Scaling of the linear response in simple ageing systems without disorder

The time-dependent scaling of the thermoremanent and zero-field-cooled susceptiblities in ferromagnetic spin systems undergoing ageing after a quench to a temperature at or below criticality is studied. A recent debate on their interpretation is resolved by showing that for systems with a short-ranged equilibrium spin-spin correlator and above their roughening temperature, the field-cooled susceptibility $\chi_{\rm FC}(t)-\chi_0\sim t^{-A}$ where $\chi_0$ is related to the equilibrium magnetization and the exponent A is related to the time-dependent scaling of the interface width between ordered domains. The same effect also dominates the scaling of the zero-field-cooled susceptibility $\chi_{\rm ZFC}(t,s)$, but does not enter into the thermoremanent susceptibility $\rho_{\rm TRM}(t,s)$. However, there may be large finite-time corrections to the scaling of $\rho_{\rm TRM}(t,s)$ which are explicitly derived and may be needed in order to extract reliable ageing exponents. Consistency with the predictions of local scale invariance is confirmed in the Glauber-Ising and spherical models.Comment: Latex2e, 14 pages, with 6 figure

Spatial clustering of interacting bugs: Levy flights versus Gaussian jumps

A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption that the reproduction rate depends on the crowding in the neighborhood. The spatial dynamics corresponds either to normal diffusion characterized by Gaussian jumps or to superdiffusion characterized by L\'evy flights. It is observed that in both cases periodic patterns occur for appropriate parameters of the model, indicating that the general macroscopic collective behavior of the system is more strongly influenced by the competition for the resources than by the type of spatial dynamics. However, some differences arise that are discussed.Comment: This version incorporates in the text the correction published as an Erratum in Europhysics Letters (EPL) 95, 69902 (2011) [doi: 10.1209/0295-5075/95/69902

Management of Febrile Neutropenia - a German Prospective Hospital Cost Analysis in Lymphoproliferative Disorders, Non-Small Cell Lung Cancer, and Primary Breast Cancer

Background: Febrile neutropenia/leukopenia (FN/FL) is the most frequent dose-limiting toxicity of myelosuppressive chemotherapy, but German data on economic consequences are limited. Patients and Methods: A prospective, multicentre, longitudinal, observational study was carried out to evaluate the occurrence of FN/FL and its impact on health resource utilization and costs in non-small cell lung cancer (NSCLC), lymphoproliferative disorder (LPD), and primary breast cancer (PBC) patients. Costs are presented from a hospital perspective. Results: A total of 325 consecutive patients (47% LPD, 37% NSCLC, 16% PBC; 46% women; 38% age >= 65 years) with 68 FN/FL episodes were evaluated. FN/FL occurred in 22% of the LPD patients, 8% of the NSCLC patients, and 27% of the PBC patients. 55 FN/FL episodes were associated with at least 1 hospital stay (LPD n = 34, NSCLC n = 10, PBC n = 11). Mean (median) cost per FN/FL episode requiring hospital care amounted to (sic) 3,950 ((sic) 2,355) and varied between (sic) 4,808 ((sic) 3,056) for LPD, (sic) 3,627 ((sic) 2,255) for NSCLC, and (sic) 1,827 ((sic) 1,969) for PBC patients. 12 FN/FL episodes (LPD n = 9, NSCLC n = 3) accounted for 60% of the total expenses. Main cost drivers were hospitalization and drugs (60 and 19% of the total costs). Conclusions: FN/FL treatment has economic relevance for hospitals. Costs vary between tumour types, being significantly higher for LPD compared to PBC patients. The impact of clinical characteristics on asymmetrically distributed costs needs further evaluation

Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model

The steady-state of a generalized coagulation-decoagulation model on a one-dimensional lattice with reflecting boundaries is studied using a matrix-product approach. It is shown that the quadratic algebra of the model has a four-dimensional representation provided that some constraints on the microscopic reaction rates are fulfilled. The dynamics of a product shock measure with two shock fronts, generated by the Hamiltonian of this model, is also studied. It turns out that the shock fronts move on the lattice as two simple random walkers which repel each other provided that the same constraints on the microscopic reaction rates are satisfied.Comment: Minor revision

Relaxation time in a non-conserving driven-diffusive system with parallel dynamics

We introduce a two-state non-conserving driven-diffusive system in one-dimension under a discrete-time updating scheme. We show that the steady-state of the system can be obtained using a matrix product approach. On the other hand, the steady-state of the system can be expressed in terms of a linear superposition Bernoulli shock measures with random walk dynamics. The dynamics of a shock position is studied in detail. The spectrum of the transfer matrix and the relaxation times to the steady-state have also been studied in the large-system-size limit.Comment: 10 page

Ergodicity breaking in one-dimensional reaction-diffusion systems

We investigate one-dimensional driven diffusive systems where particles may also be created and annihilated in the bulk with sufficiently small rate. In an open geometry, i.e., coupled to particle reservoirs at the two ends, these systems can exhibit ergodicity breaking in the thermodynamic limit. The triggering mechanism is the random motion of a shock in an effective potential. Based on this physical picture we provide a simple condition for the existence of a non-ergodic phase in the phase diagram of such systems. In the thermodynamic limit this phase exhibits two or more stationary states. However, for finite systems transitions between these states are possible. It is shown that the mean lifetime of such a metastable state is exponentially large in system-size. As an example the ASEP with the A0A--AAA reaction kinetics is analyzed in detail. We present a detailed discussion of the phase diagram of this particular model which indeed exhibits a phase with broken ergodicity. We measure the lifetime of the metastable states with a Monte Carlo simulation in order to confirm our analytical findings.Comment: 25 pages, 14 figures; minor alterations, typos correcte

Ageing in bosonic particle-reaction models with long-range transport

Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Levy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is found and analysed. Exact results for non-equilibrium exponents and scaling functions are derived. The behaviour of the fluctuation-dissipation ratio is analysed. A passage time from the quasi-stationary regime to the ageing regime is defined, in qualitative agreement with kinetic spherical models and p-spin spherical glasses.Comment: Latex2e, 24 pages, with 9 figures include

Reaction fronts in stochastic exclusion models with three-site interactions

The microscopic structure and movement of reaction fronts in reaction diffusion systems far from equilibrium are investigated. We show that some three-site interaction models exhibit exact diffusive shock measures, i.e. domains of different densities connected by a sharp wall without correlations. In all cases fluctuating domains grow at the expense of ordered domains, the absence of growth is possible between ordered domains. It is shown that these models give rise to aspects not seen in nearest neighbor models, viz. double shocks and additional symmetries. A classification of the systems by their symmetries is given and the link of domain wall motion and a free fermion description is discussed.Comment: 29 pages, 5 figure

Dynamics of an exclusion process with creation and annihilation

We examine the dynamical properties of an exclusion process with creation and annihilation of particles in the framework of a phenomenological domain-wall theory, by scaling arguments and by numerical simulation. We find that the length- and time scale are finite in the maximum current phase for finite creation- and annihilation rates as opposed to the algebraically decaying correlations of the totally asymmetric simple exclusion process (TASEP). Critical exponents of the transition to the TASEP are determined. The case where bulk creation- and annihilation rates vanish faster than the inverse of the system size N is also analyzed. We point out that shock localization is possible even for rates proportional to 1/N^a, 1<a<2.Comment: 16 pages, 8 figures, typos corrected, references added, section 4 revise

The non-equilibrium phase transition of the pair-contact process with diffusion

The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles is a simple branching-annihilation processes which exhibits a phase transition from an active into an absorbing phase with an unusual type of critical behaviour which had not been seen before. Although the model has attracted considerable interest during the past few years it is not yet clear how its critical behaviour can be characterized and to what extent the diffusive pair-contact process represents an independent universality class. Recent research is reviewed and some standing open questions are outlined.Comment: Latexe2e, 53 pp, with IOP macros, some details adde