In the paper, we describe a numerical technique allowing the solution of compressible inviscid flow with a wide range of Mach numbers. The method is based on the application of the discontinuous ...Galerkin finite element method for the space discretization of the Euler equations written in the conservative form, combined with a semi-implicit time discretization. Special attention is paid to the treatment of boundary conditions and to the stabilization of the method in the vicinity of discontinuities avoiding the Gibbs phenomenon. As a result we obtain a technique allowing the numerical solution of flows with practically all Mach numbers without any modification of the Euler equations. This means that the proposed method can be used for the solution of high speed flows as well as low Mach number flows. Presented numerical tests prove the accuracy of the method and its robustness with respect to the Mach number.
In this paper we devise an efficient and robust numerical method for a nonlocal nonlinear model of flocking dynamics. The governing equations are a hydrodynamic limit of the model of Cucker and Smale ...which consists of the compressible Euler equations with added nonlinear nonlocal interaction terms. The numerical scheme is based on the discontinuous Galerkin method. A semi-implicit scheme is used in the time discretization which requires only the solution of one linear system per time level while retaining the stability of an implicit scheme. A crucial point is the construction of a suitable linearization of the nonlocal terms which does not result in fill-in of the system matrices. Element-wise and inter-element artificial diffusion is added to the scheme along with a postprocessing procedure to deal with near-vacuum states that typically arise in the solution. We demonstrate the efficiency and robustness of the scheme on numerical experiments in 1D and 2D.
•A numerical method for a nonlinear nonlocal model of flocking dynamics is proposed.•A semi-implicit discontinuous Galerkin discretization is applied.•A linearization is constructed so the nonlocal terms do not give a full system matrix.•Stabilization is added near shocks along with a treatment of near-vacuum which arise.•Numerical experiments are given in 1D and 2D.
Recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coefficients of a polynomial. An application to the design of ...fixed-order controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed, based on linear matrix inequality optimization. The key ingredient in the design procedure resides in the choice of the central polynomial. Several numerical examples illustrate the relevance of the approach.
This paper presents a simplified parameterization of all
H
∞
static state-feedback controllers in terms of a single algebraic Riccati equation and a free parameter matrix. As a special case, ...necessary and sufficient conditions for the existence of an static output-feedback gain are given. An efficient computational algorithm is given and its correctness proven. No initial stabilizing output-feedback gain is needed. The technique is used to design an
H
∞
lateral–directional command augmentation system for the F-16 aircraft.
A general solution of the H
2
control problem is presented for linear systems described by rational transfer matrices, not necessarily proper or stable. The control system is considered in the ...standard configuration, which includes the synthesis model of the plant and the controller. The H
2
control problem consists of internally stabilizing the control system while minimizing the H
2
norm of its transfer function. The notion of internal stability is based on bounded-input bounded-output stability and means that subsystems defined by any pair of input and output signals within the control system all are bounded-input bounded-output stable. In this manner, the optimal control system is devoid of impulsive as well as non-decaying exponential modes. The solution proceeds in three steps. First, the set of all controllers that internally stabilize the control system is parameterized. Then the subset of the stabilizing controllers that achieve a finite value of the H
2
norm of the control system transfer matrix is described, also in parametric form. Finally, the optimal controller is obtained by selecting the parameter that minimizes the norm. The existence of each set of controllers described above is established in terms of the given data. There are plants that cannot be internally stabilized; there are plants that can be internally stabilized but no stabilizing controller renders the H
2
norm finite; still there are plants and internally stabilizing controllers that achieve a finite value of the norm among which, however, no one actually minimizes the norm. The mathematical tools applied are doubly coprime, proper stable factorizations of rational matrices. Based on this description of the plant, two synthesis algorithms are derived: the primal and the dual one. The symmetries thus obtained are interesting and useful. The construction of the optimal controller requires two specific operations with proper stable rational matrices, inner--outer factorization and proper stable projection. The solution obtained is general in the sense that no assumptions on the plant are made other than those requiring the outer factors to be square, which can always be achieved.
Powder metallurgy represented by mechanical alloying and spark plasma sintering was used for preparation of the AlFe16 and the AlSi20Fe16 alloys. Microstructure of the both alloys consisted of very ...fine intermetallic phases homogenously dispersed in the matrix of α-Al solid solution. Fine nature of microstructure led to promising results of compressive stress-strain tests performed at laboratory and elevated temperature of 400 °C. The compressive strengths of the AlSi20Fe16 and the AlFe16 alloys at laboratory temperature were 780 MPa and 508 MPa, respectively. Elevated temperature resulted in drop of the compressive strengths to 480 MPa and 211 MPa, respectively. However, the results of investigated alloys outperformed the thermally stable AlSi12Cu1Mg1Ni1 (wt. %) used as reference material.
A new species from Slovakia and the Czech Republic, Pseudoplectania lignicola, is described and illustrated. It is distinguished from other members of the genus by a centrally arranged globose ...membranous sheath surrounding the spores, thick ectal excipulum of oblong cells at
the apothecial base, and growth on less specifc biotopes. Comparisons with similar species and the diagnostic signifcance of membranous sheath surrounding the ascospores are also discussed.
•The application of bicultural stock in RAS has the potential to benefit culture efficiency.•Physiology of rainbow trout and burbot were affected by the arrangement of biculture.•Highest proportion ...of the burbot in the stock ensured less sediment production.•A decreasing trend of solid production suggested adaptation to cultural conditions.•Bi-cultural stocks can be applied to enhance production in RAS.
Traditional monoculture systems often face challenges related to solid waste production and nutrient use. This study addresses these concerns by investigating the impact of bicultural farming of burbot (Lota lota) and rainbow trout (Oncorhynchus mykiss) in a recirculating aquaculture system (RAS) and the subsequent alteration of production of solid waste, growth and physiological status. The rationale behind incorporating burbot lies in its potential as a supplementary species to improve overall system efficiency and sustainability. The experimental groups in triplicate represented the different ratios of rainbow trout (T) and burbot (B) in the stock: T70/B30, T85/B15 and T100/B0. Burbot, although not assessed in monoculture due to its limited commercial significance, was incorporated into the study as a supplementary species, expected to enhance the nutrient utilisation through its bottom-feeding behaviour and anticipated consumption of solid waste produced by trout. After 77 days of culture, the survival rates of trout remained consistent across experimental groups, averaging over 99%, while burbot exhibited comparable survival rates despite lower cumulative survival, averaging 88%. Feed conversion ratios showed no significant differences between the groups, indicating consistent feed utilisation. A significantly higher specific growth rate (SGR) in trout was observed in group T70/B30. The SGR values of burbot were marginally low and without significant differences between groups. Among biochemical markers of blood plasma, phosphorus concentrations were significantly higher in group T70/B30 for both trout and burbot, suggesting better access to the feed for both species. Elevated antioxidant activity and evidence of oxidative stress were found for both species in intestinal tissue. The presence of burbot in stock significantly affected the production of suspended solids per gram of applied feed. Therefore, group T100/B0 demonstrated the highest solid production at multiple time points, suggesting a relationship between burbot presence and the production of suspended solids. Starting at the 9-week, the trout monoculture group exhibited significantly higher phosphorus levels in sediments compared to group T70/B30, emphasising the role of burbot in shaping sediment nutrient dynamics in RAS, such as supplementary cleaning fish. After 11 weeks, group T100/B0 displayed significantly higher values of produced suspended solids and their composition: DM, organic DM, and phosphorus content per gram of feed applied. These results provide evidence of the influence of burbot on suspended solids production and characteristics. In conclusion, this study indicates the positive effects of burbot presence on solid production and sediment nutrient composition.
A necessary and sufficient condition for a linear system to be stabilizable via static output feedback is presented. It makes an appeal to the linear-quadratic regulator theory.
This note focuses on the control of continuous-time linear systems subject to time-domain constraints (input amplitude limitation, output overshoot) on closed-loop signals. Using recent results on ...positive polynomials, it is shown that finding a Youla-Kuc/spl breve/era polynomial parameter of fixed degree (hence, a controller of fixed order) such that time-domain constraints are satisfied amounts to solving a convex linear matrix inequality (LMI) optimization problem as soon as distinct strictly negative closed-loop poles are assigned by pole placement. Proceeding this way, time-domain constraints are handled by an appropriate choice of the closed-loop zeros.
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