Quasi-stationary Value Research Articles

Исследование нестационарного горения заряда в модельной твердотопливной регулируемой двигательной установке

Based on the coupled combustion model of mixed solid fuel, unsteady combustion of fuel was studied when the pressure was changed in the combustion chamber of a model controlled small solid fuel engine. Modeling of engine thrust control system was carried out in two ways: by changing the critical section area of the nozzle over time according to a given law and by changing the area of the burning surface of the fuel according to a given law. It is found that with a sharp increase in pressure, the combustion rate increases above the quasi-stationary value, which leads to an increase in the pressure in the combustion chamber above that calculated from the quasi-stationary rate. With a sharp decrease in pressure, the combustion rate decreases to a value less than the quasi-stationary rate at the corresponding pressure. The decrease in the combustion rate leads to a decrease in the pressure in the combustion chamber below that calculated from the quasi-stationary rate. At small values of the characteristic relaxation time of the combustion chamber, a sharp decrease in pressure in the combustion chamber will lead to the extinction of the charge combustion.

Well posedness of fluid-solid mixture models for biofilm spread

Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves in response to variations in the mechano-chemical variables. For a model of biofilm spread, we show how to improve its stability properties by characterizing the time derivatives of relevant quasi-stationary magnitudes in terms of additional boundary value problems. We also give conditions for well posedness of time dependent submodels set in moving domains depending on the motion of the boundary. After constructing solutions for transport, diffusion and elliptic submodels for volume fractions, displacements, velocities, pressures and concentrations with the required regularity, we are able to handle the full model of biofilm spread in moving domains assuming we know the dynamics of the boundary. These techniques are general and can be applied in models with a similar structure arising in biological applications.

Pulsating flows of viscous fluid in flat channel for given harmonic fluctuation of flow rate

In research work, it is pointed out the issue of a pulsating flow of a viscous incompressible fluid in a flat channel for a given harmonic fluctuation of the fluid flow rate. The study of the generation of pulsating current is used in biological mechanics, in particular, in the use of microchip systems. In addition, to ensure a constant flow of liquid, pneumatic micropumps that periodically squeeze liquid from empty volumes are widely used. In such systems, the installation of pulsating flow is shown to be economically beneficial. The transfer function of the amplitude-phase rate response is determined; with the help of these functions, the ratio of the tangential shear pressure on the channel fence to the average acceleration over the channel section is determined. In Figure 1, it can be seen that the ratio of KH = 0 of in τHC/τ0KC is close to one and α02 is less than one. If α02 takes on values greater than unity, then the ratio of to KH = 0 to τHC/τ0KC is greater than unity, and it has been shown to increase with increasing frequency of dimensionless oscillation. It was shown that in an unsteady flow of liquid, even in cases where liquid acceleration is equal to zero, it was studied that the stress on the wall of the channel exceeds its quasi-stationary value. τHC/τ0KC with the increase of the ratio KH, the increase of the parameter is explained by the fact that the change of the tensile stress on the wall advances in phases concerning the average speed along the section. Calculations determine that the non-stationary shear pressure on the channel fence increases non-monotonically with the acceleration of the liquid particle at low oscillation frequencies. The shear pressure reaches its maximum value, then decreases with increasing dimensionless oscillation rate, and asymptotically approaches the values without accelerated flow.

Activated decay of a metastable state: transient times for small and large dissipation

The time evolution of the thermally activated decay rates is considered. This evolution is of particular importance for the recent nanoscale experiments discussed in the literature, where the potential barrier is relatively low (or the temperature is relatively high). The single-molecule pulling is one example of such experiments. The decay process is modeled in the present work through computer solving the stochastic (Langevin) equations. Altogether about a hundred of high precision rates have been obtained and analyzed. The rates are registered at the absorption point located far beyond the barrier to exclude the influence of the backscattering on the value of the quasistationary decay rate. The transient time, i.e. the time lapse during which the rate attains half of its quasistationary value, has been extracted. The dependence of the transient times upon a damping parameter is compared with that of the inverse quasistationary decay rate. Two analytical formulas approximating the time-dependences of the numerical rates are proposed and analyzed.

Space-Time Finite Element Discretization of Parabolic Optimal Control Problems with Energy Regularization

In this paper, we analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be evaluated by means of the solution of an elliptic quasi-stationary boundary value problem. When eliminating the control, we end up with the reduced optimality system that is nothing but the variational formulation of the coupled forward-backward primal and adjoint equations. Using Babuška's theorem, we prove unique solvability in the continuous case. Furthermore, we establish the discrete inf-sup condition for any conforming space-time finite element discretization yielding quasi-optimal discretization error estimates. Various numerical examples confirm the theoretical findings. We emphasize that the energy regularization results in a more localized control with sharper contours for discontinuous target functions, which is demonstrated by a comparison with an $L^2$-regularization and with a sparse optimal control approach.

The Kramers problem in the energy diffusion regime: transient times

Brownian motion driven by thermal fluctuations play an important role in the work of nanomachines and in single-molecule pulling experiments. Some problems in this field are reduced to the so-called Kramers problem concerning the decay rate of a quasistationary state. Provided all Brownian particles start their motion from the potential minimum, the rate increases in time reaching a quasistationary value. We model the process of decay using the Langevin equations. This modeling makes it possible identifying the transient time required for the rate to reach its quasistationary value. We compare the numerical transient times with those known from the literature. It turns out that the difference reaches up to 70% in the case of weak friction. Increasing friction results in decreasing this difference. In order to make our results useful for a larger audience, we present them in the dimensionless form.

Determination of Fluid Flow in a Pipeline Based on Solving the Inverse Problem of Heat Transfer

We present a method of indirect measurement of fluid flow in a pipeline by solving the inverse problem of heat transfer using an exact analytic solution of the quasi-stationary boundary value problem of heat transfer and experimental data on the temperature of the fluid at discrete points along the pipe. The theoretical results are tested in an experimental installation and by a numerical calculation of the temperature using the finite element method.

Thermal ablation of an aluminium film upon absorption of a femtosecond laser pulse

We have found the time dependence of the ablation depth of aluminium irradiated by a femtosecond laser pulse. It is shown to what extent an increase in the radiation energy flux density leads to an increase in the quasi-stationary value of the ablation depth. By reducing the aluminium film thickness down to one hundred nanometres and less, the ablation depth significantly increases. At the same time, the quasi-stationary value of the ablation depth of a thin film is obtained due to the removal of heat from the focal spot region.

Constitutive relations for viscoelastic materials under thermorelaxation transition

A mathematical model of the mechanical behavior of viscoelastic bodies in a complex stress state under thermorelaxation transition is considered. The constructed constitutive equations allow one to describe the relations between the stress and strain tensors over a wide temperature interval including temperatures of relaxation transition. It is assumed that the characteristic relaxation times of the isotropic homogeneous polymer in a highly elastic state are much shorter than the characteristic times of external forces, which makes it possible to describe its behavior using the elastic model. In the glassy state, the behavior of the polymer is described in the framework of linear viscoelasticity. It is also assumed that the process of glass transition is accompanied by the formation of new intermolecular bonds, each being unstressed at the time of its appearance. It has been shown that the obtained constitutive relations of the hereditary type do not violate the second law of thermodynamics. A finite element procedure based on the stepwise integration has been developed and applied for solving quasi-stationary boundary value problems in mechanics of vitrifying polymers. The numerical technique is generalized to the case of taking into account the viscoelastic properties of the material in the glassy state. The validity of the physical and numerical models has been verified in the experiments, in which the residual stresses in the cylindrical EDT-10 epoxy resin specimens subject to non-uniform cooling are determined by the split ring method and polarization-optical method. It has been shown that the results of calculations agree well with the experimental data.

Non-linear and non-conservative quasi-variational principle of flexible body dynamics and application in spacecraft dynamics

The law of conservation of energy is one of the most fundamental laws of nature. According to the law of the conservation of energy, the non-linear and non-conservative quasi-variational principle of flexible body dynamics is established. The physical meaning of the quasi-stationary value conditions has been explained in non-linear and non-conservative flexible body dynamics. In the case study, the application in spacecraft dynamics is researched.

Rigid-Elastic Coupled Dynamics and its Application

According to energy conservation law, the functional of quasi-variational principle of rigid-elastic coupled dynamics is established. Quasi-stationary value conditions of quasi-variational principle of rigid-elastic coupled dynamics are derived. The governing equations of rigid-elastic coupled dynamics are obtained. As an application of rigid-elastic coupled dynamics, an approach of coupled vibration mode determined of unrestrained beam is established. The coupled vibration mode and coupled frequency are studied by the approach.

Extension of the Complete Flux Scheme to Systems of Conservation Laws

We present the extension of the complete flux scheme to advection-diffusion-reaction systems. For stationary problems, the flux approximation is derived from a local system boundary value problem for the entire system, including the source term vector. Therefore, the numerical flux vector consists of a homogeneous and an inhomogeneous component, corresponding to the advection-diffusion operator and the source term, respectively. For time-dependent systems, the numerical flux is determined from a quasi-stationary boundary value problem containing the time-derivative in the source term. Consequently, the complete flux scheme results in an implicit semidiscretization. The complete flux scheme is validated for several test problems.

Applying Kramers formula for the nuclear fission problem: how accurate is it?

We compare results of dynamical modeling of the fission process with predictions of the Kramers formulas. For the case of large dissipation these are two: the integral rate RI and its approximation RO . As the ratio of the fission barrier height Bf to the temperature T, ϵ, reaches 4, any analytical rate is expected to agree with the dynamical quasistationary value RD within 2%. We perform modeling using several potentials and find that the difference between the RO and the RD sometimes exceeds 20% even for ϵ > 4. Such discrepancy is not acceptable nowadays because it is comparable to the quantum, non-markovian and multidimensional effects. The features of the potentials which cause this disagreement are identified and studied. It is demonstrated that this is the RI, not the RO, which meets the expectation above irrespectively of the potential profile.

The distribution of rewards in sensorimotor maps acquired by cognitive robots through exploration

To exhibit intelligent behavior, cognitive robots must have some knowledge about the consequences of their actions and their value in the context of the goal being realized. We present a neural framework using which explorative sensorimotor experiences of cognitive robots can be efficiently ‘internalized’ using growing sensorimotor maps and planning realized using goal induced quasi-stationary value fields. Further, if there are no predefined reward functions (or the case when they are not good enough in a slightly modified world), the robot will have to try and realize its goal by exploration after which reward/penalty is given at the end. This paper proposes three simple rules for distribution of the received end reward among the contributing neurons in a high dimensional sensorimotor map. Importantly, reward/penalty distribution over hundreds of neurons in the sensorimotor map is computed one shot. This resulting reward distribution can be visualized as an additional value field, representing the new learnt experience and can be combined with other such fields in a context dependent fashion to plan/compose novel emergent behavior. The simplicity and efficiency of the approach is illustrated through the resulting behaviors of the GNOSYS robot in two different scenarios (a) learning ‘when’ to optimize ‘what constraint’ while realizing spatial goals and (b) learning to push a ball intelligently to the corners of a table, while avoiding traps randomly placed by the teacher (this scenario replicates the famous trap tube paradigm from animal reasoning carried out on chimpanzees, capuchins and infants).

Dynamic and statistical simulation of the fission of highly excited atomic nuclei with allowance for the relaxation stage

Statistical and combined dynamic-statistical approaches to simulating the fission of excited nuclei are compared. It is shown that in the statistical approach, the complete suppression of the fission pro cess during time τs does not result in double consideration of the emission of light particles. The importance of dynamic simulation of fission at the stage of relaxation of fission rate Rf(t) to its quasistationary value is demonstrated.

Horizontal convective water exchange above a sloping bottom: The mechanism of its formation and an analysis of its development

The mechanism of the formation of horizontal temperature/density gradients above underwater coastal slopes of natural basins due to heating/cooling from the surface is considered. It is shown that the time required for formation of the gradients is rather small (tens of minutes for a thermocline depth of tens of meters), but the development of the corresponding flows may not be accomplished even in a day long cycle. The time dependence of the horizontal water exchange between the shallow and deep areas is analytically treated. The spatial scale of the problem is the main parameter that defines the resulting quasi-stationary value of the flow rate. The joint analysis of the published field, laboratory, and numerical data of many authors in the range of the above-slope depths of 10−2 m < d < 3 × 102 m (d ≤ D, where D is the thickness of the upper thermally active layer of a basin) indicates that the relation between the value of the horizontal quasi-stationary volumetric flow rate and the local depth looks like Q = 0.00l3 × d 1.37 (R 2 = 0.96). The horizontal convective water exchange is shown to be generally two-layered, ageostrophic, and exhibits its maximum flow rate at the end of the slope. The inferences agree well with the field data and conclusions of other authors.

The special features of the luminescence and light resistance of europium complexes and their mixtures with lanthanum complexes in polymethyl methacrylate

The kinetics of luminescence and transformation of short-lived products of the photolysis of europium and lanthanum complexes with thenoyltrifluoroacetone and 1,10-phenanthroline and their mixtures in polymethyl methacrylate films was studied by the nanosecond laser photolysis method with recording both light emission and absorption. Fast (535 and 585 nm, 5 D 1 → 7 F 0, 7 F 3, decay time 0.7 μs) and slow (613 nm, 5 D 0 → 7 F 2, luminescence rise and decay times 0.7 μs and 0.5 ms, respectively) luminescence was studied. Induced absorption with a maximum at 600 nm and decay time ∼3 ms was observed; this absorption was assigned to triplet states of the deprotonated form of thenoyltrifluoroacetone. The dependences of luminescence intensity on the concentration of the components in a mixture of complexes were analyzed, and synergistic effects of luminescence strengthening were estimated. The kinetics of a decrease in luminescence intensity during photolysis was studied. Possible mechanisms of a decrease in the relative initial process rate and an increase in the quasi-stationary value of relative luminescence intensity as the concentration of complexes in the polymer increased were discussed.

Quasi-variational principles of single flexible body dynamics and their applications

The reasons for studying single flexible body dynamics are that on one hand, it is the basis of flexible multi-body dynamics. If the theory of the single flexible body dynamics has been deeply studied, the theory of flexible multi-body dynamics will be researched easily. On the other hand, it has its unique and important applications. Quasi-variational principle of non-conservative single flexible body dynamics is established under the cross-link of particle rigid body mechanics and deformable body mechanics. Taking the interceptor as an example, this paper has explained the physical meaning of the quasi-stationary value condition of the quasi-variational principle in non-conservative single flexible body dynamics. Taking the launch of rocket as an example, it has illustrated the features of “one force for two effects” in a single flexible body dynamics. With an example of the extending flexible beam coupled with the spacecraft attitude, it has shown the transition from the single flexible body dynamics to the flexible multi-body dynamics. Finally, a number of related problems are discussed.

Statistical theory of high-gain free-electron laser saturation.

We propose an approach, based on statistical mechanics, to predict the saturated state of a single-pass, high-gain free-electron laser. In analogy with the violent relaxation process in self-gravitating systems and in the Euler equation of two-dimensional turbulence, the initial relaxation of the laser can be described by the statistical mechanics of an associated Vlasov equation. The laser field intensity and the electron bunching parameter reach a quasistationary value which is well fitted by a Vlasov stationary state if the number of electrons N is sufficiently large. Finite N effects (granularity) finally drive the system to Boltzmann-Gibbs statistical equilibrium, but this occurs on times that are unphysical (i.e., excessively long undulators). All theoretical predictions are successfully tested by means of finite- N numerical experiments.

Effect of Thermal Resistance of the Dielectric–Metal Contact on the Temperature Field in a Dielectric Exposed to Ion Beams

Heating of MgO crystals exposed to repetitively pulsed ion beams is studied. A solution to the thermal-conductivity equation provides induced specimen-temperature variations about a mean with irradiation-pulse repetition rate. The average temperature during the variation period first increases and then saturates, approaching a quasi-stationary value . The latter depends entirely on the thermal resistance of the specimen–substrate contact under fixed irradiation conditions. A rapid method for determining the thermal resistance of the contact is put forward. The approach is based on repetitive pulsed heating of the specimen by a moderate-density electron beam and on precision measurements of average temperature.