György Károlyi

• Budapest University of Technology and Economics

Motivated by the losses of runaway electrons during disruptive events in present and future tokamaks like the ITER, we investigate the transport in mixed phase space Hamiltonian systems. We are interested in the regime where the sticky regions, remaining after the disintegration of invariant transport barriers, form layers in the phase space separa...

This research used the new ISO 23478-2022 standard as a reference for the calculation of mechanical properties of N-finity, and to understand the failure modes in compression. Previous studies have investigated the mechanical properties of laminated bamboo lumber (LBL), however no study has evaluated the mechanical properties of LBL according to th...

Computing the emerging flow in blood vessel sections by means of computational fluid dynamics is an often applied practice in hemodynamics research. One particular area for such investigations is related to the cerebral aneurysms, since their formation, pathogenesis, and the risk of a potential rupture may be flow-related. We present a study on the...

A tensile test program of Moso bamboo samples was carried out in order to obtain information on the radial distribution of elastic and strength properties. In accordance with previous studies, the elastic modulus and the tensile strength were found to increase outwards in the radial direction. This spatial dependence was compared with the distribut...

A 2001. szeptember 11-i terrortámadás óta a kiemelt építményeket megnövekedett biztonsági elvárások mellett szükséges tervezni. Ez az előírás az újonnan épített nukleáris létesítményekre, köztük a Paks II. atomerőmű-beruházásra is vonatkozik. Ezen megnövekedett biztonsági igények meghatározzák, hogy a tervezett atomerőmű konténmentjének ellen kell...

Bamboo has attracted considerable recent interest in sustainable buildings as the fastest-growing natural material retaining mechanical properties similar to structural wood while being an effective CO2 absorber during its growth. Previous efforts to estimate bamboo material properties and their behaviour using homogenisation techniques used simpli...

We argue that typical mechanical systems subjected to a monotonous parameter drift whose timescale is comparable to that of the internal dynamics can be considered to undergo their own climate change. Because of their chaotic dynamics, there are many permitted states at any instant, and their time dependence can be followed—in analogy with the real...

Motivated by the grave consequences of an aircraft impact into robust engineering structures like nuclear power plants, we investigate the time-dependent reaction force during the impact of a crushing, elongated elasto{plastic missile into a robust elastic target. We derive a set of partial differential equations on a time-dependent domain to descr...

Bamboo is one of the materials that have recently attracted considerable interest in sustainable buildings as they are fast growing, retaining thermal and mechanical properties similar to structural wood products, and considered effective CO2 absorbers. Several studies tried to assess the energy performance of bamboo-structures for residential buil...

In dissipative systems without any driving or positive feedback all motion stops ultimately since the initial kinetic energy is dissipated away during time evolution. If chaos is present, it can only be of transient type. Traditional transient chaos is, however, supported by an infinity of unstable orbits. In the lack of these, chaos in undriven di...

We argue that typical mechanical systems subjected to a monotonous parameter drift whose time scale is comparable to that of the internal dynamics can be considered to undergo their own climate change. Because of their chaotic dynamics, there are many permitted states at any instant, and their time dependence can be followed - in analogy with the r...

A 2001. szeptember 11-i terrortámadás óta a kiemelt építményeket megnövekedett biztonsági elvárások mellett szükséges tervezni. Ez az előírás az újonnan épített nukleáris létesítményekre, köztük a Paks II. atomerőmű-beruházásra is vonatkozik. Ezen megnövekedett biztonsági igények meghatározzák, hogy a tervezett atomerőmű konténmentjének ellen kell...

We develop a conceptual coupled atmosphere–phytoplankton model by combining the Lorenz'84 general circulation model and the logistic population growth model under the condition of a climate change due to a linear time dependence of the strength of anthropogenic atmospheric forcing. The following types of couplings are taken into account: (a) the te...

Abstract. We develop a conceptual coupled atmosphere–phytoplankton model by combining the Lorenz'84 general circulation model and the logistic population growth model under the condition of a climate change due to a linear time dependence of the strength of anthropogenic atmospheric forcing. The following types of couplings are taken into account:...

In this paper a generalized discrete elastica including both bending and shear elastic interactions is developed and its possible link with nonlocal beam continua is revealed. This lattice system can be viewed as the generalization of the Hencky bar-chain model, which can be retrieved in the case of infinite shear stiffness. The shear contribution...

Background: Myosin II, the motor protein driving muscle contraction, uses energy of ATP hydrolysis to produce movement along actin. The key step of energy transduction is the powerstroke, involving rotation of myosin's lever while myosin is attached to actin. Macroscopic measurements indicated high thermodynamic efficiency for energy conversion. H...

Here we carry out a systematic parametric study of a uniform cylindrical missile impacting rigid or elastic structures. We give an analytical result for the impact force in case of rigid target. A new parameter, the damage potential is introduced and it is shown that this single dimensionless combination of the parameters describes the course of th...

Impact of missiles into reinforced concrete structures can have various effects. Soft impacts (deformation of missile is more significant than deformation of target structure) might cause global failure, while hard impacts of quasi-rigid missiles only affect the impact zone and cause local failure such as cracks, penetration, perforation, etc. In o...

Computing the emerging flow in blood vessel sections by means of computational fluid dynamics is an often applied practice in hemodynamics research. One particular area for such investigations is related to the cerebral aneurysms, since their formation, pathogenesis and the risk of a potential rupture may be flow-related. We present a study on the...

A repülőgép-becsapódáshoz tartozó extrém terhek valószínűsége átlagos építmények esetén elhanyagolható, így az általános tervezési előírások, szabványok ezeket nem tartalmazzák. Kiemelt létesítmények, például atomerőművek esetében azonban a lehetséges következmények súlyossága miatt mindenképpen foglalkoznunk kell ütközések hatásaival, az előírt vi...

The behaviour of biological fluid flows is often investigated in medical practice to draw conclusions on the physiological or pathological conditions of the considered organs. One area where such investigations are proven to be useful is the flow-related formation and growth of different pathologic malformations of the cerebro vascular system. In t...

Nematic liquid crystals combined with long molecular chains to form liquid crystal elastomers are capable of large extension. When such liquid crystal elastomers contain azo dyes to constitute photoelastomers, illumination can trigger large contraction. Beams made from such photoelastomers possess a non-uniform illumination and hence photostrain ac...

The Riera approach is the most commonly used method for modelling the global effects of a deformable missile on a rigid engineering structure. The Riera approach assumes the normal impact of a rigid perfectly plastic missile that only crushes at the cross-section adjacent to the target. It also neglects the effects of target deformation. Our resear...

Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final state sensitivity observed in connection with fractal basin boundaries in conservative scattering systems and...

The to and fro motion of a bouncing ball on a flat surface is represented by a low-dimensional model. To describe the repeated reversals of the horizontal velocity of the ball, the elasticity of the ball has to be taken into account. We show that a simple fly-wheel model exhibits the observed hither and thither motion of elastic balls. The suggeste...

In a low-order chaotic model of global atmospheric circulation the effects of driving, i.e., time-dependent (periodic, chaotic, and noisy) forcing, are investigated, with particular interest in extremal behavior. An approach based on snapshot attractors formed by a trajectory ensemble is applied to represent the time-dependent likelihood of extreme...

Due to their small size molecular systems are often overdamped and they are affected by significant fluctuations due to thermal forces. In this paper we investigate the effect of over-damping on a simple mechanical model of myosin II, the motor protein responsible for muscle contraction. We demonstrate that this model, based on the experimentally o...

In this paper, a new model of the progression phase of a drifting oscillator is proposed. This is to account more accurately for the penetration of an impactor through elastoplastic solids under a combination of a static and a harmonic excitation. First, the dynamic response of the semi-infinite elasto-plastic medium subjected to repeated impacts b...

In a low-order chaotic global atmospheric circu-lation model the effects of deterministic chaotic driving are investigated. As a result of driving, peak-over-threshold type extreme events, e.g. cyclonic activity in the model, become more extreme, with increased frequency of recurrence. When the characteristic time of the driving is comparable to th...

We show that common circulatory diseases, such as stenoses and aneurysms, generate chaotic advection of blood particles. This phenomenon has major consequences on the way the biochemical particles behave. Chaotic advection leads to a peculiar filamentary particle distribution, which in turn creates a favorable environment for particle reactions. Fu...

In systems exhibiting transient chaos in coexistence with periodic attractors, the inclusion of weak noise might give rise to noise-induced chaotic attractors. When the noise amplitude exceeds a critical value, an extended attractor appears along the fractal unstable manifold of the underlying nonattracting chaotic set. A further increase of noise...

Motor proteins are special enzymes capable of transforming chemical energy into mechanical work. One of the best known motor proteins belongs to the family of myosins found in eukaryotic tissues. The most studied — and first discovered — type of myosin is the skeletal muscle myosin (myosin II) which is the motor protein responsible for the contract...

Recent advances in the field of chaotic advection provide the impetus to revisit the dynamics of particles transported by blood flow in the presence of vessel wall irregularities. The irregularity, being either a narrowing or expansion of the vessel, mimicking stenoses or aneurysms, generates abnormal flow patterns that lead to a peculiar filamenta...

Spatially chaotic bifurcations of an elastic web of links are investigated. We numerically construct the global bifurcation diagrams uniquely describing the buckled states, and show that the exponential growth of the number of equilibrium branches with the size of the web indicates spatial chaos. The types of bifurcations from the trivial equilibri...

Chaotic motion of particles in fluid flows was recognized decades ago but this phenomenon has only been acknowledged recently in civil engineering. Herein it is shown that chaotic advection has a wide range of important hydraulic and environmental applications. The most important characteristics of chaotic particle transport, such as the filamentar...

We review recent advances on the dynamics of finite–size particles advected by chaotic fluid flows, focusing on the phenomena caused by the inertia of finite–size particles which have no counterpart in traditionally studied passive tracers. Particle inertia enlarges the phase space and makes the advection dynamics much richer than the passive trace...

Due to their small sizes molecular systems are often overdamped. Conformational changes in these molecules are a consequence of the separation of the energy input between the different displacements and velocities of the different functional sites of the molecule. We show how a simple mechanical device, that splits the forces between the different...

This book is a collection of contributions on various aspects of active frontier research in the field of dynamical systems and chaos. Each chapter examines a specific research topic and, in addition to reviewing recent results, also discusses future perspectives. The result is an invaluable snapshot of the state of the field by some of its most im...

In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle tr...

In this pedagogical review we summarize recent results on reactivity in chaotic hydrodynamical flows, in both open regimes and closed containers. In open flows, reaction is concentrated on the fractal filaments of the unstable manifold of a chaotic saddle. In closed flows, the product does not show a well-defined fractal property, nevertheless, the...

In this paper we investigate the transition to chaos in the motion of particles advected by open flows with obstacles. By means of a topological argument, we show that the separation points on the surface of the obstacle imply the existence of a saddle point downstream from the obstacle, with an associated heteroclinic orbit. We argue that as soon...

We show that chemical activity in hydrodynamical flows can be understood as the outcome of three basic effects: the stirring protocol of the flow, the local properties of the reaction, and the global folding dynamics which also depends on the geometry of the container. The essence of each of these components can be described by simple functional re...

Fluid motion, like in environmental flows, may generate chaotic advection: the particles transported by the flow typically exhibit chaotic dynamics. This manifests itself in that the particles trace out complicated geometrical objects, filamentary fractal structures. The appearance of these complex fractal structures plays an important role if the...

We investigate the dynamics of inertial particles immersed in open chaotic flows. We consider the generic problem of competition between different species, e.g., phytoplankton populations in oceans. The strong influence from inertial effects is shown to result in the persistence of different species even in cases when the passively advected species...

Buckling of an elastic linkage under general loading is investigated. We show that buckling is related to an initial value problem, which is always a conservative, area-preserving mapping, even if the original static problem is nonconservative. In some special cases, we construct the global bifurcation diagrams, and argue that their complicated str...

Buckling of a cantilever under general loading is investigated using a discrete model, a clamped elastic linkage. It is shown that there is a related initial value problem which is al- ways a conservative, area preserving mapping, even if the original static problem is nonconser- vative. The global bifurcation diagrams are constructed in some speci...

Since the first invention of chaos theory, it has been found to play a very important role in many different fields, ranging from physics through biology to engineering, among others. We deal with a phenomenon called spatial chaos which is a special form of spatial complexity, when the governing equations are reminiscent of a chaotic dynamical syst...

We investigate chemical activity in hydrodynamical flows in closed containers. In contrast to open flows, in closed flows the chemical field does not show a well-defined fractal property; nevertheless, there is a transient filamentary structure present. We show that the effect of the filamentary patterns on the chemical activity can be modeled by t...

Laboratory experiments and numerical simulations have shown that the outcome of cyclic competition is significantly affected by the spatial distribution of the competitors. Short-range interaction and limited dispersion allows for coexistence of competing species that cannot coexist in a well-mixed environment. In order to elucidate the mechanisms...

The growth of filamentary micro-organisms is described in terms of the geometry of evolving planar curves in which the dynamics is determined by an underlying growth process. Steadily propagating tip shapes in two and three dimensions are found that are consistent with experimentally observed growth sequences.

Chemical and biological processes often take place in fluid flows. Many of them, like environmental or mi-crofluidical ones, generate filamentary patterns which have a fractal structure, due to the presence of chaos in the underlying advection dynamics. In such cases, hydrodynamical stirring strongly couples to the reactivity of the advected specie...

Buckling of an elastic linkage under nonconservative load is investigated. There is a related initial value problem, which is conservative and chaotic, and gives valuable aid in finding the buckled shapes of the linkage. To illustrate the equilibrium configurations, the bifurcation diagram is constructed, which turns out to be a distorted version o...

The growth dynamics of filamentary microbial colonies is investigated. Fractality of the fungal or actinomycetes colonies is shown both theoretically and in numerical experiments to play an important role. The growth observed in real colonies is described by the assumption of time-dependent fractality related to the different ages of various parts...

We study the dynamics of chemically or biologically active particles advected by open flows of chaotic time dependence, which can be modeled by a random time dependence of the parameters on a stroboscopic map. We develop a general theory for reactions in such random flows, and derive the reaction equation for this case. We show that there is a sing...

Based on a well-known discrete bifurcation problem (the discretized Euler buckling problem) displaying a highly complex bifurcation diagram, we show how to find fast, global access to the distribution patterns of classical branch-invariants (symmetry groups, nodal properties, stability characteris-tics), without actually computing the complex diagr...

The problem of information integration and resistance to the invasion of parasitic mutants in prebiotic replicator systems is a notorious issue of research on the origin of life. Almost all theoretical studies published so far have demonstrated that some kind of spatial structure is indispensable for the persistence and/or the parasite resistance o...

We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one effect of chaotic advection on the passively advected species (such as phytoplankton, or self-replicating macro-molecules) is...

We have analyzed the dynamics of metabolically coupled replicators in open chaotic flows. Replicators contribute to a common metabolism producing energy-rich monomers necessary for replication. The flow and the biological processes take place on a rectangular grid. There can be at most one molecule on each grid cell, and replication can occur only...

We investigate the effects of hyperbolic hydrodynamical mixing on the reaction kinetics of autocatalytic systems. Exact results are derived for the two dimensional open baker map as an underlying mixing dynamics for a two-component autocatalytic system, $A+B \to 2B$. We prove that the hyperboliticity exponentially enhances the productivity of the r...

Hydrodynamical phenomena play a keystone role in the population dynamics of passively advected species such as phytoplankton and replicating macromolecules. Recent developments in the field of chaotic advection in hydrodynamical flows encourage us to revisit the population dynamics of species competing for the same resource in an open aquatic syste...

1. Recent developments in the field of chaotic advection in hydrodynamical/environmental flows encourage us to revisit the population dynamics of competing species in open aquatic systems. 2. We assume that these species are in competition for a common limiting resource in open flows with chaotic advection dynamics. As an illustrative example, we...

We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive adve...

We investigate the dynamics of tracer particles in time-dependent open flows. If the advection is passive the tracer dynamics is shown to be typically transiently chaotic. This implies the appearance of stable fractal patterns, so-called unstable manifolds, traced out by ensembles of particles. Next, the advection of chemically or biologically acti...

Continuing the work of Domokos and Holmes [G. Domokos and P. Holmes, J. Nonlinear Sci. 3 (1993) 109–151] and Domokos [G. Domokos, Phil. Trans. Roy. Soc. Lond. A 355 (1997) 2099–2116], we explore global bifurcation diagrams of elastic linkages subject to quasi-static, conservative, one-parameter load. The main result is an explicit construction of a...

We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B-->2B and A+B-->2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von Kármán vortex street, a time-periodic two-dimensional flow of a viscous fluid around a cylinde...

We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B --> 2B and A+B --> 2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von K\'arm\'an vortex street, a time periodic two-dimensional flow of a viscous fluid around a...

We investigate the evolution of active particle ensembles in open chaotic flows. The active processes of the type A+B→2B and A+B→2C are considered in the limit of weak diffusion. As an illustrative advection dynamics, we choose a model of the von Kármán vortex street, and show that the backbone of the active processes is the fractal structure assoc...

We consider passive tracer advection in a model of a large planar basin of fluid with two sinks opened alternately. In spite of the incompressibility of the fluid, the phase space of the tracer dynamics contains (simple) attractors, the sinks. We show that the advection is chaotic due to the appearance of a locally Hamiltonian chaotic saddle. Prope...

Lurie (1994, 1995a, b) proved recently that variabletopology shape optimization of perforated plates in flexure for non-selfadjoint problems leads to rank-2 microstructures which are in general nonorthogonal. An extension of the same optimal microstructures to perforated plates in plane stress will be presented in Part II of this study. Using the a...

In the analysis of the problem the beam is modelled by hinge elements connected together by rigid bars while the foundation is replaced by spring elements supporting the hinges. The nonlinear behaviour of the beam and the foundation is described by specially formulated bilinear material models. The characteristics of these models are considered to...

In the celebratory dinner honouring Celso Grebogi’s 60th birthday, a number of scientists in the area of chaos were asked by James Yorke to tell the tale about how they got involved in the field. Since all the participants have played crucial roles in the development of the subject, their stories give unique insights into the historical development...

Hydrodynamical phenomena play a keystone role in the population dynamics of pas- sively advected species such as phytoplankton and replicating macromolecules. Re- cent developments in the field of chaotic advection in hydrodynamical flows encour- age us to revisit the population dynamics of species competing for the same resource in an open aquatic...

Fractal filaments in Lagrangian turbulence are present due to unstable manifolds of chaotic saddle in open flows, like the flow past an obstacle. The manifold emanates from a chaotic saddle which contains an infinity of unstable periodic orbits in the wake. We point our if reactions take place superimposed on the flow then the reaction outcomes are...

We investigate the dynamics of tracer particles in time-dependent open flows. In cases when the time-dependence is restricted to a finite region, we show that the tracer dynamics is typically chaotic but necessarily of transient type. The complex behaviour is then due to an underlying nonattracting chaotic set that is also restricted to a finite do...

Véletlen fluktuációt tartalmazó nyílt áramlásokban zajló reakciók esetén a reakciótermék eloszlásának fraktáldimenziója megjelenik a reakcióegyenletben. Zárt áramlásokban a reakciótermék eloszlásának effektív fraktáldimenziója időben változik, és az időbeli változás egyenlete csatolódik a reakciótermék mennyiségét leíró egyenlethez. Egymással cikli...

A kutatás átfogó területet jelölt meg, ezen belül azonban nyolc igen konkrét kutatási célt tűzött ki. A felemelkedő kihajlás vizsgálatával sikerült egy elméleti és gyakorlati szempontból is érdekes témában eredményeket elérnünk: modellünk a tengerfenéken húzódó kábelek geometriailag nemlineáris viselkedését segít megérteni. Növényi indák komplex té...

Foglalkoztunk a kaotikus folyadékáramlásokban zajló kémiai és biológiai reakciók leírásával, különös tekintettel a front-terjedéssel kapcsolatos reakciókra, és kimutattuk, hogy másként zajlanak le, mint álló, vagy akár jól kevert közegben. A kicsiny, de véges méretű részecskék sodródása eltér a pontszerű részecskék viselkedésétől folyadék áramlásba...