Related papers: Scaling relations between numerical simulations an…
We demonstrate that if masses and charges figuring in the equation of motion including both Newton gravitational and Coulomb electrostatic force laws are divided by mass and charge, respectively, which are derived using the relations…
A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative…
The growth of structure from scale-free initial conditions is one of the most important tests of cosmological simulation methods, providing a realistically complex problem in which numerical results can be compared to rigorous analytic…
Many hydrodynamic processes can be studied in a way that is scalable over a vastly relevant physical parameter space. We systematically examine this scalability, which has so far only briefly discussed in astrophysical literature. We show…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
We compute the time variation of the fundamental constants (such as the ratio of the proton mass to the electron mass, the strong coupling constant, the fine structure constant and Newton's constant) within the context of the so-called…
Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…
The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors…
We consider further consequences of recently [1] revealed role of cosmological constant \Lambda as of a physical constant, along with the gravitational one to define the gravity i.e. the General Relativity and its low-energy limit. We now…
Several authors have recently explored the idea that physical constants such as c and G might vary over time and have formulated theories describing this variation that can address a range of cosmological problems. Such work typically…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
Five fundamental scales of mass follow from holographic limitations, a self-similar law for angular momentum and the basic scaling laws for a fractal universe with dimension 2. The five scales correspond to the observable universe,…
Environmental science almost invariably proposes problems of extreme complexity, typically characterized by strongly nonlinear evolution dynamics. The systems under investigation have many degrees of freedom - which makes them complicated -…
Prescaling is a far-from-equilibrium phenomenon which describes the rapid establishment of a universal scaling form of distributions much before the universal values of their scaling exponents are realized. We consider the example of the…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…
The quantum dynamical evolution of atomic and molecular aggregates, from their compact to their fragmented states, is parametrized by a single collective radial parameter. Treating all the remaining particle coordinates in d dimensions…