Search

The orbital-free density functional theory (OF-DFT) based method is a convenient tool to carry out electronic structure calculations scaling almost linearly with the number of electrons. However, the main impediment in the application of this method is the unavailability of the accurate form for the non-interacting kinetic energy functional in terms of electron density. The Pauli kinetic energy functional is the unknown part of the kinetic energy functional, and the corresponding Pauli potential appears in the governing Euler equation. In the present study, we present a feed-forward neural network (NN) approach to represent the Pauli potential of a group of atomic systems possessing spherically symmetric ground-state densities. This NN-based representation of Pauli potential combined with the Hohenberg–Kohn variational principle yields self-consistent radial densities that accurately exhibit the correct atomic shell structure. For this approach, the electron density in the form of a grid serves as the input to the NN model. In addition, we calculated the non-interacting kinetic energy by summing the Pauli kinetic energy, derived from the NN-based Pauli potential, and the von Weizsäcker kinetic energy. Our results demonstrate high accuracy for smaller atoms, while larger atoms exhibit greater deviations when compared with smaller atoms. The method presented in this paper provides an efficient way to calculate the Pauli potential and the Pauli kinetic energy without the need for functional derivatives. Our study represents a significant step forward in the application of machine learning techniques to OF-DFT, showcasing the potential of NNs in improving the accuracy and efficiency of quantum mechanical calculations in atomic systems. [ABSTRACT FROM AUTHOR]

We study motility-induced phase separation in symmetric and asymmetric active binary mixtures. We start with the coarse-grained run-and-tumble bacterial model that provides evolution equations for the density fields ρ i ( r ⃗ , t). Next, we study the phase separation dynamics by solving the evolution equations using the Euler discretization technique. We characterize the morphology of domains by calculating the equal-time correlation function C(r, t) and the structure factor S(k, t), both of which show dynamical scaling. The form of the scaling functions depends on the mixture composition and the relative activity of the species, Δ. For k → ∞, S(k, t) follows Porod's law: S(k, t) ∼ k−(d+1) and the average domain size L(t) shows a diffusive growth as L(t) ∼ t1/3 for all mixtures. [ABSTRACT FROM AUTHOR]

This paper investigates the globally dynamic stabilizing effects of the geometry of the domain at which the flow locates and of the geometrical structure of the finite-energy solutions to three-dimensional (3D) incompressible Navier-Stokes and Euler systems. We have established the global existence and uniqueness of the smooth solution to the Cauchy problem for 3D incompressible Navier-Stokes and Euler equations for a class of smooth large initial data in orthogonal curvilinear coordinate systems, which has no smallness assumption on initial data for the Cartesian coordinate system. Moreover, we have also established the existence, uniqueness, and exponential decay rate of the global strong solution to the initial-boundary-value problem for 3D Navier-Stokes equations for a class of smooth large initial data and a class of special bounded domain in orthogonal curvilinear coordinate systems. Regarding application, some new classes of large-amplitude global smooth solutions with very complex geometric structures, and that are either non-axisymmetric or non-helical in $ \mathbb{R}^3 $, have been established for 3D incompressible Navier-Stokes and Euler equations. This is the first result on the global existence and uniqueness of the large smooth solution to 3D incompressible Navier-Stokes and Euler equations in general orthogonal curvilinear coordinate systems. [ABSTRACT FROM AUTHOR]

In this work, we design a new class of fully discrete Lagrangian–Eulerian schemes on triangular grids to approximate nonlinear multidimensional initial value problems for scalar models and multidimensional systems of conservation. The numerical approach is based on the improved concept of multidimensional no-flow curves. We also provide a convergence proof towards the entropy solution to the scalar problem u t (t , x) + div (f (u (t , x))) = 0 , with u 0 ∈ L ∞ (R 2) , which is analyzed in the effective setting of the properties of uniqueness and regularity of the entropy process solutions in the L t ∞ (L x 1) -norm and linked to the entropy measure-valued solutions. Additionally, we obtain optimal a priori error estimates as O (h 1 2) on equilateral triangular meshes. In the general context of multidimensional hyperbolic systems of conservation laws, we show that the Lagrangian–Eulerian scheme on triangular grids also satisfies the positivity principle proposed by Lax and Liu (J Comput Phys 5(2):133–156, 1996; J Comput Phys 187:428–440, 2003) and a type of weak positivity principle. We found a connection (given in the "Appendix") between the notion of no-flow curves (viewed as a vector field with locally bounded Γ M - v a r i a t i o n ) and the results of Bressan in the context of (local) existence and continuous dependence for discontinuous O.D.E.'s as introduced in Bressan (Proc Am Math Soc 104(3):772–778, 1988) and Bressan and Colombo (Boll Un Mat Ital 4(2):295–311, 1990). We present numerical solutions for nontrivial 2D hyperbolic problems, e.g., 4 by 4 compressible Euler equations (Double Mach Reflection problem and Mach 3 wind tunnel flow), a nonclassical 2 by 2 three-phase flow system of nonstrictly hyperbolic conservation laws (with a resonance/umbilic point), and the 3 by 3 shallow-water system (with and without bottom topography), and also 8 by 8 Orszag-Tang vortex system in magnetohydrodynamics. [ABSTRACT FROM AUTHOR]

Consider a balance law where the flux depends explicitly on the space variable. At jump discontinuities, modeling considerations may impose the defect in the conservation of some quantities, thus leading to non conservative products. Below, we deduce the evolution in the smooth case from the jump conditions at discontinuities. Moreover, the resulting framework enjoys well posedness and solutions are uniquely characterized. These results apply, for instance, to the flow of water in a canal with varying width and depth, as well as to the inviscid Euler equations in pipes with varying geometry. [ABSTRACT FROM AUTHOR]

This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by prescribing the horizontal mass flux distribution, the swirl velocity, the entropy and the Bernoulli's quantity at the entrance and the radial velocity at the exit. It can be formulated as a free boundary problem with the contact discontinuity to be determined simultaneously with the flows. Compared with the two-dimensional case, a new difficulty arises due to the singularity near the axis. An invertible modified Lagrangian transformation is introduced to overcome this difficulty and straighten the contact discontinuity. The key elements in our analysis are to utilize the deformation-curl decomposition introduced in [S. Weng and Z. Xin, A deformation-curl decomposition for three dimensional steady Euler equations, Sci. Sin. Math.49 (2019) 307–320 (in Chinese): doi:10.1360/N012018-00125] to effectively decouple the hyperbolic and elliptic modes in the steady axisymmetric Euler system and to use the implicit function theorem to locate the contact discontinuity. [ABSTRACT FROM AUTHOR]

In this paper, we consider the incompressible 3D Euler and Navier–Stokes equations in a smooth bounded domain. First, we study the 3D Euler equations endowed with slip boundary conditions and we prove the same criteria for energy conservation involving the gradient, already known for the Navier–Stokes equations. Subsequently, we utilize this finding, which is based on a proper approximation of the velocity (and does not require any estimate or additional assumption on the pressure), to explore energy conservation for Beltrami flows. Finally, we explore Beltrami solutions to the Navier–Stokes equations and demonstrate that conditions leading to energy conservation are significantly distinct from those implying regularity. This remains true even when making use of the bootstrap regularity improvement, stemming from the solution being a Beltrami vector field. [ABSTRACT FROM AUTHOR]

The phenomena of concentration and cavitation in the Riemann solutions of the relativistic Euler equations with non-ideal isothermal dusty gas are considered. The Riemann problem is solved first, and the solutions consisting of rarefaction waves and shock waves are obtained. Then, by the vanishing pressure approach, we investigate the limiting behaviors of Riemann solutions and observe the concentration and cavitation phenomena. It is rigorously proved that as the dusty gas pressure vanishes with double parameters, the solution containing two shock waves and two rarefaction waves respectively converges to the delta-shock wave and vacuum state of the pressureless relativistic Euler equations. [ABSTRACT FROM AUTHOR]

Using quantile maximization decision theory, this paper considers a quantile-based Euler equation that states that the asset price is a function of the quantiles of the payoff, consumption growth, the stochastic discount factor, risk aversion, and the distribution of the consumption growth rate. We use a more general distribution assumption (log-elliptical distributions) than the log-normality of the consumption growth rate assumed in the literature. The simulation results show that: (1) the higher the downside risk aversion, the lower the constant relative risk aversion; (2) the heavier the tails of the Student-t distribution, the higher the risk aversion for each level of downside risk aversion; and (3) the curve of the relationship between risk aversion and downside risk aversion shifts upward when the normality assumption is dropped, and the magnitude of this shift is high even for high degrees of freedom of the Student-t distribution. Our results suggest that using normally distributed errors to model stock returns and consumption growth rates could lead to an underestimation of the risk aversion coefficient. [ABSTRACT FROM AUTHOR]

The masses of galaxy clusters are commonly measured from X-ray observations under the assumption of hydrostatic equilibrium (HSE). This technique is known to underestimate the true mass systematically. The fiducial FLAMINGO (Full-hydro Large-scale structure simulations with All-sky Mapping for the Interpretation of Next Generation Observations) cosmological hydrodynamical simulation predicts the median hydrostatic mass bias to increase from |$b_\text{HSE} \equiv (M_\text{HSE,500c}-M_\text{500c})/M_\text{500c} \approx -0.1$| to −0.2 when the true mass increases from group to cluster mass scales. However, the bias is nearly independent of the hydrostatic mass. The scatter at fixed true mass is minimum for |$M_\text{500c}\sim 10^{14}~\text{M}_\odot$|⁠ , where |$\sigma (b_\text{HSE})\approx 0.1$|⁠ , but increases rapidly towards lower and higher masses. At a fixed true mass, the hydrostatic masses increase (decrease) with redshift on group (cluster) scales, and the scatter increases. The bias is insensitive to the choice of analytic functions assumed to represent the density and temperature profiles, but it is sensitive to the goodness of fit, with poorer fits corresponding to a stronger median bias and a larger scatter. The bias is also sensitive to the strength of stellar and active galactic nucleus feedback. Models predicting lower gas fractions yield more (less) biased masses for groups (clusters). The scatter in the bias at fixed true mass is due to differences in the pressure gradients rather than in the temperature at |$R_\text{500c}$|⁠. The total kinetic energies within |$r_\text{500c}$| in low- and high-mass clusters are sub- and supervirial, respectively, though all become subvirial when external pressure is accounted for. Analyses of the terms in the virial and Euler equations suggest that non-thermal motions, including rotation, account for most of the hydrostatic mass bias. However, we find that the mass bias estimated from X-ray luminosity weighted profiles strongly overestimates the deviations from HSE. [ABSTRACT FROM AUTHOR]

Ideal magnetohydrodynamic (MHD) equilibria on a Riemannian 3-manifold satisfy the stationary Euler equations for ideal fluids. A stationary solution X admits a large set of "adapted" metrics on M for which X solves the corresponding MHD equilibrium equations with the same pressure function. We prove different versions of the following statement: an MHD equilibrium with non-constant pressure on a compact three-manifold with or without boundary admits no continuous Killing symmetries for an open and dense set of adapted metrics. This contrasts with the classical conjecture of Grad which loosely states that an MHD equilibrium on a toroidal Euclidean domain in R 3 with pressure function foliating the domain with nested toroidal surfaces must admit Euclidean symmetries. [ABSTRACT FROM AUTHOR]

In this work, we study the deterministic Cucker–Smale model with topological interaction. Focusing on the solutions of the corresponding Liouville equation, we show that propagation of chaos holds. Moreover, considering monokinetic solutions, we also obtain a rigorous derivation of the hydrodynamic description given by a pressureless Euler-type system. [ABSTRACT FROM AUTHOR]

The motivation for this paper has been that standard Euler equations for aggregate investment (EEI) are known to perform poorly empirically. According to the literature, it may be because they fail to account for financial constraints. We contribute to this literature in two ways. First, we introduce a more pragmatic than the standard definition of investment. Second, we construct a modified EEI (MEEI) by combining financially constrained and unconstrained firms in the same manner as in the aggregate consumption literature. The MEEI is an "all-purpose" model in that it can be estimated both when investment and its determinants (relative price of investment, profits, cash flow, etc.) are I(0) variables and when they are I(1) and cointegrated, in which case the MEEI is a non-linear error-correction model for aggregate investment. Using United States (US) aggregate quarterly data, 1947:1–2022:2, we produce evidence supporting the model and estimate that about 30 percent of the US firms forgo attractive investment opportunities because of financial constraints, which therefore hurt economic growth. Issues like aggregation bias, structural instability, and weak identification are addressed. The MEEI can be used for forecasting macroeconomic fluctuations and for enacting stabilization and growth policies. [ABSTRACT FROM AUTHOR]

Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end‐point Triebel–Lizorkin space F1,∞sℝd$$ {F}_{1,\infty}^s\left({\mathbb{R}}^d\right) $$ with s≥d+1$$ s\ge d+1 $$ is clarified. [ABSTRACT FROM AUTHOR]

In this article, we study the asymptotic behavior of the two-dimensional Vlasov–Yukawa system with a point charge under a large external magnetic field. When the intensity of the magnetic field tends to infinity, we show that the kinetic system converges to the measure-valued Euler equation with a defect measure, which extends the results of Miot to the case of the Vlasov–Yukawa system. And compared with the Miot's work, an important improvement is that our results do not require compact support conditions for spatial variables or uniform bound conditions for second-order spatial moments. In addition, the extra small condition for initial data is also not required. [ABSTRACT FROM AUTHOR]

The stability and dynamics of solitary waves propagating along the surface of an inviscid ferrofluid jet in the absence of gravity are investigated analytically and numerically. For the axisymmetric geometry, the problem is shown to be a conservative system with total energy as the Hamiltonian; however, one of the canonical variables differs from those in the classic water-wave problem in the Cartesian coordinate system. The Dirichlet–Neumann operator appearing in the kinetic energy is then expanded as a Taylor series, described in homogeneous powers of the surface displacement. Based on the further analysis of the Dirichlet–Neumann operator, a systematic procedure is proposed to derive reduced model equations of multiple scales in various asymptotic limits from the full Euler equations in the Hamiltonian/Lagrangian framework. Particularly, a fully dispersive model arising from retaining terms valid up to the quartic order in the series expansion of the kinetic energy, which results in quadratic and cubic algebraic nonlinearities in Hamilton's equations and henceforth is abbreviated as the cubic full-dispersion model, is proposed. By comparing bifurcation curves and wave profiles of various types of axisymmetric solitary waves among different model equations, the cubic full-dispersion model is found to agree well with the full Euler equations, even for waves of considerably large amplitudes. The stability properties of axisymmetric solitary waves subjected to longitudinal disturbances are verified with the newly proposed model. Our analytical results, consistent with Saffman's theory, indicate that in the axisymmetric cylindrical system, the stability exchange subjected to superharmonic perturbations also occurs at the stationary point of the speed-energy bifurcation curve. A series of numerical experiments for the stability and dynamics of solitary waves are performed via the numerical time integration of the model equation, and collision interactions between stable solitary waves show non-elastic features. [ABSTRACT FROM AUTHOR]

The multipolar spherical vortex solutions to the Euler and Navier–Stokes equations in background cylindrical flow with swirl admit an additional background divergent radial flow with arbitrary time-dependent amplitude. In this case the radial wavenumber $k$ , fundamental frequency $\omega$ and overall amplitude $U$ of the multipolar mode superposition become time-dependent and related functions. Assumption of an additional constraint, as a constitutive equation defining the time evolution of the spatially homogeneous divergence of the background flow, is required for the time evolution of the total flow to be completely evaluated from the initial conditions. It is found that flow compression implies an increase of the absolute values of the fundamental frequency $\omega$ and overall velocity amplitude $U$ of the oscillations. [ABSTRACT FROM AUTHOR]

. We address a moving boundary problem that consists of a system of equations modeling an inviscid fluid interacting with a two-dimensional nonlinear Koiter plate at the boundary. We derive a priori estimates needed to prove the local-in-time existence of solutions. We use the Arbitrary Lagrange Euler (ALE) coordinates to fix the domain and obtain careful estimates for the nonlinear Koiter plate, ALE velocity, and pressure without any viscoelastic smoothing. For the nonlinear Koiter plate, higher order energy estimates are obtained, whereas estimates for the ALE pressure are obtained by setting up an elliptic problem. For the ALE velocity, the bounds are obtained through div-curl estimates by estimating the ALE vorticity. We then extend our results in two directions: (1) to include fractional Sobolev spaces and (2) to incorporate the normalized second fundamental form. [ABSTRACT FROM AUTHOR]

We investigate the well-posedness of \alpha-surface quasi-geostrophic (\alpha-SQG) equations in the half-plane, where \alpha =0 and \alpha =1 correspond to the 2D Euler and SQG equations respectively. For 0<\alpha \le 1/2, we prove local well-posedness in certain weighted anisotropic Hölder spaces. We also show that such a well-posedness result is sharp: for any 0<\alpha \le 1, we prove nonexistence of Hölder regular solutions (with the Hölder regularity depending on \alpha) for initial data smooth up to the boundary. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the time-periodic solutions of one-dimensional compressible Euler equations with linear damping $ \alpha(x)\rho u $. The boundary conditions have no dissipative structure on one side, which involves some physical reality. By using a delicately designed iteration scheme, we establish the existence and stability of time-periodic solutions on the perturbation of a subsonic Fanno flow. Moreover, if the boundary has a higher regularity, we show that the time-periodic solution has the same higher regularity and stability. Our results are also valid for Euler equations without damping, in that case the steady subsonic background solution is a constant state. Both isentropic and isothermal polytropic gases are considered. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in comparing solutions to stochastic Volterra equations for the convex order on the space of continuous R d -valued paths and for the monotonic convex order when d = 1 . Even if these solutions are in general neither semimartingales nor Markov processes, we are able to exhibit conditions on their coefficients enabling the comparison. Our approach consists in first comparing their Euler schemes and then taking the limit as the time step vanishes. We consider two types of Euler schemes, depending on the way the Volterra kernels are discretised. The conditions ensuring the comparison are slightly weaker for the first scheme than for the second, and this is the other way around for convergence. Moreover, we weaken the integrability needed on the starting values in the existence and convergence results in the literature to be able to only assume finite first moments, which is the natural framework for convex ordering. [ABSTRACT FROM AUTHOR]

The propagating of quasi-Scholte waves in a hydroelastic system consisting of an orthotropic plate and a compressible inviscid fluid layer were investigated. There are considered the systems in which the motion of liquid layer surface not in contact with the plate is restricted by a rigid wall (the so-called "rigid wall" case) and where it is not restricted (the so-called "free surface" case). The motion of the plate is described by the exact equations and relations of elastodynamics for orthotropic bodies, and the flow of the fluid is linearized by Euler equations. The solution of the corresponding field equations is found analytically, and the dispersion equation for the investigated waves is obtained from the corresponding boundary and compatibility conditions. The dispersion curves for the corresponding quasi-Scholte waves are found numerically solving the dispersion equation. These curves are determined for different values of the mechanical constants that characterize the anisotropy of the plate material. Based on these results, specific conclusions are drawn about the influence of mechanical constants of the plate and the acoustic properties of the components of the hydroelastic system on the propagation speed of quasi-Scholte waves. [ABSTRACT FROM AUTHOR]

The present study focuses on particular properties of transonic flows through a planar channel featuring a circular bump on the lower wall. The selected geometry is reminiscent of the region surrounding the trailing edge of an airfoil at zero angle of attack and the resulting flow pattern is indeed similar to the fishtail shock-pattern that characterizes airfoils flying at nearly sonic speed. Numerical simulations have been conducted by solving the inviscid Euler equations using both a commercial and an in-house CFD code; discontinuities are modeled using shock-capturing in the former and shock-fitting in the latter. Numerical experiments reveal different shock-patterns obtained by independently varying the inlet Mach number and the outlet-to-inlet static pressure ratio. When shock-interactions occur, shock-polar analysis reveals that the branching point can be modeled using either von Neumann's three-shock-theory or Guderley's four-wave-theory, depending on the inlet Mach number. Furthermore, for certain pairs of boundary conditions, multiple solutions have been observed. [ABSTRACT FROM AUTHOR]

We analyzed the problem of one-dimensional steady detonation wave with momentum losses caused by the presence of solid inert objects on the path of the wave. The process is modeled by reactive Euler equations with two-step kinetics with exothermic first step and endothermic second step. We showed that the steady-state solutions exist for the whole range of detonation wave velocities D from the ideal detonation velocity down to the speed of sound in the fresh mixture, and that these solutions could be divided in three categories. The solutions with high detonation wave velocities retain the typical structure of self-sustained detonation wave with embedded Chapman–Jouguet point. The solutions with very low detonation wave velocities remain fully subsonic relative to the detonation front, which make them not self-sustained. Finally, the solutions with detonation velocity values between two aforementioned cases contain the second shock wave behind the detonation front. While first two types of steady-state solutions also exist in the problems with one-step chemistry, the last type emerges only at the presence of the endothermic reaction step. [ABSTRACT FROM AUTHOR]

In this Letter, the numerical simulation of axisymmetric hydrodynamic relativistic jet propagation was performed by solving the hydrodynamic relativistic Euler equation using the computer code PLUTO [Mignone et al., Astrophys. J. Suppl. Ser. 170, 228 (2007)]. The detailed flow features involved in this relativistic jet propagation has been thoroughly discussed in this present numerical study. The effect of the jet Lorentz factor ( Γ j ) on the shock–turbulence interaction has been studied by analyzing the divergence of the Lamb vector (L = ω × U). The strong coexistence of two layers ∇ · L < 0 and ∇ · L > 0 enhances the momentum transfer due to energy difference, causing turbulence amplification. [ABSTRACT FROM AUTHOR]

Dynamical systems and physical models defined on idealized continuous phase spaces are known to exhibit non-computable phenomena; examples include the wave equation, recurrent neural networks, or Julia sets in holomorphic dynamics. Inspired by the works of Moore and Siegelmann, we show that ideal fluids, modeled by the Euler equations, are capable of simulating poly-time Turing machines with polynomial advice on compact three-dimensional domains. This is precisely the complexity class P/poly considered by Siegelmann in her study of analog recurrent neural networks. In addition, we introduce a new class of symbolic systems, related to countably piecewise linear transformations of the unit square, that is capable of simulating Turing machines with advice in real-time, contrary to previously known models. [ABSTRACT FROM AUTHOR]

A recently initiated variant of density functional theory utilizes a set of spherically symmetric densities instead of the density. The exact functionals are unknown in the new theory akin to the standard density functional theory. In order to test approximate functionals exactly solvable models are introduced. A harmonic molecular ion, the analogue to the hydrogen molecule ion and a harmonic two-electron molecule showing analogy to the hydrogen molecule are proposed. It has been found that the wave function and the density can be given analytically. The exact spherical densities and the effective potentials of the Euler equations also have analytical form. It has been shown that the models can be easily extended to several "nuclei." [ABSTRACT FROM AUTHOR]

The Pauli kinetic energy functional and its functional derivative, termed Pauli potential, play a crucial role in the successful implementation of orbital-free density functional theory for electronic structure calculations. However, the exact forms of these two quantities are not known. Therefore, perforce, one employs the approximate forms for the Pauli functional or Pauli potential for performing orbital-free density functional calculations. In the present study, we developed a feed-forward neural network-based representation for the Pauli potential using a 1-dimensional (1-D) model system. We expanded density in terms of basis functions, and the coefficients of the expansion were used as input to a feed-forward neural network. Using the neural network-based representation of the Pauli potential, we calculated the ground-state densities of the 1-D model system by solving the Euler equation. We calculated the Pauli kinetic energy using the neural network-based Pauli potential employing the exact relation between the Pauli kinetic energy functional and the potential. The sum of the neural network-based Pauli kinetic energy and the von Weizsäcker kinetic energy resulted in an accurate estimation of the total kinetic energy. The approach presented in this paper can be employed for the calculation of Pauli potential and Pauli kinetic energy, obviating the need for a functional derivative. The present study is an important step in the advancement of application of machine learning-based techniques toward the orbital-free density functional theory-based methods. [ABSTRACT FROM AUTHOR]

In this paper, two newly proposed generalized Hamiltonian Conservative Chaotic Systems (CCSs) based on integrated 4D Euler equations are first discussed. Second, another generalized Hamiltonian CCS is also proposed. Furthermore, a class of generalized Hamiltonian CCSs based on integrated 4D Euler equations is given and studied. Subsequently, numerical analysis for the class of generalized Hamiltonian CCSs is further investigated to show their advantages over most of the existing CCSs, where the corresponding Lyapunov exponents' diagrams, bifurcation diagrams and phase portraits are all given to show their multistability and complex dynamics. Finally, the class of generalized Hamiltonian CCSs is implemented by using FPGA technology, and the results observed in FPGA implementation are consistent with those observed in the numerical analysis. All these results not only show multistability from a physical point of view, but also provide new physical models for chaos applications. [ABSTRACT FROM AUTHOR]

This document explores the impact of wind on the shape of shoaling and overturning waves using a two-phase DNS model, focusing on the wind Reynolds number (Re ∗) and its effects on wave shape. The simulations reveal that wind influences wave faces' steepness and geometrical parameters of overturning waves, with pressure and viscous stresses playing a role at the air-water interface. The findings suggest that wind significantly affects wave shape and overturning dynamics, potentially impacting coastal engineering and morphological evolution. The research compiled in this document provides valuable insights into fluid mechanics, surf zone dynamics, wind wave growth, and numerical modeling of wind effects on breaking waves, published in reputable journals. [Extracted from the article]

In this paper, we consider two-dimensional periodic capillary-gravity waves traveling under the influence of a vertical electric field. The full system is a nonlinear, two-layered, free boundary problem. The interface dynamics are derived by coupling Euler equations for the velocity field of the fluid with voltage potential equations governing the electric field. We first introduce the naive flattening technique to transform the free boundary problem into a fixed boundary problem. We then prove the existence of small-amplitude electrohydrodynamic waves with constant vorticity using local bifurcation theory. Moreover, we show that these electrohydrodynamic waves are formally stable in the linearized sense. Furthermore, we obtain a secondary bifurcation curve that emerges from the primary branch, consisting of ripple solutions on the interface. As far as we know, such solutions in electrohydrodynamics are established for the first time. It is worth noting that the electric field E 0 plays a key role in controlling the shapes and types of waves on the interface. [ABSTRACT FROM AUTHOR]

This work is concerned with limit behavior of the Navier–Stokes–Voigt equation with degenerate white noise in a 3D thin domain. Although the individual solutions may be chaotic in fluid dynamics, the stationary statistical solutions are essential to capture complex dynamical behaviors in the view of statistic. We therefore prove that the stationary statistical solution of the system converges weakly to the counterpart of the 2D stochastic Euler equation as the viscosity, the elasticity parameter and the thickness of the thin domain tend to zero. [ABSTRACT FROM AUTHOR]

The entropic regularization of the conservative stable discontinuous Galerkin method (DGM) in conservative variables for three-dimensional Euler equations is constructed through the use of a special slope limiter. This limiter ensures the fulfillment of the three-dimensional analogs of the monotonicity conditions and a discrete analog of the entropic inequality. The developed method is tested on a three-dimensional model problem of a Taylor–Green vortex. [ABSTRACT FROM AUTHOR]

In this paper we consider the incompressible 2D Euler equation in an annular domain with non-penetration boundary condition. In this setting, we prove the existence of a family of non-trivially smooth time-periodic solutions at an arbitrarily small distance from the stationary Taylor-Couette flow in H s , with s < 3 2 , at the vorticity level. [ABSTRACT FROM AUTHOR]

We propose Coadjoint Orbit FLIP (CO-FLIP), a high order accurate, structure preserving fluid simulation method in the hybrid Eulerian-Lagrangian framework. We start with a Hamiltonian formulation of the incompressible Euler Equations, and then, using a local, explicit, and high order divergence free interpolation, construct a modified Hamiltonian system that governs our discrete Euler flow. The resulting discretization, when paired with a geometric time integration scheme, is energy and circulation preserving (formally the flow evolves on a coadjoint orbit) and is similar to the Fluid Implicit Particle (FLIP) method. CO-FLIP enjoys multiple additional properties including that the pressure projection is exact in the weak sense, and the particle-to-grid transfer is an exact inverse of the grid-to-particle interpolation. The method is demonstrated numerically with outstanding stability, energy, and Casimir preservation. We show that the method produces benchmarks and turbulent visual effects even at low grid resolutions. [ABSTRACT FROM AUTHOR]

We propose a novel framework for simulating ink as a particle-laden flow using particle flow maps. Our method addresses the limitations of existing flow-map techniques, which struggle with dissipative forces like viscosity and drag, thereby extending the application scope from solving the Euler equations to solving the Navier-Stokes equations with accurate viscosity and laden-particle treatment. Our key contribution lies in a coupling mechanism for two particle systems, coupling physical sediment particles and virtual flow-map particles on a background grid by solving a Poisson system. We implemented a novel path integral formula to incorporate viscosity and drag forces into the particle flow map process. Our approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by the bulging and breakup of suspension drop tails, torus formation, torus disintegration, and the coalescence of sedimenting drops. In particular, our method delivered high-fidelity ink diffusion simulations by accurately capturing vortex bulbs, viscous tails, fractal branching, and hierarchical structures. [ABSTRACT FROM AUTHOR]

This paper investigates the theoretical implications of applying Darcy's law to premixed flames, a topic of growing interest in research on flame propagation in porous media and confined geometries. A multiple-scale analysis is carried out treating the flame as a hydrodynamic discontinuity in density, viscosity, and permeability. The analysis accounts in particular for the inner structure of the flame. A simple model is derived allowing the original conservation equations to be replaced by Laplace's equation for pressure, applicable on both sides of the flame front, subject to specific conditions across the front. Such model is useful for investigating general problems under confinement including flame instabilities in porous media or Hele-Shaw channels. In this context, two Markstein numbers are identified, for which explicit expressions are provided. In particular, our analysis reveals novel contributions to the local propagation speed arising from discontinuities in the tangential components of velocity and gravitational force, which are permissible in Darcy's flows to leading order, but not in flows obeying Euler or Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

This paper presents a WENO-based upwind rotated lattice Boltzmann flux solver (WENO-URLBFS) in the finite difference framework for simulating compressible flows with contact discontinuities and strong shock waves. In the method, the original rotating lattice Boltzmann flux solver is improved by applying the theoretical solution of the Euler equation in the tangential direction of the cell interface to reconstruct the tangential flux so that the numerical dissipation can be reduced. The fluxes at each interface are evaluated using a weighted summation of lattice Boltzmann solutions in two local perpendicular directions decomposed from the direction vector so that the stability performance can be improved. To achieve high-order accuracy, both fifth and seventh-order WENO reconstructions of the flow variables in the characteristic spaces are carried out. The order accuracy of the WENO-URLBFS is evaluated and compared with the traditional Lax–Friedrichs scheme, Roe scheme, and the LBFS by simulating the advection of the density disturbance problem. It is shown that the fifth and seventh-order accuracy can be achieved by all considered flux-evaluation schemes, and the present WENO-URLBFS has the lowest numerical dissipation. The performance of the WENO-URLBFS is further examined by simulating several 1D and 2D examples, including shock tube problems, Shu–Osher problems, blast wave problems, double Mach reflections, 2D Riemann problems, K-H instability problems, and High Mach number astrophysical jets. Good agreements with published data have been achieved quantitatively. Moreover, complex flow structures, including shock waves and contact discontinuities, are successfully captured. The present WENO-URLBFS scheme seems to present an effective numerical tool with high-order accuracy, lower numerical dissipation, and strong robustness for simulating challenging compressible flow problems. [ABSTRACT FROM AUTHOR]

Purpose: Rollover of a semi-trailer vehicle is a common type of instability that can occur when turning at high speeds on roads with high adhesion coefficients, or when colliding with other vehicles. In order to design effective early warning and anti-roll control systems, it is important to accurately determine the rollover thresholds. This research aims to determine the dynamic rollover thresholds of a tractor semi-trailer vehicle during turning maneuvers based on a dynamic model. Methods: A full dynamic model of a semi-trailer vehicle with 48 degrees of freedom has been established using the Multibody Dynamic analysis method and Newton Euler equations. The non-linear tire model is used to determine tire-road interaction forces when affected by tire-road deformation, adhesion coefficient of road, road wheel angle, and vehicle velocity. To validate the accuracy of the model, experiments were conducted on a road with a radius of 40 m. The verified model was then used to investigate the vehicle's dynamics during turning maneuvers at velocities ranging from 40 to 80 km/h and the magnitude of steering wheel angles ranging from 12.5 to 300 deg. Results: The results show the combined impact of the magnitude of the steering wheel angle and initial velocity on the rollover condition of the tractor semi-trailer vehicle. The 3D maps and table of maximum values for load transfer ratio and lateral acceleration of the vehicle bodies reveal the regions of roll stability and rollover. The dynamic rollover instability threshold for the tractor ranges from 4.382 to 4.838 m/s2, while that of the semi-trailer ranges from 4.022 to 4.433 m/s2. Conclusions: The article presents a method for determining the dynamic rollover threshold of tractor semi-trailer vehicles based on a full dynamic model. The dynamics rollover thresholds are the boundaries that separate the rollover region from the stability region of the lateral acceleration of the tractor and semi-trailer bodies. The research findings in this article serve as a basis for determining input parameters for early warning and anti-rollover control systems in tractor semi-trailer vehicles. These results will be further discussed in the next articles. [ABSTRACT FROM AUTHOR]

We present a formulation of special relativistic dissipative hydrodynamics (SRDHD) derived from the well-established Müller–Israel–Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity, and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and time-scale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation time-scales, it is roughly an order of magnitude faster than standard methods near the ideal limit. [ABSTRACT FROM AUTHOR]

The article in the Journal of Fluid Mechanics discusses time-periodic generalised solitary waves with a hydraulic fall in open channel flow. The study focuses on unsteady solutions emerging from an unstable steady solution, featuring large-amplitude time-periodic ripples caused by a sudden decrease in water depth known as a hydraulic fall. The research highlights the importance of considering solution stability and the long-term trends of unstable configurations in free-boundary problems, offering insights into fluid dynamics over topography. [Extracted from the article]

The article "Exact planetary waves and jet streams" delves into the study of nonlinear waves on surfaces resembling a rotating sphere for two-dimensional inviscid incompressible flow. It examines exact wave solutions in the Lagrangian reference frame within the β-plane and γ-approximation systems, showcasing non-trivial Lagrangian mean flow akin to polar jet streams. Through numerical experiments, the research investigates the temporal evolution of these waves and their connection to vorticity, shedding light on atmospheric dynamics and climate studies. The text also discusses the derivation of governing equations for two-dimensional flow on a sphere using stereographic coordinates and β and γ approximations, highlighting the stability and symmetry of vortex waves on the sphere. [Extracted from the article]

We consider a complexification of the Euler equations introduced by Šverák in [35] which conserves energy. We prove that these complex Euler equations are nonlinearly ill-posed below analytic regularity and, moreover, we exhibit solutions which lose analyticity in finite time. Our examples are complex shear flows and, hence, one-dimensional. This motivates us to consider fully nonlinear systems in one spatial dimension which are non-hyperbolic near a constant equilibrium. We prove nonlinear ill-posedness and finite-time singularity for these models. Our approach is to construct an infinite-dimensional unstable manifold to capture the high frequency instability at the nonlinear level. [ABSTRACT FROM AUTHOR]

It is well-known that the first energy shell, $ \mathcal{S}_1^{c_0}: = \{\alpha \cos(x+\mu)+\beta\cos(y+\lambda): \alpha^2+\beta^2 = c_0\, \, \&\, \, (\mu, \lambda)\in\mathbb{R}^2\} $of solutions to the 2d Euler equation is Lyapunov stable on $ \mathbb{T}^2 $. This is simply a consequence of the conservation of energy and enstrophy. Using the idea of Wirosoetisno and Shepherd [17], which is to take advantage of conservation of a properly chosen Casimir, we give a simple and quantitative proof of the $ L^2 $ stability of single modes up to translation. In other words, each$ \mathcal{S}_1^{\alpha, \beta}: = \{\alpha \cos(x+\mu)+\beta\cos(y+\lambda): (\mu, \lambda)\in\mathbb{R}^2\} $is Lyapunov stable. Interestingly, our estimates indicate that the extremal cases $ \alpha = 0, $ $ \beta = 0 $, and $ \alpha = \pm\beta $ may be markedly less stable than the others. [ABSTRACT FROM AUTHOR]

From an open set of initial data, we construct a family of classical solutions to the 1D nonisentropic compressible Euler equations which form $ C^{0,\nu} $ cusps as a first singularity, for any $ \nu \in [\frac{1}{2}, 1) $. For this range of $ \nu $, this is the first result demonstrating the stable formation of such $ C^{0,\nu} $ cusp-type singularities, also known as pre-shocks. The proof uses a new formulation of the differentiated Euler equations along the fast acoustic characteristic, and relies on a novel set of $ L^p $ energy estimates for all $ 1

In this paper, we develop a high-order well-balanced discontinuous Galerkin method for hyperbolic balance laws based on the Gauss-Lobatto quadrature rules. Important applications of the method include preserving the non-hydrostatic equilibria of shallow water equations with non-flat bottom topography and Euler equations in gravitational fields. The well-balanced property is achieved through two essential components. First, the source term is reformulated in a flux-gradient form in the local reference equilibrium state to mimic the true flux gradient in the balance laws. Consequently, the source term integral is discretized using the same approach as the flux integral at Gauss-Lobatto quadrature points, ensuring that the source term is exactly balanced by the flux in equilibrium states. Our method differs from existing well-balanced DG methods for shallow water equations with non-hydrostatic equilibria, particularly in the aspect that it does not require the decomposition of the source term integral. The effectiveness of our method is demonstrated through ample numerical tests. [ABSTRACT FROM AUTHOR]

Euler deconvolution is widely used as a semi-automatic interpretation technique for potential field data. In its original form it uses derivatives of orders 0 and 1, while second order Euler deconvolution uses derivatives of orders 0 and 2. Complete Euler deconvolution is introduced here, and this combines both methods to use derivatives of orders 0, 1, and 2. The use of the additional information in the three orders of derivatives provides increased accuracy compared to the original method, and when combined with other Euler equations it can also determine the structural index of the source. The methods are applied to both synthetic data and to two aeromagnetic data profiles from South Africa. [ABSTRACT FROM AUTHOR]

In this article, we present a formally fourth‐order accurate hybrid‐variable (HV) method for the Euler equations in the context of method of lines. The HV method seeks numerical approximations to both cell averages and nodal solutions and evolves them in time simultaneously; and it is proved in previous work that these methods are supraconvergent, that is, the order of the method is higher than that of the local truncation error. Taking advantage of the supraconvergence, the method is built on a third‐order discrete differential operator, which approximates the first spatial derivative at each grid point using only the information in the two neighboring cells. Analyses of stability, accuracy, and pointwise convergence are conducted in the one‐dimensional case for the linear advection equation; whereas extension to nonlinear systems including the Euler equations is achieved using characteristic decomposition and the incorporation of a residual‐consistent viscosity to capture strong discontinuities. Extensive numerical tests are presented to assess the numerical performance of the method for both 1D and 2D problems. [ABSTRACT FROM AUTHOR]

In this article, we investigate the incompressible 2D Euler equations on a rotating biaxial ellipsoid, which model the dynamics of the atmosphere of a Jovian planet. We study the non-zonal Rossby–Haurwitz solutions of the Euler equations on an ellipsoid, while previous works only considered the case of a sphere. Our main results include: the existence and uniqueness of the stationary Rossby–Haurwitz solutions; the construction of the traveling-wave solutions; and the demonstration of the Lyapunov instability of both the stationary and the traveling-wave solutions. [ABSTRACT FROM AUTHOR]