Langevin equation with scale-dependent noise

A new wavelet based technique for the perturbative solution of the Langevin equation is proposed. It is shown that for the random force acting in a limited band of scales the proposed method directly leads to a finite result with no renormalization required. The one-loop contribution to the Kardar-Parisi-Zhang equation Green function for the interface growth is calculated as an example.Comment: LaTeX, 5 page

Dispersion Coefficients by a Field-Theoretic Renormalization of Fluid Mechanics

We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Peclet numbers, in contrast to finite mean-field predictions. We develop a new master equation description of the fluid mechanics that incorporates the physically relevant fluctuations, and we treat those fluctuations by a renormalization group procedure. We find a finite dispersion coefficient at low volume fraction of disorder and high Peclet numbers.Comment: 4 pages, 1 figure; to appear in Phys. Rev. Let

Numerical study of the spherically-symmetric Gross-Pitaevskii equation in two space dimensions

We present a numerical study of the time-dependent and time-independent Gross-Pitaevskii (GP) equation in two space dimensions, which describes the Bose-Einstein condensate of trapped bosons at ultralow temperature with both attractive and repulsive interatomic interactions. Both time-dependent and time-independent GP equations are used to study the stationary problems. In addition the time-dependent approach is used to study some evolution problems of the condensate. Specifically, we study the evolution problem where the trap energy is suddenly changed in a stable preformed condensate. In this case the system oscillates with increasing amplitude and does not remain limited between two stable configurations. Good convergence is obtained in all cases studied.Comment: 9 latex pages, 7 postscript figures, To appear in Phys. Rev.

Defect generation and deconfinement on corrugated topographies

We investigate topography-driven generation of defects in liquid crystals films coating frozen surfaces of spatially varying Gaussian curvature whose topology does not automatically require defects in the ground state. We study in particular disclination-unbinding transitions with increasing aspect ratio for a surface shaped as a Gaussian bump with an hexatic phase draped over it. The instability of a smooth ground state texture to the generation of a single defect is also discussed. Free boundary conditions for a single bump are considered as well as periodic arrays of bumps. Finally, we argue that defects on a bump encircled by an aligning wall undergo sharp deconfinement transitions as the aspect ratio of the surface is lowered.Comment: 24 page

Adjuvant chemotherapy for breast cancer in older women: an analysis of retrospective English cancer registration data

Aims Adjuvant chemotherapy is recommended as a treatment for women with high recurrence risk early breast cancer. Older women are less likely to receive chemotherapy than younger women. This study investigated the impact of chemotherapy on breast cancer-specific survival in women aged 70 + years using English registry data. Materials and methods Cancer registration data were obtained from two English regions from 2002 to 2012 (n = 29 728). The impact of patient-level characteristics on the probability of receiving adjuvant chemotherapy was explored using logistic regression. Survival modelling was undertaken to show the effect of chemotherapy and age/health status on breast cancer-specific survival. Missing data were handled using multiple imputation. Results In total, 11 735 surgically treated early breast cancer patients were identified. Use of adjuvant chemotherapy has increased over time. Younger age at diagnosis, increased nodal involvement, tumour size and grade, oestrogen receptor-negative or human epidermal growth factor receptor 2-positive disease were all associated with increased probability of receiving chemotherapy. Chemotherapy was associated with a significant reduction in the hazard of breast cancer-specific mortality in women with high risk cancer, after adjusting for patient-level characteristics (hazard ratio 0.74, 95% confidence interval 0.67–0.81). Discussion Chemotherapy is associated with an improved breast cancer-specific survival in older women with early breast cancer at high risk of recurrence . Lower rates of chemotherapy use in older women may, therefore, contribute to inferior cancer outcomes. Decisions on potential benefits for individual patients should be made on the basis of life expectancy, treatment tolerance and patient preference

Stability of scaling regimes in d≥2d\geq 2 developed turbulence with weak anisotropy

The fully developed turbulence with weak anisotropy is investigated by means of renormalization group approach (RG) and double expansion regularization for dimensions $d\ge 2$. Some modification of the standard minimal substraction scheme has been used to analyze stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point. This fixed point is unstable at $d=2$; thus, the infinitesimally weak anisotropy destroyes above scaling regime in two-dimensional space. The restoration of the stability of this fixed point, under transition from $d=2$ to $d=3,$ has been demonstrated at borderline dimension $2<d_c<3$. The results are in qualitative agreement with ones obtained recently in the framework of the usual analytical regularization scheme.Comment: 23 pages, 2 figure

ALA- and ALA-hexylester-induced protoporphyrin IX fluorescence and distribution in multicell tumour spheroids

Synthesis of protoporphyrin IX (PpIX) in intact murine mammary cancer cell spheroids is reported from optical sections obtained using a laser scanning confocal fluorescence microscope. EMT6 spheroids 275–350 μ m in diameter were incubated in 0.1–15 mM aminolevulinic acid (ALA) or 0.001–2 mM ALA-hexylester (h-ALA) to test the ability of both pro-drugs to diffuse into the spheroids and induce PpIX production. Spheroids incubated with ALA show significant fluorescence nonuniformity for all concentrations, with the outermost cells exhibiting greater porphyrin fluorescence. Comparable levels of fluorescence throughout the optical section are achieved with approximately 100-fold lower h-ALA concentrations, indicating that the interior cells maintain esterase activity and porphyrin synthesis and that h-ALA diffuses efficiently to the spheroid interior. Fluorescence gradients are less pronounced with h-ALA incubation, in part because of apparent saturation of esterase activity in the spheroid perimeter. Proliferating (Ki67 positive) and quiescent cell populations exhibit remarkably different h-ALA concentration dependencies. The incubation concentration resulting in maximum fluorescence with ALA is 10 mM, while the optimal concentration for h-ALA is 200-fold lower at 0.05 mM. Exceeding these optimal concentrations for both pro-drugs leads to an overall loss of fluorescence. © 2001 Cancer Research Campaign http://www.bjcancer.co

Circulation Statistics in Three-Dimensional Turbulent Flows

We study the large $\lambda$ limit of the loop-dependent characteristic functional $Z(\lambda)=$, related to the probability density function (PDF) of the circulation around a closed contour $c$. The analysis is carried out in the framework of the Martin-Siggia-Rose field theory formulation of the turbulence problem, by means of the saddle-point technique. Axisymmetric instantons, labelled by the component $\sigma_{zz}$ of the strain field -- a partially annealed variable in our formalism -- are obtained for a circular loop in the $xy$ plane, with radius defined in the inertial range. Fluctuations of the velocity field around the saddle-point solutions are relevant, leading to the lorentzian asymptotic behavior $Z(\lambda) \sim 1/{\lambda^2}$. The ${\cal O}(1 / {\lambda^4})$ subleading correction and the asymmetry between right and left PDF tails due to parity breaking mechanisms are also investigated.Comment: Computations are discussed in a more detailed way; accepted for publication in Physical Review

The use of surgery in the treatment of ER+ early stage breast cancer in England: variation by time, age and patient characteristics

AIM: To assess whether the proportion of patients aged 70 and over with ER+ operable breast cancer in England who are treated with surgery has changed since 2002, and to determine whether age and individual level factors including tumour characteristics and co-morbidity influence treatment choice. METHODS: A retrospective cohort analysis of routinely collected cancer registration data from two English regions (West Midlands, Northern & Yorkshire) was carried out (n = 17,129). Trends in surgical use over time for different age groups were assessed graphically and with linear regression. Uni- and multivariable logistic regressions were used to assess the effects of age, comorbidity, deprivation and disease characteristics on treatment choice. Missing data was handled using multiple imputation. RESULTS: There is no evidence of a change in the proportion of patients treated surgically over time. The multivariable model shows that age remains an important predictor of whether or not a woman with ER+ operable breast cancer receives surgery after covariate adjustment (Odds ratio of surgery vs no surgery, 0.82 (per year over 70)). Co-morbidity, deprivation, symptomatic presentation, later stage at diagnosis and low grade are also associated with increased probability of non-surgical treatment. CONCLUSION: Contrary to current NICE guidance in England, age appears to be an important factor in the decision to treat operable ER+ breast cancer non-surgically. Further research is needed to assess the role of other age-related factors on treatment choice, and the effect that current practice has on survival and mortality from breast cancer for older women