What is the Temperature Dependence of the Casimir Effect?

There has been recent criticism of our approach to the Casimir force between real metallic surfaces at finite temperature, saying it is in conflict with the third law of thermodynamics and in contradiction with experiment. We show that these claims are unwarranted, and that our approach has strong theoretical support, while the experimental situation is still unclear.Comment: 6 pages, REVTeX, final revision includes two new references and related discussio

On the Temperature Dependence of the Casimir Effect

The temperature dependence of the Casimir force between a real metallic plate and a metallic sphere is analyzed on the basis of optical data concerning the dispersion relation of metals such as gold and copper. Realistic permittivities imply, together with basic thermodynamic considerations, that the transverse electric zero mode does not contribute. This results in observable differences with the conventional prediction, which does not take this physical requirement into account. The results are shown to be consistent with the third law of thermodynamics, as well as being consistent with current experiments. However, the predicted temperature dependence should be detectable in future experiments. The inadequacies of approaches based on {\it ad hoc} assumptions, such as the plasma dispersion relation and the use of surface impedance without transverse momentum dependence, are discussed.Comment: 14 pages, 3 eps figures, revtex4. New version includes clarifications and new reference. Accepted for publication in Phys. Rev.

On the origin of the distribution of binary-star periods

Pre-main sequence and main-sequence binary systems are observed to have periods, P, ranging from one day to 10^(10) days and eccentricities, e, ranging from 0 to 1. We pose the problem if stellar-dynamical interactions in very young and compact star clusters may broaden an initially narrow period distribution to the observed width. N-body computations of extremely compact clusters containing 100 and 1000 stars initially in equilibrium and in cold collapse are preformed. In all cases the assumed initial period distribution is uniform in the narrow range 4.5 < log10(P) < 5.5 (P in days) which straddles the maximum in the observed period distribution of late-type Galactic-field dwarf systems. None of the models lead to the necessary broadening of the period distribution, despite our adopted extreme conditions that favour binary--binary interactions. Stellar-dynamical interactions in embedded clusters thus cannot, under any circumstances, widen the period distribution sufficiently. The wide range of orbital periods of very young and old binary systems is therefore a result of cloud fragmentation and immediate subsequent magneto-hydrodynamical processes operating within the multiple proto-stellar system.Comment: 11 pages, 4 figures, ApJ, in pres

Phase transitions in simplified models with long-range interactions

We study the origin of phase transitions in some simplified models with long range interactions. For the ring model, we show that a possible new phase transition predicted in a recent paper by Nardini and Casetti from an energy landscape analysis does not occur. Instead of such phase transitions we observe a sharp, although without any non-analiticity, change from a core-halo to an only core configuration in the spatial distribution functions for low energies. By introducing a new class of solvable simplified models without any critical points in the potential energy, we show that a similar behaviour to the ring model is obtained, with a first order phase transition from an almost homogeneous high energy phase to a clustered phase, and the same core-halo to core configuration transition at lower energies. We discuss the origin of these features of the simplified models, and show that the first order phase transition comes from the maximization of the entropy of the system as a function of energy an an order parameter, as previously discussed by Kastner, which seems to be the main mechanism causing phase transitions in long-range interacting systems

Online Games

When we agreed to edit the theme on online games for this Encyclopedia our first question was, “What is meant by online games?” Scholars of games distinguish between nondigital games (such as board games) and digital games, rather than between online and offline games. With networked consoles and smartphones it is becoming harder and harder to find players in the wealthy industrialized countries who play “offline” digital games. Most games developers now include some element of online activity in their game and the question is:What is the degree to which the gameplay experience occurs online? Is online gameplay more a multiplayer than an individual experience? If we move beyond the technological meaning of “being online” we should, as Newman (2002) argued, be concerned with varying degrees of participation during gameplay

A pilgrimage to gravity on GPUs

In this short review we present the developments over the last 5 decades that have led to the use of Graphics Processing Units (GPUs) for astrophysical simulations. Since the introduction of NVIDIA's Compute Unified Device Architecture (CUDA) in 2007 the GPU has become a valuable tool for N-body simulations and is so popular these days that almost all papers about high precision N-body simulations use methods that are accelerated by GPUs. With the GPU hardware becoming more advanced and being used for more advanced algorithms like gravitational tree-codes we see a bright future for GPU like hardware in computational astrophysics.Comment: To appear in: European Physical Journal "Special Topics" : "Computer Simulations on Graphics Processing Units" . 18 pages, 8 figure

The Promiscuous Nature of Stars in Clusters

The recent availability of special purpose computers designed for calculating gravitational interactions of N-bodies at extremely high speed has provided the means to model globular clusters on a star-by-star basis for the first time. By endeavouring to make the N-body codes that operate on these machines as realistic as possible, the addition of stellar evolution being one example, much is being learnt about the interaction between the star cluster itself and the stars it contains. A fascinating aspect of this research is the ability to follow the orbits of individual stars in detail and to document the formation of observed exotic systems. This has revealed that many stars within a star cluster lead wildly promiscuous lives, interacting, often intimately and in rapid succession, with a variety of neighbours.Comment: 15 pages, 1 figure, to appear in the Astrophysical Journa

Casimir energy and entropy between dissipative mirrors

We discuss the Casimir effect between two identical, parallel slabs, emphasizing the role of dissipation and temperature. Starting from quite general assumptions, we analyze the behavior of the Casimir entropy in the limit T->0 and link it to the behavior of the slab's reflection coefficients at low frequencies. We also derive a formula in terms of a sum over modes, valid for dissipative slabs that can be interpreted in terms of a damped quantum oscillator.Comment: 8 pages, 1 figur

Casimir Force on a Micrometer Sphere in a Dip: Proposal of an Experiment

The attractive Casimir force acting on a micrometer-sphere suspended in a spherical dip, close to the wall, is discussed. This setup is in principle directly accessible to experiment. The sphere and the substrate are assumed to be made of the same perfectly conducting material.Comment: 11 pages, 1 figure; to appear in J. Phys. A: Math. Ge