Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: on the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations

In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence

Methodology for studying the numerical speed of sound in finite differences schemes

The space and time discretization inherent to all FDTD schemesintroduce non-physical dispersion errors, i.e. deviations ofthe speed of sound from the theoretical value predicted bythe governing Euler differential equations. A generalmethodologyfor computing this dispersion error via straightforwardnumerical simulations of the FDTD schemes is presented.The method is shown to provide remarkable accuraciesof the order of 1/1000 in a wide variety of twodimensionalfinite difference schemes.

Generation of Simulated Daily Precipitation and Air and Soil Temperatures, January 2000

This paper describes a maximum likelihood method using historical weather data to estimate a parametric model of daily precipitation and maximum and minimum air temperatures. Parameter estimates are reported for Brookings, SD, and Boone, IA, to illustrate the procedure. The use of this parametric model to generate stochastic time series of daily weather is then summarized. A soil temperature model is described that determines daily average, maximum, and minimum soil temperatures based on air temperatures and precipitation, following a lagged process due to soil heat storage and other factors.

Chemistry, isotope values (δD, δ18O, δ34S(SO4)) and temperatures of the water inflows in two Gotthard tunnels, Swiss Alps

Water inflows in the Gotthard Highway Tunnel and in the Gotthard Exploration Tunnel are meteoric waters infiltrating at different elevations, on both sides of an important orographic divide. Limited interaction of meteoric waters with gneissic rocks produces Ca-HCO3 and Na-Ca-HCO3 waters, whereas prolonged interaction of meteoric waters with the same rocks generates Na-HCO3 to Na-SO4 waters. Waters circulating in Triassic carbonate-evaporite rocks have a Ca-SO4 composition. Calcium-Na-SO4 waters are also present. They can be produced through interaction of either Na-HCO3 waters with anhydrite or Ca-SO4 waters with a local gneissic rock, as suggested by reaction path modeling. An analogous simulation indicates that Na-HCO3 waters are generated through interaction of Ca-HCO3 waters with a local gneissic rock. The two main SO4-sources present in the Alps are leaching of upper Triassic sulfate minerals and oxidative dissolution of sulfide minerals of crystalline rocks. Values of delta S-34(SO4) < <similar to>+ 9 parts per thousand, are due to oxidative dissolution of sulfide minerals, whereas delta S-34(SO4) > similar to+ 9 parts per thousand are controlled either by bacterial SO4 reduction or leaching of upper Triassic sulfate minerals. Most waters have temperatures similar to the expected values for a geothermal gradient of 22 degreesC/km and are close to thermal equilibrium with rocks. However relatively large, descending flows of cold waters and ascending flows of warm waters are present in both tunnels and determine substantial cooling and heating, respectively, of the interacting rocks. The most import upflow zone of warm, Na-rich waters is below Guspisbach, in the Gotthard Highway Tunnel, at 6.2-9.0 km from the southern portal. These warm waters have equilibrium temperatures of 65-75 degreesC and therefore constitute an important low-enthalpy geothermal resource. (C) 2001 Elsevier Science Ltd. All rights reserved.

Finite sample nonparametric tests for linear regressions

We introduce several exact nonparametric tests for finite sample multivariatelinear regressions, and compare their powers. This fills an important gap inthe literature where the only known nonparametric tests are either asymptotic,or assume one covariate only.

Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

On equilibria in duopolies with finite strategy spaces

We will call a game a reachable (pure strategy) equilibria game if startingfrom any strategy by any player, by a sequence of best-response moves weare able to reach a (pure strategy) equilibrium. We give a characterizationof all finite strategy space duopolies with reachable equilibria. Wedescribe some applications of the sufficient conditions of the characterization.

Finite horizon bargaining and the consistent field

This paper explores the relationships between noncooperative bargaining games and the consistent value for non-transferable utility (NTU) cooperative games. A dynamic approach to the consistent value for NTU games is introduced: the consistent vector field. The main contribution of the paper is to show that the consistent field is intimately related to the concept of subgame perfection for finite horizon noncooperative bargaining games, as the horizon goes to infinity and the cost of delay goes to zero. The solutions of the dynamic system associated to the consistent field characterize the subgame perfect equilibrium payoffs of the noncooperative bargaining games. We show that for transferable utility, hyperplane and pure bargaining games, the dynamics of the consistent fields converge globally to the unique consistent value. However, in the general NTU case, the dynamics of the consistent field can be complex. An example is constructed where the consistent field has cyclic solutions; moreover, the finite horizon subgame perfect equilibria do not approach the consistent value.

Trichogramma acacioi (Hymenoptera, Trichogrammatidae) parasitism capacity at different temperatures and factitious hosts

It was studied the parasitism capacity of Trichogramma acacioi on Anagasta kuehniella and Sitotroga cerealella eggs at different temperatures (15, 20, 25, 30 and 35 ± 1°C). The parasitism of T. acacioi varied with temperature and host. The highest parasitism (³80%) were observed during the first days after emergence in both hosts, at all tested temperatures. The accumulated parasitism varied with both host and temperature, being higher on A. kuehniella at 20°C, what shows good parasitoid species adaptation to this temperature. Thus, we conclude that the best host and best temperature to be used at mass-rearing of T. acacioi is A. kuehniella and 20ºC, respectively. Moreover, this Trichogramma species has great potential to be used in field releases at regions where average temperature is around 20ºC.

Reproduction and fertility life table of three aphid species (Macrosiphini) at different temperatures

Temperature is a key abiotic factor influencing the development and reproduction of aphids. The effect of temperature on the reproduction of three aphid species Aulacorthum solani (Kaltenbach), Macrosiphum euphorbiae (Thomas) and Uroleucon ambrosiae (Thomas) (Aphididae, Macrosiphini) has been investigated and fertility life tables were determined. Nymphs were reared in climatic chambers at temperatures of 16, 19, 22, 25, and 28 ± 1ºC, RH 70 ± 10% and 12 h photophase. Female adult aphids developed at these temperatures were then used in experiments in which pre-reproductive and reproductive periods were evaluated every 24 h. In addition, the number of nymphs produced and longevity were determined at each temperature. The reproduction period of A. solani and M. euphorbiae decreased with increasing temperature, whereas that of U. ambrosiae was maintained between 19 and 25ºC. The total number of nymphs produced by the aphids decreased as the temperature increased. The longevities of A. solani and M. euphorbiae decreased with increasing temperature but remained stable for U. ambrosiae between 19 and 25ºC. The largest survival rate (l x) and specific fertility (m x) values were found at 16 and 22ºC for all three species. The most favourable temperature for reproduction of A. solani, M. euphorbiae and U. ambrosiae was 22ºC, as demonstrated by the l x and m x profiles, the high values of net reproductive rates and intrinsic rates of increase, and the short intervals between generation and doubling times.

Causal assessment in finite extensive-form games

Two finite extensive-form games are empirically equivalent when theempirical distribution on action profiles generated by every behaviorstrategy in one can also be generated by an appropriately chosen behaviorstrategy in the other. This paper provides a characterization ofempirical equivalence. The central idea is to relate a game's informationstructure to the conditional independencies in the empirical distributionsit generates. We present a new analytical device, the influence opportunitydiagram of a game, describe how such a diagram is constructed for a givenextensive-form game, and demonstrate that it provides a complete summaryof the information needed to test empirical equivalence between two games.

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.