Related papers: Nonlinear Dynamics of Accelerator via Wavelet Appr…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
We establish long time soliton asymptotics for the nonlinear system of Maxwell equations coupled to a charged particle. The coupled system has a six dimensional manifold of soliton solutions. We show that in the long time approximation, any…
In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight…
Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This nonlinear process adds to the nonlinear modification of the shock due to the dynamical reaction of the…
We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness of our method, we perform numerical experiments which demonstrate that…
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding…
We propose and analyze an Accelerated Rearrangement Method (ARM) for solving a class of nonconvex optimization problems involving two-phase composites. These problems include maximizing the (work) energy of a membrane governed by the…
This note gives an introduction to the theories of impedances and wakes in particle accelerators. The standard formulation assumes that the beam is traveling along a straight orbit with constant velocity $\vec{v}=v\vec{e}_z$. On this note,…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
A general framework for solving nonlinear least squares problems without the employment of derivatives is proposed in the present paper together with a new general global convergence theory. With the aim to cope with the case in which the…
While the construction of symplectic integrators for Hamiltonian dynamics is well understood, an analogous general theory for Poisson integrators is still lacking. The main challenge lies in overcoming the singular and non-linear geometric…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
This work develops a functional analytic framework for making computer assisted arguments involving transverse heteroclinic connecting orbits between hyperbolic periodic solutions of ordinary differential equations. We exploit a…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered.
We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
A novel approach is developed for analytic orbit propagation based on asymptotic expansion with respect to a small perturbative acceleration. The method improves upon existing first order asymptotic expansions by leveraging on linear…