Propagation of combustion waves in the shell-core energetic materials with external heat losses.

In this paper, the properties and stability of combustion waves propagating in the composite solid energetic material of the shell-core type are numerically investigated within the one-dimensional diffusive-thermal model with heat losses to the surroundings. The flame speed is calculated as a function of the parameters of the model. The boundaries of stability are determined in the space of parameters by solving the linear stability problem and direct integration of the governing non-stationary equations. The results are compared with the characteristics of the combustion waves in pure solid fuel. It is demonstrated that a stable travelling combustion wave solution can exist for the parameters of the model for which the flame front propagation is unstable in pure solid fuel and it can propagate several times faster even in the presence of significant heat losses.

[Autowaves in a model of growth of an invasive tumor].

A mathematical model for the invasive tumour growth has been constructed, which takes cell division, death, and motility into account. The model includes local cell density and the distribution of nutrient (oxygen) concentration. Cancer cells die in the absence of nutrients; therefore, the distribution of oxygen in tissue substantially affects both the tumour proliferation rate and structure. The model adequately describes the experimentally measured rate of tumour proliferation. The existence of autowave solutions has been demonstrated, and their properties have been investigated. The results are compared with the properties of the Kolmogorov-Petrovskii-Piskunov and Fisher equations. It is shown that the nutrient distribution influences the speed selection and the convergence of the initial conditions to the automodel solution.

Transition from an excitable to an oscillatory state in dictyostelium discoideum.

Under conditions of starvation, populations of the amoebae Dictyostelium discoideum aggregate are mediated by chemical excitation waves of cAMP. Two types of waves can be observed, either spiral or circular-shaped ones. We investigate transitions from rotating spirals to circular shaped waves (target patterns). Two different experiments demonstrating this phenomenon are presented. In the first case a continuous transition from the spiral type pattern to target waves was observed at the later stages of aggregation. In the second case the transition was induced by annihilation of waves by a spatially homogeneous cAMP pulse. Instead of the originally present spiral waves, oscillating spots bearing target patterns emerged. On the basis of a model for Dictyostelium aggregation, we provide a theoretical explanation for such transitions. It is shown that cell density can be an effective bifurcation parameter. Under certain conditions, the system is shifted from the excitable to the oscillatory state while the frequency of oscillations is proportional to the square root of the cell density. Thus, the regions with the highest cell density during the early stages of the spatial rearrangement of the cells become pacemakers and produce target patterns. The analytic results were confirmed in numerical simulations of the model.

Light-triggered pH banding profile in Chara cells revealed with a scanning pH microprobe and its relation to self-organization phenomena.

When exposed to light, Characean cells develop a pattern of alternating alkaline and acid bands along the cell length. The bands were identified with a tip-sensitive antimony pH microelectrode positioned near one end of Chara internode at a distance of 50-100 microm from the cell wall. The stage with Chara cell was moved along its longitudinal axis at a computer-controlled speed (100 or 200 microm s(-1)) relative to the pH probe over a distance of 50 mm. Under sufficient uniform illumination of the cell (from 100 to 2.5 Wm(-2)), the homogeneous pH distribution becomes unstable and a banding pattern is formed, the spatial scale of which decreases with the light intensity. If the cell is locally illuminated, bands are formed only in the region of illumination. It is shown that the inhibition of cyclosis by cytochalasin B leads to the disappearance of the banding pattern. The addition of ammonium (weak base) inhibited the banding pattern, whereas acetate (weak acid) alleviated the inhibitory effect of ammonium and restored the pH banding. A model explaining the observed phenomena is formulated in terms of proton concentration outside and bicarbonate concentration inside the cell. It contains two diffusion equations for the corresponding ions with nonlinear boundary conditions determined by ion transport processes across the cell membrane. The model qualitatively explains most of the experimental observations. It describes the dependence of the pattern characteristics on the light intensity and reveals the role of cyclosis in this phenomenon.

[Surgical treatment of bronchial fistulas after pneumonectomy]. / Khirurgicheskoe lechenie bronkhial'nykh svishchei posle pnevmonéktomii.

The results of surgical treatment of 9 patients with bronchial fistulas after pneumonectomy have been analysed. During the reoperation the bronchial stump was wrapped by the omental flap with vascular pedicle (omentoplasty). In 6 patients omentoplasty was used in urgent repeated transpleural operations, in 3--during the late operations from transsternal transpericardial approach. Wedge resection of the tracheal bifurcation with omentoplasty from transsternal transpericardial approach was performed in 2 patients with a short bronchial stump. 2 patients died after surgery: one--from cardiopulmonary failure, the other one--from the relapse of bronchial fistula. Omentoplasty in patients with primary bronchial fistulas proved to be effective. It is advisable to perform reoperations during the 1st day after complications developed.

Catastrophic extinction, noise-stabilized turbulence and unpredictability of competition in a modified Volterra-Lotka model.

Spatial coexistence and competition among species is investigated through a modified Volterra-Lotka model which takes into account sexual breeding. This allows the population specific growth rate to depend on the population density. As a result of this modification the degeneracy inherent in the classical model is eliminated and qualitatively novel regimes are observed, as demonstrated by parametric analysis of the model. In the case where the corresponding parameters of competing species do not differ significantly the model can be reduced to a single Ginzburg-Landau type equation. The spatially distributed model is analyzed both in the absence and in the presence of noise mimicking inherent fluctuations in birth and death rates. It is shown that noise can qualitatively change the behavior of the system. Not only does it induce the formation of spatial patterns, but also switches on endless turbulent-like rearrangement of the system. When initially unpopulated habitat is occupied by competing species even a very low-intensity noise makes the final state of the system totally unpredictable and sensitive to any fluctuations. (c) 1996 American Institute of Physics.

Complexity of precipitation patterns: Comparison of simulation with experiment.

Numerical simulations show that a simple model for the formation of Liesegang precipitation patterns, which takes into account the dependence of nucleation and particle growth kinetics on supersaturation, can explain not only simple patterns like parallel bands in a test tube or concentric rings in a petri dish, but also more complex structural features, such as dislocations, helices, "Saturn rings," or patterns formed in the case of equal initial concentrations of the source substances. The limits of application of the model are discussed. (c) 1994 American Institute of Physics.

[Emergence of a quasi-periodic spatial structure in the model of aggregation of moving, dividing cells, possessing chemotactic properties]. / Vozniknovenie kvazi-periodicheskoi prostranstvennoi struktury v modeli agregatsii deliashchikhsia podvizhnykh kletok, obladaiushchikh khemotaksisom.

It has been analyzed the Keller-Segel model of aggregation of divided cells possessed hemotaxis. During the cell division homogeneous stationary distribution becomes unstable due to increasing of the common cells amount. It is shown that accidental variation of the primary stable homogeneous stationary distribution result to forming of a like periodical space structure with characteristic scale that basically is defined by the cell division rate. This approach allows to explain the arising of complex space structures in the movable bacterium colonies.

[The instrumental extirpation of the esophagus via an abdominocervical approach]. / Instrumental'naia ékstirpatsiia pishchevoda iz abdominotservikal'nogo dostupa.

The authors operated on 6 patients with cancer of the lower thoracic esophagus and cardioesophageal carcinoma, Stage III. All the patients underwent esophageal extirpation from the abdominocervical access by using an extractor inserted into the esophageal lumen through a cut in its wall above the tumor. The esophagus was drawn out from the mediastinum into the abdomen, similar to subcutaneous vein removal by the Bebcock method. A single esophagoplasty was performed in 4 patients. In the postoperative period one patient died from pulmonary embolism. No complications due to the procedure of esophageal removal were observed. In the authors' opinion, during operations using the abdominocervical access, instrumental esophagectomy by means of an extractor is more traumatic and simple than manual esophageal mobilization.

A mathematical model of the mechanism of vertebrate somitic segmentation.

A mathematical model for the mechanism of periodic pattern formation in the process of somitogenesis is proposed. It is assumed that the metameric arrangement first appears before somite formation at the stage of transition of mesodermal cells into a polarized state. The model is based on the assumption that besides the mechanism of contact cell polarization there exists a mechanism of polarization suppression due to excretion of some chemical substance by polarized cells. Periodicity appears as a result of interaction of a kinematic wave of somitogenic cell determination with the cell cycles of mesodermal cells.

[A mechanism of development of spatial-temporal orderliness in bacterial systems]. / Mekhanizm vozniknoveniia prostranstvenno-vremennoi uporiadochennosti v bakterial'nykh sistemakh.

Peculiarities of the mechanism of intercellular regulation capable of initiating nonhomogeneous spatial structures in different experimental bacterial systems are analysed. A model of band formation of bacterial density in agar-stabilized bacterial system with opposite gradients of the substrate and oxygen is suggested. It is shown that for the appearance of spatial structures in the bacterial systems a time delay in the cell response to the external signal is of principal importance, as well as the hysteresis of transitions between differentiated bacterial states.

Mathematical modelling of intercellular regulation causing the formation of spatial structures in bacterial colonies.

Bacterial colonies may grow forming stable spatial, particularly circular, structures. For instance, motile bacteria Proteus vulgaris or Escherichia coli grown on agar under certain conditions may form concentric rings with the centre in the inoculation point (Rüss-Münzer, 1935, Bact. Parasit Kde (Abt 1) 7, 214; Budriené, 1985, Dokl. Acad. Nauk SSR, 283, 470). A similar picture can be observed in a different situation, i.e. when a lawn of non-motile Salmonella typhimurium bacteria is cultivated on a solid agar with the locally introduced substrate (Hoppensteadt & Jäger, 1980, Lecture Notes in Biomath. 38, 68). This paper describes a mechanism of bacterial interactions through a hypothetical mediator released by the organisms. A mathematical model has been built. Its analysis has shown that the selected laws of secretion and reception of the mediator can adequately account for the formation of circular structures in the case of both motile and non-motile bacteria.

[Prevention of bronchial fistula and empyema after resection and removal of the lung]. / Profilaktika bronkhial'nogo svishcha i émpiemy plevry posle rezektsii i udaleniia legkogo.

Pulmonectomies in 231 patients and resections of a lung in 320 patients were followed by the development of bronchial fistulas in 33 patients (5.9%): after pneumonectomy--in 17 patients (7.3%) and after lobe- and bilobectomy in 16 patients (5%). Empyema of the pleura was noted in 20 patients (3.6%): in 12 patients (5.2%) and 8 patients (2.5%) correspondingly. Seventeen of 53 patients with these complications died. The use of a manual method of suturing the bronchus without a stump with the local application of fibrinogen, complex bronchological sanitation and intraoperative bronchofibroscopy (drainage of the pleural cavity after pneumonectomy with the following filling of the cavity with an antiseptic solution and formation of the selective pneumoperitoneum) allowed to decrease the incidence of bronchial fistulas in 102 patients to 2.9%, and empyema of the pleura--to 1.9%.

On the possibility of reduction of dissipative structure models to a simple form.

A multicomponent reaction-diffusion system containing two different space scales (contrasting system) is considered. It is shown that if the system answers several conditions enumerated, it can be reduced to a bicomponent system which describes a dissipative structure either of a peak or of a step type. While in the first case the original and the final systems are equivalent only in the neighbourhood of zero, in the second case the equivalence is more general as the solution of these systems does not leave the region for which the procedure of reduction was developed.

Cell surface and cell division.

A mathematical model of the regulation of cell division is suggested. The model is based on the hypothesis that the process giving rhythm to cell division is located in the cell membrane: i.e., the process of free-radical oxidation of membrane lipids. Much depends on the physical state of the membrane. In the membrane, phase transitions take place because of the changes in lipid composition. These transitions differ in normal and tumor cells: in normal cells they are sharp and hysteretic owing to the presence of a framework (membrane skeleton) on the surface of the membrane, while in tumor cells the integrity of the surface is violated so that the transitions are smooth. This model makes it possible to explain differences in the regulation of normal and cancer cell proliferation. Within the limits of the model, such phenomena as density dependent inhibition of growth, reverse transformation, influence of cyclic AMP and ions of Ca2+ on the cell cycle, the actions of serum and of proteases on the cycle, and so on, are explained. A rational scheme for the appearance of the selective damage found in tumor cells is proposed.

On the possible mechanism of cell cycle synchronization.

The influence of exchanges of lipids and antioxidants (AO) between the cells on the cell proliferation is studied in the frame of the membrane model of the cell cycle. It is shown theoretically that the easy-oxidative lipids exchange favours the synchronization of cell division, while the AO exchange leads to desynchronization. The analytical consideration and some numerical estimations are carried out. The qualitative consequences accessible to experimental verification are discussed.