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One of the specialized spectroscopic techniques used to analyze the interaction of a light field with a target atom or molecule is nonlinear four-wave mixing in the extreme ultraviolet (XUV) region. In this paper, we investigate the fundamental interaction of atomic argon and molecular nitrogen gases with a light field in the perturbative nonlinear regime by cascading high-order harmonic generation (HHG) radiation with a multi-color laser. We optimize the phase-matching of collinear, multiple-cycle laser pulses with incommensurate frequencies (800 nm, 1400 nm and 560 nm) in third-order nonlinear wave-mixing with HHG-XUV radiation. Using a single-gas-cell interaction chamber, we reveal the electron wave packet dynamics in atomic and molecular systems by examining the time-dependent spectral features of the wave-mixing field, including intensity and frequency modulation patterns. This simple experimental setup presents a novel spectroscopy technique that can provide deeper insights into target systems, and potentially more complex molecular gases, involving multi-electron interaction regimes.

Flat bands – single-particle energy bands – in tight-binding lattices, aka networks, have attracted attention due to the presence of macroscopic degeneracies and their sensitivity to perturbations. They support compact localized eigenstates protected by destructive interference. This makes them natural candidates for emerging exotic phases and unconventional orders. In this review we consider the recently proposed systematic ways to construct flat band networks based on symmetries or fine-tuning. We then discuss how the construction methods can be further extended, adapted or exploited in presence of perturbations, both single-particle and many-body. This strategy has lead to the discovery of non-perturbative metal-insulator transitions, fractal phases, nonlinear and quantum caging and many-body nonergodic quantum models. We discuss what implications these results may have for the design of fine-tuned nanophotonic systems including photonic crystals, nanocavities, and metasurfaces.

Studying the nonlinear photoresponse of different materials, including III-V semiconductors, two-dimensional materials and many others, is attracting burgeoning interest in the terahertz (THz) field. Especially, developing field-effect transistor (FET)-based THz detectors with preferred nonlinear plasma-wave mechanisms in terms of high sensitivity, compactness and low cost is a high priority for advancing performance imaging or communication systems in daily life. However, as THz detectors continue to shrink in size, the impact of the hot-electron effect on device performance is impossible to ignore, and the physical process of THz conversion remains elusive. To reveal the underlying microscopic mechanisms, we have implemented drift-diffusion/hydrodynamic models via a self-consistent finite-element solution to understand the dynamics of carriers at the channel and the device structure dependence. By considering the hot-electron effect and doping dependence in our model, the competitive behavior between the nonlinear rectification and hot electron-induced photothermoelectric effect is clearly presented, and it is found that the optimized source doping concentrations can be utilized to reduce the hot-electron effect on the devices. Our results not only provide guidance for further device optimization but can also be extended to other novel electronic systems for studying THz nonlinear rectification.

In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in the cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme and an arc length method are used in the solution of nonlinear equations by finite element method to determine the mechanical effect. The Carrera-Unified formulation (CUF) is used to solve nonlinear, low or high order kinematic refined structure theories for finite beam elements. In the study, displacement area and stress distributions of composite structures with different angles and functionally graded (FG) structures are presented for Lagrange polynomial expansions. The results show the accuracy and computational efficiency of the method used and give confidence for new research.

The stability of a circular vortex is studied in the thermal quasi-geostrophic (TQG) model. Several radial distributions of vorticity and buoyancy (temperature) are considered for the mean flow. First, the linear stability of these vortices is addressed. The linear problem is solved exactly for a simple flow, and two stability criteria are then derived for general mean flows. Then, the growth rate and most unstable wavenumbers of normal-mode perturbations are computed numerically for Gaussian and cubic exponential vortices, both for elliptical and higher mode perturbations. In TQG, contrary to usual QG, short waves can be linearly unstable on shallow vorticity profiles. Linearly, both stratification and bottom topography (under specific conditions) have a stabilizing role. In a second step, we use a numerical model of the nonlinear TQG equations. With a Gaussian vortex, we show the growth of small-scale perturbations during the vortex instability, as predicted by the linear analysis. In particular, for an unstable vortex with an elliptical perturbation, the final tripolar vortices can have a turbulent peripheral structure, when the ratio of mean buoyancy to mean velocity is large enough. The frontogenetic tendency indicates how small-scale features detach from the vortex core towards its periphery, and thus feed the turbulent peripheral vorticity. We confirm that stratification and topography have a stabilizing influence as shown by the linear theory. Then, by varying the vortex and perturbation characteristics, we classify the various possible nonlinear regimes. The numerical simulations show that the influence of the growing small-scale perturbations is to weaken the peripheral vortices formed by the instability, and by this, to stabilize the whole vortex. A finite radius of deformation and/or bottom topography also stabilize the vortex as predicted by linear theory. An extension of this work to stratified flows is finally recommended.

The rheological behavior of an ionic liquid was investigated by means of molecular dynamics simulations with experimental contribution, under conditions close to those found in the elastohydrodynamic and the very-thin film lubrication regimes. The molecular model was applied to nearly 200 temperature–pressure–shear rate cases, without any parameter adjustment. Experiments were conducted on a rheometer and a high-pressure falling-body viscometer. This unique combination of numerical and experimental tools has enabled the full description of the ionic liquid rheological response to extreme conditions of temperature, pressure and shear rate. In the linear domain, a very good consistency between the two computational approaches (nonequilibrium molecular dynamics, equilibrium molecular dynamics via the Green–Kubo formalism) and the experiments was obtained on the Newtonian viscosity. Reliable values of the pressure–viscosity coefficient, another rheological characteristic necessary for predicting film thickness in the regimes of interest in this work, were inferred. Compared with a conventional lubricant of almost identical Newtonian viscosity, the pressure–viscosity coefficient of the ionic fluid is much lower, its variations with temperature remaining, however, very similar. The application of the time–temperature–pressure superposition principle and the regression to the Carreau equation for describing the nonlinear domain have revealed, for the first time, significant variations in the exponent of the Carreau model which have been correlated with the changes in temperature and pressure.

In this article, we present the current status of the derivation of a viscous Serre–Green–Naghdi system. For this goal, the flow domain is separated into two regions. The upper region is governed by inviscid Euler equations, while the bottom region (the so-called boundary layer) is described by Navier–Stokes equations. We consider a particular regime binding the Reynolds number and the shallowness parameter. The computations presented in this article are performed in the fully nonlinear regime. The boundary layer flow reduces to a Prandtl-like equation that we claim to be irreducible. Further approximations are necessary to obtain a tractable model.

Characterising the passive anisotropic properties of soft tissues has been largely limited to the linear viscoelastic regime and shear loading is rarely done in the large deformation regime, despite the physiological significance of such properties. This paper demonstrates the use of eccentric rheology, which allows the anisotropy of skeletal muscle to be investigated. The large amplitude oscillatory strain properties of skeletal muscle were also investigated using Fourier Transform-rheology. Histology was used to qualitatively assess the microstructure changes induced by large strain. Results showed that skeletal muscle was strongly anisotropic in the linear regime. The storage and loss moduli were found to be significantly different (p<0.05) between the three fibre alignment groups; for the group tested with fibres perpendicular to plane of shear was 12.3±1.3kPa and 3.0±0.35kPa, parallel to shear direction was 10.6±1.2kPa and 2.4±0.23kPa, and perpendicular to shear direction was 5.5±0.90kPa and 1.3±0.21kPa. The appearance and growth of higher order harmonics at large strain was different in the three testing directions indicating that the anisotropy of muscle affects skeletal muscle behaviour in the nonlinear regime. Histological analysis showed an increasing destruction of extracellular matrix and the rearrangement of fibres with increasing strain indicating mechanical damage at strains of larger than 10%. These microstructural changes could contribute to the complex nonlinear behaviour in skeletal muscle. This paper demonstrates a method of characterising the anisotropic properties in skeletal muscle under large strain whilst giving meaningful information on the physical response of tissue at various strains.

The effect of high-frequency vibrations on the nonlinear regimes of thermal convection in a two-layer system composed of a horizontal pure fluid layer and fluid-saturated porous layer heated from below is studied in the framework of the average approach. For large porous layer thicknesses it has been found, that at low vibration intensities the evolution of convective regimes with the growth of the Rayleigh number proceeds as follows: stationary regime—oscillatory regime—stationary regime. At high vibration intensities the stationary convective regimes take place at any values of the supercriticality used in the calculations. At close values of the fluid layer and porous layer thicknesses the interaction between the short-wave and long-wave instability modes is investigated. It has been found that at high vibration intensities the ambiguity of the stationary solutions is observed in a certain range of supercriticalities.

In recent decades, the Laurentian Great Lakes have undergone rapid surface warming with the summertime trends substantially exceeding the warming rates of surrounding land. Warming of the deepest (Lake Superior) was the strongest, and that of the shallowest (Lake Erie)—the weakest of all lakes. To investigate the dynamics of accelerated lake warming, we considered single-column and multi-column thermodynamic lake–ice models coupled to an idealized two-layer atmosphere. The variable temperature of the upper atmospheric layer—a proxy for the large-scale atmospheric forcing—consisted, in the most general case, of a linear trend mimicking the global warming and atmospheric interannual variability, both on top of the prescribed seasonal cycle of the upper-air temperature. The atmospheric boundary layer of the coupled model exchanged heat with the lake and exhibited lateral diffusive heat transports between the adjacent atmospheric columns. In simpler single-column models, we find that, for a certain range of periodic atmospheric forcing, each lake possesses two stable equilibrium seasonal cycles, which we call “regimes”—with and without lake-ice occurrence in winter and with corresponding cold and warm temperatures in the following summer, respectively, all under an identical seasonally varying external forcing. Deeper lakes exhibit larger differences in their summertime surface water temperature between the warm and cold regimes, due to their larger thermal and dynamical inertia. The regime behavior of multi-column coupled models is similar but more complex, and in some cases, they admit more than two stable equilibrium seasonal cycles, with varying degrees of wintertime ice-cover. The simulated lake response to climate change in the presence of the atmospheric noise rationalizes the observed accelerated warming of the lakes, the correlation between wintertime ice cover and next summer’s lake-surface temperature, as well as higher warming trends of the (occasionally wintertime ice-covered) deep-lake vs. shallow-lake regions, in terms of the corresponding characteristics of the forced transitions between colder and warmer lake regimes. Since the regime behavior in our models arises due to nonlinear dynamics rooted in the ice–albedo feedback, this feedback is also the root cause of the accelerated lake warming simulated by these models. In addition, our results imply that if Lake Superior eventually becomes largely ice-free (<10% maximum ice cover every winter) under continuing global warming, the surface warming trends of the deeper regions of the lake will become modest, similar to those of the shallower regions of the lake.