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Universe structure emerges in the unreduced, complex-dynamic interaction process with the simplest initial configuration (two attracting homogeneous fields, quant-ph/9902015). The unreduced interaction analysis gives intrinsically creative…
Using the maximal Lie algebra of point symmetries of a system of nonlinear equations used in geophysical fluid dynamics, two conservation laws are found in addition to the conservation of energy.
The dynamics of a system of particles subject to a 4th order potential field modeling the space-time evolution of wedge disclinations is studied, focusing on finite systems of disclinations within a circular domain. Existence theorems for…
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory…
Relativistic quantum theories are usually thought of as being quantum field theories, but this is not the only possibility. Here we consider relativistic quantum theories with a fixed number of particles that interact neither through…
We draw a picture of physical systems that allows us to recognize what is this thing called "time" by requiring consistency not only with our notion of time but also with the way time enters the fundamental laws of Physics, independently of…
New method of quantization is presented. It is based on classical Newton-Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is…
We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of…
A new approach to the dynamics of the universe based on work by O Murchadha, Foster, Anderson and the author is presented. The only kinematics presupposed is the spatial geometry needed to define configuration spaces in purely relational…
We find a first--order partial differential equation whose solutions are all ultralocal scalar combinations of gravitational constraints with Abelian Poisson brackets between themselves. This is a generalisation of the Kucha\v{r} idea of…
Hydrodynamic equations for a one-component plasma are derived as a generalization of the Euler equations to include the effects of the long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
We extend the geometrical theory presented in [5] for collisional and frictional particle abrasion to include an independent physical equation for the evolution of mass and volume. We introduce volume weight functions as multipliers of the…
We present a new formalism which allows to derive the general Lagrangian dynamical equations for the motion of gravitating particles in a non--flat Friedmann universe with arbitrary density parameter $\Omega$ and no cosmological constant.…
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the…
In this work, a methodology is proposed for formulating general dynamical equations in mechanics under the umbrella of the principle of energy conservation. It is shown that Lagrange's equation, Hamilton's canonical equations, and…