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.

Phase-field model of Hele-Shaw flows in the high-viscosity contrast regime

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady-state finger.

Influence of disorder strength on phase-field models of interfacial growth

We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.

Side-branch growth in two-dimensional dendrits. Part II: Phase-field model

The development of side-branching in solidifying dendrites in a regime of large values of the Peclet number is studied by means of a phase-field model. We have compared our numerical results with experiments of the preceding paper and we obtain good qualitative agreement. The growth rate of each side branch shows a power-law behavior from the early stages of its life. From their birth, branches which finally succeed in the competition process of side-branching development have a greater growth exponent than branches which are stopped. Coarsening of branches is entirely defined by their geometrical position relative to their dominant neighbors. The winner branches escape from the diffusive field of the main dendrite and become independent dendrites.

Universality in models for disorder induced phase transitions

We have systematically analyzed six different reticular models with quenched disorder and no thermal fluctuations exhibiting a field-driven first-order phase transition. We have studied the nonequilibrium transition, appearing when varying the amount of disorder, characterized by the change from a discontinuous hysteresis cycle (with one or more large avalanches) to a smooth one (with only tiny avalanches). We have computed critical exponents using finite size scaling techniques and shown that they are consistent with universal values depending only on the space dimensionality d.

Intrinsic noise-induced phase transitions: Beyond the noise interpretation

We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Itô vs Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Itô. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau-type model. A detailed discussion of a different numerical algorithm valid for both interpretations is also presented.

Phase-field approach to spatial perturbations in normal Saffman-Taylor fingers

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.

Sequential partitioning: an alternative to understanding size distributions of avalanches in first-order phase transitions

We study the problem of the partition of a system of initial size V into a sequence of fragments s1,s2,s3 . . . . By assuming a scaling hypothesis for the probability p(s;V) of obtaining a fragment of a given size, we deduce that the final distribution of fragment sizes exhibits power-law behavior. This minimal model is useful to understanding the distribution of avalanche sizes in first-order phase transitions at low temperatures.

Phase-field model for Hele-Shaw flows with arabitrary contrast II: numerical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit, and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.

Phase I study of sorafenib combined with radiation therapy and temozolomide as first-line treatment of high-grade glioma.

BACKGROUND: Sorafenib (Sb) is a multiple kinase inhibitor targeting both tumour cell proliferation and angiogenesis that may further act as a potent radiosensitizer by arresting cells in the most radiosensitive cell cycle phase. This phase I open-label, noncontrolled dose escalation study was performed to determine the safety and maximum tolerated dose (MTD) of Sb in combination with radiation therapy (RT) and temozolomide (TMZ) in 17 patients with newly diagnosed high-grade glioma. METHODS: Patients were treated with RT (60 Gy in 2 Gy fractions) combined with TMZ 75 mg m(-2) daily, and Sb administered at three dose levels (200 mg daily, 200 mg BID, and 400 mg BID) starting on day 8 of RT. Thirty days after the end of RT, patients received monthly TMZ (150-200 mg m(-2) D1-5/28) and Sb (400 mg BID). Pharmacokinetic (PK) analyses were performed on day 8 (TMZ) and on day 21 (TMZ&Sb) (Clinicaltrials ID: NCT00884416). RESULTS: The MTD of Sb was established at 200 mg BID. Dose-limiting toxicities included thrombocytopenia (two patients), diarrhoea (one patient) and hypercholesterolaemia (one patient). Sb administration did not affect the mean area under the curve(0-24) and mean Cmax of TMZ and its metabolite 5-amino-imidazole-4-carboxamide (AIC). Tmax of both TMZ and AIC was delayed from 0.75 (TMZ alone) to 1.5 h (combined TMZ/Sb). The median progression-free survival was 7.9 months (95% confidence interval (CI): 5.4-14.55), and the median overall survival was 17.8 months (95% CI: 14.7-25.6). CONCLUSIONS: Although Sb can be combined with RT and TMZ, significant side effects and moderate outcome results do not support further clinical development in malignant gliomas. The robust PK data of the TMZ/Sb combination could be useful in other cancer settings.

EORTC 26083 phase I/II trial of dasatinib in combination with CCNU in patients with recurrent glioblastoma.

The treatment of patients with recurrent glioblastoma remains a major oncologic problem, with median survival after progression of 7-9 months. To determine the maximum tolerated dose and dose-limiting toxicity (DLT), the combination of dasatinib and cyclonexyl-chloroethyl-nitrosourea (CCNU) was investigated in this setting. The study was designed as multicenter, randomized phase II trial, preceded by a lead-in safety phase. The safety component reported here, which also investigated pharmacokinetics and preliminary clinical activity, required expansion and is therefore considered a phase I part to establish a recommended dosing regimen of the combination of CCNU (90-110 mg/m(2)) and dasatinib (100-200 mg daily). Overall, 28 patients were screened, and 26 patients were enrolled. Five dose levels were explored. DLTs, mainly myelosuppression, occurred in 10 patients. Grade 3 or 4 neutropenia was recorded in 7 patients (26.9%) and thrombocytopenia in 11 patients (42.3%). No significant effect of CCNU coadministration on dasatinib pharmacokinetics was found. Median progression-free survival (PFS) was 1.35 months (95% confidence interval: 1.2-1.4) and 6-month PFS was 7.7%. In this phase I study of recurrent glioblastoma patients, the combination of CCNU and dasatinib showed significant hematological toxicities and led to suboptimal exposure to both agents.