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Detailed observations of the temperature fluctuations in the microwave background radiation indicate that we live in an open universe. From the size of these fluctuations it is concluded that the geometry of the universe is quite close to…
Growth occurs in a wide range of systems ranging from biological tissue to additive manufacturing. This work considers surface growth, in which mass is added to the boundary of a continuum body from the ambient medium or from within the…
The concept of turnaround surface in an accelerating universe is generalized to arbitrarily large deviations from spherical symmetry, to close the gap between the idealized theoretical literature and the real world observed by astronomers.…
The "external" or "bulk" motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition, and velocity are allowed as long as there is no direct…
A phenomenological formalism is presented in which the apparent acceleration of the universe is generated by large-scale structure formation, thus eliminating the magnitude and coincidence fine-tuning problems of the Cosmological Constant…
In this paper we consider the motion of a rigid body immersed in a two dimensional unbounded incompressible perfect fluid with vorticity. We prove that when the body shrinks to a massless pointwise particle with fixed circulation, the…
The semiclassical description of the dynamics of wave packets in periodic potentials and subject to an applied force relies on the concepts of effective mass and anomalous transport. This picture is valid if the force changes slowly in time…
A phenomenological formalism is presented in which the apparent acceleration of the universe is generated by large-scale structure formation, thus eliminating the coincidence and magnitude fine-tuning problems of the Cosmological Constant…
In the present paper a new concept is introduced that: `mass is a complex quantity'. The concept of complex-mass suggests that the total mass M of a moving body is complex sum of: (i) the real-part (grain or rest) mass $m_{g}$ establishing…
Chaplygin's equations describing the planar motion of a rigid body in an unbounded volume of an ideal fluid involved in a circular flow around the body are considered. Hamiltonian structures, new integrable cases, and partial solutions are…
We show that the late-time acceleration of the universe can be understood as a codimension-one bifurcation of the Friedmann dynamical system in the variables $(H,\Omega)$. At a critical value of the density-parameter combination, a…
We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface…
We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the…
We investigate the motion of a hard cylinder rolling down a soft inclined plane. The cylinder is subjected to a viscous drag force and stochastic fluctuations due to the surrounding medium. In a wide range of parameters we observe…
A pseudo-velocity concept, based on the extension of a linear body, is defined by a special relativity experiment. It suggests an analogy with the covariance properties of Wiener's process, ultimately implying that the scaling behavior of…
We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two…
Contemporary observational and theoretical studies on the temporal nature of microscopic measurements renewed the discussion about the fundamental constants, leading to the possibility of light speed variation and superluminal pulse…
In this work we discuss different interpretations of mass in the relativistic dynamics. A new way to introduce mass is proposed. Our way is based on the relativistic equation of motion expressed in the form of the Newton$'$s second law. In…
We point out that, due to the nonlinearity of the Einstein equations, a homogeneous approximation in cosmology leads to the appearance of an additional term in the Friedmann equation. This new term is associated with the spatial…
Large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity we find two types of…