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Entropy solutions of a diffusion equation with discontinuous hysteresis and their finite volume approximation
Get PDFWe provide a finite volume approximation in dimension d≥1 to a quasilinear parabolic equation with discontinuous hysteresis modelling a phase change, arising as a singluar limit of a pseudo-parabolic regularisation of a foward-backward diffusion equation. The convergence of the numerical solution to a suitable weak entropy solutions is shown under a parallelism assumption between the nonlinearities driving the evolution in each phase. The main challenge lies in the treatment of the discontinuous hysteresis operator in the proof of the compactness of the sequence of approximate solutions. This is achieved by regularising the hysteresis operator with a continuous one for which Hilpert inequalities are accessible and let us obtain crucial uniform translation estimates in L1 in space. Numerical simulations, computed using a Julia-based framework for the finite volume discretisation of reaction-diffusion equations, are shown
Less Interaction with Forward Models in Langevin Dynamics: Enrichment and Homotopy
No full textEnsemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted covariance estimates rely on successive evaluations of the forward model or its gradient. A main drawback of these methods hence is their vast number of required forward calls as well as their possible lack of convergence in the case of more involved posterior measures such as multimodal distributions. The goal of this paper is to address these challenges to some extend. First, several possible adaptive ensemble enrichment strategies that successively enlarge the number of particles in the underlying Langevin dynamics are discusses that in turn lead to a significant reduction of the total number of forward calls. Second, analytical consistency guarantees of the ensemble enrichment method are provided for linear forward models. Third, to address more involved target distributions, the method is extended by applying adapted Langevin dynamics based on a homotopy formalism for which convergence is proved. Finally, numerical investigations of several benchmark problems illustrates the possible gain of the proposed method, comparing it to state-of-the-art Langevin samplers
A Stabilized Total Pressure-Formulation of the Biot's Poroelasticity Equations in Frequency Domain: Numerical Analysis and Applications
No full textThis work focuses on the numerical solution of the dynamics of a poroelastic material in the frequency domain. We provide a detailed stability analysis based on the application of the Fredholm alternative in the continuous case, considering a total pressure formulation of the Biot's equations. In the discrete setting, we propose a stabilized equal order finite element method complemented by an additional pressure stabilization to enhance the robustness of the numerical scheme with respect to the fluid permeability. Utilizing the Fredholm alternative, we extend the well-posedness results to the discrete setting, obtaining theoretical optimal convergence for the case of linear finite elements. We present different numerical experiments to validate the proposed method. First, we consider model problems with known analytic solutions in two and three dimensions. As next, we show that the method is robust for a wide range of permeabilities, including the case of discontinuous coefficients. Lastly, we show the application for the simulation of brain elastography on a realistic brain geometry obtained from medical imaging
Synchronization between Kerr cavity solitons and broad laser pulse injection
Get PDFThe synchronization of a soliton frequency comb in a Kerr cavity with pulsed laser injection is studied numerically. A neutral delay differential equation is used to model the light dynamics in the cavity. This model allows for the investigation of both cases where the pulse repetition period is close to the cavity round-trip time and where the repetition period of the injection pulses is close to a rational fraction M/N of the round-trip time. It is demonstrated that solitons can exist in this latter case, provided that the injection pulses are of a higher amplitude, which is directly proportional to the number M. Furthermore, it is shown that the synchronization range of the solitons is also proportional to the number M . The solitons excited by pulses with a period slightly different from the M : N -resonance can be destabilized by the Andronov--Hopf bifurcation, which occurs when the injection level at the soliton position decreases to M times the injection amplitude corresponding to the saddle-node bifurcation in a model equation with uniform injection
ICSI 2024
No full textThis two-volume set LNCS 14788 and 14789 constitutes the refereed post-conference proceedings of the 15th International Conference on Advances in Swarm Intelligence, ICSI 2024, held in Xining, China, during August 23–26, 2024. The 74 revised full papers presented in these proceedings were carefully reviewed and selected from 156 submissions. The papers are organized in the following topical sections: Part I - Particle swarm optimization; Swarm intelligence computing; Differential evolution; Evolutionary algorithms; Multi-agent reinforcement learning & Multi-objective optimization. Part II - Route planning problem; Machine learning; Detection and prediction; Classification; Edge computing; Modeling and optimization & Analysis of review
Bayesian Estimation of Laser Linewidth From Delayed Self-Heterodyne Measurements
No full textWe present a statistical inference approach to estimate the frequency noise characteristics of ultra-narrow linewidth lasers from delayed self-heterodyne beat note measurements using Bayesian inference. Particular emphasis is on the estimation of the intrinsic (Lorentzian) laser linewidth. The approach is based on a statistical model of the measurement process, taking into account the effects of the interferometer as well as the detector noise. Our method therefore yields accurate results even when the intrinsic linewidth plateau is obscured by detector noise. The regression is performed on periodogram data in the frequency domain using a Markov chain Monte Carlo method. By using explicit knowledge about the statistical distribution of the observed data, the method yields good results already from a single time series and does not rely on averaging over many realizations, since the information in the available data is evaluated very thoroughly. The approach is demonstrated for simulated time series data from a stochastic laser rate equation model with 1/f-type non-Markovian noise
Modeling and Simulation of a Cascaded Polarization-Coupled System of Broad-Area Semiconductor Lasers
No full textWe consider a brightness- and power-scalable rectified polarization beam combining scheme for high-power, broad-area edge-emitting semiconductor laser diodes. The coupling of 2m emitters is achieved through Lyot-filtered optical reinjection from a specially designed multi-stage external cavity, which forces individual diodes to lase on interleaved frequency combs with overlapping envelopes. Simulations of up to sixteen coupled emitters and analysis of the calculated beams suggest that, under ideal conditions, a beam coupling efficiency of approximately 90% can be expected. Reducing optical losses within the external cavity is crucial for improving this efficiency in experimental systems
Design of very-large area photonic crystal surface emitting lasers with an all-semiconductor photonic crystal
No full textWe report on the design of a photonic crystal surface emitting laser (PCSEL) with an all-semiconductor (InGaP/GaAs) photonic crystal suitable for very-large-area emission and high-power operation. Using coupled-wave theory for PCSELs we model infinite- and finite-size cavity PCSELs and show that a photonic crystal unit cell with square lattice periodicity and a rotated and stretched triangular feature is suitable for the realization of PCSELs with very large areas (1 mm<L < 3 mm for a square cavity of size L × L) while maintaining high mode discrimination between the fundamental laser mode and higher order cavity modes as well as high external efficiency. This was achieved by exploiting a single-lattice photonic crystal unit cell design that minimizes one-dimensional coupling in the photonic crystal, providing a promising alternative to double-lattice PCSELs
All spatial graphs with weak long-range effects have chemical distance comparable to Euclidean distance
Get PDFThis note provides a sufficient condition for linear lower bounds on chemical distances (compared to the Euclidean distance) in general spatial random graphs. The condition is based on the scarceness of long edges in the graph and weak correlations at large distances and is valid for all translation invariant and locally finite graphs that fulfil these conditions. The proof is based on a renormalisation scheme introduced by Berger [arXiv: 0409021 (2004)]
Persistent hubs in CMJ branching processes with independent increments and preferential attachment trees
Get PDFA sequence of trees (Tn) n ∈ N contains a emphpersistent hub, or displays emphdegree centrality, if there is a fixed node of maximal degree for all sufficiently large n ∈ N. We derive sufficient criteria for the emergence of a persistent hub in genealogical trees associated with Crump-Mode-Jagers branching processes with independent waiting times between births of individuals, and sufficient criteria for the non-emergence of a persistent hub. We also derive criteria for uniqueness of these persistent hubs. As an application, we improve results in the l iterature concerning the emergence of unique persistent hubs in generalised preferential attachment trees, in particular, allowing for cases where there may not be a emphMalthusian parameter associated with the process. The approach we use is mostly self-contained, and does not rely on prior results about Crump-Mode-Jagers branching processe