Biomedical subjects

Roman O Grigoriev

Publications and source records attributed to Roman O Grigoriev.

6 recordsLinked to original sources

PubMed2006

Transient dynamics and nonlinear stability of spatially extended systems.

As studies of various systems have shown, the sole focus on the eigenvalues in a linear stability analysis can be misleading, especially when the dynamics of disturbances is characterized by strong transient growth. The aim of this paper is to extend the generalized stability analysis, in the context of spatially extended systems, by examining the role of the nonlinear terms in the destabilization process. The critical noise level leading to destabilization is often found to scale as a power of the magnitude of transient amplification. In what follows we show that the power law exponent sensitively depends on the type of nonlinear terms and their potential for generating self-sustaining noise amplification cycles (bootstrapping). We find, however, that the exponents are not universal and also depend on the more subtle details of the transient dynamics. We also show that the basin of attraction of a spatially uniform state is bounded by the stable manifold(s) of nearby saddle(s) which play a major role in the transition.

Journal Article↗

PubMed2006

Chaotic mixing in microdroplets.

We describe a general methodology for introducing thorough chaotic mixing in microdroplets. The mixing properties of fluid flows in microdroplets are governed by their symmetries, which give rise to invariant surfaces serving as barriers to transport. Complete three-dimensional mixing by chaotic advection requires destruction of all flow invariants. To illustrate this idea, we demonstrate that complete mixing can be obtained in a time-dependent flow produced by moving a microdroplet along a two-dimensional path. The theoretical predictions are confirmed by experiments that use the thermocapillary effect to manipulate microdroplets.

Diffusion↗

PubMed2005

Pattern selection and control via localized feedback.

Many theoretical analyses of feedback control of pattern-forming systems assume that feedback is applied at every spatial location, something that is often difficult to accomplish in experiments. This paper considers an experimentally more feasible scenario where feedback is applied at a sparse array of discrete spatial locations. We show how such feedback can be computed analytically for a class of reaction-diffusion systems and use generalized linear stability analysis to determine how dense the actuator array needs to be to select or maintain control of a given pattern state in the presence of noise. The one-dimensional Swift-Hohenberg equation is used to illustrate our theoretical results and explain earlier experimental observations on the control of the Rayleigh-Bénard convection.

Journal Article↗

PubMed2003

Optical manipulation of microscale fluid flow.

A novel optical method is used both to probe and to control dynamics in experiments on the spreading of microscale liquid films over solid substrates. The flow is manipulated by thermally induced surface-tension gradients that are regulated by controlling the absorption of light in the substrate. This approach permits, for the first time, the measurement of the dispersion relation for the well-known contact line instability; the measurements are compared with theoretical predictions from the slip model for spreading films. The experiments also demonstrate the use of feedback control to suppress instability. These results show that optical control can provide dynamically reconfigurable manipulations of fluid flow, thereby suggesting a general approach for constructing reprogrammable microfluidic devices.

Journal Article↗

PubMed2002

Spectral theory for the failure of linear control in a nonlinear stochastic system.

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems described by linearly stable but strongly non-normal evolution operators. In spatially extended systems the non-normality manifests itself in two different but complementary ways: transient amplification and spectral focusing of disturbances. We show that temporal and spatial aspects of the non-normality and the type of nonlinearity are all crucially important to understand and describe the mechanism of nonlinear instability. Presented results are expected to apply equally to other physical systems where strong non-normality is due to the presence of mean flow rather than the action of control.

Journal Article↗

PubMed2002

Non-normality and the localized control of extended systems.

The idea of controlling the dynamics of spatially extended systems using a small number of localized perturbations is very appealing-such a setup is easy to implement in practice. However, when the distance between controllers generating the perturbations becomes large, control fails due to extreme sensitivity of the system to noise. This sensitivity results from strong non-normality of the evolution operator governing the dynamics of disturbances in the controlled system. We investigate how non-normality can arise in an originally normal system and study how the noise amplification depends on the distance between controllers.

Journal Article↗