A Unitarity-Conserving Higgs Inflation Model

Scalar field models of inflation based on a large nonminimal coupling to gravity xi, in particular, Higgs inflation, may violate unitarity at an energy scale ~ M_p / xi << M_p. In this case the model is incomplete at energy scales relevant to inflation. Here we propose a new unitarity-conserving model of Higgs inflation. The completion of the theory is achieved via additional interactions which are proportional to products of the derivatives of the Higgs doublet. The resulting model differs from the original version of Higgs inflation in its prediction for the spectral index, with a classical value n = 0.974. In the case of a nonsupersymmetric model, quantum corrections are likely to strongly modify the tree-level potential, suggesting that supersymmetry or a gauge singlet scalar inflaton is necessary for a completely successful model.Comment: 5 pages, published versio

Stress correlations in glasses

We rigorously establish that, in disordered three-dimensional (3D) isotropic solids, the stress autocorrelation function presents anisotropic terms that decay as $1/r^3$ at long-range, with $r$ the distance, as soon as either pressure or shear stress fluctuations are normal. By normal, we mean that the fluctuations of stress, as averaged over spherical domains, decay as the inverse domain volume. Since this property is required for macroscopic stress to be self-averaging, it is expected to hold generically in all glasses and we thus conclude that the presence of $1/r^3$ stress correlation tails is the rule in these systems. Our proof follows from the observation that, in an infinite medium, when both material isotropy and mechanical balance hold, (i) the stress autocorrelation matrix is completely fixed by just two radial functions: the pressure autocorrelation and the trace of the autocorrelation of stress deviators; furthermore, these two functions (ii) fix the decay of the fluctuations of sphere-averaged pressure and deviatoric stresses for windows of increasing volume. Our conclusion is reached because, due to the precise analytic relation (i) fixed by isotropy and mechanical balance, the constraints arising via (ii) from the normality of stress fluctuations demand the spatially anisotropic stress correlation terms to decay as $1/r^3$ at long-range. For the sake of generality, we also examine situations when stress fluctuations are not normal

Spectral Variations in Early-Type Galaxies as a Function of Mass

We report on the strengths of three spectral indicators - Mg_2, Hbeta, and Hn/Fe - in the integrated light of a sample of 100 field and cluster E/S0 galaxies. The measured indices are sensitive to age and/or and metallicity variations within the galaxy sample. Using linear regression analysis for data with non-uniform errors, we determine the intrinsic scatter present among the spectral indices of our galaxy sample as a function of internal velocity dispersion. Our analysis indicates that there is significantly more intrinsic scatter in the two Balmer line indices than in the Mg_2 index, indicating that the Balmer indices provide more dynamic range in determining the age of a stellar population than does the Mg_2 index. Furthermore, the scatter is much larger for the low velocity dispersion galaxies, indicating that star formation has occurred more recently in the lower mass galaxies.Comment: 4 pages, 1 figure, 1 table, to appear in the Astrophysical Journal Letter

A finite difference scheme for the equilibrium equations of elastic bodies

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques

A compact finite difference scheme for div(Rho grad u) - q2u = 0

A representative class of elliptic equations is treated by a dissipative compact finite difference scheme and a general solution technique by relaxation methods is discussed in detail for the Laplace equation

Control of broad-area vertical-cavity surface emitting laser emission by optically induced photonic crystals

We control the emission properties of a broad-area vertical-cavity surface emitting laser by coupling it to an external feedback cavity containing a photorefractive crystal with an optically induced photonic lattice. The periodic modulation of the refractive index serves as a tunable filter and enables the dynamic suppression of unwanted spatial instabilities and modes, as originally suggested by Gomila et al

Governing behaviour: Habits and the science of behaviour change

In this chapter I examine the emergence and characteristics of ‘behavioural science’ and its claim to provide the basis for governing behaviour through science. I explore some of the different forms that such a behavioural science has taken, and in particular the extent to which it does seek to govern through the shaping and reshaping of habits. This is exemplified with examples from the management of the coronavirus (COVID-19) pandemic in the United Kingdom in 2020. Following a brief account of the neurobiology of habits that has largely been based on research with animals, I consider its take-up within social psychology in accounting for human habitual conduct. This involves a renewed emphasis on the power of the situation, entailing some ambiguity about the role of conscious goals in eliciting habitual behaviour. Overall, I argue that the behavioural science strategy of governing conduct through communication of ‘scientific evidence’ has the aim of intensifying each individual’s responsibility to care for themselves at the very same time as they enact their ‘citizenship’ responsibilities to others. The hope, which might be misplaced, is that one can govern the behaviour of millions by governing the ways that each individual behaves themselves