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At least 847 records · Page 47

Coaction and double-copy properties of configuration-space integrals at genus zero

We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension α' or the dimensional-regularization parameter ϵ of Feynman integrals. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in (p, 2) minimal models, which can be normalized to become uniformly transcendental in the p → ∞ limit.

Conformal Field Theory↗

Femtoscopy in s NN = 5.02 TeV p+Pb collisions with ATLAS

Bose-Einstein correlations between identified charged pions are measured for p+Pb collisions at $ \sqrt{sNN}=5.02 $ TeV with the ATLAS detector using a total integrated luminosity of 28 nb -1 . Pions are identified using ionisation energy loss measured in the pixel silicon detector. Two-particle correlation functions and the extracted source radii are presented as a function of collision centrality as well as average transverse pair momentum (k T ), rapidity (y* $\pi$$\pi$ ), and azimuthal angle with respect to the second-order event plane. Pairs are selected with a rapidity -2 < y* $\pi$$\pi$ <1 and with an average transverse momentum 0.1 < k T < 0.8 GeV. The effect on the two-particle correlation function from jet fragmentation is studied, and a new method for constraining its contributions to the measured correlations is described. The measured source sizes are substantially larger in more central collisions and are observed to decrease with increasing pair k T . A correlation with the local single-particle multiplicity dN ch /dy* is demonstrated. The cross term R ol , which couples radial and longitudinal expansion, is measured as a function of rapidity, and a departure from zero is observed with 5.1σ combined significance for y* $\pi$$\pi$ > -1 in the most central events. Lastly, the azimuthal modulation of the radii in central events is observed to be consistent with that predicted by hydrodynamics and observed in A+A collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Notes on the D = 11 pure spinor superparticle

The D = 11 pure spinor superparticle has been shown to describe linearized D = 11supergravityinamanifestlycovariantway. Anumberofauthorshaveproposedthat its correlation functions be used to compute amplitudes. The use of the scalar structure of the eleven-dimensional pure spinor top cohomology introduces a natural measure for computing such correlation functions. This prescription requires the construction of ghost number one and zero vertex operators. In these notes, we construct explicitly a ghost number one vertex operator but show the incompatibiliy of a ghost number zero vertex operator satisfying a standard descent equation for D = 11 supergravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Anomalous structural evolution and liquid fragility signatures in Cu-Zr and Cu-Hf liquids and glasses

The results of high energy X-ray scattering studies of equilibrium and supercooled Cu 100-x Zr x (x = 46 and 54) and Cu x Hf 100-x (x = 55 and 60.8) liquids and the corresponding glasses are presented. The liquid data were obtained in a containerless environment using the beamline electrostatic levitation (BESL) technique. The total structure factor and total pair correlation functions were measured as a function of temperature for the liquids, and for the glasses at room temperature. A developing asymmetry in the peak of the first coordination shell in the total pair correlation function suggests chemical ordering in the liquids with cooling. This asymmetry takes the form of two prominent peaks, suggesting two prominent ordering length scales. When the magnitudes of these peaks are extrapolated to the glass transition temperature a discontinuity is observed, indicating that an abrupt increase in the magnitude is required to match the observed peak heights in the glass. This suggests that the structure of the supercooled liquid orders more rapidly near the glass transition temperature, a conclusion that is supported by molecular dynamics simulations. This observed structural evolution of the liquid indicates that the concept of fragility, typically defined from the behavior of viscosity with temperature, has a measurable structural signature as well, which can be observed in X-ray diffraction studies.

Mauro, N. A.↗

Coherent (photon) vs incoherent (current) detection of multidimensional optical signals from single molecules in open junctions

The nonlinear optical response of a current-carrying single molecule coupled to two metal leads and driven by a sequence of impulsive optical pulses with controllable phases and time delays is calculated. Coherent (stimulated, heterodyne) detection of photons and incoherent detection of the optically induced current are compared. Using a diagrammatic Liouville space superoperator formalism, the signals are recast in terms of molecular correlation functions which are then expanded in the many-body molecular states. Two dimensional signals in benzene-1,4-dithiol molecule show cross peaks involving charged states. The correlation between optical and charge current signal is also observed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On hierarchical solutions to the BBGKY hierarchy

It is thought that the gravitational clustering of galaxies in the universe may approach a scale-invariant, hierarchical form in the small separation, large-clustering regime. Past attempts to solve the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. It is shown here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has cluster-cluster correlations equal to galaxy-galaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dyamical role in the large-clustering regime. These results are a particular property of the specific separable model assumed for the correlation functions in phase space, not an intrinsic property of spatially hierarchical solutions to the BBGKY hierarchy. The observed distribution of galaxies does not satisfy the required conditions. The disagreement between theory and observation may be traced, at least in part, to initial conditions which, if Gaussian, already have cluster correlations greater than galaxy correlations.

Hamilton, A. J. S.↗

Studying the effects of overlapping objects in dark energy

Observing the clustering of galaxies allows us to calculate cosmological parameters necessary for understanding dark energy. However, as the density of observed objects increases, the probability of these objects blending likewise increases, causing multiple galaxies to be observed as one. This affects the inferred values of parameters such as the galaxy bias (b) and the matter energy density (ΩM). To see whether the bias from incorrectly inferring the galaxy count is significant, we compare the correlation functions in simulated data for “true” and “observed” data sets with one-to-one and multiple-to-one correspondences, respectively. For each data set, we create two correlation functions: one “measured” function directly relying on the galaxies’ positions using the TreeCorr python library, and one “model” derived mathematically from the galaxies’ power spectrum using the Cosmological Core Library (CCL). By minimizing the residual between these two functions, we compute the ideal values for b and ΩM across the various possible redshifts that position the galaxies in three dimensional space. This minimization is done with an Markov chain Monte Carlo (MCMC) estimate that finds one value of ΩM and ten values for b corresponding to the ten redshift bins ranging from z = 0.2 to z = 1.2. We find that neither b nor ΩM is particularly affected by inclusion of blended galaxies. Though there is room for improvement, the data suggests that the fluctuations we found are a result of noise or limitations on the modeling rather than blending explicitly.

79 ASTRONOMY AND ASTROPHYSICS↗

Geometry of conformal manifolds and the inversion formula

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed using Euclidean and Lorentzian inversion formulae, which combine the operator content of the conformal field theory into an analytic function. Analogously, operators of fixed dimension define bundles over the conformal manifold whose curvatures can also be computed using inversion formulae. These results relate curvatures to integrated four-point correlation functions which are sensitive only to the behavior of the theory at separated points. We apply these inversion formulae to derive convergent sum rules expressing the curvature in terms of the spectrum of local operators and their three-point function coefficients. We further show that the curvature can smoothly diverge only if a conserved current appears in the spectrum, or if the theory develops a continuum. We verify our results explicitly in 2d examples. In particular, for 2d (2,2) superconformal field theories we derive a lower bound on the scalar curvature, which is saturated by free theories when the central charge is a multiple of three.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Spatial density fluctuations and selection effects in galaxy redshift surveys

One of the main problems of observational cosmology is to determine the range in which a reliable measurement of galaxy correlations is possible. This corresponds to determining the shape of the correlation function, its possible evolution with redshift and the size and amplitude of large scale structures. Different selection effects, inevitably entering in any observation, introduce important constraints in the measurement of correlations. In the context of galaxy redshift surveys selection effects can be caused by observational techniques and strategies and by implicit assumptions used in the data analysis. Generally all these effects are taken into account by using pair-counting algorithms to measure two-point correlations. We review these methods stressing that they are based on the a-priori assumption that galaxy distribution is spatially homogeneous inside a given sample. We show that, when this assumption is not satisfied by the data, results of the correlation analysis are affected by finite size effects. In order to quantify these effects, we introduce a new method based on the computation of the gradient of galaxy counts along tiny cylinders. We show, by using artificial homogeneous and inhomogeneous point distributions, that this method identifies redshift dependent selection effects and disentangles them from the presence of large scale density fluctuations. We then apply this new method to several redshift catalogs and we find evidence that galaxy distribution, in those samples where selection effects are small enough, is characterized by power-law correlations with exponent γ=0.9 up to 20 Mpc/h followed by a change of slope that, in the range 20–100 Mpc/h, corresponds to a power-law exponent γ=0.25. Whether a crossover to spatial uniformity occurs at ∼ 100 Mpc/h or larger scales cannot be clarified by the present data.

79 ASTRONOMY AND ASTROPHYSICS↗

Coupled π π , K K ¯ scattering in P -wave and the ρ resonance from lattice QCD

In this study, we determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering in $P$-wave, by calculating correlation functions using lattice QCD with light quark masses such that $m_\pi = 236$ MeV in a cubic volume of $\sim (4 \,\mathrm{fm})^3$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $\pi\pi$, $K\overline{K}$ and $q\bar{q}$, in several moving frames and several lattice irreducible representations, leads to discrete energy spectra from which scattering amplitudes are extracted. In the elastic $\pi\pi$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $\rho$ resonance, and we extend the analysis into the coupled-channel $K\overline{K}$ region for the first time, finding a small coupling between the channels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Superclustering and the large-scale structure of the Universe

A complete redshift survey of nearby rich galactic clusters is analyzed in terms of a spatial correlation function, the growth of supercluster, the presence of superclusters around the Bootes void and the discovery of a 300 Mpc void. Abell's (1958) statistical sampling of rich clusters is used for the study. Attention is given to the dependence of the correlation function on the richness of the system, with finding that chances are greater of finding rich neighbors closer together than poor neighbors. Samples of redshifts of 4 or less correlate well with clusters of redshift 5 or more. The size of intergalactic voids is proportional to the surrounding galactic excesses. Finally, the superclusters exist on scales of about 100 Mpc/h, which is larger than expected.

Bahcall, N. A.↗

Testing the Large-scale Environments of Cool-core and Non-cool-core Clusters with Clustering Bias

There are well-observed differences between cool-core (CC) and non-cool-core (NCC) clusters, but the origin of this distinction is still largely unknown. Competing theories can be divided into internal (inside-out), in which internal physical processes transform or maintain the NCC phase, and external (outside-in), in which the cluster type is determined by its initial conditions, which in turn leads to different formation histories (i.e., assembly bias). We propose a new method that uses the relative assembly bias of CC to NCC clusters, as determined via the two-point cluster-galaxy cross-correlation function (CCF), to test whether formation history plays a role in determining their nature. We apply our method to 48 ACCEPT clusters, which have well resolved central entropies, and cross-correlate with the SDSS-III/BOSS LOWZ galaxy catalog. We find that the relative bias of NCC over CC clusters is b = 1.42 ± 0.35 (1.6 σ different from unity). Our measurement is limited by the small number of clusters with core entropy information within the BOSS footprint, 14 CC and 34 NCC clusters. Future compilations of X-ray cluster samples, combined with deep all-sky redshift surveys, will be able to better constrain the relative assembly bias of CC and NCC clusters and determine the origin of the bimodality.

79 ASTRONOMY AND ASTROPHYSICS↗

Signal processing considerations for low signal to noise ratio laser Doppler and phase Doppler signals

The relative performance of current methods used for estimating the phase and the frequency in LDV and phase Doppler applications in low signal to noise ratio conditions is analyzed. These methods include the Fourier analysis and the correlation techniques. Three methods that use the correlation function for frequency and phase estimations are evaluated in terms of accuracy and speed of processing. These methods include: (1) the frequency estimation using zero crossings counting of the auto-correlation function, (2) the Blackman-Tukey method, and (3) the AutoRegressive method (AR). The relative performance of these methods is evaluated and compared with the Fourier analysis method which provides the optimum performance in terms of the Maximum Likelihood (ML) criteria.

Ibrahim, K. M.↗

Dynamic Light Scattering From Colloidal Gels

We present a brief, preliminary account of the interpretation of dynamic light scattering from fractal colloidal gels. For small scattering angles, and for high initial colloid particle volume fractions, the correlation functions exhibit arrested decay, reflecting the non-ergodic nature of these systems and allowing us to directly determine the elastic modulus of the gels. For smaller initial volume fractions, the correlation functions decay completely. In all cases, the initial decay is not exponential, but is instead described by a stretched exponential. We summarize the principles of a model that accounts for these data and discuss the scaling behavior of the measured parameters.

Krall, A. H.↗

Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces

The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.

Hou, Thomas Y.↗

Efficient Parallelization of Irregular Applications on GPU Architectures

With the enlarging computation capacity of general Graphics Processing Units (GPUs), leveraging GPUs to accelerate parallel applications has become a critical topic in academia and industry. However, a wide range of irregular applications with the computation-/memory-intensive nature cannot easily achieve high GPU utilization. The challenges mainly involve the following aspects: first, data dependence leads to coarse-grained kernel and inefficient parallelism; second, heavy GPU memory usage may cause frequent memory evictions and extra overhead of I/O; third, specific computation patterns produce memory redundancies; last, workload balance and data reusability conjunctly benefit the overall performance, but there may exist a dynamic trade-off between them. Targeting these challenges, this dissertation proposes multiple optimizations to accelerate two real-world applications: many-body correlation functions to simulate nuclear physics in a large-scale scientific system; the other is the eALS-based matrix factorization recommendation system. To accelerate the calculations of many-body correlation functions, this dissertation presents three frameworks in GPU memory management and multi-GPU scheduling. Firstly, an optimized systematic GPU memory management framework, MemHC, utilizes a series of new memory reduction designs in GPU memory allocation, CPU/GPU communications, and GPU memory oversubscription. Secondly, an enhanced multi-GPU scheduling framework, MICCO, particularly by taking both data dimension (e.g., data reuse and data eviction) and computation dimension into account. MICCO designs a heuristic scheduling algorithm and a machine learning-based regression model to generate the optimal settings of a proposed new concept to manage the trade-off. Thirdly, a locality-aware multi-GPU scheduling framework. This scheduler leverages pipeline batch generation with a looking-ahead strategy by building local dependency graphs for memory transfer reduction and better data reuse, achieving up to 79.92% memory cost reduction and 1.67x speedup. To parallelize the eALS-based recommendation system, this dissertation proposes an efficient CPU/GPU heterogeneous recommendation system, HEALS. HEALS employs newly designed architecture-adaptive data formats to achieve load balance and good data locality on CPU and GPU. To mitigate the data dependence, HEALS presents a CPU/GPU collaboration model for both task parallelism and data parallelism with multiple kernel computation optimizations. In summary, this dissertation efficiently accelerates two typical irregular applications on GPUs by building four frameworks, including CPU/GPU collaboration, GPU memory management, and multi-GPU scheduling.

Wang, Qihan↗

On the Virasoro six-point identity block and chaos

We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge $c$ and a sparse spectrum, the leading contribution to this correlation function is the six-point Virasoro identity block - corresponding to each distinct pair of operators fusing into the identity and its descendants. We call this the star channel. One particular term in the star channel identity block is the stress tensor $SL(2,\mathbb{R})$ (global) block, for which we derive an explicit expression. In the holographic context, this object corresponds to a direct measure of nonlinear effects in pure gravity. We calculate additional terms in the star channel identity block that contribute at the same order at large $c$ as the global block using the novel theory of reparametrizations, which extends the shadow operator formalism in a natural way. We investigate these blocks' relevance to quantum chaos in the form of six-point scrambling in an out-of time ordered correlator. Interestingly, the global block does not contribute to the scrambling mode of this correlator, implying that, to leading order, six-point scrambling is insensitive to the three-point graviton coupling in the bulk dual. Finally, we compare our findings with a different OPE channel, called the comb channel, and find the same result for the chaos exponent in this decomposition.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Bottomonium properties in the quark-gluon plasma from a lattice-QCD informed 𝑇-matrix approach

Recent computations of bottomonium correlation functions with extended sources in lattice-discretized quantum chromodynamics (lQCD) provide new insights into heavy-quark dynamics at distance scales which are of the order of the inverse temperature. We analyze these results employing the thermodynamic 𝑇-matrix framework, in a continued effort to interpret lQCD data for quarkonium correlation functions in a nonperturbative and self-consistently solved quantum-many-body approach to a strongly coupled quark-gluon plasma (QGP). Its key inputs are the in-medium driving kernel (potential) of the scattering equation and an interference function which implements 3-body effects in the quarkonium coupling to the thermal medium. A simultaneous description of lQCD results for the bottomonium correlators with extended operators and the previously analyzed Wilson line correlators only requires minor refinements of the potential but calls for stronger interference effects at larger separation of the bottom quark and antiquark. We then analyze the poles of the self-consistent 𝑇 matrices on the real axis to assess the survival of the various bound states. Here, we estimate the pertinent temperatures where the poles disappear for the various bottomonium states and discuss the relation to the corresponding peaks in the bottomonium spectral functions. We also recalculate the spatial diffusion coefficient of the QGP and find it to be similar to that in our previous study.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗