Divergence of Dipole Sums and the Nature of Non-Lorentzian Exponentially Narrow Resonances in One-Dimensional Periodic Arrays of Nanospheres

Origin and properties of non-Lorentzian spectral lines in linear chains of nanospheres are discussed. The lines are shown to be super-exponentially narrow with the characteristic width proportional to exp[-C(h/a)^3] where C is a numerical constant, h the spacing between the nanospheres in the chain and a the sphere radius. The fine structure of these spectral lines is also investigated.Comment: 9 pages, 4 figure

On the Convergence of the Born Series in Optical Tomography with Diffuse Light

We provide a simple sufficient condition for convergence of Born series in the forward problem of optical diffusion tomography. The condition does not depend on the shape or spatial extent of the inhomogeneity but only on its amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem

Coherently tunable third-order nonlinearity in a nanojunction

A possibility of tuning the phase of the third-order Kerr-type nonlinear susceptibility in a system consisting of two interacting metal nanospheres and a nonlinearly polarizable molecule is investigated theoretically and numerically. It is shown that by varying the relative inter-sphere separation, it is possible to tune the phase of the effective nonlinear susceptibility \chi^{(3)}(\omega;\omega,\omega,-\omega)$in the whole range from 0 to$2\pi$.Comment: 10 pages 5 figure

Comment on "Optical Response of Strongly Coupled Nanopraticles in Dimer Arrays" (Phys. Rev. B 71(4), 045404, 2005)

I have re-calculated the extinction spectra of aggregates of two silver nanospheres shown in Figs.~2 and 3 of Ref.~8. I have used the approximate method of images according to Ref.~8 and an exact numerical technique. I have found that the three sets of data (those I have obtained by the method of images, the numerical results, and the results published in Ref.~8) do not coincide. In this Comment, I discuss the reasons for these discrepancies and the general applicability of the method of images to the quasi-static electromagnetic problem of two interacting nanospheres.Comment: 4 pages, 4 figures, submitted to Phys. Rev.

Revisiting the Taxation of Punitive Damages

In our recent article, Taxing Punitive Damages, available at http://ssrn.com/abstract=1421879, we argued (1) that plaintiffs in punitive damages cases should be allowed to introduce to the jury evidence regarding the deductibility of those damages by defendants, and (2) that this jury tax-awareness approach is better than the Obama Administration’s suggested alternative of disallowing those deductions. To our delight, Professor Larry Zelenak and Paul Mogin have each provided published comments to our piece on Virginia Law Review\u27s In Brief companion website. Professor Zelenak’s thoughtful response focuses on our prescriptive claim that jury tax-awareness is better than nondeductibility, while Mr. Mogin disputes our doctrinal claim that the tax evidence is admissible. In this reply, we offer our answers to these and related challenges

Taxing Punitive Damages

There is a curious anomaly in the law of punitive damages. Jurors assess punitive damages in the amount that they believe will best “punish” the defendant. But, in fact, defendants are not always punished to the degree that the jury intends. Under the Internal Revenue Code, punitive damages paid by business defendants are tax deductible and, as a result, these defendants often pay (in real dollars) far less than the jury believes they deserve to pay.To solve this problem of under-punishment, many scholars and policymakers, including President Obama, have proposed making punitive damages nondeductible in all cases. In our view, however, such a blanket nondeductibility rule would, notwithstanding its theoretical elegance, be ineffective in solving the under-punishment problem. In particular, defendants could easily circumvent the nondeductibility rule by disguising punitive damages as compensatory damages in pre-trial settlements.Instead, the under-punishment problem is best addressed at the state level by making juries “tax-aware.” Tax-aware juries would adjust the amount of punitive damages to impose the desired after-tax cost on the defendant. As we explain, the effect of tax awareness cannot be circumvented by defendants through pre-trial settlements. For this and a number of other reasons, tax awareness would best solve the underpunishment problem even though it does come at the cost of enlarging plaintiff windfalls. However, given the defendant-focused features of current punitive damages doctrine, this cost is not particularly troubling

Local anisotropy and giant enhancement of local electromagnetic fields in fractal aggregates of metal nanoparticles

We have shown within the quasistatic approximation that the giant fluctuations of local electromagnetic field in random fractal aggregates of silver nanospheres are strongly correlated with a local anisotropy factor S which is defined in this paper. The latter is a purely geometrical parameter which characterizes the deviation of local environment of a given nanosphere in an aggregate from spherical symmetry. Therefore, it is possible to predict the sites with anomalously large local fields in an aggregate without explicitly solving the electromagnetic problem. We have also demonstrated that the average (over nanospheres) value of S does not depend noticeably on the fractal dimension D, except when D approaches the trivial limit D=3. In this case, as one can expect, the average local environment becomes spherically symmetrical and S approaches zero. This corresponds to the well-known fact that in trivial aggregates fluctuations of local electromagnetic fields are much weaker than in fractal aggregates. Thus, we find that, within the quasistatics, the large-scale geometry does not have a significant impact on local electromagnetic responses in nanoaggregates in a wide range of fractal dimensions. However, this prediction is expected to be not correct in aggregates which are sufficiently large for the intermediate- and radiation-zone interaction of individual nanospheres to become important.Comment: 9 pages 9 figures. No revisions from previous version; only figure layout is change

Historical Evolution of theWave Resource and Energy Production off the Chilean Coast over the 20th Century

The wave energy resource in the Chilean coast shows particularly profitable characteristics for wave energy production, with relatively high mean wave power and low inter-annual resource variability. This combination is as interesting as unusual, since high energetic locations are usually also highly variable, such as the west coast of Ireland. Long-term wave resource variations are also an important aspect when designing wave energy converters (WECs), which are often neglected in resource assessment. The present paper studies the long-term resource variability of the Chilean coast, dividing the 20th century into five do-decades and analysing the variations between the different do-decades. To that end, the ERA20C reanalysis of the European Centre for Medium-Range Weather Forecasts is calibrated versus the ERA-Interim reanalysis and validated against buoy measurements collected in different points of the Chilean coast. Historical resource variations off the Chilean coast are compared to resource variations off the west coast in Ireland, showing a significantly more consistent wave resource. In addition, the impact of historical wave resource variations on a realistic WEC, similar to the Corpower device, is studied, comparing the results to those obtained off the west coast of Ireland. The annual power production off the Chilean coast is demonstrated to be remarkably more regular over the 20th century, with variations of just 1% between the different do-decades.The authors with the Centre for Ocean Energy Research in Maynooth University are supported by Science Foundation Ireland under Grant No. 13/IA/1886. It is also supported by grant CGL2016-76561-R, MINECO/ERDF, UE. Additional funding was received from the University of Basque Country (UPV/EHU, GIU17/002)