Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum

In this paper we consider the question of the degree to which negative and positive energy are intertwined. We examine in more detail a previously studied quantum state of the massless minimally coupled scalar field, which we call a ``Helfer state''. This is a state in which the energy density can be made arbitrarily negative over an arbitrarily large region of space, but only at one instant in time. In the Helfer state, the negative energy density is accompanied by rapidly time-varying energy fluxes. It is the latter feature which allows the quantum inequalities, bounds which restrict the magnitude and duration of negative energy, to hold for this class of states. An observer who initially passes through the negative energy region will quickly encounter fluxes of positive energy which subsequently enter the region. We examine in detail the correlation between the energy density and flux in the Helfer state in terms of their expectation values. We then study the correlation function between energy density and flux in the Minkowski vacuum state, for a massless minimally coupled scalar field in both two and four dimensions. In this latter analysis we examine correlation functions rather than expectation values. Remarkably, we see qualitatively similar behavior to that in the Helfer state. More specifically, an initial negative energy vacuum fluctuation in some region of space is correlated with a subsequent flux fluctuation of positive energy into the region. We speculate that the mechanism which ensures that the quantum inequalities hold in the Helfer state, as well as in other quantum states associated with negative energy, is, at least in some sense, already ``encoded'' in the fluctuations of the vacuum.Comment: 21 pages, 7 figures; published version with typos corrected and one added referenc

The evolution of sperm morphometry in pheasants

Postcopulatory sexual selection is thought to be a potent evolutionary force driving the diversification of sperm shape and function across species. In birds, insemination and fertilisation are separated in time and sperm storage increases the duration of sperm female interaction and hence the opportunity for sperm competition and cryptic female choice. We performed a comparative study of 24 pheasant species (Phasianidae, Galliformes) to establish the relative importance of sperm competition and the duration of sperm storage for the evolution of sperm morphometry (i.e. size of different sperm traits). We found that sperm size traits were negatively associated with the duration of sperm storage but were independent of the risk of sperm competition estimated from relative testis mass. Our study emphasises the importance of female reproductive biology for the evolution of sperm morphometry particularly in sperm storing taxa

Weighted Radon transforms for which the Chang approximate inversion formula is precise

We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given

Wrapping an adhesive sphere with a sheet

We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss'Theorema Egregium shows that this operation necessarily generates metric distortions (i.e. stretching) as well as bending. As a result, a large variety of contact patterns ranging from simple disks to complex branched shapes are observed as a function of both geometrical and material properties. We describe these different morphologies as a function of two non-dimensional parameters comparing respectively bending and stretching energies to adhesion. A complete configuration diagram is finally proposed

Josephson junction between anisotropic superconductors

The sin-Gordon equation for Josephson junctions with arbitrary misaligned anisotropic banks is derived. As an application, the problem of Josephson vortices at twin planes of a YBCO-like material is considered. It is shown that for an arbitrary orientation of these vortices relative to the crystal axes of the banks, the junctions should experience a mechanical torque which is evaluated. This torque and its angular dependence may, in principle, be measured in small fields, since the flux penetration into twinned crystals begins with nucleation of Josephson vortices at twin planes.Comment: 6 page

Bernoulli type polynomials on Umbral Algebra

The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating functions, we provide to deriving identities for these polynomials

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

Feasibility of sulfur concrete for martian constructions

A significant step in space exploration during the 21st century will be the human settlement on Mars. Instead of transporting all the construction materials from Earth to the red planet with incredibly high cost, using Martian soil to construct a site on Mars is a superior choice. Mars has long been considered a “sulfur-rich planet”. Studies of Martian meteorites suggest elevated sulfur concentrations in the interior, and Martian surface deposits contain high levels of sulfur (SO3 up to ~37 wt%, average ~6 wt%), likely in the form of sulfate salts1. To let the thoughts become facts, a new construction material using simulated Martian soil and molten sulfur is developed. In fact, sulfur concrete is not a new concept. The utilization of sulfur as a molten bonding agent can be traced back to prehistoric times2. Sulfur concretes are being produced by first hot-mixing sulfur (or modified sulfur) and aggregates, which allows the sulfur binder crystalize as monoclinic sulfur (Sβ), then letting the mixture cool down while sulfur transform to the stable orthorhombic polymorph (Sα) to achieve a reliable building material. In addition to the raw material availability, the utilization of sulfur concrete has many advantages compared to conventional Portland cement concrete. The strength reaches similar levels while the fatigue life, low temperature sustainability, and the curing time are superior, a minimum of 70-80 % of the ultimate compressive strength is reached within 24 hours