Existence and stability of limit cycles for pressure oscillations incombustion chambers

In this paper, we discuss two problems. First, using a second order expansion in the pressure amplitude, some analytical results on the existence, stability and amplitude of limit cycles for pressure oscillations in combusticm chambers are presented. A stable limit cycle seems to be unique. The conditions for existence and stability are found to be dependent only on the linear parameters. The nonlinear parameter affects only the wave amplitude. The imaginary parts of the linear responses, to pressure oscillations, of the different processes in the chamber play an important role in the stability of the limit cycle. They also affect the direction of flow of energy among modes. In the absence of the imaginary parts, in order for an infinitesimal perturbation in the flow to reach a finite amplitude, the lowest mode must be unstable while the highest must be stable; thus energy flows from the lowest mode to the highest one. The same case exists when the imaginary parts are non-zero, but in addition, the contrary situation is possible. There are conditions under which an infinitesimal perturbation may reach a finite amplitude if the lowest mode is stable while the highest is unstable. Thus energy can flow "backward" from the highest mode to the lowest one. It is also shown that the imaginary parts increase the final wave amplitude. Second, the triggering of pressure oscillations in solid propellant rockets is discussed. In order to explain the triggering of the oscillations to a nontrivial stable: limit cycle, the treatment of two modes and the inclusion in the combustion response of either a second order nonlinear velocity coupling or a third order nonlinear pressure coupling seem to be sufficient

Measurements of interactions between acoustic fields and nonuniform mean flow

Two problems crucial to the stability of longitudinal acoustic waves in solid rocket motors are examined experimentally. The first is the dissipation of energy associated with an average flow inward at the lateral boundary. Measurements reported here, though subject to considerable experimental error, show that the actual losses are much larger than predicted by the approximate one dimensional analysis. The second problem is the attenuation of waves accompanying reflection by the nonuniform flow in a choked exhaust nozzle. Empahsis in this work has been on technique, to provide data relatively easily and inexpensively. It appears that good results can be obtained in a routine manner using small supersonic wind tunnel operated as an open cycle. At least for Mach numbers up to 0.04 at the nozzle entrance, difficulties with signal/noise are satisfactorily overcome with a tracking filter

Strength and Deformation Characteristics of Plain Concrete Subjected to High Repeated and Sustained Loads

The investigation was concerned with the response of plain concrete when subjected to repeated or sustained high compressive loads. The objectives were: (1) to study the strength and deformation characteristics of concrete under such loading conditions, and (2) to propose an analytical procedure to predict concrete behavior under high repeated loads. The first objective was realized through an experimental program. Plain concrete prisms (4 in. by 4 in. by 12 in.) were subjected to high repeated and sustained loads. Compressive loads were concentrically applied. Strains in the longitudinal and lateral directions were recorded throughout the life of a specimen. The test program was divided into three phases. Phase One dealt with the effect of maximum stress, stress range and concrete age at time of loading. Phase Two concerned with the effect of speed of testing on static and repeated load behavior. The relationship between the damage, caused by high repeated and sustained loads, less than those necessary to cause failure, and the remaining load carrying capacity of a specimen, was studied in Phase Three. To achieve the second objective, two analytical models were formulated. These were based on the cycle and time-dependence of damage and of strains of concrete when subjected to high repeated or sustained stresses. For a given set of parameters, a damage model was proposed to predict the number of cycles required to cause failure, while a failure strain model was developed to predict the total longitudinal strain accumulated at failure. The experimental program showed that concrete response to high repeated loads is very much controlled by the time concrete has to resist stresses higher than its sustained load strength. For a maximum stress higher than the sustained load strength, a decrease in the stress range and /or the stress rate (test frequency) significantly increases the “sustained load” contribution to the overall behavior. The number of cycles to failure are smaller, and the exhibited strains throughout the loading history and at failure are larger, the greater the “sustained load” effect. Even if the effect of hydration during a test is excluded, concrete age at loading appears to have a significant effect on behavior of concrete subjected to high loads. In addition, it was shown by experiment that plain concrete, subjected to high repeated and sustained loads, undergoes a “hardening” stage manifested by an increase in the static strength over the static strength prior to sustained or repeated load test. This “hardening” is dominant during the earlier portion of the life of the specimen. The last portion is characterized by progressive crack propagation and a stress decrease until failure. In the analytical study, a damage model was developed in which the cycle and time-dependent effects are expressed separately. The damage model was revised successively until excellent agreement, between calculated and observed failure cycles, was achieved. Also, an analytical model to determine the failure strain model was derived. The total strain was assumed to consist of an initial elastic strain, a cycle-dependent and a time-dependent strain. The agreement between calculated and observed failure strains ranged from poor to satisfactory, but the failure strains, calculated from the analytical model, gave the general tendencies which were observed in the experiments.National Science Foundation. Research Grant GK-180

Underdetermined blind source separation based on Fuzzy C-Means and Semi-Nonnegative Matrix Factorization

Conventional blind source separation is based on over-determined with more sensors than sources but the underdetermined is a challenging case and more convenient to actual situation. Non-negative Matrix Factorization (NMF) has been widely applied to Blind Source Separation (BSS) problems. However, the separation results are sensitive to the initialization of parameters of NMF. Avoiding the subjectivity of choosing parameters, we used the Fuzzy C-Means (FCM) clustering technique to estimate the mixing matrix and to reduce the requirement for sparsity. Also, decreasing the constraints is regarded in this paper by using Semi-NMF. In this paper we propose a new two-step algorithm in order to solve the underdetermined blind source separation. We show how to combine the FCM clustering technique with the gradient-based NMF with the multi-layer technique. The simulation results show that our proposed algorithm can separate the source signals with high signal-to-noise ratio and quite low cost time compared with some algorithms

Enteral reduction and oblique anastomosis: a novel technique in the treatment of small bowel atresia

Background: Jejunoileal atresias are major causes of neonatal intestinal obstruction, and various surgical techniques were described for their treatment. Resection and/or tapering of the proximal dilated pouch and end-toend or end-to-back enteral anastomosis are the most commonly used techniques. Either of these techniques, however, has shortcomings such as loss of bowel length, kink obstruction, and anastomotic leak due to anastomotic line mismatch.Objective: The aim of this study was to describe an alternative surgical technique for bowel atresia repair, enteral reduction and oblique anastomosis.Patients and methods: The technique involves reduction of the dilated bowel diameter by removing an elliptical fullthickness part of the anterior wall of the proximal dilated pouch and oblique anastomosis of the resultant window with a longitudinally incised posterior wall of the distal bowel.Results: This technique was used in seven successive neonates, four female and three male, in 1 year. Their ages at operation ranged between 2 and 30 days (median 3 days). Six neonates recovered well. Enteral feeds were tolerated in 7–10 days and the length of hospital stay ranged between 15 and 36 days. One baby, who underwent surgical repair at the age of 30 days, died following severe sepsis and anastomotic leak.Conclusion: Enteral reduction and oblique anastomosis is an easy and safe alternative to current surgical techniques used for the treatment of small intestinal atresia. No bowel resection is required while proximal bowel tapering is achieved.Keywords: oblique anastomosis, small bowel atresia, taperin

Degenerate Bogdanov-Takens bifurcations in a bulk viscous cosmology

Using the dynamical system theory we show that the Friedmann-Robertson-Walker (FRW) cosmological model with bulk viscous fluid in the presence of cosmological constant is equivalent to a degenerate two dimensional Bogdanov-Takens normal form. The equation of state parameter, $\omega$, the bulk viscosity coefficient, $\xi$, and the cosmological constant, $\Lambda$, define the necessary parameters for unfolding the degenerate Bogdanov-Takens system. The fixed points of the system are discussed together with the variation of their stability properties upon changing the relevant parameters $\omega$, $\Lambda$ and $\xi$. The variation of the stability properties are visualized by the appropriate bifurcation diagrams. Phase portrait for finite domain and global phase portrait are displayed and the issue of the structural stability are discussed. Typical issues such as late acceleration or inflation that can be induced by viscosity and could have relevance to observational cosmology are also discussed.Comment: 46 pages, 21 figures, 4 tables, typos are corrected, new references are added, new material is adde