A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Improved integrated nucleus-nucleus inelastic cross sections for light nuclides in Geant4

We propose a new root-mean-square radius parameterization for light nuclei A≤30 suitable for use in Geant4 calculations of nucleus-nucleus total hadronic inelastic scattering cross sections. The new approach takes into account the proton-neutron asymmetry of the reactants, and was fit to 360 measured total inelastic cross sections from the EXFOR database. Measured nuclear radii are better described in the new approach than the current Geant4 implementation, particularly for unstable nuclides, and there is better agreement with measured cross sections for both stable and unstable nuclides. The improved parameterization should help in carbon-ion therapy applications in particular

Influence of track structure and condensed history physics models of Geant4 to nanoscale electron transport in liquid water

The Geant4 toolkit offers a range of electromagnetic (EM) models for simulating the transport of charged particles down to sub-keV energies. They can be divided to condensed-history (CH) models (like the Livermore and Penelope models) and the track-structure (TS) models included in the Geant4-DNA low-energy extension of Geant4. Although TS models are considered the state-of-the-art for nanoscale electron transport, they are difficult to develop, computationally intensive, and commonly tailored to a single medium (e.g., water) which prohibits their use in a wide range of applications. Thus, the use of CH models down to sub-keV energies is particularly intriguing in the context of general-purpose Monte Carlo codes. The aim of the present work is to compare the performance of the CH models of Geant4 against the recently implemented TS models of Geant4-DNA for nanoscale electron transport. Calculations are presented for two fundamental quantities, the dose-point-kernel and the microdosimetric lineal energy. The influence of user-defined simulation parameters (tracking and production cuts, and maximum step size) on the above calculations is also examined. It is shown that Livermore offers the best performance among the CH models of Geant4 for nanoscale electron transport. However, even under optimally-chosen simulation parameters, the differences between the CH and TS models examined may be sizeable for low energy electrons (\u3c1 keV) and/or nanometer size targets (\u3c100 nm)

Evaluation of the influence of physical and chemical parameters on water radiolysis simulations under MeV electron irradiation using Geant4-DNA

This paper presents the influence of electron elastic scattering models, electron thermalization models, and chemical parameters on Geant4-DNA simulations of liquid water radiolysis under mega-electron-volt electron irradiation. The radiochemical yields are simulated using a new Geant4-DNA example. In particular, the influence of the new elastic scattering model recently developed is presented as well as the influence of improved electron thermalization models. The influence of a new chemistry constructor using parameters of another Monte Carlo track structure code is also described. The results calculated using these different models are compared with each other and with experimental data. For sub-mega-electron-volt electron simulations, the combination of the G4EmDNAPhysics-option2 physics constructor with the recently developed elastic scattering model, the Meesungnoen electron thermalization model, and the G4EmDNAChemistry-option1 chemistry constructor is recommended

Multiplicity dependence of the average transverse momentum in pp, p-Pb, and Pb-Pb collisions at the LHC

The average transverse momentum versus the charged-particle multiplicity $N_{ch}$ was measured in p-Pb collisions at a collision energy per nucleon-nucleon pair $\sqrt{s_{NN}}$ = 5.02 TeV and in pp collisions at collision energies of $\sqrt{s}$ = 0.9, 2.76, and 7 Tev in the kinematic range 0.15 with $N_{ch}$ is observed, which is much stronger than that measured in Pb-Pb collisions. For pp collisions, this could be attributed, within a model of hadronizing strings, to multiple-parton interactions and to a final-state color reconnection mechanism. The data in p-Pb and Pb-Pb collisions cannot be described by an incoherent superposition of nucleon-nucleon collisions and pose a challenge to most of the event generators

Charge correlations using the balance function in Pb?Pb collisions at ?sNN = 2.76 TeV

In high-energy heavy-ion collisions, the correlations between the emitted particles can be used as a probe to gain insight into the charge creation mechanisms. In this article, we report the first results of such studies using the electric charge balance function in the relative pseudorapidity \Delta\eta and azimuthal angle \Delta\phi in Pb-Pb collisions at sqrt{s_{NN}} = 2.76 TeV with the ALICE detector at the Large Hadron Collider. The width of the balance function decreases with growing centrality (i.e. for more central collisions) in both projections. This centrality dependence is not reproduced by HIJING, while AMPT, a model which incorporates strings and parton rescattering, exhibits qualitative agreement with the measured correlations in \Delta\phi but fails to describe the correlations in \Delta\eta. A thermal blast wave model incorporating local charge conservation and tuned to describe the p_T spectra and v_2 measurements reported by ALICE, is used to fit the centrality dependence of the width of the balance function and to extract the average separation of balancing charges at freeze-out. The comparison of our results with measurements at lower energies reveals an ordering with sqrt{s_{NN}}: the balance functions become narrower with increasing energy for all centralities. This is consistent with the effect of larger radial flow at the LHC energies but also with the late stage creation scenario of balancing charges. However, the relative decrease of the balance function widths in \Delta\eta and \Delta\phi with centrality from the highest SPS to the LHC energy exhibits only small differences. This observation cannot be interpreted solely within the framework where the majority of the charge is produced at a later stage in the evolution of the heavy-ion collision