Fraction of uninfected walkers in the one-dimensional Potts model

The dynamics of the one-dimensional q-state Potts model, in the zero temperature limit, can be formulated through the motion of random walkers which either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is investigated numerically and found to decay algebraically, U(t) \sim t^{-\phi(q)}, with a nontrivial exponent \phi(q). Our study is extended to include the coupled diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as \rho(t) \sim t^{-1/2}. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t) \sim t^{-\theta} with \theta \simeq 1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t) \sim t^{-\phi}, where \phi \simeq 1.13 when infection occurs between like particles only, and \phi \simeq 1.93 when we also include cross-species contamination.Comment: Expanded introduction with more discussion of related wor

Growth Based Morphogenesis of Vertebrate Limb Bud

Many genes and their regulatory relationships are involved in developmental phenomena. However, by chemical information alone, we cannot fully understand changing organ morphologies through tissue growth because deformation and growth of the organ are essentially mechanical processes. Here, we develop a mathematical model to describe the change of organ morphologies through cell proliferation. Our basic idea is that the proper specification of localized volume source (e.g., cell proliferation) is able to guide organ morphogenesis, and that the specification is given by chemical gradients. We call this idea “growth-based morphogenesis.” We find that this morphogenetic mechanism works if the tissue is elastic for small deformation and plastic for large deformation. To illustrate our concept, we study the development of vertebrate limb buds, in which a limb bud protrudes from a flat lateral plate and extends distally in a self-organized manner. We show how the proportion of limb bud shape depends on different parameters and also show the conditions needed for normal morphogenesis, which can explain abnormal morphology of some mutants. We believe that the ideas shown in the present paper are useful for the morphogenesis of other organs

Revisiting the HD 21749 planetary system with stellar activity modelling

HD 21749 is a bright (V = 8.1 mag) K dwarf at 16 pc known to host an inner terrestrial planet HD 21749c as well as an outer sub-Neptune HD 21749b, both delivered by Transiting Exoplanet Survey Satellite (TESS). Follow-up spectroscopic observations measured the mass of HD 21749b to be 22.7 ± 2.2 M with a density of 7.0^{+1.6}_{-1.3} g cm-3, making it one of the densest sub-Neptunes. However, the mass measurement was suspected to be influenced by stellar rotation. Here, we present new high-cadence PFS RV data to disentangle the stellar activity signal from the planetary signal. We find that HD 21749 has a similar rotational time-scale as the planet's orbital period, and the amplitude of the planetary orbital RV signal is estimated to be similar to that of the stellar activity signal. We perform Gaussian process regression on the photometry and RVs from HARPS and PFS to model the stellar activity signal. Our new models reveal that HD 21749b has a radius of 2.86 ± 0.20 R, an orbital period of 35.6133 ± 0.0005 d with a mass of Mb = 20.0 ± 2.7 M and a density of 4.8^{+2.0}_{-1.4} g cm-3 on an eccentric orbit with e = 0.16 ± 0.06, which is consistent with the most recent values published for this system. HD 21749c has an orbital period of 7.7902 ± 0.0006 d, a radius of 1.13 ± 0.10 R, and a 3σ mass upper limit of 3.5 M. Our Monte Carlo simulations confirm that without properly taking stellar activity signals into account, the mass measurement of HD 21749b is likely to arrive at a significantly underestimated error bar

First measurement of Xi(-) polarization in photoproduction

Despite decades of studies of the photoproduction of hyperons, both their production mechanisms and their spectra of excited states are still largely unknown. While the parity-violating weak decay of hyperons offers a means of measuring their polarization, which could help discern their production mechanisms and identify their excitation spectra, no such study has been possible for doubly strange baryons in photoproduction, due to low production cross sections. However, by making use of the reaction γp→K+K+Ξ−, we have measured, for the first time, the induced polarization, P, and the transferred polarization from circularly polarized real photons, characterized by Cx and Cz, to recoiling Ξ−s. The data were obtained using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab for photon energies from just over threshold (2.4 GeV) to 5.45 GeV. These first-time measurements are compared, and are shown to broadly agree, with model predictions in which cascade photoproduction proceeds through the decay of intermediate hyperon resonances that are produced via relativistic meson exchange, offering a new step forward in the understanding of the production and polarization of doubly-strange baryons

First measurement of the helicity asymmetry E in eta photoproduction on the proton

Results are presented for the first measurement of the double-polarization helicity asymmetry E for the $\eta$ photoproduction reaction $\gamma p \rightarrow \eta p$. Data were obtained using the FROzen Spin Target (FROST) with the CLAS spectrometer in Hall B at Jefferson Lab, covering a range of center-of-mass energy W from threshold to 2.15 GeV and a large range in center-of-mass polar angle. As an initial application of these data, the results have been incorporated into the J\"ulich model to examine the case for the existence of a narrow $N^*$ resonance between 1.66 and 1.70 GeV. The addition of these data to the world database results in marked changes in the predictions for the E observable using that model. Further comparison with several theoretical approaches indicates these data will significantly enhance our understanding of nucleon resonances

Photon beam asymmetry Sigma for eta and eta ' photoproduction from the proton

Measurements of the linearly-polarized photon beam asymmetry $\Sigma$ for photoproduction from the proton of $\eta$ and $\eta^\prime$ mesons are reported. A linearly-polarized tagged photon beam produced by coherent bremsstrahlung was incident on a cryogenic hydrogen target within the CEBAF Large Acceptance Spectrometer. Results are presented for the $\gamma p \to \eta p$ reaction for incident photon energies from 1.070 to 1.876 GeV, and from 1.516 to 1.836 GeV for the $\gamma p \to \eta^\prime p$ reaction. For $\gamma p \to \eta p$, the data reported here considerably extend the range of measurements to higher energies, and are consistent with the few previously published measurements for this observable near threshold. For $\gamma p \to \eta^\prime p$, the results obtained are consistent with the few previously published measurements for this observable near threshold, but also greatly expand the incident photon energy coverage for that reaction. Initial analysis of the data reported here with the Bonn-Gatchina model strengthens the evidence for four nucleon resonances -- the $N(1895)1/2^-$, $N(1900)3/2^+$, $N(2100)1/2^+$ and $N(2120)3/2^-$ resonances -- which presently lack the "four-star" status in the current Particle Data Group compilation, providing examples of how these new measurements help refine models of the photoproduction process.Comment: 10 pages, 3 figure

First measurement of the polarization observable E in the p→(γ→,π⁺)n reaction up to 2.25 GeV

First results from the longitudinally polarized frozen-spin target (FROST) program are reported. The double-polarization observable E, for the reaction $\vec \gamma \vec p \to \pi^+n$, has been measured using a circularly polarized tagged-photon beam, with energies from 0.35 to 2.37 GeV. The final-state pions were detected with the CEBAF Large Acceptance Spectrometer in Hall B at the Thomas Jefferson National Accelerator Facility. These polarization data agree fairly well with previous partial-wave analyses at low photon energies. Over much of the covered energy range, however, significant deviations are observed, particularly in the high-energy region where high-L multipoles contribute. The data have been included in new multipole analyses resulting in updated nucleon resonance parameters. We report updated fits from the Bonn-Gatchina, J\"ulich, and SAID groups.Comment: 6 pages, 3 figure