Scalar potential

About: Scalar potential is a research topic. Over the lifetime, 3642 publications have been published within this topic receiving 78868 citations. The topic is also known as: potential.

A generalized cable equation for magnetic stimulation of axons

Abstract: During magnetic stimulation, electric fields are induced both on the inside (intracellular region) and the outside (extracellular region) of nerve fibers. The induced electric fields in each region can be expressed as the sum of a primary and a secondary component. The primary component arises due to an applied time varying magnetic field and is the time derivative of a vector potential. The secondary component of the induced field arises due to charge separation in the volume conductor surrounding the nerve fiber and is the gradient of a scalar potential. The question, "What components of intracellular fields and extracellular induced electric fields contribute to excitation?" has, so far, not been clearly addressed. Here, the authors address this question while deriving a generalized cable equation for magnetic stimulation and explicitly identify the different components of applied fields that contribute to excitation. In the course of this derivation, the authors review several assumptions of the core-conductor cable model in the context of magnetic stimulation. It is shown that out of the possible 4 components, only the first spatial derivative of the intracellular primary component and the extracellular secondary component of the fields contribute to excitation of a nerve fiber. An earlier form of the cable equation for magnetic stimulation has been shown to result in solutions identical to three-dimensional (3D) volume-conductor model for the specific configuration of an isolated axon in a located in an infinite homogenous conducting medium. The authors extend and generalize this result by demonstrating that their generalized cable equation results in solutions identical to 3D volume conductor models even for complex geometries of volume conductors surrounding axons such as a nerve bundle of different conductivity surrounding axons. This equivalence in the solutions is valid for several representations of a nerve bundle such as anisotropic monodomain and bidomain models.

Fibre Inflation: Observable Gravity Waves from IIB String Compactifications

Abstract: We introduce a simple string model of inflation, in which the inflaton field can take trans-Planckian values while driving a period of slow-roll inflation. This leads naturally to a realisation of large field inflation, inasmuch as the inflationary epoch is well described by the single-field scalar potential $V = V_0 (3-4 e^{-\hat\varphi/\sqrt{3}})$. Remarkably, for a broad class of vacua all adjustable parameters enter only through the overall coefficient $V_0$, and in particular do not enter into the slow-roll parameters. Consequently these are determined purely by the number of \e-foldings, $N_e$, and so are not independent: $\varepsilon \simeq \frac32 \eta^2$. This implies similar relations among observables like the primordial scalar-to-tensor amplitude, $r$, and the scalar spectral tilt, $n_s$: $r \simeq 6(n_s - 1)^2$. $N_e$ is itself more model-dependent since it depends partly on the post-inflationary reheat history. In a simple reheating scenario a reheating temperature of $T_{rh}\simeq 10^{9}$ GeV gives $N_e\simeq 58$, corresponding to $n_s\simeq 0.970$ and $r\simeq 0.005$, within reach of future observations. The model is an example of a class that arises naturally in the context of type IIB string compactifications with large-volume moduli stabilisation, and takes advantage of the generic existence there of Kahler moduli whose dominant appearance in the scalar potential arises from string loop corrections to the Kahler potential. The inflaton field is a combination of Kahler moduli of a K3-fibered Calabi-Yau manifold. We believe there are likely to be a great number of models in this class -- `high-fibre models' -- in which the inflaton starts off far enough up the fibre to produce observably large primordial gravity waves.

Quasi-Newtonian dust cosmologies

Abstract: Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function N (the relativistic acceleration scalar potential) which evolves along the reference congruence according to , we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearizing the dynamical equations about a (non-comoving) FLRW background. In this case, on properly accounting for the first-order momentum density relating to the non-relativistic peculiar motion of the matter, additional source terms arise in the evolution and constraint equations describing small-amplitude energy density fluctuations that do not appear in similar gravitational instability scenarios in the standard literature.