We construct a general class of new time dependent solutions of non-linear σ-models coupled to gravity. These solutions describe configurations of expanding or contracting codimension two solitons which are not subject to a constraint on the total tension. The two dimensional metric on the space transverse to the defects is determined by the Liouville equation. This space can be compact or non-...

We study the action of a lattice Γ in the group G = SL(2,R) on the plane. We obtain a formula which simultaneously describes visits of an orbit Γu to either a fixed ball, or an expanding or contracting family of annuli. We also discuss the ‘shrinking target problem’. Our results are valid for an explicitly described set of initial points: all u ∈ R in the case of a cocompact lattice, and all u ...

We recently reported a new motion illusion where dots in expanding random dot patterns appear to move faster than those in rotation patterns despite having the same physical speed distributions. In the current paper, we compared expansion and rotation motion to translational motion and found that the perceived dot speed in translation patterns was between that of expansion and rotation. We also...

Kaluza-Klein theory admits “bubble” configurations, in which the circumference of the fifth dimension shrinks to zero on some compact surface. A three parameter family of such bubble initial data at a moment of timesymmetry (some including a magnetic field) has been found by Brill and Horowitz, generalizing the (zero-energy) “Witten bubble” solution. Some of these data have negative total energ...

The primordial Universe might be highly inhomogeneous. We perform the 3+1D Numerical Relativity simulation for evolution of scalar field in an initial inhomogeneous expanding Universe, and investigate how it populates landscape with both de Sitter (dS) AdS vacua. results show that eventually either different region separates into vacua, so dS or bubbles (the bubble wall is but spacetime inside ...

It is folklore that Albert Einstein’s greatest blunder occurred in 1917 when he introduced the cosmological constant term into his theory of general relativity [5]. At the time Einstein believed the universe to be static, and yet his original field equations, which describe how the gravitational influence of matter bends space-time, predicted an expanding (or contracting) one. To resolve this a...

Abstract Typical observers in the universe do not follow smooth Hubble expansion, but move relative to it. Such bulk peculiar motions introduce a characteristic scale that is closely analogous familiar Jeans length. This “peculiar length” marks threshold below which relative-motion effects dominate linear kinematics. There, cosmological measurements can vary considerably between bulk-flow frame...

BACKGROUND The metformin label has recently been changed from serum creatinine (sCr)-based to estimated glomerular filtration rate (eGFR)-based indication, which is expected to expand its use for patients with mild renal insufficiency. However, because the sCr level is lower in Asians than in Caucasians at the same level of renal function, this change might not expand metformin use in the Asian...

We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting, and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them, previously predicted hyperbolicity is confirmed. The third one provides an example of a ...

We discuss a robotic system composed of Crystalline modules. Crystaline modules can aggregate together to form distributed robot systems. Crystalline modules can move relative to each other by expanding and contracting. This actuation mechanism permits automated shape metamorphosis. We describe the crystalline module concept and show the basic motions that enable a crystalline robot system to s...