AI for Science

A regularized Boussinesq equation is studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi-Pasta-Ulam lattice with a general cubic interaction force. Explicit periodic traveling wave solutions in terms of Jacobi elliptic functions are classified, and their solitary-wave, kink, and trigonometric limits are obtained. The Whitham modulation equations describing slow modulations of periodic traveling wave solutions are derived using an averaged variational principle. The convexity (strict hyperbolicity, genuine nonlinearity) of the resulting hydrodynamic-type equations is examined numerically in general and analytically in the solitary-wave and harmonic limits. In particular, the loss of hyperbolicity and the formation of complex conjugate characteristic speeds is shown to lead to modulational instability of periodic traveling waves. The onset of modulational instability is verified by numerical computations of linearized spectra for periodic traveling waves and initial value problems that also reveal additional short-wave instabilities.

Arrays of neutral atoms present a promising system for quantum computing, quantum sensors, and other applications, several of which would profit from the ability to load, cool, and image the atoms in a finite magnetic field. In this work, we develop a technique to image and prepare $^{87}$Rb atom arrays in a finite magnetic field by combining EIT cooling with fluorescence imaging. We achieve an average readout fidelity of $99.7(1)\,\%$ at $98.2(3)\,\%$ survival probability and up to $68(2)\%$ single-atom stochastic loading probability in a 2.3 G magnetic field, with performance validated at fields up to 10 G. We further develop a model to predict the survival probability, which also agrees well with several other atom array experiments. Our technique cools both the axial and radial directions, and will enable future continuously-operated neutral atom quantum processors and quantum sensors.

Two-path complementarity in polarized interferometric fields is reconsidered by retaining the complete path--polarization density matrix instead of reducing the description to the path degree of freedom from the outset. The familiar relation connecting the Cartesian visibility components, path predictability, and reduced-state mixedness is recovered as a marginal consequence of the reduced path state and is not interpreted as a new complementarity law. Attention is focused instead on the full path--polarization description in a real reference basis adapted to the path and linear-polarization degrees of freedom. Within this framework, the normalized purity separates naturally into path, polarization, and path--polarization-correlation contributions, while the antisymmetric sector provides a sector-resolved measure of cohesion. The resulting decomposition identifies which parts of the complete state store phase-sensitive interferometric coherence and which contributions are removed when polarization is traced out. The formalism therefore provides a sector-resolved accounting of complementarity within the full path--polarization state and clarifies the connection between reduced visibility loss, polarization marking, path--polarization correlations, and quantum-eraser recovery. The present article establishes the framework and associated purity decomposition; a more detailed exploration of full path--polarization complementarity and its dynamical aspects is left for future work.

We determine the fully resolved equilibrium density profiles for two binary hard-sphere crystal structures using classical density functional theory through the White Bear II functional from fundamental measure theory. While for the substitutional crystal, in which some hard spheres are replaced by spheres of slightly smaller diameter, the density profiles are rather similar to the single-component case (narrow Gaussian peaks centered at fcc lattice sites), we observe a more complex behavior for the case of interstitial solid solutions, where the small species is fairly delocalized in the unit cell. Further, we compute the species-resolved inhomogeneous two-body direct correlation functions, depending on two three-dimensional vectors, for these two types of binary crystals. The large--large components are mainly determined by the vacancy concentration $n_\text{vac}$ and show a characteristic magnitude $\sim 1/n_\text{vac}$. Based on this observation, we propose a simple geometric picture. The components of the direct correlation function involving the small spheres substantially differ in interstitial solid solutions from those of the substitutional crystal.

Surfactants are amphiphilic molecules that are generally anisotropic rather than spherical. Their orientation is therefore governed by the interplay between shear-induced reorientation, thermal rotational diffusion, and energetic alignment with the interface. The relative importance of these processes is characterized by the rotational Peclet number, $Pe_r$. We show that this microscopic coupling between flow and surfactant orientation can give rise to new macroscopic interfacial phenomena, including a shear-dependent effective surface tension and non-trivial droplet deformation. To investigate this mechanism, we develop a phase-field model that incorporates both the surfactant concentration and its local average orientation (polarization field). Using perturbation theory, we derive an analytical expression for the effective surface tension, which depends not only on the surfactant concentration but also on the local shear rate. We then employ a hybrid numerical method to study the deformation of a surfactant-covered droplet under imposed shear flow. For small $Pe_r$, droplet deformation can be accurately captured by a modified Taylor and Maffettone-Minale theories. For large $Pe_r$, shear-induced reorientation strongly distorts the surfactant polarization, and the droplet deformation progressively approaches that of a pure (surfactant-free) droplet.

The surface states of certain topological phases can be linked to a quantum anomaly: the violation of a classical symmetry by a field theory via a non-conserved current. This has been generalized to the case of a non-Hermitian (NH) chiral anomaly affecting the surfaces states of an NH Weyl phase. Here, we show that the NH anomaly inflow is mediated by continnum Landau modes (CLMs): special eigenstates exhibiting both spatial localization and a continuous spectrum, contrary to the usual distinction between bound and free states. The number of anomaly-induced surface modes scales with the sample volume rather than its surface area, which is shown to be tied to the unusual multiplicity of the CLMs. The other properties of the CLMs, including their normalization conditions and localization scale, closely match the predictions of the NH field theory. Finally, we discuss the conditions under which these phenomena can be probed experimentally using metamaterials.

This article studies the temporal approximation of hyperbolic semilinear stochastic evolution equations with multiplicative Gaussian noise by Milstein-type schemes. We take the term hyperbolic to mean that the leading operator generates a contractive, not necessarily analytic $C_0$-semigroup. Optimal convergence rates are derived for the pathwise uniform strong error \[ E_h^\infty := \Big(\mathbb{E}\Big[\max_{1\le j \le M}\|U_{t_j}-u_j\|_X^p\Big]\Big)^{1/p} \] on a Hilbert space $X$ for $p\in [2,\infty)$. Here, $U$ is the mild solution and $u_j$ its Milstein approximation at time $t_j=jh$ with step size $h>0$ and final time $T=Mh>0$. For sufficiently regular nonlinearity and noise, we establish strong convergence of order one, with the error satisfying $E_h^\infty\lesssim h\sqrt{\log(T/h)}$ for rational Milstein schemes and $E_h^\infty \lesssim h$ for exponential Milstein schemes. This extends previous results from parabolic to hyperbolic SPDEs and from exponential to rational Milstein schemes. Moreover, root-mean-square error estimates are strengthened to pathwise uniform estimates. Numerical experiments validate the convergence rates for the stochastic Schrödinger equation. Further applications to Maxwell's and transport equations are included.

The open quantum Rabi model describes a two-level system coupled to a harmonic oscillator. A Gaussian phase transition for the nonequilibrium steady states has been predicted when the bosonic mode is soft and subject to damping. We show that oscillator dephasing is a relevant perturbation, which leads to a non-Gaussian phase transition and an intriguing cascade of instabilities for $k$-th order bosonic operators, as well as a jump in the steady-state qubit polarization. For the soft-mode limit, the equations of motion form a closed hierarchy and spectral properties can be efficiently studied. To this purpose, we establish a fruitful connection to non-Hermitian Hamiltonians. The results for the phase diagram, stability boundaries, and relevant observables are based on mean-field analysis, exact diagonalization, perturbation theory, and Keldysh field theory.

Kemeny's constant measures the efficiency of a Markov chain in traversing its states. We investigate whether structure-preserving perturbations to the transition probabilities of a reversible Markov chain can improve its connectivity while maintaining a fixed stationary distribution. Although the minimum achievable value for Kemeny's constant can be estimated, the required perturbations may be infeasible. We reformulate the problem as an optimization task, focusing on solution existence and efficient algorithms, with an emphasis on the problem of minimizing Kemeny's constant under sparsity constraints.

We investigate the dimension dependence of Bramble--Pasciak--Xu (BPX) preconditioners for high-dimensional partial differential equations and establish that the condition numbers of BPX-preconditioned systems grow only polynomially with the spatial dimension. Our analysis requires a careful derivation of the dimension dependence of several fundamental tools in the theory of finite element methods, including elliptic regularity, the Bramble--Hilbert lemma, trace inequalities, and inverse inequalities. We further analyze an averaged Scott--Zhang-type quasi-interpolation operator, and show that its associated constants scale polynomially with the dimension. Building on these ingredients, we prove a multilevel norm equivalence theorem and derive a BPX preconditioner with explicit polynomial bounds on its dimensional dependence. The analysis is motivated in part by recent tensor and quantum finite element methods, where dimension-explicit conditioning estimates for BPX preconditioners play an important role.

Photonic molecules support the excitation of higher-order states, which are otherwise hard to access at individual waveguides. In this work, we demonstrate the resonant excitation of photonic molecular states which evanescently couple to single-mode waveguides. We implement the experiments on femtosecond laser written photonic structures and demonstrate an efficient resonant excitation of higher-orbital states, optimized at specific wavelengths and propagation distances. We suggest the use of long photonic molecules as long-distance photonic links, and demonstrate strong coupling for very distant waveguides separated by 127 μm. We apply this concept to a one-dimensional lattice and demonstrate the excitation of topological edge states emerging due to the third-order next-neighbour interactions. Our findings demonstrate effective long-range evanescent coupling which could be a concrete solution for fiber-based photonic chips, topological physics emerging from long-range interactions, or fundamental studies of initially uncoupled systems.

Whether it is for solving nonlinear equations, optimization problems, or autonomous dynamical systems, fixed-point-type iterations are widely used in numerical sciences. On-the-fly reduced-order modelling (ROM) enables the construction of a low-dimensional, self-correcting approximation of the solution to this system during the iterative process, while removing the need to do an offline training phase and any dependence on a precomputed reduced basis (e.g., a fixed geometry or mesh). This technique has been used in specific fields before, including fluid-structure interactions and topology optimization, but no general study of this method has been done to the knowledge of the authors. A general method for accelerating fixed point schemes will be presented. We show that when the iteration mapping is contractive, the error of the approximate solution is guaranteed to be within the user-defined tolerance using inexact fixed-point theory. This methodology is then applied to the solution of systems of PDEs with a block Gauss-Seidel scheme. Errors due to the ROM are propagated through each iteration with respect to the computational graph of the system, which allows one to estimate whether the current iteration is still within the user-defined tolerance. Some working hypotheses necessary to observe a significant speedup and the limitations of the method are explored as well. As a numerical illustration, the methodology is applied to a multiphysics lid-driven cavity flow in two and three dimensions.

A highly exotic phenomenon in solid-state physics is the observation of magnetic quantum oscillations in insulators. For instance, in the Kondo insulator YbB$_{12}$ various groups reported the observation of such oscillations seemingly originating from Fermi surfaces, though this contradicts the concept of an insulator having no charged quasiparticles. In this study, we searched for quantum oscillations in YbB$_{12}$ by using bulk-sensitive ultrasonic experiments in high magnetic fields up to 65 T and down to 485 mK. For that, we utilized an YbB$_{12}$ single crystal that, in previous experiments, revealed oscillations in the magnetoresistance in the insulating state. We confirmed oscillation-like behavior of the magnetoresistance as well as field-dependent oscillations in the magnetocaloric effect. However, we could not observe magnetoacoustic quantum oscillations in the insulating state, only in the field-induced metallic state. In the insulating state, we found some anomalies in our ultrasound data, the origin of which remains elusive. Our findings provide further information on the puzzling behavior of the insulating state of YbB$_{12}$.

Dynamical systems are fundamental to modeling the natural world, yet modeling them involves a persistent trade-off: manually prescribed mechanistic models are interpretable by design but often overly simplistic and misspecified; in contrast, flexible data-driven neural methods lack physical insight. Hybrid modeling aims for the best of both worlds by combining a prescribed or symbolic, physics-based component with a flexible neural network. A critical challenge, however, is that the neural component may relearn mechanistic parts, yielding redundant and uninterpretable models, especially when the symbolic structure itself is discovered from data. Existing methods based on standard $L^2$ regularization rely on a projection argument that breaks when the symbolic component is learned through sparse discovery, allowing the neural augmentation to overlap with symbolic structure. We introduce \textbf{OrthoReg} (Orthogonal Regularization), which directly penalizes overlap between the symbolic and neural components, preventing symbolic structure from being absorbed by the neural residual. This yields a complementary decomposition: the symbolic part captures what the library can express, and the neural part captures what remains. On benchmark dynamical systems with partial library mismatch, OrthoReg improves symbolic recovery and out-of-distribution behavior.

Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a graph-based NCDE forecasting method that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, and offers both a lightweight graph-constrained variant and a more expressive variant, learning additional graph connections from data via adaptive graph convolutions. To systematically study when graph informedness is beneficial in forecasting, we devise a continuous advection simulation on directed graphs, yielding synthetic spatio-temporal datasets with known ground-truth flow structure. We then evaluate INDEQS on two real-world tasks: river discharge forecasting on a hydrological network and traffic flow prediction on PeMS08. Across these synthetic and real-world benchmarks, outer informedness consistently improves mean absolute error over an uninformed NCDE with comparable parameter count, particularly on larger graphs, while inner informedness offers a more parameter-efficient alternative when strict adherence to a known adjacency is desired. A comparison of discrete convolutional and continuous-time decoders further shows that continuous decoders yield better accuracy and greater temporal flexibility on real-world tasks. An implementation of INDEQS and the advection simulation is available at https://github.com/Mitchi1/indeqs.

This work investigates the application of a domain-shift aware neural network for regression tasks aimed at estimating unbalance masses in rotating shafts under varying operating conditions. Experimental data were collected from a test rig in which a primary shaft, equipped with a flange carrying unbalanced masses, was driven at different rotational speeds, while a secondary shaft could be optionally activated to introduce domain discrepancy. The unbalance masses were positioned at a fixed radial distance, and the dynamic response of the system was recorded using triaxial accelerometers. The inverse problem of mass estimation is formulated within a domain adaptation framework, where the network is trained with a maximum mean discrepancy strategy to align feature representations across source and target distributions. The results demonstrate the effectiveness of explicitly addressing domain shift in improving prediction accuracy, especially when the system's physical behavior and sources of domain discrepancy are not fully known and fall outside the training conditions. These findings highlight the potential of domain-shift aware models for regression tasks in Structural Health Monitoring.

We study the propagation of coupled surface and internal equatorial internal waves. A model of two vertically stratified fluid layers with different constant densities is employed. Taking Coriolis forces into account, we derive explicit solutions to the linearized governing equations which assumes irrotational fluid motion in both layers separately, and further obtain the dispersion relation which determines the phase speeds of propagating surface and internal waves. We prove a result on solutions to the dispersion relations which greatly simplifies our subsequent analysis of the nonlinear dynamical systems which describe the motion of the fluid in the upper layer. Phase portraits for all possible streamlines in both fluid layers are presented, while furthermore a Lagrangian description of the fluid flow is obtained, and the particle trajectories of the fluid particles are determined.

In a standard two-level Ramsey interferometer, the measured phase accumulates linearly during the interrogation time. Here, we introduce three-level Ramsey interferometry that employs a noncyclic geometric phase response to enhance phase sensing, with projected internal-path interference reshaping the mapping from accumulated signal phase to readout phase. Near a geodesic-closure transition, a small accumulated signal phase produces a sharply amplified readout-phase shift. We quantify the accompanying gain--visibility tradeoff and identify a finite operating window in which the amplified response yields a net signal-to-noise-ratio gain under technical-noise-limited conditions. By tuning an initial Ramsey phase offset, this high-slope window can be positioned at a desired operating point and sampled repeatedly with shorter cycles, providing a geometric shortcut to improved projected stability. More broadly, these results establish a multilevel Ramsey route to enhanced phase sensitivity in quantum platforms, where two signal-collecting internal paths interfere to produce a noncyclic geometric response.

We characterize two nested Walsh parity-check filters implemented on Quandela's Belenos cloud photonic processor in a single-photon eight-mode spatial register. The modes are indexed by the vertices of the cube $Q_3$. The filters realize the classical $[8,7,2]$ single-parity-check code, the zero-sum neutral subspace $\mathcal{N}$ and the $[8,4,4]$ extended Hamming code, the parity-checked subspace $\mathcal{S}\subset\mathcal{N}$ with one DC and three face-parity syndrome channels. These are first-quantized path/mode encodings of classical codes: the experiment verifies leakage suppression and syndrome routing, not error correction or protection against photon loss, and all probabilities are conditional on postselected single-photon detections. Across more than 340,000 detections, neutral inputs show residual DC-port leakage of $0.02\%$-$1.1\%$ (mean $0.6\%$), corresponding to $\approx21\times$ suppression relative to the ideal $0.125$ DC-capture baseline and $31.6\times$ relative to the measured non-neutral control. Injected DC contamination gives a monotonic soft error signal, and the three face-parity syndrome channels route to their predicted ports with $94$-$99\%$ selectivity. A sector-preserving unitary core keeps leakage far below non-neutral controls over one to three applications, with differences dominated by calibration and compilation systematics rather than gate-cycle physics. We quantify these limits, including fixed-pattern separator bias, $\pm 0.02$ calibration offsets, and compilation scatter near the $10^{-3}$ leakage level, and report a Hong-Ou-Mandel degradation episode in which suppression vanished and recovered after recalibration.

Interference of time-bin encoded signals over free-space optical channels typically requires stringent mode filtering on receivers due to wavefront distortions from atmospheric turbulence, conventionally addressed with adaptive optics. Passive multimode receivers based on field-widened interferometers present a compelling alternative, enabling direct interference without the overhead of wavefront correction. We demonstrate a field-widened interferometer design that is implemented solely with reflective surfaces and achieves a high interference visibility (greater than 0.97) for spatially multimode beams. The interference of the multimode beams is enabled by two imaging systems that consist of a cavity configuration between a spherical concave mirror and a flat mirror. The configuration enables small form-factors, is inherently achromatic, and is based on standard spherical mirrors which reduces the complexity of the system. The interferometer is applicable for spatially multimode and turbulent optical channels, such as satellite communication, and is designed for quantum systems that use time-bin encoded qubits.

We report the design, commissioning, and operation of deuterium-deuterium (DD) and deuterium-tritium (DT) gas delivery systems developed to load a diamond anvil cell (DAC) beam target for muon-catalyzed fusion (muCF). The DAC approach enables DT fuel to be compressed to GPa pressures at more than twice the liquid density and heated from cryogenic temperatures through 500 K, opening access to a substantially expanded parameter range for muCF kinetics and yield measurements. In this approach, DT is cryo-condensed to a liquid in a minichamber and then compressed in the DAC using a helium-driven pneumatic membrane, achieving high pressures in a millimeter-scale DT sample volume. A DD gas delivery system was designed and used to validate the experimental apparatus, measure the gas quantities needed for filling, develop operational experience, and collect kinetics and yield data with DD targets. The DT gas delivery system adds tritium-specific capabilities for inventory minimization, secondary containment, and activity monitoring. The DT system integrates depleted uranium storage beds and a liquid helium cryogenic condenser used for pressure building and cryopumping. High-purity delivery is provided by a rapid-response palladium permeator. The system is housed in a helium-atmosphere glovebox held at negative pressure with continuous cleanup. We present the process and instrumentation design, a failure modes and effects analysis (FMEA), and data from the experiment's in situ Raman spectrometer, which provides direct confirmation of target loading and composition through the optically clear diamond anvils. The 2024 and 2025 DT campaigns achieved repeatable target fills and operation with no measurable tritium releases to the stack, demonstrating safe, high-purity DT loading at novel density-temperature conditions for muCF studies.

Ionization stabilization is a well-known phenomenon in strongly driven Soft-Coulomb atomic models, where the ionization probability decrease as the field amplitude increases. In this work, we investigate how this mechanism is affected by introducing a repulsive Morse barrier into the binding potential, leading to a Morse-Soft-Coulomb (MsC) model. A systematic comparison between the Soft-Coulomb and Morse-Soft-Coulomb systems is performed for different values of the softening parameter. Ionization probabilities, escape-time maps computed on the field-free energy shell and representative trajectories reveal that the stabilization window observed in the Soft-Coulomb model is strongly suppressed in the Morse-Soft-Coulomb system. To elucidate the origin of this behavior, we analyze the corresponding Kramers-Henneberger effective potentials. While the Soft-Coulomb model develops a symmetric double-well structure supporting two equivalent trapping regions, the Morse-Soft-Coulomb potential exhibits a single effective minimum as a consequence of the broken left-right symmetry introduced by the Morse branch. The combined analysis of ionization probabilities, escape dynamics, representative trajectories, and Kramers-Henneberger potentials indicates that the suppression of stabilization is closely associated with the modification of the phase-space transport structures and the reduction of the effective trapping region induced by the Morse

The weakly nonlinear response of a homogeneous magnetised plasma is usually written as a double cyclotron-harmonic expansion. This representation is explicit, but the repeated use of the Jacobi-Anger expansion produces long sums of Bessel functions and nested resonance denominators. In the linear problem we recently obtained an alternative formulation by keeping the Larmor phase unexpanded and by evaluating the characteristic integral in terms of the newly introduced incomplete-Bessel function $G_μ(z,ψ)$. In this article we apply the same idea directly to the first nonlinear Vlasov-Maxwell equation. The nonlinear source contains the linear response of an inner mode. When this linear response is written in incomplete-Bessel form, the outer characteristic integral produces a bivariate orbit-resolvent $G_{μ,ν}^{(r)}(z,ψ;w,χ)$. This function emerges therefore as the natural orbit integral generated by the first nonlinear characteristic problem. We derive the nonlinear distribution function in terms of these bivariate functions, collect the identities needed for the current projection, recover an extension of the classical double-harmonic Liu-Tripathi formula by expansion, and indicate how the nonlinear susceptibility tensor is obtained from bivariate angular contractions.

Quantum technologies are rapidly advancing across multiple research domains, with a growing impact on biomedical imaging and sensing. We examine their emerging role in ophthalmology through four complementary directions: photon-limited retinal imaging, correlation based imaging, nanoscale optical probes, and quantum-limited visual perception. Advances in optical coherence tomography and single-photon detection enable imaging under strict photon budget constraints, reducing phototoxicity while preserving image quality. Correlation-based approaches, including ghost imaging, offer alternative strategies for image formation in low-light and scattering environments, although practical implementation remains limited by detection efficiency and acquisition time. In parallel, nanoscale optical platforms such as quantum dots provide tunable and photostable probes for enhanced contrast and targeted delivery, with ongoing challenges related to biocompatibility and clinical translation. Finally, experiments at the single-photon level and with structured light fields demonstrate how the visual system itself operates near physical detection limits and can be probed using controlled optical states. While many of these approaches remain at an early stage, they collectively illustrate how quantum and quantum-inspired methods may augment current ophthalmic imaging and diagnostic technologies while providing new tools for studying visual function under well-defined physical constraints.

Optical skyrmions possess topological polarization textures that can maintain topological robustness under external perturbations, making them promising carriers for disturbance-resistant optical information transmission. However, existing optical skyrmion generation schemes mostly rely on static optical elements or fixed nanostructures, making high-speed dynamic switching of the topological state difficult. Here, we propose a high-speed switchable optical skyrmion generator based on a patterned liquid-crystal spin-orbit device. The device employs the in-plane orientation of liquid crystals to imprint a fixed Pancharatnam-Berry geometric phase, while an applied voltage rapidly tunes the liquid-crystal retardance, enabling reversible switching between skyrmion and non-skyrmion states. Experimental results show that the device exhibits millisecond electrical response, with bidirectional response times of 1.76 ms and 0.72 ms, corresponding to an ideal cycling rate of approximately 403 Hz, making it the fastest switchable optical skyrmion generator to date. Furthermore, by exploiting this rapid topological refreshing capability, we demonstrate image encoding and decoding, providing a new liquid-crystal device platform for high-speed, refreshable, and disturbance-resistant topological optical information transmission.

High-refractive-index materials underpin a wide range of optical technologies, including communications, imaging, lasers, and integrated photonic systems. Here, we demonstrate a self-assembled metamaterial platform based on gold nanoparticle aggregates with nanometer-scale gaps exhibit remarkably high effective refractive indices exceeding 15 in the mid-infrared regime, while simultaneously producing gap-field enhancements of at least two-orders of magnitude. This combination of high refractive index and extreme field enhancement enables exceptionally strong light-matter interactions. We demonstrate this by designing a compact high-index metamaterial device supporting an anapole, which further enhances the nanogap field. By placing quantum emitters with terahertz transitions inside the plasmonic gaps, we show a stimulated-emission response enhanced by at least three orders of magnitude, highlighting applications in non-linear optics, frequency up-conversion and vibrational strong coupling.

We consider stratified steady water waves in a two dimensional channel. Our subject is branches of Stokes waves, bifurcating from laminar flows. We assume that the mass flux and the Bernoulli constant are fixed and consider the period of the wave as a parameter, which can change its value along the branch. A new class of density and Bernoulli functions is presented, for which laminar flows generate global bifurcation branches. The laminar flows are not necessary unidirectional and we show that the bifurcation branch can bifurcate from the laminar flow with arbitrary large period.

Intermittency is one of the central features of turbulent transfer: the multi-scale energy cascade is mediated by rare and intense fluctuations. We investigate this phenomenon in a multi-branch shell model, which combines quasi-local triadic nonlinear interactions with a branching structure that mimics the growth of degrees of freedom toward small scales. Comparison with the standard Sabra model shows that branching enhances intermittency, as measured by anomalous scaling exponents of energy-flux structure functions. We further use multiplier statistics and large deviation estimates to characterize the multiplicative nature of the cascade. Our results suggest that reduced descriptions of turbulent intermittency should retain both nonlinear dynamics and geometrical organization. Implications on Navier-Stokes turbulence are discussed.

This paper explores the effectiveness of various novel deterministic and traditional stochastic data assimilation (DA) and parameter recovery (PR) algorithms given noisy data from chaotic systems. We use semi-analytic methods to numerically construct synthetic data from the Lorenz '63 and multiscale Lorenz '96 chaotic dynamical systems, adding white noise. Our findings show that, for different noise levels, deterministic PR algorithms paired with deterministic DA algorithms are shown computationally to be overall more accurate and stable than stochastic PR algorithms. Additionally, deterministic PR methods have demonstrated greater speed and efficiency, requiring less computational power than stochastic PR methods. This suggests that future work should consider exploring the full potential of deterministic PR algorithms in the presence of noise.

We study the reflection of a weak planar shock from a rigid wall in the joint limit of weak shock strength and nearly glancing incidence. In the distinguished scaling (M=1+λα^2), where (M) is the incident-shock Mach number and (α) is the glancing angle, the inner reflection region is governed by the unsteady transonic small-disturbance (UTSD) equation. The corresponding canonical shock-reflection problem is controlled by the single parameter[a=\fracα{\sqrt{2(M^2-1)}}=\frac{1}{2\sqrtλ}+O(α^2),]so the limiting inner parameter (a_0=1/(2\sqrtλ)) is independent of (γ). Consequently, the detachment value (a_d=\sqrt2) maps to the physical scaling threshold (λ_d=1/8), with Guderley--Mach reflection for (λ>1/8). The physical trajectory angle is obtained from the canonical UTSD trajectory function (g(a)) by the Mach-number strength scale[χ_{\rm phys}\sqrt{2(M^2-1)},g(a)+O(M^2-1) 2\sqrtλ,α,g(a_0)+O(α^3).]We derive the self-similar UTSD reduction, the sonic parabola, the UTSD shock polar and its regular-reflection cubic, recovering (a_d=\sqrt2) directly. We also give the local linearisation and formal adjoint solvability condition defining the first correction (H(a;γ)), without claiming a computed correction curve. Finally, a time-marching solver for the full leading-order canonical UTSD system is benchmarked against the Hunter--Tesdall (a_0=0.5) triple point: once transverse compression (u>1) behind the Mach stem is retained, the computed (u=0.5) contour passes through ((ξ,η)=(1.007,0.514)), compared with the published ((1.008,0.514)).