Transient phenomena in multiphase queueing systems

Institute of Mathematics and Cybernetics, Lithuanian Academy of Sciences. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 1, pp. 136–145, January–March, 1991.     

Transient chaos and crisis phenomena in butterfly valves driven by solenoid actuators

Chilled water systems used in the industry and on board ships are critical for safe and reliable operation. It is hence important to understand the fundamental physics of these systems. This paper focuses in particular on a critical part of the automation system, namely, actuators and valves that are used in so-called “smart valve” systems. The system is strongly nonlinear, and necessitates a nonlinear dynamic analysis to be able to predict all critical phenomena that affect effective operation and efficient design. The derived mathematical model includes electromagnetics, fluid mechanics, and mechanical dynamics. Nondimensionalization has been carried out in order to reduce the large number of parameters to a few critical independent sets to help carry out a broad parametric analysis. The system stability analysis is then carried out with the aid of the tools from nonlinear dynamic analysis. This reveals that the system is unstable in a certain region of the parameter space. The system is also shown to exhibit crisis and transient chaotic responses; this is characterized using Lyapunov exponents and power spectra. Knowledge and avoidance of these dangerous regimes is necessary for successful and safe operation.     

Experimental and theoretical investigation of PLC bands

In this paper, the nucleation and propagation of PLC deformation bands in AlMg3 alloy are studied experimentally and theoretically. The morphology and kinematics of PLC bands are investigated using both mechanical and thermal measurement methods. In particular, the latter is based on the use of a thermal camera which captures the temperature changes resulting from mechanical dissipation during nucleation and propagation of PLC bands. On the modeling side, two models are investigated via finite-element and finite-difference methods. Here, attention is focused on the influence of the specimen geometry and the thermomechanical coupling on PLC band nucleation and propagation. A comparison of experimental and simulation results is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Filtering method in backlash phenomena analysis

The behavior of robotic manipulators with backlash is analyzed. Based on the pseudo-phase plane two indices are proposed to evaluate the backlash effect upon the robotic system: the root mean square error and the fractal dimension. For the dynamical analysis the noisy signals captured from the system are filtered through wavelets. Several tests are developed that demonstrate the coherence of the results.     

Lineability and algebrability of pathological phenomena in analysis

We show that, in analysis, many pathological phenomena occur more often than one could expect, that is, in a linear or algebraic way. We show this by means of the construction of large algebraic structures (infinite dimensional vector spaces or infinitely generated algebras) enjoying some special or pathological properties.     

Modeling and analysis of tilt-rotor aeromechanical phenomena

The paper presents a recent effort to explore tilt-rotor aeromechanical phenomena with an emphasize on aeroelastic stability in forward flight (airplane mode). A general tilt-rotor model has been developed and implemented using a numerical technique that preserves symbolic exactness of the equations of motion. The stability study is based on an eigenvalue analysis about a nonlinear periodic trim solution. The present method enables both high resolution periodic response, and clear tracing of the instability drivers by providing the exact partial derivatives of the involved degrees of freedom in each one of the associated equations of motion. In addition to the common way of identifying trends and sensitivities by parametric study, the present approach supplies information about the effectiveness of possible mechanisms that are not included in the baseline model. The present results demonstrate the ability of the method to provide such unique insight into the aeromechanical phenomena in forward flight. Illustrative indications regarding required tilt-rotor design features that will postpone the instability phenomena are discussed.     

Transient phenomena for random walks in the absence of the expected value of jumps

Let ξ, ξ₁, ξ₂, ... be independent identically distributed random variables, and S _n :=Σ _j=1 ⁿ ,ξ _j , $ \bar S $ \bar S := sup _n≥0 S _n . If Eξ = −a < 0 then we call transient those phenomena that happen to the distribution $ \bar S $ \bar S as a → 0 and $ \bar S $ \bar S tends to infinity in probability. We consider the case when Eξ fails to exist and study transient phenomena as a → 0 for the following two random walk models:

Experimental and theoretical modeling of shrinkage damage formation in fiber composites

The cure of a thermoset matrix in the formation of composites is always accompanied by chemical shrinkage that generates internal stresses. In composites with high fiber content, the matrix is cured under three-dimensionally constrained conditions. The results of the previous experimental and theoretical modeling of formation of shrinkage damage under these conditions in epoxy-amine systems are briefly discussed. The effect of the model geometry (tube and plate models), scale factor, cure schedule, and chemical structure of composites is analyzed. A theoretical model for predicting the possibility of formation of shrinkage damage in fiber composites is proposed. A regular square structure was considered. Analysis showed that the maximum level of shrinkage stress in the matrix at the ultimate fiber fraction ⁺ was close to the stress level ⁺ in an experimental long tube model, where the formation of shrinkage damage took place. The experimental results for the short tube model showed that the shrinkage damage in epoxy-amine systems occurred up to approximately ⁺/3. The damage development took place within the whole range of fiber content from ⁺ to ^* (where the shrinkage stress level was about ⁺/3). In the long tube model, cohesive defects always nucleated inside the matrix. The damage grew, reached the inner surface of the tube, and then extended as adhesive debondings. A similar situation is expected in composites with a high fiber content. The damage considered is local, and the total monolithic character of a composite product is conserved.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998. Riga, Latvia.Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka 142432, Moscow Region, Russia. Translated form Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 264–275, March–April, 1998.     

Extension phenomena in multidimensional complex analysis: correction of the historical record

Conclusion  Even though Bochner should not be credited with the proof of any version of theCR extension theorem, his 1943 paper remains a landmark in the history of the Hartogs extension phenomenon. His vision to enlarge his horizon from holomorphic functions to certain harmonic functions set the stage for further generalizations by himself (for example [Bochner 1954]) as well as for Ehrenpreis’s investigations on related problems for solutions of more general elliptic partial-differential operators. In closing, it should be pointed out that Bochner’s 1943 paper, in an ironic twist, includes an important result for which Bochner did not receive any credit until recently [Range 1986, p. 188]. Bochner proved the solution of ∂ on polydiscs (for (0, l)-forms in the real-analytic case, which was the case of interest to him), via the Cauchy transform with parameters in dimension one, and by induction on the number of differentialsdzj appearing in the given form (Theorem 11,op. cit., p. 665). This result, with essentially the same proof, 10 years later became widely known as the Dolbeault-Grothendieck Lemma. But this is another story….     

Multiscaling comparative analysis of time series and geophysical phenomena

Different methods are used to determine the scaling exponents associated with a time series describing a complex dynamical process, such as those observed in geophysical systems. Many of these methods are based on the numerical evaluation of the variance of a diffusion process whose step increments are generated by the data. An alternative method focuses on the direct evaluation of the scaling coefficient of the Shannon entropy of the same diffusion distribution. The combined use of these methods can efficiently distinguish between fractal Gaussian and Lévy‐walk time series and help to discern between alternative underling complex dynamics. © 2005 Wiley Periodicals, Inc. Complexity 10: 51–56, 2005     

Experimental and theoretical investigation of a composite beam for bridge structures

Results of an experimental and theoretical investigation of composite beams as elements of bridge superstructure are presented. Experiments on beams of two types — made of wood and the same beams with a composite sheath — were carried out. The rigidity of the beams of the second type was about twice as high as that of the first ones. The classical bending model of composite beams gave deflections smaller than experimental ones. To reconcile these results, the model is refined by including the effect of shear. The deflections are represented as classical ones multiplied by a shear factor which depends on the bending and shear stiffnesses and the span length of the beams. As a result, a good agreement between calculations and experiments is achieved. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 449–462, July–August, 2006.     

Experimental and theoretical investigation on soft tissue remodeling enhanced by cell activity

The aim of the present work is to investigate the remodeling phenomenon of a cell-seeded tissue. In experiments, a cell seeded condensed collagen gel is mechanically stimulated in a bioreactor for four weeks, after which the specimen is tested in compression to measure its change of stiffness. The change, regarded as remodeling, is assumed to be the result of newly synthesized collagen type II; a constitutive equation is proposed for the remodeling effect. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and theoretical investigation of creep groan of brakes through minimal models

Creep groan of brake systems is a low frequency vibration phenomenon occurring at low speeds which can make passengers feel uncomfortable. This phenomenon is caused by the stick-slip-effect resulting in limit cycle oscillations with frequencies lower than 200 Hz. For the experimental investigation of this problem, an idealized brake test rig is designed concentrating on the investigation of the frictional contact by realizing low damping and small disturbances in the system. Different sensors are utilized in the test rig. Limit cycles and bifurcation effects can be observed in the experimental results. With respect to modeling, a one degree-of-freedom (DOF) model using Coulomb's friction law and a two DOF model using the bristle friction law are considered. In a comparative study of experimental and simulation results, the parameters of both friction laws can be identified from the dynamic experimental results, such as the static and dynamic friction coefficients, contact stiffness and Stribeck velocity. Experimental and theoretical results show a very good concordance. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and theoretical investigation on the microstructure of aluminum alloys during extrusion

The purpose of this work is the investigation of the material behavior of aluminum alloys during extrusion and cooling. In particular, the alloys of the 6000 series (Al–Mg–Si) and 7000 series (Al–Zn–Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. For the development of a suitable material model EBSD measurements are done on different parts of an extruded Al6060 specimen. For this sample a microstructure picture is generated and a statistical analysis is performed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transient analysis of two queues in parallel with jockeying

Recently, Tarabia (Appl. Math. Model., 2008, 802) studied the steady-state probabilities of two parallel queues with jockeying and restricted capacities, using the matrix-analytical technique. In this paper, the differential–difference equations which describe the transient state case are derived. Using the fourth order Runge–Kutta method and randomization methods, transient-state probabilities of the Tarabia (2008) model are computed. It is shown that these two methods are closely related, but that the randomization method is superior to the Runge–Kutta method. In the transient case, a numerical comparison between Tarabia's model and Conolly's (J. Appl. Prob., 1984, 394) model is presented to highlight the effect of jockeying on the average of the queue length and the waiting time. Finally, some illustrative numerical results are provided, and conclusions are presented.     

Random irreversible phenomena: entropy in subordination

Having been motivated by the processing of astrophysical data, we formulate a stochastic model of transmitting random information. It may be assumed that the information source is taken to be white noise, while the observed data are viewed as sample functions of a stable process. Thus our model of the system of the transmitting signal is realized by the so-called Bochner theory of subordination. As a characteristic of this phenomena we observe the loss of entropy.     

Expected value analysis: Experimental considerations and convergence properties

In a companion paper, we developed a method, EVA (expected value analysis), to analyze the effect of the uncertainty of parameters in multiparameter systems described by ordinary differential equations. In this paper, we first interpret the output mean of EVA from an experimental point of view. Secondly, we discuss the convergence properties of EVA. The only approximation is the truncation of higher order correlation effects. A quantitative analysis of the approximations is presented, justifying the methodology.