Subexponential Algorithm for d-Cluster Edge Deletion: Exception or Rule?

The correlation clustering problem is a fundamental problem in both theory and practice, and it involves identifying clusters of objects in a data set based on their similarity. A traditional modeling of this question as a graph theoretic problem involves associating vertices with data points and indicating similarity by adjacency. Clusters then correspond to cliques in the graph. The resulting optimization problem, Cluster Editing (and several variants) are very well-studied algorithmically. In many situations, however, translating clusters to cliques can be somewhat restrictive. A more flexible notion would be that of a structure where the vertices are mutually ``not too far apart'', without necessarily being adjacent. One such generalization is realized by structures called s-clubs, which are graphs of diameter at most s. In this work, we study the question of finding a set of at most k edges whose removal leaves us with a graph whose components are s-clubs. Recently, it has been shown that unless Exponential Time Hypothesis fail (ETH) fails Cluster Editing (whose components are 1-clubs) does not admit sub-exponential time algorithm STACS, 2013]. That is, there is no algorithm solving the problem in time 2 degrees((k))n(O(1)). However, surprisingly they show that when the number of cliques in the output graph is restricted to d, then the problem can be solved in time O(2(O(root dk)) + m + n). We show that this sub-exponential time algorithm for the fixed number of cliques is rather an exception than a rule. Our first result shows that assuming the ETH, there is no algorithm solving the s-Club Cluster Edge Deletion problem in time 2 degrees((k))n(O(1)). We show, further, that even the problem of deleting edges to obtain a graph with d s-clubs cannot be solved in time 2 degrees((k))n(O)(1) for any fixed s, d >= 2. This is a radical contrast from the situation established for cliques, where sub-exponential algorithms are known.

Flexibility in flapping foil suppresses meandering of induced jet in absence of free stream

Thrust-generating flapping foils are known to produce jets inclined to the free stream at high Strouhal numbers St = fA/U-infinity, where f is the frequency and A is the amplitude of flapping and U-infinity is the free-stream velocity. Our experiments, in the limiting case of St —> infinity (zero free-stream speed), show that a purely oscillatory pitching motion of a chordwise flexible foil produces a coherent jet composed of a reverse Benard-Karman vortex street along the centreline, albeit over a specific range of effective flap stiffnesses. We obtain flexibility by attaching a thin flap to the trailing edge of a rigid NACA0015 foil; length of flap is 0.79 c where c is rigid foil chord length. It is the time-varying deflections of the flexible flap that suppress the meandering found in the jets produced by a pitching rigid foil for zero free-stream condition. Recent experiments (Marais et al., J. Fluid Mech., vol. 710, 2012, p. 659) have also shown that the flexibility increases the St at which non-deflected jets are obtained. Analysing the near-wake vortex dynamics from flow visualization and particle image velocimetry (PIV) measurements, we identify the mechanisms by which flexibility suppresses jet deflection and meandering. A convenient characterization of flap deformation, caused by fluid-flap interaction, is through a non-dimensional effective stiffness', EI* = 8 EI/(rho V-TEmax(2) s(f) c(f)(3)/2), representing the inverse of the flap deflection due to the fluid-dynamic loading; here, EI is the bending stiffness of flap, rho is fluid density, V-TEmax is the maximum velocity of rigid foil trailing edge, s(f) is span and c(f) is chord length of the flexible flap. By varying the amplitude and frequency of pitching, we obtain a variation in EI* over nearly two orders of magnitude and show that only moderate EI*. (0.1 less than or similar to EI * less than or similar to 1 generates a sustained, coherent, orderly jet. Relatively `stiff' flaps (EI* greater than or similar to 1), including the extreme case of no flap, produce meandering jets, whereas highly `flexible' flaps (EI* less than or similar to 0.1) produce spread-out jets. Obtained from the measured mean velocity fields, we present values of thrust coefficients for the cases for which orderly jets are observed.

Trace Formulae for Curvature of Jet Bundles over Planar Domains

For a domain Omega in C and an operator T in B-n(Omega), Cowen and Douglas construct a Hermitian holomorphic vector bundle E-T over Omega corresponding to T. The Hermitian holomorphic vector bundle E-T is obtained as a pull-back of the tautological bundle S(n, H) defined over by Gr(n, H) a nondegenerate holomorphic map z bar right arrow ker(T - z), z is an element of Omega. To find the answer to the converse, Cowen and Douglas studied the jet bundle in their foundational paper. The computations in this paper for the curvature of the jet bundle are rather intricate. They have given a set of invariants to determine if two rank n Hermitian holomorphic vector bundle are equivalent. These invariants are complicated and not easy to compute. It is natural to expect that the equivalence of Hermitian holomorphic jet bundles should be easier to characterize. In fact, in the case of the Hermitian holomorphic jet bundle J(k)(L-f), we have shown that the curvature of the line bundle L-f completely determines the class of J(k)(L-f). In case of rank Hermitian holomorphic vector bundle E-f, We have calculated the curvature of jet bundle J(k)(E-f) and also obtained a trace formula for jet bundle J(k)(E-f).

Large carbon cluster thin film gauges for measuring aerodynamic heat transfer rates in hypersonic shock tunnels

Different types of Large Carbon Cluster (LCC) layers are synthesized by a single-step pyrolysis technique at various ratios of precursor mixture. The aim is to develop a fast responsive and stable thermal gauge based on a LCC layer which has relatively good electrical conduction in order to use it in the hypersonic flow field. The thermoelectric property of the LCC layer has been studied. It is found that these carbon clusters are sensitive to temperature changes. Therefore suitable thermal gauges were developed for blunt cone bodies and were tested in hypersonic shock tunnels at a flow Mach number of 6.8 to measure aerodynamic heating. The LCC layer of this thermal gauge encounters high shear forces and a hostile environment for test duration in the range of a millisecond. The results are favorable to use large carbon clusters as a better sensor than a conventional platinum thin film gauge in view of fast responsiveness and stability.

DEEP WASHINGTON PHOTOMETRY OF INCONSPICUOUS STAR CLUSTER CANDIDATES IN THE LARGE MAGELLANIC CLOUD

We present deep Washington photometry of 45 poorly populated star cluster candidates in the Large Magellanic Cloud (LMC). We have performed a systematic study to estimate the parameters of the cluster candidates by matching theoretical isochrones to the cleaned and dereddened cluster color-magnitude diagrams. We were able to estimate the basic parameters for 33 clusters, out of which 23 are identified as single clusters and 10 are found to be members of double clusters. The other 12 cluster candidates have been classified as possible clusters/asterisms. About 50% of the true clusters are in the 100-300 Myr age range, whereas some are older or younger. We have discussed the distribution of age, location, and reddening with respect to field, as well as the size of true clusters. The sizes and masses of the studied sample are found to be similar to that of open clusters in the Milky Way. Our study adds to the lower end of cluster mass distribution in the LMC, suggesting that the LMC, apart from hosting rich clusters, also has formed small, less massive open clusters in the 100-300 Myr age range.

NUMERICAL SIMULATIONS OF LIQUID JET BREAK UP IN A CROSSFLOW

Atomization is the process of disintegration of a liquid jet into ligaments and subsequently into smaller droplets. A liquid jet injected from a circular orifice into cross flow of air undergoes atomization primarily due to the interaction of the two phases rather than an intrinsic break up. Direct numerical simulation of this process resolving the finest droplets is computationally very expensive and impractical. In the present study, we resort to multiscale modelling to reduce the computational cost. The primary break up of the liquid jet is simulated using Gerris, an open source code, which employs Volume-of-Fluid (VOF) algorithm. The smallest droplets formed during primary atomization are modeled as Lagrangian particles. This one-way coupling approach is validated with the help of the simple test case of tracking a particle in a Taylor-Green vortex. The temporal evolution of the liquid jet forming the spray is captured and the flattening of the cylindrical liquid column prior to breakup is observed. The size distribution of the resultant droplets is presented at different distances downstream from the location of injection and their spatial evolution is analyzed.

Acoustic response of vortex breakdown modes in a coaxial isothermal unconfined swirling jet

The present experimental work is concerned with the study of amplitude dependent acoustic response of an isothermal coaxial swirling jet. The excitation amplitude is increased in five distinct steps at the burner's Helmholtz resonator mode (i.e., 100 Hz). Two flow states are compared, namely, sub-critical and super-critical vortex breakdown (VB) that occur before and after the critical conical sheet breakdown, respectively. The geometric swirl number is varied in the range 2.14-4.03. Under the influence of external pulsing, global response characteristics are studied based on the topological changes observed in time-averaged 2D flow field. These are obtained from high resolution 2D PIV (particle image velocimetry) in the longitudinal-mid plane. PIV results also illustrate the changes in the normalized vortex core coordinates (r(vcc)/(r(vcc))(0) (Hz), y(vcc)/(y(vcc))(0) (Hz)) of internal recirculation zone (IRZ). A strong forced response is observed at 100 Hz (excitation frequency) in the convectively unstable region which get amplified based on the magnitude of external forcing. The radial extent of this forced response region at a given excitation amplitude is represented by the acoustic response region (b). The topological placement of the responsive convectively unstable region is a function of both the intensity of imparted swirl (characterized by swirl number) and forcing amplitude. It is observed that for sub-critical VB mode, an increase in the excitation amplitude till a critical value shifts the vortex core centre (particularly, the vortex core moves downstream and radially outwards) leading to drastic fanning-out/widening of the IRZ. This is accompanied by similar to 30% reduction in the recirculation velocity of the IRZ. It is also observed that b < R (R: radial distance from central axis to outer shear layer-OSL). At super-critical amplitudes, the sub-critical IRZ topology transits back (the vortex core retracts upstream and radially inwards) and finally undergoes a transverse shrinkage ((r(vcc))/(r(vcc))(0 Hz) decreases by similar to 20%) when b >= R. In contrast, the vortex core of super-critical breakdown mode consistently spreads radially outwards and is displaced further downstream. Finally, the IRZ fans-out at the threshold excitation amplitude. However, the acoustic response region b is still less than R. This is explained based on the characteristic geometric swirl number (S-G) of the flow regimes. The super-critical flow mode with higher S-G (hence, higher radial pressure drop due to rotational effect which scales as Delta P similar to rho u theta(2) and acts inwards towards the center line) compared to sub-critical state imposes a greater resistance to the radial outward spread of b. As a result, the acoustic energy supplied to the super-critical flow mode increases the degree of acoustic response at the pulsing frequency and energizes its harmonics (evident from power spectra). As a disturbance amplifier, the stronger convective instability mode within the flow structure of super-critical VB causes the topology to widen/fan-out severely at threshold excitation amplitude. (C) 2015 AIP Publishing LLC.

Jet substructure and probes of CP violation in Vh production

We analyse the hVV (V = W, Z) vertex in a model independent way using Vh production. To that end, we consider possible corrections to the Standard Model Higgs Lagrangian, in the form of higher dimensional operators which parametrise the effects of new physics. In our analysis, we pay special attention to linear observables that can be used to probe CP violation in the same. By considering the associated production of a Higgs boson with a vector boson (W or Z), we use jet substructure methods to define angular observables which are sensitive to new physics effects, including an asymmetry which is linearly sensitive to the presence of CP odd effects. We demonstrate how to use these observables to place bounds on the presence of higher dimensional operators, and quantify these statements using a log likelihood analysis. Our approach allows one to probe separately the hZZ and hWW vertices, involving arbitrary combinations of BSM operators, at the Large Hadron Collider.

Associated jet and subjet rates in light-quark and gluon jet discrimination

We show that in studies of light quark- and gluon-initiated jet discrimination, it is important to include the information on softer reconstructed jets (associated jets) around a primary hard jet. This is particularly relevant while adopting a small radius parameter for reconstructing hadronic jets. The probability of having an associated jet as a function of the primary jet transverse momentum (PT) and radius, the minimum associated jet pi, and the association radius is computed up to next-to-double logarithmic accuracy (NDLA), and the predictions are compared with results from Herwig++, Pythia6 and Pythia8 Monte Carlos (MC). We demonstrate the improvement in quark-gluon discrimination on using the associated jet rate variable with the help of a multivariate analysis. The associated jet rates are found to be only mildly sensitive to the choice of parton shower and hadronization algorithms, as well as to the effects of initial state radiation and underlying event. In addition, the number of k(t) subjets of an anti-k(t) jet is found to be an observable that leads to a rather uniform prediction across different MC's, broadly being in agreement with predictions in NDLA, as compared to the often used number of charged tracks observable.

A model supersonic buried-nozzle jet: instability and acoustic wave scattering and the far-field sound

We consider sound source mechanisms involving the acoustic and instability modes of dual-stream isothermal supersonic jets with the inner nozzle buried within an outer shroud-like nozzle. A particular focus is scattering into radiating sound waves at the shroud lip. For such jets, several families of acoustically coupled instability waves exist, beyond the regular vortical Kelvin-Helmholtz mode, with different shapes and propagation characteristics, which can therefore affect the character of the radiated sound. In our model, the coaxial shear layers are vortex sheets while the incident acoustic disturbances are the propagating shroud modes. The Wiener-Hopf method is used to compute their scattering at the sharp shroud edge to obtain the far-field radiation. The resulting far-field directivity quantifies the acoustic efficiency of different mechanisms, which is particularly important in the upstream direction, where the results show that the scattered sound is more intense than that radiated directly by the shear-layer modes.

A Computational Study of the Factors Influencing the PVC-Triggering Ability of a Cluster of Early Afterdepolarization-Capable Myocytes

Premature ventricular complexes (PVCs), which are abnormal impulse propagations in cardiac tissue, can develop because of various reasons including early afterdepolarizations (EADs). We show how a cluster of EAD-generating cells (EAD clump) can lead to PVCs in a model of cardiac tissue, and also investigate the factors that assist such clumps in triggering PVCs. In particular, we study, through computer simulations, the effects of the following factors on the PVC-triggering ability of an EAD clump: (1) the repolarization reserve (RR) of the EAD cells; (2) the size of the EAD clump; (3) the coupling strength between the EAD cells in the clump; and (4) the presence of fibroblasts in the EAD clump. We find that, although a low value of RR is necessary to generate EADs and hence PVCs, a very low value of RR leads to low-amplitude EAD oscillations that decay with time and do not lead to PVCs. We demonstrate that a certain threshold size of the EAD clump, or a reduction in the coupling strength between the EAD cells, in the clump, is required to trigger PVCs. We illustrate how randomly distributed inexcitable obstacles, which we use to model collagen deposits, affect PVC-triggering by an EAD clump. We show that the gap-junctional coupling of fibroblasts with myocytes can either assist or impede the PVC-triggering ability of an EAD clump, depending on the resting membrane potential of the fibroblasts and the coupling strength between the myocyte and fibroblasts. We also find that the triggering of PVCs by an EAD clump depends sensitively on factors like the pacing cycle length and the distribution pattern of the fibroblasts.

Delineation of homogeneous hydrometeorological regions using wavelet-based global fuzzy cluster analysis

Identification of homogeneous hydrometeorological regions (HMRs) is necessary for various applications. Such regions are delineated by various approaches considering rainfall and temperature as two key variables. In conventional approaches, formation of regions is based on principal components (PCs)/statistics/indices determined from time series of the key variables at monthly and seasonal scales. An issue with use of PCs for regionalization is that they have to be extracted from contemporaneous records of hydrometeorological variables. Therefore, delineated regions may not be effective when the available records are limited over contemporaneous time period. A drawback associated with the use of statistics/indices is that they do not provide effective representation of the key variables when the records exhibit non-stationarity. Consequently, the resulting regions may not be effective for the desired purpose. To address these issues, a new approach is proposed in this article. The approach considers information extracted from wavelet transformations of the observed multivariate hydrometeorological time series as the basis for regionalization by global fuzzy c-means clustering procedure. The approach can account for dynamic variability in the time series and its non-stationarity (if any). Effectiveness of the proposed approach in forming HMRs is demonstrated by application to India, as there are no prior attempts to form such regions over the country. Drought severity-area-frequency (SAF) curves are constructed corresponding to each of the newly formed regions for the use in regional drought analysis, by considering standardized precipitation evapotranspiration index (SPEI) as the drought indicator.

Flow Investigation of Linear Cluster Plug Nozzle

Computational and experimental tools have been used to understand the linear cluster plug nozzle flowfield for a range of pressure ratios. The experimental cluster configuration is arrived at from a linear plug nozzle by introducing splitter plates in the primary nozzle, and computational analysis of corresponding geometry is also carried out. The flow development on the plug surface has been analyzed for two different cluster module spacings. The interactions between the cluster module jets is a complex one with a three-dimensional shock structure because of the differential end condition the shock experiences on the plug wall and freejet boundary. A prominent streamwise vorticity resulting from curvature of the shock is also seen along the length of the plug downstream of the module junctions. The out-of-phase wave interactions occurring along the module centerline and the splitter plate centerline, resulting in a wavy surface-limiting streamline pattern, particularly at lower pressure ratios, is explained.

The impact of latent heating on the location and strength of the tropical easterly jet

The tropical easterly jet (TEJ) is a prominent atmospheric circulation feature observed during the Asian summer monsoon. It is generally assumed that sensible heating over the Tibetan Plateau directly influences the location of the TEJ. However, other studies have suggested the importance of latent heating in determining the jet location. In this paper, the relative importance of latent heating on the maintenance of the TEJ is explored through simulations with a general circulation model. The simulation of the TEJ by the Community Atmosphere Model, version 3.1 is discussed in detail. These simulations showed that the location of the TEJ is well correlated with the location of the precipitation. Significant zonal shifts in the location of the precipitation resulted in similar shifts in the zonal location of the TEJ. These zonal shifts had minimal effect on the large-scale structure of the jet. Further, provided that precipitation patterns were relatively unchanged, orography did not directly impact the location of the TEJ. These changes were robust even with changes in the cumulus parameterization. This suggests the potential important role of latent heating in determining the location and structure of the TEJ. These results were used to explain the significant differences in the zonal location of the TEJ in the years 1988 and 2002. To understand the contribution of the latitudinal location of latent heating on the strength of the TEJ, aqua-planet simulations were carried out. It has been shown that for similar amounts of net latent heating, the jet is stronger when heating is in the higher tropical latitudes. This may partly explain the reason for the jet to be very strong during the JJA monsoon season.

Cold gas in cluster cores: global stability analysis and non-linear simulations of thermal instability

We perform global linear stability analysis and idealized numerical simulations in global thermal balance to understand the condensation of cold gas from hot/virial atmospheres (coronae), in particular the intracluster medium (ICM). We pay particular attention to geometry (e.g. spherical versus plane-parallel) and the nature of the gravitational potential. Global linear analysis gives a similar value for the fastest growing thermal instability modes in spherical and Cartesian geometries. Simulations and observations suggest that cooling in haloes critically depends on the ratio of the cooling time to the free-fall time (t(cool)/t(ff)). Extended cold gas condenses out of the ICM only if this ratio is smaller than a threshold value close to 10. Previous works highlighted the difference between the nature of cold gas condensation in spherical and plane-parallel atmospheres; namely, cold gas condensation appeared easier in spherical atmospheres. This apparent difference due to geometry arises because the previous plane-parallel simulations focused on in situ condensation of multiphase gas but spherical simulations studied condensation anywhere in the box. Unlike previous claims, our non-linear simulations show that there are only minor differences in cold gas condensation, either in situ or anywhere, for different geometries. The amount of cold gas depends on the shape of tcool/tff; gas has more time to condense if gravitational acceleration decreases towards the centre. In our idealized plane-parallel simulations with heating balancing cooling in each layer, there can be significant mass/energy/momentum transfer across layers that can trigger condensation and drive tcool/tff far beyond the critical value close to 10.