Instytut Podstawowych Problemów Techniki

Streszczenie:

As follows from experiments, waves of calcium concentration in biological tissues can be easily excited by a local mechanical stimulation. Therefore the complete theory of calcium waves should also take into account coupling between mechanical and chemical processes. In this paper we consider the existence of travelling waves for buffered systems, as in [22], completed, however, by an equation for mechanical equilibrium and respective mechanochemical coupling terms. Thus the considered, coupled system consists of reaction-diffusion equations (for the calcium and buffers concentrations) and equations for the balance of mechanical forces.

Słowa kluczowe:

Calcium waves, reaction-diffusion systems, mechanochemical coupling

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The propagation of weak discontinuities for quasilinear systems with coefficients functionally dependent on the solution is studied. We demonstrate that, similarly to the case of usual quasilinear systems, the transport equation for the intensity of weak discontinuity is quadratic in this intensity. However, the contribution from the (nonlocal) functional dependence appears to be in principle linear in the jump intensity (with some exceptions). For illustration, several examples, including two hyperbolic systems (with functional dependence), the dispersive Maxwell equations and fluid equations of the Hall plasma thruster, are considered.

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In the paper we consider the existence of calcium travelling waves for systems with fast buffers. We prove the convergence of the travelling waves to an asymptotic limit as the kinetic coefficients characterizing the interaction between calcium and buffers tend to infinity. To be more precise, we prove the convergence of the speeds as well as the calcium component concentration profile to the profile of the travelling wave of the reduced equation. Additionally, we take into account the effect of coupling between the mechanical and chemical processes and show the existence as well the monotonicity of the profiles of concentrations. This property guarantees their positivity.

Słowa kluczowe:

Calcium waves, Reaction–diffusion systems, Mechanochemical coupling

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The underlying mechanism of low-frequency oscillations in Hall accelerators is investigated theoretically. It is shown that relaxation oscillations arise from a competition between avalancheionization and the advective transport of the working gas. The model derived recovers the slow progression and fast recession of the ionization front. Analytical approximations of the shape of current pulses and of the oscillation frequency are provided for the case of large amplitude oscillations.

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In this paper we consider the coupling between chemical and mechanical effects accompanying the diffusion of calcium, either in biological tissues or in a single long cell. The tissue is treated either as a 3-D, or as a quasi-2-D thin layer, of visco- elastic medium, whereas the cell is represented as a thin long cylinder. In particular, the influence of viscosity on the properties of calcium travelling waves is studied. In principle, we explore here the simplest model of calcium diffusion which is based on an effective diffusion coefficient, thus neglecting the details of the role played by buffers. The mechano-chemical coupling in the model is realized by the presence of a traction tensor, in addition to the viscoelastic stress tensor in the mechanical equations, and the strain tensor in the source term of the calcium diffusion equation, as proposed in [1–4]. Our aim is to provide a simple and effective theory, which can be useful in studying various effects influencing propagation of calcium waves. Since in the absence of viscosity the whole mechano-chemical system for calcium and buffers is easily reduced to the “chemical one”, i.e. it consists only of reaction diffusion equations, therefore we decided to perform expansion with respect to the viscosity. Treating, thus, viscous forces as a perturbation, we reduce the problem in each case to a single reaction diffusion equation for the calcium concentration. In this way we avoid the question of the existence of travelling wave solutions as for the so obtained models, their existence follows simply from already known theorems [5–9].

Słowa kluczowe:

calcium waves, reaction-diffusion systems, mechano-chemical coupling

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The work presents the results of the simulations of water flows through narrow channels (Poiseuille flows) performed using the molecular dynamics method, for two different channel widths (equal to 5 and 10 diameters of the water molecule) and for two different materials of the channel walls (copper and quartz).
In the simulations, physical properties of the materials and their electrostatic interactions were considered. The obtained results are compared with the analytical solutions for a micropolar fluid flow taking account of the experimentally obtained rheological constants of water.

Słowa kluczowe:

nanoflows, micropolar fluid, molecular dynamics simulation, nanochannels

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Hall-effect thruster plasma oscillations recorded by means of probes located at the channel exit are analyzed using the empirical mode decomposition (EMD) method. This self-adaptive technique permits to decompose a nonstationary signal into a set of intrinsic modes, and acts as a very efficient filter allowing to separate contributions of different underlying physical mechanisms. Applying the Hilbert transform to the whole set of modes allows to identify peculiar events and to assign them a range of instantaneous frequency and power. In addition to 25kHz breathing-type oscillations which are unambiguously identified, the EMD approach confirms the existence of oscillations with instantaneous frequencies in the range of 100–500kHz typical for ion transit-time oscillations. Modeling of high-frequency modes (ν∼10MHz) resulting from EMD of measured wave forms supports the idea that high-frequency plasma oscillations originate from electron-density perturbations propagating azimuthally with the electron drift velocity.

Słowa kluczowe:

Plasma oscillations, Interplanetary magnetic fields, Plasma waves, Wavelets, High frequency discharges

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Streszczenie:

The influence of mechano-chemical coupling on calcium concentration waves is considered. The propagation of calcium waves is described by a reaction–diffusion equation with the reaction term dependent on the mechanical stress responsible for the release of calcium. Similarly the balance of mechanical forces is influenced by the calcium concentration through the so-called traction force.

Słowa kluczowe:

Calcium waves, Reaction–diffusion systems, Mechano-chemical coupling

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A spectroscopic study of a low-pressure supersonic jet of laser-heated argon plasma is presented. The experimental set-up consisted of a high-pressure convergent nozzle and a supersonic nozzle. The supersonic nozzle was placed just behind the convergent nozzle and was connected to a low-pressure chamber. A continuous wave laser with output power of 2 kW was used to maintain the plasma in the stream of argon gas flowing from the convergent nozzle. The plasma then expanded through the supersonic nozzle. Emission spectra from the laser-sustained plasma and supersonic jet were measured with a 1.3 m focal length spectrograph and 1254 silicon intensified target (SIT) detector connected to an EG&G PARC optical multichannel analyser (OMA) III. We found that the supersonic stream of argon plasma had an electron density of - and a temperature of 6 - 7 kK.

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The boundaries of the existence of a laser-sustained argon plasma in forced convective flow were investigated experimentally and numerically. The plasma was maintained by a cw CO2 laser with an output power of 2.5 kW and burnt in free space at atmospheric pressure. Flow velocities changed from 2.3 m s-1 to 8 m s-1. The f number was 8.8. The results show that a quasi-2D model in which the axial flow is given by the relation rho u= rho 0u0( rho / rho 0)12/, where rho 0 and u0 are the density and velocity of the cold gas respectively, describes the observed phenomena fairly well.

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Discharge current and local plasma oscillations are studied in a high voltage Hall effect thruster PPS®-X000. Characteristic time scales that appear in different operating conditions are resolved with the use of Hilbert-Huang spectra (HHS) which display time dependenc of instantaneous frequency and power. Sets of intrinsic mode functions (imfs) that are used for HHS calculation result due to application of empirical mode decomposition method (EMD) to nonstationary multicomponent signals. In the experiment the signals are captured in the electric circuit of the thruster as well locally, in the vicinity of the thruster exhaust region. Classical electric probes spaced along the azimuth and/or thruster axis let us study correlations of signals which were captured in different locations. In this way azimuthal and axial propagation of disturbances is inspected. The discharge voltage is varied in the range of 200÷900 V while xenon mas flow rate of 5÷9 mg/s. LF, MF, and HF characteristic bands that are known from previous studies of PPS®-100 thruster have been also detected here. However, expanding discharge current onto a set of intrinsic modes we can resolve MF mode more reliably than before. Moreover, for higher discharge voltages, this irregular mode turns into more regular waveform and tends to dominate in the discharge current masking almost completely the breathing mode (LF oscillations of the discharge current). In such a case triggering of HF oscillations is correlated with the phase of MF mode while in the case of PPS®-100 thruster it was correlated with the appropriate phase of the breathing mode (LF band). Regular HF emission that can be unambiguously interpreted as azimuthal electrostatic wave now is observed only in the specific operating conditions of the thruster. However, even if irregular HF emission is observed the time delay of cross-correlated signals which are captured in different azimuthal locations corresponds to the velocity of azimuthal electron drift in the field of magnetic barrier.

Słowa kluczowe:

High voltage direct current transmission, Electrical circuits, Electrostatic discharges, Electrostatic waves, Plasma oscillations

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Using the fluid equations of Hall thruster plasma we analyze the influence of the electron energy balance on the stability of ion sound modes. For frequencies lower than ωc = 107 s−1 the gains and losses in the source term are approximately equal, thus the temperature can be in principle determined in terms of other dependent variables. This permits to reduce the number of equations. It appears however, that the new system can have complex characteristics in some regions. This in turn implies instability of certain modes with frequencies lower than ωc.

Słowa kluczowe:

Energy balance, Acoustic analysis, Fluid equations, Instability analysis, Plasma instabilities

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