Elastic cavitation, tube hollowing, and differential growth in plants and biological tissues

Elastic cavitation is a well-known physical process by which elastic materials under stress can open cavities. Usually, cavitation is induced by applied loads on the elastic body. However, growing materials may generate stresses in the absence of applied loads and could induce cavity opening. Here, we demonstrate the possibility of spontaneous growth-induced cavitation in elastic materials and consider the implications of this phenomenon to biological tissues and in particular to the problem of schizogenous aerenchyma formation

New Innovation Models in Medical AI

In recent years, scientists and researchers have devoted considerable resources to developing medical artificial intelligence (AI) technologies. Many of these technologies—particularly those that resemble traditional medical devices in their functions—have received substantial attention in the legal and policy literature. But other types of novel AI technologies, such as those related to quality improvement and optimizing use of scarce facilities, have been largely absent from the discussion thus far. These AI innovations have the potential to shed light on important aspects of health innovation policy. First, these AI innovations interact less with the legal regimes that scholars traditionally conceive of as shaping medical innovation: patent law, FDA regulation, and health insurance reimbursement. Second, and perhaps related, a different set of innovation stakeholders, including health systems and insurers, are conducting their own research and development in these areas for their own use without waiting for commercial product developers to innovate for them. The activities of these innovators have implications for health innovation policy and scholarship. Perhaps most notably, data possession and control play a larger role in determining capacity to innovate in this space, while the ability to satisfy the quality standards of regulators and payers plays a smaller role relative to more familiar biomedical innovations such as new drugs and devices

The Problem of Inertia in Friedmann Universes

In this paper we study the origin of inertia in a curved spacetime, particularly the spatially flat, open and closed Friedmann universes. This is done using Sciama's law of inertial induction, which is based on Mach's principle, and expresses the analogy between the retarded far fields of electrodynamics and those of gravitation. After obtaining covariant expressions for electromagnetic fields due to an accelerating point charge in Friedmann models, we adopt Sciama's law to obtain the inertial force on an accelerating mass $m$ by integrating over the contributions from all the matter in the universe. The resulting inertial force has the form $F = -kma$, where $k < 1$ depends on the choice of the cosmological parameters such as $\Omega_{M}$, $\Omega_{\Lambda}$, and $\Omega_{R}$ and is also red-shift dependent.Comment: 10 page

Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing

We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her with the previously found constraints, these form a sufficient number of second class constraints so that the phase space is reduced to one pair of canonically conjugate variables: \Ac_2\and\Sc^2. The formalism is related to both the Bondi-Sachs and the Newman-Penrose methods of studying the gravitational field at null infinity. Asymptotic solutions in the vicinity of null infinity which exclude logarithmic behavior require the connection to fall off like $1/r^3$ after the Minkowski limit. This, of course, gives the previous results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off more slowly leads to logarithmic behavior which leaves null infinity intact, allows for meaningful gravitational radiation, but the peeling theorem does not extend to $\Psi_1$ in the terminology of Newman-Penrose. The conclusions are in agreement with those of Chrusciel, MacCallum, and Singleton. This work was begun as a preliminary study of a reduced phase space for quantization of general relativity.Comment: magnification set; pagination improved; 20 pages, plain te

Transverse frames for Petrov type I spacetimes: a general algebraic procedure

We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars $\Psi_{1}$ and $\Psi_{3}$ equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov Type I spacetime, setting $\Psi_{1}$ and $\Psi_{3}$ to zero makes apparent the superposition of a Coulomb-type effect $\Psi_{2}$ with transverse degrees of freedom $\Psi_{0}$ and $\Psi_{4}$.Comment: 10 pages, submitted to Classical Quantum Gravit

New Innovation Models in Medical AI

In recent years, scientists and researchers have devoted considerable resources to developing medical artificial intelligence (AI) technologies. Many of these technologies—particularly those that resemble traditional medical devices in their functions—have received substantial attention in the legal and policy literature. But other types of novel AI technologies, such as those related to quality improvement and optimizing use of scarce facilities, have been largely absent from the discussion thus far. These AI innovations have the potential to shed light on important aspects of health innovation policy. First, these AI innovations interact less with the legal regimes that scholars traditionally conceive of as shaping medical innovation: patent law, FDA regulation, and health insurance reimbursement. Second, and perhaps related, a different set of innovation stakeholders, including health systems and insurers, are conducting their own research and development in these areas for their own use without waiting for commercial product developers to innovate for them. The activities of these innovators have implications for health innovation policy and scholarship. Perhaps most notably, data possession and control play a larger role in determining capacity to innovate in this space, while the ability to satisfy the quality standards of regulators and payers plays a smaller role relative to more familiar biomedical innovations such as new drugs and devices

Lightcone reference for total gravitational energy

We give an explicit expression for gravitational energy, written solely in terms of physical spacetime geometry, which in suitable limits agrees with the total Arnowitt-Deser-Misner and Trautman-Bondi-Sachs energies for asymptotically flat spacetimes and with the Abbot-Deser energy for asymptotically anti-de Sitter spacetimes. Our expression is a boundary value of the standard gravitational Hamiltonian. Moreover, although it stands alone as such, we derive the expression by picking the zero-point of energy via a ``lightcone reference.''Comment: latex, 7 pages, no figures. Uses an amstex symbo

Integration of the Friedmann equation for universes of arbitrary complexity

An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models consisting of an arbitrary number of non-interacting species. The inheritance of constants of the motion from simpler models as more species are added is stressed. It is then argued that all FLRW models admit what amounts to a unique candidate for a gravitational epoch function (a dimensionless scalar invariant derivable from the Riemann tensor without differentiation which is monotone throughout the evolution of the universe). The same relations that lead to the construction of constants of the motion allow an explicit evaluation of this function. In the simplest of all models, the $\Lambda$CDM model, it is shown that the epoch function exists for all models with $\Lambda > 0$, but for almost no models with $\Lambda \leq 0$.Comment: Final form to appear in Physical Review D1

(2,2)-Formalism of General Relativity: An Exact Solution

I discuss the (2,2)-formalism of general relativity based on the (2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian signature. In this formalism general relativity is describable as a Yang-Mills gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge symmetry is the group of the diffeomorphisms of the 2-dimensional fibre manifold. After presenting the Einstein's field equations in this formalism, I solve them for spherically symmetric case to obtain the Schwarzschild solution. Then I discuss possible applications of this formalism.Comment: 2 figures included, IOP style file neede