Successive Splittings Research Articles

Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large- N QCD to N=3 via the SU(N) analog of Wigner 6‐j symbols

Consider a high-energy parton showering as it traverses a QCD medium such as a quark-gluon plasma. Interference effects between successive splittings in the shower are potentially very important but have so far been calculated (even in idealized theoretical situations) only in soft emission or large-$N_{\rm c}$ limits, where $N_{\rm c}$ is the number of quark colors. In this paper, we show how one may remove the assumption of large $N_{\rm c}$ and so begin investigation of $N_{\rm c}{=}3$ without soft-emission approximations. Treating finite $N_{\rm c}$ requires (i) classifying different ways that four gluons can form a color singlet and (ii) calculating medium-induced transitions between those singlets, for which we find application of results for the generalization of Wigner 6-$j$ symbols from angular momentum to SU($N_{\rm c}$). Throughout, we make use of the multiple scattering ($\hat q$) approximation for high-energy partons crossing quark-gluon plasmas, and we find that this approximation is self-consistent only if the transverse-momentum diffusion parameter $\hat q$ for different color representations satisfies Casimir scaling (even for strongly-coupled, and not just weakly-coupled, quark-gluon plasmas). We also find that results for $N_{\rm c}{=}3$ depend, mathematically, on being able to calculate the propagator for a coupled non-relativistic quantum harmonic oscillator problem in which the spring constants are operators acting on a 5-dimensional Hilbert space of internal color states. Those spring constants are represented by constant $5{\times}5$ matrices, which we explicitly construct. We are unaware of any closed form solution for this type of harmonic oscillator problem, and we discuss prospects for using numerical evaluation.

Forward trijet production in proton–nucleus collisions

Using the formalism of the light-cone wave function in perturbative QCD together with the hybrid factorization, we compute the cross-section for three particle production at forward rapidities in proton–nucleus collisions. We focus on the quark channel, in which the three produced partons — a quark accompanied by a gluon pair, or two quarks plus one antiquark — are all generated via two successive splittings starting with a quark that was originally collinear with the proton. The three partons are put on-shell by their scattering off the nuclear target, described as a Lorentz-contracted “shockwave”. The three-parton component of the quark light-cone wave function that we compute on this occasion is also an ingredient for other interesting calculations, like the next-to-leading order correction to the cross-section for the production of a pair of jets.

Pomeron interaction in the perturbative QCD

Formation of the triple pomeron vertices in processes P→PP→PPP and PP→P→PP is studied in the BFKL-Bartels approach. It is demonstarted that successive splittings of the pomeron indeed generate the standard triple pomeron vertex in agreement with the dipole approach. In contrast, in the process PP→P→PP the improper part of the vertex is found missing. Significance of this result is discussed in the framework of the theory of interacting pomerons.

Coulomb chronometry to probe the decay mechanism of hot nuclei

In 129 Xe+ nat Sn central collisions from 8 to 25 MeV/A, the three-fragment exit channel occurs with a significant cross section. We show that these fragments arise from two successive binary splittings of a heavy composite system. The sequence of fragment production is determined. Strong Coulomb proximity effects are observed in the three-fragment final state. A comparison with Coulomb trajec-tory calculations shows that the time scale between the consecutive break-ups decreases with increasing bombarding energy, becoming quasi-simultaneous above excitation energy E * = 4.0$\pm$0.5 MeV/A. This transition from sequential to simultaneous break-up was interpreted as the signature of the onset of multifragmentation for the three-fragment exit channel in this system.

Sequential fissions of heavy nuclear systems

In Xe+Sn central collisions from 12 to 20 MeV/A measured with the INDRA 4$\pi$ multidetector, the three-fragment exit channel occurs with a significant cross section. In this contribution, we show that these fragments arise from two successive binary splittings of a heavy composite system. Strong Coulomb proximity effects are observed in the three-fragment final state. By comparison with Coulomb trajectory calculations, we show that the time scale between the consecutive break-ups decreases with increasing bombarding energy, becoming compatible with quasi-simultaneous multifragmentation above 18 MeV/A.

Final state dipole showers and the DGLAP equation

We study a parton shower description, based on a dipole picture, of the final state in electron-positron annihilation. In such a shower, the distribution function describing the inclusive probability to find a quark with a given energy depends on the shower evolution time. Starting from the exclusive evolution equation for the shower, we derive an equation for the evolution of the inclusive quark energy distribution in the limit of strong ordering in shower evolution time of the successive parton splittings. We find that, as expected, this is the DGLAP equation. This paper is a response to a recent paper of Dokshitzer and Marchesini that raised troubling issues about whether a dipole based shower could give the DGLAP equation for the quark energy distribution.

O.258 3D control of resection margins in oral cancer based on PET/CT image-fusion

Background & Aims: Neoadjuvant chemoradiotherapy has become a standard treatment of locally advanced rectal carcinomas, even though the responsiveness varies from complete response to resistance. The aim of the study was to evaluate the capacity of gene expression signatures to identify responders and nonresponders pretherapeutically. Methods: By using microarray technology we generated gene expression profiles of 43 biopsy specimens of locally advanced rectal carcinomas. The transcription profile then was compared with histopathologic response and used to identify a set of genes discriminating responders from nonresponders. Results: We identified a gene expression signature of 42 genes, mostly encoding proteins that either play a role in the nucleus, such as the transcription factor ETS2, or are associated with transport function, such as the solute carrier SLC35E1, or the regulation of apoptosis, such as caspase-1. In leave-one-out cross-validation the correct classification of a responder was 71%, the specificity of the analysis for a correct classification of a nonresponder was 86%. By applying an additional statistical method of 200 successive splittings into training and test data sets we generated an individual prediction accuracy measure for each predicted response. Conclusions: Our study shows that pretherapeutic prediction of response of rectal carcinomas to neoadjuvant chemoradiotherapy is feasible, and may represent a new valuable and practical tool of therapeutic stratification.

Parton showers with quantum interference: leading color, with spin

We have previously described a mathematical formulation for a parton shower based on the approximation of strongly ordered virtualities of successive parton splittings. Quantum interference, including interference among different color and spin states, was included. A practical numerical implementation strategy was left unspecified. In a subsequent paper, we showed that if we add the further approximations of taking only the leading color limit and averaging over spins, we obtain a shower evolution that can be implemented as a Markov process. In this paper, we outline a strategy for including the correlations induced by parton spins.

Parton showers with quantum interference: leading color, spin averaged

We have previously described a mathematical formulation for a parton shower based on the approximation of strongly ordered virtualities of successive parton splittings. Quantum interference, including interference among different color and spin states, is included. In this paper, we add the further approximations of taking only the leading color limit and averaging over spins, as is common in parton shower Monte Carlo event generators. Soft gluon interference effects remain with this approximation. We find that the leading color, spin averaged shower in our formalism is similar to that in other shower formulations. We discuss some of the differences.

Microarray-Based Prediction of Tumor Response to Neoadjuvant Radiochemotherapy of Patients With Locally Advanced Rectal Cancer

Neoadjuvant chemoradiotherapy has become a standard treatment of locally advanced rectal carcinomas, even though the responsiveness varies from complete response to resistance. The aim of the study was to evaluate the capacity of gene expression signatures to identify responders and nonresponders pretherapeutically. By using microarray technology we generated gene expression profiles of 43 biopsy specimens of locally advanced rectal carcinomas. The transcription profile then was compared with histopathologic response and used to identify a set of genes discriminating responders from nonresponders. We identified a gene expression signature of 42 genes, mostly encoding proteins that either play a role in the nucleus, such as the transcription factor ETS2, or are associated with transport function, such as the solute carrier SLC35E1, or the regulation of apoptosis, such as caspase-1. In leave-one-out cross-validation the correct classification of a responder was 71%, the specificity of the analysis for a correct classification of a nonresponder was 86%. By applying an additional statistical method of 200 successive splittings into training and test data sets we generated an individual prediction accuracy measure for each predicted response. Our study shows that pretherapeutic prediction of response of rectal carcinomas to neoadjuvant chemoradiotherapy is feasible, and may represent a new valuable and practical tool of therapeutic stratification.

Vortex avalanches and magnetic flux fragmentation in superconductors.

We report the results of numerical simulations of nonisothermal dendritic flux penetration in type-II superconductors. We propose a generic mechanism of dynamic branching of a propagating hot spot of a flux flow/normal state triggered by a local heat pulse. The branching occurs when the flux hot spot reflects from inhomogeneities or the boundary on which magnetization currents either vanish, or change direction. The hot spot then undergoes a cascade of successive splittings, giving rise to a dissipative dendritic-type flux structure. This dynamic state eventually cools down, turning into a frozen multifilamentary pattern of magnetization currents.

Accessibilité hiérarchique des groupes de présentation finie

We prove that a finitely presented group admits a finite hierarchy obtained by successive splittings along a family of elementary subgroups.

Splitting trees

Splitting a tree is defined as removing all edges of a chain and disconnecting one from the other edges incident with that chain. Splitting a forest is simultaneously splitting each of its non-trivial trees. The splitting number σ( T) of a tree T is the minimum number of successive forest splittings which lead to deletion of all of T's edges. An O( N) algorithm is proposed to get an upper bound σ′( t), the connected splitting number, on the splitting number σ( t) of a tree T and an O( N log N) algorithm to compute this last number, where N is the number of vertices of the tree. Subject to a mild condition, these numbers lead to find a ‘black-and-white coloring’ of a tree T. In such a coloring a large part of T's vertices are colored in black or white and no two adjacent vertices receive a different color.

Changes of longitudinal vortex roll structure in a mixed convective air flow through a horizontal plane channel: an experimental study

Flow visualization and temperature measurement were conducted to investigate the buoyancy induced longitudinal vortex flow structure in a mixed convective air flow through a bottom heated horizontal plane channel for the Reynolds number ranging from 20 to 50 and Rayleigh number from 6000 to 30 000. The results suggested that at low buoyancy-to-inertia ratio a longitudinal roll pair with spanwise symmetry is first induced near the duct sides and more rolls are induced adjacent to the existing rolls as the flow moves downstream. Steady vortex flow prevails after the initial transient. At high buoyancy-to-inertia ratio the splitting and merging of the rolls take place frequently causing the flow to become unsteady and highly asymmetric at high Rayleigh numbers. Several types of the roll splitting processes were identified, namely, the splitting of one roll to three rolls and two rolls to four rolls, formation of two new rolls and two successive roll splittings of the above types. The reverse processes were noted during the roll merging. The data from the measured time histories of the air temperature indicated that the flow oscillation is position dependent with the oscillation amplitude being higher in the downstream core regions. Besides, the oscillation amplitude inside a roll is determined largely by the spanwise or axial position adjustment during the roll splitting and merging processes. Finally, the data for the onset of steady and unsteady vortex flows were empirically correlated.

Excitability, wave reflection, and wave splitting in a cubic autocatalysis reaction-diffusion system

The excitability properties of a two-variable cubic autocatalysis model for chemical oscillations are examined. The reaction-diffusion behaviour of this model is studied in a one-dimensional configuration with differing relative diffusivities of the species. Wave reflection at no-flux boundaries is examined and described in terms of reactant depletion in the wave front and reactant influx in the wave back. Waves are also reflected upon collision with other waves. Wave splitting, the spontaneous initiation of a wave from the trailing edge of another wave, is found to occur for some relative diffusivities. Successive wave splittings give rise to stationary Turing patterns at long times.

Rapid decrease of fragment emission time in the range of 3–5 MeV/u excitation energy

Multifragment emission processes from highly excited nuclei produced in 40Ar + 197Au reactions at incident energies of 30 and 60 MeV/u are compared. At the lowest bombarding energy and 3.3 MeV/u excitation energy, the composite system decay process supports the hypothesis of long-lived equilibrated nucleu decaying by successive binary splittings. For excited nuclei around 5 MeV/u, the depletion observed at small relative angles in the correlation functions is interpreted as the result of a strong reduction in the fragment emission time scale.

Theoretical determination of conformational paths in citrate synthase.

Two methods are developed for the theoretical determination of a conformational path between two well-documented forms, a closed form and the open form [Remington et al. (1982) J. Mol. Biol. 158, 111-152] of pig heart citrate synthase, a dimeric enzyme of 2 x 437 residues. The first method uses the minimization of the sum of the potential energies at a set of equidistant points, according to Elber and Karplus [(1987) Chem. Phys. Lett. 139, 375-380]. The initialization of the algorithm is modified to account for large-angle rotations of many groups by performing the interpolations in the space of internal polar coordinates of a set of generalized Jacobi vectors earlier introduced by Durup [(1991) J. Phys. Chem. 95, 1817-1829] and by carefully testing all choices of directions of rotation for determining the initialized midpoint between the known forms. The path includes intermediate points, created by successive splittings of each interval into two equal parts, with a partial energy minimization performed after each splitting. The minimization encounters the well-known local-minima problem, which here is handled by low-temperature molecular dynamics annealing. It is shown that the best ratio of potential energy decrease to rms deviation is achieved by running the dynamics at 50 K, as compared to 100 K and above. The main character of the path obtained is the occurrence of strong to-and-fro variations of some dihedral angles at specific stages along the path. The second method, which we name directed dynamics, uses only low-temperature molecular dynamics simulations by starting trajectories from each of the two known forms with initial velocities directed toward the other one. The procedure is iterated by restarting trajectory pairs after the points of closest approach of the preceding pair. The two half-paths thus built eventually meet after 70 iterations. This method provides a second path with strong similarities, as well as some differences, with respect to the path obtained by the first method.

Propagation of the normal zone in composite superconductors with high contact resistance

The propagation of the normal zone in composite superconductors with high thermal resistance and high electrical contact resistance between the superconducting and the normal components of the conductor is analysed. It is shown that in certain conditions propagation can result from successive multiple splittings of the resistive domain generated. The minimum initiation current of this process has been found and has been analysed as a function of the composite parameters and external conditions.

Separating, incompressible surfaces in 3-manifolds

Incompressible surfaces (see definition below) are one of the fundamental tools in the topological theory of 3-manifolds. The elementary fact that a compact, connected, orientable 3-manifold M with non-empty boundary contains a nonseparating, two-sided (definition below) incompressible surface is the starting point for Haken's theorem ([5], Theorem 13.3) that if M is also irreducible (w then it has a "hierarchy", i.e. can be reduced to a ball by successive splittings along two-sided incompressible surfaces. Most of the deeper known results on 3manifolds depend on this. For many purposes, separating incompressible surfaces seem more useful than non-separating ones. This is apparent, for example, to anyone who has studied fundamental groups of 3-manifolds by using hierarchies: a separating incompressible surface in M yields a decomposition of zrl(M ) as a free product with amalgamation, whereas a non-separating one gives only an " H N N decomposition" of nl(M), from which group-theoretical experience shows that it is much harder to extract information. On the other hand, separating incompressible surfaces which are non-triviali.e. not boundary-parallel (see below) have, until now, seemed very hard to come by, except in examples. The main theorem of this paper, Theorem 1 of Sect. 4, guarantees that a compact connected orientable 3-manifold M will have a non-trivial separating incompressible surface provided that H I (M;Q) is carried by the boundary of M and that some boundary component of M has genus > 1. This is used to prove Theorem 2 of Sect. 5, which asserts that if in addition M is irreducible and every incompressible torus in M is boundary-parallel, then M can be reduced to a disjoint union of solid tori and products of 2-tori with closed intervals by successive splittings along separating incompressible surfaces. As a corollary we get an analogous result for a large class of homology 3-spheres. Theorem 1 is quite deep, for it depends on William Thurston's recent work on hyperbolic structures in 3-manifolds. The proof combines one of Thurston's results with an algebraic result of Hyman Bass's (based on work of Serre's) and some elementary algebraic geometry. This material is reviewed in Sects. 1 and 3.

Polymorphism and Twinning in Synthetic Fluorophlogopite

Optical and X-ray studies of large, clear flakes of synthetic fluorophlogopite reveal that approximately 29 per cent are not single crystals as has been previously assumed. Instead these are composed of two or more 1M polymorphs that possess a common (001) direction but are twinned about the [310] axis or, much more rarely, about [110]. The composition surface is irregular, and the boundary between twinned individual crystals of successive splittings generally cannot be superposed. Layers of the 3T polymorph are infrequently present either interleaved between layers of the much more abundant 1M type or sometimes, in single cleavage flakes, as islands surrounded by the 1M type. The direction of layer stagger probably varies even within a single phlogopite layer. Variations of 60° or 180° in this direction are attributed to irregularities in the location of the magnesium ions. The far more frequently observed variations of 120° in the layer-stagger direction for phlogopite are the result of irregularities in the location of the fluoride (or hydroxyl) ions.