplings of both species was exhibited over variable distances. No spatial cross-correlation was found between overstorey basal area (DBH ? 10 cm) and regeneration (h ? 1.3 m, DBH < 10 cm) at any study area. The results confirm the importance of disturbed microsites for seedling establishment, but suggest that undisturbed microsites may sometimes be more advantageous for long-term tree survival. The regeneration gap concept may not be useful in describing the regeneration dynamics of late-successional boreal forests.

Paleoseismological evidence of surface faulting along the northeastern Himalayan front, India: Timing, size, and spatial extent of great earthquakes

The similar to 2500 km long Himalayan arc has experienced three large to great earthquakes of M-w 7.8 to 8.4 during the past century, but none produced surface rupture. Paleoseismic studies have been conducted during the last decade to begin understanding the timing, size, rupture extent, return period, and mechanics of the faulting associated with the occurrence of large surface rupturing earthquakes along the similar to 2500 km long Himalayan Frontal Thrust (HFT) system of India and Nepal. The previous studies have been limited to about nine sites along the western two-thirds of the HFT extending through northwest India and along the southern border of Nepal. We present here the results of paleoseismic investigations at three additional sites further to the northeast along the HFT within the Indian states of West Bengal and Assam. The three sites reside between the meizoseismal areas of the 1934 Bihar-Nepal and 1950 Assam earthquakes. The two westernmost of the sites, near the village of Chalsa and near the Nameri Tiger Preserve, show that offsets during the last surface rupture event were at minimum of about 14 m and 12 m, respectively. Limits on the ages of surface rupture at Chalsa (site A) and Nameri (site B), though broad, allow the possibility that the two sites record the same great historical rupture reported in Nepal around A.D. 1100. The correlation between the two sites is supported by the observation that the large displacements as recorded at Chalsa and Nameri would most likely be associated with rupture lengths of hundreds of kilometers or more and are on the same order as reported for a surface rupture earthquake reported in Nepal around A.D. 1100. Assuming the offsets observed at Chalsa and Nameri occurred synchronously with reported offsets in Nepal, the rupture length of the event would approach 700 to 800 km. The easternmost site is located within Harmutty Tea Estate (site C) at the edges of the 1950 Assam earthquake meizoseismal area. Here the most recent event offset is relatively much smaller (<2.5 m), and radiocarbon dating shows it to have occurred after A.D. 1100 (after about A.D. 1270). The location of the site near the edge of the meizoseismal region of the 1950 Assam earthquake and the relatively lesser offset allows speculation that the displacement records the 1950 M-w 8.4 Assam earthquake. Scatter in radiocarbon ages on detrital charcoal has not resulted in a firm bracket on the timing of events observed in the trenches. Nonetheless, the observations collected here, when taken together, suggest that the largest of thrust earthquakes along the Himalayan arc have rupture lengths and displacements of similar scale to the largest that have occurred historically along the world's subduction zones.

Weighted subspace methods and spatial smoothing: analysis and comparison

The effect of using a spatially smoothed forward-backward covariance matrix on the performance of weighted eigen-based state space methods/ESPRIT, and weighted MUSIC for direction-of-arrival (DOA) estimation is analyzed. Expressions for the mean-squared error in the estimates of the signal zeros and the DOA estimates, along with some general properties of the estimates and optimal weighting matrices, are derived. A key result is that optimally weighted MUSIC and weighted state-space methods/ESPRIT have identical asymptotic performance. Moreover, by properly choosing the number of subarrays, the performance of unweighted state space methods can be significantly improved. It is also shown that the mean-squared error in the DOA estimates is independent of the exact distribution of the source amplitudes. This results in a unified framework for dealing with DOA estimation using a uniformly spaced linear sensor array and the time series frequency estimation problems.

Further results in spatial smoothing

The paper analyses the effect of spatial smoothing on the performance of MUSIC algorithm. In particular, an attempt is made to bring out two effects of the smoothing: (i) reduction of effective correlation between the impinging signals and (ii) reduction of the noise perturbations due to finite data. For the case of a two-source scenario with widely spaced sources, simplified expressions for improvement with smoothing have been obtained which provide more insight into the impact of smoothing. Specifically, a pessimistic estimate of the minimum value of source correlation beyond which the smoothing is beneficial is brought out by these expressions. Computer simulations are used to demonstrate the usefulness of the analytical results.

Spatial distribution of oil in groundnut and sunflower seeds by nuclear magnetic resonance imaging

The nuclear magnetic resonance imaging technique has been used to obtain images of different transverse and vertical sections in groundnut and sunflower seeds. Separate images have been obtained for oil and water components in the seeds. The spatial distribution of oil and water inside the seed has been obtained from the detailed analysis of the images. In the immature groundnut seeds obtained commercially, complementary oil and water distributions have been observed. Attempts have been made to explain these results.

The determination of spatial pattern in Dictyostelium discoideum

Free-living amoebae of the cellular slime mould Dictyostelium discoideum aggregate when starved and give rise to a long and thin multicellular structure, the slug. The slug resembles a metazoan embryo, and as with other embryos it is possible to specify a fate map. In the case of Dictyostelium discoideum the map is especially simple: cells in the anterior fifth of the slug die and form a stalk while the majority of those in the posterior differentiate into spores. The genesis of this anterior-posterior distinction is the subject of our review. In particular, we ask: what are the relative roles of individual pre-aggregative predispositions and post-aggregative position in determining cell fate? We review the literature on the subject and conclude that both factors are important. Variations in nutritional status, or in cell cycle phase at starvation, can bias the probability that an amoeba differentiates into a stalk cell or a spore. On the other hand, isolates, or slug fragments, consisting of only prestalk cells or only prespore cells can regulate so as to result in a normal range of both cell types. We identify three levels of control, each being responsible for guiding patterning in normal development: (i) 'coin tossing', whereby a cell autonomously exhibits a preference for developing along either the stalk or the spore pathway with relative probabilities that can be influenced by the environment; (ii) 'chemical kinetics', whereby prestalk and prespore cells originate from undifferentiated amoebae on a probabilistic basis but, having originated, interact (e.g. via positive and negative feedbacks), and the interaction influences the possibility of conversion of one cell type into the other, and (iii) 'positional information', in which the spatial distribution of morphogens in the slug influences the pathway of differentiation. In the case of possibilities (i) and (ii), sorting out of like cell types leads to the final spatial pattern. In the case of possibility (iii), the pattern arises in situ.

Spatial gradients of calcium in the slug of Dictyostelium discoideum

Starved amoebae of D. discoideum aggregate and give rise to a long and thin multicellular structure called the slug. The cells within the slug eventually differentiate according to a simple anterior/posterior dichotomy. This motivates a search for gradients of putative morphogens along its axis. Calcium may be one such morphogen. On the basis of observations made by using the calcium-sensitive fluorescent dyes fura-2 and chlortetracyline, we report that there are spatial gradients in cytoplasmic and sequestered calcium in the slug. Anteriorly located and genetically defined prestalk cells (ecmA/pstA, ecmB/pstAB) contain significantly higher levels of calcium than the prespore cells in the posterior. However, the proportion of 'calcium-rich' cells in the slug is greater than that of the subset of prestalk cells defined by the expression of the ecmA or ecmB genes.

The precision of regulation in Dictyostelium discoideum: implications for cell-type proportioning in the absence of spatial pattern

We have made careful counts of the exact number of spore, stalk and basal disc cells in small fruiting bodies of Dictyostelium discoideum (undifferentiated amoebae are found only rarely and on average their fraction is 4.96 x 10(-4)). (i) Within aggregates of a given size, the relative apportioning of amoebae to the main cell types occurs with a remarkable degree of precision. In most cases the coefficient of variation (c.v.) in the mean fraction of cells that form spores is within 4.86%. The contribution of stalk and basal disc cells is highly variable when considered separately (c.v.'s upto 25% and 100%, respectively), but markedly less so when considered together. Calculations based on theoretical models indicate that purely cell-autonomous specification of cell, fate cannot account for die observed accuracy of proportioning. Cell-autonomous determination to a prestalk or prespore condition followed by cell type interconversion, and stabilised by feedbacks, suffices to explain the measured accuracy. (ii) The fraction of amoebae that differentiates into spores increases monotonically with the total number of cells. This fraction rises from an average of 73.6% for total cell numbers below 30 and reaches 86.0% for cell numbers between 170 and 200 (it remains steady thereafter at around 86%). Correspondingly, the fraction of amoebae differentiating into stalk or basal disc decreases viith total size. These trends are in accordance with evolutionary expectations and imply that a mechanism for sensing the overall size of the aggregate also plays an essential role in the determination of cell-type proportions.