Neighboring mapping points theorem

Let f be a continuous map from a metric space X to M. We say that points in a subset N of X are f-neighbors if there exists a sphere S in M such that f(N) lies on S and there are no points of f(X) inside of S. We prove that if X is a unit sphere of any dimension and M is a contractible metric space then there are two f-neighbors in X such that the distance between them is greater than one. This theorem can be derived from the fact that for every non-null-homotopic closed covering C of X there is a set of f-neighbors N in X such that every member of C contains a point of N.Comment: 7 pages, 1 figur

Neighboring clusters in Bernoulli percolation

We consider Bernoulli percolation on a locally finite quasi-transitive unimodular graph and prove that two infinite clusters cannot have infinitely many pairs of vertices at distance 1 from one another or, in other words, that such graphs exhibit ``cluster repulsion.'' This partially answers a question of H\"{a}ggstr\"{o}m, Peres and Schonmann.Comment: Published at http://dx.doi.org/10.1214/009117906000000485 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Radiative energy loss of neighboring subjets

We compute the in-medium energy loss probability distribution of two neighboring subjets at leading order, in the large-$N_c$ approximation. Our result exhibits a gradual onset of color decoherence of the system and accounts for two expected limiting cases. When the angular separation is smaller than the characteristic angle for medium-induced radiation, the two-pronged substructure lose energy coherently as a single color charge, namely that of the parent parton. At large angular separation the two subjets lose energy independently. Our result is a first step towards quantifying effects of energy loss as a result of the fluctuation of the multi-parton jet substructure and therefore goes beyond the standard approach to jet quenching based on single parton energy loss. We briefly discuss applications to jet observables in heavy-ion collisions.Comment: 34 pages, 15 figure

Radiative Heat Transfer between Neighboring Particles

The near-field interaction between two neighboring particles is known to produce enhanced radiative heat transfer. We advance in the understanding of this phenomenon by including the full electromagnetic particle response, heat exchange with the environment, and important radiative corrections both in the distance dependence of the fields and in the particle absorption coefficients. We find that crossed terms of electric and magnetic interactions dominate the transfer rate between gold and SiC particles, whereas radiative corrections reduce it by several orders of magnitude even at small separations. Radiation away from the dimer can be strongly suppressed or enhanced at low and high temperatures, respectively. These effects must be taken into account for an accurate description of radiative heat transfer in nanostructured environments.Comment: 22 pages, 9 figures, fully self-contained derivation

Raman scattering mediated by neighboring molecules

Raman scattering is most commonly associated with a change in vibrational state within individual molecules, the corresponding frequency shift in the scattered light affording a key way of identifying material structures. In theories where both matter and light are treated quantum mechanically, the fundamental scattering process is represented as the concurrent annihilation of a photon from one radiation mode and creation of another in a different mode. Developing this quantum electrodynamical formulation, the focus of the present work is on the spectroscopic consequences of electrodynamic coupling between neighboring molecules or other kinds of optical center. To encompass these nanoscale interactions, through which the molecular states evolve under the dual influence of the input light and local fields, this work identifies and determines two major mechanisms for each of which different selection rules apply. The constituent optical centers are considered to be chemically different and held in a fixed orientation with respect to each other, either as two components of a larger molecule or a molecular assembly that can undergo free rotation in a fluid medium or as parts of a larger, solid material. The two centers are considered to be separated beyond wavefunction overlap but close enough together to fall within an optical near-field limit, which leads to high inverse power dependences on their local separation. In this investigation, individual centers undergo a Stokes transition, whilst each neighbor of a different species remains in its original electronic and vibrational state. Analogous principles are applicable for the anti-Stokes case. The analysis concludes by considering the experimental consequences of applying this spectroscopic interpretation to fluid media; explicitly, the selection rules and the impact of pressure on the radiant intensity of this process

The Coherence of Evolutionary Theory with Its Neighboring Theories

Evolutionary theory coheres with its neighboring theories, such as the theory of plate tectonics, molecular biology, electromagnetic theory, and the germ theory of disease. These neighboring theories were previously unconceived, but they were later conceived, and then they cohered with evolutionary theory. Since evolutionary theory has been strengthened by its several neighboring theories that were previously unconceived, it will be strengthened by infinitely many hitherto unconceived neighboring theories. This argument for evolutionary theory echoes the problem of unconceived alternatives. Ironically, however, the former recommends that we take the realist attitude toward evolutionary theory, while the latter recommends that we take the antirealist attitude toward it