Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction-diffusion (RD) partial differential equations. Ho...

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function ...

Quantum mechanics is different from most other branches of science in that it uses complex numbers in a fundamental way. Complex numbers were originally created as a mathematical curiosity: i = √−1 was the asserted “imaginary” solution to the polynomial equation x2 = −1. As time went on, an entire mathematical edifice was constructed with these “imaginary” numbers. Complex numbers have kept lon...

Computational techniques adapted from classical mechanics and used in image analysis run the gamut from Lagrangian action principles to HamiltonJacobi field equations: witness the popularity of the fast marching and fast sweeping methods which are essentially fast Hamilton-Jacobi solvers. In sharp contrast, there are very few applications of quantum mechanics inspired computational methods. Giv...

The reflection of an object can be distorted by undulations of the reflector, be it a funhouse mirror or a fluid surface. Painters and photographers have long exploited this effect, for example, in imaging scenery distorted by ripples on a lake. Here, we use this phenomenon to visualize micrometric surface waves generated as a millimetric droplet bounces on the surface of a vibrating fluid bath...

Current models of evoked otoacoustic emissions explain the striking periodicity in their frequency spectra by suggesting that it originates through the reflection of forward-traveling waves by a corresponding spatial corrugation in the mechanics of the cochlea. Although measurements of primate cochlear anatomy find no such corrugation, they do indicate a considerable irregularity in the arrange...

The problems solving of a quantum mechanics is obtained by a classic way or with the help of a corpuscular quantum mechanics In this chapter we shall analyze fundamentals of a modern quantum mechanics. It as a matter of fact not corpuscular and wave. Will be shown, that though it and operates with mass and energy of a particle, as a matter of fact properties of particles in it are skipped in a ...

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be tak...

The quantum formalism is a \measurement" formalism|a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schrr odinger's equation for a system of particles when we merely insist that \particles" means particles. While distinctly non-Newtonian, Bohmian mecha...