Search results for "Lagrange"
showing 10 items of 60 documents
Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral
2014
A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…
A New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal
1999
In this paper we summarize the main features of a new time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin, Osher and Fatemi. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on an ENO Hamilton-Jacobi version of Roe's scheme. We show numerical evidence of the speed, resolution and stability of this simple explicit procedure in two representative 1D and 2D numerical examples.
On thermoeconomics of energy systems at variable load conditions: integrated optimization of plant design and operation
2007
Abstract Thermoeconomics has been assuming a growing role among the disciplines oriented to the analysis of energy systems, its different methodologies allowing solution of problems in the fields of cost accounting, plant design optimisation and diagnostic of malfunctions. However, the thermoeconomic methodologies as such are particularly appropriate to analyse large industrial systems at steady or quasi-steady operation, but they can be hardly applied to small to medium scale units operating in unsteady conditions to cover a variable energy demand. In this paper, the fundamentals of thermoeconomics for systems operated at variable load are discussed, examining the cost formation process an…
Abelian Powers and Repetitions in Sturmian Words
2016
Richomme, Saari and Zamboni (J. Lond. Math. Soc. 83: 79-95, 2011) proved that at every position of a Sturmian word starts an abelian power of exponent $k$ for every $k > 0$. We improve on this result by studying the maximum exponents of abelian powers and abelian repetitions (an abelian repetition is an analogue of a fractional power) in Sturmian words. We give a formula for computing the maximum exponent of an abelian power of abelian period $m$ starting at a given position in any Sturmian word of rotation angle $\alpha$. vAs an analogue of the critical exponent, we introduce the abelian critical exponent $A(s_\alpha)$ of a Sturmian word $s_\alpha$ of angle $\alpha$ as the quantity $A(s_\a…
A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing
2006
Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L^1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existe…
Ostrogradsky's Hamilton formalism and quantum corrections
2010
By means of a simple scalar field theory it is demonstrated that the Lagrange formalism and Ostrogradsky's Hamilton formalism in the presence of higher derivatives, in general, do not lead to the same results. While the two approaches are equivalent at the classical level, differences appear due to the quantum corrections.
Numerical simulation of unsteady MHD flows and applications
2009
International audience; We present a robust numerical method for solving the compressible Ideal Magneto-Hydrodynamic equations. It is based on the Residual Distribution (RD) algorithms already successfully tested in many problems. We adapted the scheme to the multi-dimensional unsteady MHD model. The constraint ∇ · B = 0 is enforced by the use a Generalized Lagrange Multiplier (GLM) technique. First, we present this complete system and the keys to get its eigensystem, as we may need it in the algorithm. Next, we introduce the numerical scheme built in order to get a compressible, unsteady and implicit solver which has good shock-capturing properties and is second-order accurate at the conve…
Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential
2020
Abstract We consider a two phase eigenvalue problem driven by the ( p , q ) -Laplacian plus an indefinite and unbounded potential, and Robin boundary condition. Using a modification of the Nehari manifold method, we show that there exists a nontrivial open interval I ⊆ R such that every λ ∈ I is an eigenvalue with positive eigenfunctions. When we impose additional regularity conditions on the potential function and the boundary coefficient, we show that we have smooth eigenfunctions.
Normalizing biproportional methods
2002
International audience; Biproportional methods are used to update matrices: the projection of a matrix Z to give it the column and row sums of another matrix is R Z S, where R and S are diagonal and secure the constraints of the problem (R and S have no signification at all because they are not identified). However, normalizing R or S generates important mathematical difficulties: it amounts to put constraints on Lagrange multipliers, non negativity (and so the existence of the solution) is not guaranteed at equilibrium or along the path to equilibrium.
Large eddy simulation of inertial particles dispersion in a turbulent gas-particle channel flow bounded by rough walls
2020
The purpose of this paper is to understand the capability and consistency of large eddy simulation (LES) in Eulerian–Lagrangian studies aimed at predicting inertial particle dispersion in turbulent wall-bounded flows, in the absence of ad hoc closure models in the Lagrangian equations of particle motion. The degree of improvement granted by LES models is object of debate, in terms of both accurate prediction of particle accumulation and local particle segregation; therefore, we assessed the accuracy in the prediction of the particle velocity statistics by comparison against direct numerical simulation (DNS) of a finer computational mesh, under both one-way and two-way coupling regimes. We p…