Related papers: A Multipoint Method for Approximation of Wavefunct…
A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from…
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…
This paper deals with the multivalued non-autonomous random dynamical system generated by the non-autonomous stochastic wave equations on unbounded domains, which has a non-Lipschitz nonlinearity with critical exponent in the three…
In my thesis I study mesoscopic corrections on diffuse transport. I first describe the diffuse transport of light, using the scalar approximation and the radiative transfer approach. Next, I focus on the correlations in transmission, I…
Multiplex networks describe a large variety of complex systems, whose elements (nodes) can be connected by different types of interactions forming different layers (networks) of the multiplex. Multiplex networks include social networks,…
We show the appearance of multifractal wave functions on a one-dimensional quasiperiodic system that has a monofractal energy spectrum. Using the Mantica technique, we construct the model as an inverse problem from the energy spectrum of a…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the…
We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint…
We highlight some recent developments that widen the scope and reach of mesoscopic thin-film (or long-wave) hydrodynamic models employed to describe the dynamics of thin films, drops and contact lines of simple and complex liquids on solid…
The behavior of monochromatic electromagnetic waves in stationary media is shown to be ruled by a frequency dependent function, which we call Wave Potential, encoded in the structure of the Helmholtz equation. Contrary to the common belief…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…
This paper is concerned with the study of interaction of waves originating from the Riemann problem centred at two different points for a system of equations modelling propagation of elastic waves. The system consists of two equations for…
In this paper,we present a detailed formulation to solve the scattering wave function for a multi-terminal mesoscopic system with spin-orbit coupling. In addition to terminal currents, all local quantities can be calculated explicitly by…
Controlling the polarization and wavefront of light is essential for compact photonic systems in modern science and technology. This may be achieved by metasurfaces, a new platform that has radically changed the way people engineer…
We study the diffusion of monochromatic classical waves in a disordered acoustic medium by scattering theory. In order to avoid artifacts associated with mathematical point scatterers, we model the randomness by small but finite insertions.…
Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging…
A simple procedure to derive the transformation of a wavefunction under a change of reference frame is applied to some examples and its relation with the transformation of the Hamilton principal function is studied.