Ageing, dynamical scaling and conformal invariance

Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local free field theories. The scaling form of two-point functions is completely fixed by the requirement of local scale invariance. These predictions are confirmed through tests in the 3D ANNNI model at its Lifshitz point and in ageing phenomena of simple ferromagnets, here studied through the kinetic Ising model with Glauber dynamics.Comment: Latex2e, 12 pages, 3 figures. Talk given at TH2002, Paris July 200

On the new approach to variable separation in the time-dependent Schr\"odinger equation with two space dimensions

We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit separation of variables. Besides that, we carry out separation of variables in the Schr\" odinger equation with the anisotropic harmonic oscillator potential $V=k_1x_1^2+k_2x_2^2$ and obtain a complete list of coordinate systems providing its separability. Most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schr\" odinger equation ($V=0$).Comment: 21 pages, latex, to appear in the "Journal of Mathematical Physics" (1995

The social media life of climate change: Platforms, publics, and future imaginaries

Social media is a transformative digital technology, collapsing the “six degrees of separation” which have previously characterized many social networks, and breaking down many of the barriers to individuals communicating with each other. Some commentators suggest that this is having profound effects across society, that social media have opened up new channels for public debates and have revolutionized the communication of prominent public issues such as climate change. In this article we provide the first systematic and critical review of the literature on social media and climate change. We highlight three key findings from the literature: a substantial bias toward Twitter studies, the prevalent approaches to researching climate change on social media (publics, themes, and professional communication), and important empirical findings (the use of mainstream information sources, discussions of “settled science,” polarization, and responses to temperature anomalies). Following this, we identify gaps in the existing literature that should be addressed by future research: namely, researchers should consider qualitative studies, visual communication and alternative social media platforms to Twitter. We conclude by arguing for further research that goes beyond a focus on science communication to a deeper examination of how publics imagine climate change and its future role in social life

REGULATION OF CORONARY BLOOD FLOW DURING ETHER AND HALOTHANE ANAESTHESIA

SUMMARY The effects of ether (6-10%) and halothane (1-2%) were studied on coronary flow regulation in dogs. In one group of experiments the kft coronary artery was perfused mechanically, coronary perfusion pressure being either kept constant or adjusted to aortic pressure, and the heart itself had to pump the blood to all other arteries. The preload on the heart was changed by varying die intravascular volume. In another group, bodi coronary arteries were perfused mechanically under constant pressure; the other arteries were also perfused mechanically by a cardiopulmonary bypass. In this group measurements were carried out on the empty beating heart. Halothane had a direct effect on die heart, myocardial contractility was reduced, cardiac work and myocardial oxygen consumption were diminished and coronary vasoconstriction followed. Edier effects on the heart were principally die same as diose due to halodiane, but to a lesser degree. Coronary vasoconstriction caused by halodiane did not produce myocardial hypoxia. Coronary vasoconstriction occurred as an autorcgulatory mechanism preventing "unnecessary ” hyperperfusion as long as cardiac work and oxygen consumption were diminished. Bodi edier and halodiane reduced systemic vascular resistanc

Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential

We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear effects, can be described quite precisely. This includes semi-classical regimes, as well as finite time blow-up and scattering issues. We present the tools used for these problems, as well as their limitations, and outline the arguments of the proofs.Comment: 20 pages; survey of previous result

Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities

We perform the complete group classification in the class of nonlinear Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$ $\gamma$ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.Comment: 10 page

An analysis of the spatial arrangement of the myocardial aggregates making up the wall of the left ventricle

Objective: We used the technique of peeling of myocardial aggregates, usually described as ‘fibres', to determine the spatial arrangement of the myocytes in the left ventricular wall of a healthy autopsied human heart. Methods: We digitised the left ventricular outer and inner boundaries, as well as the pathways in space, of almost 3000 aggregates harvested from the left ventricular myocardium. During the process of gradual peeling, we sought to identify the myocardial aggregates as uniformly as possible. Despite this, interpolation was necessary to complete the pattern so as to construct a unit vector field that represented the preferred direction of the myocardial aggregates throughout the entirety of the walls of the left ventricle of this individual human heart. Results: Apart from the overall systematic arrangement of the aggregates necessary to achieve physiologic ventricular contraction, we documented substantial local heterogeneities in the orientation of the myocardial aggregates. In particular, a significant proportion of aggregates was found to intrude obliquely with respect to the ventricular boundaries, with markedly heterogeneous distribution. Moreover, the distribution of the helical angle of the aggregates relative to the ventricular base varied notably throughout the left ventricular free walls and the septum. Within the generally quite uniform and continuous structure of the ventricular mass, we were, however, unable to identify any organised tracts or functional subunits such as a ‘helical ventricular band', nor did we find radial fibrous lamellas coursing across the ventricular wall. Conclusion: We suggest that the impact of local anatomical inhomogeneities, associated with gradients in regional contractile function on global ventricular dynamics, has been systematically underestimated in the past. Our analysis confirms furthermore the continuous nature of the myocardium associated with an overall gross organisation of the fibre direction field; however, there is no evidence of substructures compartmentalising the ventricle

Symmetry based determination of space-time functions in nonequilibrium growth processes

We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations, we derive expressions for the universal scaling functions of two-time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion. The usefulness of the space-time functions is illustrated through the investigation of two atomistic growth models, the Family model and the restricted Family model, which are shown to belong to a unique universality class in 1+1 and in 2+1 space dimensions. This corrects earlier studies which claimed that in 2+1 dimensions the two models belong to different universality classes.Comment: 18 pages, three figures included, submitted to Phys. Rev.