Related papers: Critical Parameterisation of the Brill Wave Initia…
We address several estimation problems in quantum optics by means of the maximum-likelihood principle. We consider Gaussian state estimation and the determination of the coupling parameters of quadratic Hamiltonians. Moreover, we analyze…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
We consider the flow of multiple particles in a Bingham fluid in an anti-plane shear flow configuration. The limiting situation in which the internal and applied forces balance and the fluid and particles stop flowing, that is, when the…
A new Hamilton principle of convolutional type, completely compatible with the initial conditions of an IVP, has been proposed in a recent publication arXiv:1912.08490v1 [math-ph]. In the present paper the possible use of this principle for…
The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem…
Brill waves are the simplest (non-trivial) solutions to the vacuum constraints of general relativity. They are also rich enough in structure to allow us believe that they capture, at least in part, the generic properties of solutions of the…
We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the three-wave equation: \[p_{ij,t}-\frac{b_i-b_j}{a_i-a_j}p_{ij,x}+\sum_k(\frac{b_k-b_j}{a_k-a_j}-\frac{b_i-b_k}{a_i-a_k})p_{ik}p_{kj}=0,\quad…
As a first application of the new adaptive mesh functionality of the the pseudospectral numerical relativity code bamps, we evolve twist-free, axisymmetric gravitational waves close to the threshold of collapse. We consider six different…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
The approximate radial wave functions for the Cornell potential describing quark-antiquark interaction are constructed in the framework of a variational method. The optimal values of the variational parameters are fixed by the fulfillment…
The population of stellar-mass, compact object binaries that merge with non-negligible eccentricity may be large enough to motivate searches with ground-based gravitational wave detectors. Such events could be exceptional laboratories to…
In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations…
Using the variational approach and the critical point theory, we established several criteria for the existence of at least one nontrivial solution for a discrete elliptic boundary value problem with a weight $p(\cdot, \cdot)$ and depending…
The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…
A global network of laser interferometric gravitational wave detectors is projected to be in operation by around the turn of the century. Here, the noisy output of a single instrument is examined. A gravitational wave is assumed to have…
A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…
For the string baryon model "triangle" the initial-boundary value problem is stated and solved in general. This problem implies defining a classical motion of the system on the base of given initial position and initial velocities of string…
A fully implicit numerical approach based on the space-time finite element method is implemented for the semilinear wave equation in 1(space) + 1(time) and 2 + 1 dimensions to explore critical collapse and search for self-similar solutions.…
We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at…
We propose, as an alternative theory of quantum mechanics, a relativistically covariant variational principle (VP) capable of describing both wavefunction collapse and, as an appropriate limiting case, evolution of the wavefunction…