Mean-value identities as an opportunity for Monte Carlo error reduction

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

Erratum: Suppression of localization in kronig-penney models with correlated disorder (Vol. 49, PG 147, 1994)

We consider the electron dynamics and transport properties of one-dimensional continuous models with random, short-range correlated impurities. We develop a generalized Poincare map formalism to cast the Schrodinger equation for any potential into a discrete set of equations, illustrating its application by means of a specific example. We then concentrate on the case of a Kronig-Penney model with dimer impurities. The previous technique allows us to show that this model presents infinitely many resonances (zeroes of the reflection coefficient at a single dimer) that give rise to a band of extended states, in contradiction with the general viewpoint that all one-dimensional models with random potentials support only localized states. We report on exact transfer-matrix numerical calculations of the transmission coefFicient, density of states, and localization length for various strengths of disorder. The most important conclusion so obtained is that this kind of system has a very large number of extended states. Multifractal analysis of very long systems clearly demonstrates the extended character of such states in the thermodynamic limit. In closing, we brieBy discuss the relevance of these results in several physical contexts.

Cosmological perturbations in coherent oscillating scalar field models

The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V(ϕ) = λ|ϕ|^n /n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained c_eff^ 2  = ω = (n − 2)/(n + 2) with ω the effective equation of state. We also obtain the first order correction in k^ 2/ω_eff^ 2 , when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ω_eff. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet’s theorem.

Comprehensive Validation Of A Measure Of Student School Engagement: A Pilot Study Of Middle School Students

Although it may sound reasonable that American education continues to be more effective at sending high school students to college, in a study conducted in 2009, The Council of the Great City Schools states that "slightly more than half of entering ninth grade students arrive performing below grade level in reading and math, while one in five entering ninth grade students is more than two years behind grade level...[and] 25% received support in the form of remedial literacy instruction or interventions" (Council of the Great City Schools, 2009). Students are distracted with technology (Lei & Zhao, 2005), family (Xu & Corno, 2003), medical illnesses (Nielson, 2009), learning disabilities and perhaps the most detrimental to academic success, the very lack of interest in school (Ruch, 1963). In a Johns Hopkins research study, Building a Graduation Nation - Colorado (Balfanz, 2008), warning signs were apparent years before the student dropped out of high school. The ninth grade was often referenced as a critical point that indicated success or failure to graduate high school. The research conducted by Johns Hopkins illustrates the problem: students who become disengaged from school have a much greater chance of dropping out of high school and not graduating. The first purpose of this study was to compare different measurement models of the Student School Engagement (SSE) using Factor Analysis to verify model fit with student engagement. The second purpose was to determine the extent to which the SSE instrument measures student school engagement by investigating convergent validity (via the SSE and Appleton, Christenson, Kim and Reschly's instrument and Fredricks, Blumenfeld, Friedel and Paris's instrument), discriminant validity (via Huebner's Student Life Satisfaction Survey) and criterion-related validity (via the sub-latent variables of Aspirations, Belonging and Productivity and student outcome measures such as achievement, attendance and discipline). Discriminant validity was established between the SSE and the Appleton, Christenson, Kim and Reschly's model and Fredricks, Blumenfeld, Friedel and Paris's (2005) Student Engagement Instruments (SEI). When confirming discriminant validity, the SSE's correlations were weak and statistically not significant, thus establishing discriminant validity with the SLSS. Criterion-related validity was established through structural equation modeling when the SSE was found to be a significant predictor of student outcome measures when both risk score and CSAP scores were used. The third purpose of this study was to assess the factorial invariance of the SSE instrument across gender to ensure the instrument is measuring the intended construct across different groups. Conclusively, configural, weak and metric invariances were established for the SSE as a non-significant change in chi-square indicating that all parameters including the error variances were invariant across groups of gender. Engagement is not a clearly defined psychological construct; it requires more research in order to fully comprehend its complexity. Hopefully, with parental and teacher involvement and a sense of community, student engagement can be nurtured to result in a meaningful attachment to school and academic success.

USLE and WEPP Soil Erosion Models: Their Applicability and Use in Generating Cover Values to Stabilize Soil in the Los Alamos, New Mexico Area

Soil erosion is a naturally occurring process that involves the detachment, transport, and deposition of soil particles. Disturbances such as thinning and wildfire can reduce cover greatly and increase erosion rates. Forest managers may use erosion prediction tools, such as the Universal Soil Loss Equation (USLE) and Water Erosion Prediction Project (WEPP) to estimate erosion rates and develop techniques to manage erosion. However, it is important to understand the differences and the applications of each model. Erosion rates were generated by each model and the model most applicable to the study site, Los Alamos, New Mexico was determined. It was also used to find the amount of cover needed to stabilize soil. The USLE is a simpler model and less complicated than a computer model like WEPP, and thus easier to manipulate to estimate cover values. Predicted cover values were compared to field cover values. Cover is necessary to establish effective erosion control guidelines.

GE models and algorithms for condensed phase equilibrium data regression in ternary systems: limitations and proposals

Phase equilibrium data regression is an unavoidable task necessary to obtain the appropriate values for any model to be used in separation equipment design for chemical process simulation and optimization. The accuracy of this process depends on different factors such as the experimental data quality, the selected model and the calculation algorithm. The present paper summarizes the results and conclusions achieved in our research on the capabilities and limitations of the existing GE models and about strategies that can be included in the correlation algorithms to improve the convergence and avoid inconsistencies. The NRTL model has been selected as a representative local composition model. New capabilities of this model, but also several relevant limitations, have been identified and some examples of the application of a modified NRTL equation have been discussed. Furthermore, a regression algorithm has been developed that allows for the advisable simultaneous regression of all the condensed phase equilibrium regions that are present in ternary systems at constant T and P. It includes specific strategies designed to avoid some of the pitfalls frequently found in commercial regression tools for phase equilibrium calculations. Most of the proposed strategies are based on the geometrical interpretation of the lowest common tangent plane equilibrium criterion, which allows an unambiguous comprehension of the behavior of the mixtures. The paper aims to show all the work as a whole in order to reveal the necessary efforts that must be devoted to overcome the difficulties that still exist in the phase equilibrium data regression problem.

Applying reactive models to column experiments to assess the hydrogeochemistry of seawater intrusion: optimising ACUAINTRUSION and selecting cation exchange coefficients with PHREEQC

Three sets of laboratory column experimental results concerning the hydrogeochemistry of seawater intrusion have been modelled using two codes: ACUAINTRUSION (Chemical Engineering Department, University of Alicante) and PHREEQC (U.S.G.S.). These reactive models utilise the hydrodynamic parameters determined using the ACUAINTRUSION TRANSPORT software and fit the chloride breakthrough curves perfectly. The ACUAINTRUSION code was improved, and the instabilities were studied relative to the discretisation. The relative square errors were obtained using different combinations of the spatial and temporal steps: the global error for the total experimental data and the partial error for each element. Good simulations for the three experiments were obtained using the ACUAINTRUSION software with slight variations in the selectivity coefficients for both sediments determined in batch experiments with fresh water. The cation exchange parameters included in ACUAINTRUSION are those reported by the Gapon convention with modified exponents for the Ca/Mg exchange. PHREEQC simulations performed using the Gains-Thomas convention were unsatisfactory, with the exchange coefficients from the database of PHREEQC (or range), but those determined with fresh water – natural sediment allowed only an approximation to be obtained. For the treated sediment, the adjusted exchange coefficients were determined to improve the simulation and are vastly different from those from the database of PHREEQC or batch experiment values; however, these values fall in an order similar to the others determined under dynamic conditions. Different cation concentrations were simulated using two different software packages; this disparity could be attributed to the defined selectivity coefficients that affect the gypsum equilibrium. Consequently, different calculated sulphate concentrations are obtained using each type of software; a smaller mismatch was predicted using ACUAINTRUSION. In general, the presented simulations by ACUAINTRUSION and PHREEQC produced similar results, making predictions consistent with the experimental data. However, the simulated results are not identical to the experimental data; sulphate (total S) is overpredicted by both models, most likely due to such factors as the kinetics of gypsum, the possible variations in the exchange coefficients due to salinity and the neglect of other processes.

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.

Minimizing the IOL Power Error Induced by Keratometric Power

Purpose. To evaluate theoretically in normal eyes the influence on IOL power (PIOL) calculation of the use of a keratometric index (nk) and to analyze and validate preliminarily the use of an adjusted keratometric index (nkadj) in the IOL power calculation (PIOLadj). Methods. A model of variable keratometric index (nkadj) for corneal power calculation (Pc) was used for IOL power calculation (named PIOLadj). Theoretical differences ($PIOL) between the new proposed formula (PIOLadj) and which is obtained through Gaussian optics (PIOL Gauss) were determined using Gullstrand and Le Grand eye models. The proposed new formula for IOL power calculation (PIOLadj) was prevalidated clinically in 81 eyes of 81 candidates for corneal refractive surgery and compared with Haigis, HofferQ, Holladay, and SRK/T formulas. Results. A theoretical PIOL underestimation greater than 0.5 diopters was present in most of the cases when nk = 1.3375 was used. If nkadj was used for Pc calculation, a maximal calculated error in $PIOL of T0.5 diopters at corneal vertex in most cases was observed independently from the eye model, r1c, and the desired postoperative refraction. The use of nkadj in IOL power calculation (PIOLadj) could be valid with effective lens position optimization nondependent of the corneal power. Conclusions. The use of a single value of nk for Pc calculation can lead to significant errors in PIOL calculation that may explain some IOL power overestimations with conventional formulas. These inaccuracies can be minimized by using the new PIOLadj based on the algorithm of nkadj.

Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

Estimation of the Central Corneal Power in Keratoconus: Theoretical and Clinical Assessment of the Error of the Keratometric Approach

Purpose: The aim of this study was to analyze theoretically the errors in the central corneal power calculation in eyes with keratoconus when a keratometric index (nk) is used and to clinically confirm the errors induced by this approach. Methods: Differences (DPc) between central corneal power estimation with the classical nk (Pk) and with the Gaussian equation (PGauss c ) in eyes with keratoconus were simulated and evaluated theoretically, considering the potential range of variation of the central radius of curvature of the anterior (r1c) and posterior (r2c) corneal surfaces. Further, these differences were also studied in a clinical sample including 44 keratoconic eyes (27 patients, age range: 14–73 years). The clinical agreement between Pk and PGauss c (true net power) obtained with a Scheimpflug photography–based topographer was evaluated in such eyes. Results: For nk = 1.3375, an overestimation was observed in most cases in the theoretical simulations, with DPc ranging from an underestimation of 20.1 diopters (D) (r1c = 7.9 mm and r2c = 8.2 mm) to an overestimation of 4.3 D (r1c = 4.7 mm and r2c = 3.1 mm). Clinically, Pk always overestimated the PGauss c given by the topography system in a range between 0.5 and 2.5 D (P , 0.01). The mean clinical DPc was 1.48 D, with limits of agreement of 0.71 and 2.25 D. A very strong statistically significant correlation was found between DPc and r2c (r = 20.93, P , 0.01). Conclusions: The use of a single value for nk for the calculation of corneal power is imprecise in keratoconus and can lead to significant clinical errors.

3D models created from ROV videos and their corresponding subtransect dimensions

Underwater video transects have become a common tool for quantitative analysis of the seafloor. However a major difficulty remains in the accurate determination of the area surveyed as underwater navigation can be unreliable and image scaling does not always compensate for distortions due to perspective and topography. Depending on the camera set-up and available instruments, different methods of surface measurement are applied, which make it difficult to compare data obtained by different vehicles. 3-D modelling of the seafloor based on 2-D video data and a reference scale can be used to compute subtransect dimensions. Focussing on the length of the subtransect, the data obtained from 3-D models created with the software PhotoModeler Scanner are compared with those determined from underwater acoustic positioning (ultra short baseline, USBL) and bottom tracking (Doppler velocity log, DVL). 3-D model building and scaling was successfully conducted on all three tested set-ups and the distortion of the reference scales due to substrate roughness was identified as the main source of imprecision. Acoustic positioning was generally inaccurate and bottom tracking unreliable on rough terrain. Subtransect lengths assessed with PhotoModeler were on average 20% longer than those derived from acoustic positioning due to the higher spatial resolution and the inclusion of slope. On a high relief wall bottom tracking and 3-D modelling yielded similar results. At present, 3-D modelling is the most powerful, albeit the most time-consuming, method for accurate determination of video subtransect dimensions.

Age models for sediment cores off Peru

Planktonic foraminiferal faunas of the southeast Pacific indicate that sea surface temperatures (SST) have varied by as much as 8-10°C in the Peru Current, and by ?5-7°C along the equator, over the past 150,000 years. Changes in SST at times such as the Last Glacial Maximum reflect incursion of high-latitude species Globorotalia inflata and Neogloboquadrina pachyderma into the eastern boundary current and as far north as the equator. A simple heat budget model of the equatorial Pacific shows that observed changes in Peru Current advection can account for about half of the total variability in equatorial SSTs. The remaining changes in equatorial SST, which are likely related to local changes in upwelling or pycnocline depth, precede changes in polar climates as recorded by d18O. This partitioning of processes in eastern equatorial Pacific SST reveals that net ice-age cooling here reflects first a rapid response of equatorial upwelling to insolation, followed by a later response to changes in the eastern boundary current associated with high-latitude climate (which closely resembles variations in atmospheric CO2 as recorded in the Vostok ice core). Although precise mechanisms responsible for the equatorial upwelling component of climate change remain uncertain, one likely candidate that may operate independently of the ice sheets is insolation-driven changes in El Niño/Southern Oscillation (ENSO) frequency. Early responses of equatorial SST detected both here and elsewhere highlight the sensitivity of tropical systems to small changes in seasonal insolation. The scale of tropical changes we have observed are substantially greater than model predictions, suggesting a need for further quantitative assessment of processes associated with long-term climate change.

The development of a numerical solution to transport equation /

"Prepared for U.S. Army Engineer District, Mobile."