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We investigate rate-independent strain paths in a granular material generated by periodically oscillating stress cycles using a particular constitutive model within the hypoplasticity theory of Kolymbas type. It is assumed that the irreversible hypoplastic effects decay to zero when the void ratio reaches its theoretical minimum, while the void ratio is in turn related to the evolution of the volumetric strain through the mass conservation principle. We show that under natural assumptions on material parameters, both isotropic and anisotropic stress cycles are described by a differential equation whose solution converges asymptotically to a limiting periodic process taking place in the shakedown state when the number of loading cycles tends to infinity. Furthermore, an estimation of how fast, in terms of the number of cycles, the system approaches the limit state is derived in explicit form. It is shown how it depends on the parameters of the model, on the initial void ratio, and on the prescribed stress interval.

Perturbed parameters are considered in a hypoplastic model of granular materials. For fixed parameters, the model response to a periodic stress loading and unloading converges to a limit state of strain. The focus of this contribution is the assessment of the change in the limit strain caused by varying model parameters.

PDF file - 695K, S. figure 1mRNA from CD19+ cells of healthy individuals. S. figure 2 Expression of Wnt-5a in the samples shown in Fig. 1 was determined by qRT-PCR. S. figure 3 Viability of primary CLL cells stimulated with the indicated compounds have been assessed by the WST1 test. S. figure 4 mRNA from MEC1 cells and from B-cells of healthy individuals was isolated and the expression of the indicated genes was analyzed by real time qRT-PCR. S. figure 5 Flow-cytometric analysis of apoptosis in patient CLL cells used for transplantation. S. Figure 6 Expression of PRICKLE1.

The full quasistatic thermomechanical system of PDEs, describing water diffusion with the possibility of freezing and melting in a visco-elasto-plastic porous solid, is studied in detail under the hypothesis that the pressure-saturation hysteresis relation is given in terms of the Preisach hysteresis operator. The resulting system of balance equations for mass, momentum, and energy coupled with the phase dynamics equation is shown to admit a global solution under general assumptions on the data., 52 pages

A PDE system consisting of the mechanical equilibrium and mass balance equations for displacement and capillary pressure as a model for fluid diffusion in a partially saturated viscoelastoplastic p...

A problem of motion of a piezoelectric actuator in contact with an elasto-plastic obstacle is reformulated as a PDE in one spatial dimension with hysteresis in the bulk and on the contact boundary. The model is shown to dissipate energy in agreement with the principles of thermodynamics. The main result includes existence, uniqueness, and continuous data dependence of solutions.

The author reviews the book Nadezhda Stalyanova and Elena Kreychova. Rechnik na lingvistichnite termini za studenti slavisti A–N (balgarski ezik – cheshki ezik – polski ezik). Sofia: Paradigma 2019, 142 p., ISBN 978-954-326-387-5; Rechnik na lingvistichnite termini za studenti slavisti O–Ya (balgarski ezik – cheshki ezik – polski ezik). Sofia: Paradigma 2020, 118 p., ISBN 978-954-326-425-4 .

A controllability problem for a diffusion equation with a complex hysteresis operator is proposed here and consists in finding a control which guarantees that the solution reaches a desired value at a given time. We propose a constructive method based on a two-parameter penalty argument. One small parameter penalizes the distance of the solution at final time from the expected value, the second one is used to approximate the underlying rate independent variational inequalities in the hysteresis term by smooth viscous constitutive relations. We prove that a solution to the controllability problem can be obtained by passing to the limit in a doubly degenerate control system, and the convergence is strong in space and uniform in time.

Luciferase reporter assays represent a simple and sensitive experimental system in cell and molecular biology to study multiple biological processes. However, the application of these assays is often limited by the costs of conventional luminometer instruments and the versatility of their use in different experimental conditions. Therefore, we aimed to develop a small, affordable luminometer allowing continuous measurement of luciferase activity, designed for inclusion into various kinds of tissue culture incubators. Here we introduce LuminoCell - an open-source platform for the construction of an affordable, sensitive, and portable luminometer capable of realtime monitoring in-cell luciferase activity. The LuminoCell costs $40, requires less than 1 hour to assemble, and it is capable of performing real-time sensitive detection of both magnitude and duration of the activity of major signalling pathways in cell cultures, including receptor tyrosine kinases (EGF, FGF), WNT/β-catenin, and NF-κB. Additionally, we show that the LuminoCell is suitable to be used in cytotoxicity assays as well as for monitoring periodic circadian gene expression.

We study stress paths that are obtained under proportional deformations within the rate-independent hypoplasticity theory of Kolymbas type describing granular materials like soil and broken rock. For a particular simplified hypoplastic constitutive model by Bauer, a closed-form solution of the corresponding system of non-linear ordinary differential equations is available. Since only negative principal stresses are relevant for the granular body, the feasibility of the solution consistent with physics is investigated in dependence of the direction of a proportional strain path and constitutive parameters of the model.

Piezoelectricity of some materials has shown to have many applications, in particular in energy harvesting. Due to the inherent hysteresis in the characteristic of such materials, a number of hysteretic models have been proposed minding the fact that hysteresis losses may influence the efficiency of the process. However, hysteresis dissipation is accompanied with heat production, which in turn increases the temperature of the device and may change its physical characteristics. In this paper we propose a phenomenological model for electromechanical coupling in piezoelectric materials where temperature and feedback effects are taken into account. We prove the existence of solution for the resulting PDE system and show that the model is thermodynamically consistent. The main analytical tool is the inverse Preisach operator with temperature-dependent density.

Clanek se zabýva starsimi a aktualnimi významy srbochorvatských onym vyjadřujicich zakladni spolecensko-politicke realie soucasne Bosny a Hercegoviny (Bosanac, Bosnjak, Musliman, Srpska), významy adjektiv bosanski a bosnjacki a jejich překladovými ekvivalenty v cestině. Dochazi k zavěru, že ceske ekvivalenty Bosňan a Bosňak navzdory udajům ve starsich slovnicich cestiny nelze v soucasnosti chapat jako synonyma, a to same plati i o adjektivech bosenský a bosňacký, ceských ekvivalentech přislusných srbochorvatských adjektiv. Při uživani pojmů spjatých se složitou spolecensko-politickou situaci v Bosně a Hercegovině v cizich jazycich je třeba postupovat velice obezřetně.

We propose a mathematical model describing the process of filling the pores of a building material with lime water solution with the goal to improve the consistency of the porous solid. Chemical reactions produce calcium carbonate which glues the solid particles together at some distance from the boundary and strengthens the whole structure. The model consists of a 3D convection-diffusion system with a nonlinear boundary condition for the liquid and for calcium hydroxide, coupled with the mass balance equations for the chemical reaction. The main result consists in proving that the system has a solution for each initial data from a physically relevant class. A 1D numerical test shows a qualitative agreement with experimental observations., Comment: 22 pages

After the Second World War, Serbo-Croatian was formally declared on the basis of the so-called Novi Sad Agreement (1954). Its demise is connected to the demise of the Yugoslav Federation (1992). The sociological, historical, political and ideological reasons of the rejection of this glottonym (and with it the rejection of the common language) were clearly the decisive factor, but they were not always the same. The Serbs, Croats, Bosniaks and Montenegrins had specific reasons for this. These reasons can be revealed, inter alia, by analyzing a number of declarative, proclaiming, explanatory, defending, shorter or longer texts on the language generated by all the above-mentioned national communities which used Serbo-Croatian as their first (mother) tongue after 1990. The most recent Declaration on the Common Language (2017) is unique in this sense. Srbochorvatština byla po druhé světové válce oficializována tzv. novosadskou dohodou (1954). Její zánik souvisí se zánikem jugoslávské federace (1992). Sociologické, historické, politické a ideologické důvody odmítnutí tohoto složeného lingvonyma (a tím i odmítnutí takto manifestovaného společného jazyka) byly jednoznačně rozhodujícím faktorem, ale nebyly pokaždé stejné. Srbové, Chorvati, Bosňáci i Černohorci pro to měli vlastní důvody. Tyto důvody lze mimo jiné odhalit analýzou řady deklarativních, proklamačních, vysvětlujících, obhajujících, kratších i delších textů o jazyce generovaných lingvisty (ovšem nejen jimi) ze všech výše uvedených národních společenství, která jako první (mateřský) jazyk používala srbochorvatštinu po roce 1990. Nejnovější Deklarace o společném jazyce (2017) je v tomto smyslu unikát.

The paper gives insights into modeling and well-posedness analysis driven by cyclic behavior of particular rate-independent constitutive equations based on the framework of hypoplasticity and on the elastoplastic concept with nonlinear kinematic hardening. Compared to the classical concept of elastoplasticity, in hypoplasticity there is no need to decompose the deformation into elastic and plastic parts. The two different types of nonlinear approaches show some similarities in the structure of the constitutive relations, which are relevant for describing irreversible material properties. These models exhibit unlimited ratchetting under cyclic loading. In numerical simulation it will be demonstrated, how a shakedown behavior under cyclic loading can be achieved with a slightly enhanced simple hypoplastic equations proposed by Bauer

We show that sweeping processes with possibly non-convex prox-regular constraints generate a strongly continuous input-output mapping in the space of absolutely continuous functions. Under additional smoothness assumptions on the constraint we prove the local Lipschitz continuity of the input-output mapping. Using the Banach contraction principle, we subsequently prove that also the solution mapping associated with the state-dependent problem is locally Lipschitz continuous., Some comments have been added; Acknowledgment and Bibliogrphy sections have been expanded. To appear in "Applied Mathematics and Optimization"

We propose to model the lungs as a viscoelastic deformable porous medium with a hysteretic pressure–volume relationship described by the Preisach operator. Breathing is represented as an isothermal time-periodic process with gas exchange between the interior and exterior of the body. The main result consists in proving the existence of a periodic solution under an arbitrary periodic forcing in suitable function spaces.

The long time behavior of solutions to the autonomous PDE system describing fluid diffusion in a viscoelastic porous medium with capillary hysteresis is studied with homogeneous Dirichlet condition...

The problem of optimal energy harvesting for a piezoelectric element driven by mechanical vibrations is stated in terms of an ODE system with hysteresis under the time derivative coupling a mechanical oscillator with an electric circuit with or without inductance. In the piezoelectric constitutive law, both the self-similar piezoelectric butterfly character of the hysteresis curves and feedback effects are taken into account in a thermodynamically consistent way. The physical parameters of the harvester are chosen to be the control variable, and the goal is to maximize the harvested energy for a given mechanical load and a given time interval. If hysteresis is modeled by the Preisach operator, the system is shown to be well-posed with continuous data dependence. For the special case of the play operator, we derive first-order necessary optimality conditions and an explicit form of the gradient of the total harvested energy functional in terms of solutions to the adjoint system.

Specimens of magnetostrictive materials can transform a variation of their stress-induced size into a variation of a produced magnetic field and vice versa. These phenomena are utilized in magnetostrictive energy harvesters, vibration sensors, etc. Mathematical models of magnetostrictive materials vary from complex hysteretic models to relatively simple non-hysteretic models. In this paper, three mathematical models of Galfenol are considered, namely a non-hysteretic model, a non-hysteretic model with a feedback loop, and a model where the hysteresis is represented by the Preisach operator with a simplified Preisach density function. The parameters of these models are identified from measured magnetic and magneto-elastic curves. All the models are applicable in technical praxis. The output of the non-hysteretic model with a feedback loop best fits the measured data and, to some extent, reproduces fine features of magneto-elastic curves.

Magnetostrictive behavior is characterized by a complex coupling between magnetic and mechanical quantities. While this behavior can be quite easily exploited for both actuation and sensing or energy conversion purposes, the complex hysteresis interaction between magnetization and magnetic field and mechanical stress and strain is hard to model. Nevertheless, magnetic and magnetostrictive experimental curves are quite self-similar, assuming stress as self-similarity parameter. The quantification of this concept would help modeling. Here, this concept is quantified and experimentally confirmed over different types of magnetostrictive samples.

In this paper, a continuum model is introduced for fluid flow in a deformable porous medium, where the fluid may undergo phase transitions. Typically, such problems arise in modeling liquid–solid phase transformations in groundwater flows. The system of equations is derived here from the conservation principles for mass, momentum, and energy and from the Clausius–Duhem inequality for entropy. It couples the evolution of the displacement in the matrix material, of the capillary pressure, of the absolute temperature, and of the phase fraction. Mathematical results are proved under the additional hypothesis that inertia effects and shear stresses can be neglected. For the resulting highly nonlinear system of two PDEs, one ODE and one ordinary differential inclusion with natural initial and boundary conditions, existence of global in time solutions are proved by means of cut-off techniques and suitable Möser-type estimates.

It is well known that the Prandtl-Ishlinskii hysteresis operator is locally Lipschitz continuous in the space of continuous functions provided its primary response curve is convex or concave. This property can easily be extended to any absolutely continuous primary response curve with derivative of locally bounded variation. Under the same condition, the Prandtl-Ishlinskii operator in the Kurzweil integral setting is locally Lipschitz continuous also in the space of regulated functions. This paper shows that the Prandtl-Ishlinskii operator is still continuous if the primary response curve is only monotone and continuous, and that it may not even be locally Holder continuous for continuously differentiable primary response curves.

The research orientation of the Department of technics, Faculty of Education, University of Hradec Kralove focuses on finding new ways for development of polytechnic and science education. The research is motivated by the fact that children’s interest in technical and science subjects is decreasing in recent years in the Czech Republic. The research aims are to prove the applicability and effectiveness of multidisciplinary methods in teaching of technical and science subjects. The research observed the effect of the use of construction activity in teaching of physics in lower secondary school. The results of research confirmed that working and construction activity can develop technical and science thinking of children. Keywords: polytechnic education, science education, lower secondary school, construction activity, construction kit.

We prove the null controllability of the relaxed Stefan problem, which models phase transitions in two-phase systems. The technique relies on the penalty approximation of the differential inclusion describing the phase dynamics, solving a constrained minimization problem, and passing to the limit.

We propose to model the mammalian lungs as a viscoelastic deformable porous medium with a hysteretic pressure–volume relationship described by the Preisach operator. Breathing is represented as an isothermal time-periodic process with the gas exchange between the interior and exterior of the body. The main result consists of proving the existence of a periodic solution under an arbitrary periodic forcing in suitable function spaces.

Classification of inner processes during loading and unloading tests in models of hypoplasticity developed by D. Kolymbas for the constitutive behavior of granular materials is the main aim of this work. We focus on a modified model proposed by Bauer. By introducing a dimensionless time parameter s, we transform the constitutive equation into a rate-independent form, and study the stress paths in different proportional loading regimes.

Certain financial market strategies are known to exhibit a hysteretic structure similar to the memory observed in plasticity, ferromagnetism, or magnetostriction. The main difference is that in financial markets, the spontaneous occurrence of discontinuities in the time evolution has to be taken into account. We show that one particular market model considered here admits a representation in terms of Prandtl-Ishlinskii hysteresis operators, which are extended in order to include possible discontinuities both in time and in memory. The main analytical tool is the Kurzweil integral formalism, and the main result proves the well-posedness of the process in the space of right-continuous regulated functions.

A hybrid model is proposed for characterization of the hysteresis nonlinearity of the well-known play operator. The proposed model holds the hysteresis nonlinearity and the memory effects of the play operator. Simulation results are also presented to show the capability of the hybrid model to present the hysteresis nonlinearity with memory effects.

We propose a hysteretic model for electromechanical coupling in piezoelectric materials, with the strain and the electric field as inputs and the stress and the polarization as outputs. This constitutive law satisfies the thermodynamic principles and exhibits good agreement with experimental measurements. Moreover, when it is coupled with the mechanical and electromagnetic balance equations, the resulting PDE system is well-posed under the hypothesis that hysteretic effects take place only in one preferred direction. We prove the existence and uniqueness of its global weak solutions for each initial data with prescribed regularity. One of the tools is a new Lipschitz continuity theorem for the inverse Preisach operator with time dependent coefficients.

The prediction of compressive properties of foams at large strains and in a wide range of strain rates is still an open issue. In this work we propose a visco-hyperelastic formulation, suitable for large finite strain applications, for the prediction of the compressive response of foams that takes into account the viscoelasticity of the polymer, nonlinear damping, nonlinear behaviour of the cellular structure and effect of gas permeability through the pores at high strain rates. A mathematical expression of the continuous relaxation spectrum is proposed to model the viscoelastic behaviour of the polymer. The relaxation spectrum is then discretized with the desired accuracy required for the subsequent numerical simulations. The model parameters are identified by coupling dynamic measurements at small strain with static ones at large strain. The results are validated by comparing numerical predictions with experimental data from compressive tests up to 50% strain performed at strain rates spanning over 6 degrees of magnitude.

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We consider piecewise-linear, discrete-time, macroeconomic models that have a continuum of feasible equilibrium states. The non-trivial equilibrium set and resulting path-dependence are induced by stickiness in either expectations or the response of the Central Bank. For a low-dimensional variant of the model with one representative agent, and also for a multi-agent model, we show that when exogenous noise is absent from the system the continuum of equilibrium states is the global attractor and each solution trajectory converges exponentially to one of the equilibria. Further, when a uniformly bounded noise is present, or the equilibrium states are destabilized by an imperfect Central Bank policy (or both), we estimate the size of the domain that attracts all the trajectories. The proofs are based on introducing a family of Lyapunov functions and, for the multi-agent model, deriving a formula for the inverse of the Prandtl-Ishlinskii operator acting in the space of discrete-time inputs and outputs.

The article deals with the technical literacy and implementation of the Industry 4.0 at elementary schools. It deals with the importance of construction kit in development of children’s technical thinking. The article presents the results of research taken at elementary schools in the Hradec Kralove Region. The research is dealing with the problematic of teaching the subject “Polytechnic creation” and is dealing with the use of construction kits during that subject.

Hysteresis is an important issue in modeling piezoelectric materials, for example, in applications to energy harvesting, where hysteresis losses may influence the efficiency of the process. The main problem in numerical simulations is the inversion of the underlying hysteresis operator. Moreover, hysteresis dissipation is accompanied with heat production, which in turn increases the temperature of the device and may change its physical characteristics. More accurate models therefore have to take the temperature dependence into account for a correct energy balance. We prove here that the classical Preisach operator with a fairly general parameter-dependence admits a Lipschitz continuous inverse in the space of right-continuous regulated functions, propose a time-discrete and memory-discrete inversion algorithm, and show that higher regularity of the inputs leads to a higher regularity of the output of the inverse., Submitted version in Discrete Contin. Dyn. Syst. Ser. B

We propose a model for unsaturated poro-plastic flow derived from the thermodynamic principles. For the isothermal case, the problem consists of a degenerate coupled system of two PDEs with two independent hysteresis operators describing hysteresis phenomena in both the solid and the pore fluids. Under natural hypotheses, we prove the existence of a global strong solution for this system. Copyright © 2015 John Wiley & Sons, Ltd.

We consider a system of operator equations involving play and Prandtl-Ishlinskii hysteresis operators. This system generalizes the classical mechanical models of elastoplasticity, friction and fatigue by introducing coupling between the operators. We show that under quite general assumptions the coupled system is equivalent to one effective Prandtl-Ishlinskii operator or, more precisely, to a discontinuous extension of the Prandtl-Ishlinskii operator based on the Kurzweil integral of the derivative of the state function. This effective operator is described constructively in terms of the parameters of the coupled system. Our result is based on a substitution formula which we prove for the Kurzweil integral of regulated functions integrated with respect to functions of bounded variation. This formula allows us to prove the composition rule for the generalized (discontinuous) Prandtl-Ishlinskii operators. The composition rule, which underpins the analysis of the coupled model, then establishes that a composition of generalized Prandtl-Ishlinskii operators is also a generalized Prandtl-Ishlinskii operator provided that a monotonicity condition is satisfied.

We pursue the study of fatigue accumulation in an oscillating elastoplastic beam under the additional hypothesis that the material can partially recover by the effect of melting. The full system consists of the momentum and energy balance equations, an evolution equation for the fatigue rate, and a differential inclusion for the phase dynamics. The main result consists in proving the existence and uniqueness of a strong solution.

Rate independent evolutions can be formulated as operators, called hysteresis operators, between suitable function spaces. In this paper, we present some results concerning the existence and the form of directional derivatives and of Hadamard derivatives of such operators in the scalar case, that is, when the driving (input) function is a scalar function.

The third-body concept is a pragmatic tool used to understand the friction and wear of sliding materials. The wear particles play a crucial role in this approach and constitute the main part of the third-body. This paper aims to introduce a mathematical model for the motion of a third-body interface separating two surfaces in contact. This model is written in accordance with the formalism of hysteresis operators as solution operators of the underlying variational inequalities. The existence result for this dynamical problem is obtained by using a priori estimates established for Faedo–Galerkin approximations, and some more specific techniques such as anisotropic Sobolev embedding theory.

The diffusion equation with a bounded saturation range under the time derivative and with Robin boundary conditions is shown to admit a regular bounded solution provided that the saturation function and the permeability coefficient have controlled decay at infinity. The result remains valid even if Preisach hysteresis is present in the pressure-saturation relation. The method of proof is based on a Moser-Alikakos iteration scheme which is compatible with a generalized Preisach energy dissipation mechanism.