Euler's formula ≈ Euler's formula
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UpSetR: an R package for the visualization of intersecting sets and their properties Open
Motivation Venn and Euler diagrams are a popular yet inadequate solution for quantitative visualization of set intersections. A scalable alternative to Venn and Euler diagrams for visualizing intersecting sets and their properties is neede…
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Hydrodynamic Diffusion in Integrable Systems Open
We show that hydrodynamic diffusion is generically present in many-body, one-dimensional interacting quantum and classical integrable models. We extend the recently developed generalized hydrodynamic (GHD) to include terms of Navier-Stokes…
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Physics-informed neural networks for inverse problems in supersonic\n flows Open
Accurate solutions to inverse supersonic compressible flow problems are often\nrequired for designing specialized aerospace vehicles. In particular, we\nconsider the problem where we have data available for density gradients from\nSchliere…
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Diffusion in generalized hydrodynamics and quasiparticle scattering Open
We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be reach…
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Euler approximations with varying coefficients: The case of superlinearly growing diffusion coefficients Open
A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these…
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Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves Open
In this paper we are concerned with a class of double phase energy functionals arising in the theory of transonic flows. Their main feature is that the associated Euler equation is driven by the Baouendi-Grushin operator with variable coef…
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Exact solutions for the static bending of Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model Open
Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using th…
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Topological Euler Class as a Dynamical Observable in Optical Lattices Open
The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology-the Euler class-in such a dynamical setting. The enigmatic invariant (…
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UpSetR: An R Package for the Visualization of Intersecting Sets and their Properties Open
Venn and Euler diagrams are a popular yet inadequate solution for quantitative visualization of set intersections. A scalable alternative to Venn and Euler diagrams for visualizing intersecting sets and their properties is needed. We devel…
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On the maximal cut of Feynman integrals and the solution of their differential equations Open
The standard procedure for computing scalar multi-loop Feynman integrals\nconsists in reducing them to a basis of so-called master integrals, derive\ndifferential equations in the external invariants satisfied by the latter and,\nfinally, …
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nVenn: generalized, quasi-proportional Venn and Euler diagrams Open
Motivation Venn and Euler diagrams are extensively used for the visualization of relationships between experiments and datasets. However, representing more than three datasets while keeping the proportions of each region is still not feasi…
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Finite time singularities for the free boundary incompressible Euler equations Open
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the interface breaks dow…
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Holographic thermodynamics requires a chemical potential for color Open
The thermodynamic Euler equation for high-energy states of large-$N$ gauge\ntheories is derived from the dependence of the extensive quantities on the\nnumber of colors $N$. This Euler equation relates the energy of the state to\nthe tempe…
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Solution Properties of a 3D Stochastic Euler Fluid Equation Open
We prove local well-posedness in regular spaces and a Beale–Kato–Majda blow-up criterion for a recently derived stochastic model of the 3D Euler fluid equation for incompressible flow. This model describes incompressible fluid motions whos…
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A New Feature of the Fractional Euler–Lagrange Equations for a Coupled Oscillator Using a Nonsingular Operator Approach Open
In this new work, the free motion of a coupled oscillator is investigated. First, a fully description of the system under study is formulated by considering its classical Lagrangian, and as a result, the classical Euler–Lagrange equations …
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Perfect fluids Open
We present a systematic treatment of perfect fluids with translation and rotation symmetry, which is also applicable in the absence of any type of boost symmetry. It involves introducing a fluid variable, the kinetic mass density , which i…
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A new and general fractional Lagrangian approach: A capacitor microphone case study Open
In this study, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system. Initially, for both displacement and electrical charge, the classical Euler–Lagrange equa…
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The Implicit Discretization of the Supertwisting Sliding-Mode Control Algorithm Open
A preliminary version of this article was presented at the 15th Int. Workshop on Variable Structure Systems VSS’2018, Graz, Austria, July 2018.
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Generalized hydrodynamics of the classical Toda system Open
We obtain the exact generalized hydrodynamics for the integrable Toda system. The Toda system can be seen in a dual way, both as a gas and as a chain. In the gas point of view, using the elastic and factorized scattering of Toda particles,…
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Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment and stability Open
Solving stochastic differential equations (SDEs) numerically, explicit Euler–Maruyama (EM) schemes are used most frequently under global Lipschitz conditions for both drift and diffusion coefficients. In contrast, without imposing the glob…
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Discrete maximal regularity of time-stepping schemes for fractional evolution equations Open
In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. Th…
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The Motion of a Bead Sliding on a Wire in Fractional Sense Open
In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form.We first introduce the classical Lagrangian from the system model under consideration and obtain the classical Euler-Lagrange equation of …
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Subdiffusion with a time-dependent coefficient: Analysis and numerical solution Open
In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear fin…
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On Tamed Euler Approximations of SDEs Driven by Lévy Noise with Applications to Delay Equations Open
We extend the taming techniques for explicit Euler approximations of\nstochastic differential equations (SDEs) driven by L\\'evy noise with\nsuper-linearly growing drift coefficients. Strong convergence results are\npresented for the case …
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Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker–Smale models Open
This paper deals with the derivation and analysis of a compressible Euler-type equation with singular commutator, which is derived from a hyperbolic limit of the kinetic description to the Cucker–Smale model of interacting individuals.
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A New Banach Space Defined By Euler Totient Matrix Operator Open
The main object of this paper is to introduce a new Banach space derived by using a matrix operator which is comprised of Euler's totient function.Also, we determine α , β , γ -duals of this space and characterize some matrix classes on th…
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Physics-Informed Neural Networks for Solving Forward and Inverse Problems in Complex Beam Systems Open
This article proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theories, where the double beams ar…
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A well-balanced finite volume scheme for the Euler equations with gravitation Open
Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure…
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Fluctuations in Ballistic Transport from Euler Hydrodynamics Open
We propose a general formalism, within large-deviation theory, giving access to the exact statistics of fluctuations of ballistically transported conserved quantities in homogeneous, stationary states. The formalism is expected to apply to…
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Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions Open
We consider solving the forward and inverse partial differential equations (PDEs) which have sharp solutions with physics-informed neural networks (PINNs) in this work. In particular, to better capture the sharpness of the solution, we pro…