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Souvislost mezi principem nejmenší akce a termodynamickou podmínkou stability
Maršík, František; Trávníček, Zdeněk; Antošová, Zuzana
2023 - English
The extended principle is formulated for a material point (M.P.) X, which has nonzero mass, temperature, and trajectory x(X,t). The Lagrangian of this variation principle is equal to the kinetic energy from which, the internal energy of the material point (which depends on the entropy) and the additional energy caused by the frictional force are subtracted. The relation between the inertial force and the entropy gradient is found and the gravitational force is completely replaced by the entropy gradient. Thanks to the mentioned properties of the total enthalpy, the Thermodynamic criterion of stability of the state of M.P., is formulated.
Keywords:
principle of the least action; thermodynamic stability condition; annular swirl flow
Fulltext is available at external website.
Souvislost mezi principem nejmenší akce a termodynamickou podmínkou stability
The extended principle is formulated for a material point (M.P.) X, which has nonzero mass, temperature, and trajectory x(X,t). The Lagrangian of this variation principle is equal to the kinetic ...
Texture Spectral Similarity Criteria Comparison
Havlíček, Michal; Haindl, Michal
2023 - English
Criteria capable of texture spectral similarity evaluation are presented and compared. From the fifteen evaluated criteria, only four criteria guarantee zero or minimal spectral ranking errors. Such criteria can support texture modeling algorithms by comparing the modeled texture with corresponding synthetic simulations. Another possible application is the development of texture retrieval, classification, or texture acquisition system. These criteria thoroughly test monotonicity and mutual correlation on specifically designed extensive monotonously degrading experiments.
Keywords:
Texture Comparison; Texture Modeling; Texture Retrieval; Texture Classification; Texture Acquisition
Fulltext is available at external website.
Texture Spectral Similarity Criteria Comparison
Criteria capable of texture spectral similarity evaluation are presented and compared. From the fifteen evaluated criteria, only four criteria guarantee zero or minimal spectral ranking errors. Such ...
Statistical Method Selection Matters: Vanilla Methods in Regression May Yield Misleading Results
Kalina, Jan
2023 - English
The primary aim of this work is to illustrate the importance of the choice of the appropriate methods for the statistical analysis of economic data. Typically, there exist several alternative versions of common statistical methods for every statistical modeling task\nand the most habitually used (“vanilla”) versions may yield rather misleading results in nonstandard situations. Linear regression is considered here as the most fundamental econometric model. First, the analysis of a world tourism dataset is presented, where the number of international arrivals is modeled for 140 countries of the world as a response of 14 pillars (indicators) of the Travel and Tourism Competitiveness Index. Heteroscedasticity is clearly recognized in the dataset. However, the Aitken estimator, which would be the standard remedy in such a situation, is revealed here to be very inappropriate. Regression quantiles represent a much more suitable solution here. The second illustration with artificial data reveals standard regression quantiles to be unsuitable for data contaminated by outlying values. Their recently proposed robust version turns out to be much more appropriate. Both\nillustrations reveal that choosing suitable methods represent an important (and often difficult) part of the analysis of economic data.
Keywords:
linear regression; assumptions; non-standard situations; robustness; diagnostics
Fulltext is available at external website.
Statistical Method Selection Matters: Vanilla Methods in Regression May Yield Misleading Results
The primary aim of this work is to illustrate the importance of the choice of the appropriate methods for the statistical analysis of economic data. Typically, there exist several alternative versions ...
Bohl-Marek decomposition applied to a class of biochemical networks with conservation properties
Papáček, Štěpán; Matonoha, Ctirad; Duintjer Tebbens, Jurjen
2023 - English
This study presents an application of one special technique, further called as Bohl-Marek decomposition, related to the mathematical modeling of biochemical networks with mass conservation properties. We continue in direction of papers devoted to inverse problems of parameter estimation for mathematical models describing the drug-induced enzyme production networks [3]. However, being aware of the complexity of general physiologically based pharmacokinetic (PBPK) models, here we focus on the case of enzyme-catalyzed reactions with a substrate transport chain [5]. Although our ultimate goal is to develop a reliable method for fitting the model parameters to given experimental data, here we study certain numerical issues within the framework of optimal experimental design [6]. Before starting an experiment on a real biochemical network, we formulate an optimization problem aiming to maximize the information content of the corresponding experiment. For the above-sketched optimization problem, the computational costs related to the two formulations of the same biochemical network, being (i) the classical formulation x˙(t) = Ax(t) + b(t) and (ii) the 'quasi-linear' Bohl-Marek formulation x˙M(t) = M(x(t)) xM(t), can be determined and compared.
Keywords:
Mathematical modeling; Biochemical network; Pharmacokinetic (PBPK) models
Fulltext is available at external website.
Bohl-Marek decomposition applied to a class of biochemical networks with conservation properties
This study presents an application of one special technique, further called as Bohl-Marek decomposition, related to the mathematical modeling of biochemical networks with mass conservation properties. ...
Validation of numerical simulations of a simple immersed boundary solver for fluid flow in branching channels
Keslerová, R.; Lancmanová, Anna; Bodnár, Tomáš
2023 - English
This work deals with the flow of incompressible viscous fluids in a two-dimensional branching channel. Using the immersed boundary method, a new finite difference solver was developed to interpret the channel geometry. The numerical results obtained by this new solver are compared with the numerical simulations of the older finite volume method code and with the results obtained with OpenFOAM. The aim of this work is to verify whether the immersed boundary method is suitable for fluid flow in channels with more complex geometries with difficult grid generation.
Keywords:
immersed boundary method; finite volume method; OpenFOAM
Available in digital repository of the ASCR
Validation of numerical simulations of a simple immersed boundary solver for fluid flow in branching channels
This work deals with the flow of incompressible viscous fluids in a two-dimensional branching channel. Using the immersed boundary method, a new finite difference solver was developed to interpret the ...
Rooting algebraic vertices of convergent sequences
Hartman, David; Hons, T.; Nešetřil, J.
2023 - English
Structural convergence is a framework for convergence of graphs by Nešetřil and Ossona de Mendez that unifies the dense (left) graph convergence and Benjamini-Schramm convergence. They posed a problem asking whether for a given sequence of graphs (Gn) converging to a limit L and a vertex r of L it is possible to find a sequence of vertices (rn) such that L rooted at r is the limit of the graphs Gn rooted at rn. A counterexample was found by Christofides and Král’, but they showed that the statement holds for almost all vertices r of L. We offer another perspective to the original problem by considering the size of definable sets to which the root r belongs. We prove that if r is an algebraic vertex (i.e. belongs to a finite definable set), the sequence of roots (rn) always exists.
Keywords:
rooting; algebraic vertices; convergent sequences
Available in digital repository of the ASCR
Rooting algebraic vertices of convergent sequences
Structural convergence is a framework for convergence of graphs by Nešetřil and Ossona de Mendez that unifies the dense (left) graph convergence and Benjamini-Schramm convergence. They posed a problem ...
On the problem of singular limit
Caggio, Matteo; Ducomet, B.; Nečasová, Šárka; Tang, T.
2023 - English
We consider the problem of singular limit of the compressible Euler system confined to a straight layer Ωδ = (0, δ)×R², δ > 0. In the regime of low Mach number limit and reduction of dimension the convergence to the strong solution of the 2D incompressible Euler system is shown.
Keywords:
compressible Euler equations; dissipative measure-valued solutions; low Mach number; thin domain
Available in digital repository of the ASCR
On the problem of singular limit
We consider the problem of singular limit of the compressible Euler system confined to a straight layer Ωδ = (0, δ)×R², δ > 0. In the regime of low Mach number limit and reduction of dimension the ...
Deep learning methods for the acoustic emission methods to evaluate an onset of plastic straining
Parma, Slavomír; Kovanda, Martin; Chlada, Milan; Štefan, Jan; Kober, Jan; Feigenbaum, H. P.; Plešek, Jiří
2023 - English
Development of phenomenological plasticity models, hardening rules, and plasticity theories relies on experimental data of plastic straining. The experimental data are usually measured as the stress–strain response of the material being loaded and do not provide any clues or information about the local response of\nmaterial. In this paper, we analyze the plastic deformation of the material using the acoustic emission method and current state-of-the-art neural network models such as the InceptionTime architecture.
Keywords:
metal plasticity; strain hardening; acoustic emission; neural networks
Fulltext is available at external website.
Deep learning methods for the acoustic emission methods to evaluate an onset of plastic straining
Development of phenomenological plasticity models, hardening rules, and plasticity theories relies on experimental data of plastic straining. The experimental data are usually measured as the ...
Model order reduction for particle-laden flows: systems with rotations and discrete transport operators
Kovárnová, A.; Isoz, Martin
2023 - English
In the present work, we concentrate on particle-laden flows as an example of industry-relevant transport-dominated systems. Our previously-developed framework for data-driven model order reduction (MOR) of such systems, the shifted proper orthogonal decomposition with interpolation via artificial neural networks, is further extended by improving the handling of general transport operators. First, even with intrusive MOR approaches, the underlying numerical solvers can provide only discrete realizations of transports linked to the movement of individual particles in the system. On the other hand, our MOR methodology requires continuous transport operators. Thus, the original framework was extended by the possibility to reconstruct continuous approximations of known discrete transports via another artificial neural network. Second, the treatment of rotation-comprising transports was significantly improved.
Keywords:
model order reduction; shifted POD; artificial neural networks; CFD-DEM; Open- FOAM
Fulltext is available at external website.
Model order reduction for particle-laden flows: systems with rotations and discrete transport operators
In the present work, we concentrate on particle-laden flows as an example of industry-relevant transport-dominated systems. Our previously-developed framework for data-driven model order reduction ...
Can extended bodies follow geodesic trajectories?
Lukes-Gerakopoulos, Georgios; Mukherjee, Sajal
2023 - English
We provide an extension of the analysis on whether an extended test body can follow a geodesic trajectory given by Mukherjee et al. (2022). In particular, we consider a test body in a pole-dipole-quadrupole approximation under the Ohashi-Kyrian-Semer´ak spin supplementary condition moving in the Schwarzschild and Kerr background. Using orbital setups under which a pole-dipole body can follow geodesic motion, we explore under which conditions this can also take place in the pole-dipole-quadrupole approximation when only the mass quadrupole is taken into account. For our analysis, we employ the assumption that the dipole contribution and the quadrupole contribution vanish independentlly.
Keywords:
Mathisson–Papapetrou–Dixon equations; particle dynamics; black holes; chaos
Fulltext is available at external website.
Can extended bodies follow geodesic trajectories?
We provide an extension of the analysis on whether an extended test body can follow a geodesic trajectory given by Mukherjee et al. (2022). In particular, we consider a test body in a ...
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