Related papers: Kinetic equations: computation
Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…
A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Robots sense, move and act in the physical world. It is therefore natural that algorithmic problems in robotics and automation have a geometric component, often central to the problem. Below we review ten challenging problems at the…
We consider here kinematical quantization: a first and often overlooked step in quantization procedures. $\mathbb{R}$, $\mathbb{R}_+$ and the interval are considered, as well as direct (Cartesian) products thereof. Some simple…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
The purpose of physics is to describe nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this spectrum of events is desirable, this would…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
We report on recent study [1] of the role of the kinematical constraint in the CCFM equation and its non-linear extension. We compare numerical results obtained by solving the CCFM equation and argue that kinematical constraint represents…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
Perhaps the most basic question we can ask about cosmological correlations is how their strength changes as we smoothly vary kinematic parameters. The answer is encoded in differential equations that govern this evolution in kinematic…
The kinetic theory for a fluid of hard spheres which undergo endothermic and/or exothermic reactions with mass transfer is developed. The exact balance equations for concentration, density, velocity and temperature are derived. The Enskog…
Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the…
Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this…
General relativity poses serious problems for counterfactual propositions peculiar to it as a physical theory. Because these problems arise solely from the dynamical nature of spacetime geometry, they are shared by all schools of thought on…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
Master equations are commonly used to model the dynamics of physical systems, including systems that implement single-valued functions like a computer's update step. However, many such functions cannot be implemented by any master equation,…