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In this paper, we propose a high order conservative semi-Lagrangian scheme (SL) for the ellipsoidal BGK model of the Boltzmann transport equation. To avoid the time step restriction induced by the convection term, we adopt the semi-Lagrangian approach. For treating the nonlinear stiff relaxation operator with small Knudsen number, we employ high order $L$-stable diagonally implicit Runge-Kutta time discretization or backward difference formula. The proposed implicit schemes are designed to update solutions explicitly without resorting to any Newton solver. We present several numerical tests to demonstrate the accuracy and efficiency of the proposed methods. These methods allow us to obtain accurate approximations of the solutions to the Navier-Stokes equations or the Boltzmann equation for moderate or relatively large Knudsen numbers, respectively.

Metasurface-based optical components are becoming increasingly important due to their unparalleled ability to shape and manipulate electromagnetic waves across a wide range of frequencies, from microwave and terahertz to visible light. In particular, planar meta-mirrors with high efficiency and broad operational bandwidth are expected to play a significant role in shaping channel characteristics for 6G communication links due to their reduced SWaP (size, weight, and power) and integrability. However, achieving large fractional bandwidth and high efficiency simultaneously using metasurface-based mirrors or reflectors have been challenging. In this work, highly efficient broadband focusing meta-mirror has been designed, fabricated and experimentally demonstrated. The device operates in the D-Band (110-170 GHz) and beyond (up to 200 GHz), and exhibits unmatched performance in terms of combined fractional bandwidth (58\%) and energy efficiency, exceeding 53\% over the entire bandwidth with a peak of 77.4\% at frequency 135 GHz. The high performance and advantageous design tradeoffs of this meta-mirror are discussed in terms of the principles of low Fresnel number optics.

Chirality, an intrinsic preference for a specific handedness, is a fundamental characteristic observed in nature. In magnetism, magnetic chirality arises from the anti-symmetric Dzyaloshinskii-Moriya interaction in competition with the symmetric Heisenberg exchange interaction. Traditionally, the anti-symmetric interaction has been considered minor relative to the symmetric interaction. In this study, we demonstrate an observation of giant magnetic chirality during the dimensionality crossover of magnetic materials from three-dimensional to two-dimensional. The ratio between the anti-symmetric and symmetric interactions exhibits a reversal in their dominance over this crossover, overturning the traditional consideration. This observation is validated theoretically using a non-local interaction model and tight-binding calculation with distinct pairing schemes for each exchange interaction throughout the crossover. Additional experiments investigating the asphericity of orbital moments corroborate the robustness of our findings. Our findings highlight the critical role of dimensionality in shaping magnetic chirality and offer strategies for engineering chiral magnet states with unprecedented strength, desired for the design of spintronic materials., Comment: 21 pages, 4 figures

The dimensionality of vortical structures has recently been extended beyond two dimensions, providing higher-order topological characteristics and robustness for high-capacity information processing and turbulence control. The generation of high-dimensional vortical structures has mostly been demonstrated in classical systems through the complex interference of fluidic, acoustic, or electromagnetic waves. However, natural materials rarely support three- or higher-dimensional vortical structures and their physical interactions. Here, we present a high-dimensional gradient thickness optical cavity (GTOC) in which the optical coupling of planar metal-dielectric multilayers implements topological interactions across multiple dimensions. Topological interactions in high-dimensional GTOC construct non-trivial topological phases, which induce high-dimensional vortical structures in generalized parameter space in three, four dimensions, and beyond. These emergent high-dimensional vortical structures are observed under electro-optic tomography as optical vortex dynamics in two-dimensional real-space, employing the optical thicknesses of the dielectric layers as synthetic dimensions. We experimentally demonstrate emergent vortical structures, optical vortex lines and vortex rings, in a three-dimensional generalized parameter space and their topological transitions. Furthermore, we explore four-dimensional vortical structures, termed optical vortex sheets, which provide the programmability of real-space optical vortex dynamics. Our findings hold significant promise for emulating high-dimensional physics and developing active topological photonic devices., Comment: 21 pages,5 figures

Lens tension is essential for accommodative vision but remains challenging to measure with precision. Here, we present an optical coherence elastography (OCE) technique that quantifies both the tension and elastic modulus of lens tissue and capsule. This method derives mechanical parameters from surface wave dispersion across a critical frequency range of 1-30 kHz. Using isolated lenses from six-month-old pigs, we measured intrinsic anterior capsular tensions of 0-20 kPa and posterior capsular tensions of 40-50 kPa, induced by intra-lenticular pressure at the cortical surface. Young's modulus (E) was 1.9 MPa for anterior capsules and 1.2 MPa for posterior capsules. Tensions in cortical tissue (E ~ 10 kPa) were below 1 kPa. Biaxial zonular stretching (~4% strain) increased anterior capsular tension from near zero to 64 kPa. This acousto-optical method holds significant promise for diagnosing and managing accommodative dysfunctions through lens mechanics assessment in clinical settings.

Brillouin Light Scattering (BLS) spectroscopy is a non-invasive, non-contact, label-free optical technique that can provide information on the mechanical properties of a material on the sub-micron scale. Over the last decade it has seen increased applications in the life sciences, driven by the observed significance of mechanical properties in biological processes, the realization of more sensitive BLS spectrometers and its extension to an imaging modality. As with other spectroscopic techniques, BLS measurements not only detect signals characteristic of the investigated sample, but also of the experimental apparatus, and can be significantly affected by measurement conditions. The aim of this consensus statement is to improve the comparability of BLS studies by providing reporting recommendations for the measured parameters and detailing common artifacts. Given that most BLS studies of biological matter are still at proof-of-concept stages and use different--often self-built--spectrometers, a consensus statement is particularly timely to assure unified advancement., Comment: Main Text & Supplementary Text: 56 pages, 3 Figures, 2 Supplementary Figures, 1 Supplementary Table

BGK (Bhatnagar-Gross-Krook) model is a relaxation-type model of the Boltzmann equation, which is popularly used in place of the Boltzmann equation in physics and engineering. In this paper, we address the ill-posedness problem for the BGK model, in which the solution instantly escapes the initial solution space. For this, we propose two ill-posedness scenarios, namely, the homogeneous and the inhomogeneous ill-posedness mechanisms. In the former case, we find a class of spatially homogeneous solutions to the BGK model, where removing the small velocity part of the initial data triggers ill-posedness by increasing temperature. For the latter, we construct a spatially inhomogeneous solution to the BGK model such that the local temperature constructed from the solution has a polynomial growth in spatial variable. These ill-posedness properties for the BGK model pose a stark contrast with the Boltzmann equation for which the solution map is, at least for a finite time, stable in the corresponding solution spaces., Comment: 79 pages, 1 figures; remark 1.5 and acknowledgement modified, references added for section 1

In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling high-dimensional partial differential equations (PDEs), challenges arise when applying quadrature rules for accurate integral evaluation in the BGK operator, which can compromise the mesh-free benefit and increase computational costs. To address this, we leverage the canonical polyadic decomposition structure of SPINNs and the linear nature of moment calculation, achieving a substantial reduction in computational expense for quadrature rule application. The multi-scale nature of the particle density function poses difficulties in precisely approximating macroscopic moments using neural networks. To improve SPINN training, we introduce the integration of Gaussian functions into SPINNs, coupled with a relative loss approach. This modification enables SPINNs to decay as rapidly as Maxwellian distributions, thereby enhancing the accuracy of macroscopic moment approximations. The relative loss design further ensures that both large and small-scale features are effectively captured by the SPINNs. The efficacy of our approach is demonstrated through a series of five numerical experiments, including the solution to a challenging 3D Riemann problem. These results highlight the potential of our novel method in efficiently and accurately addressing complex challenges in computational physics.

Nano-scale lasers harnessing metallic plasmons hold promise across physical sciences and industrial applications. Plasmons are categorized as surface plasmon polaritons (SPP) and localized surface plasmons (LSP). While SPP has gained popularity for nano-lasers by fitting a few cycles of SPP waves into resonators, achieving LSP lasing in single nanoparticles remains an elusive goal. Here, we highlight the equivalence of LSP and SPP within resonant systems and present lasers oscillating in the lowest-order LSP or, equivalently, half-cycle SPP. This diffraction-limited dipolar emitter is realized through strong coupling of plasmonic oscillation in gold and dielectric resonance in high-gain III-V semiconductor in the near infrared away from surface plasmon frequencies. The resulting single-mode stimulated emission peak exhibits linewidth Q factors over 50 at room temperature, with wide tunability spanning from 1190 to 1460 nm determined by resonator sizes ranging from 190 to 280 nm. A semiconductor laser model elucidates the temporal and spectral buildup dynamics under optical pumping. Notably, linewidth Q values surpassing 250 are attained from higher-order, isolated laser particles within live biological cells. These results offer fresh perspectives in nanophotonics and indicate promising opportunities for multiplexed biological applications.

Shear wave elastography (SWE) has emerged as a new imaging modality that brings tissue mechanical properties as biomarkers potentially useful for early and precise diagnosis. While different SWE methods have been proposed, how to relate the frequency SWE measurements to quasi-static stiffnesses of tissues sensed by cells when prestresses are involved remains challenging. Here we suggest an incremental dynamics theory for prestressed viscoelastic solids and investigate its application in SWE across a broad frequency range. To model the power-law dispersion relation with minimal parameters, we introduce the Kelvin-Voigt fractional derivation model (KVFD) in the constitutive modeling of material viscoelasticity. To validate the usefulness of the theory, we performed experiments on prestressed soft materials and biological tissues. The results show that the theoretical solution fits the experimental dispersion curve well over a broad frequency range and accurately captures the effect of prestress. The theory also reveals the correlation of phase velocities and attenuations of shear waves with principal stresses and leads to a method for probing the prestress in a viscoelastic solid without prior knowledge of the constitutive parameters as validated by our numerical experiments. Taken together, our results show that the theory presented here enables the development of spatially resolved SWE when high-frequency shear waves get involved, and provides insights into wave motions in soft materials subject to prestresses.

Dynamic locomotion in legged robots is close to industrial collaboration, but a lack of standardized testing obstructs commercialization. The issues are not merely political, theoretical, or algorithmic but also physical, indicating limited studies and comprehension regarding standard testing infrastructure and equipment. For decades, the approaches we have been testing legged robots were rarely standardizable with hand-pushing, foot-kicking, rope-dragging, stick-poking, and ball-swinging. This paper aims to bridge the gap by proposing the use of the linear impactor, a well-established tool in other standardized testing disciplines, to serve as an adaptive, repeatable, and fair disturbance rejection testing equipment for legged robots. A pneumatic linear impactor is also adopted for the case study involving the humanoid robot Digit. Three locomotion controllers are examined, including a commercial one, using a walking-in-place task against frontal impacts. The statistically best controller was able to withstand the impact momentum (26.376 kg$\cdot$m/s) on par with a reported average effective momentum from straight punches by Olympic boxers (26.506 kg$\cdot$m/s). Moreover, the case study highlights other anti-intuitive observations, demonstrations, and implications that, to the best of the authors' knowledge, are first-of-its-kind revealed in real-world testing of legged robots., Comment: A modified version of this preprint has been accepted at IEEE International Conference on Robotics and Automation (ICRA) 2024

Synthesis of thin films has traditionally relied upon slow, sequential processes carried out with substantial human intervention, frequently utilizing a mix of experience and serendipity to optimize material structure and properties. With recent advances in autonomous systems which combine synthesis, characterization, and decision making with artificial intelligence (AI), large parameter spaces can be explored autonomously at rates beyond what is possible by human experimentalists, greatly accelerating discovery, optimization, and understanding in materials synthesis which directly address the grand challenges in synthesis science. Here, we demonstrate autonomous synthesis of a contemporary 2D material by combining the highly versatile pulsed laser deposition (PLD) technique with automation and machine learning (ML). We incorporated in situ and real-time spectroscopy, a high-throughput methodology, and cloud connectivity to enable autonomous synthesis workflows with PLD. Ultrathin WSe2 films were grown using co-ablation of two targets and showed a 10x increase in throughput over traditional PLD workflows. Gaussian process regression and Bayesian optimization were used with in situ Raman spectroscopy to autonomously discover two distinct growth windows and the process-property relationship after sampling only 0.25% of a large 4D parameter space. Any material that can be grown with PLD could be autonomously synthesized with our platform and workflows, enabling accelerated discovery and optimization of a vast number of materials.

Understanding corneal stiffness is valuable for improving refractive surgery, detecting corneal abnormalities, and assessing intraocular pressure. However, accurately measuring the elastic properties, particularly the tensile and shear moduli that govern mechanical deformation, has been challenging. To tackle this issue, we have developed guided-wave optical coherence elastography that can simultaneously excite and analyze symmetric (S0) and anti-symmetric (A0) elastic waves in the cornea at frequencies around 10 kHz and allows us to extract tensile and shear properties from measured wave dispersion curves. By applying acoustoelastic theory that incorporates corneal tension and a nonlinear constitutive tissue model, we verified the technique using elastomer phantoms and ex vivo porcine corneas and investigated the dependence on intraocular pressure. For two healthy human subjects, we measured a mean tensile modulus of 3.6 MPa and a mean shear modulus of 76 kPa in vivo with estimated errors of < 4%. This technique shows promise for the quantitative biomechanical assessment of the cornea in a clinical setting.

Objective: The mechanical properties of corneal tissues play a crucial role in determining corneal shape and have significant implications in vision care. This study aimed to address the challenge of obtaining accurate in vivo data for the human cornea. Methods: We have developed a high-frequency optical coherence elastography (OCE) technique using shear-like antisymmetric (A0)-mode Lamb waves at frequencies above 10 kHz. Results: By incorporating an anisotropic, nonlinear constitutive model and utilizing the acoustoelastic theory, we gained quantitative insights into the influence of corneal tension on wave speeds and elastic moduli. Our study revealed significant spatial variations in the shear modulus of the corneal stroma on healthy subjects for the first time. The central cornea exhibited a shear modulus of 74 kPa, while the corneal periphery showed a decrease to 41 kPa. The limbus demonstrated an increased shear modulus exceeding 100 kPa. We obtained wave displacement profiles that are consistent with highly anisotropic corneal tissues. Conclusion: Our approach enabled precise measurement of corneal tissue elastic moduli in situ with high precision (< 7%) and high spatial resolution (< 1 mm). Significance: The high-frequency OCE technique holds promise for biomechanical evaluation in clinical settings, providing valuable information for refractive surgeries, degenerative disorder diagnoses, and intraocular pressure assessments.

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs and approximate highly complex solution functions. The number of training points (collocation points) required on these challenging PDEs grows substantially, but it is severely limited due to the expensive computational costs and heavy memory overhead. To overcome this issue, we propose a network architecture and training algorithm for PINNs. The proposed method, separable PINN (SPINN), operates on a per-axis basis to significantly reduce the number of network propagations in multi-dimensional PDEs unlike point-wise processing in conventional PINNs. We also propose using forward-mode automatic differentiation to reduce the computational cost of computing PDE residuals, enabling a large number of collocation points (>10^7) on a single commodity GPU. The experimental results show drastically reduced computational costs (62x in wall-clock time, 1,394x in FLOPs given the same number of collocation points) in multi-dimensional PDEs while achieving better accuracy. Furthermore, we present that SPINN can solve a chaotic (2+1)-d Navier-Stokes equation significantly faster than the best-performing prior method (9 minutes vs 10 hours in a single GPU), maintaining accuracy. Finally, we showcase that SPINN can accurately obtain the solution of a highly nonlinear and multi-dimensional PDE, a (3+1)-d Navier-Stokes equation. For visualized results and code, please see https://jwcho5576.github.io/spinn.github.io/., Comment: To appear in NeurIPS 2023 (28 pages, 13 figures). workshop paper: arXiv:2211.08761

Unlike the case for classical particles, the literature on BGK type models for relativistic gas mixture is extremely limited. There are a few results %\cite{Kremer,Kremer3,KP} in which such relativistic BGK models for gas mixture are employed to compute transport coefficients. However, to the best knowledge of authors, relativistic BGK models for gas mixtures with complete presentation of the relaxation operators are missing in the literature. In this paper, we fill this gap by suggesting a BGK model for relativistic gas mixtures for which the existence of each equilibrium coefficients in the relaxation operator is rigorously guaranteed in a way that all the essential physical properties are satisfied such as the conservation laws, the H-theorem, the capturing of the correct equilibrium state, the indifferentiability principle, and the recovery of the classical BGK model in the Newtonian limit.

In this work, we suggest a system of differential equations that quantitatively models the formulation and evolution of a trend cycle through the consideration of underlying dynamics between the trend participants. Our model captures the five stages of a trend cycle, namely, the onset, rise, peak, decline, and obsolescence. It also provides a unified mathematical criterion/condition to characterize the fad, fashion and classic. We prove that the solution of our model can capture various trend cycles. Numerical simulations are provided to show the expressive power of our model.

In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We obtain sharp estimates on the dynamic regret of the algorithm when the regular part of the cost is convex and smooth. If the Bregman distance is given by the Euclidean distance, our result also improves the previous work in two ways: (i) We establish a sharper regret bound compared to the previous work in the sense that our estimate does not involve $O(T)$ term appearing in that work. (ii) We also obtain the result when the domain is the whole space $\mathbb{R}^n$, whereas the previous work was obtained only for bounded domains. We also provide numerical tests for problems involving the errors in the gradient and proximal operator., Comment: 16 pages, 5 figures

Gradient-push algorithm has been widely used for decentralized optimization problems when the connectivity network is a direct graph. This paper shows that the gradient-push algorithm with stepsize $\alpha>0$ converges exponentially fast to an $O(\alpha)$-neighborhood of the optimizer under the assumption that each cost is smooth and the total cost is strongly convex. Numerical experiments are provided to support the theoretical convergence results.

Bhatnagar-Gross-Krook (BGK) equation is a relaxation model of the Boltzmann equation which is widely used in place of the Boltzmann equation for the simulation of various kinetic flow problems. In this work, we study the asymptotic stability of the BGK model when the initial data is not necessarily close to the global equilibrium pointwisely. Due to the highly nonlinear structure of the relaxation operator, the argument developed to derive the bootstrap estimate for the Boltzmann equation leads to a weaker estimate in the case of the BGK model, which does not exclude the possible blow-up of the perturbation. To overcome this issue, we carry out a refined analysis of the macroscopic fields to guarantee that the system transits from a highly nonlinear regime into a quadratic nonlinear regime after a long but finite time, in which the highly nonlinear perturbative term relaxes to essentially quadratic nonlinearity., Comment: 34 pages, 1 figures

Nanolasers have great potential as both on-chip light sources and optical barcoding particles. We demonstrate ultrasmall InGaP and InGaAsP disk lasers with diameters down to 360 nm (198 nm in height) in the red spectral range. Optically pumped, room-temperature, single-mode lasing was achieved from both disk-on-pillar and isolated particles. When isolated disks were placed on gold, plasmon polariton lasing was obtained with Purcell-enhanced stimulated emission. UV lithography and plasma ashing enabled the fabrication of nanodisks on a wafer-scale, with intended random size variation. Silica-coated nanodisk particles generated stable sub-nanometer spectra from within biological cells across an 80 nm bandwidth from 635 to 715 nm., Comment: 25 pages, 5 main figures, 8 supplementary figures, 3 supplementary tables

Visualizing elastic waves by noninvasive imaging has been useful for analyzing the mechanical properties of materials and tissues. However, the maximum wave frequency of elastography has been limited to ~10 kHz due to the finite sensitivity to small vibration and finite imaging speed. Here, we present an optical coherence elastography technique that extends the frequency range to MHz by noise reduction, anti-aliasing demodulation, and advanced wave analysis. Our system can measure the stiffness of hard (GPa) materials including bones with mm-scale resolution and characterize soft, viscoelastic materials from 100 Hz to 1 MHz. The dispersion of Rayleigh surface waves over the wide frequency range allowed us to profile depth-dependent shear modulus (10 kPa to 100 MPa) in cartilages ex vivo and the human skin in vivo. This technique opened a new window for the characterization of materials in situ with 3-dimensional resolution.

In this paper, we perform the convergence analysis of unsupervised Legendre--Galerkin neural networks (ULGNet), a deep-learning-based numerical method for solving partial differential equations (PDEs). Unlike existing deep learning-based numerical methods for PDEs, the ULGNet expresses the solution as a spectral expansion with respect to the Legendre basis and predicts the coefficients with deep neural networks by solving a variational residual minimization problem. Since the corresponding loss function is equivalent to the residual induced by the linear algebraic system depending on the choice of basis functions, we prove that the minimizer of the discrete loss function converges to the weak solution of the PDEs. Numerical evidence will also be provided to support the theoretical result. Key technical tools include the variant of the universal approximation theorem for bounded neural networks, the analysis of the stiffness and mass matrices, and the uniform law of large numbers in terms of the Rademacher complexity.

Physics-informed neural networks (PINNs) have emerged as new data-driven PDE solvers for both forward and inverse problems. While promising, the expensive computational costs to obtain solutions often restrict their broader applicability. We demonstrate that the computations in automatic differentiation (AD) can be significantly reduced by leveraging forward-mode AD when training PINN. However, a naive application of forward-mode AD to conventional PINNs results in higher computation, losing its practical benefit. Therefore, we propose a network architecture, called separable PINN (SPINN), which can facilitate forward-mode AD for more efficient computation. SPINN operates on a per-axis basis instead of point-wise processing in conventional PINNs, decreasing the number of network forward passes. Besides, while the computation and memory costs of standard PINNs grow exponentially along with the grid resolution, that of our model is remarkably less susceptible, mitigating the curse of dimensionality. We demonstrate the effectiveness of our model in various PDE systems by significantly reducing the training run-time while achieving comparable accuracy. Project page: https://jwcho5576.github.io/spinn/, Comment: To appear in NeurIPS 2022 Workshop on The Symbiosis of Deep Learning and Differential Equations (DLDE) - II, 12 pages, 5 figures, full paper: arXiv:2306.15969

Predicting volatility is important for asset predicting, option pricing and hedging strategies because it cannot be directly observed in the financial market. The Black-Scholes option pricing model is one of the most widely used models by market participants. Notwithstanding, the Black-Scholes model is based on heavily criticized theoretical premises, one of which is the constant volatility assumption. The dynamics of the volatility surface is difficult to estimate. In this paper, we establish a novel architecture based on physics-informed neural networks and convolutional transformers. The performance of the new architecture is directly compared to other well-known deep-learning architectures, such as standard physics-informed neural networks, convolutional long-short term memory (ConvLSTM), and self-attention ConvLSTM. Numerical evidence indicates that the proposed physics-informed convolutional transformer network achieves a superior performance than other methods., Comment: Submitted to Quantitative Finance (under final review); Revised Version

Embodying bosonic and electrically interactive characteristics in two-dimensional space, excitons in transition-metal dichalcogenides (TMDCs) have garnered considerable attention. The realisation and application of strong-correlation effects, long-range transport, and valley-dependent optoelectronic properties require customising exciton decay dynamics. Strains, defects, and electrostatic doping effectively control the decay dynamics but significantly disturb the intrinsic properties of TMDCs, such as electron band structure and exciton binding energy. Meanwhile, vacuum-field manipulation provides an optical alternative for engineering radiative decay dynamics. Planar mirrors and cavities have been employed to manage the light-matter interactions of two-dimensional excitons. However, the conventional flat platforms cannot customise the radiative decay landscape in the horizontal TMDC plane or independently control vacuum field interference at different pumping and emission frequencies. Here, we present a meta-mirror resolving the issues with more optical freedom. For neutral excitons of the monolayer MoSe2, the meta-mirror manipulated the radiative decay rate by two orders of magnitude, depending on its geometry. Moreover, we experimentally identified the correlation between emission intensity and spectral linewidth. The anisotropic meta-mirror demonstrated polarisation-dependent radiative decay control. We expect that the meta-mirror platform will be promising to tailor the two-dimensional distributions of lifetime, density, and diffusion of TMDC excitons in advanced opto-excitonic applications.