High-energy strong interactions: from ‘hard’ to ‘soft’

We discuss the qualitative features of the recent data on multiparticle production observed at the LHC. The tolerable agreement with Monte Carlos based on LO DGLAP evolution indicates that there is no qualitative difference between ‘hard’ and ‘soft’ interactions; and that a perturbative QCD approach may be extended into the soft domain. However, in order to describe the data, these Monte Carlos need an additional infrared cutoff k _min with a value k _min∼2–3 GeV which is not small, and which increases with collider energy. Here we explain the physical origin of the large k _min. Using an alternative model which matches the ‘soft’ high-energy hadron interactions smoothly on to perturbative QCD at small x, we demonstrate that this effective cutoff k _min is actually due to the strong absorption of low k _t partons. The model embodies the main features of the BFKL approach, including the diffusion in transverse momenta, ln k _t , and an intercept consistent with resummed next-to-leading log corrections. Moreover, the model uses a two-channel eikonal framework, and includes the contributions from the multi-Pomeron exchange diagrams, both non-enhanced and enhanced. The values of a small number of physically-motivated parameters are chosen to reproduce the available total, elastic and proton dissociation cross section (pre-LHC) data. Predictions are made for the LHC, and the relevance to ultra-high-energy cosmic rays is briefly discussed. The low x inclusive integrated gluon PDF, and the diffractive gluon PDF, are calculated in this framework, using the parameters which describe the high-energy pp and p[`(p)]p\bar{p} ‘soft’ data. Comparison with the PDFs obtained from the global parton analyses of deep inelastic and related hard scattering data and from diffractive deep inelastic data looks encouraging.     

The rate of molecular collisions in gases composed of ‘soft’ molecules

Equations are derived for the number of collisions per unit time in which the centres of the molecules approach to some arbitrary distance, d, or less, for molecules with spherical intermolecular potentials. The collision rates based upon this criterion of closeness-of-approach have a different dependence on temperature from those based upon cross sections determined from the viscosity. It is suggested that the rates calculated in this paper are the more appropriate for the discussion of experiments on the exchange of molecular energy and on the kinetics of chemical reactions.     

Study on‘soft＇ and ‘hard＇ interactions in ^-pp （pp） collisions using HIJING and PYTHIA

This paper presents a study on ＇hard＇ and ＇soft＇ interactions in ^-pp （pp） collisions using a phenomenological model of HIJING, the jet-cone reconstruction method is employed to select the ＇hard＇ and ＇soft＇ event sub-samples from minimum bias events. It is found that the HIJING model can reproduce the energy scaling behaviour of mean transverse momentum （〈PT〉） distributions of charged hadrons versus multiplicity （Nch） in ＇soft＇ events. From the PYTHIA simulation comparing with the HIJING model, the enhancement of the kaon and proton yields from ＇hard＇ interactions comparing with ＇soft＇ interactions is observed to be due to the mini-jets effect. These mechanisms responsible for the increase of charged hadron＇s （PT） are different in ＇soft＇ and ＇hard＇ interactions.     

Photoluminescence in “hard” and “soft” ferroelectric ceramics

In the previous years the ferroelectrics perovskites has shown an increase in the study for optical applications. What do materials take advantage of, the so-called soft or hard dopants? In this work we try to clarify some of these aspects analyzing a classic perovskite-type structure system like Pb _0.95 Sr _0.05(Zr _0.53 Ti _0.47)_1?y Cr _y O _3?y/2 (PSZTC) andPb _1?3x/2 La _x (Zr _0.53 Ti _0.47)_1?y Nb _y O _3?y/2 (PLZTN), hard and soft respectively. Photoluminescence, optical absorption spectroscopy, Raman spectroscopy, structural and micro-structural measurements have been carried out. The results revealed the role of the Cr, La and Nb ion substitutions in photoluminescence spectra, energy gap, Raman response, morphology grain size and the symmetry presented in these materials near the morphotropic phase boundary (MPB).     

Out-of-roundness and thermal energy effects on ‘ideally soft ferromagnets’

Infinite initial susceptibility is predicted in certain micro-magnetic computations of sufficiently small spheres and circular discs made of isotropic magnetic material. In this letter, it is argued that this result pertains only to perfectly round samples in the absence of thermal energy. It is expected, therefore, that much lower values of the initial susceptibility will be found on experimentally realizable samples at room temperature.     

Ramanujan’s ‘‘Lost Notebook’’ and the Virasoro Algebra

By using the theory of vertex operator algebras, we gave a new proof of the famous Ramanujans modulus 5 modular equation from his Lost Notebook (p. 139 in [R]). Furthermore, we obtained an infinite list of q-identities for all odd moduli; thus, we generalized the result of Ramanujan.Acknowledgements It was indeed hard to trace all the known proofs of (1.1), (1.2) and (1.3). We apologize if some important references are omitted. We would like to thank Jim Lepowsky for conversations on many related subjects. A few years ago Lepowsky and the author were trying to relate classical Rogers-Ramanujan identities and Zhus work [Z]. We also thank Bruce Berndt for pointing us to [BrO] and Steve Milne for bringing [Mi] to our attention.     

Response to ‘On the orthogonality of the phase velocity and its feasibility for plane waves’

A recent theoretical study of plane waves with orthogonal phase velocity is premised on incorrect assumptions. The conclusion reached therein – namely, that “a plane wave with orthogonal phase velocity cannot possess linear momentum” and therefore “cannot propagate at all” – is incorrect in general.     

Per cent ‘covalency’ and the nephelauxetic effect in lanthanide complexes

The use of the nephelauxetic ratio for the calculation of percent covalency is examined. Values of F_k and E^k obtained from four parameter fits (e.g. F ₂, F ₄, F ₆ and ζ_4f) neglecting configuration interaction for Pr³⁺ in various host lattices are compared to those of the free ion. By including the effects of 4f-ligand overlap one can account for the empirically obtained order of sensitivity to the environment for F_k : F ₂ > F ₄ > F ₆ and for E^k : E ² > E ³ > E ¹. The results further indicate that by using the nephelauxetic effect and the relationship b = (1 - β)/2 one is likely to overestimate the degree of covalency of a complex.     

‘Planetodiversity’: the variety of planets and planetary systems in the Universe

‘Planetodiversity’ is a composite word from planetary diversity. This denomination wants to parallel the common use of the term biodiversity employed in biology but translated here to the context of planetary sciences due to the proliferating variety of planets discovered outside the Solar System and theoretically proposed to exist. There are two properties that allow us a classification of a body as a planet or more generally as a ‘planetary mass object’: the orbital configuration and the physical structure (mass, energy and chemical composition). This leads respectively to the concepts that we term the ‘orbital planetodiversity’ and the ‘physical planetodiversity’. We present in a comparative way the basic planetary types observed or expected to exist within the framework of these two concepts.     

Arthur Cayley and the ‘Gruppen Pest’

The original contributions of Arthur Cayley to the Philosophical Magazine on group theory and his ‘trees’ are revisited and to some extend reinterpreted. Both topics were and are of enormous importance not only in physics (group theory, graph theory), but also in quite a few other disciplines as diverse as information technology or, for example, linguistics (trees, graph theory). In order to show that these two topics originally arose from interests in the theory of permutations also Cayley’s ‘Mousetrap’ game is briefly mentioned.     

‘Percolative’ dynamics in the hexagonal lattice

We study a percolative dynamic model for the hexagonal lattice. Random trajectories are generated and their critical behaviour is studied. The critical behaviour corresponds to that of simple percolatio in some of the parameter space, but elsewhere the exponents reveal new universality classes. We calculate the fractal dimension of extended trajectories for different critical points.     

Constraints on the nuclear symmetry energy and its density slope from the α decay process

We study the impact of the nuclear symmetry energy and its density dependence on the α-decay process.Within the framework of the preformed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state(EOS). Each EOS is characterized by a particular symmetryenergy coefficient(a_(sym)) and a corresponding density-slope parameter L. The stepwise trends of the neutron(proton) skin thickness of the involved nuclei with both asym and L do not clarify the oscillating behaviors of the α-decay half-life T_α with these quantities. We find that the change of the skin thickness after α-decay satisfactorily explains these behaviors. The presented results provide constraints on asym centered around an optimum value a_(sym) = 32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an α-decay,yield a minimum calculated half-life with the same extracted value of the α-preformation factor inside the parent nucleus.     

Simulating Suppression Effects in Pulsed ENDOR, and the ‘Hole in the Middle’ of Mims and Davies ENDOR Spectra

All pulsed electron-nuclear double resonance (ENDOR) techniques, and in particular the Mims and Davies sequences, suffer from detectability biases (‘blindspots’) that are directly correlated to the size of the hyperfine interactions of coupled nuclei. Our efforts at ENDOR ‘crystallography’ and ‘mechanism determination’ with these techniques have led our group to refine our simulations of pulsed ENDOR spectra to take into account these biases, and we here describe the process and illustrate it with several examples. We first focus on an issue whose major significance is not widely appreciated, the ‘hole in the middle’ of pulsed ENDOR spectra caused by the n = 0 suppression hole in Mims ENDOR and by the analogous A → 0 suppression in Davies ENDOR for I = ½ and for ²H (I = 1). We then discuss the general treatment of suppression effects for I = 1, illustrating it with a treatment of Mims suppression for ¹⁴N.     

Heat release rate as represented by [OH] × [CH2O] and its role in autoignition

Data from a recent instantaneous, simultaneous, high-resolution imaging experiment of Rayleigh temperature and laser induced fluorescence (LIF) of OH and CH₂O at the base of a turbulent lifted methane flame issuing into a hot vitiated coflow are analysed and contrasted to reference flames to further investigate the stabilization mechanisms involved. The use of the product of the quantified OH and semi-quantified CH₂O images as a marker for heat release rate is validated for transient autoigniting laminar flames. This is combined with temperature gradient information to investigate the flame structure. Super-equilibrium OH, the nature of the profiles of heat release rate with respect to OH mole fraction, and comparatively high peak heat release rates at low temperature gradients is found in the kernel structures at the flame base, and found to be indicative of autoignition stabilization.     

Soft processes at the LHC,II: soft–hard factorisation breaking and gap survival

We calculate the probability that the rapidity gaps in diffractive processes survive both eikonal and enhanced rescattering. We present arguments that enhanced rescattering, which violates soft–hard factorisation, is not very strong. Accounting for NLO effects, there is no reason to expect that the black-disc regime is reached at the LHC. We discuss the predictions for the survival of the rapidity gaps for exclusive Higgs production at the LHC.