Biomedical subjects

Tamás Tél

Publications and source records attributed to Tamás Tél.

9 recordsLinked to original sources

PubMed2005

Chemical transients in closed chaotic flows: the role of effective dimensions.

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 the use of time-dependent effective dimensions. We derive a new chemical rate equation, which turns out to be coupled to the dynamics of the effective dimension, and predicts an exponential convergence. Previous results concerning activity in open flows are special cases of this new rate equation.

Journal Article↗

PubMed2005

Multifractal spectra of chemical fields in fluid flows.

In the filamental phase of reactions embedded in fluid flows, where the concentration distribution is strongly fluctuating, we show that a chemical measure can be defined based on the absolute value of the concentration gradients. We express the generalized dimensions in terms of the roughness exponents of the structure functions as well as of the cancellation exponents of the chemical concentration. This measure is of basically different character than the natural distribution of the passive advection. It is similar to the SRB measures of dissipative systems, although the advection problem is area preserving. This approach is shown to be a useful tool in analyzing sea surface temperature anomalies.

Journal Article↗

PubMed2004

Reactive particles in random flows.

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 singular enhancement of the reaction in random flows, and this enhancement is increased as compared to the nonrandom case. We verify our theory in a model flow generated by four point vortices moving chaotically.

Models, Biological↗

PubMed2004

Coarse-grained entropy and information dimension of dynamical systems: The driven Lorentz gas.

We study the resolution dependence of the steady-state saturation values of coarse-grained entropies characterizing general dynamical systems. For dissipative maps they are proportional to the information codimension of the chaotic attractor. Thus, they provide a highly accurate method for determining the information dimension and related characteristics of the dynamical system. This general result is demonstrated for the field-driven Lorentz gas. In the discussion, we take the results on the resolution dependence of the entropy as the starting point to revisit different approaches to define thermodynamic entropy production for transport processes in dynamical systems, and discuss the role of local equilibrium in this enterprise.

Journal Article↗

PubMed2004

Universality in active chaos.

Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem through partial differential equations difficult. Here we present a simple approach for the activity in inhomogeneously stirred flows. We show that the fractal patterns serving as skeletons and catalysts lead to a rate equation with a universal form that is independent of the flow, of the particle properties, and of the details of the active process. One aspect of the universality of our approach is that it also applies to reactions among particles of finite size (so-called inertial particles).

Computer Simulation↗

PubMed2003

Advection of finite-size particles in open flows.

It is known that small, spherical particles with inertia do not follow the local velocity field of the flow. Here we investigate the motion of such particles and particle ensembles immersed in open, unsteady flows which, in the case of ideal pointlike tracers, generate chaotic Lagrangian trajectories. Due to the extra force terms in the equations of motion (such as Stokes drag, added mass) the inertial tracer trajectories become described by a high-dimensional (2d+1, with d being the flow's dimension) chaotic dynamics, which can drastically differ from the (d+1)-dimensional ideal tracer dynamics. As a consequence, we find parameter regimes (in terms of density and size), where long-term tracer trapping can occur for the inertial particle, even for flows in which no ideal, pointlike passive tracers can be trapped. These studies are performed in a model of a two-dimensional channel flow past a cylindrical obstacle. Since the Lagrangian tracer dynamics is sensitive to the particle density and size parameters, a simple geometric setup in such flows could be used as a (low-density) particle mixture segregator.

Journal Article↗

PubMed2003

Competing populations in flows with chaotic mixing.

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 the possibility of coexistence of more species than that limited by the number of niches they occupy. We derive a novel set of dynamical equations for competing populations.

Competitive Behavior↗

PubMed2002

Dynamics of "leaking" Hamiltonian systems.

In order to understand the dynamics in more detail, in particular for visualizing the space-filling unstable foliation of closed chaotic Hamiltonian systems, we propose to leak them up. The cutting out of a finite region of their phase space, the leak, through which escape is possible, leads to transient chaotic behavior of nearly all the trajectories. The never-escaping points belong to a chaotic saddle whose fractal unstable manifold can easily be determined numerically. It is an approximant of the full Hamiltonian foliation, the better the smaller the leak is. The escape rate depends sensitively on the orientation of the leak even if its area is fixed. The applications for chaotic advection, for chemical reactions superimposed on hydrodynamical flows, and in other branches of physics are discussed.

Journal Article↗

PubMed2002

Finite-size effects on active chaotic advection.

A small (but finite-size) spherical particle advected by fluid flows obeys equations of motion that are inherently dissipative, due to the Stokes drag. The dynamics of the advected particle can be chaotic even with a flow field that is simply time periodic. Similar to the case of ideal tracers, whose dynamics is Hamiltonian, chemical or biological activity involving such particles can be analyzed using the theory of chaotic dynamics. Using the example of an autocatalytic reaction, A+Bright arrow2B, we show that the balance between dissipation in the particle dynamics and production due to reaction leads to a steady state distribution of the reagent. We also show that, in the case of coalescence reaction, B+Bright arrowB, the decay of the particle density obeys a universal scaling law as approximately t(minus sign1) and that the particle distribution becomes restricted to a subset with fractal dimension D2, where D2 is the correlation dimension of the chaotic attractor in the particle dynamics.

Journal Article↗