Search results for "Euler"
showing 10 items of 159 documents
Hypergestures in Complex Time: Creative Performance Between Symbolic and Physical Reality
2015
Musical performance and composition imply hypergestural transformation from symbolic to physical reality and vice versa. But most scores require movements at infinite physical speed that can only be performed approximately by trained musicians. To formally solve this divide between symbolic notation and physical realization, we introduce complex time (\(\mathbb {C}\)-time) in music. In this way, infinite physical speed is “absorbed” by a finite imaginary speed. Gestures thus comprise thought (in imaginary time) and physical realization (in real time) as a world-sheet motion in space-time, corresponding to ideas from physical string theory. Transformation from imaginary to real time gives us…
A geometrical constructive approach to infinitesimal analysis: epistemological potential and boundaries of tractional motion
2014
Recent foundational approaches to Infinitesimal Analysis are essentially algebraic or computational, whereas the first approaches to such problems were geometrical. From this perspective, we may recall the seventeenth-century investigations of the “inverse tangent problem.” Suggested solutions to this problem involved certain machines, intended as both theoretical and actual instruments, which could construct transcendental curves through so-called tractional motion. The main idea of this work is to further develop tractional motion to investigate if and how, at a very first analysis, these ideal machines (like the ancient straightedge and compass) can constitute the basis of a purely geome…
On the interior regularity of weak solutions to the 2-D incompressible Euler equations
2016
We study whether some of the non-physical properties observed for weak solutions of the incompressible Euler equations can be ruled out by studying the vorticity formulation. Our main contribution is in developing an interior regularity method in the spirit of De Giorgi–Nash–Moser, showing that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result $$\begin{aligned} u \in L_\mathrm{loc}^{2+\varepsilon }(\Omega _T) \implies \mathrm{local\ regularity} \end{aligned}$$ for weak solutions in the energy space $$L_t^\infty L_x^2$$ , satisfying appropriate vorticity estimates. We also obtain impr…
Equilibrium real gas computations using Marquina's scheme
2003
Marquina's approximate Riemann solver for the compressible Euler equations for gas dynamics is generalized to an arbitrary equilibrium equation of state. Applications of this solver to some test problems in one and two space dimensions show the desired accuracy and robustness
Numerical Simulation of Friction Stir Welding by Natural Element Methods
2008
In this work we address the problem of numerically simulating the Friction Stir Welding process. Due to the special characteristics of this welding method (i.e., high speed of the rotating pin, very large deformations, etc.) finite element methods (FEM) encounter several difficulties. While Lagrangian simulations suffer from mesh distortion, Eulerian or Arbitrary Lagrangian Eulerian (ALE) ones still have difficulties due to the treatment of convective terms, the treatment of the advancing pin, and many others. Meshless methods somewhat alleviate these problems, allowing for an updated Lagrangian framework in the simulation. Accuracy is not affected by mesh distortion (and hence the name mes…
Meshless Simulation of Friction Stir Welding
2007
This paper encompasses our first efforts towards the numerical simulation of friction stir welding by employing a Lagrangian approach. To this end, we have employed a meshless method, namely the Natural Element Method (NEM). Friction Stir welding is a welding process where the union between the work pieces is achieved through the extremely high deformation imposed by a rotating pin, which moves between the two pieces. This extremely high strain is the main responsible of the difficulties associated with the numerical simulation of this forming process. Eulerian and Arbitrary Lagrangian-Eulerian (ALE) frameworks encounter difficulties in some aspects of the simulation. For instance, these ap…
An analytical study of the ageostrophic motion of an air parcel
1978
The complete ageostrophic motion of an individual air parcel is discussed. It is shown that the general velocity solution of the equation describing this motion may be expressed in terms of the well-known series approximation of Philipps and a rest term; this term describes the inertial motion of the air parcel about a given initial state.
On the moving load problem in beam structures equipped with tuned mass dampers
2017
This paper proposes an original and efficient approach to the moving load problem on Euler–Bernoulli beams, with Kelvin–Voigt viscoelastic translational supports and rotational joints, and in addition, equipped with Kelvin–Voigt viscoelastic tuned mass dampers (TMDs). While supports are taken as representative of external devices such as grounded dampers or in-span supports with flexibility and damping, the rotational joints may model rotational dampers or connections with flexibility and damping arising from imperfections or damage. The theory of generalised functions is used to treat the discontinuities of the response variables, which involves deriving exact complex eigenvalues and eigen…
On the number of factors of Sturmian words
1991
Abstract We prove that for m ⩾1, card( A m ) = 1+∑ m i =1 ( m − i +1) ϕ ( i ) where A m is the set of factors of length m of all the Sturmian words and ϕ is the Euler function. This result was conjectured by Dulucq and Gouyou-Beauchamps (1987) who proved that this result implies that the language (∪ m ⩾0 A m ) c is inherently ambiguous. We also give a combinatorial version of the Riemann hypothesis.
An order-adaptive compact approximation Taylor method for systems of conservation laws
2021
Abstract We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered ( 2 p + 1 ) -point stencils, where p may take values in { 1 , 2 , … , P } according to a new family of smoothness indicators in the stencils. The methods are based on a combination of a robust first order scheme and the Compact Approximate Taylor (CAT) methods of order 2p-order, p = 1 , 2 , … , P so that they are first order accurate near discontinuities and have order 2p in smooth regions, where ( 2 p + 1 ) is the size of the biggest stencil in which large gradients are n…