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We use the dynamical analysis to study the evolution of the universe at late time for the model in which the interaction between dark energy and dark matter is inspired by disformal transformation. We extend the analysis in the existing…
Based on superfluid behavior of a (boson) dark matter as the light itself, a unified model for dark matter and quintessence is proposed. Inspired by (O'Dell et al. 2000) which in an exciting study showed that particular configurations of…
Using techniques from harmonic analysis, we derive several sharp stability estimates for the second order Heisenberg Uncertainty Principle. We also present the explicit lower and upper bounds for the sharp stability constants and compute…
It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
The $S$-deformation method is a useful way to show the linear mode stability of a black hole when the perturbed field equation takes the form of the Schr\"odinger equation. While previous works where many explicit examples are studied…
The phenomenologically observed flatness - or near flatness - of spacetime cannot be understood as emerging from continuum Planck (or sub-Planck) scales using known physics. Using dimensional arguments it is demonstrated that any…
Recent gravitational wave observations show evidence for the presence of higher harmonics, thus possibly indicating that these waves were generated in the inspiral of compact objects with asymmetric mass ratios. Signals with higher…
Location dependence of physical parameters such as the electromagnetic fine structure constant and Newton's G produce body accelerations which violate universality of free fall rates testable with laboratory and space experiments.…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
The fine-structure constant alpha approximately 1/137 is traditionally regarded as a fundamental dimensionless parameter. I argue instead that alpha is a scaled quantity that arises only where the structural scales contributed by classical…
Dynamical stability is a prerequisite for control and functioning of desired nano-machines. We utilize the Caldeira-Leggett master equation to investigate dynamical stability of molecular cogwheels modeled as a rigid, propeller-shaped…
The current observational and experimental bounds on the time variation of the constants of nature (the fine structure constant $\alpha$, the gravitational constant $G$ and the proton-electron mass ratio $\mu=m_p/m_e$) are reviewed.
It has been more than a century since first Lorentz and later Einstein explored relativistic events and still important consequences of that remains unclear to everybody. The present study extensively focus on Lorentz (Length) contraction…
In the early seventies, Alan Sandage defined cosmology as the search for two numbers: Hubble parameter ${{H}_{0}}$ and deceleration parameter ${{q}_{0}}$. The first of the two basic cosmological parameters (the Hubble parameter) describes…
We consider a nonlinear damped hyperbolic equation in $\real^n$, $1 \le n \le 4$, depending on a positive parameter $\epsilon$. If we set $\epsilon=0$, this equation reduces to the well-known Kolmogorov-Petrovski-Piskunov equation. We…
If the fine structure constant is not really constant, is this due to a variation of $e$, $\hbar$, or $c$? It is argued that the only reasonable conclusion is a variable speed of light.
We consider the nonlinear Dirac equation in 1+1 dimension with scalar-scalar self interaction $ \frac{g^2}{\kappa+1} ({\bar \Psi} \Psi)^{\kappa+1}$ and with mass $m$. Using the exact analytic form for rest frame solitary waves of the form…
Studies of the effective regime of loop quantum gravity (LQG) revealed that, in the limit of Planckian curvature scales, spacetime may undergo a transition from the Lorentzian to Euclidean signature. This effect is a consequence of quantum…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…