A mean spherical model for soft potentials: The hard core revealed as a perturbation

The mean spherical approximation for fluids is extended to treat the case of dense systems interacting via soft-potentials. The extension takes the form of a generalized statement concerning the behavior of the direct correlation function c(r) and radial distribution g(r). From a detailed analysis that views the hard core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions

Complementarity and Scientific Rationality

Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the acceptance of his approach to quantum mechanics over de Broglie's had no reasonable foundation. But Bohr's interpretation changed little from the time of its first appearance, and stood independent of any philosophical presuppositions. The principle of complementarity is itself best read as a conjecture of unusually wide scope, on the nature and future course of explanations in the sciences (and not only the physical sciences). If it must be judged a failure today, it is not because of any internal inconsistency.Comment: 29 page

Density Functional for Anisotropic Fluids

We propose a density functional for anisotropic fluids of hard body particles. It interpolates between the well-established geometrically based Rosenfeld functional for hard spheres and the Onsager functional for elongated rods. We test the new approach by calculating the location of the the nematic-isotropic transition in systems of hard spherocylinders and hard ellipsoids. The results are compared with existing simulation data. Our functional predicts the location of the transition much more accurately than the Onsager functional, and almost as good as the theory by Parsons and Lee. We argue that it might be suited to study inhomogeneous systems.Comment: To appear in J. Physics: Condensed Matte

Conventional and manipulated growth of Cu-Cu(111)

Molecular beam epitaxy of Cu on Cu(111) was studied using thermal energy He scattering, in the temperature range between 100 and 450 K. Three-dimensional growth was observed in the whole temperature range. To determine the onset of various diffusion processes, submonolayer films formed by deposition at low temperature were annealed. Annealing proceeds in two steps. The first step is interpreted as a change in island shape, the second as Ostwald-ripening. A comparison with homoepitaxy on Pt(111) and Ag(111) is made. Growth manipulation was carried out by artificially increasing the island number density via intervention in the nucleation stage of each layer. The procedures applied were temperature reduction during nucleation as well as pulsed ion bombardment. These techniques enabled the convenient growth of good quality films consisting of a large number of monolayers. Finally, the use of oxygen as a surfactant modifying the growth mode was investigated. Under some growth conditions, pre-exposure of the surface to oxygen was found to induce weak He-intensity oscillations during deposition. The quality of the films grown in this way was, however, low

Noether symmetries, energy-momentum tensors and conformal invariance in classical field theory

In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on board, we next discuss in detail, for Poincar\'e invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincar\'e symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincar\'e. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincar\'e invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved bakground.Comment: 31 pa

The 2024 Cardozo Colloquium on Global and Constitutional Theory Presents: Linda Greenhouse on the Roberts Court

Join Linda Greenhouse, Senior Research Scholar in Law at Yale Law School, to discuss the exceptional trajectory of the Roberts Court. Greenhouse is also a Pulitzer Prize-winning reporter who has covered the United States Supreme Court for nearly three decades for The New York Times.https://larc.cardozo.yu.edu/event-invitations-2024/1004/thumbnail.jp

Phase behaviour of additive binary mixtures in the limit of infinite asymmetry

We provide an exact mapping between the density functional of a binary mixture and that of the effective one-component fluid in the limit of infinite asymmetry. The fluid of parallel hard cubes is thus mapped onto that of parallel adhesive hard cubes. Its phase behaviour reveals that demixing of a very asymmetric mixture can only occur between a solvent-rich fluid and a permeated large particle solid or between two large particle solids with different packing fractions. Comparing with hard spheres mixtures we conclude that the phase behaviour of very asymmetric hard-particle mixtures can be determined from that of the large component interacting via an adhesive-like potential.Comment: Full rewriting of the paper (also new title). 4 pages, LaTeX, uses revtex, multicol, epsfig, and amstex style files, to appear in Phys. Rev. E (Rapid Comm.

Lightweight Heat Pipes Made from Magnesium

Magnesium has shown promise as a lighter-weight alternative to the aluminum alloys now used to make the main structural components of axially grooved heat pipes that contain ammonia as the working fluid. Magnesium heat-pipe structures can be fabricated by conventional processes that include extrusion, machining, welding, and bending. The thermal performances of magnesium heat pipes are the same as those of equal-sized aluminum heat pipes. However, by virtue of the lower mass density of magnesium, the magnesium heat pipes weigh 35 percent less. Conceived for use aboard spacecraft, magnesium heat pipes could also be attractive as heat-transfer devices in terrestrial applications in which minimization of weight is sought: examples include radio-communication equipment and laptop computers

Spherical Collapse in Chameleon Models

We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse depends on the initial comoving size of the inhomogeneity.Comment: matches printed versio