On the dynamics of random neuronal networks

We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with the classical integrate-and-fire model. The ergodicity properties of the Markov process associated to finite networks are investigated. We derive the limit in distribution of the sample path of the state of a neuron of the network when its size gets large. The invariant distributions of this limiting stochastic process are analyzed as well as their stability properties. We show that the system undergoes transitions as a function of the averaged connectivity parameter, and can support trivial states (where the network activity dies out, which is also the unique stationary state of finite networks in some cases) and self-sustained activity when connectivity level is sufficiently large, both being possibly stable.Comment: 37 pages, 3 figure

Magnetic Nernst effect

The thermodynamics of irreversible processes in continuous media predicts the existence of a Magnetic Nernst effect that results from a magnetic analog to the Seebeck effect in a ferromagnet and magnetophoresis occurring in a paramagnetic electrode in contact with the ferromagnet. Thus, a voltage that has DC and AC components is expected across a Pt electrode as a response to the inhomogeneous magnetic induction field generated by magnetostatic waves of an adjacent YIG slab subject to a temperature gradient. The voltage frequency and dependence on the orientation of the applied magnetic induction field are quite distinct from that of spin pumping.Comment: 4 pages, 1 figur

Nano-structures at martensite macrotwin interfaces in Ni65Al35Ni_{65}Al_{35}

The atomic configurations at macrotwin interfaces between microtwinned martensite plates in $Ni_{65}Al_{35}$ material are investigated using transmission electron microscopy. The observed structures are interpreted in view of possible formation mechanisms for these interfaces. A distinction is made between cases in which the microtwins, originating from mutually perpendicular \{110\} austenite planes, enclose a final angle larger or smaller than $90^{\circ}$. Two different configurations, a crossing and a step type are described. Depending on the actual case, tapering, bending and tip splitting of the smaller microtwin variants are observed. The most reproducible deformations occur in a region of approximately 5-10nm width around the interface while a variety of structural defects are observed further away from the interface. These structures and deformations are interpreted in terms of the coalescence of two separately nucleated microtwinned martensite plates and the need to accommodate remaining stresses

A periodic microfluidic bubbling oscillator: insight into the stability of two-phase microflows

This letter describes a periodically oscillating microfoam flow. For constant input parameters, both the produced bubble volume and the flow rate vary over a factor two. We explicit the link between foam topology alternance and flow rate changes, and construct a retroaction model where bubbles still present downstream determine the volume of new bubbles, in agreement with experiment. This gives insight into the various parameters important to maintain monodispersity and at the same time shows a method to achieve controlled polydispersity.Comment: 4 page

A rigorous proof of the Landau-Peierls formula and much more

We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by T. Kjeldaas and W. Kohn in 1957.Comment: 30 pages - Accepted for publication in A.H.

Testing and tuning symplectic integrators for Hybrid Monte Carlo algorithm in lattice QCD

We examine a new 2nd order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, \bra\Delta H^2\ket^{1/2}, is about 10 times smaller than that of the standard 2nd order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a factor 2 increase in cost, the new integrator is about 50% more efficient than the 2LF integrator. Integrating over positions first, then momenta, is slightly more advantageous than the reverse. Further parameter tuning is possible. We find that the optimal parameter for the new integrator is slightly different from the value obtained by Omelyan et al., and depends on the simulation parameters. This integrator could also be advantageous for the Trotter-Suzuki decomposition in Quantum Monte Carlo.Comment: 14 pages, 6 figure

Computation of maximal local (un)stable manifold patches by the parameterization method

In this work we develop some automatic procedures for computing high order polynomial expansions of local (un)stable manifolds for equilibria of differential equations. Our method incorporates validated truncation error bounds, and maximizes the size of the image of the polynomial approximation relative to some specified constraints. More precisely we use that the manifold computations depend heavily on the scalings of the eigenvectors: indeed we study the precise effects of these scalings on the estimates which determine the validated error bounds. This relationship between the eigenvector scalings and the error estimates plays a central role in our automatic procedures. In order to illustrate the utility of these methods we present several applications, including visualization of invariant manifolds in the Lorenz and FitzHugh-Nagumo systems and an automatic continuation scheme for (un)stable manifolds in a suspension bridge problem. In the present work we treat explicitly the case where the eigenvalues satisfy a certain non-resonance condition.Comment: Revised version, typos corrected, references adde

Auto-dual connected operators based on iterative merging algorithms

This paper proposes a new set of connected operators that are autodual. Classical connected operators are analyzed within the framework of merging algorithms. The discussion highlights three basic notions: merging order , merging criterion and region model. As a result a general merging algorithm is proposed. It can be used to create new connected operators and in particular autodual operators. Implementation issues are also discussed.Peer ReviewedPostprint (published version