Publisher's Note: Impact of diffusion on surface clustering in random hydrodynamic flows [Phys. Rev. E 95, 013109 (2017)].

This corrects the article DOI: 10.1103/PhysRevE.95.013109.

Impact of diffusion on surface clustering in random hydrodynamic flows.

Buoyant material clustering in a stochastic flow, which is homogeneous and isotropic in space and stationary in time, is addressed. The dynamics of buoyant material in three-dimensional hydrodynamic flows can be considered as the motion of passive tracers in a compressible two-dimensional velocity field. The latter is of interest in the present study. It is well known that the clustering of the density of passive tracers occurs in this case. We evaluate the impact of diffusion on the clustering process by using a numerical model. In general, the effect of diffusion is negligible in the very beginning of the evolution of initially uniformly distributed passive tracers. Therefore, the clustering of the density of passive tracers can emerge in accordance with the general theory. We analyze the long time clustering affected by diffusion and show that the emerged cluster structure persists in time in spite of the diffusion effect. However, the clusters split in time.

[DELAYED AND PRIMARY RECONSTRUCTION OF MAMMARY GLAND IN PATIENTS WITH THE BREAST CANCER].

Immediate and late follow­up results of oncoplastic operations, performed in 75 patients, suffering mammary gland cancer (MGC), including in 22­a delayed, and in 53­primary reconstruction of the breast, were analyzed. In 66 patients musculo­ cutaneous flaps on nutrient pedicle, taken up from the back and abdominal wall tissues, with underlying mammary gland endoprosthesis,were applied as a transplant. Ductal invasive MGC was diagnosed in 70 patients, invasive lobular one ­ in 5. After delayed reconstruction of the breast 81.8% patients have survived five years, and after primary reconstruction ­ 73.6%. Performance of oncoplastic operations in patients, suffering MGC, have permitted to achieve satisfactory immediate and late follow­up results of treatment, it constitutes essential element in complex of rehabilitation measures after performance of radical mastectomy.

Anomalous sea surface structures as an object of statistical topography.

By exploiting ideas of statistical topography, we analyze the stochastic boundary problem of emergence of anomalous high structures on the sea surface. The kinematic boundary condition on the sea surface is assumed to be a closed stochastic quasilinear equation. Applying the stochastic Liouville equation, and presuming the stochastic nature of a given hydrodynamic velocity field within the diffusion approximation, we derive an equation for a spatially single-point, simultaneous joint probability density of the surface elevation field and its gradient. An important feature of the model is that it accounts for stochastic bottom irregularities as one, but not a single, perturbation. Hence, we address the assumption of the infinitely deep ocean to obtain statistic features of the surface elevation field and the squared elevation gradient field. According to the calculations, we show that clustering in the absolute surface elevation gradient field happens with the unit probability. It results in the emergence of rare events such as anomalous high structures and deep gaps on the sea surface almost in every realization of a stochastic velocity field.

[Immediate and late follow-up results of surgical and combined treatment of patients with colonic cancer of various localization in right half of the colon].

Comparative estimation of immediate and late follow-up results of treatment was con- ducted in 520 patients, suffering cancer of the colonic right half, including coecum - in 227 (43.7% ± 2.1%), colon ascendum - in 159(30.7% ± 2.0%), right colonic flexure - in 66 (12.9% ± 1.3%), right half of colon transversum - in 66 (12.9% ± 4.2%). In 463 (89.0% ± 1.4%) patients radical operations were performed, while in 57 (11.0% ± 1.7%) - the symptomatic. After radical operations 8 (1.7% ± 0.5%) patients died, and after the symptomatic - 3 (5.3% ± 3.0%). Definite surgical treatment was performed in 258 (60,8% ± 2,4%) patients, the combined one - in 166 (39.2% ± 2.4%). Five-year survival have constituted (64.2% ± 5.5%) for the patients, operated on for the colon ascendumcancer, and (19.1% ± 5.7%) - for cancer of right colonic flexure; while after combined treatment - (40.4% ± 5.8%) in patients, operated on for cancer of coecum, (29.4% ± 11.9%) - right half of colon transversum; ten-year survival have constituted (16.8% ± 2.7%) for the patients, who were radically operated for cancer of coecum, and (4.8% ± 2.6%) - for cancer of right colonic flexure (p<0,005). Late follow-up results of radical treatment of the colonic right half depends essentially on localization and degree of the cancer spread.

Determination of the optimal excitation frequency range in background flows.

The chaotization of a vortical flow caused by a nonstationary incident flow is studied by the examples of several dynamically consistent models. It is shown that for relatively small values of excitation amplitude, the chaotization of such flows and, correspondingly, chaotic transport of passive scalars is determined by a small number of nonlinear resonances with frequencies close to the excitation frequency. Hence, the analysis of locations and overlaps of these resonances in the considered models makes it possible to derive fairly good estimates of excitation frequencies that are optimal for the chaotic transport.

[The effect of low-molecular-weight heparin on the late follow-up results of the combined and complex treatment of patients with rectal cancer].

The late follow-up results of combined and complex treatment of 305 patients, suffering cancer recti, were analyzed. After the operation in 250 (82%) patients the anticoagulants were administered, including the low-molecular-weight heparin (calcium nadroparine)--129 (42.3%), and nonfractionized heparin--in 121 (39.7%). In 55 (18%) patients the complex and combined treatment was conducted, according to the present standards, without application of anticoagulants. There was proved, that administration of calcium nadroparine in combined and complex treatment of patients, suffering cancer recti, had promoted the patients three-year and five-year survival indices increase due to reduction of the tumors generalization.

[Complex estimation of proliferative activity of epithelial cells of the large intestine damaged by polyps and cancer]. / Kompleksna otsinka proliferatyvnoï aktyvnosti klityn epiteliiu slyzovoï obolonky tovstoï kyshky vrazhenoï polipamy ta rakom.

Peculiarities of mitotic regime and expression of proliferating cell nuclear antigen were investigated in 18 polyps and 35 cases of colorectal cancer. Direct relationship between spectrum and degree of manifestation of proliferative activity, level of morphological malignant tumors and accumulation of oncopathology in the patient pedigrees was established.