Quasi-stationary Process Research Articles

Performance Analysis of Linear Cooperative Multi-Hop Networks Subject to Composite Shadowing-Fading

We consider a cooperative multi-hop line network, where a group of nodes cooperatively transmits the same message to another group of nodes, and model the transmission from one group to another as a discrete-time quasi-stationary Markov process. We derive the transition probability matrix of the Markov chain by considering the wireless channel exhibiting composite shadowing-fading. The shadowing is modeled as a log-normal random variable (RV) and the multipath fading as a Rayleigh RV, where the multiplicative model for the mixture distribution known as Suzuki (Rayleigh-lognormal) distribution has been considered. The sum distribution of the multiple Suzuki RVs is approximated by a single log-normal RV by using the moment generating function (MGF)-based technique. This MGF-based technique uses Gauss-Hermite integration to present the sum distribution in closed form. We quantify the signal-to-noise ratio (SNR) margin required to achieve a certain quality of service (QoS) under standard deviation of the shadowing. We also provide the optimal level of cooperation required for obtaining maximum coverage of a line network under a given QoS. Two topologies for linear network are considered and the performance of each topology under various system parameters is provided. The analytical results have been validated by matching with the simulation results.

Dynamical features of the quasi-stationary microRNA-mediated protein translation process supported by eIF4F translation initiation factors

Mathematical modeling of kinetic processes with different time scales allows a reduction of the governing equations on the basis of quasi-steady-state approximations (QSSA). Below the QSSA theorem is applied to a modified mathematical model of the microRNA repression on the protein translation with participation of eIF4F translation initiation factors. In accordance with the terminology of the QSSA theorem two of the protein concentrations are denoted as ‘fast varying‘, such that the corresponding kinetic equations form a system attached to the system for ‘slow‘ variables that consists of equations for the other four concentrations. We obtain analytic solutions related to the steady-state values of the fast varying concentrations and the slow varying ones, and the interpretation of these solutions are as restrictions on the regulatory role of microRNAs on the protein translation process.

Photodissociation of IF2CCOF clusters by resonant IR radiation

Results of studies on the dissociation of (IF2CCOF) n clusters upon resonant excitation of IF2CCOF molecules by pulsed (~10-7 s) IR laser radiation are reported. Two different channels of the cluster excitation, via vibrations of C–F (~9 μm) and C = O (~5.3 μm) bonds in chromophore molecules, were used. It has been shown that, in both cases, the number of clusterized molecules decreases exponentially with increasing IR radiation fluence Φ IR . A dissociation lag has been revealed; i.e. the dissociation of (IF2CCOF) n clusters has been found to occur only at values of Φ IR that exceed a certain threshold value, Φ IR > Δ Φ th . The efficiency of cluster dissociation has been shown to depend only on the amount of absorbed energy and not to depend on the used channel of excitation. A phenomenological model of the cluster IR dissociation has been developed, which ensure a clear interpretation of experimental results. In particular, the energy required to evaporate the molecule and the mean size of the clusters under study have been estimated. It is concluded that, on a time scale ~10-7 s, the process of the IR dissociation of (IF2CCOF) n clusters can be considered as a quasi-stationary process of successive evaporation of molecules in the course of cluster heating by resonant IR radiation.

DIFFUSION-CONTROLLED QUASI-STATIONARY MASS TRANSFER FOR AN ISOLATED SPHERICAL PARTICLE IN AN UNBOUNDED MEDIUM

A consolidated mathematical formulation of the spherically symmetric mass transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the diffusion-controlled quasi-stationary process, a mathematically complete set of the exact analytical solutions is obtained in implicit forms to cover the entire parameter range. Furthermore, accurate explicit formulas for the particle radius as a function of time are also constructed semi-empirically for convenience in engineering practice. Both dissolution of a particle in a solvent and growth of it by precipitation in a supersaturated environment are considered in the present work.

Entropy increase during physical processes for black holes in Lanczos-Lovelock gravity

We study quasi-stationary physical process for black holes within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasi-stationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary state. This result reinforces the physical interpretation of Wald entropy for Lanczos-Lovelock models and takes a step towards proving the analogue of the black hole area increase-theorem in a wider class of gravitational theories.

A model of thermoelectroplasticity of variations in the mechanical properties of metals based on defect structure reorganization under the action of pulse electric current

We consider variations in the mechanical properties of prestrained samples made of metallic materials with defects like microcracks and micropores under the action of pulse high-energy electric currents of certain intensity and duration. It was experimentally shown [1–5] that the treatment with a high-energy electromagnetic field of a prestretched sample with defects like microcracks that are located normally to the sample tension axis increases the sample limit plastic strain, which simplifies the treatment of hard-to-deform alloys in various technological processes. We consider a slow quasi-stationary process of thermal-electric treatment of samples, which permits obtaining materials with desired mechanical properties including samples with a high limit plastic strain.

Computation of the entropy of a two-phase elastic medium in the problem of thermoelasticity

We find an explicit expression for the entropy of a homogeneous isotropic two-phase elastic medium in the problem describing the quasistationary process of changing the temperature. Based on the limit behavior of the entropy, we can conclude whether this process is reversible or not. Bibliography: 4 titles.

Numerical simulation of quasi-stationary ring spinning process linear elastic yarn

This article reports a theoretical investigation on the ring spinning balloon in the textile industry. Theoretical equations incorporating yarn elasticity are obtained, which has been ignored by most previous models. This model differs from the earlier ones in that their choice of yarn was perfectly flexible and inextensible; those used here we presume to be more realistic. Discussions in this paper deal with the significance of various yarn elasticity parameters on varying yarn tension and balloon shape. Some results are given, from which the model seems to be very efficient and reliable in the simulation of the ring spinning process. Restrictions on the applicability of the theory are also pointed out.

On the Problem of Formulating Principles in Nonequilibrium Thermodynamics

In this work, we consider the choice of a system suitable for the formulation of principles in nonequilibrium thermodynamics. It is argued that an isolated system is a much better candidate than a system in contact with a bath. In other words, relaxation processes rather than stationary processes are more appropriate for the formulation of principles in nonequilibrium thermodynamics. Arguing that slow varying relaxation can be described with quasi-stationary process, it is shown for two special cases, linear nonequilibrium thermodynamics and linearized Boltzmann equation, that solutions of these problems are in accordance with the maximum entropy production principle.

Stabilization of the process of electrohydrodynamic dispersion of metals with electron-beam heating

The stability of the process of nanostructure formation during the electrohydrodynamic dispersion of metals with electron-beam heating has been studied. The main factors responsible for the process breakage are considered and conditions under which the passage to a stable setup operation regime does not lead to a decrease in the efficiency of nanoparticle formation are determined. It is established that the formation of nanoparticles in this regime is a quasi-stationary process, in which the particle flux appears as a constant background with pulsations of 50% amplitude.

THOUGHTS ON THE AREA THEOREM

Hawking's area theorem can be understood from a quasistationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual Banados–Teitelboim–Zanelli (BTZ) black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon "can decrease," rather than increase, with the quasistationary process. However, I find that the area for the outer horizon "never decrease" such as the usual area theorem still works in our examples, though this is quite nontrivial in general. I also find that the recently proposed new entropy formulae for the above mentioned, recently discovered black holes satisfy the second law of thermodynamics.

Notes on the area theorem

Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon ‘can decrease’, rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon ‘never decreases’ such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons.

Direct observations of non-stationary bridge deck aeroelastic vibration in wind tunnel

It is useful to study the ambient non-stationary response of a cable-supported bridge to monitor the “aeroelastic status” of the structure. In the absence of effective non-stationary analyzing tools, it is suitable to have signal processing techniques to pre-examine the measured ambient responses for the time scale at which the aeroelastic system varies to know if the recording can be treated as a quasi-stationary process or must be treated as non-stationary one. Among the factors contributing to the non-stationarity, the effect of signature turbulence is studied in this paper by joint time–frequency analysis on wind tunnel experiments with a partially streamlined box girder sectional model. Hilbert transform combined with empirical mode decomposition method is used. Instantaneous frequency domain properties of the aeroelastic vibration are obtained. Time-dependant features of the interactive system are partially revealed.

A correlation-spectral identification method for quasi-stationary time processes

Parametric identification algorithms are designed for a quasi-stationary linear filter, which is an adequate model for the formation of a quasi-stationary time process if noise is fed to the filter input.

Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model

We perform a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-Field model, a prototype for long-range interactions in N-particle dynamics. In particular, we point out the role played by the infinity of stationary states of the associated N→∞ Vlasov dynamics. In this context, we derive a new general criterion for the stability of any spatially homogeneous distribution, and compare its analytical predictions with numerical simulations of the Hamiltonian, finite N, dynamics. We then propose, and verify numerically, a scenario for the relaxation process, relying on the Vlasov equation. When starting from a nonstationary or a Vlasov unstable stationary state, the system shows initially a rapid convergence towards a stable stationary state of the Vlasov equation via nonstationary states: we characterize numerically this dynamical instability in the finite N system by introducing appropriate indicators. This first step of the evolution towards Boltzmann–Gibbs equilibrium is followed by a slow quasi-stationary process, that proceeds through different stable stationary states of the Vlasov equation. If the finite N system is initialized in a Vlasov stable homogeneous state, it remains trapped in a quasi-stationary state for times that increase with the nontrivial power law N 1.7. Single particle momentum distributions in such a quasi-stationary regime do not have power-law tails, and hence cannot be fitted by the q-exponential distributions derived from Tsallis statistics.

A model of electromagnetic radiation signals of loaded rocks

UDC 622.831 Since the time of discovering electromagnetic radiation (EMR) accompanying the formation and growth of cracks [1] investigations of this phenomenon have developed in the direction of studying the physics of the process, in particular, a study of the kinetics of cracking of loaded rocks and in applied directions [2, 3]. On the basis of data on recording EMR pulses models of the kinetics of accumulation of cracks as a quasi-stationary stochastic process with independent increments [2] and correlated persistent (trend-preserving) pulsed process [3] were constructed. An experimental check of these models was based on calculating the number of pulses recorded during loading of the rock specimens under laboratory conditions, in which case the shape of the EMR signal, possibility of superposition of pulses in time, polarization of the signal, distance of the detector from the EMR sources (cracks), etc., were not taken into account. Consideration of the aforemen- tioned factors becomes especially urgent when investigating the process of cracking in large rock masses, where the rate of flow of EMR pulses can be considerable. In connection with this, it is necessary to develop a model of the EMR signal in interrelation to the kinetics of accumulation of cracks and shape of the EMR pulses from cracks taken individually. The purpose of the present work was to develop a model of the EMR signal occurring during cracking of rocks in interrelation to the kinetics of accumulation of cracks and shape of the EMR pulses from individually taken cracks.

Increase of black hole entropy in higher curvature gravity.

We examine the Zeroth Law and the Second Law of black hole thermodynamics within the context of effective gravitational actions including higher curvature interactions. We show that entropy can never decrease for quasi-stationary processes in which a black hole accretes positive energy matter, independent of the details of the gravitational action. Within a class of higher curvature theories where the Lagrangian consists of a polynomial in the Ricci scalar, we use a conformally equivalent theory to establish that stationary black hole solutions with a Killing horizon satisfy the Zeroth Law, and that the Second Law holds in general for any dynamical process. We also introduce a new method for establishing the Second Law based on a generalization of the area theorem, which may prove useful for a wider class of Lagrangians. Finally, we show how one can infer the form of the black hole entropy, at least for the Ricci polynomial theories, by integrating the changes of mass and angular momentum in a quasistationary accretion process.

A stationary model of coherent text generation*

Abstract The present paper is an attempt to develop the theoretical foundations of the concept of statistical arrangement of words in a coherent text on the basis of a variation model. Text generation is considered as a quasistationary process, and the theoretical consequences of this approach are examined.

Evaluation of the functional connectivity in the nervous system using time dependent scatter diagrams

We investigated spike trains of the feline nervous system, which are considered to be non-stationary point processes characterized by changes of the functional interneuronal connectivities. Ordinary long-term averaged correlation methods are useful as processing time series data as a quasi-stationary point process, but not as a non-stationary point process. We depicted the joint impulse configuration scatter diagram proposed by D.H. Perkel et al. for subsets of the neural spike train to find changes of functional connectivities The time-dependent scatter diagram wasgenerated by arranging these scatter diagrams in chronological order. Time-dependent scatter diagrams were generated for spike trains derived from the anterior ectosylvius sulcus, the coronal sulcus, the lateral bank of the presylvius sulcus, the medial wall of the presylvius sulcus, the medial wall of the cruciate sulcus. The patterns of time-dependent scatter diagrams for these cortices are considered to change in relation to eye movement. Changes of these patterns correspond to those of the functional connectivities related to the dynamics of eye movement in the neural system.

Effect of coating porosity on the process of heat transfer with gas-thermal deposition

Features are considered for the thermal state of layered-inhomogeneous systems of a multilayer coating—underlayer—base with plasma deposition of cladding composite powders. Typical results are presented for mathematical modeling of the quasistationary process of heat transfer for the system in question. Regularities of the effect of coating porosity on the temperature schedule for the system and the effect of coating thickness on porosity are studied.