**391**

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**Numerical modeling of magnetostrictive materials**

Kholmetska, I.; Chleboun, J.; Krejčí, Pavel

2016 - English
An operator-differential model for magnetostrictive energy harvesting proposed in the literature is used to calculate the amount of harvested energy under some uncertainty in the Preisach density function. The uncertainty is modeled through a fuzzy set approach. In galfenol, an alloy of gallium and iron, however, the hysteresis phenomenon is present only weakly. This allows to propose a simpler, but computationally faster model without hysteresis. The new, simpler model has been identified from the measured magnetic and magnetostrictive cycles. The amount of harvested energy is of the same order in both models. Again, an uncertainty in the identified model can be considered and its impact on the amount of the harvested energy calculated.
Keywords:
*magnetostrictive materials; hysteresis; energy harvesting*
Available in digital repository of the ASCR
Numerical modeling of magnetostrictive materials

An operator-differential model for magnetostrictive energy harvesting proposed in the literature is used to calculate the amount of harvested energy under some uncertainty in the Preisach density ...

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**Anthropic principle and the local Hubble expansion**

Křížek, Michal; Somer, L.

2016 - English
We claim that a local expansion of the universe, whose rate is comparable with the Hubble constant H0, had an essential influence on the development of intelligent life on the Earth. We present more than 10 examples showing that some antigravitational effects of the cosmological constant are observable locally in the Solar system. It is known that the luminosity of the Sun increased approximately linearly within the last 4.5Gyr starting at 70% of its present value. We give several independent arguments showing that the average Earth-Sun distance increases about 5m/yr due to antigravitational forces and such a large recession speed cannot be explained by solar wind, tidal forces, plasma outbursts from the Sun, or by the decrease of the Solar mass due to nuclear reactions. Models based on Newtonian mechanics can explain only a few cm per year.
Keywords:
*antigravity; habitable zone; law of conservation of energy*
Available in digital repository of the ASCR
Anthropic principle and the local Hubble expansion

We claim that a local expansion of the universe, whose rate is comparable with the Hubble constant H0, had an essential influence on the development of intelligent life on the Earth. We present more ...

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**Word problems of a given structure in the perspective of teacher training**

Tichá, Marie; Hošpesová, A.

2015 - English
The paper reports on the results of a research study focusing on how to train prospective teachers for guiding their pupils through the process of solving word problems. The teaching experiment involved prospective teachers’ work with graphical representations called branched chains to solve and pose word problems. The paper shows the difficulties the students were facing, presents ideas from discussions during joint reflection, tries to describe the changes in the students’ skills and attitudes. It also points at the differences between prospective primary and secondary mathematics teachers.
Keywords:
*inquiry based mathematics education; prospective teaching training; subject matter knowledge; knowledge base for teaching*
Fulltext is available at external website.
Word problems of a given structure in the perspective of teacher training

The paper reports on the results of a research study focusing on how to train prospective teachers for guiding their pupils through the process of solving word problems. The teaching experiment ...

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**Error patterns in computation in concept cartoons**

Samková, L.; Tichá, Marie; Hošpesová, A.

2015 - English
The paper focuses on an educational tool called Concept Cartoons, and its possible usage in primary school mathematics, especially in promoting discussion in the classroom. We show in detail how to prepare Concept Cartoons displaying various mental computation strategies and error patterns.
Keywords:
*concept Cartoons; error patterns; mental computation strategies*
Available at various institutes of the ASCR
Error patterns in computation in concept cartoons

The paper focuses on an educational tool called Concept Cartoons, and its possible usage in primary school mathematics, especially in promoting discussion in the classroom. We show in detail how to ...

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**Reasoning of pupils in the solving process of a geometrical inquiry-stimulating task**

Roubíček, Filip

2015 - English
The poster focuses on the issue of solving geometrical problems in the context of inquiry based education, namely on the use of inquiry by pupils and on classroom mathematics discourse. The poster describes communicative situations in solving of inquiry based problems and presents examples of pupils’ solutions and discussion in the classroom.
Keywords:
*inquiry based education; teaching of geometry; problem solving; mathematical discourse*
Available at various institutes of the ASCR
Reasoning of pupils in the solving process of a geometrical inquiry-stimulating task

The poster focuses on the issue of solving geometrical problems in the context of inquiry based education, namely on the use of inquiry by pupils and on classroom mathematics discourse. The poster ...

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**Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability**

Kůs, Pavel

2015 - English
In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this particular problém are discussed. Our numerical tests confirm the convergence of the method, but for some very special choices of parameters, this convergence has very uncommon properties.
Keywords:
*convergence; finite element method; Turing instability; reaction-diffusion*
Available in digital repository of the ASCR
Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability

In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this ...

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**On the problem of singular limits in a model of radiative flow**

Ducomet, B.; Nečasová, Šárka

2015 - English
We consider a "semi-relativistic" model of radiative viscous compressible Navier-Stokes-Fourier system coupled to the radiative transfer equation extending the classical model introduced in [8] and we study diffusion limits in the case of well-prepared initial data and Dirichlet boundary condition for the velocity field.
Keywords:
*radiation hydrodynamics; Navier-Stokes-Fourier system; weak solution*
Fulltext is available at external website.
On the problem of singular limits in a model of radiative flow

We consider a "semi-relativistic" model of radiative viscous compressible Navier-Stokes-Fourier system coupled to the radiative transfer equation extending the classical model introduced in [8] and we ...

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**Some notes about the homogenization problem for the Navier-Stokes equations**

Feireisl, Eduard; Namlyeyeva, Yuliya; Nečasová, Šárka

2015 - English
We study the homogenization problem for the evolutionary Navier-Stokes system under the critical size of obstacles. Convergence towards the limit system of Brinkman's type is shown under very mild assumptions concerning the shape of the obstacles and their mutual distance.
Keywords:
*Navier-Stokes system; homogenization; Brinkman's law*
Fulltext is available at external website.
Some notes about the homogenization problem for the Navier-Stokes equations

We study the homogenization problem for the evolutionary Navier-Stokes system under the critical size of obstacles. Convergence towards the limit system of Brinkman's type is shown under very mild ...

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**Badatelské úlohy ve vyučování geometrii**

Roubíček, Filip

2015 - Czech
Podnětem badatelských aktivit ve vyučování geometrii je geometrická úloha, která popisuje neznánou, neurčitou nebo nejednoznačnou situaci a požaduje její komplexní prozkoumání. V příspěvku je popsáno šest badatelských úloh z různých oblastí elementární geometrie. The stimulus of inquire activities in the teaching of geometry is a geometrical problem which describes an unknown, undefined or ambiguous situation and requires its complexe exploration. Six inquiry-stimulating problems of various areas of elementary geometry are described in the paper.
Keywords:
*inquiry-based teaching; inquiry activities; geometrical problem*
Available at various institutes of the ASCR
Badatelské úlohy ve vyučování geometrii

Podnětem badatelských aktivit ve vyučování geometrii je geometrická úloha, která popisuje neznánou, neurčitou nebo nejednoznačnou situaci a požaduje její komplexní prozkoumání. V příspěvku je popsáno ...

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**Different approaches to interface weights in the BDDC method in 3D**

Čertíková, M.; Šístek, Jakub; Burda, P.

2015 - English
In this paper, we discuss the choice of weights in averaging of local (subdomain) solutions on the interface for the BDDC method (Balancing Domain Decomposition by Constraints). We try to find relations among different choices of the interface weights and compare them numerically on model problems of the Poisson equation and linear elasticity in 3D. Problems with jumps in coefficients of material properties are considered and both regular and irregular interfaces between subdomains are tested.
Keywords:
*BDDC; interface weights; coefficient jumps*
Available in digital repository of the ASCR
Different approaches to interface weights in the BDDC method in 3D

In this paper, we discuss the choice of weights in averaging of local (subdomain) solutions on the interface for the BDDC method (Balancing Domain Decomposition by Constraints). We try to find ...

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