Kramers-Kronig relations and the properties of conductivity and permittivity in heterogeneous media

The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exists Kramers-Kronig relations for conductivity, which are mathematically equivalent to the Hilbert transform. These relations impose strong constraints that models of heterogeneous media should satisfy to have a physically plausible frequency dependence of the conductivity and permittivity. We illustrate these relations and constraints by a few examples of known physical media. These extended relations constitute important constraints to test the consistency of past and future experimental measurements of the electric properties of heterogeneous media.Comment: 17 pages, 2 figure

Macroscopic models of local field potentials and the apparent 1/f noise in brain activity

The power spectrum of local field potentials (LFPs) has been reported to scale as the inverse of the frequency, but the origin of this "1/f noise" is at present unclear. Macroscopic measurements in cortical tissue demonstrated that electric conductivity (as well as permittivity) is frequency dependent, while other measurements failed to evidence any dependence on frequency. In the present paper, we propose a model of the genesis of LFPs which accounts for the above data and contradictions. Starting from first principles (Maxwell equations), we introduce a macroscopic formalism in which macroscopic measurements are naturally incorporated, and also examine different physical causes for the frequency dependence. We suggest that ionic diffusion primes over electric field effects, and is responsible for the frequency dependence. This explains the contradictory observations, and also reproduces the 1/f power spectral structure of LFPs, as well as more complex frequency scaling. Finally, we suggest a measurement method to reveal the frequency dependence of current propagation in biological tissue, and which could be used to directly test the predictions of the present formalism

Generalized cable formalism to calculate the magnetic field of single neurons and neuronal populations

Neurons generate magnetic fields which can be recorded with macroscopic techniques such as magneto-encephalography. The theory that accounts for the genesis of neuronal magnetic fields involves dendritic cable structures in homogeneous resistive extracellular media. Here, we generalize this model by considering dendritic cables in extracellular media with arbitrarily complex electric properties. This method is based on a multi-scale mean-field theory where the neuron is considered in interaction with a "mean" extracellular medium (characterized by a specific impedance). We first show that, as expected, the generalized cable equation and the standard cable generate magnetic fields that mostly depend on the axial current in the cable, with a moderate contribution of extracellular currents. Less expected, we also show that the nature of the extracellular and intracellular media influence the axial current, and thus also influence neuronal magnetic fields. We illustrate these properties by numerical simulations and suggest experiments to test these findings.Comment: Physical Review E (in press); 24 pages, 16 figure

The Evolution of Cost Control Systems: a Cultural Phenomenon

This paper only aims at stimulating research and debate, starting from two ideas:• historically, cost control systems have undergone major changes by integrating an increasing level of instability;• the same pattern of evolution can be found in other areas.Evolutions seem to have gone through four stages:1. A static period. Individuals think in terms of a stable environment in which there is only one truth. Problems are solved through an analytical approach.2. A period of static balance. Although there is some movement, unchanging laws prevail. The environment is a deterministic one in which the future is modelled on the past. The only systems that can be conceived are closed , dependent ones.3. A period of dynamic balance. Some change is introduced in the laws regulating trends. The environment may thus be transformed and tentatively brought under control. Systems tend to become open ended and adaptable.4. A period when the probabilistic order of confusion prevails. Although the movement has become widespread, it cannot be foreseen in detail. However, major events are somehow predictable according to statistical laws. Overall transformations remain undetermined. Systems improve and become more effective by constant updating and upgrading.Those four stages have been observed in five different fields:• cost control systems in organisations• the history of economic theory• natural sciences• information technology• philosophy.This evolution of course did not affect the five fields in the same manner or at the same pace. It is however important to note that the stages are identical whatever the field i.e. that changes in thinking patterns shifted from one stage to another.management control

Age differences in fMRI adaptation for sound identity and location

We explored age differences in auditory perception by measuring fMRI adaptation of brain activity to repetitions of sound identity (what) and location (where), using meaningful environmental sounds. In one condition, both sound identity and location were repeated allowing us to assess non-specific adaptation. In other conditions, only one feature was repeated (identity or location) to assess domain-specific adaptation. Both young and older adults showed comparable non-specific adaptation (identity and location) in bilateral temporal lobes, medial parietal cortex, and subcortical regions. However, older adults showed reduced domain-specific adaptation to location repetitions in a distributed set of regions, including frontal and parietal areas, and to identity repetition in anterior temporal cortex. We also re-analyzed data from a previously published 1-back fMRI study, in which participants responded to infrequent repetition of the identity or location of meaningful sounds. This analysis revealed age differences in domain-specific adaptation in a set of brain regions that overlapped substantially with those identified in the adaptation experiment. This converging evidence of reductions in the degree of auditory fMRI adaptation in older adults suggests that the processing of specific auditory “what” and “where” information is altered with age, which may influence cognitive functions that depend on this processing

A fractal approach to the rheology of concentrated cell suspensions

Results on the rheological behavior of novel CHO cell suspensions in a large range of concentrations are reported. The concentration dependent yield stress and elastic plateau modulus are formalized in the context of fractal aggregates under shear, and quite different exponents are found as compared to the case of red blood cell suspensions. This is explained in terms of intrinsic microscopic parameters such as the cell-cell adhesion energy and cell elasticity but also the cell individual dynamic properties, found to correlate well with viscoelastic data at large concentrations (phi>0.5).Comment: 4 pages, 5 figure

Entropic fluctuations in thermally driven harmonic networks

We consider a general network of harmonic oscillators driven out of thermal equilibrium by coupling to several heat reservoirs at different temperatures. The action of the reservoirs is implemented by Langevin forces. Assuming the existence and uniqueness of the steady state of the resulting process, we construct a canonical entropy production functional which satisfies the Gallavotti--Cohen fluctuation theorem, i.e., a global large deviation principle with a rate function I(s) obeying the Gallavotti--Cohen fluctuation relation I(-s)-I(s)=s for all s. We also consider perturbations of our functional by quadratic boundary terms and prove that they satisfy extended fluctuation relations, i.e., a global large deviation principle with a rate function that typically differs from I(s) outside a finite interval. This applies to various physically relevant functionals and, in particular, to the heat dissipation rate of the network. Our approach relies on the properties of the maximal solution of a one-parameter family of algebraic matrix Riccati equations. It turns out that the limiting cumulant generating functions of our functional and its perturbations can be computed in terms of spectral data of a Hamiltonian matrix depending on the harmonic potential of the network and the parameters of the Langevin reservoirs. This approach is well adapted to both analytical and numerical investigations

A Detailed Fluctuation Theorem for Heat Fluxes in Harmonic Networks out of Thermal Equilibrium

We continue the investigation, started in [J. Stat. Phys. 166, 926-1015 (2017)], of a network of harmonic oscillators driven out of thermal equilibrium by heat reservoirs. We study the statistics of the fluctuations of the heat fluxes flowing between the network and the reservoirs in the nonequilibrium steady state and in the large time limit. We prove a large deviation principle for these fluctuations and derive the fluctuation relation satisfied by the associated rate function

Couplings in parametrically excited inclined cables systems

Cables in stayed bridges are subjected to important dynamic solicitations for which dynamic model are now well established. Due to their design, such structures highlight resonance phenomena and instabilities frequently observed. Nevertheless, some structures exhibit important vibration amplitudes that can not be explained simply. Measurement recently performed on a bridge point a coupling of the cable with the deck or the pillar. The present paper suggests to consider the deck flexibility coupled to the nonlinear dynamic of the inclined cable. Results of previous study are used. The retained nonlinear model of the cable include two degrees of freedom for the in-plane motion. Considering the bridge mass and deck rigidity adds one DOF, assumed linear in a first approach. The excitation is created on the deck, which produce an external force(such as the wind or the car traffic for example). An experimental set-up uses a specific device in order to highlight expected coupling phenomena on the parametric instabilities. It is composed of a flexible blade which represents the deck, and an inclined cable. Both elements are linked to a mass forced to move vertically, and which represent the anchor point and the equivalent mass of a section of the deck. Therefore, the cable has a given initial static tension. An electrodynamic shaker applies a force close to blade clumping. The transmitted force from the shaker to the structure is measured thanks to a piezo-electric sensor. The instantaneous cable tension is measured via a Shape force sensor. And a high resolution laser sensor captures without contact the in-plane motion of the cable. Analytically, the multiple scales method is applied to solve the nonlinear equations of motion. In-plane vibration of the cable and stability in the vicinity of the primary resonance w1 and sub-harmonic resonance 2w1 are computed. The competition between the behaviour at 2w1 and w2 are of particular interest, as it is observed experimentally

On the steady state correlation functions of open interacting systems

We address the existence of steady state Green-Keldysh correlation functions of interacting fermions in mesoscopic systems for both the partitioning and partition-free scenarios. Under some spectral assumptions on the non-interacting model and for sufficiently small interaction strength, we show that the system evolves to a NESS which does not depend on the profile of the time-dependent coupling strength/bias. For the partitioned setting we also show that the steady state is independent of the initial state of the inner sample. Closed formulae for the NESS two-point correlation functions (Green-Keldysh functions), in the form of a convergent expansion, are derived. In the partitioning approach, we show that the 0th order term in the interaction strength of the charge current leads to the Landauer-Buettiker formula, while the 1st order correction contains the mean-field (Hartree-Fock) results