On-the-fly Uniformization of Time-Inhomogeneous Infinite Markov Population Models

This paper presents an on-the-fly uniformization technique for the analysis of time-inhomogeneous Markov population models. This technique is applicable to models with infinite state spaces and unbounded rates, which are, for instance, encountered in the realm of biochemical reaction networks. To deal with the infinite state space, we dynamically maintain a finite subset of the states where most of the probability mass is located. This approach yields an underapproximation of the original, infinite system. We present experimental results to show the applicability of our technique

Measuring the Polarization of a Rapidly Precessing Deuteron Beam

This paper describes a time-marking system that enables a measurement of the in-plane (horizontal) polarization of a 0.97-GeV/c deuteron beam circulating in the Cooler Synchrotron (COSY) at the Forschungszentrum J\"ulich. The clock time of each polarimeter event is used to unfold the 120-kHz spin precession and assign events to bins according to the direction of the horizontal polarization. After accumulation for one or more seconds, the down-up scattering asymmetry can be calculated for each direction and matched to a sinusoidal function whose magnitude is proportional to the horizontal polarization. This requires prior knowledge of the spin tune or polarization precession rate. An initial estimate is refined by re-sorting the events as the spin tune is adjusted across a narrow range and searching for the maximum polarization magnitude. The result is biased toward polarization values that are too large, in part because of statistical fluctuations but also because sinusoidal fits to even random data will produce sizeable magnitudes when the phase is left free to vary. An analysis procedure is described that matches the time dependence of the horizontal polarization to templates based on emittance-driven polarization loss while correcting for the positive bias. This information will be used to study ways to extend the horizontal polarization lifetime by correcting spin tune spread using ring sextupole fields and thereby to support the feasibility of searching for an intrinsic electric dipole moment using polarized beams in a storage ring. This paper is a combined effort of the Storage Ring EDM Collaboration and the JEDI Collaboration.Comment: 28 pages, 15 figures, prepared for Physical Review ST - Accelerators and Beam

Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions

Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A + B -> C, or A + A -> C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site).Comment: 33 pages, submitted to Physical Biolog

Wind-US Code Physical Modeling Improvements to Complement Hypersonic Testing and Evaluation

This report gives an overview of physical modeling enhancements to the Wind-US flow solver which were made to improve the capabilities for simulation of hypersonic flows and the reliability of computations to complement hypersonic testing. The improvements include advanced turbulence models, a bypass transition model, a conjugate (or closely coupled to vehicle structure) conduction-convection heat transfer capability, and an upgraded high-speed combustion solver. A Mach 5 shock-wave boundary layer interaction problem is used to investigate the benefits of k- s and k-w based explicit algebraic stress turbulence models relative to linear two-equation models. The bypass transition model is validated using data from experiments for incompressible boundary layers and a Mach 7.9 cone flow. The conjugate heat transfer method is validated for a test case involving reacting H2-O2 rocket exhaust over cooled calorimeter panels. A dual-mode scramjet configuration is investigated using both a simplified 1-step kinetics mechanism and an 8-step mechanism. Additionally, variations in the turbulent Prandtl and Schmidt numbers are considered for this scramjet configuration

Dependence of pp->pp pi0 near Threshold on the Spin of the Colliding Nucleons

A polarized internal atomic hydrogen target and a stored, polarized beam are used to measure the spin-dependent total cross section Delta_sigma_T/sigma_tot, as well as the polar integrals of the spin correlation coefficient combination A_xx-A_yy, and the analyzing power A_y for pp-> pp pi0 at four bombarding energies between 325 and 400 MeV. This experiment is made possible by the use of a cooled beam in a storage ring. The polarization observables are used to study the contribution from individual partial waves.Comment: 6 pages, 1 table, 4 figures, corrected equations 2 and

Toward polarized antiprotons: Machine development for spin-filtering experiments

The paper describes the commissioning of the experimental equipment and the machine studies required for the first spin-filtering experiment with protons at a beam kinetic energy of $49.3\,$MeV in COSY. The implementation of a low-$\beta$ insertion made it possible to achieve beam lifetimes of $\tau_{\rm{b}}=8000\,$s in the presence of a dense polarized hydrogen storage-cell target of areal density $d_{\rm t}=(5.5\pm 0.2)\times 10^{13}\,\mathrm{atoms/cm^{2}}$. The developed techniques can be directly applied to antiproton machines and allow for the determination of the spin-dependent $\bar{p}p$ cross sections via spin filtering

Spin tune mapping as a novel tool to probe the spin dynamics in storage rings

Precision experiments, such as the search for electric dipole moments of charged particles using storage rings, demand for an understanding of the spin dynamics with unprecedented accuracy. The ultimate aim is to measure the electric dipole moments with a sensitivity up to 15 orders in magnitude better than the magnetic dipole moment of the stored particles. This formidable task requires an understanding of the background to the signal of the electric dipole from rotations of the spins in the spurious magnetic fields of a storage ring. One of the observables, especially sensitive to the imperfection magnetic fields in the ring is the angular orientation of stable spin axis. Up to now, the stable spin axis has never been determined experimentally, and in addition, the JEDI collaboration for the first time succeeded to quantify the background signals that stem from false rotations of the magnetic dipole moments in the horizontal and longitudinal imperfection magnetic fields of the storage ring. To this end, we developed a new method based on the spin tune response of a machine to artificially applied longitudinal magnetic fields. This novel technique, called \textit{spin tune mapping}, emerges as a very powerful tool to probe the spin dynamics in storage rings. The technique was experimentally tested in 2014 at the cooler synchrotron COSY, and for the first time, the angular orientation of the stable spin axis at two different locations in the ring has been determined to an unprecedented accuracy of better than $2.8\mu$rad.Comment: 32 pages, 15 figures, 7 table

Phase Measurement for Driven Spin Oscillations in a Storage Ring

This paper reports the first simultaneous measurement of the horizontal and vertical components of the polarization vector in a storage ring under the influence of a radio frequency (rf) solenoid. The experiments were performed at the Cooler Synchrotron COSY in J\"ulich using a vector polarized, bunched $0.97\,\textrm{GeV/c}$ deuteron beam. Using the new spin feedback system, we set the initial phase difference between the solenoid field and the precession of the polarization vector to a predefined value. The feedback system was then switched off, allowing the phase difference to change over time, and the solenoid was switched on to rotate the polarization vector. We observed an oscillation of the vertical polarization component and the phase difference. The oscillations can be described using an analytical model. The results of this experiment also apply to other rf devices with horizontal magnetic fields, such as Wien filters. The precise manipulation of particle spins in storage rings is a prerequisite for measuring the electric dipole moment (EDM) of charged particles

Exclusive Measurements of pp -> dpi+pi0: Double-Pionic Fusion without ABC Effect

Exclusive measurements of the reaction pp -> dpi+pi0 have been carried out at T_p = 1.1 GeV at the CELSIUS storage ring using the WASA detector. The isovector pi+pi0 channel exhibits no enhancement at low invariant pipi masses, i. e. no ABC effect. The differential distributions are in agreement with the conventional t-channel Delta-Delta excitation process, which also accounts for the observed energy dependence of the total cross section. This is an update of a previously published version -- see important note at the end of the article