497 Search Results

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic andmore » parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.« less

Reflected computer vision targets are a powerful tool for measurement of mirror surface shape, with several important advantages over traditional fringe deflectometry methods. This method was first presented in 2021 and has undergone significant improvement and demonstration since. We describe a new baseline system using reflected computer vision targets, and present results from a large-scale measurement campaign conducted on both commercial heliostats and test mirrors in the laboratory. Calibration of the measurement system with photogrammetry allows for accurate measurement without careful control of target shape or camera position. Overall, the results show that a baseline setup using this method achievesmore » measurement uncertainties in the slope error root-mean-square less than ±0.11 milliradian due to a series of repeatability conditions, varying sample position, rotation, lighting, camera settings, and system rebuild and recalibration. We present a detailed description of the setup, the results generated by this measurement tool, repeated measurement results, and the strengths and limitations of this metrology system.« less

The propagation of intense, partially spatially coherent laser beams in a medium with instantaneous third-order susceptibility is studied analytically and numerically. For sufficiently high power relative to that required for nonlinear self-focusing, the propagation initially proceeds in two stages. In the first stage, spatial coherence builds up, and in the second stage, the number of speckles reduces. Once the degree of coherence is sufficiently high, whole-beam self-focusing occurs. The beam power is mostly confined within the initial spot radius. Two analytical approaches for describing the evolution of the beam are presented. The method of moments leads to an analytical solutionmore » for the rms spot radius that is in excellent agreement with simulations. This method does not require any knowledge of the field statistics beyond the initial conditions and provides no information about the evolution of the individual speckles. The other approach employs a self-similar solution for the second-order coherence function of the field and assumes that the fourth-order coherence function is factorizable and obeys complex circular Gaussian random statistics. The latter method also leads to an analytical expression for the spot radius, but its predictions for the qualitative evolution of the speckles disagree with wave-optics simulations.« less

Urbanization, i.e., increasing urban development areas in a watershed, is well known as a major cause of increasing flood magnitudes. This study analyzes the observed flood peaks at 262 watersheds in the U.S. Mid-Atlantic region with varying levels of urban development and free from reservoir impacts. Our analysis reveals an interesting, V-shaped nonlinear behavior: flood peaks first decrease and then increase with increasing percentage of urban development area at the watershed scale (PDAW), with the shift occurring at a PDAW threshold of around 10%. Regression analyses suggest that the V-shaped pattern primarily results from complex interactions among climate conditions (e.g.,more » storm-event rainfall) and landscape properties (e.g., elevation, distance to the coast). A neural network model was then developed to capture such interactions, satisfactorily reproducing the V-shaped pattern with an R-squared value of 0.58, RMSE of 6.72 mm/day, and NSE of 0.55. These findings highlight the need to account for nonlinear dynamics in flood prediction and management in the coastal environment.« less

Temperature variation is often considered an undesirable factor in ultrasonic testing, as wave velocity is highly sensitive to thermal fluctuations. However, completely eliminating the temperature effect is difficult, particularly in tests requiring precise velocity measurements. Recently, a method called Thermal Modulation of Nonlinear Ultrasonics (TMNL) has been developed. Instead of eliminating the thermal effect, the TMNL method leverages the temperature variation as a driving force to stimulate the nonlinear response of the medium and modulate the ultrasonic waves propagating in it. These modulated waves can then be used to evaluate the nonlinear behaviours of the test medium. This paper presentsmore » a focused review of the TMNL technique, including its theoretical foundations, particularly the conceptual challenges in integrating thermal effects into classical acoustoelastic theory, and recent applications in non-destructive evaluation (NDE). Three case studies are presented to demonstrate TMNL’s application in detecting microcracking in concrete, assessing ageing in polymer materials, and enabling temperature compensation in acoustoelastic tests. In conclusion, the review also summarises related studies, including photothermal crack modulation, and discusses current limitations and future directions of TMNL in elastic media.« less

Triggered by advances in atomic-layer exfoliation and growth techniques, along with the identification of a wide range of extraordinary physical properties in self-standing films consisting of one or a few atomic layers, two-dimensional (2D) materials such as graphene, transition metal dichalcogenides (TMDs), and other van der Waals (vdW) crystals now constitute a broad research field expanding in multiple directions through the combination of layer stacking and twisting, nanofabrication, surface-science methods, and integration into nanostructured environments. Photonics encompasses a multidisciplinary subset of those directions, where 2D materials contribute remarkable nonlinearities, long-lived and ultraconfined polaritons, strong excitons, topological and chiral effects, susceptibilitymore » to external stimuli, accessibility, robustness, and a completely new range of photonic materials based on layer stacking, gating, and the formation of moiré patterns. These properties are being leveraged to develop applications in electro-optical modulation, light emission and detection, imaging and metasurfaces, integrated optics, sensing, and quantum physics across a broad spectral range extending from the far-infrared to the ultraviolet, as well as enabling hybridization with spin and momentum textures of electronic band structures and magnetic degrees of freedom. The rapid expansion of photonics with 2D materials as a dynamic research arena is yielding breakthroughs, which this Roadmap summarizes while identifying challenges and opportunities for future goals and how to meet them through a wide collection of topical sections prepared by leading practitioners.« less

Digital signal processing is the cornerstone of several modern-day technologies, yet in multiple applications it faces critical bottlenecks related to memory and speed constraints. Thanks to recent advances in metasurface design and fabrication, light-based analog computing has emerged as a viable option to partially replace or augment digital approaches. Several light-based analog computing functionalities have been demonstrated using patterned flat optical elements, with great opportunities for integration in compact nanophotonic systems. So far, however, the available operations have been restricted to the linear regime, limiting the impact of this technology to a compactification of Fourier optics systems. In this paper,more » we introduce nonlinear operations to the field of metasurface-based analog optical processing, demonstrating that nonlinear optical phenomena, combined with nonlocality in flat optics, can be leveraged to synthesize kernels beyond linear Fourier optics, paving the way to a broad range of new opportunities. As a practical demonstration, we report the experimental synthesis of a class of nonlinear operations that can be used to realize broadband, polarization-selective analog-domain edge detection.« less

Recently, a new class of nonlinearly partitioned Runge–Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations y' = F(y, y). The target class of problems are those in which different scales, stiffnesses, or physics are coupled in a nonlinear way, wherein the desired partition cannot be written in a classical additive or component-wise fashion. Here we use a rooted-tree analysis to derive full-order conditions for NPRKM methods, where M denotes the number of nonlinear partitions. Due to the nonlinear coupling and thereby the mixed product differentials, it turns out that the standard node-colored rooted treemore » analysis used in analyzing ODE integrators does not naturally apply. Instead we develop a new edge-colored rooted-tree framework to address the nonlinear coupling. The resulting order conditions are enumerated, are provided directly for up to fourth order with M = 2 and third order with M = 3, and are related to existing order conditions of additive and partitioned RK methods. We conclude with an example that shows how the nonlinear order conditions can be used to obtain an embedded estimate of the state-dependent nonlinear coupling strength in a dynamical system.« less

Agriculture is crucial for global food supply and dominates the Earth's land surface. It is unknown, however, how slow but relentless changes in climate mean state, versus random extreme conditions arising from changing variability, will affect agroecosystems' carbon fluxes, energy fluxes, and crop production. We used an advanced weather generator to partition changes in mean climate state versus variability for both temperature and precipitation, producing forcing data to drive factorial-design simulations of US Midwest agricultural regions in the Energy Exascale Earth System Model. We found that an increase in temperature mean lowers stored carbon, plant productivity, and crop yield, andmore » tends to convert agroecosystems from a carbon sink to a source, as expected; it also can cause local to regional cooling in the earth system model through its effects on the Bowen Ratio. The combined effect of mean and variability changes on carbon fluxes and pools was nonlinear, that is, greater than each individual case. For instance, gross primary production reduces by 9%, 1%, and 13% due to change in mean temperature, change in temperature variability, and change in both temperature mean and variability, respectively. Overall, the scenario with change in both temperature and precipitation means leads to the largest reduction in carbon fluxes (-16% gross primary production), carbon pools (-35% vegetation carbon), and crop yields (-33% and -22% median reduction in yield for corn and soybean, respectively). By unambiguously parsing the effects of changing climate mean versus variability and quantifying their nonadditive impacts, this study lays a foundation for more robust understanding and prediction of agroecosystems' vulnerability to 21st-century climate change.« less

We demonstrate for the first time that the nonlinear saturation of neoclassical tearing modes (NTMs) can be found directly using a variational principle based on Taylor relaxation, without needing to simulate the intermediate, resistivity-dependent dynamics. As in previous investigations of classical tearing mode saturation (Loizu et al 2020 Phys. Plasmas 27 070701; Loizu and Bonfiglio 2023 J. Plasma Phys. 89 905890507), we make use of Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), an equilibrium solver based on the variational principle of the multi-region relaxed magnetohydrodynamics (MHDs), featuring stepped pressure profiles and arbitrary magnetic topology.more » We work in slab geometry and employ a simple bootstrap current model J_bs = C$$\boldsymbol{\nabla}$$p to study the bootstrap-driven tearing modes, scanning over the asymptotic matching parameter Δ' and bootstrap current strength. Saturated island widths produced by SPEC agree well with the predictions of an initial value resistive MHDs code (Huang and Bhattacharjee 2016 Astrophys. J. 818 20) while being orders of magnitude faster to calculate. Additionally, we observe good agreement with a simple analytical modified Rutherford equation, without requiring any fitting coefficients. The match is obtained for both linearly unstable classical tearing modes in the presence of bootstrap current, and NTMs, which are linearly stable but nonlinear-unstable due to the effects of the bootstrap current.« less