Three-dimensional rogue waves in non-stationary parabolic potentials

Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1)-dimensional case to the variety of solutions of integrable NLS equation of (1+1)-dimensional case. As an example, we illustrated our technique using two lowest order rational solutions of the NLS equation as seeding functions to obtain rogue wave-like solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wave-like solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and BECs.Comment: 7 pages, 6 figure

Projected-Dipole Model for Quantum Plasmonics

Quantum effects of plasmonic phenomena have been explored through ab-initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer is mapped from the free-electron distribution near the metal surface as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects of nonlocal response and a finite work function with TDDFT-level accuracy. Applying the theory to dimers we find quantum-corrections to the hybridization even in mesoscopic dimers as long as the gap is sub-nanometric itself.Comment: Supplemental Material is available upon request to author

Collisionless relaxation in non-neutral plasmas

A theoretical framework is presented which allows to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study relaxation of charged-particles beams. It is shown that a fully matched beam relaxes to the Lynden-Bell distribution. However, when a mismatch is present and the beam oscillates, parametric resonances lead to a core-halo phase separation. The approach developed accounts for both the density and the velocity distributions in the final stationary state.Comment: Accepted in Phys. Rev. Let

Liquid-state theory of charged colloids

A simple theory of the fluid state of a charged colloidal suspension is proposed. The full free energy of a polyelectrolyte solution is calculated. It is found that the counterions condense onto the polyions forming clusters composed of one polyion and n counterions. The distribution of cluster sizes is determined explicitly. In agreement with the current experimental and Monte Carlo results, no liquid-gas phase separation was encountered.Comment: 4 pages, 2 Postscript figures, uses multicol.sty; changed conten

Donnan equilibrium and the osmotic pressure of charged colloidal lattices

We consider a system composed of a monodisperse charge-stabilized colloidal suspension in the presence of monovalent salt, separated from the pure electrolyte by a semipermeable membrane, which allows the crossing of solvent, counterions, and salt particles, but prevents the passage of polyions. The colloidal suspension, that is in a crystalline phase, is considered using a spherical Wigner-Seitz cell. After the Donnan equilibrium is achieved, there will be a difference in pressure between the two sides of the membrane. Using the functional density theory, we obtained the expression for the osmotic pressure as a function of the concentration of added salt, the colloidal volume fraction, and the size and charge of the colloidal particles. The results are compared with the experimental measurements for ordered polystyrene lattices of two different particle sizes over a range of ionic strengths and colloidal volume fractions.Comment: 8 pages, 4 Postscript figures, uses multicol.sty, to be published in European Physical Journal

Characterizing Uncertainty in Air Pollution Damage Estimates

This study uses Monte Carlo methods to characterize the uncertainty associated with per-ton damage estimates for 100 power plants in the contiguous United States (U.S.) This analysis focuses on damage estimates produced by an Integrated Assessment Model (IAM) for emissions of two local air pollutants: sulfur dioxide (SO2) and .ne particulate matter (PM2:5). For each power plant, the Monte Carlo procedure yields an empirical distribution for the damage per ton of SO2 and PM2:5:For a power plant in New York, one ton of SO2 produces $5,160 in damages with a 90$1,000 and $14,090. A ton of PM2:5 emitted from the same facility causes$17,790 worth of damages with a 90% percentile interval of $3,780 and$47,930. Results for the sample of 100 fossil-fuel .red power plants shows a strong spatial pattern in the marginal damage distributions. The degree of variability increases by plant location from east to west. This result highlights the importance of capturing uncertainty in air quality modeling in the empirical marginal damage distributions. Further, by isolating uncertainty at each module in the IAM we .nd that uncertainty associated with the dose-response parameter, which captures the in.uence of exposure to PM2:5 on adult mortality rates, the mortality valuation parameter, and the air quality model exert the greatest in.uence on cumulative uncertainty. The paper also demonstrates how the marginal damage distributions may be used to guide regulators in the design of more efficient market-based air pollution policy in the U.S.Monte Carlo, Air Pollution, Market-based Pollution Policy