How thin can a microfiber be and still guide light?

For the adiabatically deformed optical fiber the intermode transmission amplitudes and loss vanish exponentially with the characteristic length of the fiber's nonuniformity. For this reason smoothly deformed optical fiber tapers can have very small losses. However, losses dramatically increase with a thinning of the microfiber down to a diameter much smaller than the radiation wavelength. The theory of nonadiabatic intermode transitions is briefly discussed and, by using this theory, the problem of the smallest diameter of a microfiber that can transmit evanescent radiation is studied. It is shown that even for an extremely high uniformity of microfiber the ability of light transmission does not leave much space for microfiber thinning: the propagating mode vanishes at a threshold value of the microfiber's diameter, that is smaller than the radiation wavelength by only an order of magnitude.     

How different is a hard-sphere fluid from a suspension of hard-sphere colloids near the glass transition?

This paper compares simulation and experiment to verify how a hard-sphere fluid is different from a suspension of hard-sphere colloids near the glass transition at 6% polydispersity. This is done by performing extensive molecular-dynamic simulations and by analyzing the resultant mean-square displacement from a unified viewpoint based on the mean-field theory proposed recently by Tokuyama [Physica A 364 (2006) 23–62]. The remarkable similarities are found in various physical quantities between two systems, except their phase diagrams, in which the experiment shows the glass transition, while the simulation shows the temporal re-entrant melting (transition from crystal to supercooled liquid) followed by the glass transition within a limited waiting time of order 8.4×10⁴$8.4\times {10}^4$ in a dimensionless unit.     

How random is a random vector?

Over 80 years ago Samuel Wilks proposed that the “generalized variance” of a random vector is the determinant of its covariance matrix. To date, the notion and use of the generalized variance is confined only to very specific niches in statistics. In this paper we establish that the “Wilks standard deviation” –the square root of the generalized variance–is indeed the standard deviation of a random vector. We further establish that the “uncorrelation index” –a derivative of the Wilks standard deviation–is a measure of the overall correlation between the components of a random vector. Both the Wilks standard deviation and the uncorrelation index are, respectively, special cases of two general notions that we introduce: “randomness measures” and “independence indices” of random vectors. In turn, these general notions give rise to “randomness diagrams”—tangible planar visualizations that answer the question: How random is a random vector? The notion of “independence indices” yields a novel measure of correlation for Lévy laws. In general, the concepts and results presented in this paper are applicable to any field of science and engineering with random-vectors empirical data.     

How fat is a fat bundle?

Let P M be a principal G-bundle with connection 1-form and curvature . For a subset S of g^* the given connection is S-fat (Weinstein, [5]) if for every in S the form ° is nondegenerate on each horizontal subspace in TP.Let K be a compact group and K/H be its coadjoint orbit. The orthogonal projection t h defines a connection on the principal H-bundle K K/H. We show that this connection is fat off certain walls of Weyl chambers in h^*. We then apply the result to the construction of symplectic fiber bundles over K/H. As an example, we show how higher-dimensional coadjoint orbits fiber symplectically over lower-dimensional orbits.     

How bosonic is a pair of fermions?

Composite particles made of two fermions can be treated as ideal elementary bosons as long as the constituent fermions are sufficiently entangled. In that case, the Pauli principle acting on the parts does not jeopardise the bosonic behaviour of the whole. An indicator for bosonic quality is the composite boson normalisation ratio \(\chi _{N+1}/\chi _{N}\) of a state of \(N\) composites. This quantity is prohibitively complicated to compute exactly for realistic two-fermion wavefunctions and large composite numbers \(N\) . Here, we provide an efficient characterisation in terms of the purity \(P\) and the largest eigenvalue \(\lambda _1\) of the reduced single-fermion state. We find the states that extremise \(\chi _N\) for given \(P\) and \(\lambda _1\) , and we provide easily evaluable, saturable upper and lower bounds for the normalisation ratio. Our results strengthen the relationship between the bosonic quality of a composite particle and the entanglement of its constituents.     

How interdisciplinary is nanotechnology?

Facilitating cross-disciplinary research has attracted much attention in recent years, with special concerns in nanoscience and nanotechnology. Although policy discourse has emphasized that nanotechnology is substantively integrative, some analysts have countered that it is really a loose amalgam of relatively traditional pockets of physics, chemistry, and other disciplines that interrelate only weakly. We are developing empirical measures to gauge and visualize the extent and nature of interdisciplinary interchange. Such results speak to research organization, funding, and mechanisms to bolster knowledge transfer. In this study, we address the nature of cross-disciplinary linkages using “science overlay maps” of articles, and their references, that have been categorized into subject categories. We find signs that the rate of increase in nano research is slowing, and that its composition is changing (for one, increasing chemistry-related activity). Our results suggest that nanotechnology research encompasses multiple disciplines that draw knowledge from disciplinarily diverse knowledge sources. Nano research is highly, and increasingly, integrative—but so is much of science these days. Tabulating and mapping nano research activity show a dominant core in materials sciences, broadly defined. Additional analyses and maps show that nano research draws extensively upon knowledge presented in other areas; it is not constricted within narrow silos.

How probable is inflation?

The Henneaux-Gibbons-Hawking-Stewart canonical measure on the set of classical universes is applied to a Friedmann-Robertson-Walker model containing a massive scalar field. Although a uniform probability distribution in this measure would solve the flatness problem, it gives an ambiguous probability for inflation, since both the set of inflationary solutions and the set of noninflationary solutions have infinite measure.     

How adiabatic is quantum tunneling?

We consider the coupling between collective and intrinsic degrees of freedom of a many-dimensional quantum system. We give a criterion for the validity of the adiabatic approximation in tunneling processes and derive an equation for the “lag” of the intrinsic wave function with respect to the adiabatic groundstate. Solutions for several simple cases are presented.     

How old is surface science?

Philosophical and literary testimonies from the Classical World (5th century b.c. to 3rd century a.d.) involving solid surfaces are reviewed. Plato thought the surface to be a real entity, whereas Aristotle considered it to possess an unqualified existence, i.e. not to be a substance, but just an accidental entity. The Old Stoics asserted that surfaces do not possess any physical existence, although the Stoic philosopher Posidonius—apparently the only exception in his school—held them to exist both in thought and reality. While both the Atomists and the Epicureans were very little interested in them, the Sceptic philosopher Sextus Empiricus considered surfaces to be the limits of a body, although he maintained that both the view that they are corporeal or the view that they are incorporeal present unsurmountable difficulties.Among Roman authors, the testimony from Pliny the Elder is mostly concerned with metallic surfaces, chemical change occurring there, and surface treatments used in antiquity.Besides the philosophical motivations, the implications of the testimonies are discussed in the light of surface science. The purely geometrical surface of Plato is found to compare favorably to single-crystal surface, Posidonius’ “corporeal” surface is best likened to an air-oxidized, or otherwise ambient-modified surface, and ancient accounts on mixture are compared to XPS results obtained in adhesion studies of enameled steels. I argue that the long-standing dominance of Aristotle’s view from antiquity onwards may have had a part in delaying theoretical speculation into solid surfaces.     

Reentrant phases in the ± J spin glass

We consider an enlarged phase space of the ±J spin glass which includes the dilute Ising model and the frustrated system. The three orthogonal axes in this space are: (i) The fraction of ferro- to antiferro-magnetic bonds, p; (ii) the ratio of the strengths of the antiferro- to ferromagnetic interacions, q; and (iii) the temperature, T. Within this phase space we observe extended regions of the low-temperature spin-glass phase which is characterized by a unique distribution of the local-order parameter. We observe reentrant phase transitions: for fixed p and q with varying T the distribution of the local order parameter shows paramagnetic, ferromagnetic and then spin-glass phases; for fixed p and T and varying q the distribution shows ferromagnetic to paramagnetic and then spin-glass phases.     

How does crystalline substrate plasticity modify thin film buckling?

We report experimental atomic force microscopy observations and analytical modeling of buckling structures of thin films deposited on single crystal substrates. The formation of straight-sided blisters just above the step structures resulting from the dislocations emergence has been observed and explained in the framework of the F?ppl-von Karman theory of thin plates. A critical step height above which the buckling may occur has been determined and the asymmetry of the resulting blisters has been explained. Finally, the new buckling criterion has been compared with the classical one in the plane case and allows us to explain the blisters localization on step structures.     

How Magnetic is the Dirac Neutrino?

We derive model-independent, "naturalness" upper bounds on the magnetic moments munu of Dirac neutrinos generated by physics above the scale of electroweak symmetry breaking. In the absence of fine-tuning of effective operator coefficients, we find that current information on neutrino mass implies that[EQUATION: SEE TEXT] bohr magnetons. This bound is several orders of magnitude stronger than those obtained from analyses of solar and reactor neutrino data and astrophysical observations.     

How big is the universe today?

If one defines the size of the present universe in terms of a hypersurface of simultaneity generated by the spatial geodesies orthogonal to our world line today, then it is finite in all expanding Big Bang Friedmann models.