Related papers: On the Physical Problem of Spatial Dimensions: An …
In 1946, Erd\H{o}s posed the distinct distance problem, which seeks to find the minimum number of distinct distances between pairs of points selected from any configuration of $n$ points in the plane. The problem has since been explored…
In this work, we explore the de Broglie-Bohm Quantum Cosmology for a stiff matter, $p = \rho$, anisotropic n-dimensional Universe. One begins by considering a Gaussian wave function for the Universe, which depends on the momenta parameters…
We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is…
In this paper, we give an instability criterion for the Prandtl equations in three space variables, which shows that the monotonicity condition of tangential velocity fields is not sufficient for the well-posedness of the three dimensional…
Relativistic kinematics is usually considered only as a manifestation of pseudo-Euclidean (Lorentzian) geometry of space-time. However, as it is explicitly stated in General Relativity, the geometry itself depends on dynamics, specifically,…
One often distinguishes between a line and a plane by saying that the former is one-dimensional while the latter is two. But, what does it mean for an object to have $d-$dimensions? Can we define a consistent notion of dimension rigorously…
We consider a $(4 + 2k)$ - dimensional Einstein-Gauss-Bonnet model with the cosmological $\Lambda$-term. Exact stable solutions with three constant Hubble-like parameters in this model are obtained. In this case, the multidimensional…
Large extra dimensional theories attempt to solve the hierarchy problem by assuming that the fundamental scale of the theory is at the electroweak scale. This requires the size of the extra dimensions to be stabilized at a scale which is…
In this article it is shown that a careful analysis of Kant's "Thoughts on the True Estimation of Living Forces" leads to a conclusion that does not match the usually accepted interpretation of Kant's reasoning in 1747, according to which…
Noticing that really the fermions of the Standard Model are best thought of as Weyl - rather than Dirac - particles (relative to fundamental scales located at some presumably very high energies) it becomes interesting that the experimental…
We use the model of L. Randall et al to investigate the stability of allowed quantum field configurations. Firstly, we find that due to the topology of this 5 dimensional model, there are 2 possible configurations of the scalar field,…
A longstanding belief has been that the semimajor axes, in the Newtonian planetary problem, are stable. In the course of the XIX century, Laplace, Lagrange and others gave stronger and stronger arguments in this direction, thus culminating…
We present a new systematic way of setting up galactic gas disks based on the assumption of detailed hydrodynamic equilibrium. To do this, we need to specify the density distribution and the velocity field which supports the disk. We first…
This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework. We define dimensional stability as an invariant within the…
The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…
There is no known fundamental reason to demand as a cosmological initial condition that the bulk possess an SO(3,1) isometry. On the contrary, one expects bulk curvature terms that violate the SO(3,1) isometry at early epochs, leading to a…
Supersymmetry has been studied for over three decades by physicists, its superset even longer by mathematicians, and superspace has proven to be very useful both conceptually and in facilitating computations. However, the (1) necessary…
We investigate cosmologies with homogeneous extra dimensions that can be described by generalised Friedmann-Robertson-Walker metrics and give a brief review on a general setup to describe a broad range of standard stabilization and…
The problem of having an accurate description of the spacetime around neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a…
We present a canonical quantization framework for static spherically symmetric spacetimes described by the Einstein-Hilbert action with a cosmological constant. In addition to recovering the classical Schwarzschild-(Anti)-de Sitter…