154 research outputs found
Front dynamics during diffusion-limited corrosion of ramified electrodeposits
Experiments on the diffusion-limited corrosion of porous copper clusters in
thin gap cells containing cupric chloride are reported. By carefully comparing
corrosion front velocities and concentration profiles obtained by phase-shift
interferometry with theoretical predictions, it is demonstrated that this
process is well-described by a one-dimensional mean-field model for the generic
reaction A + B (static) -> C (inert) with only diffusing reactant (cupric
chloride) and one static reactant (copper) reacting to produce an inert product
(cuprous chloride). The interpretation of the experiments is aided by a
mathematical analysis of the model equations which allows the reaction-order
and the transference number of the diffusing species to be inferred. Physical
arguments are given to explain the surprising relevance of the one-dimensional
mean-field model in spite of the complex (fractal) structure of the copper
clusters.Comment: 26 pages, 10 figures, submitted to J. Phys. Chem. B, high quality eps
figures available at http://www-math.mit.edu/~bazant/paper
Mechanical Sensing of Living Systems â From Statics to Dynamics
Living systems are fascinating sensing machines that outmatch all artificial machines. Our aim is to put a focus on the dynamics of mechanosensing in cellular systems through concepts and experimental approaches that have been developed during the past decades. By recognizing that a cellular system is not simply the intricate assembly of active and passive macromolecular actors but that it can also manifest scale-invariant and/or highly nonlinear global dynamics, biophysicists have opened a new domain of investigation of living systems. In this chapter, we review methods and techniques that have been implemented to decipher the cascade of temporal events which enable a cell to sense a mechanical stimulus and to elaborate a response to adapt or to counteract this perturbation. We mainly describe intrusive (mechanical probes) and nonintrusive (optical devices) experimental methods that have proved to be efficient for real-time characterization of stationary and nonstationary cellular dynamics. Finally, we discuss whether thermal fluctuations, which are inherent to living systems, are a source of coordination (e.g., synchronization) or randomization of the global dynamics of a cell
A non-parametric probabilistic model for soil-structure interaction
International audienceThe paper investigates the effect of soil-structure interaction on the dynamic response of structures. A non-parametric probabilistic formulation for the modelling of an uncertain soil impedance is used to account for the usual lack of information on soil properties. Such a probabilistic model introduces the physical coupling stemming from the soil heterogeneity around the foundation. Considering this effect, even a symmetrical building displays a torsional motion when submitted to earthquake loading. The study focuses on a multi-story building modeled by using equivalent Timoshenko beam models which have different mass distributions. The probability density functions of the maximal internal forces and moments in a given building are estimated by Monte Carlo simulations. Some results on the stochastic modal analysis of the structure are also given
Emergence of log-normal type distributions in avalanche processes in living systems : a network model
Funding We acknowledge financial support from the Agence Nationale de la Recherche (ANR grant number ANR-18-CE45-0012-01) and from the French Research Minister (MESRI) for SP. PhD funding. Acknowledgments We are very grateful for the participants of the second ISINP meeting at Lake Como for stimulating exchanges about our talk. We are thanful to P. Argoul, A. Guillet, E. HartĂš, L. Delmarre for fruitful discussions. SP wishes to thank T. Matteuzzi for his inspiring considerations. We are indebted to Erika Polizzi for her graphical help.Peer reviewedPublisher PD
Multi-scaled analysis of the damped dynamics of an elastic rod with an essentially nonlinear end attachment
We study multi-frequency transitions in the transient dynamics of a viscously damped dispersive finite rod with an essentially nonlinear end attachment. The attachment consists of a small mass connected to the rod by means of an essentially nonlinear stiffness in parallel to a viscous damper. First, the periodic orbits of the underlying hamiltonian system with no damping are computed, and depicted in a frequencyâenergy plot (FEP). This representation enables one to clearly distinguish between the different types of periodic motions, forming back bone curves and subharmonic tongues. Then the damped dynamics of the system is computed; the rod and attachment responses are initially analyzed by the numerical Morlet wavelet transform (WT), and then by the empirical mode decomposition (EMD) or HilbertâHuang transform (HTT), whereby, the time series are decomposed in terms of intrinsic mode functions (IMFs) at different characteristic time scales (or, equivalently, frequency scales). Comparisons of the evolutions of the instantaneous frequencies of the IMFs to the WT spectra of the time series enables one to identify the dominant IMFs of the signals, as well as, the time scales at which the dominant dynamics evolve at different time windows of the responses; hence, it is possible to reconstruct complex transient responses as superposition of the dominant IMFs involving different time scales of the dynamical response.
Moreover, by superimposing the WT spectra and the instantaneous frequencies of the IMFs to the FEPs of the underlying hamiltonian system, one is able to clearly identify the multi-scaled transitions that occur in the transient damped dynamics, and to interpret them as âjumpsâ between different branches of periodic orbits of the underlying hamiltonian system. As a result, this work develops a physics-based, multi-scaled framework and provides the necessary computational tools for multi-scaled analysis of complex multi-frequency transitions of essentially nonlinear dynamical systems
Spiral Waves in Chaotic Systems
Spiral waves are investigated in chemical systems whose underlying
spatially-homogeneous dynamics is governed by a deterministic chaotic
attractor. We show how the local periodic behavior in the vicinity of a spiral
defect is transformed to chaotic dynamics far from the defect. The
transformation occurs by a type of period doubling as the distance from the
defect increases. The change in character of the dynamics is described in terms
of the phase space flow on closed curves surrounding the defect.Comment: latex file with three postscript figures to appear in Physical review
Letter
A propensity criterion for networking in an array of coupled chaotic systems
We examine the mutual synchronization of a one dimensional chain of chaotic
identical objects in the presence of a stimulus applied to the first site. We
first describe the characteristics of the local elements, and then the process
whereby a global nontrivial behaviour emerges. A propensity criterion for
networking is introduced, consisting in the coexistence within the attractor of
a localized chaotic region, which displays high sensitivity to external
stimuli,and an island of stability, which provides a reliable coupling signal
to the neighbors in the chain. Based on this criterion we compare homoclinic
chaos, recently explored in lasers and conjectured to be typical of a single
neuron, with Lorenz chaos.Comment: 4 pages, 3 figure
Does ohmic heating influence the flow field in thin-layer electrodeposition?
In thin-layer electrodeposition the dissipated electrical energy leads to a
substantial heating of the ion solution. We measured the resulting temperature
field by means of an infrared camera. The properties of the temperature field
correspond closely with the development of the concentration field. In
particular we find, that the thermal gradients at the electrodes act like a
weak additional driving force to the convection rolls driven by concentration
gradients.Comment: minor changes: correct estimation of concentration at the anode,
added Journal-re
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Tissue multifractality and Born approximation in analysis of light scattering: a novel approach for precancers detection
Multifractal, a special class of complex self-affine processes, are under recent intensive investigations because of their fundamental nature and potential applications in diverse physical systems. Here, we report on a novel light scattering-based inverse method for extraction/quantification of multifractality in the spatial distribution of refractive index of biological tissues. The method is based on Fourier domain pre-processing via the Born approximation, followed by the Multifractal Detrended Fluctuation Analysis. The approach is experimentally validated in synthetic multifractal scattering phantoms, and tested on biopsy tissue slices. The derived multifractal properties appear sensitive in detecting cervical precancerous alterations through an increase of multifractality with pathology progression, demonstrating the potential of the developed methodology for novel precancer biomarker identification and tissue diagnostic tool. The novel ability to delineate the multifractal optical properties from light scattering signals may also prove useful for characterizing a wide variety of complex scattering media of non-biological origin
Diffusion-limited aggregation as branched growth
I present a first-principles theory of diffusion-limited aggregation in two
dimensions. A renormalized mean-field approximation gives the form of the
unstable manifold for branch competition, following the method of Halsey and
Leibig [Phys. Rev. A {\bf 46}, 7793 (1992)]. This leads to a result for the
cluster dimensionality, D \approx 1.66, which is close to numerically obtained
values. In addition, the multifractal exponent \tau(3) = D in this theory, in
agreement with a proposed `electrostatic' scaling law.Comment: 13 pages, one figure not included (available by request, by ordinary
mail), Plain Te
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