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Aluminium gallium nitride ((Al,Ga)N) has gained significant attention in recent years due to its potential for highly efficient light emitters operating in the deep ultra-violet (UV) range (< 280 nm). However, given that current devices exhibit extremely low efficiencies, understanding the fundamental properties of (Al,Ga)N-based systems is of key importance. Here, using a multi-scale simulation framework, we study the impact of alloy disorder on carrier transport, radiative and non-radiative recombination processes in a c-plane Al 0.7 Ga 0.3 N/Al 0.8 Ga 0.2 N quantum well embedded in a p-i-n junction. Our calculations reveal that alloy fluctuations can open "percolative" pathways that promote transport for the electrons and holes into the quantum well region. Such an effect is neglected in conventional, and widely used transport simulations. Moreover, we find also that the resulting increased carrier density and alloy induced carrier localization effects significantly increase non-radiative Auger-Meitner recombination in comparison to the radiative process. Thus, to avoid such non-radiative process and potentially related material degradation, a careful design (wider well, multi quantum wells) of the active region is required to improve the efficiency of deep UV light emitters.

We show the importance of using a thermodynamically consistent flux discretization when describing drift-diffusion processes within light emitting diode simulations. Using the classical Scharfetter-Gummel scheme with Fermi-Dirac statistics is an example of such an inconsistent scheme. In this case, for an (In,Ga)N multi quantum well device, the Fermi levels show steep gradients on one side of the quantum wells which are not to be expected. This result originates from neglecting diffusion enhancement associated with Fermi-Dirac statistics in the numerical flux approximation. For a thermodynamically consistent scheme, such as the SEDAN scheme, the spikes in the Fermi levels disappear. We will show that thermodynamic inconsistency has far reaching implications on the current-voltage curves and recombination rates.

International audience; The efficient and reliable computation of guided modes in photonic crystal wave-guides is of great importance for designing optical devices. Transparent boundary conditions based on Dirichlet-to-Neumann operators allow for an exact computation of well-confined modes and modes close to the band edge in the sense that no modelling error is introduced. The well-known super-cell method, on the other hand, introduces a modelling error which may become prohibitively large for guided modes that are not well-confined. The Dirichlet-to-Neumann transparent boundary conditions are, however, not applicable for all frequencies as they are not uniquely defined and their computation is unstable for a countable set of frequencies that correspond to so called Dirichlet eigenvalues. In this work we describe how to overcome this theoretical difficulty introducing Robin-to-Robin transparent boundary conditions whose construction do not exhibit those forbidden frequencies. They seem, hence, well suited for an exact and reliable computation of guided modes in photonic crystal wave-guides.

International audience; Despite considerable progress in their process technology during the last years, vertical GaN power transistors are currently not finding market entry due to the small size and high cost of native GaN substrates. This issue can in principle be circumvented by using heteroepitaxial GaN on more affordable substrates. Recently, first demonstrations of vertical diodes [1] and transistors [2] for GaN-on-silicon have been published where vertical current flow was enabled by backside removal of the silicon substrate and the isolating buffer layers.

We propose a new numerical 2-point flux for a quasilinear convection-diffusion equation. This numerical flux is shown to be an approximation of the numerical flux derived from the solution of a two-point Dirichlet boundary value problem for the projection of the continuous flux onto the line connecting neighboring collocation points. The later approach generalizes an idea first proposed by Scharfetter and Gummel for linear drift-diffusion equations. We establish first that the new flux satisfies sufficient properties ensuring the convergence of the associate finite volume scheme, while respecting the maximum principle. Then, we pay attention to the long time behavior of the scheme: we show relative entropy decay properties satisfied by the new numerical flux as well as by the generalized Scharfetter-Gummel flux. The proof of these properties uses a generalization of some discrete (and continuous) log-Sobolev inequalities. The corresponding decay of the relative entropy of the continuous solution is proved in the appendix. Some 1D numerical experiments confirm the theoretical results.

In this work, we study the impact that random alloy fluctuations have on the distribution of electrons and holes across the active region of a (In,Ga)N/GaN multi-quantum well based light emitting diode (LED). To do so, an atomistic tight-binding model is employed to account for alloy fluctuations on a microscopic level and the resulting tight-binding energy landscape forms input to a drift-diffusion model. Here, quantum corrections are introduced via localization landscape theory and we show that when neglecting alloy disorder our theoretical framework yields results similar to commercial software packages that employ a self-consistent Schroedinger-Poisson-drift-diffusion solver. Similar to experimental studies in the literature, we have focused on a multi-quantum well system where two of the three wells have the same In content while the third well differs in In content. By changing the order of wells in this multicolor quantum well structure and looking at the relative radiative recombination rates of the different emitted wavelengths, we (i) gain insight into the distribution of carriers in such a system and (ii) can compare our findings to trends observed in experiment. Our results indicate that the distribution of carriers depends significantly on the treatment of the quantum well microstructure. When including random alloy fluctuations and quantum corrections in the simulations, the calculated trends in the relative radiative recombination rates as a function of the well ordering are consistent with previous experimental studies. The results from the widely employed virtual crystal approximation contradict the experimental data. Overall, our work highlights the importance of a careful and detailed theoretical description of the carrier transport in an (In,Ga)N/GaN multi-quantum well system to ultimately guide the design of the active region of III-N-based LED structures., 12 pages, 6 figures

In this paper, we consider a drift-diffusion charge transport model for perovskite solar cells, where electrons and holes may diffuse linearly (Boltzmann approximation) or nonlinearly (e.g. due to Fermi-Dirac statistics). To incorporate volume exclusion effects, we rely on the Fermi-Dirac integral of order −1 when modeling moving anionic vacancies within the perovskite layer which is sandwiched between electron and hole transport layers. After non-dimensionalization, we first prove a continuous entropy-dissipation inequality for the model. Then, we formulate a corresponding two-point flux finite volume scheme on Voronoi meshes and show an analogous discrete entropy-dissipation inequality. This inequality helps us to show the existence of a discrete solution of the nonlinear discrete system with the help of a corollary of Brouwer's fixed point theorem and the minimization of a convex functional. Finally, we verify our theoretically proven properties numerically, simulate a realistic device setup and show exponential decay in time with respect to the L2 error as well as a physically and analytically meaningful relative entropy.

We derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we provide rigorous proof to the results introduced by Forest, Pradel, and Sab (Int. J. Solids Struct. 38 (26-27): 4585-4608 ’01). Depending on how different characteristic lengths of the domain scale with respect to the Cosserat intrinsic length, we obtain either an effective classical Cauchy continuum or an effective Cosserat continuum. Moreover, we provide some corrector type results for each case.

This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and uniqueness theorems for sweeping trajectories corresponding to various classes of control functions acting in moving sets. Then we establish quantitative stability results, which provide efficient estimates on the sweeping trajectory dependence on controls and initial values. Our final topic, accomplished in finite-dimensional state spaces, is deriving new necessary optimality and suboptimality conditions for sweeping control systems with endpoint constrains by using constructive discrete approximations.

Wick polynomials and Wick products are studied in the context of noncommutative probability theory. It is shown that free, Boolean, and conditionally free Wick polynomials can be defined and related through the action of the group of characters over a particular Hopf algebra. These results generalize our previous developments of a Hopf-algebraic approach to cumulants and Wick products in classical probability theory.

In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regularity of the target function and is optimal both for the least-square (prediction) error and for the reproducing kernel Hilbert space (reconstruction) norm error. It is based on a modified Lepskii balancing principle using a varying family of norms.

We construct an explicit transitive free action of a Banach space of H\"older functions on the space of branched rough paths, which yields in particular a bijection between theses two spaces. This endows the space of branched rough paths with the structure of a principal homogeneous space over a Banach space and allows to characterize its automorphisms. The construction is based on the Baker-Campbell-Hausdorff formula, on a constructive version of the Lyons-Victoir extension theorem and on the Hairer-Kelly map, which allows to describe branched rough paths in terms of anisotropic geometric rough paths., Comment: Final version to appear in Proceedings of the London Mathematical Society. 34 pages

Existence and uniqueness for rough flows, transport and continuity equations driven by general geometric rough paths are established., 20 pages

International audience; In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order sufficient conditions relying on the Goh transform.

In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions. The appendix provides an example illustrating the applicability of our results., Comment: This is the first part of a work on optimality conditions for a control problem of a semilinear heat equation. More precisely, the full version, available at arXiv:1906.00237v1, has been divided in two, resulting in the current manuscript (that corresponds to Part I) and arXiv:1909.05056 (which is Part II)

International audience; We study a non-linear statistical inverse problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization) approach to estimate the quantity for the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonov functional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoretical analysis for the minimizer of the Tikhonov regularization scheme using the concept of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions.

Spin structures realized in magnetic materials with competing exchange interactions depend crucially on weak additional interactions, such as relativistic magnetic anisotropies, farther-neighbor exchanges, etc. This is the case in the natural magnetic mineral linarite, which has attracted a lot of attention due to its rich phase diagram. Electron spin resonance (ESR) is a sensitive experimental technique that allows to probe the presence and magnitude of magnetic anisotropies. The authors have measured the ESR modes in linarite over a broad frequency range and for various field geometries. The accompanying theoretical analysis provides accurate estimates for the magnetic anisotropy constants that, in turn, influence the presence of exotic multipolar states.

Malliavin calculus is implemented in the context of [M. Hairer, A theory of regularity structures, Invent. Math. 2014]. This involves some constructions of independent interest, notably an extension of the structure which accomodates a robust, and purely deterministic, translation operator, in $L^2$-directions, between "models". In the concrete context of the generalized parabolic Anderson model in 2D - one of the singular SPDEs discussed in the afore-mentioned article - we establish existence of a density at positive times., Minor revision of [v1]. This version published in Journal of Functional Analysis, Volume 272, Issue 1, 1 January 2017, Pages 363-419

International audience; We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Rie-mannian geometry. The results are new and extend the class of equations studied so far by the last two authors.

We consider one-dimensional Mott variable-range hopping with a bias, and prove the linear response as well as the Einstein relation, under an assumption on the exponential moments of the distances between neighboring points. In a previous paper \cite{FGS} we gave conditions on ballisticity, and proved that in the ballistic case the environment viewed from the particle approaches, for almost any initial environment, a given steady state which is absolutely continuous with respect to the original law of the environment. Here, we show that this bias--dependent steady state has a derivative at zero in terms of the bias (linear response), and use this result to get the Einstein relation. Our approach is new: instead of using e.g. perturbation theory or regeneration times, we show that the Radon-Nikodym derivative of the bias--dependent steady state with respect to the equilibrium state in the unbiased case satisfies an $L^p$-bound, $p>2$, uniformly for small bias. This $L^p$-bound yields, by a general argument not involving our specific model, the statement about the linear response., 35 pages, 1 figure

International audience; Few-cycle pulse characterization methods face a serious challenge in providing sufficient signal-to-noise ratios together with superior spectral fidelity, as imposed by phase-matching conditions and linear dispersion effects. Here we investigate the effect of linear dispersion inside the nonlinear medium inherently present in such arrangements. We demonstrate that pulse characterization using a cross-polarized wave generation dispersion scan is surprisingly insensitive to the group-velocity dispersion itself. We characterize sub-4 fs pulses at 780 nm center the wavelength utilizing crystals of different thicknesses, yielding nearly identical pulse shapes. Numerical simulations shed light on this behavior indicating practical limits of usable medium lengths.

In the current version we present a translation into English of the main derivations, which first appeared on September 2, 2018 in Russian, extend the analysis from the case of strongly convex objective to the case of uniformly convex objectives and add the numerical analysis of our results; International audience; We consider convex optimization problems with the objective function having Lipshitz-continuous $p$-th order derivative, where $p\geq 1$. We propose a new tensor method, which closes the gap between the lower $O\left(\varepsilon^{-\frac{2}{3p+1}} \right)$ and upper $O\left(\varepsilon^{-\frac{1}{p+1}} \right)$ iteration complexity bounds for this class of optimization problems. We also consider uniformly convex functions, and show how the proposed method can be accelerated under this additional assumption. Moreover, we introduce a $p$-th order condition number which naturally arises in the complexity analysis of tensor methods under this assumption. Finally, we make a numerical study of the proposed optimal method and show that in practice it is faster than the best known accelerated tensor method. We also compare the performance of tensor methods for $p=2$ and $p=3$ and show that the 3rd-order method is superior to the 2nd-order method in practice.

International audience

Coherent beam combining (CBC) of high brightness tapered amplifiers (TPAs) is a promising approach for the development of high power semiconductor laser sources with excellent beam quality and offers a pathway to future direct diode high brightness system [1]. Operation of the amplifiers in quasi continuous wave (QCW) mode allows to overcome the thermal limitations in the amplifiers and to test their full power scaling potential. Additionally, high brightness QCW sources with high spectral purity are in demand as NIR pump sources for nonlinear frequency conversion to address medical applications of modulated high power visible laser sources. In this paper we discuss dynamic effects in pulsed high brightness tapered amplifiers and demonstrate their coherent superposition for brightness scaling. We use state-of the art TPAs with the so called ELOD2 epitaxial design, which allows us to maintain close-to-diffraction limited beam quality at high powers [2,3].

The paper is devoted to evolution equations of the form $$\begin{aligned} \frac{\partial }{\partial t}u(t) = -(A + B(t))u(t), \quad t \in {\mathcal {I}}= [0,T], \end{aligned}$$ on separable Hilbert spaces where A is a non-negative self-adjoint operator and \(B(\cdot )\) is family of non-negative self-adjoint operators such that \(\mathrm {dom}(A^{\alpha }) \subseteq \mathrm {dom}(B(t))\) for some \({\alpha }\in [0,1)\) and the map \(A^{-{\alpha }}B(\cdot )A^{-{\alpha }}\) is Holder continuous with the Holder exponent \({\beta }\in (0,1)\). It is shown that the solution operator U(t, s) of the evolution equation can be approximated in the operator norm by a combination of semigroups generated by A and B(t) provided the condition \({\beta }> 2{\alpha }-1\) is satisfied. The convergence rate for the approximation is given by the Holder exponent \({\beta }\). The result is proved using the evolution semigroup approach.

International audience; High brightness diode laser beam combining techniques are in demand for efficient high power nonlinear conversion. Coherent beam combining (CBC) is the only method that has the potential for brightness scaling by maintaining one single narrow spectral linewidth. CBC in a master oscillator power amplifier (MOPA) configuration using a small number of efficiently cooled tapered amplifiers is a promising approach for efficient brightness scaling in a simple architecture. We present the application of such a source based on CBC of three tapered amplifiers seeded by a DFB laser at λ = 976 nm for second harmonic generation (SHG). A maximum power of 2.1 W at 488 nm was generated by SHG in a MgO:PPLN bulk crystal limited by thermal effects. A clear benefit of the beam clean-up resulting from the CBC setup was documented leading to an improved nonlinear efficiency. As part of our ongoing studies into further brightness scaling in CBC architectures, we present an experimental analysis of the phase dynamics of tapered amplifiers in quasi continuous operation (QCW) at high currents. Furthermore, we are investigating different amplifier designs for improved beam quality at high powers and therefore improved combining efficiency.

We report on a coherent beam combination of three high-brightness tapered amplifiers, which are seeded by a single-frequency laser at λ = 976 nm in a simple architecture with efficiently cooled emitters. The maximal combined power of 12.9 W is achieved at a combining efficiency of > 65%, which is limited by the amplifiers’ intrinsic beam quality. The coherent combination cleans up the spatial profile, as the central lobe’s power content increases by up to 86%. This high-brightness infrared beam is converted into the visible by second harmonic generation. This results in a high non-linear conversion efficiency of 4.5%/W and a maximum power over 2 W at 488 nm, which is limited by thermal effects in the periodically poled lithium niobate (PPLN).

A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture parsimoniously key stylized facts of the entire implied volatility surface, including extreme skews that were thought to be outside the scope of stochastic volatility. On the mathematical side, Markovianity and, partially, semi-martingality are lost. In this paper we show that Hairer's regularity structures, a major extension of rough path theory, which caused a revolution in the field of stochastic partial differential equations, also provides a new and powerful tool to analyze rough volatility models., Dedicated to Professor Jim Gatheral on the occasion of his 60th birthday

International audience; Special issue, containing papers by leading specialists in control theory and optimisation, dedicated to Guenter Leugering. It is continued as the next, also special, issue (2/2019)

International audience; The optimal stopping problem arising in the pricing of American options can be tackled by the so called dual martingale approach. In this approach, a dual problem is formulated over the space of adapted martingales. A feasible solution of the dual problem yields an upper bound for the solution of the original primal problem. In practice, the optimization is performed over a finite-dimensional subspace of martingales. A sample of paths of the underlying stochastic process is produced by a Monte-Carlo simulation, and the expectation is replaced by the empirical mean. As a rule the resulting optimization problem, which can be written as a linear program, yields a martingale such that the variance of the obtained estimator can be large. In order to decrease this variance, a penalizing term can be added to the objective function of the pathwise optimization problem. In this paper, we provide a rigorous analysis of the optimization problems obtained by adding different penalty functions. In particular, a convergence analysis implies that it is better to minimize the empirical maximum instead of the empirical mean. Numerical simulations confirm the variance reduction effect of the new approach.

In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise. In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants. We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature. We present these invariant features in an algebraic framework, and we develop some of their basic properties., 18 pages, 1 figure

International audience; We demonstrate coherent beam combining of four high brightness tapered amplifiers in pulsed, quasi continuous wave (QCW) operation, seeded by a 976 nm laser diode. The maximum power of 22.7 W was achieved with > 64 % combining efficiency in a close to diffraction limited beam. We discuss turn-on dynamics of tapered amplifiers operated in pulsed mode in detail.

Stochastic geometry models are used to study wireless networks, particularly cellular phone networks, but most of the research focuses on the typical user, often ignoring atypical events, which can be highly disruptive and of interest to network operators. We examine atypical events when a unexpected large proportion of users are disconnected or connected by proposing a hybrid approach based on ray launching simulation and point process theory. This work is motivated by recent results using large deviations theory applied to the signal-to-interference ratio. This theory provides a tool for the stochastic analysis of atypical but disruptive events, particularly when the density of transmitters is high. For a section of a European city, we introduce a new stochastic model of a single network cell that uses ray launching data generated with the open source RaLaNS package, giving deterministic path loss values. We collect statistics on the fraction of (dis)connected users in the uplink, and observe that the probability of an unexpected large proportion of disconnected users decreases exponentially when the transmitter density increases. This observation implies that denser networks become more stable in the sense that the probability of the fraction of (dis)connected users deviating from its mean, is exponentially small. We also empirically obtain and illustrate the density of users for network configurations in the disruptive event, which highlights the fact that such bottleneck behaviour not only stems from too many users at the cell boundary, but also from the near-far effect of many users in the immediate vicinity of the base station. We discuss the implications of these findings and outline possible future research directions., 8 pages, 11 figures

International audience; We devise and analyze arbitrary-order nonconforming methods for the discretization of the viscosity-dependent Stokes equations on simplicial meshes. We keep track explicitly of the viscosity and aim at pressure-robust schemes that can deal with the practically relevant case of body forces with large curl-free part in a way that the discrete velocity error is not spoiled by large pressures. The method is inspired from the recent Hybrid High-Order (HHO) methods for linear elasticity. After elimination of the auxiliary variables by static condensation, the linear system to be solved involves only discrete face-based velocities, which are polynomials of degree $k \ge 0$, and cell-wise constant pressures. Our main result is a pressure-independent energy-error estimate on the velocity of order $(k+1)$. The main ingredient to achieve pressure-independence is the use of a divergence-preserving velocity reconstruction operator in the discretization of the body forces. We also prove an $L^2$-pressure estimate of order $(k+1)$ and an $L^2$-velocity estimate of order $(k+2)$, the latter under elliptic regularity. The local mass and momentum conservation properties of the discretization are also established. Finally, two-and three-dimensional numerical results are presented to support the analysis.

The requirements for coherent combination of high power GaAs-based single-pass tapered amplifiers are studied. Changes to the epitaxial layer structure are shown to bring higher beam quality and hence improved combining efficiency for one fixed device geometry. Specifically, structures with large vertical near field and low wave-guiding from the active region show 10% higher beam quality and coherent combining efficiency than reference devices. As a result, coherent combining efficiency is shown to be limited by beam quality, being directly proportional to the power content in the central lobe across a wide range of devices with different construction. In contrast, changes to the in-plane structure did not improve beam quality or combining efficiency. Although poor beam quality does correlate with increased optical intensities near the input aperture, locating monolithically-integrated absorption regions in these areas did not lead to any performance improvement. However, large area devices with subsequently improved cooling do achieve higher output powers. Phase noise can limit coherent combining, but this is shown to be small and independent of device design. Overall, tapered amplifiers are well suited for high power coherent combining applications.

International audience; We give a review of results on the operator-norm convergence of the Trotter product formula on Hilbert and Banach spaces, which is focused on the problem of its convergence rates. Some recent results concerning evolution semigroups are presented in details.

International audience; We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold diffusion is called drifted Oscillating Brownian motion.For this continuously observed diffusion, the maximum likelihood estimator coincide with a quasi-likelihood estimator with constant diffusion term. We show that this estimator is the limit, as observations become dense in time, of the (quasi)-maximum likelihood estimator based on discrete observations. In long time, the asymptotic behaviors of the positive and negative occupation times rule the ones of the estimators. Differently from most known results in the literature, we do not restrict ourselves to the ergodic framework: indeed, depending on the signs of the drift, the process may be ergodic, transient or null recurrent. For each regime, we establish whether or not the estimators are consistent; if they are, we prove the convergence in long time of the properly rescaled difference of the estimators towards a normal or mixed normal distribution. These theoretical results are backed by numerical simulations.

We revise the operator-norm convergence of the Trotter product formula for a pair {A,B} of generators of semigroups on a Banach space. Operator-norm convergence holds true if the dominating operator A generates a holomorphic contraction semigroup and B is a A-infinitesimally small generator of a contraction semigroup, in particular, if B is a bounded operator. Inspired by studies of evolution semigroups it is shown in the present paper that the operator-norm convergence generally fails even for bounded operators B if A is not a holomorphic generator. Moreover, it is shown that operator norm convergence of the Trotter product formula can be arbitrary slow., 12 pages

In this paper we study the Brinkman model as a unified framework to allow the transition between the Darcy and the Stokes problems. We propose an unconditionally stable low-order finite element approach, which is robust with respect to the whole range of physical parameters, and is based on the combination of stabilized equal-order finite elements with a non-symmetric penalty-free Nitsche method for the weak imposition of essential boundary conditions. In particular, we study the properties of the penalty-free Nitsche formulation for the Brinkman setting, extending a recently reported analysis for the case of incompressible elasticity (Boiveau and Burman, IMA J. Numer. Anal. 36 (2016) 770-795). Focusing on the two-dimensional case, we obtain optimal a priori error estimates in a mesh-dependent norm, which, converging to natural norms in the cases of Stokes or Darcy ows, allows to extend the results also to these limits. Moreover, we show that, in order to obtain robust estimates also in the Darcy limit, the formulation shall be equipped with a Grad-Div stabilization and an additional stabilization to control the discontinuities of the normal velocity along the boundary. The conclusions of the analysis are supported by numerical simulations.

Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results.

International audience

International audience; Improved diode laser beam combining techniques are in strong demand for applications in material processing. Coherent beam combining (CBC) is the only combining approach that has the potential to maintain or even improve all laser properties, and thus has high potential for future systems. As part of our ongoing studies into CBC of diode lasers, we present recent progress in the coherent superposition of high-power single-pass tapered laser amplifiers. The amplifiers are seeded by a DFB laser at λ = 976 nm, where the seed is injected into a laterally single-mode ridge-waveguide input section. The phase pistons on each beam are actively controlled by varying the current in the ridge section of each amplifier, using a sequential hill-climbing algorithm, resulting in a combined beam with power fluctuations of below 1%. The currents into the tapered sections of the amplifiers are separately controlled, and remain constant. In contrast to our previous studies, we favour a limited number of individual high-power amplifiers, in order to preserve a high extracted power per emitter in a simple, low-loss coupling arrangement. Specifically, a multi-arm interferometer architecture with only three devices is used, constructed using 6 mm-long tapered amplifiers, mounted junction up on C-mounts, to allow separate contact to single mode and amplifier sections. A maximum coherently combined power of 12.9 W is demonstrated in a nearly diffraction-limited beam, corresponding to a 65% combining efficiency, with power mainly limited by the intrinsic beam quality of the amplifiers. Further increased combined power is currently sought.

We develop Gibbs sampling based techniques for learning the optimal content placement in a cellular network. A collection of base stations are scattered on the space, each having a cell (possibly overlapping with other cells). Mobile users request for downloads from a finite set of contents according to some popularity distribution. Each base station can store only a strict subset of the contents at a time; if a requested content is not available at any serving base station, it has to be downloaded from the backhaul. Thus, there arises the problem of optimal content placement which can minimize the download rate from the backhaul, or equivalently maximize the cache hit rate. Using similar ideas as Gibbs sampling, we propose simple sequential content update rules that decide whether to store a content at a base station based on the knowledge of contents in neighbouring base stations. The update rule is shown to be asymptotically converging to the optimal content placement for all nodes. Next, we extend the algorithm to address the situation where content popularities and cell topology are initially unknown, but are estimated as new requests arrive to the base stations. Finally, improvement in cache hit rate is demonstrated numerically., 32 pages

International audience; Periodic self-organization of matter beyond the diffraction limit is a puzzling phenomenon, typicalboth for surface and bulk ultrashort laser processing. Here we compare the mechanisms of periodicnanostructure formation on the surface and in the bulk of fused silica. We show that volumenanogratings and surface nanoripples having subwavelength periodicity and oriented perpendicularto the laser polarization share the same electromagnetic origin. The nanostructure orientation isdefined by the near-field local enhancement in the vicinity of the inhomogeneous scattering centers.The periodicity is attributed to the coherent superposition of the waves scattered at inhomogeneities.Numerical calculations also support the multipulse accumulation nature of nanogratings formationon the surface and inside fused silica. Laser surface processing by multiple laser pulses promotes thetransition from the high spatial frequency perpendicularly oriented nanoripples to the low spatialfrequency ripples, parallel or perpendicular to the laser polarization. The latter structures also share theelectromagnetic origin, but are related to the incident field interference with the scattered far-field ofrough non-metallic or transiently metallic surfaces. The characteristic ripple appearances are predictedby combined electromagnetic and thermo-mechanical approaches and supported by SEM images of thefinal surface morphology and by time-resolved pump-probe diffraction measurements.

International audience; We describe the coherent beam combining of three high-power tapered laser amplifiers seeded by a DFB laser at λ = 976 nm, and demonstrate a combined power of 12.9 W in a close to diffraction-limit beam at a combining efficiency of > 65%. We use individual devices on C-mounts in a multi-arm interferometer. The phase pistons of each beam are matched by automatically controlling the ridge current of the amplifiers. Increased power per element was achieved by making use of a simplified, efficiently cooled single emitter-based optical system.

International audience; Fully implicit time-space discretizations applied to the two-phase Darcy flow problem lead to the systems of nonlinear equations, which are traditionally solved by some variant of Newton's method. The efficiency of the resulting algorithms heavily depends on the choice of the primary unknowns since Newton's method is not invariant with respect to a nonlinear change of variable. In this regard the role of capillary pressure/saturation relation is paramount because the choice of primary unknowns is restricted by its shape. We propose an elegant mathematical framework for two-phase flow in heterogeneous porous media resulting in a family of formulations, which apply to general monotone capillary pressure/saturation relations and handle the saturation jumps at rocktype interfaces. The presented approach is applied to the hybrid dimensional model of two phase water-gas Darcy flow in fractured porous media for which the fractures are modeled as interfaces of co-dimension one. The problem is discretized using an extension of Vertex Approximate Gradient scheme. As for the phase pressure formulation, the discrete model requires only two unknowns by degree of freedom.

The recent findings of line narrowing in Raman-active continuous-wave-pumped gas [1] showed that the Stokes scattering occurs in a Lamb-Dicke regime and is associated to formation of array of deep subwavelength nanotraps, which resulted in a sub-recoil linewidth Stokes radiation [1]. The results also showed that this nanotrap lattice exhibits a macroscopic motion. Here we present theoretical and numerical analysis of this phenomenon, addressing the peculiarities of field distribution and fascinating effect of nanotrap lattice in motion.

Recent results in laser beam delivery and ultra-short pulse (USP) compression using hypocycloid-core Kagome hollow-core photonic crystal fibers (HC-PCFs) [1] proved that this type of optical fiber is an excellent candidate as a photonic component for these applications. For example, it has been demonstrated that the fiber guides up to 1 mJ of600 fs long pulses with no damage, and by a simple choice of gas and fiber dispersion, the authors achieved both USP guidance with no pulse broadening nor narrowing, guidance with self-phase modulation (SPM) spectral broadening, and finally guidance with over 10-fold self-compression using solitonic dynamics. However, these compression results necessitated both fiber gas-loading-system and tailored fiber-fabrication, which are not necessarily accessible to the broader research community. Here, we report on a set of results of self-compression of a USP laser based on a commercially available Kagome fiber (PMC-C-YB-7C from GLOphotonics [2]) and with no need of gas loading management. The compression relies on pulse dynamics near the photoionization threshold, which shows a strong and abrupt self-compression via the formation of a soliton at a well-defined pulse energy value and then its breakup at higher energy values [3]. By simply adjusting the fiber length from 10 cm to 4 m, we achieved compression of an initial 600 fs from Yb-doped USP-laser down to ∼20 fs (a compression ratio ∼30) over an energy span of 10–500 μJ. Figure 1(a) shows a summary of calculated (dotted curves) and measured (solid curves) pulse duration evolution with input energy for different fiber lengths. All curves show a “step shape” corresponding to this sudden compression, and the input energy value at which the self-compression occurs increases with shortening fiber length. A typical experimental FROG [4] evolution of such dynamic is shown in Figure 1 (c) for the case of 2 m fiber length resulting in a spectral broadening, a soliton red-shift and a strong pulse compression as the energy is increased. For this conditions, the maximum compression occurs at an energy around 60 μΐ. For higher energy, the pulse breaks up via soliton fission.

Results are presented for optimizing device-to-device communications in cellular networks, while maintaining spectral efficiency of the base-station-to-device downlink channel. We build upon established and tested stochastic geometry models of signal-to-interference ratio in wireless networks based on the Poisson point process, which incorporate random propagation effects such as fading and shadowing. A key result is a simple formula, allowing one to optimize the device-to-device spatial throughput by suitably adjusting the proportion of active devices. These results can lead to further investigation as they can be immediately applied to more sophisticated models such as studying multi-tier network models to address coverage in closed access networks., 6 pages, 4 figures. Submitted

International audience; Coherent beam combining (CBC) aims at increasing the spatial brightness of lasers. It consists in maintaining a constant phase relationship between different emitters, in order to combine them constructively in one single beam. We have investigated the CBC of an array of five individually-addressable high-power tapered laser diodes at λ = 976 nm, in two architectures: the first one utilizes the self-organization of the lasers in an interferometric extended-cavity, which ensures their mutual coherence; the second one relies on the injection of the emitters by a single-frequency laser diode. In both cases, the coherent combining of the phase-locked beams is ensured on the front side of the array by a transmission diffractive grating with 98% efficiency. The passive phase-locking of the laser bar is obtained up to 5 A (per emitter). An optimization algorithm is implemented to find the proper currents in the five ridge sections that ensured the maximum combined power on the front side. Under these conditions we achieve a maximum combined power of 7.5 W. In the active MOPA configuration, we can increase the currents in the tapered sections up to 6 A and get a combined power of 11.5 W, corresponding to a combining efficiency of 76%. It is limited by the beam quality of the tapered emitters and by fast phase fluctuations between emitters. Still, these results confirm the potential of CBC approaches with tapered lasers to provide a high-power and high-brightness beam, and compare with the current state-of-the-art with laser diodes.