Replies are given to arguments advanced in this journal that claim to show that it is to nonlinear classical mechanics rather than quantum mechanics that one must look for the physical underpinnings of consciousness. ∗This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy und...

We show that the four-dimensional U(1) gauge theory in the continuum formulation has a confining phase (exhibiting area law of the Wilson loop) in the strong coupling region above a critical coupling gc. This result is obtained by taking into account topological non-trivial sectors in U(1) gauge theory. The derivation is based on the reformulation of gauge theory as a deformation of a topologic...

We discuss the early history of an important field of ‘‘sturm and drang’’ in modern theory of nonlinear waves. It is demonstrated how scientific demand resulted in independent and almost simultaneous publications by many different authors on modulation instability, a phenomenon resulting in a variety of nonlinear processes such as envelope solitons, envelope shocks, freak waves, etc. Examples f...

Memristive System is a class on non-linear systems with very interesting properties. It is considered to be the fourth basic circuit element like Resistors, Capacitors and Inductors. Till date most of the works on memristive systems concentrated on its applications in the field of designing super dense non volatile memory, crossbar latches, neural networks, modeling of neural synapses, nonlinea...

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochast...

Theory of nonlinear resonance, including stochastic one, is developed on the basis of the statistical field theory and using variables action-angle. Explicit expressions of action, proper frequency and nonlinearity parameter as functions of the system energy and the external signal frequency are found for the cases of nonlinear pendulum and double well potential. PACS: 02.50.-r; 05.10.Gg; 05.45.-a

This paper presents a thermoelastic bending analysis of functionally graded sandwich plates by using a new quasi-3D hybrid type higher order shear deformation theory (HSDT). The mathematical model contains only 5 unknowns as the first order shear deformation theory (FSDT). The nonlinear term of the temperature field is modeled in such way that can be different from the shape functions of the di...

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves.