Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?

We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. Within the class of Filippov solutions, if $\Sigma$ is attractive, one should expect solution trajectories to slide on $\Sigma$. It is well known, however, that the classical Filippov convexification methodology is ambiguous on $\Sigma$. The situation is further complicated by the possibility that, regardless of how sliding on $\Sigma$ is taking place, during sliding motion a trajectory encounters so-called generic first order exit points, where $\Sigma$ ceases to be attractive. In this work, we attempt to understand what behavior one should expect of a solution trajectory near $\Sigma$ when $\Sigma$ is attractive, what to expect when $\Sigma$ ceases to be attractive (at least, at generic exit points), and finally we also contrast and compare the behavior of some regularizations proposed in the literature. Through analysis and experiments we will confirm some known facts, and provide some important insight: (i) when $\Sigma$ is attractive, a solution trajectory indeed does remain near $\Sigma$, viz. sliding on $\Sigma$ is an appropriate idealization (of course, in general, one cannot predict which sliding vector field should be selected); (ii) when $\Sigma$ loses attractivity (at first order exit conditions), a typical solution trajectory leaves a neighborhood of $\Sigma$; (iii) there is no obvious way to regularize the system so that the regularized trajectory will remain near $\Sigma$ as long as $\Sigma$ is attractive, and so that it will be leaving (a neighborhood of) $\Sigma$ when $\Sigma$ looses attractivity. We reach the above conclusions by considering exclusively the given piecewise smooth system, without superimposing any assumption on what kind of dynamics near $\Sigma$ (or sliding motion on $\Sigma$) should have been taking place.Comment: 19 figure

The stabilization of unstable detonation waves for the mixture of nitromethane/methanol

Mass velocity profiles of detonation waves in mixtures of nitromethane with acetone and methanol with added diethylenetriamine sensitizer were measured using a VISAR laser interferometer. It was found that even small, about 1%, concentrations of acetone and methanol, inert diluents, led to instability of the one-dimensional detonation front in nitromethane. The results of the experiment show that the use of the sensitizer is an effective method of flow stabilization and if the concentration of the inert diluent does not exceed 10%, the detonation front becomes stable with the addition of 1% diethylenetriamine. At a higher diluent concentration, the sensitizer does not suppress the instability but decreases the oscillation amplitude by several times. The addition of diethylenetriamine to the mixture has been found to increase the detonation velocity

Activity of the right cardiac ventricle and metabolism in healthy persons during an orthostatic test after short term immobilization

A 15 minute orthostatic test was performed on healthy male volunteers under conditions of catheterization of the right ventricle of the heart and the radial (or brachial) artery before and after 5 day bedrest in an antiorthostatic position of the body (with the foot of the bed raised 4.5 degrees). The change to a vertical position after immobilization was attended by a more marked increase in the rate of cardiac contractions, an increase of max dp/dt pressure in the right ventricle, and a decrease of cardiac and stroke indices. The decrease of the cardiac index was compensated for, to a certain measure, by a further increase in the extraction and utilization of O2 by the tissues. The arterial blood pH did not change essentially, while the decrease in pCO2 and content of standard bicarbonate was more marked

Influence of Carboxylic Acids on Filterability and Quality Level of Synthetic Low Alkaline Calcium Sulfonate (Detergent-Dispersant Motor Oil Additive)

The study examined the conditions of synthetic low alkaline calcium sulfonate (SLCS) synthesis, which is added to motor oils as a detergent-dispersant additive. In particular, the effect of the introduction of carboxylic acids at the stage of SLCS synthesis on such characteristics of the additive as the observable filterability, volume filtration rate, volume fraction of sediment and kinematic viscosity was studied. For the obtained additive samples the average sizes of particles dispersed in the volume were measured using the dynamic light scattering method (DLS) and the basic physicochemical parameters were determined

Sliding mode control of quantum systems

This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e., eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum sliding mode control systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of main features of the proposed method is that the designed control laws can guarantee desired control performance in the presence of uncertainties in the system Hamiltonian. This sliding mode control approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.Comment: 18 pages, 4 figure

The Environmental Agenda in the Election Programs of Russian Political Parties

The article is devoted to the study of environmental agenda in the Russian political field on the example of the analysis of the election programs of Russian political parties. The study analyzes the factors and features of the inclusion of the environmental issues in the political programs of Russian political parties. The main environmental problems raised by political parties and the dynamics of its considering were highlighted, and the specific of their discursive representation were analyzed. The study revealed the following features of the appeal of political actors to environmental issues: techno-utopianism as an unconditional belief in “green technologies” that does not imply major institutional changes; eco-populism, manifested in the connection of environmental problems with more popular social issues; ritualization as a formal mention of the “green” agenda, which does not receive careful consideration. Special attention was paid to the (un)formation of the climate agenda in Russia, which showed the limitations of the global process influence on the Russian political agenda. The study was carried out on the basis of a qualitative methodology

Flow and Noise Control in High Speed and High Reynolds Number Jets Using Plasma Actuators

The idea of manipulating flow to change its characteristics is over a century old. Manipulating instabilities of a jet to increase its mixing and to reduce its radiated noise started in the 1970s. While the effort has been successful in low-speed and low Reynolds number jets, available actuators capabilities in terms of their amplitude, bandwidth, and phasing have fallen short in control of high-speed and high Reynolds number jets of practical interest. Localized arc filament plasma actuators have recently been developed and extensively used at Gas Dynamics and Turbulence Laboratory (GDTL) for control of highspeed and high Reynolds number jets. While the technique has been quite successful and is very promising, all the work up to this point had been carried out using small high subsonic and low supersonic jets from a 2.54 cm diameter nozzle exit with a Reynolds number of about a million. The preliminary work reported in this paper is a first attempt to evaluate the scalability of the technique. The power supply/plasma generator was designed and built in-house at GDTL to operate 8 actuators simultaneously over a large frequency range (0 to 200 kHz) with independent control over phase and duty cycle of each actuator. This allowed forcing the small jet at GDTL with azimuthal modes m = 0, 1, 2, 3, plus or minus 1, plus or minus 2, and plus or minus 4 over a large range of frequencies. This power supply was taken to and used, with minor modifications, at the NASA Nozzle Acoustic Test Rig (NATR). At NATR, 32 actuators were distributed around the 7.5 in. nozzle (a linear increase with nozzle exit diameter would require 60 actuators). With this arrangement only 8 actuators could operate simultaneously, thus limiting the forcing of the jet at NATR to only three azimuthal modes m = plus or minus 1, 4, and 8. Very preliminary results at NATR indicate that the trends observed in the larger NASA facility in terms of the effects of actuation frequency and azimuthal modes are similar in both small GDTL and larger NASA jets. However, the actuation authority seems to fall short in the larger jet at higher Mach numbers, resulting in decreased amplitude response compared to the small jet, which is attributed at this point to the lack of sufficient number of actuators. The preliminary results seem also to suggest that amplitude of actuation tones is similar in both the small and larger jets

Optimizing integrated steelworks process off-gas distribution through Economic Hybrid Model Predictive Control and Echo State Networks

Steel production in integrated steelworks involves the simultaneous production of various byproducts, including process off-gases that are usually exploited for generating electricity in the internal power plant, heat and steam. Their discontinuous production is managed through complex network, gasholders and torches, which must be managed with stringent operational constraints. In this paper we present a supervision and control system designed to optimize the economic management of the distribution of process off-gases that also allows minimizing the environmental impact. The system implements a digital twin based mainly on machine learning techniques, including Echo State Networks, and a hierarchical optimization system, which first level is based on an economic model predictive approach and the second level is based on the economic hybrid model predictive control. This system allows to effectively maximize the use of off-gases while minimizing the environmental impact of their use up to 97%