Ultrahigh harmonics from laser-assisted ion-atom collisions

We present a theoretical analysis of high-order harmonic generation from ion-atom collisions in the presence of linearly polarized intense laser pulses. Photons with frequencies significantly higher than in standard atomic high-harmonic generation are emitted. These harmonics are due to two different mechanisms: (i) collisional electron capture and subsequent laser-driven transfer of an electron between projectile and target atom; (ii) reflection of a laser-driven electron from the projectile leading to recombination at the parent atom.Comment: 5 pages, 4 figure

Selective amplification of scars in a chaotic optical fiber

In this letter we propose an original mechanism to select scar modes through coherent gain amplification in a multimode D-shaped fiber. More precisely, we numerically demonstrate how scar modes can be amplified by positioning a gain region in the vicinity of specific points of a short periodic orbit known to give rise to scar modes

Reality Check: Combining Survey and Market Data to Estimate the Importance of Product Attributes

Discrete choice models estimated using hypothetical choices made in a survey setting (i.e., choice experiments) are widely used to estimate the importance of product attributes in order to make product design and marketing mix decisions. Choice experiments allow the researcher to estimate preferences for product features that do not yet exist in the market. However, parameters estimated from experimental data often show marked inconsistencies with those inferred from the market, reducing their usefulness in forecasting and decision making. We propose an approach for combining choice-based conjoint data with individual-level purchase data to produce estimates that are more consistent with the market. Unlike prior approaches for calibrating conjoint models so that they correctly predict aggregate market shares for a “baseline” market, the proposed approach is designed to produce parameters that are more consistent with those that can be inferred from individual-level market data. The proposed method relies on a new general framework for combining two or more sources of individual-level choice data to estimate a hierarchical discrete choice model. Past approaches to combining choice data assume that the population mean for the parameters is the same across both data sets and require that data sets are sampled from the same population. In contrast, we incorporate in the model individual characteristic variables, and assert only that the mapping between individuals\u27 characteristics and their preferences is the same across the data sets. This allows the model to be applied even if the sample of individuals observed in each data set is not representative of the population as a whole, so long as appropriate product-use variables are collected that can explain the systematic deviations between them. The framework also explicitly incorporates a model for the individual characteristics, which allows us to use Bayesian missing-data techniques to handle the situation where each data set contains different demographic variables. This makes the method useful in practice for a wide range of existing market and conjoint data sets. We apply the method to a set of conjoint and market data for minivan choice and find that the proposed method predicts holdout market choices better than a model estimated from conjoint data alone or a model that does not include demographic variables

Improved Semiclassical Approximation for Bose-Einstein Condensates: Application to a BEC in an Optical Potential

We present semiclassical descriptions of Bose-Einstein condensates for configurations with spatial symmetry, e.g., cylindrical symmetry, and without any symmetry. The description of the cylindrical case is quasi-one-dimensional (Q1D), in the sense that one only needs to solve an effective 1D nonlinear Schrodinger equation, but the solution incorporates correct 3D aspects of the problem. The solution in classically allowed regions is matched onto that in classically forbidden regions by a connection formula that properly accounts for the nonlinear mean-field interaction. Special cases for vortex solutions are treated too. Comparisons of the Q1D solution with full 3D and Thomas-Fermi ones are presented.Comment: 14 pages, 5 figure

Multi-filament structures in relativistic self-focusing

A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review

Modeling the Effect of Images on Product Choices

Conjoint is one of the most popular methods in marketing research, widely used to understand how customers trade-off features of a product. Since product images have a strong influence on customer choice, it is natural to want to include images in conjoint studies, yet this has proven to be difficult, since images are difficult to parsimoniously characterize in the utility function. This paper proposes a novel approach to account for the effect of images on respondents’ choices, in which consumer heterogeneity in the appeal of the images is modeled through the covariance structure in a probit model. The covariance structure is informed by a separate task where respondents rate the images included in the study. In our application to midsize crossover vehicles, we show that our approach readily scales to a large number of images, fits better than several alternatives commonly used in practice, and makes more reasonable predictions about product substitution when a new product enters the market. We discuss how this approach could be used predict the effect of other difficult-to-characterize product attribute such as sound quality or taste on product choice

Approximate Analytic Solution for the Spatiotemporal Evolution of Wave Packets undergoing Arbitrary Dispersion

We apply expansion methods to obtain an approximate expression in terms of elementary functions for the space and time dependence of wave packets in a dispersive medium. The specific application to pulses in a cold plasma is considered in detail, and the explicit analytic formula that results is provided. When certain general initial conditions are satisfied, these expressions describe the packet evolution quite well. We conclude by employing the method to exhibit aspects of dispersive pulse propagation in a cold plasma, and suggest how predicted and experimental effects may be compared to improve the theoretical description of a medium's dispersive properties.Comment: 17 pages, 4 figures, RevTe

Time-dependent unitary perturbation theory for intense laser driven molecular orientation

We apply a time-dependent perturbation theory based on unitary transformations combined with averaging techniques, on molecular orientation dynamics by ultrashort pulses. We test the validity and the accuracy of this approach on LiCl described within a rigid-rotor model and find that it is more accurate than other approximations. Furthermore, it is shown that a noticeable orientation can be achieved for experimentally standard short laser pulses of zero time average. In this case, we determine the dynamically relevant parameters by using the perturbative propagator, that is derived from this scheme, and we investigate the temperature effects on the molecular orientation dynamics.Comment: 16 pages, 6 figure

Azimuthally polarized spatial dark solitons: exact solutions of Maxwell's equations in a Kerr medium

Spatial Kerr solitons, typically associated with the standard paraxial nonlinear Schroedinger equation, are shown to exist to all nonparaxial orders, as exact solutions of Maxwell's equations in the presence of vectorial Kerr effect. More precisely, we prove the existence of azimuthally polarized, spatial, dark soliton solutions of Maxwell's equations, while exact linearly polarized (2+1)-D solitons do not exist. Our ab initio approach predicts the existence of dark solitons up to an upper value of the maximum field amplitude, corresponding to a minimum soliton width of about one fourth of the wavelength.Comment: 4 pages, 4 figure

Economical adjunction of square roots to groups

How large must an overgroup of a given group be in order to contain a square root of any element of the initial group? We give an almost exact answer to this question (the obtained estimate is at most twice worse than the best possible) and state several related open questions.Comment: 5 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2: minor correction