Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Microscopic Theory of Anchoring Transitions at the Surfaces of Pure Liquid-Crystals and their Mixtures .1. The Fowler Approximation

We have generalized earlier work on anchoring of nematic liquid crystals by Sullivan, and Sluckin and Poniewierski, in order to study transitions which may occur in binary mixtures of nematic liquid crystals as a function of composition. Microscopic expressions have been obtained for the anchoring energy of (i) a liquid crystal in contact with a solid aligning surface; (ii) a liquid crystal in contact with an immiscible isotropic medium; (iii) a liquid crystal mixture in contact with a solid aligning surface. For (iii), possible phase diagrams of anchoring angle versus dopant concentration have been calculated using a simple liquid crystal model. These exhibit some interesting features including re-entrant conical anchoring, for what are believed to be realistic values of the molecular parameters. A way of relaxing the most drastic approximation implicit in the above approach is also briefly discussed.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Phase III trial of consolidation therapy with yttrium-90-ibritumomab tiuxetan compared with no additional therapy after first remission in advanced follicular lymphoma.

PURPOSE: We conducted an international, randomized, phase III trial to evaluate the efficacy and safety of consolidation with yttrium-90 ((90)Y)-ibritumomab tiuxetan in patients with advanced-stage follicular lymphoma in first remission. PATIENTS AND METHODS: Patients with CD20(+) stage III or IV follicular lymphoma, who achieved a complete response (CR)/unconfirmed CR (CRu) or partial response (PR) after first-line induction treatment, were randomly assigned to receive (90)Y-ibritumomab tiuxetan (rituximab 250 mg/m(2) on day -7 and day 0 followed on day 0 by (90)Y-ibritumomab tiuxetan 14.8 MBq/kg; maximum of 1,184 MBq) or no further treatment (control). The primary end point was progression-free survival (PFS), which was calculated from the time of random assignment. RESULTS: A total of 414 patients (consolidation, n = 208; control, n = 206) were enrolled at 77 centers. (90)Y-ibritumomab tiuxetan consolidation significantly prolonged median PFS (after a median observation time of 3.5 years) in all patients (36.5 v 13.3 months in control arm; hazard ratio [HR] = 0.465; P < .0001) and regardless of whether patients achieved PR (29.3 v 6.2 months in control arm; HR = 0.304; P < .0001) or CR/CRu (53.9 v 29.5 months in control arm; HR = 0.613; P = .0154) after induction treatment. Median PFS with consolidation was prolonged in all Follicular Lymphoma International Prognostic Index risk subgroups. After (90)Y-ibritumomab tiuxetan consolidation, 77% of patients in PR after induction converted to CR/CRu, resulting in a final CR rate of 87%. The most common toxicity with (90)Y-ibritumomab tiuxetan was hematologic, and grade 3 or 4 infections occurred in 8% of patients. CONCLUSION: Consolidation of first remission with (90)Y-ibritumomab tiuxetan in advanced-stage follicular lymphoma is highly effective with no unexpected toxicities, prolonging PFS by 2 years and resulting in high PR-to-CR conversion rates regardless of type of first-line induction treatment.

Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization

The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that the space subdivision process is in accordance with the premises of the Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the time dependency of nucleation and growth rates. We have also developed an approximate analytical cell size probability density function. Finally, we have applied our approach to the distributions resulting from solid phase crystallization under isochronal heating conditions

The influence of Bone Morphogenic Protein-2 on the consolidation phase in a distraction osteogenesis model.

We asked whether locally applied recombinant-Bone Morphogenic Protein-2 (rh-BMP-2) with an absorbable Type I collagen sponge (ACS) carrier could enhance the consolidation phase in a callotasis model. We performed unilateral transverse osteotomy of the tibia in 21 immature male rabbits. After a latency period of 7 days, a 3-weeks distraction was begun at a rate of 0.5mm/12h. At the end of the distraction period (Day 28) animals were randomly divided into three groups and underwent a second surgical procedure: 6 rabbits in Group I (Control group; the callus was exposed and nothing was added), 6 rabbits in Group II (ACS group; receiving the absorbable collagen sponge soaked with saline) and 9 rabbits in Group III (rh-BMP-2/ACS group; receiving the ACS soaked with 100μg/kg of rh-BMP-2, Inductos(®), Medtronic). Starting at Day 28 we assessed quantitative and qualitative radiographic parameters as well as densitometric parameters every two weeks (Days 28, 42, 56, 70 and 84). Animals were sacrificed after 8 weeks of consolidation (Day 84). Qualitative radiographic evaluation revealed hypertrophic calluses in the Group III animals. The rh-BMP-2/ACS also influenced the development of the cortex of the calluses as shown by the modified radiographic patterns in Group III when compared to Groups I and II. Densitometric analysis revealed the bone mineral content (BMC) was significantly higher in the rh-BMP-2/ACS treated animals (Group III).

Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at T=0.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics.

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

Random-field Potts model with dipolarlike interactions: Hysteresis avalanches and microstructure

A model for the study of hysteresis and avalanches in a first-order phase transition from a single variant phase to a multivariant phase is presented. The model is based on a modification of the random-field Potts model with metastable dynamics by adding a dipolar interaction term truncated at nearest neighbors. We focus our study on hysteresis loop properties, on the three-dimensional microstructure formation, and on avalanche statistics.

Liquid-gas phase transition in nuclear matter from realistic many-body approaches

The existence of a liquid-gas phase transition for hot nuclear systems at subsaturation densities is a well-established prediction of finite-temperature nuclear many-body theory. In this paper, we discuss for the first time the properties of such a phase transition for homogeneous nuclear matter within the self-consistent Green's function approach. We find a substantial decrease of the critical temperature with respect to the Brueckner-Hartree-Fock approximation. Even within the same approximation, the use of two different realistic nucleon-nucleon interactions gives rise to large differences in the properties of the critical point.

Noise-induced phase separation: Mean-field results

We present a study of a phase-separation process induced by the presence of spatially correlated multiplicative noise. We develop a mean-field approach suitable for conserved-order-parameter systems and use it to obtain the phase diagram of the model. Mean-field results are compared with numerical simulations of the complete model in two dimensions. Additionally, a comparison between the noise-driven dynamics of conserved and nonconserved systems is made at the level of the mean-field approximation.

Studying Avalanches in the ground-state of the two-dimensional random field Ising model driven by an external field

We study the exact ground state of the two-dimensional random-field Ising model as a function of both the external applied field B and the standard deviation ¿ of the Gaussian random-field distribution. The equilibrium evolution of the magnetization consists in a sequence of discrete jumps. These are very similar to the avalanche behavior found in the out-of-equilibrium version of the same model with local relaxation dynamics. We compare the statistical distributions of magnetization jumps and find that both exhibit power-law behavior for the same value of ¿. The corresponding exponents are compared.

90Yttrium-Ibritumomab Tiuxetan Consolidation of First Remission in Advanced-Stage Follicular Non-Hodgkin Lymphoma: Updated Results After a Median Follow-Up of 7.3 Years From the International, Randomized, Phase III First-Line Indolent Trial.

PURPOSE Updated results are presented after a median follow-up of 7.3 years from the phase III First-Line Indolent Trial of yttrium-90 ((90)Y) -ibritumomab tiuxetan in advanced-stage follicular lymphoma (FL) in first remission. PATIENTS AND METHODS Patients with CD20(+) stage III or IV FL with complete response (CR), unconfirmed CR (CRu), or partial response (PR) after first-line induction treatment were randomly assigned to (90)Y-ibritumomab consolidation therapy (rituximab 250 mg/m(2) days -7 and 0, then (90)Y-ibritumomab 14.8 MBq/kg day 0; maximum 1,184 MBq) or no further treatment (control). Primary end point was progression-free survival (PFS) from date of random assignment. Results For 409 patients available for analysis ((90)Y-ibritumomab, n = 207; control, n = 202), estimated 8-year overall PFS was 41% with (90)Y-ibritumomab versus 22% for control (hazard ratio [HR], 0.47; P < .001). For patients in CR/CRu after induction, 8-year PFS with (90)Y-ibritumomab was 48% versus 32% for control (HR, 0.61; P = .008), and for PR patients, it was 33% versus 10% (HR, 0.38; P < .001). For (90)Y-ibritumomab consolidation, median PFS was 4.1 years (v 1.1 years for control; P < .001). Median time to next treatment (TTNT) was 8.1 years for (90)Y-ibritumomab versus 3.0 years for control (P < .001) with approximately 80% response rates to second-line therapy in either arm, including autologous stem-cell transplantation. No unexpected toxicities emerged during long-term follow-up. Estimated between-group 8-year overall survival rates were similar. Annualized incidence rate of myelodysplastic syndrome/acute myeloblastic leukemia was 0.50% versus 0.07% in (90)Y-ibritumomab and control groups, respectively (P = .042). CONCLUSION (90)Y-ibritumomab consolidation after achieving PR or CR/CRu to induction confers 3-year benefit in median PFS with durable 19% PFS advantage at 8 years and improves TTNT by 5.1 years for patients with advanced FL.

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.