Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial... Show moreExcitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic or electrical scroll waves in the heart. Here we show that such phenomena can be extended to a space of four or more dimensions and propose that connections of excitable elements in a network setting can be regarded as additional spatial dimensions. Numerical simulations are performed in four dimensions using the FitzHugh-Nagumo model, showing that the vortices rotate around a twodimensional surface which we define as the superfilament. Evolution equations are derived for general superfilaments of codimension two in an N-dimensional space, and their equilibrium configurations are proven to be minimal surfaces. We suggest that biological excitable systems, such as the heart or brain which have nonlocal connections can be regarded, at least partially, as multidimensional excitable media and discuss further possible studies in this direction. Show less
In holographic inflation, the 4D cosmological dynamics is postulated to be dual to the renormalization group flow of a 3D Euclidean conformal field theory with marginally relevant operators. The... Show moreIn holographic inflation, the 4D cosmological dynamics is postulated to be dual to the renormalization group flow of a 3D Euclidean conformal field theory with marginally relevant operators. The scalar potential of the 4D theory—in which inflation is realized—is highly constrained, with use of the Hamilton–Jacobi equations. In multifield holographic realizations of inflation, fields additional to the inflaton cannot display underdamped oscillations (that is, their wave functions contain no oscillatory phases independent of the momenta). We show that this result is exact, independent of the number of fields, the field space geometry, and the shape of the inflationary trajectory followed in multifield space. In the specific case where the multifield trajectory is a straight line or confined to a plane, it can be understood as the existence of an upper bound on the dynamical masses m of extra fields of the form m≤3H/2 up to slow roll corrections. This bound corresponds to the analytic continuation of the well-known Breitenlohner–Freedman bound found in anti–de Sitter spacetimes in the case when the masses are approximately constant. The absence of underdamped oscillations implies that a detection of “cosmological collider” oscillatory patterns in the non-Gaussian bispectrum would not only rule out single-field inflation, but also holographic inflation or any inflationary model based on the Hamilton–Jacobi equations. Hence, future observations have the potential to exclude, at once, an entire class of inflationary theories, regardless of the details involved in their model building. Show less
García-García, A.M.; Loureiro, B.; Romero, Bermudez A.; Tezuka, M. 2018
Local contact line pinning prevents droplets from rearranging to minimal global energy, and models for droplets without pinning cannot predict their shape. We show that experiments are much better... Show moreLocal contact line pinning prevents droplets from rearranging to minimal global energy, and models for droplets without pinning cannot predict their shape. We show that experiments are much better described by a theory, developed herein, that does account for the constrained contact line motion, using as an example droplets on tilted plates. We map out their shapes in suitable phase spaces. For 2D droplets, the critical point of maximum tilt depends on the hysteresis range and Bond number. In 3D, it also depends on the initial width, highlighting the importance of the deposition history. Show less
We describe the breakup of a confined gas thread in a cross-flowing stream of liquid at capillary numbers Ca < 10(-2). The breakup is initiated, not by a Plateau-Rayleigh instability, but by... Show moreWe describe the breakup of a confined gas thread in a cross-flowing stream of liquid at capillary numbers Ca < 10(-2). The breakup is initiated, not by a Plateau-Rayleigh instability, but by liquid that flows from the tip of the thread to the neck where pinch-off occurs. This flow, faster than previously estimated, is driven by different curvatures at the tip and neck and runs through large gaps between thread and channel walls. Understanding how these curvatures evolve during bubble formation leads to accurate predictions of the moment of pinch-off. Show less
The effect of a Zeeman magnetic field coupled to the spin of the electrons on the conducting properties of the disordered Hubbard model is studied. Using the determinant quantum Monte Carlo method,... Show moreThe effect of a Zeeman magnetic field coupled to the spin of the electrons on the conducting properties of the disordered Hubbard model is studied. Using the determinant quantum Monte Carlo method, the temperature- and magnetic-field-dependent conductivity is calculated, as well as the degree of spin polarization. We find that the Zeeman magnetic field suppresses the metallic behavior present for certain values of interaction and disorder strength and is able to induce a metal-insulator transition at a critical field strength. It is argued that the qualitative features of magnetoconductance in this microscopic model containing both repulsive interactions and disorder are in agreement with experimental findings in two-dimensional electron and hole gases in semiconductor structures. Show less
Marchevsky, M.; Aarts, J.; Kes, P.H.; Indenbom, M.V. 1997
